MATHEMATICS HIGH SCHOOL

Simplifying rational expressions1. (c+8)(c-8)/(c-8)(c+3)
2. n^2+4n-12/n^2+2n-8
3. 42x^2y^3/28x^3y
4. m^2-3m-10/m-5

Answers

Answer 1
Answer: 1. ((c + 8)(c - 8))/((c - 8)(c + 3))_,_
    (c + 8)/(c + 3)_,_

2. (n^(2) + 4n - 12)/(n^(2) + 2n - 8)_,_
    (n^(2) + 6n - 2n - 12)/(n^(2) + 4n - 2n - 8)_,_
    (n(n) + n(6) - 2(n) - 2(6))/(n(n) + n(4) - 2(n) - 2(4))_,_
    (n(n + 6) - 2(n + 6))/(n(n + 4) - 2(n + 4))_,_
    ((n - 2)(n + 6))/((n - 2)(n + 4))_,_
    (n + 6)/(n + 4)_,_

3. (42x^(2)y^(3))/(28x^(3)y)_,_
    (3y^(2))/(2x)_,_

4. (m^(2) - 3m - 10)/(m - 5)_,_
    (m^(2) - 5m + 2m - 10)/(m - 5)_,_
    (m(m) - m(5) + 2(m) - 2(5))/(m - 5)_,_
    (m(m - 5) + 2(m - 5))/(m - 5)_,_
    ((m + 2)(m - 5))/(m - 5)_,_
    m + 2_,_

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Solve two step equation 3=9+n/2

Answers

Answer:

n = -12

Step-by-step explanation:

hope it helped , darling .

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Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle? 6(10x2 + 8x + 2) 12(5x2 + 4x + 2) 6x(10x2 + 8x + 2) 12x(5x2 + 4x + 2)

Answers

12(5x^2+4x+2) is correct answer because divide everything by 12 and that is factorization that you get. It is the furthest simplified for of this factorization.

The factorization could represent the number of water bottles and weight of each water bottle is 12.

Given that,

The water bottles weighed a total of  =60x^(2) +48x+24 ounces.

We have to find,

The factorization could represent the number of waterbottles and weight of each water bottle.

According to the question,

The water bottles weighed a total of

=60x^(2) +48x+24

Taking 12 as the highest common factor gives:

= 12 (5x^(2) + 4x+2)

Where 12 is the number of bottles and (5x^(2) + 4x+2) is the weight of eachone.

Hence , The factorization could represent the number of water bottles and weight of each water bottle is 12.

For more information about HCF click the link given below.

brainly.com/question/17240111

After plotting the data where x equals the length of the side of a polygon, and f(x) represents the area of the polygon, Jack used technology and determined the appropriate model to approximate the area of the polygon, f(x) = x2 + 2x + 3. Use the model Jack created to predict the area of a polygon that has a side length of 3.10
18
19
20

Answers

The area of polygon is 18 sq. units.

What is polygon?

In geometry, a polygon is any closed curve made up of a collection of continuous line segments, without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons.

Given that jack has a model f(x) = x² + 2x +3

where f(x) is area of polygon and x shows length of side

area when length is 3

substitute value of x in equation

f(x) = x² + 2x +3

f(3) = 3² + 2ₓ3 + 3

f(3) = 9 + 6+ 3

f(3) = 18

Hence area of polygon according to given equation is 18 sq. units

Learn more about polygon

brainly.com/question/28276384

#SPJ5

We are given the model to approximate the are of the polygon to be
f(x) = x² + 2x + 3
where x is the length of the side
For a polygon with a side length of 3, x = 3
f(3) = 3² + 2(3) + 3
f(3) = 18
The area is 18

The length of a swimming pool is 8m longer than its width and the area is 105m2

Answers

width : w \n length : \ l = w + 8 \n A = 105 \ m^2 \n \nA= w \cdot l \n \nw(w+l)=105 \n \nw^2+w = 105 \n \nw^2+w-105 =0 \n \n(w+15)(w-7)=0 \n \nw+15 =0 \ \ or \ \ w-7 = 0 \n \nw = -15 \ \ or \ \ w=7 \n \n width \ cant \ be \ negative, \ so \n \n w = 7 \ and \ l = w+8 = 7 +8 =15 \n \nchek : \n \n A=w\cdot l \n \nA=7\cdot 15=105 \ m^2
l\ \rightarrow\ the\ length\nw\ \rightarrow\ the\ width \n\nl=w+8\ \ \ and\ \ \ l\cdot w=105\ \ \ and\ \ \ l>0,\ w>0\n\n(w+8)\cdot w=105\ \ \ \Rightarrow\ \ \ w^2+8w=105\n\n w^2+2\cdot4w+4^2=105+4^2\n\n (w+4)^2=105+16\ \ \ \Rightarrow\ \ \ (w+4)^2=121\n\nw+4=11\ \ \ or\ \ \ w+4=-11\n\nw=7\ \ \ \ \ \ \ \ \ \ or\ \ \ w=-15<0\n\nw=7\ \ \ \Rightarrow\ \ \ l=7+8=15\n\nAns.\ the\ length\ is\ 15\ m\ \ and\ \ the\ width\ is\ 7\ m.

Calcylate the volume of this regular solidWhat is the volume of the rectangular prism
6 cm
5 cm
9 cm​

Answers

Answer:

V = 270 cm³

Step-by-step explanation:

Remember your volume formula: V=lwh

So, plug in all your variables and multiply:

(6)(5)(9) = 270

And we have our final answer!

Each child ticket for a ride costs $3, while each adult ticket costs $5. The ride collected a total of $150, and 40 tickets were sold. How many of each type of ticket were sold?A. 150 child and 40 adult
B. 24 adult and 10 child
C. 30 child and 10 adult
D. 25 child and 15 adult

Answers

The way to go about this is to think logically about the answers
A) isn't possible as 40 tickets were sold and 150 plus 40 = 190
B) is similar to above only there was less than 40 tickets sold
C) very possible
D) very possible
next step:
C) (30 x 3) + (10 x 5) = 90 + 50 = $140 (by this we should assume that the answer is D) 
D) (25 x 3) + (15 x 5) = 75 + 75 =  $150 ( yay answer is D :) )
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