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1 year ago

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The sum of two numbers is negative seventeen, and one number is nine less than the other.Using the variables m and n to represen

t the two numbers, write a system of equations that describe the situation. Enter the equations below, separated by comma.Find the two numbers. Enter them below, separated by a comma.

2 answers:

Romashka-Z-Leto [24]1 year ago

5 0

Answer:

Step-by-step explanation:

given
m+n=-17,m-n=9

hence m=9+n apply in the 1 st eq

(9+n)+n=-17

2n=-17-9

n=8/2

n=4==>m=9+4

m=13,n=4

Orlov [11]1 year ago

3 0

ANSWER:

m + n = -17, m - 9 = n

-4, -13

STEP-BY-STEP EXPLANATION:

According to the statement, we can establish the following system of equations:

$\begin{gathered} m+n=-17 \\ \: m-9=n \\ \\ m+n=-17,m-9=n \end{gathered}$

We substitute the second equation in the first and solve:

$\begin{gathered} m+m-9=-17 \\ 2m=-17+9 \\ m=\frac{-8}{2} \\ m=-4 \\ \\ \text{ Now, for n, replacing the value of m:} \\ n=-4-9 \\ n=-13 \end{gathered}$

Therefore, the numbers are -4 and -13

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Please help ! 20 pts please

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The given ratios expresses the number of time a value is larger or smaller

than another value.

The correct responses are;

3. <u>(B) 12 and 24</u>

4. <u>(D) 6, 9, 21</u>

5. $\underline{(E) \ \displaystyle \frac{11}{2}}$

6. $\underline{(E) \ \displaystyle \frac{5}{14}}$

7. (B) $\overline{EF}$ =<u> 6</u>, $\overline{AC}$ = <u>9·√5</u>

8. <u>(C) The values are equal</u>

9. <u>(A) The value in column A is greater</u>

Reasons:

3. Given that the perimeter of the rectangle = 72

The ratio of the lengths of the sides = 1:2

Let <em>a</em> and <em>b</em> represent the sides, we have;

2·a + 2·b = 72

$\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}$

Which gives;

2·a = b

2·a + 2·(2·a) = 72

6·a = 72

a = 72 ÷ 6 = 12

b = 2·a = 2 × 12 = 24

The lengths of the sides are; <u>(B) 12 and 24</u>

4. Extended ratio = 2:3:7

The perimeter = 36

The lengths of the sides are;

$\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}$

$\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}$

$\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}$

The lengths are; <u>(D) 6, 9, 21</u>

5. The given equation is presented as follows;

$\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}$

5 × (x + 2) = 3 × (x + 7)

5·x + 10 = 3·x + 21

5·x - 3·x = 21 - 10

2·x = 11

$\displaystyle x = \mathbf{ \frac{11}{2}}$

The correct option is; $\displaystyle \underline{(E) \ \frac{11}{2}}$

6. The width to length ratio is $\displaystyle \mathbf{\frac{2.5}{7.0}}$

The simplified ratio is therefore;

$\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}$

The correct option is (E) $\displaystyle \underline{(E) \ \frac{5}{14}}$

7. The given ratio of the lengths is 3:1

Therefore;

$\overline{BC}$ : $\overline{EF}$ = 3:1

Which gives;

$\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}$

$\overline{BC}$ = 18

Therefore;

$\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}$

18 × 1 = 3 × $\overline{EF}$

$\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6$

$\overline{EF}$ = 6

By Pythagorean theorem, we have;

$\overline{DF}$ ² = $\mathbf{\overline{DE}}$ ² + $\mathbf{\overline{EF}}$ ²

Which gives;

$\overline{DF}$ ² = 3² + 6² = 45

$\overline{DF}$ = √(45) = 3·√5

Using the given ratio, we have;

$\overline{AC}$ = 3 × $\mathbf{\overline{DF}}$

Which gives;

$\overline{AC}$ = 3 × 3·√5 = 9·√5

$\overline{AC}$ = 9·√5

The correct option is; (B) $\overline{EF}$ =<u> 6</u>, $\overline{AC}$ = <u>9·√5</u>

8. EF = 1, AB = 2

CD = 2, CE = 4

Therefore;

$\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}$

$\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}$

Which gives;

$\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}$

<u>(C) The values are equal</u>

9. AC = 6, BE = 8

DF = 3, BD = 6

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$\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}$

Column B

$\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}$

$\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}$

Therefore;

Column A is greater than column B

<u>(A) The value in column A is greater</u>

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