MATHEMATICS MIDDLE SCHOOL

Solve the system of equations and choose the correct answer from the list of options. (4 points)x − y = 7
y = 3x + 12

Select one:
a. 2 /19 comma 2 / 33
b. negative 2 / 19 comma negative 33 / 2
c. negative 19 / 2 comma negative 33 / 2
d. 19 / 2 comma 33 / 2

Answers

Answer 1

Answer:

Answer:

c. negative 19 / 2 , negative 33 / 2

Step-by-step explanation:

x − y = 7

y = 3x + 12

Substitute y = 3x + 12 into x − y = 7

x − (3x + 12) = 7

x - 3x - 12 = 7

-2x - 12 = 7

-2x = 19

x = -19/2

Substitute x = -5/2 into x − y = 7

-19/2 − y = 7

y = -19/2 - 7

y = - 5/2 - 14/2

y = -33/2

Answer:

x = -19/2, y = -33/2

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20 POINTS!! Help me please! Will pass out Brainliest Answer!

1) A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree.

Approximately how high up the tree does the top of the pole reach?

A. 7.0 feet

B. 12.7 feet

C. 7.0 feet

D. 1.9 feet

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2) A tree is 132 inches tall. The distance from the top of the tree to the tip of the tree's shadow is 166 inches.

Approximately how long is the tree's shadow?

A. 212 inches

B. 149 inches

C. 101 inches

D. 34 inches

Answers

Hello! Lets do this step by step my sweet kitty! ;)
So for the first question to solve we are going to be using the Pythagorean theorem which is a^2 + b^2 = c^2. So with the given numbers we are going to plug them into our equation. :) So C is the hypotenuse and a and b are gonna be the legs. We don't know what our height is so for that we are going to use the variable of n. So we get 15^2 = 8^2 + n^2
So we can rewrite our equation 225 = 64 + n^2 Now to isolate n we are going to subtract 64 from both sides of the equation giving us 161=n^2
Now we find the square root of 161 which is equal to = 12.6885 which can be rounded off to 12.7 which makes B our answer! :)

Problem 2).
We are going to use the same process so plugging in our numbers to the equation just as we did previously gives us 166^2 = 132^2 + n^2
Rewriting the equation as 27556= 17424 +n^2 Now subtract 17424 from both sides leaves us with 10132=n^2 Now just find the square root of 10132 which is 100.657 which can be rounded to about 101 which gives us our answer! Option C 101 inches. :)

Hope I helped! If you have any other questions or would like further explanation just let me know! :)

pythagorean theorem
if yo have a right traignel, then
if a and b are legs (sides that touch the right angle) and c is the hypotonuse (longest side and side ooposite right angle)
a^2+b^2=c^2 so

1. 15 foot pole leans agains tree
bottom is 8 feet
we can see a right traignel
the pole is the hypotonuse and 8 is 1 leg so the other leg is the height that the pole reaches
8^2+b^2=15^2
64+b^2=225
subtract 64
b^2=161 take square root of both sides using calculator
b=12.68 ft
closest answer is 12.7
answer is B, 12.7

2. tree is132 tall
distance from tree to shadow is 166
how long is shadow?
tree height is standing height or one of the legs
distance from tree to shadow is 166 aka hypotonuse
shadow=bottom leg so
132^2+b^2=166^2
17424+b^2=27556
subtract 17424 from both sides
b^2=10132 take square root using calculator
b=100.65
closest is 100.1
answer is C, 100.1
diagram below

Gina charges $28 for 3 hours of lessons. Hector charges $18 for 2 hours of lessons. Who offers a better deal????

Answers

Gina because if u get 6 hours of a lesson from hector it is going to be $64 but gina will charge $56for 6 hours

3 goes in to 28hrs 9.3 times so i see each hour as her being paid 9.30. the other is gettin paid 9 so i see the 2nd as better

Will give branist if done correctly..it would really help me out.. Thank you in advance!Instructions:

Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.

Complete the following. Show all work for calculations.

1. List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

2. Describe the shape of the cross section when the box is cut parallel to the base.

3. What is the surface area of the box?

4. What is the surface area of the box if it is scaled up by a factor of 10?

5. What is the volume of the box?

6. What is the volume of the box if it is scaled down by a factor of $1/10$?

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