The quadratic function f(x) has a vertex at (1, 6) and opens downward.

If g(x) = (x - 7)2 + 1, which statement is true?
A.
The axis of symmetry of f(x) is x = 1, and the axis of symmetry of g(x) is x = 7.
B.
The axis of symmetry of f(x) is x = 1, and the axis of symmetry of g(x) is x = -7.
C.
The axis of symmetry of f(x) is x = -1, and the axis of symmetry of g(x) is x = -7.
D.
The axis of symmetry of f(x) is x = -1, and the axis of symmetry of g(x) is x = 7.

The complete equation is 3 lb/sec ≈ 4897.0806 kg/h.

From the question, we have the following parameters that can be used in our computation:

3 Ib/sec ≈ ? kg/h

To convert pounds per second (lb/sec) to kilograms per hour (kg/h), we can use the conversion factor: 1 lb = 0.45359237 kg.

So, 3 lb/sec = 3 * 0.45359237 kg/sec = 1.361 kg/sec

To convert from per second to per hour, we multiply by the number of seconds per hour:

1.3607771 kg/sec * 3600 sec/hour = 4897.0806 kg/h

Therefore, 3 lb/sec ≈ 4897.0806 kg/h.

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Answer:

0.58

Step-by-step explanation:

First, we need to find the total number of pieces of clothing in the dryer. We do this by adding up the number of black shirts, gray shirts, black sweaters, and gray sweaters: 3 + 8 + 13 + 7 = 31

Next, we need to find the number of gray pieces of clothing in the dryer. We do this by adding up the number of gray shirts and gray sweaters: 8 + 7 = 15

Now we can find the probability of Bill taking out a gray piece of clothing by dividing the number of gray pieces of clothing by the total number of pieces of clothing: 15/31

To find the probability of Bill taking out a shirt, we add the number of black shirts and gray shirts: 3 + 8 = 11

Now we can find the probability of Bill taking out a shirt by dividing the number of shirts by the total number of pieces of clothing: 11/31

To find the probability that the piece of clothing Bill takes out is gray or is a shirt, we add the probability of Bill taking out a gray piece of clothing and the probability of Bill taking out a shirt.

So the probability that the piece of clothing Bill takes out is gray or is a shirt is: (15/31)+(11/31)= 0.58 rounded to the nearest hundredth.

The required total number of innings are 7.5.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

We have,

1 (2/3) innings on Monday and 3 (1/3) innings on Wednesday.

Total innings =  1 (2/3) +  3 (1/3)

= 5/2 + 10/2

= 15/2

= 7.5 innings.

Thus, total innings are 7.5.

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The sketch of the function z = 6 − 2x − 3y is illustrated below graph.

The term in math called function is defined as special relationship where each input has a single output.

Here we have the function as z = 6 − 2x − 3y

Now, we have to plot the function into graph.

In order to plot the graph, first we have to identify the variable in the function here in the function we have 3 variable. then we plot the graph on the 3 dimensional plane.

If you want to understand how to draw 3−D plot, then assume one of the coordinate is zero and draw line of remaining two coordinate,

In a similarly draw for other two coordinates too, you will get purview of

3−D plot of that function that has been look like as follows.

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Lisa’s average speed is: 11.4 miles/hours

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formulas and procedures we will use to solve this exercise are:

Where:

Given info:

Applying the time formula we get:

t2= 135 mi / 15 mi/h

t2= 9 h

Calculating t1 we get:

t1= 9h -1 h

t1= 8 h

Applying the average velocity formula we get:

vm= x(total)/t(total)

vm= (60 mil + 135 mil) /( 9h + 8h)

vm= 195 mil/17 h

vm= 11.4 mil/h

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Therefore , the solution of the given problem of domain comes out to be its range is [2,-2] and domain is [-1.5,-4].

A function's domain is the range of possible arguments that it can receive. These integers indicate the cross of a functional like f. (x). The range of potential values that can be used with a function is known as its domain. The value that method returns after inserting the x value belongs to this set. The formula for a function with y as the predictor variables and x as the predictor variables is y = f. (x). When a single value of y can be successfully produced from a value of x, that value is said to be in the domain of the function.

Here,

Given :

A graph with the extreme values of 2 and -2.

So.

Its range is [2,-2]

and

its start from [-1.5,-4]  

so its domain is [-1.5,-4] .

Therefore , the solution of the given problem of domain comes out to be

its range is [2,-2] and domain is [-1.5,-4].

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The relation's domain is 0, 1, 2, 3, and 4.The relation's range is: 0, 1, 4, 9, and 16.

The set of x-values or relational inputs can be thought of as the domain of a relation.

The collection of all results, or y-values, that match an ordered set of pairs' x-values.

With respect to the relationship, (0, 0), (1, -1), (2, -4), (3, -9), and (4, -16)

The relation's range is 0, 1, 2, 3, and 4. (these are all the input of the relation).

The relation's range is: 0, 1, 4, 9, and 16 (these are all the output of the relation).

The relation's domain is 0, 1, 2, 3, and 4.The relation's range is: 0, 1, 4, 9, and 16

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Answer: 3x^2 + x + 2

Step-by-step explanation:

1. The slope-intercept form of the equation of each line given the slope and y-intercept are as follows:

2. The given slopes are:

3. Two slopes of the parallel lines are:

The slope of the line parallel is 2/3.

The slope of the line parallel is 9/5

4. The slopes of all perpendicular lines are:

The slope-intercept form of the equation of a line given is given below:

where;

m is the slope

c is the intercept

a. Slope-10, y-intercept = -5

The equation will be: y = -10x - 5

b. Slope 7, y-intercept = 5

The equation will be: y = 7x + 5

c. Slope = -9/5, y-intercept =- 4

The equation will be: y = -9/5x - 4

d. Slope = -5/4, y-intercept - 5

The equation will be: y = -5/4x - 5

2. Slope = y₂ - y₁ / x₂ - x₁

a. (17,-6), (-11,7)

slope = 7 - (-6) / -11 - 17

slope = -13/28

b. (3,4), (-4,-5)

slope = -5 - 4 / -4 - 3

slope = -9/7

c. (-20, 14),(17, 15)

slope = 15 - 14 / 17 - (-20)

slope = 1/37

d. (11,-18), (-1,-7)

slope = -7 - (-18) / -1 - 11

slope = -11/12

3. Two lines are parallel if the slopes are equal.

a. y = 2/3x - 4

The slope of its line is 2/3

The slope of the line parallel is 2/3.

b. y = 9/5x - 5

The slope of its line is 9/5

The slope of the line parallel is 9/5

4. The slope of all perpendicular lines is the negative reciprocal, that is, (-1/m).

a. y = -1/2x -2

slope, m = -1/2

The slope of a perpendicular line = -1/(-1/2)

The slope of a perpendicular line = 2

b.  y = -x -1

slope, m = -1

The slope of a perpendicular line = -1/(-1)

The slope of a perpendicular line = 1

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It is going to take 140 seconds to walk from first floor to the fifth floor.

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

Time taken for walking up 3 floors = 84 seconds

Time taken for walking up 1 floor = 84 seconds/3 = 28 seconds/floor

Time it is going to take for walking up 5 floors =  28 second/floor* 5  floor

Time it is going to take for walking up 5 floors = 140 seconds

We can conclude, it will take 140 seconds to walk from the first floor to the fifth floor.

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Her bi-weekly gross earnings if she works 47 hours during a week of her pay period is $4110.525.

The answer is determined by calculating the income earned for the additional hours she works multiplied by the income earned for the additional hours. This is then added with the gross income for the week and the total is calculated by taking the sum of the two.

Given that her bi-weekly gross earnings are $913.45, and she earns additional compensation for all hours over 40 worked in one week.

For 47 hours, the extra hours worked are 7.

Hence, the compensation for additional hour is:

a = 7 (913.45/2)

a = 3197.075

The gross income would be:

Total = bi-weekly pay + additional hours

T = 913.45 + 3197.075

T = 4110.525

Hence, her bi-weekly gross earnings if she works 47 hours during a week of her pay period is $4110.525.

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The total amount Ofelia had was $ 15.

The equations are mathematical statements with two algebraic expressions flanking the equal to the sign on either side.

It can demonstrate the equality of the relationship between the expressions printed on the left and right sides.

There are some components of an equation, that are:

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign.

The "=" sign determines on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is equal to the original amount of money

The amount Ofelia spends = $ 12

The remaining amount of money Ofelia had=(1/5)A

So, the equation will be

subtract the original amount of money A - amount Ofelia spends = remaining amount of money Ofelia had

By substituting the values in the equation, we get

A - 12 = ( 1/5 )A

Add 12 on both sides of the equation, and we get

A = (1/5)A + 12

Subtract (1/5 )A on both sides of the equation, and we get

A - ( 1/5 )A = 12

On simplifying the equation, we get

(5A - A)/5 = 12

4A/5 = 12

Multiplying by 5 on both sides of the equation, we get

4A = 60

Divide by 4 into both sides of the equation, and we get

A = $ 15

The value of A is $ 15

Hence, the original amount is $ 15

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Answer: the smallest number out of the four is 0.13

Step-by-step explanation:

First, let's think about the number 13. It's a whole number and it's pretty big. It's definitely larger than the other numbers we're looking at today.

Next, let's take a look at 0.13. This number is a decimal, which means it's a number that has a whole number part and a fractional part. The whole number part is 0 and the fractional part is 13. So, 0.13 is smaller than 13.

Now, let's move on to 1.03. This is also a decimal and it's a little bit bigger than 0.13, but smaller than 13.

Finally, we have 1.3. This number is a decimal with a whole number part of 1 and a fractional part of 3. It is bigger than 0.13 and 1.03 but smaller than 13.

So, we can see that the smallest number out of the four is 0.13.

On U.S. converting to Metric System , the Advantages are Standardization , Improved Science and Technology and the Disadvantages are Cost , Resistance to change .

The Advantages of the U.S. converting to the metric system:

(i) Standardization: The metric system is used by the majority of countries in the world, making international trade and communication easier and more efficient.

(ii) Improved Science and Technology: The metric system is the standard system used in science and technology, making it easier for the U.S. to collaborate with other countries and to participate in international research.

The Disadvantages of the U.S. converting to the metric system:

(i) Cost: The conversion to the metric system would be a costly and time-consuming process, involving changes to products, labeling, and infrastructure.

(ii) Resistance to change: There may be resistance from people who are used to the imperial system and are comfortable with it.

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Answer:

C' - (6, -6)

D' - (8, -6)

E' - (10, -8)

F' - (8, -10)

Step-by-step explanation:

Hey there!

To solve this problem, we must first know what the rule for rotating a shape 90 degrees clockwise is:

(x, y) --> (y, -x)

Now, we can apply this rule to all of the points/vertices

C' - (6, -6)

D' - (8, -6)

E' - (10, -8)

F' - (8, -10)

These are the points and their coordinates after the rotation has been applied.

The equation of the line that passes through two points (1, 4) and (3, 10) is,

y = 3x + 1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line passes through two points (1, 4) and (3, 10).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

y - 4 = 6/2 (x - 1)

y = 3x + 1

Therefore, the equation of the line is y = 3x + 1.

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Answer: I think you got number 1 correct.

Step-by-step explanation: I think you can search online XD.

The pearson correlation coefficient is equal to 4.6/1.25, or 3.68. This is approximately equal The closest answer is e. 0.98.

Coefficient is a numerical or statistical value used to measure the strength or magnitude of a relationship between two or more variables. It is commonly used in mathematics, physics, engineering, and economics to quantify the strength of a linear relationship between two variables. In mathematics, coefficients are used to measure the degree of influence of a certain variable on the relationship between two variables.

The correlation between x and y can be found by calculating the Pearson correlation coefficient. This can be done by first calculating the covariance of x and y, which is equal to 4.6, and then dividing it by the standard deviation of x multiplied by the standard deviation of y, which is equal to 1.25.

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Answer:

Answer is 382.5 square inch

Step-by-step explanation:

calculate all the area of the surface

Answer is 382.5 square inch

The surface area of the prism is given by the equation A = 382.5 inches²

The surface area of the prism is calculated as

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

Given data ,

Let the surface area of the prism be represented as A

Now , the prism consists of 2 right angled triangles and 3 faces of rectangles

So , the base of the triangle b = 9 inches

The height of the triangle h = 10 inches

So , the area of the 2 triangles = 2 ( bh ) / 2

On simplifying the equation , we get

The area of 2 triangles = 9 x 10 = 90 inches²

The area of first rectangle = 9 x 10 = 90 inches²

The area of second rectangle = 9 x 9 = 81 inches²

The area of third rectangle = 13.5 x 9 = 121.5 inches²

So , the area of the prism = area of 2 triangles + area of first rectangle + area of second rectangle + area of third rectangle

Substituting the values in the equation , we get

The area of the prism A = 90 + 90 + 81 + 121.5

The area of the prism A = 382.5 inches²

Hence , the surface area of prism is 382.5 inches²

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The intersection of events A and B is the event of exactly two tails. This is because event A is defined as exactly two tails and event B is defined as at least two tails.

Since two tails is both exactly two tails and at least two tails, the intersection of the two events is exactly two tails.

The intersection of two sets is the set of all elements that are common to both sets. This is also known as the intersection of two conjunctions. To find the intersection of two sets, you take the elements from both sets and keep only the elements that are found in both sets. For example, given the sets A = {1, 2, 3} and B = {2, 3, 4}, the intersection of A and B would be {2, 3}.

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The probability that she will select a chicken would be =7/23.

Probability is defined as the expression that represents that possible outcome of an event.

The amount of pigs in the farm = 6

The amount of chicken in the farm = 7

The amount of cows in the farm = 10

The total animals in the farm = 10+7+6 = 23

The probability of selecting a chicken out from the whole farm = 7/23.

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Complete question:

Giovanna owns a farm. She is going to randomly select one animal to present at the state fair. She has 6 pigs, 7 chickens, and 10 cows. What is P (chicken) ?

Answer:

I'm sorry I don't know

Step-by-step explanation:

but I think that you do need to multiply it by 1pp just asyou multiply the amp by 100 from Ma to A

The top 25 percent, a data point would need to have a z score greater than 0.67.

A z score is a measure of how many standard deviations a data point is from the mean of a data set.

To determine the minimum z score, we first need to find the mean and standard deviation of the data set. The mean represents the center of the data and the standard deviation tells us how spread out the data is.

If a data point has a z score greater than 0, it is above the mean and considered in the top half of the data set.

To be in the top 25 percent, the data point would need to have a z score greater than the value that separates the top 75 percent from the bottom 25 percent.

This value can be found using a table of standard normal distributions or using software that calculates z scores.

In a standard normal distribution, the value that separates the top 75 percent from the bottom 25 percent is about 0.67.

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one-sided limits of a function f(x) at x = 1 is  lim x → 2[f(x) - f(2)]/(x - 2) = 20

Since  function f(x) = 5(x² - 1) and we want to find its derivative, we can proceed thus.

Let x = h + 2

So,  

f(x) = 5(x² - 1)

f(2) = 5[(2)² - 1]

= 5[4 - 1]

= 5(3)

= 15

f(2 + h) = 5[(2 + h)² - 1)

= 5(4 + 4h + h² - 1)

= 5(3 + 4h + h²)

= 15 + 20h + 5h²

So, f(2 + h) - f(2) = 15 + 20h + 5h² - 15

= 20h + 5h²

So, we have that

[f(2 + h) - f(2)]/h = (20h + 5h²)/h

= 20 + 5h

Now, taking the limit as h → 0, we have

= 20 + 5(0)

= 20 + 0

= 20

So,  lim h → 0[f(2 + h) - f(x)]/h = lim x → 2[f(x) - f(2)]/(x - 2) = 20

So,  lim x → 2[f(x) - f(2)]/(x - 2) = 20

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A stick has a length of 5 units and the stick is then broken at two points, chosen at random, then the probability that all three resulting pieces are shorter than 3 units is 16%.

Total length of the stick = 5 units

The stick is broken into pieces = 3

The equal length of the stick = 5/3

The equal length of the stick = 1.67

The probability that all three resulting pieces are shorter than 3 units = 2/5 × 2/5

The probability that all three resulting pieces are shorter than 3 units = 4/25

The probability that all three resulting pieces are shorter than 3 units = 0.16

The probability that all three resulting pieces are shorter than 3 units = 16%

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Answer: The Fourth One

Step-by-step explanation:

Answer:

Bottom right corner

Step-by-step explanation:

Note that the proof that ΔABC ≅ ΔEDC is given as follows:

According to the ASA rule, if any two angles and sides included between the angles of one triangle are comparable to the corresponding two angles and sides included between the angles of the second triangle, the two triangles are said to be congruent.

Thus, given the above statements, it is clear that ΔABC ≅ ΔEDC

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Full Question:

Angle BAC is congruent to Angle DEC: Given

C is the midpoint of AE: Given

Prove triangle ABC is congruent to triangle EDC

What are the statements and reasons for this proof?

If ABC is a right angled triangle and angle BAC = 90°. If AD perpendicular to BC and BD=DC then BC² = 4AD² is 4 * AD^2.

How to prove that BC² = 4AD²?​

In right triangle ABC, by Pythagorean theorem, we have:

AC^2 + BC^2 = AB^2

Since AD is perpendicular to BC, by similarity, triangle ABD is similar to triangle ADC. Therefore, we have:

BD/AD = AD/DC

BD = AD^2/DC

Substituting BD into the first equation, we get:

AC^2 + BC^2 = AB^2 = AD^2 + (AD^2/DC)^2

AC^2 + BC^2 = AD^2 + AD^4/DC^2

AC^2 + BC^2 = AD^2(1 + AD^2/DC^2)

Since BD = DC, we have:

AC^2 + BC^2 = AD^2(1 + AD^2/BD^2)

And substituting DC = BD:

AC^2 + BC^2 = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2)

Since AB^2 = AC^2 + BC^2, we have:

BC^2/AD^2 = AB^2/AD^2 - AC^2/AD^2 = (AB^2 + AC^2)/AD^2 - AC^2/AD^2 = (BC^2 + AC^2)/AD^2 = 4

Therefore, BC^2 = 4 * AD^2.

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The required simplified value of the f + g(x) =  3x² + 5x + 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x)=3x²-2x+6

g(x) = 7x - 4

f+g = f(x) + g(x)
      = 3x²-2x+6 + 7x - 4
      = 3x² + 5x + 2

Thus, the required simplified value of the f + g(x) =  3x² + 5x + 2.

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Answer:

  B.  y -6 = 2(x -2)

Step-by-step explanation:

You want the point-slope equation of the line with slope 2 through point (2, 6).

The point-slope equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Then the equation for the line with slope 2 through point (2, 6) is ...

  y -6 = 2(x -2) . . . . . choice B

__

Additional comment

If any function goes through the point (0, 0), it can be translated so that it goes through the point (h, k) by the replacements ...

A line with slope 2 through the origin is y = 2x. When that is translated so it goes through (2, 6), the equation becomes ...

  y -6 = 2(x -2)

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