List all the angles which are congruent to angle A!! ( a pair of parallel lines is cut by a transversal as shown in the figure)

The length of the stretched wire is required.

The length of the wire is 9.43 feet.

b = Length of the pole = 8 ft

a = Distance between bracket and base of pole = 5 ft

c = Length of wire

The two lengths form a right triangle.

From the Pythagoras theorem we have

[tex]c^2=a^2+b^2\\\Rightarrow c=\sqrt{a^2+b^2}\\\Rightarrow c=\sqrt{8^2+5^2}\\\Rightarrow c=9.43\ \text{feet}[/tex]

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The student needs to apply the formula for the volume of a pyramid, V = 1/3 * a² * h. Since the height is 3 cm less than the side length, this introduces a variable in the equation, (x - 3), to solve for x.

The question relates to pyramid volume and the formulation of mathematical equations. First, it requires understanding that the volume of a pyramid is derived using the formula V = 1/3 * a² * h, where V is the volume, a is the length of the side of the square base, and h is the height of the pyramid. Since the height is stated as 3 cm less than the base (x), we can interpret this in the formula as h = x - 3.

Replacing these values in the volume formula gives us V = 1/3 * x² * (x-3). As the volume given is 162 cubic centimeters, this forms the equation: 162 = 1/3 * x² * (x-3). Simplifying this equation would provide the base length x in cm.

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Solution:

we are given that

The population of a city in 2005 was 18000.

By 2010, the city’s population had grown to 45,000.

Economists have determined that the growth is exponential.

As we know the exponential growth is defined by the relation

[tex]P=p_0e^{rt}\\ \\ \text{where P is the population at time t and initial population is } p_0\\[/tex]

Here we have [tex]p_0=18000, P=45000, t=5[/tex]

substitute these values we get

[tex]45000=18000e^{5r}\\ \\ r=0.183[/tex]

So we get

[tex]P(t)=18000e^{0.183t}[/tex]

So For population is 2015 substitute t=10

[tex]P(10)=18000e^{0.183*10}[/tex]

[tex]P(10)=112209.9598 [/tex]

The projected population for 2015 is 112210

Final answer:

Vivien would use her handspan, which measures 18.5 centimeters, approximately 9 times to measure a length of 1 meter 75 centimeters. This estimate assumes precision in her handspan measurement.

Explanation:

To estimate the number of times Vivien uses her handspan to measure a length of 1 meter 75 centimeters, we need to divide the total length by the length of her handspan. Since Vivien's handspan measures 18.5 centimeters, and the total length to measure is 1 meter 75 centimeters (which equals 175 centimeters), we perform the following calculation:

This is an estimation technique that assumes Vivien's measurement with her handspan is accurate. The accuracy of this measurement can vary based on several factors, including the precision of Vivien's handspan and the method used for measuring.

Answer:

The data we have is:

He works for $8 an hour.

He mows lawns for $10 an hour.

He wants to work no more than 20 hours per week, and wants to hearn at least $120 week.

So if S is the number of hours he works in the store, and M is the number of hours that he mowns lawns, we have the inequalities:

S + M ≤ 20

S*$8 + M*$10 ≥ $120

So let's choose a possible solution:

Let's select M = 12 and S = 0

in this way, he worsk

0h + 12 h = 12 h that is less than 20 hours, and he wins:

0*$8 + 12*$10 = $120, which is the minimum amount of money that he wants to win.

and we have a lot of other possible solutions:

S= 1, M = 12

S = 2, M= 12.. and so on.

Answer: x=9

Step-by-step explanation:

In the given picture, we have a circle in which we have given two congruent arcs [tex]\overarc{RS}\text{ and }\overarc{TS}[/tex]

And [tex]\overline{RS}=59\text{ and }\overline{ST}=10x-31[/tex]

Since, we know that congruent arcs have congruent chords.

Therefore,  [tex]\overline{RS}=\overline{ST}[/tex]

[tex]59=10x-31\\\\\Rightarrow\ 10x=59+31\\\\\Rightarrow 10x=90\\\\\Rightarrow x=\frac{90}{10}\\\\\Rightarrow x=9[/tex]

To solve the problem we must know the Chord's Equidistant From The Center Of A Circle Theorem.

If two chords of a circle are equidistant from the center then they are congruent to each other and their corresponding arcs are also congruent.

The value of x is 9.

Chord RS and chord ST are equidistant from the center. therefore,

RS = ST

[tex]59 = 10x-31\\ 59+31 = 10x\\ 90 = 10x\\\\ x= \dfrac{90}{10}\\\\ x= 9[/tex]

Hence, the value of x is 9.

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Final answer:

To solve the expression 13(9−6m)+14(12m−8), distribute the numbers and combine like terms to get the sum, which is 90m + 5.

Explanation:

To find the sum of the expression 13(9−6m)+14(12m−8), we need to distribute the numbers outside the parentheses across the terms inside the parentheses and then combine like terms.

Distribute the numbers:

13 × 9 = 117

13 × (−6m) = −78m

14 × 12m = 168m

14 × (−8) = −112

Now we combine like terms:

117 (−78m) + (168m − 112)

Simplifying this we get:

−78m + 168m = 90m

−112 + 117 = 5

So the sum is 90m + 5.

You have to formulate an equation for this problem.

Let x = the number asked in the problem

5x – 4 = 3x + 6

Solve the equation.

5x – 3x = 6 + 4

2x = 10

X = 5

Therefore, the number is 5.

Final answer:

Two-thirds of each poster are not covered with opaque paper. Multiplying (2/3) by 5 gives us 10/3, which can be converted to 3 and 1/3, indicating that three whole posters plus one-third of another are not covered.

Explanation:

If one third of each of 5 same sized posters is covered with opaque paper, then two thirds of each poster are not covered. To find what fraction of the posters are not covered by opaque paper, you apply multiplication. You start with one poster: one-third covered means two-thirds are not covered. Represent this as 2/3. Since the question concerns 5 identical posters, you multiply the fraction of one poster (2/3) by the number of posters (5).

Mathematically, this looks like:

(2/3) × 5 = 10/3

However, 10/3 represents more than one whole, and it can be converted into a mixed number to represent the total unobstructed fraction of the posters. This is 3 and 1/3, meaning that in total, you have three whole posters and one-third of another poster not covered by opaque paper.

Final answer:

To rewrite the equation 19x - 20y = -13 in slope-intercept form, you subtract 19x on both sides and then divide by -20 to isolate y. The resulting equation is y = (19/20)x + 13/20.

Explanation:

To rewrite the equation 19x - 20y = -13 in slope-intercept form, follow these steps:

Move 19x to the other side by subtracting it from both sides: -20y = -19x - 13

Divide by -20 to isolate y: y = (19/20)x + 13/20

Therefore, the equation in slope-intercept form is y = (19/20)x + 13/20.

The value of cos (11pi/6), is -sqrt(3)/2.

To determine the exact value of cos (11π/6), we first need to understand the trigonometric values at certain angles. In this case, 11π/6 radians is equivalent to 330 degrees. Using the unit circle, we know that at 330 degrees, cosine is equivalent to -√3 / 2.