A fogpole casts a 13-foot shadow on the ground when the sun is at a 68° angle of elevation. Which of the following expressions can be used to determine the height (h), in feet, of the fogpole? (Assume the flagpole is perpendicular to the ground.) Draw a picture

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Answer:

[tex]y=3(x-7)^2[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

Parent function

[tex]y=x^2[/tex]

Translated 7 units to the right

Subtract 7 from the x-value:

[tex]f(x-7) \implies y=(x-7)^2[/tex]

Vertically stretched by a factor of 3

Multiply the whole function by 3:

[tex]3f(x) \implies y=3(x-7)^2[/tex]

Streched 7 units right means change in x

So new equation

Vertically streched by 3

Answer:(x-1)(x+8)

Step-by-step explanation: You need to set it up as (x+y)(x+z) format. To get that you need to flip the zeroes making them the opposite. So the answer in this case would be (x-1)(x+8).

Answer:

48 sides

Step-by-step explanation:

A nonagon has 9 sides

A decagon has 10 sides

10 + 10 + 10 = 30

9+9 = 18

30 + 18 = 48

48 sides in total

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The number is 276999

Answer:

440x4=2200

Step-by-step explanation:

I'm guessing you meant 1/4, which is also known as 0.25, and if you know that 440 meters is equal to 1/4th of the whole race track you just have to multiply 440 by 4.

Answer:

B, C, D

Step-by-step explanation:

Square roots are not in polynomials

Since the specific conclusion is based on a general premise, this is a case of deductive reasoning.

The term deductive reasoning has to do with the process of arriving at a specific conclusion based on a more general premise.

In this case, the conclusion arrived at was based on the fact that Mia saw a general sign that read that 3 grapefruit cost $2.50. Hence, this is a case of deductive reasoning.

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An expression for the total cost of the daycare for Lucy's dog this week is T = 3F + 2H and the total cost is equal to $114.

In this exercise, you're required to write an expression for the total cost of the daycare for Lucy's dog this week. Thus, we would assign a variable to the cost for full-day and half-day day care as follows:

Thus, the total cost of the daycare is given by:

T = 3F + 2H

Evaluating the expression, we have:

T = 3(28) + 2(15)

T = 84 + 30

T = $114.

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Answer:

The volume of the cylinder is approximately 1570.8 cm³.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume Formula [Cylinder]:
[tex]\displaystyle V = \pi r^2 h[/tex]

Step-by-step explanation:

Step 1: Define

Identify given variables.

h = 5 cm

r = 10 cm

Step 2: Find Volume

∴ the volume of a cylinder whose height is 5 cm and radius is 10 cm is approximately 1570.8 cm³.

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Topic: Geometry

Answer:

A. 17.35 mm³

Step-by-step explanation:

Volume of a Pyramid

[tex]V = \frac{1}{3}Bh[/tex]

V ... volume

B ... area of base

h ... height

The base of this pyramid is a square. Area of a square is side times side.

[tex]B = 3.5 \times 3.5[/tex]

Let's substitute in the formula.

[tex]V = \frac{1}{3}Bh\\\\V = \frac{1}{3}(3.5\times 3.5)(4.25)\\\\V = \frac{1}{3}(12.25)(4.25)\\\\V \approx 17.35417 \text{ mm}^3[/tex]

Now let's round to the nearest hundredth.

V = 17.35 mm³

Check the picture below.

The six values of 0 shown on the dot plot represent that 6 students out of the 30 sampled did not send any text messages daily.

With the sample being representative of the population, a dot plot for the entire population would have the same proportions as the sample but with a larger number of students.

The number of dots above a number indicates the number of students who send that number of text messages daily.

As there are 6 dots over 0, it means that 6 students do not send any text messages daily.

Seeing as the sample is representative of the entire population, a dot plot for the whole school would have a larger number of dots over each number but the proportions would be the same as the sample.

For instance, the proportion of total students who don't send any messages per day is:

= 6 / 30

= 20%

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[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ 2^3~~ = ~~8\implies \log_2(8)~~ = ~~3[/tex]

The value of (26 - 7) and (5 - 24) when they're multiplied will be -399.

From the information given, we are told to multiply (26 - 7) and (5 - 24). This goes thus:

= (26 - 7) × (5 - 24)

= 21 × -19

= -399

In this case, value of (26 - 7) and (5 - 24) when they're multiplied will be -399.

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Answer:

7-B (congruent)

8-D (supplement)

9-B (congruent)

10-B (congruent)

11-D (supplement)

Step-by-step explanation:

7- 1 and 3 are congruent using the corresponding angles theorem

8- they are supplements using the same side interior angle theorem

9- they are congruent using alternate interior angle theorem

10- they are congruent using the alternate exterior angle theorem

11- they are supplements using the same side exterior angle theorem

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brainliest?

Answer:

(a^2)+4a-5

Step-by-step explanation:

(3+a+2)(a+2-3)

(a+5)(a-1)

use FOIL or box method

5a-5+(a^2)-a simplifyes to

(a^2)+4a-5

Answer:

Least 8.06, 8.295, 8.3, 8.31 Greatest

Answer:

x=70+30-60

Step-by-step explanation:

Word to my mother

Step-by-step explanation:

Given: x=5 and y=6

=>4x2+3y

=> 8+3(6)

=> 8+18

=> 26

Hope it helps

The value of this expression is 58

Algebraic expression is a mathematical sentence that involves all mathematical operations.

In an algebra - a real number is always accompanied by some letter, which can represent a variable or unknown.

— To solve this expression, just: change the letters for the numbers and multiply/add.

⚘ Resolution

[tex]\large \sf 4x2+3y[/tex]

[tex]\large \sf 4 \cdot 5 \cdot 2 +3 \cdot 6[/tex]

[tex]\large \sf 40 +18[/tex]

[tex]\red{\boxed{\boxed{\green{\large \sf \ 58 \ }}}}\\[/tex]

Therefore, the value of this expression will be 58

Answer:

You add 33 on both sides to solve for the variable.

Step-by-step explanation:

The options that are true of the triangles include:

It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.

This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.

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Answer:

∆XYZ ~∆X'Y'Z'

AngleXZY ≅ AngleY'Z'X'

XZ = 2X'Z'

Step-by-step explanation:

took test

Answer:

[tex]d = \sqrt{109}[/tex]

Step-by-step explanation:

Use the distance formula.

[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Your points are (-4, 11) and (6, 8).

[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]

Answer:

B

Step-by-step explanation:

the absolute value function always gives a positive result

However, the value inside can be positive or negative, that is

5x + 30 = 10x or - (5x + 30) = 10x

solving both

5x + 30 = 10x (subtract 5x from both sides )

30 = 5x ( divide both sides by 5 )

6 = x

or

- (5x + 30) = 10x

- 5x - 30 = 10x ( add 5x to both sides )

- 30 = 15x ( divide both sides by 15 )

- 2 = x

As a check

substitute these values into the equation and if both sides are equal then it is a solution.

x = 6

left side = | 5(6) + 30 | = | 30 + 30 | = | 60| = 60

right side = 10(6) = 60

Then x = 6 is a solution

x = - 2

left side = | 5(- 2) + 30 | = | - 10 + 30 | = | 20 | = 20

right side = 10(- 2) = - 20 ≠ 20

Thus x = - 2 is an extraneous solution

Answer:

If the arcs are the same

4x+25=5x

x=25

So, QPR is 4(25)+25

QPR is 125

Answer: rectangle

Step-by-step explanation:

From the options, it is implied that it is a parallelogram.

From inspection, we can tell that not all the sides are congruent, so it is not a rhombus or a square.

To determine if it is a rectangle, we can use the slope formula to see if there is a pair of perpendicular sides (if this is the case, then this will be a parallelogram with a right angle, making it a rectangle)

[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC} \text{ because} \left(m_\overline{AB} \right) \left(m_{\overline{BC} \right)=1[/tex]

So, the most specific classification is a rectangle.

Answer:

640[tex]x^{6}[/tex]

Step-by-step explanation:

(5x³)(4x) ³2

(4x) ³ is the same as

4³ * x³ = 64x³

--

(5x³)(64x³)2

5*64*2 = 640

x³ * x³ = [tex]x^{6}[/tex]

640[tex]x^{6}[/tex]