A'BC' is a dilation of ABC.
If the center of dilation was (0,0), what was the scale factor used to create the dilation?

I’m literally sobbing- I have no clue what this question means

Using the calorie count C for a serving of food C =5h + 8f + 5​p, the formula for f is derived to be; f = (C - 5h  - 5​p) / 8

An equation is an expression that shows the relationship between two or more numbers and variables.

WE have been Given data that C =5h + 8f + 5​p

Where C is the calorie count, h is the number of grams of carbohydrate, f is the number of grams of fat and p is the number of grams of protein

Now solving for f in the given equation;

C = 5h + 8f + 5​p

Then f the subject of formula;

C - 5h  - 5​p = + 8f

8f = C - 5h  - 5​p

Now dividing through by 8

f = (C - 5h  - 5​p) / 8

Hence, The number of grams of fat, f, contained in a serving of food is; f = (C - 5h  - 5​p) / 8

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Answer:

AB and CD are congruent.

Step-by-step explanation:

Given points:

To determine if AB and CD are congruent, calculate the length of the two lines using the distance formula.

[tex]\boxed{\begin{minipage}{7.8 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

[tex]\begin{aligned}\implies AB & = \sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& = \sqrt{(2-4)^2+(6-1)^2}\\& = \sqrt{(-2)^2+(5)^2}\\& = \sqrt{4+25}\\& = \sqrt{29}\end{aligned}[/tex]

[tex]\begin{aligned}\implies CD & = \sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\& = \sqrt{(-4-(-2))^2+(-3-2)^2\\& = \sqrt{(-2)^2+(-5)^2}\\& = \sqrt{4+25}\\& = \sqrt{29}\end{aligned}[/tex]

Therefore, as AB = CD, we can conclude that AB and CD are congruent.

The equation in terms of x that represents the given relationship is (7 + x)x = 555

The given parameters are

Length = L

Width = x

Area = 555 yd^2

From the question, we have

L = 7 + x

The area of a rectangle is

A = Lx

Substitute 7 + x for L

So, we have

A = (7 + x)x

Substitute 555 for A

So, we have

(7 + x)x = 555

Hence, the equation in terms of x that represents the given relationship is (7 + x)x = 555

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Answer:

×=2 , y= -2

Step-by-step explanation:

3x+y=4______(1)

x-3y=8_______(2)

by substitution method...

multiplying eq (1) by 3..

9x+3y=12_____(3)

x-3y=8_______(4)

10x=20

x=2

putting the value of x in eq (1)

3x+y=4

3(2)+y=4

6+y=4

y=4-6

y=-2

×=2 , y= -2

Answer:

5, -35, 3.75, 4a + 4b + 5

Step-by-step explanation:

1. f(0) = 3(0)^2 - 2(0) + 5 = 5

2. f(-4) = 3(-4)^2 - 2(-4) + 5 = -35

3. f(-1/2) = 3(-1/2)^2 - 2(-1/2) + 5 = 3.75

4. f(a+b) = 3(a+b)^2 - 2(a+b) +5 = 4a + 4b + 5

3(a+b)(a+b) - 2a -2b + 5

6a + 6b -2a -2b +5

4a + 4b + 5  

I think

Answer:

Step-by-step explanation:

30.8%

Explanation- Did the maths

Answer:the problem is kinda confusing on the (three-cent five-cent and 10-cent lollipops) part ) but if she needs to spend 1$ exactly the answer is 14( reason show below.)

Step-by-step explanation

First I did

(3x5=15)

then I did

(15x4=60)

Then

60+15+15=90

Lastly

90+5+5=100(aka 1$)

In conclusion she can buy 14

Answer:

Team A scored 12 pts

Team B scored 17 pts

The linear equation that passes through (-1, 8) and (5,-2) is:

y = (5/3)*x + 29/3

A general linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope, and b is the y-intercept.

If we know that this line passes trhough the points (-1, 8) and (5, -2) then we can write the slope as:

a = (-2 - 8)/(5 + 1) = -10/6 = 5/3

Then we can write:

y = (5/3)*x + b

Now to find the value of b we can replace the values of one of the points in the line, if we use (-1, 8) we will get:

8 = (5/3)*-1 + b

8 + 5/3 = b

24/3+  5/3 = b

29/3 = b

We conclude that the linear equation is:

y = (5/3)*x + 29/3

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These are our two tables of values for the following functions using the integers from -4 to 4.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The given functions using the integers from -4 to 4 are

a. F(x)=6/x-2b.

r(x)=6x+12/x²-4

According to given question we have

f(x) = 6/x - 2

Now we just need to evaluate the function in all the given points:

a) f(x) = 6/x - 2

Now we can put the value

f(-4) = 6/(-4) - 2 =  -3/2 - 4/2 = -7/2

f(-3) = 6/-3 - 2 = -4

f(-2) = 6/-2 - 2 = -5

f(-1) = 6/-1 - 2 = -8

f(0) is undefined

f(1) = 6/1 - 2 = 4

f(2) = 6/2 - 2 = 1

f(3) = 6/3 - 2 = 0

f(4) = 6/4 - 2 = -1/2

b. r(x)=6x+12/x²-4

Now we can put the value

r(-4) = 6(-4)+12/(-4)²-4=-27.25

r(-3) = 6(-3)+12/(-3)²-4=-20.66

r(-2) = 6(-2)+12/(-2)²-4=-13

r(-1) = 6(-1)+12/(-1)²-4= 2

r(0) = 6(0)+12/(0)²-4= ∞

r(1) = 6(1)+12/(1)²-4 =14

r(2) = 6(2)+12/(2)²-4=11

r(3) = 6(3)+12/(3)²-4 =15.33

r(4) = 6(4)+12/(4)²-4=20.75

Therefore, these are our two tables of values for the following functions using the integers from -4 to 4.

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Answer:

60/7 ft

Step-by-step explanation:

Using similar triangles, if we let the height of the tree in ft be x,

[tex]\frac{x}{24}=\frac{5}{14} \\ \\ x=\frac{60}{7}[/tex]

The number of pounds of steak she buys is 0.82 pounds

From the question, we have the following parameters:

3.5 pounds of steak = $36.75

From the question, we understand that

Hannah spent $8.61 on steak

This means that

x pounds = $8.61

So, we have the following system of equations

3.5 pounds of steak = $36.75

x pounds = $8.61

Cross multiply in the above equation

So, we have

36.75 * x = 3.5 * 8.61

Divide both sides of the equation by 36.75

x = 3.5 * 8.61/36.75

Evaluate the quotient

x = 0.82

Hence, the number of pounds of steak she buys is 0.82 pounds

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Step-by-step explanation:

If n= -1

input -1 for n in the equation

e.g. 3(-1)³-4(-1)

From there solve for n and you should get -23n

The distinction between present value and future value is that the former is required now and the latter is needed at a future period

What is the difference between present value and future value?

The present value indicates today's worth or dollars of a future value  of a  flow whereas the future value determines the future worth of an investment or deposit made today or deposits over a number of years at a time in the future

The amount that Claudia would have in a year's time is future value because the present value is the initial deposit made today

The amount that Steven would  have to deposit today in order to accumulate $400,000 in 15 years is the present value

The amount that a deposit of $4,500 made today would worth in 6 years is the future value because the initial deposit is the present value.

Joe would have to deposit payments in expectation of future value after 3 years and the deposit required today to earn a rate of return of 5% in order to have $1000 in 5 years is a present value

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The general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.

A line that only touches a curve once is said to be tangent to it. The point (x₀ , y₀) where a line with the equation of a tangent to a curve

y = f ( x ) is given by:

T' (x) = f'(x) (x ₋ x₀)  ₊ y₀

The slope of the tangent line to a curve at a point is computed by getting the first derivative of the curve.

y(x)=2x²y

y'(x) = (2)2x²⁻¹ ₊ (1)2x¹⁻¹

y'(x) = 4x¹ ₊ 2x°

y'(x) = 4x ₊ 2(1)

y'(x) = 4x ₊ 2

The slope at a point

P (x, y) is computed by substituting the x-coordinate of the point to the first derivative. This is the general expression for the slope:

m = y'(x) = 4x + 2

For x = - 3

m = 4 (- 3) + 2

m = - 12 + 2

m = - 10

For x = 0.5

m = 4 (0.5) + 2

m = 2 + 2

m = 4

Therefore, the general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.

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Answer:

Step-by-step explanation:

The area of a triangle is equal to half the product of the base by the height drawn to that base

Hence,

1)

[tex]\displaystyle\\S_\triangle=\frac{1}{2}(4)(1.5)\\\\S_\triangle=2(1.5)\\\\S_\triangle=3 \ square\ inches[/tex]

2)

[tex]\displaystyle\\S_\triangle=\frac{1}{2}(16)(9.4)\\\\S_\triangle=8(9.4)\\\\S_\triangle=75,2 \ square\ km[/tex]

3)

The area of a trapezoid is equal to the product of the half sum of the trapezoid bases by the height

Hence,

1 ft=12 in

[tex]\displaystyle\\S_{trapezoid}=\frac{a+b}{2}h \\\\S_{trapezoid}=\frac{16.8+33.6}{2}(12)\\\\ S_{trapezoid}=\frac{50.4}{2} (12)\\\\S_{trapezoid}=25.2(12)\\\\S_{trapezoid}=302,4 \ square \ inches[/tex]

4)

[tex]\displaystyle\\S_{trapezoid}=\frac{7.9+2.3}{2}(4.6)\\\\S_{trapezoid}=\frac{10.2}{2}(4.6)\\\\ S_{trapezoid}=5.1(4.6)\\\\ S_{trapezoid}=23.46\ square\ meters[/tex]

5)

The area of a rectangle is equal to the length times the width of its sides

Hence,

[tex]S=ab\\\\S=6(5.1)\\\\S=30.6\ square\ meters[/tex]

6)

[tex]S=6(4)-2(4-3)\\\\S=24-2(1)\\\\S=24-2\\\\S=22 \ square\ cm[/tex]

A) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ exactly​ three is;

P(X = 3) = 0.2397

B) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ at least​ four is;

P(x ≥ 4) = 0.50748

C) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ less than eight is;

P(x < 8) = 0.99051

The formula for binomial Probability distribution is;

P(X = x) = ⁿCₓ * p^(x) * (1 - p)^(n - x)

We are told that 36​% adults favor the use of unmanned drones by police agencies. Thus;

p = 30% = 0.3

sample size; n = 12

A) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ exactly​ three is;

P(X = 3) = ¹²C₃ * 0.3³ * (1 - 0.3)^(12 - 3)

P(X = 3) =  ¹²C₃ * 0.3³ * 0.7⁹

P(X = 3) = 0.2397

B) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ at least​ four is;

P(x ≥ 4) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)

P(x ≥ 4) = 0.50748

C) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ less than eight is;

P(x < 8) = 1 - (P(8) + P(9) + P(10) + P(11) + P(12))

P(x < 8) = 1 - 0.00949

P(x < 8) = 0.99051

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Answer:

85+75+160=v

Step-by-step explanation:

correct answer

Use the roster method to write each of the given sets. the set of natural numbers x that satisfy x + 6 = 5.

There is no set of natural numbers of x that satisfy the condition for x+6=5

Roster method is nothing but listing the items of a set inside brackets, the roster method provides a means to display the set's components.

For Example, A={1,2,3,4,5}

The Natural numbers is the category of numbers known as "natural numbers" (n) contains only positive values. They are used in numerical ordering and counting.

They are {N=0,1,2,3,4,......}

Here, x+6=5

Only an integer can meet the condition from the given parameters. This is because an integer has two possible values: positive and negative.

i.e

By adding (-6) to both sides, we have:

x+6-6=5-6

x=-1

Therefore here only one integer satisfy the equation x+6=5 that is {-1} but -1 is not a natural number.

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Answer: (5, -6)

Step-by-step explanation:

I'm not really 100% sure if i can put in detail but this is the correct answer

Answer: Yes it is proportional

Step-by-step explanation: First I used two points on paper and used the formula y2-y1/x2-x1 and used these two points (20,100) and (15,175) and got -15, And finally it is proportional at a negative rate!

Hope This helps owo

The graph of the quadratic equation is shown in the image attached below.

In accordance with algebra fundamental theorem, we can construct a quadratic equation by knowing the locations of at least three points on Cartesian plane. Herein we find a quadratic equation in vertex form, whose formula is described below:

y - k = C · (x - h)²

Where:

By using this expression, we can find the locations of the vertex and intercepts of the parabola. Now we proceed to find all the required information:

Vertex

y = (x + 5)²

(h, k) = (- 5, 0)

x-Intercepts

(x + 5)² = 0

x = - 5

y-Intercept

y = (0 + 5)²

y = 25

Another point

x = - 1

y = (- 1 + 5)²

y = 4²

y = 16

Finally, we mark the three points on the Cartesian plane and pass a curve through them. The result is shown in the image attached below.

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Answer:51.25

Step-by-step explanation:

The number that have a digit in the ones place is 1/10 of the value in the tens place are 3,222 and 1,055.

What is Place value?

The value of each digit is called place value.

The given condition to find the number is;

Number that have a digit in the ones place is 1/10 of the value in the tens place.

Now, In the number 3,222;

2 is 1/10 of the 20 in the tens place.

And, In the number 1,055

5 is 1/10 of the tens value of 50.

So, The number that have a digit in the ones place is 1/10 of the value in the tens place are 3,222 and 1,055.

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Answer:

The answer A,B,C