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3 years ago

G(x) = 3x + 1; Find g(-8)

Mathematics

2 answers:

gregori [183]3 years ago

5 0

Answer:

g(-8) = -23

Step-by-step explanation:

g(x) = 3x + 1 Plug in g(-8)

g(-8) = 3(-8) + 1 Multiply 3 by -8

g(-8) = -24 + 1 Add 1 to -24

g(-8) = -23

Fiesta28 [93]3 years ago

3 0

$\text{Hello there!}\\\\\text{Plug -8 to the x variable:}\\\\g(x)=3(-8)+1\\\\\text{Solve:}\\\\g(x)=3(-8)+1\\\\g(x)=-24+1\\\\g(x)=-23\\\\\boxed{\text{g(-8)=-23}}$

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Yuliya22 [10]

Yes, this answer is correct.

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Sergeeva-Olga [200]

Answer: 114.37 ft

Step-by-step explanation:

If we model this situation as a right triangle, where the hypotenuse is the length of the ladder ( $110 ft$ ), the opposite leg is the height the ladder will reach $h$ , and the adjacent leg is the distance between the base of the ladder and the building ( $28 ft$ ); we have two options:

1) Using trigonometric functions, since we are given the angle $\theta=75\°$

2) Using the Pithagorean Theorem

Any of the options will give a similiar result. So, let's choose the Pithagorean Theorem:

$(hypotenuse)^{2}=(opposite-leg)^{2}+(adjacent-leg)^{2}$

$(110 ft)^{2}=(h)^{2}+(28 ft)^{2}$

Isolating $h$ :

$h=\sqrt{(110 ft)^{2}-(28 ft)^{2}}$

$h=106.37 ft$

Adding to this height the extra height of $8 ft$ (since the base of the ladder is at this distance above the ground, perhaps held by a firefighter truck):

$h=106.37 ft+8 ft=114.37 ft$ This is the height the ladder will reach

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3 years ago

Kylie Matsumoto is a set designer. Her annual salary is $ 45,320. Kylie's semi-monthly salary is $ _________. (Round to the near

ivanzaharov [21]

The answer to this question would be: $1888.33/semi-month

To answer this question you need to convert the annual into semi-monthly. Annual mean every 1 year or every 12 months. Semi-monthly mean two times a month. Then the equation would be: $45,320 / year x (1 year/12month) x (1 month/2 semi-month) = $1888.33/semi-month

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3 years ago

Mike spent half of his allowance going to the movies. He washed the family car and earned 7 dollars. What is his weekly allowanc

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What a wack question, confused on either he spent that 7 or didn't. But imma say he didnt so, i think 8$ if thats even an answer, spent half his allowance and earned 7 dollars and ended off with 15 at the end of the week. So that means 8 doesn't it?

Step-by-step explanation:

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3 years ago

Bhaskar went for hiking with scouts’ team and there the scouts were given a task to build tents with the help of bamboos, ropes

dimulka [17.4K]

The triangles on Bhaskar's tent are similar triangles.

The length of IJ is 4.5 m
The applicable theorem is the mid-point theorem
The appropriate formula for area is the Heron's formula
The ratio of ABC to DEF is 1 : 9

(a) The length of IJ

The given parameter are:

$\mathbf{EF = 9m}$

I and J are at the midpoint of DE and DF

The above highlight means that

$\mathbf{IJ= \frac 12 \times EF}$ --- midpoint theorem

Substitute 9 for EF

$\mathbf{IJ= \frac 12 \times 9m}$

$\mathbf{IJ= 4.5\ m}$

(b) The property used to find GH and IJ

In (a), the midpoint theorem is used to calculate IJ

GH and IJ are corresponding sides of similar triangles,

So the midpoint theorem can also be used to calculate the length of GH

(c) The area of the triangle

For the given triangles, the lengths of the sides are known.

When side lengths are known, the formula to use for finding the triangle's area is the Heron's formula.

The Heron's formula is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

Where:

$\mathbf{s = a + b + c}\\\mathbf{a,b,c \to sides\ of\ the\ triangle}$

(d): The ratio of the areas:

For the small triangle, we have:

$\mathbf{a= 3.8,\ b = 4,\ c = 3}$

So, we have:

$\mathbf{s = 3.8 + 4 + 3 = 10.8}$

So, the area is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

$\mathbf{A_{small} = \sqrt{10.8 \times (10.8 -3.8) \times (10.8 - 4) \times (10.8 - 3)}}$

$\mathbf{A_{small} = \sqrt{4009.824}}$

For the big triangle, we have:

$\mathbf{a= 11.4,\ b = 12,\ c = 9}$

So, we have:

$\mathbf{s = 11.4 + 12 + 9 = 32.4}$

So, the area is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

$\mathbf{A_{big} = \sqrt{32.4 \times (32.4 -11.4) \times (32.4 - 12) \times (32.4 - 9)}}$

$\mathbf{A_{big} = \sqrt{324795.744}}$

The ratio of the small triangle to the big triangle is:

$\mathbf{Ratio = A_{small} : A_{big}}$

$\mathbf{Ratio = \sqrt{4009.824}:\sqrt{324795.744}}$

Divide by 4009.824

$\mathbf{Ratio = \sqrt{1}:\sqrt{81}}$

Take square roots

$\mathbf{Ratio = 1 : 9}$

Hence, the ratio of ABC to DEF is 1 : 9

Read more about similar triangles at:

brainly.com/question/24874611

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