MATHEMATICS MIDDLE SCHOOL

Factor 20x2 + 25x – 12x – 15 by grouping.

Answers

Answer 1

Answer:

Answer:

(4x+5) (5x-3)

Step-by-step explanation:

20x^2 + 25x – 12x – 15

From the first two terms factor out 5x and the last two terms factor out -3

5x(4x+5) -3(4x+5)

Now we can factor out (4x+5)

(4x+5) (5x-3)

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Need help with the whole page

Help please! this is due tomorrow so please help out! will mark as brainiest!!

Answers

Answer:

$\large\boxed{\bold{Q1}\ -(128)/(9)}\n\boxed{\bold{Q2}\ 2^(25)}$

Step-by-step explanation:

$\bold{Q1}\n\n(-2(3^2\cdot3^3)^2)/(3^(12)\cdot2^(-6))\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\n\n=-(2(3^(2+3))^2)/(3^(12)\cdot2^(-6))=-(2(3^5)^2)/(3^(12)\cdot2^(-6))\qquad\text{use}\ (a^n)^m=a^(nm)\n\n=-(2\cdot3^(5\cdot2))/(3^(12)\cdot2^(-6))=-(2\cdot3^(10))/(3^(12)\cdot2^(-6))\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\n\n=-2^(1-(-6))\cdot3^(10-12)=-2^(7)\cdot3^(-2)\qquad\text{use}\ a^(-n)=(1)/(a^n)\n\n=-2^7\cdot(1)/(3^2)=-(2^7)/(3^2)=-(128)/(9)$

$\bold{Q2}\n\n(4^2)/(4^(-7))\cdot(2^4\cdot2^3)\cdot(3^(-2))^0\qquad\text{use}\ (a^n)/(a^m)=a^(n-m),\ a^n\cdot a^m=a^(n+m),\ a^0=1\n\n=4^(2-(-7))\cdot2^(4+3)\cdot1=4^(9)\cdot2^7=(2^2)^(9)\cdot2^7\qquad\text{use}\ (a^n)^m=a^(nm)\n\n=2^(2\cdot9)\cdot2^7=2^(18)\cdot2^7\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\n\n=2^(18+7)=2^(25)$

I need help on 12 stunts in 4 movies it is unit rate

Answers

To find out how many stunts per movie (unit rate) we have to divide the amount of stunts (12) by the amount of movies (4). Then we will check our work. to make sure we are right. Lets do it:-

12 ÷ 4 = 3
3 stunts per movie

CHECK OUR WORK:-

3 × 4 = 12
We were RIGHT!!

So, the unit rate for 12 stunts in 4 movies is 3 stunts per movie.

Hope i helped ya!! xD

$12\ stunts\ in\ 4\ movies.\n\nDivide\ the\ number\ of\ stunts\ by\ the\ number\ of\ movies.\n\n (12)/(4)=3\n\nThat's\ an\ average\ of\ 3\ stunts\ per\ movie.\n\n{\boxed{3}$

I need help with the answer

Answers

Your answer would be 25/12 improper or as a mixed fraction 2 1/12

Answer: 2 1/12 hope this helps

Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2

Answers

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

1. 2x^2 - 7x + 3

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

a = 2
b = -7
c = 3

we can use the quadratic formula: $x = (-b~\pm~√(b^2~-~4ac) )/(2a)$

Substitute the a, b, and c values into the quadratic formula: $x=(-(-7)\pm√((-7)^2-4(2)(3)) )/(2(2))$

Now simplify using the laws of pemdas: $x=(7\pm√((49)-(24)) )/(4)$

Simplify even further: $x=(7\pm√((25)) )/(4) \rightarrow x=(7\pm (5) )/(4)$

Now split this equation into two equations to solve for x: $x=(12 )/(4) ~~and~~ x=(2 )/(4)$

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

$\boxed {x=3,(1)/(2) }$

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

x - 3 = 0
2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

2. 3x^2 + 7x + 2

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

3x + 1 = 0
x + 2 = 0

Solve.

First factor: 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

Second factor: x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

$\boxed {x = -(1)/(3) , -2}$

PLEASE HELP; Part 1Iris made a large model of a butterfly. The actual butterfly has a body length of 3 inches and and wing span of 8 inches. The wing span in the model is 32 inches.

Which proportion shows how long the butterfly body should be for the model?

A.8/3=x/32

B.3/32=8/x

C.4/x=32/3

D.3/8=x/32

Part 2

Based on the information from Part 1, determine whether each statement is True or False.

1.The length of the butterfly body in the model should be 15 inches. TRUE OR FALSE

2.Iris can make the model out of a piece of cardboard measuring 13 x 36. TRUE OR FALSE

3.If the wingspan on the model was 22 inches, Iris could make the body 8 inches. TRUE OR FALSE

4.If Iris made the body first and it was 18 inches long, the wingspan would need to be 60 inches.

Answers

The actual butterfly and the model are similar.

The ratio of corresponding parts of similar figures is the same.

The ratio of the fly's wingspan to that of the model is 8 to 32 or 8/32.

The ratio of the fly's body to that of the model is 3 is to x where x is the length of the fly model's body.

3/x = 8/32

That proportion does not appear in the options but a proportion that is equivalent to it does.

3/x = 8/32 cross multiplies to 3*32 = 8*x

Looking at option D which is 3/8 = x/32, notice that it cross multiplies to 8*x = 3*32 .

Therefor, option D is the same as the proportion and is the answer to the question.

Which pair of rectangles is similar ? A 3,8 and 2,6 B 3,8 and 2,5
C 3,9 and 2,6
D 3,6 and 2,9 ?

Answers

D because they are equal the same if you do 3×6=18 and 2×9=18
They have the same area amount.
~JZ
Hope it helps

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