The length of a picture is 2 more than the width. There is a frame of uniform width around the picture that is 3 inches wide. If the area of everything is 224 in 2 , find the dimensions of the picture.

The missing sides or angles that makes the triangle ABC congruent to PDF by ASA are ∠A and ∠P, ∠B and ∠D and AB and PD

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal . In other words, two triangles are congruent when the corresponding sides and angles are equal.

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent by ASA(angle side angle)

Therefore, the missing side or the angles that would make the triangle ABC congruent to triangle PDF by ASA is as follows:

AB≅ PD

∠A ≅ ∠P

∠B ≅ ∠D

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As per the unitary method, the original price of the watch is 217.11

The term unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Here we have given that the price of a watch was decreased by 35% and sold for $75. 99.

Let us consider that x be the original price of watch.

Here we have given that the amount of discount is calculated as,

=> 35% of x = 75.99

=> 35/100 of x = 75.99

When we simplify this then we get,

=> 0.35 of x = 75.99

Then the value of x is calculated as,

=> x = 75.99/0.35

=> x = 217.11

Therefore, the correct option is (D).

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The solutions to the equation y/ (y- 4) - 4/ (y + 4) = 32/ y are approximately 30.948, 4.627 and -3.575.

The given equation is y/ (y- 4) - 4/ (y + 4) = 32/ y

Let us simplify the left hand side (LHS) :

Make the denominator same to (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y/ (y- 4))×((y + 4)/(y + 4)) - (4/ (y + 4))×((y - 4)/(y - 4))

y/ (y- 4) - 4/ (y + 4) = ( y(y + 4) - 4(y - 4))/ (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y² + 4y - 4y + 16)/ (y² - 16)

y/ (y- 4) - 4/ (y + 4) = (y² + 16)/ (y² - 16)

Now plugging this simplified version in LHS

(y² + 16)/ (y² - 16) = 32/ y

y(y² + 16) = 32(y² - 16)

y³ - 32y² + 16y + 32×16 = 0

The solutions are approximately 30.948, 4.627 and -3.575.

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Answer: Since he is in school for 5 days a week, in a school week he will have a balance of 25.

Step-by-step explanation:

The correct answer would be an option (B) which graph represents a linear function.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

A linear function is defined as a function in the form of f(x) = mx + c where 'm' and 'c' are real numbers.

It represents the line's slope-intercept form, which is written as y = mx+ c.

As per graph (B),

This is a linear function that represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line

'c' is the y-intercept of the line

'x' is the independent variable

'y' (or f(x)) is the dependent variable

Hence, the correct answer would be an option (B).

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The solution for the given quadratic equation is  x = -11 or x = -1.

A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.

The standard form of a quadratic equation is ax² + bx + c = 0.

Where a, b and c are constants.

here, given that,

The given quadratic equation is,

x² + 12x + 11 = 0.

The graph of the equation is, plotted below.

From the graph,

The solutions are x = -1 and x = -11

The second approach to find the solution for the given quadratic equation is factorization method,

x² + 12x + 11 = 0

x² + 11x + x + 11 = 0

x(x + 11) + 1(x + 11) = 0

(x + 11) (x + 1) = 0

x = -11 or x = -1

So, the required solution is x = -11 or x = -1.

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On solving the provided question, we can say that the equation representing the path of each kangaroo. x = 4ft and y = 11ft

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

equation

let X be kangaroo 1

and Y be kangaroo 2.

So the equation

X = 3ft + 1ft

while

Y = 5ft + 1ft +.5ft.

and now,

x = 4ft and y = 11ft

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Answer:

[tex]m = \frac{y2 - y1}{x2 - x1} where \: m \: is \: slope[/tex]

(8,3)=(x1,y1)

(10,3)=(x2, y2)

Now,

[tex]m = \frac{3 - 3}{10 - 8} \\ = 0[/tex]

It is difficult to estimate the exact number of smartphones in the group and the standard deviation, as this depends on what type of smartphones each person has. It could take between 1 and 8 people to find a smartphone, depending on the number of smartphones already in the group.

The number of smartphones in the group of 8 people is difficult to estimate, as it depends on the type of smartphone each person has. For example, if there are 2 people with iPhones, 3 people with Android phones, and 3 people with Windows phones, then there would be 8 smartphones in the group. However, if there is only one person with an iPhone and the other 7 have different types of phones, then there would be only 4 smartphones in the group. The standard deviation of the number of smartphones in the group would depend on how many different types of smartphones are present and the total number of smartphones in the group. The amount of time it would take to find a smartphone would depend on the number of smartphones already in the group. If there are already 4 or more smartphones, then it would take only 1 person to find a smartphone. If there are only 3 smartphones, then it could take up to 8 people before one of them has a smartphone.

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T(60) > T(10) + T(30) means that the number of tenants living on 60th floor is greater than the sum of tenants that are living in 10th and 30th floor.

n = number of floor of the Princess Tower (Floor Number)

T(n) is a function of n (floor number) which tells how many tenants are beings living on the nth floor

Tenant means a person occupying a rented land or property (A resident for simple understanding)

Therefore:

The statement:  T(60) > T(10) + T(30)

Means that: The number of tenants living on 60th floor is greater than the sum of tenants living on 10th and 30th floor.

Just for an example If we have T(60) = 30, T(10) = 10, T(30) = 5

Then T(60) > T(10) + T(30) means that 30 > 10 + 5 which becomes 30 > 15

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The interpretation of the standard error of the mean is the amount of time it takes for students taking this statistics class to complete this multiple-choice assessment item would vary by 0.27 minutes.

The sample mean duration of time required to complete this question would normally deviate from the population mean by roughly 0.27 minutes if we randomly sampled a large number of students enrolled in this statistics course.

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The main difference between an equation and an inequality is in an equation the elements are equal but in an inequality the elements are compared.

A relationship between two expressions or values that are not equal to each other is called inequality.

An equation has an answer that equals a number. An inequality has an answer that could be less than or more than or less than or equal to or more than or equal to.

For example:  You have some money in your pocket. You want to buy some snacks for tonight's match, but your wife told you to buy one pizza on your way back to home that costs $10. That means that on snacks you can spend (y) :

y ≤ x - 10     where x represents money in your pocket.

This means that from money in your pocket you have to subtract $10 for pizza and out of the remaining money you can spend some part of it on snacks or all of it.

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Leading coefficient: 23

Degree: 8 (The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of the variable "u" is 8, so the degree of the polynomial is 8.)

Answer:

i) 23

ii) 8

Step-by-step explanation:

i) leading coefficient:

23

ii) Degree

The degree of the polynomial is the highest power in the polynomial.

So,

degree of polynomial=8

Answer:

2 gallons

Step-by-step explanation:

Make a proportion of gallons of vinegar to batches of salad dressing

[tex]\frac{\frac{2}{5} }{1}[/tex] = [tex]\frac{x}{5}[/tex]

1 x 5 = 5, so

[tex]\frac{2}{5}[/tex] x5  or

[tex]\frac{2}{5}[/tex] x [tex]\frac{5}{1}[/tex] = [tex]\frac{10}{5}[/tex] = 2

Answer:

0.27

Step-by-step explanation:

I hope this helps :)

Answer:

yes to all 3

Step-by-step explanation:

A

3z = 21 ( isolate z by dividing both sides by 3 )

z = 7

B

n + 14 = 36 ( subtract 14 from both sides )

n = 22

C

[tex]\frac{3}{4}[/tex] v = 12 ( multiply both sides by 4 to clear the fraction )

3v = 48 ( divide both sides by 3 )

v = 16

Answer: Part A. a student must find the missing length by using the Pythagorean theorem.

The answer should come out to be x=2√26 or x=−2√26 (Decimal: 10.19803902…, -10.19803902…) or (Rounded to the nearest tenth: 10.20, -10.20)

Step-by-step explanation:

Let's make x the missing length. The Pythagorean theorem says the way to set up this equation is the leg^2 + leg^2 = hypotnues^2.

Set up the problem and solve, I'll show you how to do it: x²+11²2=15²

Step 1: Simplify both sides of the equation.

x² + 121=225

Step 2: Subtract 121 from both sides.

x² + 121−121=225−121

x² = 104

Step 3: Take square root.

x = ± √104

The answer should come out to be x = 2√26 or x = −2√26 (Decimal: 10.19803902…, -10.19803902…) or (Rounded to the nearest tenth: 10.20, -10.20)

Answer:

m(w) = $25+$20w

Step-by-step explanation:

Let m be the amount saved and w the weeks since the account was opened.  Greta starts with $25, so m(0) = $25.

She saves $20 each week, w.  m(1), the end of the first week, Greta would have $25 + $20 = $45.  This continues for future weeks.  We could write this as the follwoing:

 m(w) = $25+$20w

Week 5, for example, would end with m(5) = $25+$20*(5)

       m(5) = $125.

Answer:

To find the solution to the system of equations, we need to find the values of x and y that make both equations true at the same time.

The pairs of points you provided are coordinates (x,y) which we can use to find the solution.

For the pair of points (1.8, 11.4) and (-2.8, -2.4)

We can substitute the x and y values of the first point into both equations and check if they are true.

f(1.8) = 31.8 + 6 = 7.4

g(1.8) = 1.8^2 + 41.8 + 1 = 11.16

As we can see the first equation is not true, we can safely assume that this is not the solution of the system of equations.

For the pair of points (0,6) and (0, 1)

We can substitute the x and y values of the first point into both equations and check if they are true.

f(0) = 30 + 6 = 6

g(0) = 0^2 + 40 + 1 = 1

As we can see both equations are true at the same time, this is the solution of the system of equations.

For the pair of points (-3.7,0) and (-0.27,0)

We can substitute the x and y values of the first point into both equations and check if they are true.

f(-3.7) = 3*(-3.7) + 6 = -7.1

g(-3.7) = (-3.7)^2 + 4*(-3.7) + 1 = 13.69

As we can see the first equation is not true, we can safely assume that this is not the solution of the system of equations.

For the pair of points (2.8, 5.1) and (3.6, 1.2)

We can substitute the x and y values of the first point into both equations and check if they are true.

f(2.8) = 32.8 + 6 = 11.4

g(2.8) = 2.8^2 + 42.8 + 1 = 21.96

As we can see the first equation is not true, we can safely assume that this is not the solution of the system of equations.

So the solution of the system of equations is (0,6) and (0, 1)

The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

Let the number of green marbles be 'g'.

The probability of selecting a red marble before the number of green marbles is doubled is[tex]$\frac{4}{g+4} * 100 = x\%$[/tex]

The probability of selecting one of the four red marbles from the box after the number of green marbles is doubled is [tex]$\frac{4}{2g+4} * 100 = (x - 15)\%$[/tex]

Rearranging the equations and solving for g, we get:

[tex]\frac{4}{g+4} * 100 = x$\frac{4}{2g+4} * 100 = (x - 15)$$2g+4 = \frac{4}{x-15}$$g = \frac{4 - 4x + 60}{2x - 30}$[/tex]

Therefore, the number of green marbles before the number of green marbles is doubled is [tex]$\frac{4 - 4x + 60}{2x - 30}[/tex]

The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

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Isabella fills her pool at a rate of 18 liters per minute as per the given condition.

The slope of the volume can be used to determine how quickly it changes when given Time t in minutes and Volume V in liters. That represents a change in volume relative to a change in time.

m = (v2-v1)/(t2-t1).

selecting the first two points (2, 184) and from the provided data (7, 94).

Volume remains in the pool at what rate =

(94-184)/(7-2) = -90/5 = -18.

Therefore the rate at which Isabella fills her pool is 18 liters/minute as per the given question.

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If Angel is trying to find the height of a radio antenna on the roof of a local building. The height of the antenna (the distance from point A to point B) is 8m.

Given data:

Horizontal distance = 18 meters

Angle of elevation from his eyes to the roof (point A) = 21°

Angle of elevation from his eyes to the top of the antenna (point B) = 39°

So,

AB= 18 × (Tan 39° - Tan 21°)

AB = 18 × ( 0.8098 - 0.3839)

AB = 18 × 0.4259

AB = 7.67

AB = 8m (Approximately)

Therefore the height of the antenna (the distance from point A to point B) is 8m.

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To find the domain and range of a system of inequalities, you need to solve the system of inequalities, plot the solution, determine inequality sign for solution, shade area of solution, then the x-values of the area represent domain and y values represent range.

Solve the system of inequalities for x and y in terms of each other.

Plot the solutions on a coordinate plane. Each solution will be a boundary line for the solution set.

Determine the inequality signs for each solution. Solutions with < or > signs will be represented as a dashed line, while solutions with ≤ or ≥ signs will be represented as a solid line.

Shade the portion of the coordinate plane that satisfies all of the inequalities.

The shaded area represents the solution set for the system of inequalities.

The domain is the set of all x-values that are included in the solution set and the range is the set of all y-values that are included in the solution set.

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Answer:

x = 9

Step-by-step explanation:

the intersecting secants theorem states that IH * IS = IF * IT

here, x = IH

x * 16 = 8 * (10+8)

16x  = 144

divide both sides by 16 to get x

x = 9

if we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. but the probability that such a coin will come up heads exactly half the time in 16 tosses is 1 in 65536 (2^16).

This can be calculated using the binomial probability formula which states that the probability of getting a certain number of heads in a certain number of tosses is given by (Number of ways to get the desired number of heads) / (Total number of possible outcomes). In this case, the number of ways to get 8 heads in 16 tosses is equal to 16C8, or 120.

The total number of possible outcomes is equal to 2^16, or 65536. Thus, the probability of getting 8 heads in 16 tosses is 120/65536, which is approximately equal to 1/65536.

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The final answers are as follows gross profit $321,600, cost of goods sold of $528,000 and balance due $782,980.

(a) The terms of the sale are 3/10, n/30 which means that if Cullumber Company pays the invoice within 10 days, they will receive a 3% discount on the total invoice amount. However, if they pay within 30 days, they will not receive a discount.

To calculate the amount due if Cullumber Company takes the discount:

$914,000 x 3/100 = $27,420

$914,000 - $27,420 = $886,580

To calculate the gross profit:

$914,000 - $592,400 = $321,600

(b) The return of merchandise means that Cullumber Company is returning $104,600 worth of merchandise and thus the amount due to Marin will be:

$886,580 - $104,600 = $782,980

And the cost of goods sold will be:

$592,400 - $64,400 = $528,000

(c) On March 12, Marin Company received the balance due from Cullumber Company which is $782,980.

This means that the net amount received by Marin Company after the discount and return of merchandise is $782,980.

Therefore, The final answers are as follows gross profit $321,600, cost of goods sold of $528,000 and balance due $782,980.

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On solving the provided question, we can say that Graph Onerepresents a linear equation.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

Graph One

The graph is linear, commonly known as being in a straight line. Other graphs are not, though. Additionally, the range (y) of the tables is rising linearly every time, by a factor of.5 (1/2).

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Answer:

A.) (0,5)

B.) -3/2

C.) y= (-3/2)x + 5

Step-by-step explanation:

A.) The y-intercept of a graph is the point where the function crosses the y-intercept. For the function shown in the graph, the y-intercept would be (0,5) or y=5.

B.) Slope can be determined by using rise over run. To determine the rise and run, we will need to look at 2 points. Let's use the points (0,5) and (2,2). Instead of "rising" from (0,5) to (2,2), we must "sink" 3, giving us a rise of -3. Next, to get from (0,5) to (2,2), we must "run to the right 2. So, our "rise over run" or "rise/run" would be -3/2. This means our slope is -3/2.

C.) When writing an equation for the line, we are going to want to write it in slope-intercept form. Slope-intercept form is often shown as y=mx+b, when m is the slope and b is the y-intercept. Since we know both the slope and y-intercept, we can plug those values into the slope-intercept form equation. This then changes y=mx+b into y=(-3/2)x+5.

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Answer:

y= -3/2x+6

Point of intersection: (0,6)

Y Intercept: 6

Slope: -3/2

You can check slope by counting the number of units it goes down and to the side. it is rise/run so the amount of y values it goes down and x values goes to the side is the denominator.

Slope: rise/run= y1-y2/x2-x1

Step-by-step explanation:

The correct dotplot for the given data is option D, which displays the number of errors for the week for each workstation.

Error in math is any mistake made in the process of solving a mathematical problem or problem-solving process. It could mean a mistake in the calculations, incorrect steps taken, or incorrect assumptions made. It can also include making a wrong interpretation of the problem, or not being able to solve it at all. Errors in math can occur due to a lack of understanding of the concepts, mistakes in calculations, errors in reasoning, or incorrect application of the rules and formulas. Errors can also be made in the process of writing down the equations, or in the process of simplifying the equation.

The graph begins with 0 and goes up to 254201 in intervals of 5. The data points for each work station are marked on the graph, showing the number of errors each work station made. This visual display of data points allows for an easy comparison of the number of errors across all workstations.

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