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3 years ago

Raise the following fractions to a higher term...

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

7 0

Answer:

1. B

2. B

Step-by-step explanation:

To find the missing term, find the scale factor between the fractions - the number which multiplies to one to make the other.

1. 7 x __ = 35

7x 5 = 35 therefore 5 is the scale factor. Multiply 15 x 5 = 75

2. 8 x ___ = 32

8 x 4 - 32 therefore the scale factor is 4. Multiply 1 x 4 = 4.

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3 years ago

A rectangle is 6yards longer than it is wide. Find the dimensions of the rectangle if it’s area is 187 square yards

emmasim [6.3K]

Answer:

Width = 11 yards

Length = 17 yards

Step-by-step explanation:

First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where w is width, and l, for length.

We know the area of a rectangle is A = width x length

For our case 187 = w . (w + 6)

Using the Distributive Property for the multiplication we obtain

$187 = w^{2} +6w$

$w^{2} +6w-187 =0,$

Using the quadratic formula $w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}$ where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:

$w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}$

$w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}$

We have two options: $w=\frac{-6+28}{2}=\frac{22}{2}=11 yards$

$w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards$ But a distance (width) can not be negative so, this answer for w must be discarded.

The answer must be width = 11 yards.

To find the length $l =\frac{187}{11}=17 yards$

6 0

3 years ago

1. Solve the following equations for x:

worty [1.4K]

Answer:

A. X=-12
B. X=102
C. X=44
D. X=15

Step-by-step explanation:

Isolate the term of x from one side of the equation.

First, add by 9 from both sides.

x-9+9=-21+9

Solve.

-21+9=-12

X=-12

Switch sides.

x+10=112

Subtract by 10 from both sides.

x+10-10=112-10

Solve.

112-10=102

X=102

Switch sides.

x-30=14

Add by 30 from both sides.

x-30+30=14+30

Solve.

x=44

Switch sides.

x-12=3

Add by 12 from both sides.

x-12+12=3+12

Solve.

Add the numbers from left to right.

3+12=15

x=15

Therefore, the correct answer is part A: x=-12, part B: x=102, part C: x=44, and part D: x=15.

I hope this helps you! Let me know if my answer is wrong or not.

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