3. a. Which of the numbered angles are exterior angles?

b. Name the remote interior angles for each exterior angle.

C. How are exterior angles 6 and 8 related?

(Picture included) please help

Answer: The answer is 9/8 = 27/24

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The height of the pole above the level of the observer's eyes is 31.42 ft

Let the angle of elevation of the top of the pole from a point 47 ft away be α.

Let the angle of elevation of the top of the pole from the point 13 ft away be β.

Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.

If the height of the pole above the level of the observer's eye is h, we have that

tanβ = tan2α = h/13 and tanα = h/47

From trigonometric identities tan2α = 2tanα/(1 - tan²α)

Substituting the values of the variables into the equation, we have

tan2α = 2tanα/(1 - tan²α)

h/13 = 2h/47 ÷ [1 - (h/47)²]

Dividing through by h, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

Cross-multiplying, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

1 - (h/47)² = 2/47 × 13

1 - (h/47)² = 26/47

(h/47)² = 1 - 26/47

(h/47)² = (47 - 26)/47

(h/47)² = 21/47

Taking square-root of both sides, we have

h/47 = √(21/47)

Cross-multiplyng, we have

h = √(21/47) × 47

h = √(21 × 47)

h = √987

h = 31.42 ft

The height of the pole above the level of the observer's eyes is 31.42 ft

Learn more about height of a pole here:

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Answer:

D. 0.343

Step-by-step explanation:

You can see the first three options as 0.340 so if you substract this number with 0.343 the remainder is positive 3.

This strategy also can be applied to the number 0.3409 but in this occasion the result is different:

[tex]0.343 - 0.3409 = 2.1\times 10^{-3}[/tex]

That is small number but still is positive that's meaning that between 0.343 and 0.3409 the greatest value is 0.343 .

Answer:

f ( 3 ) = 81

Step-by-step explanation:

→ Substitute in x = 3

9 × 3² - 3

→ Simplify

9 × 9 - 3

→ Simplify again

78

Answer:

(3*5)+(19*3)

Step-by-step explanation:

both numbers GCF is 3.

(3*5)=15

(19*3)=57

15+57=72

Hope that helps

Answer:

4.5

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation:

Use the distance formula

d= √(x2-x1)² +(y2-y1)² , where x1, x2, y1, y2 are the coordinates of the points

A(x1 = −1, y1 =  5) and B(x2 = 0, y2 = 4)

d= √(0 - -1 )² +(4 - 5)²

d= √(1)² +(-1)²

d= √2

d= 1.414213562, round to the nearest tenth

d≈ 1.4

Answer:

No, it is not a linear function, rather a rational function

Step-by-step explanation:

Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:

2yx=4

yx=2

y=2/x

Answer:

they are technically congruent due to same angles n same or equal sides

Answer:

Step-by-step explanation:

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

so your amswer is A. True

Answer:

450

Step-by-step explanation:

150* 3

hope this helps

Answer:

450

Step-by-step explanation:

150 feet in 1/3 min

? -----  1 min

150 * 1 = x * 1/3

x = 150 * 3

= 450

Answer:

16 = y

Step-by-step explanation:

So you have the equation 6=-y+42+-2y

Find the y first

6=-y+42+-2y

add all y's together

6=-3y+42

subtract 42 on both sides

-48 = -13y

16 = y

------------------------------------------------

Now do the check:

Plug in 16 where ever it says y in the original equation

6= -(16) + 42 + -2(16)

open the brackets

6= -16+42-32

solve

6=26-32

6 = 6

Hope this helps

The confidence interval can be calculated from the margin of error, and vice versa,

The margin of error of the confidence interval is 2.156

The confidence interval is given as:

[tex]\mathbf{CI = 3.2 \pm 1.96 \cdot 1.1}[/tex]

The formula of confidence interval is:

[tex]\mathbf{CI = \bar x\pm E}[/tex]

Where E represents the margin of error.

So, by comparison:

[tex]\mathbf{E = 1.96 \cdot 1.1}[/tex]

Multiply

[tex]\mathbf{E = 2.156}[/tex]

Hence, the margin of error of the confidence interval is 2.156

Read more about margin of errors at:

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Answer:

Money for coach tickets is $1280 and money for first class is $7600

Step-by-step explanation:

8 x 160 = 1280

8x 950 = 7600

Answer:

D) (6, -4)

Step-by-step explanation:

pt C has coordinates of (6,4)

if you reflect that point across the x-axis the x-value remains the same and the y-value continues to be 4 units from the x-axis, but below it instead of above it

- BRAINLIEST answerer

Answer: 32 hours

Step-by-step explanation: 51/6 = 8.5

So, Erica makes 8.5 dollars per hour. 272/8.5 = 32. Thus, Erica will need 32 hours.

Brainliest?

Answer:

2x^3-2x^2+x

Step-by-step explanation:

Just trust me!

Step-by-step explanation:

7 √(1/3) - 2 1/3 √(1/3) +3√147

→7(1/√3) - (7/3)(1/√3) +3√(3×7×7)

→ (7/√3) - (7/3√3) +3×7√3

→ (7/√3) - (7/3√3) + 21√3

On Rationalising the denominators then

→ [ 7√3/(√3×√3)]-[7√3/(3×√3×√3) +21√3

The Rationalising factor of√3 =√3

→ (7√3/3)-[7√3/(3×3)]+21√3

→ (7√3/3)-(7√3/9)+21√3

LCM of 3 and 9 = 9

→ [(3×7√3)-(7√3)+(9×21√3)]/9

→ (21√3-7√3+189√3)/9

→[(21-7+189)√3]/9

→ [(210-7)√3]/9

→ 203√3/9 Ans.

Hope this helps.

Answer:

y = 1/3 x + 14/3

Step-by-step explanation:

We can identify the two points shown easily.

They are (-2, 4) and (4, 6).

First, we find the line of the slope of the line that contains those two points.

slope = m = (y2 - y1)/(x2 - x1) = (6 - 4)/[4 - (-2)] = 2/6 = 1/3

Now we use one point and the slope to find the y-intercept.

y = mx + b

Let's use point (4, 6) and the slope, 1/3.

6 = (1/3)(4) + b

18/3 = 4/3 + b

b = 18/3 - 4/3

b = 14/3

The equation is

y = mx + b

y = 1/3 x + 14/3

a) x²+6x

b)5x²-x

c)12x²+15x

d)8x²-12xy

Answer:

250

Step-by-step explanation:

You can take the explicit formula and simply substitute the n value with 64:

-2 + 4 * (64 - 1)

-2 + 4 * (63)

-2 + 252

250

Answer:

447

Step-by-step explanation:

Using probability of complementary events, it is found that there is a 0.41 probability that such a person moves to one of the higher income classes fifteen years later.

When two events are complementary, the sum of their probabilities are 1.

In this problem, either a person moves to a higher income class or they do not, hence, the events are complementary.

A similar problem is given at https://brainly.com/question/24084986

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-4)}}}\implies \cfrac{-1}{-2+4}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{-\cfrac{1}{2}}[x-\stackrel{x_1}{(-4)}] \\\\\\ y-6=-\cfrac{1}{2}(x+4)\implies y-6=-\cfrac{1}{2}x-2\implies \underset{\textit{slope-intercept form}}{y=-\cfrac{1}{2}x+4}[/tex]