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3 years ago

PLEASE HELP ME ASAP!!

Mathematics

1 answer:

mote1985 [20]3 years ago

7 0

Answer:

Step-by-step explanation:

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Please help ! 20 pts please

Ksenya-84 [330]

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

than another value.

The correct responses are;

3. (B) 12 and 24

4. (D) 6, 9, 21

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

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

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

8. (C) The values are equal

9. (A) The value in column A is greater

Reasons:

3. Given that the perimeter of the rectangle = 72

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

Let a and b 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; (B) 12 and 24

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; (D) 6, 9, 21

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) $\overline{EF}$ = 6, $\overline{AC}$ = 9·√5

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;

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

(C) The values are equal

9. AC = 6, BE = 8

DF = 3, BD = 6

Column A

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

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

(A) The value in column A is greater

Learn more about ratios here:

brainly.com/question/2774839

7 0

3 years ago

Evaluate the expression 2/5 divided by 1/5 plus 4/5 divided by 1/3

Anna007 [38]

Answer:

The answer I got is 4 2/5.

Step-by-step explanation: 2/5 divided by 1/5 is 2. 4/5 divided by 1/3 is 2 2/5. 2 plus 2 2/5 is 4 2/5.

6 0

3 years ago

What is the domain of the quadratic function graphed below?

lora16 [44]

The domain of the graph is the set of all real values

<h3>How to determine the domain?</h3>

The domain is the set of x values of the graph

From the graph, the x values extend in both directions without end

This means that the x values can accommodate all real values

Hence, the domain of the graph is the set of all real values

Read more about domain at:

brainly.com/question/13113489

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3 0

2 years ago

Hello! So, Given the equation y = 2x - 8, what is the slope and the y-intercept? Please help with a good explanation of how you

elena55 [62]

Answer:

m = 2 and b = -8.

Step-by-step explanation:

One of the most commonly used equations of straight lines is y = mx + b, where m is the slope and b is the y-intercept.

Comparing the given y = 2x - 8 to y = mx + b, we see that m = 2 and b = -8.

3 0

4 years ago

Read 2 more answers

If you invested $600 at 3% simple interest for 2 years, how much interest do you earn? Show work and answer in complete sentence

zzz [600]

Answer:

I would rather do the second option of which uses Compound interest that will give a profit of $47.85

Step-by-step explanation:

In this problem we will be exploring the two formulas

1. simple interest

A= P(1+r*t)

2. compound interest

A= P(1+r/n)^nt

Where A= final amount

P= initial amount

r= rate

t= time.

n= number of periods Compounded

1.given data

P= $600

r= 3%= 3/100= 0.03

t= 2 years

A= 600(1+0.03*2)

A= 600(1+0.06)

A= 600(1.06)

A= $636

Interest = 636-600= $36

2. Given data

P= $600

r= 4%= 4/100= 0.04

n= 24

t= 2

A= 600(1+0.04/24)^24*2

A=600(1+0.0016)^48

A=600(1.0016)^48

A= 600*1.07975

A= 647.85

Interest = 647.85-600= $47.85

7 0

3 years ago