Rewrite in simplest terms:
−
6
(
6
p
−
9
)
−
10
p
−6(6p−9)−10p

Triangles AED and BEC are congruent by AAS rule, so DE ≅ CE by CPCTC

When corresponding sides and angles of two triangles are congruent, they are said to be congruent triangles.

Given is figure of triangles,

In Δ ADC and Δ BCD,

AD ≅ BC (given)

∠ BCD ≅ ∠ ADC (given)

DC is common segment in both,

Therefore,  Δ ADC ≅  Δ BCD by SAS rule

∠ DAE ≅ ∠ CBE by CPCTC

∠ AED ≅ ∠ BEC by vertically opposite angles postulate.

Δ AED ≅ Δ BEC by AAS rule

DE ≅ CE by CPCTC

Hence, Triangles AED and BEC are congruent by AAS rule, so DE ≅ CE by CPCTC

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The number of cars sold that were not white based on the dot plot is 19

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

The dot plot represents the given parameter

From the dot plot, we have the following values represented as follows:

The above parameters means that the following cars are not white cars

So, we have the following representation

When these frequencies are added, we have

Total = 5 + 8 + 1 + 4 + 1

Evaluate the sum

Total = 19

Hence, the number of cars is 19

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Answer: it is A.

Step-by-step explanation: I did the quiz

The ratios are as follows

Ratio of boys to girls = 2:3

Ratio of girls to boys = 3:2

Ratio of tomato plants to lettuce plants = 1:2

Ratio of lettuce plants to cucumber plants = 4:1

Unit rate = $4

Cost of buying 20 copies = $80

What are ratios?

Ratios compare two numbers, usually by dividing them.

If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B.

For example, if A is five and B is 10, your ratio will be 5/10.

According to the given question:

1) There were 6 boys and 9 girls on the camping trip.

Ratio of boys to girls = 6:9 = 2:3

Ratio of girls to boys = 9:6 = 3:2

2) There are 4 tomato plants, 8 lettuce plants, and 2 cucumber plants in Jill's garden.

Ratio of tomato plants to lettuce plants = 4:8 = 1:2

Ratio of lettuce plants to cucumber plants = 8:2 = 4:1

3)  If Jan can buy 10 copies of a certain book for $40

Unit rate = 40/10 = $4

Cost of buying 20 copies = 20 x 4 = $80

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Answer:

4.) m > 7

5.) k + (-5) > 30 (The ">" has a line under It)

6.) 0.875

I don't know what it means when it says "graph the solution set" but I simplified it for you!

Answer:

Step-by-step explanation:

Start with the slope intercept equation: y=mx+b

y=-2x+1

m=-2 and b=1

Now draw a graph on your paper, place a point at +1 on the Y axis.

Next, solve for y with x=1.

y=-2(1)+1

y=-2+1

y=-1

Now graph (1,-1)

Answer: 3 [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Answer:

7 1/5

Step-by-step explanation:

Answer:

[tex]C. \; \dfrac{x+2}{x+1}[/tex]

Step-by-step explanation:

Since the vertical asymptotes are at x = -1

This means the denominator must have x + 1 in it

The only expression is the one in choice C

Answer: I'm pretty sure the answer is either 18.6, or 90

Tell me in the comments if I'm wrong

The values of the unknown angles are ∠1 = 92°, ∠2 = 24°, ∠3 = 64°, ∠4 = 35°, ∠5 = 81°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal). For example, in the below-given figure, angle p and angle w are the corresponding angles.

∠1 + 88 = 180°( angles on a straight line)

∠1 = 180 - 88 which is 92°

∠3 = 64°( corresponding angles are equal)

∠2 + ∠1 + ∠3 = 180( sum of angles in a triangle)

∠2 + 92° + 64° = 180

∠2 = 180 - 92 - 64

∠2 = 24°

∠4 + 81 + ∠3 = 180 ( angles on a straight line)

∠4 + 81 + 64 = 180

∠4 = 180 - 64 -81

∠4 = 35°

∠5 = 81°( alternate angles are equal)

In conclusion the values of ∠1, ∠2, ∠3, ∠4, ∠5 are 92°, 24°, 64°, 35° and 81° respectively.

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Answer:

16

Step-by-step explanation:

You must use the Pythagorean theorem to find w. Because you are looking for a leg, you must do a² - b² = c². This translates to 20² - 12² = w². If you enter the numbers into your calculator 20²- 12² = 256. You must then square root 256, and if you input √256 into your calculator you will get your final answer of w = 16.

Answer:

4.5 or equivalently 4 1/2 or 9/2

All are equivalent

Units are miles/hour

Step-by-step explanation:

Take any two points on the graph. Divide the change in y values to the change in x values and you get the rate

Chosen points: (0, 0) and (2, 9)

Rate of change = (9-0)/(2-0) = 9/2 = 4.5

Answer:

∠1 = 52

∠2 = 128

∠3 = 52

Step-by-step explanation:

∠2 = ∠4 Because of vertical angles

∠1 = ∠3 Because of vertical angles

∠1 + ∠4 = 180 Because of supplementary angles

Here, we are given that ∠4 = 128°

∠4 = ∠2 So ∠2 = 128°

∠1 + ∠4 = 180

∠4 = 128°

∠1 + 128° = 180

==> subtract 128 from both sides

∠1 = 52

∠1 = ∠3

∠1 = 52 meaning that ∠3 = 52

Answer:

m<1 = 52°

m<3 = 52°

m<4 = 128°

Step-by-step explanation:

Given: m<2 = 128°

<1 is supplementary to <2.

m<1 + m<2 = 180°

m<1 + 128° = 180°

m<1 = 52°

Angles 1 and 3 are vertical angles, so they are congruent.

m<3 = 52°

Angles 2 and 4 are vertical angles, so they are congruent.

m<4 = 128°

Answer:

Step-by-step explanation:

Answer: The sale price per dozen would we around $6.80 with no tax included.

Step-by-step explanation:

Answer:a

Step-by-step explanation:

Answer:

(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.

(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.

(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.

Step-by-step explanation:

The area that represent the wall the poster will cover is as follows:

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Therefore, One poster has a width of x + 5 inches, and the other has a width of x + 3 inches.

The expression  to represent the area of wall that the posters will cover can be calculated as follows:

area = w²

area of the first poster = (x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25

area of the second poster = (x + 3)² = (x +3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9

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Answer: 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

2+0 is zero I mean two and 1+1 is two and 5+ I forgot something and you know you just need to add them up together in it at all your answer

Answer: y=7x+1

Step-by-step explanation:

y=mx+b

Given:

slope= 7

point is (1,8)

Replace x and y for those numbers:

8=7(1)+b

Solve for b:

8=7+b

b=1

Final equation:

y=7x+1

The value of angle RPQ in the circle is 115°.

The products of the measurements of the segments of two chords are equal if they intersect in a circle.

When two chords intersect inside a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175°

arc angle SA = 55°

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115°.

Therefore, the angle is 115°.

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Answer:

[tex]\textsf{a)} \quad y=3\left(\dfrac{5}{3}\right)^x[/tex]

[tex]\textsf{b)} \quad y=40\left(\dfrac{1}{3}\right)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

From inspection of the diagram, two points on the graph are:

The y-intercept is the y-value when x = 0.

As a is the y-intercept, and the y-intercept is 3:

[tex]\implies y=3 \cdot b^x[/tex]

Substitute point (1, 5) into the equation and solve for b:

[tex]\begin{aligned}(1,5) \implies 5&=3 \cdot b^1\\5&=3b\\b&=\dfrac{5}{3}\end{aligned}[/tex]

Therefore, the equation of the exponential function is:

[tex]y=3\left(\dfrac{5}{3}\right)^x[/tex]

From inspection of the diagram, two points on the graph are:

The y-intercept is the y-value when x = 0.

As a is the y-intercept, and the y-intercept is 40:

[tex]\implies y=40 \cdot b^x[/tex]

Substitute point (-1, 120) into the equation and solve for b:

[tex]\begin{aligned}(-1,120) \implies 120&=40 \cdot b^{-1}\\\dfrac{120}{40}&=\dfrac{1}{b}\\b&=\dfrac{40}{120}\\ b&=\dfrac{1}{3}\end{aligned}[/tex]

Therefore, the equation of the exponential function is:

[tex]y=40\left(\dfrac{1}{3}\right)^x[/tex]

Answer:

Step-by-step explanation:

You have a piecewise defined function f(x) and you want the values of f(-5), f(-2), and f(1).

The first step in finding the value of a piecewise defined function is to determine the function definition on the domain containing the x-value of interest.

The value x=-5 is in the interval x < -2, so the first part of the function definition applies: f(x) = 3.

  f(-5) = 3

The value x = -2 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².

  f(-2) = -(-2 -1)² = -(-3)²

  f(-2) = -9

The value x = 1 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².

  f(1) = -(1 -1)² = -(0)²

  f(1) = 0

The required value of f(5) would be 81.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

We have been given the function below as:

f(n) = f(n-1) - 3   ....(i)

f(1) = 3

To determine the value of f(5)

Substitute the value of n = 2 in the equation (i);

f(2) = - 3f(1) = - 3;

n = 3,

f(3) = - 3f(2) = 9;

n = 4,

f(4) = - 3f(3) = - 27,

n = 5,

f(5) = - 3f(4) = 81

Thus, the required value of f(5) would be 81.

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The maximum width and area of rectangle are 475 feet and 225625 sq. feet respectively.

Any given rectangle  has ONE region - there is no base or most extreme, simply a region. To find the region of a rectangle  shape, increase the length times the width. For instance, a rectangle  shape 4′ long by 5′ wide will have an area of 20 square feet.

We have

l×w = area of rectangle-------------------------(1)

2w + l = 950

l = 950 - 2w

Put the value if l in equation (1)

(950 - 2w) × w = area

This is a quadratic equation for maximum value of w we have of it one zeros is zero

so,

950 - 2w = 0

w = 950/2

W =475 feet

Te

Then length = 950 - 475 =475

Area of rectangle = 475 × 475 = 225625 sq. feet

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