How to solve (x-4)^2-9=0

Answers

Answer 1

Answer:

Step-by-step explanation:

(x-4)^2-9=0

Let's assume a=x-4 and b=3

We know that,

[tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]

substituting values a, and b in above equation we get,

(x-4+3)(x-4-3)==

(x-1)(x-7)=0

x=1,7

Answer 2

Answer:

[tex]\displaystyle{x=7,1}[/tex]

Step-by-step explanation:

Given the equation:

[tex]\displaystyle{\left(x-4\right)^2-9=0}[/tex]

Add 9 both sides:

[tex]\displaystyle{\left(x-4\right)^2-9+9=0+9}\\\\\displaystyle{\left(x-4\right)^2=9}[/tex]

Square root both sides:

[tex]\displaystyle{\sqrt{\left(x-4\right)^2}=\sqrt{9}}[/tex]

Cancel square root for left side and add plus-minus to right side:

[tex]\displaystyle{x-4=\pm \sqrt{9}}[/tex]

Evaluate the surd of 9:

[tex]\displaystyle{x-4=\pm 3}[/tex]

Add 4 both sides:

[tex]\displaystyle{x-4+4=\pm 3 +4}\\\\\displaystyle{x=\pm 3 +4}[/tex]

Two solutions can be either:

[tex]\displaystyle{x=3+4}[/tex] or [tex]\displaystyle{x = -3+4}[/tex]

Hence:

[tex]\displaystyle{x=7,1}[/tex]


Related Questions

Tell how many polygons can be formed by each set of points​

Answers

The number of polygons that can be formed are

(0, 1) and (2, 3): Zero polygon(4, 5), (6, 7), and (8, 9): One polygon (triangle)(3, 5) and the x-axis: One polygon (triangle)

How to determine the number of polygons

Points (0, 1) and (2, 3)

The set of points (0, 1) and (2, 3) cannot form a polygon as they are collinear (i.e., lie on the same straight line) and do not enclose an area.

Points  (4, 5), (6, 7), and (8, 9)

These are three different points.

Because a triangle has three sides, one triangle can be formed by the set of points (4,5), (6,7), and (8,9). i.e. One polygon

Points (3, 5) and the x-axis.

One polygon can be formed by the set of points (3,5) and the x-axis: a triangle with vertices at (3,5), (0,0), and (6,0).

How to determine the areas and the perimeters

Polygon (4)

This is a rectangle with the dimension:

6 units by 5 units

So, we have

Perimeter = 2 * (6 + 5) = 22 units

Area = 6 * 5 = 30 squared units

Polygon (5)

This is a composite figure with the following dimensions:

Square of 4 units

Rectangle: 6 units by 2 units

So, we have

Perimeter = 4 * 4 + 2 * (6 + 2) = 32 units

Area = 4 * 4 + 6 * 2 = 28 squared units

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Determine whether -(p « › q) and p «> -q are logically equivalent.

Answers

No, -(p « › q) and p «> -q are not logically equivalent.

What is logical equivalence?

When two logical assertions have the same truth value for all conceivable truth value assignments to their constituent propositions, the two statements are said to be logically equivalent. In other words, two assertions are comparable logically if and only if all feasible permutations of the truth values of their component propositions are equal.

First, let's rewrite the statements using the standard logical operators of negation, conjunction, and implication:

-(p « › q) is equivalent to ¬(p ∧ ¬q)

p «> -q is equivalent to ¬p → ¬¬q, which simplifies to p → q

Now, we can construct a truth table with columns for p, q, ¬(p ∧ ¬q), and p → q:

p |      q |   ¬(p ∧ ¬q)    |    p → q

--|----------|------------------|-----

T        T          F               T

T        F          T               F

F       T           T               T

F       F           T               T

We can see that the truth values of the two statements are not always the same.

For example, when p is true and q is false, ¬(p ∧ ¬q) is true and p → q is false.

Therefore, -(p « › q) and p «> -q are not logically equivalent.

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All of the following employee information is included on a W-2 form EXCEPT..

Answers

Overall, the W-2 form is an important document for employees to receive and keep for tax purposes, but it is not comprehensive in terms of all the financial details of their employment.

What is equation?

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

A W-2 form is an Internal Revenue Service (IRS) tax form that employers are required to provide to their employees every year. It reports the employee's annual wages and the amount of taxes withheld from their paychecks. While a W-2 form contains a lot of important information about an employee's earnings and tax withholding, it does not include every detail about their employment or financial situation. Some examples of information that are not included on a W-2 form include:

Information about non-wage income, such as interest or dividends

Information about benefits received, such as health insurance or retirement plan contributions

Information about deductions or credits, such as charitable contributions or education expenses

Information about stock options or other forms of equity compensation

Information about expenses related to employment, such as travel or equipment costs.

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Una fabrica ganaba $80 por hora hombre de mano de obra cuando se abrió Cada año, la fabrica obtiene un 5% adicional por hora hombre

Answers

As a result, after five years, the business makes $102.10 per hour of work performed by men.

What are a company's earnings?

The gains that a company makes are its earnings. They are obtained by deducting revenue from cost of products sold, running costs, and taxes. The creation and ongoing running of a company are primarily motivated by the desire to generate profits. Dividend payments to stockholders can then be made with the earnings.

If the factory earned $80 per man-hour of labor when it opened, and each year earns an additional 5% per man-hour, we can calculate the earnings for any given year using the formula:

E = $80 × (1 + r)ⁿ

where E is the earnings per man-hour, r is the annual rate of increase (5% = 0.05), and n is the number of years since the factory opened.

For example, if we want to find the earnings per man-hour after 3 years, we would plug in n=3:

E = $80 × (1 + 0.05)³

E = $80 × 1.157625

E = $92.61

Therefore, after 3 years, the factory earns $92.61 per man-hour of labor.

Similarly, if we want to find the earnings per man-hour after 5 years, we would plug in n=5:

E = $80 × (1 + 0.05)⁵

E = $80 × 1.276282

E = $102.10

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The correct question is:

A factory earned $80 per man-hour of labor when it opened Each year, the factory earns an additional 5% per man-hour

A school needs to go buy new notebooks and desk computers for it s computer lap the notebook cost $250 each, and the desktop computers cost $175

Answers

Answer:

I'm sorry, it seems like you didn't complete the question. Can you please provide me with the rest of the question so I can assist you?

he three data sets have the same mean and range, but is the variation the same? Prove your answer by computing the standard deviation. Assume the data were obtained from samples. (a) 4, 5, 11, 13, 13, 14 (b) 5, 7, 10, 10, 13, 15 (c) 3, 10, 11, 11, 12, 13

Answers

The standard deviations of the data are different.

Standard deviation:

The formula used to calculate the standard deviation of data is given by

         Standard deviation = √[ ∑(x[tex]_{i}[/tex] - x)² /n ]  

x - mean of the data and n = number of observations

Here we have

(a) 4, 5, 11, 13, 13, 14

Mean of the data = [4 + 5 + 11 + 13 + 13 + 14 ]/6 = 60/6 = 10

On calculating deviations

=> ∑(x[tex]_{i}[/tex] - x)² = 96

=> √[ ∑(x[tex]_{i}[/tex] - x)²/n ] = √[ 96/ 6 ] = 4    

(b) 5, 7, 10, 10, 13, 15

Since the mean of the data is equal for all  

On calculating deviations

=> ∑(x[tex]_{i}[/tex] - x)² = 68

=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 68/ 6 ] = 3.36

(c) 3, 10, 11, 11, 12, 13

On calculating deviations

=> ∑(x[tex]_{i}[/tex] - x)² = 64

=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 64/ 6 ] = 3.26  

Therefore,

The standard deviations of the data are different.

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I need help! Please include an explanation.

Answers

The location of A ' given the rotation about the origin and the xy coordinate plane is D. In Quadrant IV.

How to find the location ?

To rotate a point 180° about the origin, we switch the signs of both coordinates. For instance, if you have ( x, y ) rotated, then it becomes ( - x ,  - y ).

So, if A is located at (-4, 3), then A' is located at (4, -3).

The point A' is located in Quadrant IV, because it has a positive x-coordinate and a negative y-coordinate, which is the characteristic of points in this quadrant.

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The family likes peaches and other fruits. The local farmer’s market is selling fresh peaches at a discounted price. If the farmer’s market sold 35% of its produce and has 260 peaches remaining, how many peaches did it originally have on hand? Show all your work and explain how you used equivalent ratios to solve the problem.

Answers

The farmer's market originally had 400 peaches on hand.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.

Let's use x to represent the original number of peaches the farmer's market had on hand.

We know that the farmer's market sold 35% of its produce, which means it sold 0.35x peaches. The remaining number of peaches can be calculated by subtracting the number of peaches sold from the original number of peaches:

remaining peaches = x - 0.35x

We also know that there are 260 peaches remaining, so we can set up an equation:

260 = x - 0.35x

Simplifying this equation, we can combine like terms:

260 = 0.65x

To solve for x, we need to isolate the variable by dividing both sides by 0.65:

x = 260 / 0.65

x = 400

Therefore, the farmer's market originally had 400 peaches on hand.

To explain how we used equivalent ratios, we used the fact that the farmer's market sold 35% of its produce. This can be represented as a ratio of 35/100 or 0.35. We then used this ratio to find the number of peaches sold, which is 0.35x. We also used the fact that the remaining peaches are the original peaches minus the peaches sold, or x - 0.35x. Finally, we set up an equation using the remaining peaches and solved for x to find the original number of peaches.

Hence, the farmer's market originally had 400 peaches on hand.

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An isosceles triangle has a perimeter of 19 inches. A leg is 2 inches longer than the base. How long is the
base?

Answers

Answer:

Base = 5inches

Step-by-step explanation:

2(x+2) + x
2x+4+x
3x+4=19
3x=15
x=5

Answer:x5

Step-by-step explanation:

could you help with the question pls?

Answers

By using distributive property, an estimate for sin((π/6 + ε)(1 - ε)) is approximately 0.5108.

What is sinx ?

sinx is a trigonometric function that represents the ratio of the length of the side opposite to an angle x in a right-angled triangle to the length of the hypotenuse of the triangle. In other words, it is the sine of the angle x.

The sine function is typically denoted as sin(x), where x is the measure of an angle in radians. It is defined as follows:

sin(x) = opposite side / hypotenuse

According to the question:
We can use the small angle approximation sin(x) ≈ x for small angles x to estimate[tex]sin((\pi /6 + \epsilon)(1 - \epsilon))[/tex], where ε = 0.01.

First, we can expand the expression using the distributive property:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) = sin(\pi /6 - \epsilon^2 +\epsilon /6)[/tex]

Since ε is small, we can use the small angle approximation to estimate the value of sin(ε/6):

[tex]sin(\epsilon /6) =\epsilon/6[/tex]

Next, we can use the fact that [tex]sin(\pi /6) = 1/2[/tex] to estimate [tex]sin(\pi /6 - \epsilon ^2)[/tex] :

[tex]sin(\pi /6 - \epsilon ^2) ≈ sin(\pi /6) = 1/2[/tex]

Substituting these approximations into the original expression, we get:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) =sin(\pi /6 - \epsilon^{2} + \epsilon/6) =sin(\pi /6) + sin(\epsilon/6) - sin(\epsilon^{2} )sin((\pi /6 + \epsilon)(1 - \epsilon)) = 1/2 + \epsilon/6 - sin(\epsilon^{2} )[/tex]

Finally, we can use the fact that sin(x) is approximately equal to x for small values of x to approximate [tex]sin(\epsilon^{2} ) as \epsilon^{2}[/tex]:

[tex]sin(\epsilon^2) = \epsilon^2[/tex]

Substituting this approximation into the previous expression, we get:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) ≈ 1/2 + \epsilon/6 - \epsilon^2[/tex]

Now, we can substitute the value of ε = 0.01 into this expression to get an estimate:

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) ≈ 1/2 + 0.01/6 - 0.01^2[/tex]

[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) =0.5108[/tex]

Therefore, an estimate for sin((π/6 + ε)(1 - ε)) is approximately 0.5108.

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39.6​% of consumers believe that cash will be obsolete in the next 20 years. Assume that 6 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.

Answers

The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.

The binomial probability:

The binomial probability formula is used to calculate the probability of getting exactly k successes in n independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is denoted as p. The formula is:

[tex]P(X=k) = C(n,k)\times p^k\times(1-p)^{(n-k)[/tex]

Here we have  

39.6​% of consumers believe that cash will be obsolete in the next 20 years.

Let p be the probability that a consumer believes that cash will be obsolete

=> p = 39.6% or 0.396.

Then, the probability that a consumer does not believe that cash will be obsolete is q = 1 - p = 0.604.  

We need to find the probability that less than 3 of the selected consumers believe that cash will be obsolete.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial probability formula, we have:

[tex]P(X = k) = C(n,k) \times p^k\times q^{(n-k)[/tex]

=> P(X = 0) = C(6, 0) × (0.396)⁰ × (0.604)⁶ = 0.048

=> P(X = 1) = C(6, 1) × (0.396)¹ × (0.604)⁵ = 0.18

=> P(X = 1) = C(6, 2) × (0.396)² × (0.604)⁴ = 0.3

P(X < 3) = 0.048 + 0.18 + 0.3 = 0.528        

         

Therefore,

The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.

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Summarize in your own words a quantity in the life-science that is modelled by a function of time. For your function, if you knew some values of its derivative, what would those values be telling you about your model? Be specific (don’t just say “rate-of-change”).

Answers

One example of a quantity in the life sciences that is modeled by a function of time is the population size of a species.

How can this be modeled?

This can be modeled using a differential equation, where the rate of change of the population size is proportional to the current population size.

If we knew the values of the derivative of this function (i.e., the first derivative), we would be able to make inferences about the growth or decline of the population.

A positive derivative value would indicate that the population is growing, while a negative derivative value would indicate that the population is declining. The magnitude of the derivative would also give us information about the rate of growth or decline of the population. If the derivative is large, the population is changing quickly, while a small derivative indicates slower change.

If we had information about the second derivative of the function (i.e., the rate of change of the derivative), we would be able to make further inferences about the behavior of the population.

A positive second derivative value would indicate that the population is accelerating in its growth, while a negative second derivative value would indicate that the population is decelerating in its growth. This information could be useful in predicting future trends in population size and in making decisions about conservation efforts or resource management.

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Algebra question, multiple choice, photo attached

Answers

The graph of the linear inequality y ≥ 2·x - 1 is the region on or above the graph of the line y = 2·x - 1

Option A is correct;

(A) On or above

What is an inequality?

An inequality is a comparison that expresses an unequal relationship between two expressions.

An example of an inequality is; V < W, R > Q, X ≥ W, etc

The region of the graph of a linear inequality is indicated by shading above the line when the inequality is >, and below the line when the inequality symbol is <

The specified linear inequality can be presented as follows;

y ≥ 2·x - 1

Therefore, w get;

The values of y are larger than 2·x - 1

The shaded region is the region on or above the graph of the line y = 2·x - 1

The correct option is therefore; (A) On or above the line y = 2·x - 1

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What is the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labeled 1-10?

Answers

The probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

What is meant by probability?

An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur.

In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.

It is said that there are 10 balls in a bag, labelled 1-10.

Now,

The number of ways the ball labelled 1 is picked is 1

The number of ways the ball labelled 2 is picked is 2

So the number of ways a ball labelled certain number is picked is 1.

Now there is no replacement.

So the total number of balls decreases by 1 when 1 ball is taken.

Then,

The probability of choosing the ball numbered 1 = 1/10

The probability of choosing 2 = 1/9

The probability of choosing 3 = 1/8

.

.

.

the probability of choosing 10 = 1

Total probability of choosing the balls in consecutive order = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.

Therefore the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

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Suppose your boss proposes an alternative form of payment. For the first day of each month, you’ll earn a penny. Thereafter, each workday your wages will double what they were the day before. If there are 20 workdays in a month, how much would you make for the month?

Answers

We will make ₹1,048,575 for the month. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four basic operations, often referred to as "arithmetic operations", are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.

We are given that for the first day of each month, a penny is earned. Thereafter, each workday wages will double what they were the day before.

Now, since there are 20 workdays in a month so, the total amount earned is as follows:

⇒ 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1,024 + 2,048 + 4,096 + 8,192 + 16,384 + 32,768 + 65,536 + 131,072 + 262,144 + 524,288

⇒ ₹ 1,048,575

Hence, we will make ₹ 1,048,575 for the month.

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I think of a number, treble it and take 6 from my answer.
If the result is 18, find the number.

Answers

Answer:

number is 8

Step-by-step explanation:

let the number be n then trebling it ( multiplying it by 3 ) is 3n, then subtracting 6 from this is 3n - 6 , so

3n - 6 = 18 ( add 6 to both sides )

3n = 24 ( divide both sides by 3 )

n = 8

that is the number thought of is 8

Julia needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on
sale contains 6 glasses, use the drop-down menu below to write an inequality
representing s, the number of sets of glasses Julia should buy

Answers

Answer:

Julia should buy at least 5 sets of glasses.

Step-by-step explanation:

The inequality will be

286 +6s ≥ 316

Solve for s to get s ≥ 5

State whether each investment below realized a profit or loss. Compute the percent of increase or decrease.
Purchase Price: $12.00
Selling Price: $8.25

Answers

The given investment realized a loss of $3.75 with 31.25% decrease.

What is profit?

The amount made by selling a product, which should be greater than the product's cost price, is generally referred to as the profit. It is the profit generated by all business activities. In other words, a product is deemed to have made a profit if its selling price (SP) exceeds its cost price (CP). It explains the financial gain realised when the revenue from a company activity outpaces the costs, like as taxes and expenses, involved in maintaining a business activity.

Given : Purchase Price: $12.00

            Selling Price: $8.25

Since the purchase price is more than the selling prize, So the investment has been sold at a loss.

The loss on investment = Purchasing price - Selling price

                                       = $ 12 - 8.25

                                       = $3.75.

% of decrease = (loss/ purchasing price) × 100

                        = 3.75/12 × 100

                        = 31.25 %

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Macroeconomics
The regular price for a set of four tires is $250, but Erin finds a store that has the tires she needs on sale for $175?

Which graph correctly illustrates this scenario?

Answers

The graph for the given question is mentioned below.

What is graph?

A graph is a visual representation of data or information that is used to display and communicate relationships between variables or categories. Graphs can take many forms, including line graphs, bar graphs, pie charts, and scatter plots, among others. They are commonly used in fields such as science, economics, and statistics.

As the price of a set of four tires has decreased from $250 to $175, we can illustrate this scenario using a demand and supply graph with  quantity on the horizontal and size on the vertical axis.

The graph should show a leftward shift of the demand curve, indicating that consumers are willing to buy more tires at a lower price. The supply curve remains constant, indicating that the supplier is willing to sell the same quantity of tires at a lower price. Therefore, the correct graph should be:

               |      P

       250 |     \

               |       \ Supply

               |         \

               |           \

       175  |              \    

               |                \

               |                  \ Demand (after discount)

               |                    \

                     Q

where P is the price, Q is the quantity, and the demand curve has shifted to the right.

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What is the answer to this photo

Answers

The required number of tubs are 17.55 tubs.

How to find number of tubs?

To solve the problem, we need to find the total amount of ice cream used in ounces and then convert it to pounds to find the number of tubs used.

Number of scoops for regular cones = 2 scoops/cone

Number of scoops for large cones = 3 scoops/cone

Total number of scoops of ice cream used for regular cones = 2 scoops/cone x 234 cones = 468 scoops

Total number of scoops of ice cream used for large cones = 3 scoops/cone x 156 cones = 468 scoops

Total number of scoops of ice cream used = 468 scoops + 468 scoops = 936 scoops

Total amount of ice cream used in ounces = 936 scoops x 3 ounces/scoop = 2808 ounces

Total amount of ice cream used in pounds = 2808 ounces / 16 ounces/pound = 175.5 pounds

Number of tubs of ice cream used = 175.5 pounds / 10 pounds/tub = 17.55 tubs

Rounding up to the nearest whole number, we get:

Answer: (C) 17.55 tubs.

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A group of students is painting a background piece for the school play. What is the area of the part that is painted blue?

Answers

The area of the part that is painted blue is 679 ft.

What are the basic arithmetic operations?

The four basic arithmetic operations are addition, subtraction, multiplication, and division.

Arithmetic operations are the building blocks for all mathematical processes and methods. (Yeah, they’re kind of a big deal!) These types of operations are part of the “arithmetic” branch of math.

Arithmetic operations strip math down to the basics that we use every day, whether we realize it or not. Those basics are addition, subtraction, multiplication, and division.

The area

= 20×30+(1/2)×20×(40-30) -3x5 - 2×3

= boot 10x10- 15-6

= 700-21

= 679

Hence, The area of the part that is painted blue is 679 ft.

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Gabriel's father has a garden in the back yard. The dimensions of the garden are shown here.

A green rectangle is shown. The width is labeled as 2 and two-thirds feet. The length is labeled as 7 and three-fourths feet.

Part A

Calculate the area of the garden. Show at least one step before you show your solution.

Part B

You found the area of the garden in Part A. Explain briefly, without doing any calculations, how you would find

5/6 of this area.

Answers

The Area of Garden is 62/3 feet².

What is area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm² and m² are used to measure area. A shape's area is a two-dimensional measurement.

Given:

Length = 7 3/4 feet = 31/4 feet

Width = 2 2/3 feet = 8/3 feet

So, Area of Garden

= l w

= 31/4 x 8/3

= 62/3 feet²

and, Now, 5/6th of the Garden

= 62/3 x 5/6

= 31 / 3 x 5 / 2

= 155 / 6 feet²

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RIDDLE: Why was the Mathematician Late for Work?
Directions: Find the slope between each pair of points Show all work on a separate sheet of paper. After completing each set, find matching answers. One will have a letter and the other a number. Write the letter in the matching numbered box at the bottom of the page.
SET 2
T. (7, 5) and (10, 9) ______________ 16. (-5, -2) and (9, 2) ______________
B. (-8, 2) and (-5, -4) ______________ 8. (-10, -6) and (2, -8) ______________
H. (2, -2) and (-4, -1) ______________ 3. (-2, 1) and (-8, -7) ______________
S. (-4, 9) and (-11, 7) ______________ 5. (-4, -2) and (-3, 3) ______________
O. (5, -1) and (4, -6) ______________ 14. (-2, -4) and (-7, 6) ______________
SET 3
K. (1, -3) and (2, -3) ______________ 9. (8, -1) and (6, -4) ______________
R. (3, 0) and (-3, 5) ______________ 1. (-11, -6) and (-8, -5) ______________
E. (12, 4) and (8, -2) ______________ 15. (-5, 4) and (-5, 3) ______________
U. (7, -3) and (7, -9) ______________ 12. (-2, -3) and (-5, 9) ______________
O. (3, 1) and (2, 5) ______________ 6. (-3, 8) and (7, 8) ______________
H. (-1, -6) and (-7, -8) ______________ 10. (-5, 3) and (7, -7) ______________
TAKE YOUR TIME!!! THIS IS 60 POINTS!

Answers

Set 2:

T. Slope = (9-5)/(10-7) = 4/3 __16.  Slope = (2-(-2))/(9-(-5)) = 4/14

B. Slope = (-4-2)/(-5-(-8)) = -6/3 __ 8.  Slope = (-8-(-6))/(2-(-10)) = -2/12

H.  Slope = (-1-(-2))/(-4-2) = -3/-6 __ 3.  Slope = (-7-1)/(-8-(-2)) = -8/6

S.  Slope = (7-9)/(-11-(-4)) = -2/-7 __ 5. Slope = (3-(-2))/(-3-(-4)) = 5/1

O. Slope = (-6-(-1))/(4-5) = -5/-1 __ 14.  Slope = (6-(-4))/(-7-(-2)) = 10/-5

Set 3:

K. Slope = (-3-(-3))/(2-1) = 0/1 __ 9.  Slope = (-4-(-1))/(6-8) = -3/-2

R. Slope = (5-0)/(-3-3) = 5/-6 __ 1.  Slope = (-5-(-6))/(-8-(-11)) = 1/3

E. Slope = (-2-4)/(8-12) = -6/-4 __ 15. Slope = (3-4)/(-5-(-5)) = -1/0

U.  Slope = (-9-(-3))/(7-7) = -6/0 __ 12. Slope = (9-(-3))/(-5-(-2)) = 12/3

O.  Slope = (5-1)/(2-3) = 4/-1 ____ 6.  Slope = (8-8)/(7-(-3)) = 0/10

H.  Slope = (-8-(-6))/(-7-(-1)) = -2/-6 _ 10. (-5, 3) and (7, -7) Slope = (-7-3)/(7-(-5)) = -10/12

What are sets?

A set is a collection of distinct objects, usually numbers, that are grouped together in a manner that follows specific rules. Sets can be used to determine if an element belongs to the set or not, and can also be used to perform operations such as unions and intersections. Sets are an important tool in mathematics, and they can help simplify complex problems.

The Mathematician had to calculate the slope between two points for each of the sets given. To calculate the slope, the Mathematician had to subtract the y-values of the two points and divide by the difference between the x-values of the two points. The Mathematician then had to match the answers to the corresponding letter or number and write the letter in the matching numbered box at the bottom of the page. By doing this, the Mathematician was able to solve the riddle and arrive at work on time.

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Please Help!
Solve each inequality:

1) P=a+b+2c

2) y=2ab-C

Answers

We can write the expression for {P} as -

P = a + b + 4ab - 2y

What is inequality?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

Given are the expressions as -

P = a + b + 2c

y = 2ab - C

We can write -

C = 2ab - y

Putting the values in the equation -

P = a + b + 2c

P = a + b + 2(2ab - y)

P = a + b + 4ab - 2y

Therefore, we can write the expression for {P} as -

P = a + b + 4ab - 2y

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mean is 75 beats per min . s/d is 12.5 if 16 female adults randomly selected find the probability that they have pulse rates with mean less than 78 beats per min

Answers

The value of probability that they have pulse rates with mean less than 78 beats per min is,

⇒ 0.5948

What is mean by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Given that;

Mean is 75 beats per min.

And, Standard deviation is, 12.5

Hence, We get;

z = (78 - 75) / 12.5

z = 3/12.5

z = 0.24

Hence, The probability is, 0.5948

Thus, The value of probability that they have pulse rates with mean less than 78 beats per min is,

⇒ 0.5948

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I need help please!!! It for geometry

Answers

Answer:

Below

Step-by-step explanation:

The diagonals  WY  and  XZ   are equal for a rectangle

14x+10 = 11x+ 22

3x = 12

x = 4

then use this value to calculate the length

  WY = 14 x + 10

         = 14 (4) + 10 = 66 units


Critique Reasoning Mario says that he drew two tangents to a circle
that meet at a point outside the circle. He also says that the two points
where the two tangents meet the circle separate the circle into two
semicircles. Is it possible for Mario to have drawn this figure? Explain.

Answers

No, it is not possible for Mario to have drawn this figure.

What are the properties of the circle?

The circumference, which is the distance around the object, the diameter, which is the length of a circle measured from one end to the other and passing through its center, and the radius, which is equal to half of the diameter, are the three key characteristics.

If two tangents to a circle meet at a point outside the circle, they must be parallel to each other.

If the two points where the two tangents meet the circle separate the circle into two semicircles, then the center of the circle must lie on the line containing the two points.

However, since the tangents are parallel, they do not intersect the line containing the two points, and therefore, the center of the circle cannot lie on this line.

This contradicts the definition of a circle, which states that the center of a circle is equidistant from all points on the circle.

Therefore, Mario's reasoning is flawed, and it is not possible for him to have drawn this figure.

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What are the possible values for From the diagram you know that the triangles have two pairs of congruent corresponding sides, that LM< _, and that m Please imma give brainlest
Help

Answers

The converse of the [tex]H[/tex]inge theorem indicates that the angle subtended by the segment [tex]\overline{LM}[/tex], (∠K) which is less than the length of the segment [tex]\overline{OP}[/tex], will be less than the measure of the angle subtended by the segment [tex]\overline{OP}[/tex], which is 90°

The possible values for angle ∠K is; m∠K < 90°What is the H-i-n-g-e Theorem?

The h-i-n-g-e theorem, which is also known as the open mouth theorem states that two triangles that have a pair of corresponding congruent sides and which have different measure of the included angle between the sides, then the third side of the triangle with the larger included angle will be longer.

The h-i-n-g-e theorem can be deduced from the triangle inequality theorem.

The corresponding congruent sides in the two triangles are;

[tex]\overline{KL}[/tex] is congruent to [tex]\overline{ON}[/tex], [tex]\overline{KM}[/tex] is congruent to [tex]\overline{NP}[/tex]

[tex]\overline{LM}[/tex] = 7 is less than [tex]\overline{OP}[/tex] = 9

Therefore;

[tex]\overline{LM}[/tex] < [tex]\overline{OP}[/tex]

m∠N = 90°, therefore, the converse of the h-i-n-g-e theorem, indicates that the angle subtended by the segment [tex]\overline{LM}[/tex] is less than the angle subtended by the angle [tex]\overline{OP}[/tex], which is 90°

The angle ∠K is less than the angle ∠N

m∠K < m∠N = 90°

m∠K < 90°

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Which solid figures do NOT have a vertex or vertices? (Check all that apply.)

cylinders
cones
prisms
pyramids

Answers

Cylinders do NOT have vertices!

Answer: Cylinders and Cones don't have a vertex or vertices.

Step-by-step explanation: I had the same question and got it right.

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Ben drew a rectangle. The length of his rectangle is the width of the rectangle.
1/3
Let & = length.
Let w = width.
W
Complete the table, and graph

Answers

Based on the relationship between the length and width of the rectangle, the length of the rectangle for the various values of the width is given below:

when width, W = 1, Length, l = 1/3when width, W = 3, Length, l = 1when width, W = 7, Length, l = 7/3

What is the relationship between the length and the width of the rectangle?

The relationship between the length and the width of the rectangle is a linear relationship given by the linear equation below:

l = w/3

where;

l is the length of the rectangle

w is the width of the rectangle

When w = 1

l = 1/3

When w = 3

l = 3/3

l = 1

when w = 7

l = 7/3

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