MATHEMATICS MIDDLE SCHOOL

The length and breath of a rectangle are (a^2 +ab +b^2) units and (a-b) units.Find the area of the rectangle.

Answers

Answer 1

Answer:

Answer:

a^3 - b^3.

Step-by-step explanation:

Area = length * breadth

= (a - b)(a^2 + ab + b^2)

= a(a^2 + ab + b^2) - b(a^2 + ab + b^2)

= a^3 + a^2b + ab^2 - a^2b - ab^2 - b^3

Note: the 4 middle terms cancel out. So the answer is

a^3 - b^3.

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10. angle GHI is an isosceles triangle with GI HI. IF GH is three more than x, HI is 17 less than fourtimes x, and GI is 45 less than six times x, find x and the measure of each side.

Answers

Answer:

GH = 17 units

GI = 39 units

HI = 39 units

Step-by-step explanation:

We are given the following information in the question:

Triangle GHI is an isosceles triangle.

$GI = HI$

The measures of side are:

$GH = 3 + x\nHI = 4x-17\nGI = 6x - 45$

It is given that

GI = HI

$4x - 17 = 6x -45\n6x - 4x = 45-17\n2x = 28\nx = 14$

Thus, the measures of three sides are:

$GH = 3 + x=14+3 = 17\nHI = 4x-17 = 4(14)-17 = 39\nGI = 6x - 45=6(14) - 45 = 39$

A painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?

Answers

pythagorean theorem
legnth of lader is hypotonuse (leaning against wall and wall is one leg and distance from wall to bottom of ladder is other leg)

so
a^2+b^2=c^2 where a and b are legs and c=hypotonuse

a=8

c=24
8^2+b^2=24^2
64+b^2=576
subtract 64
b^2=512
square root both sides
22.62
round to tenth
22.6

answer is 22.6 ft

PLS I NEED IT FAST I HAVE A 5 MIN LIMIT!!Which table shows a proportional relationship?

a

b

c

d

Answers

Answer:

Its B

Step-by-step explanation:

Its B because the values of c are all 2 times the values of b. This is an example of direct proportion.

We write it as c = 2b

Laura earns $ 255 by working 20 hours each week .Part A
Write an equation to find how much Laura earns per hour. Use H to represent the hourly
Equation

Part B
Solve the equation to find Laura's hourly rate

part C
Laura earns $2.90 more per hour than her friend ,Jess . Write an equation to show how much Jess earns per hour .Use J to represent her hourly

Answers

you will have to figure out the last equation but here is the rest:

Helppp with number 10

Answers

I think number 10 is (A) and (D). Hope I helped!

Two students participated in a fund-raiser. Each sold a combination of pencils and notebooks. The first student sold 2 pencils and 8 notebooks for a total of $17. The second student sold 10 pencils and 3 notebooks for a total of $11. Find the price of each item.Write a system of equations (two equations), and define the variables also.
x=
y=
1)
2)
9 POINTS! Please help!

Answers

2x + 8y = 17
10x + 3y = 11

We need to solve the system of equations.

x = pencils
y = notebooks

If we solve by graphing, we get the answer:

One pencil costs 0.50 dollars
One notebook costs 2.00 dollars

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Ignore my errors please. how would i solve these problems... please explain step by step