please help ! 20 pts please

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

than another value.

The correct responses are;

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

[tex]\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}[/tex]

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;

[tex]\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}[/tex]

[tex]\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}[/tex]

[tex]\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}[/tex]

The lengths are; (D) 6, 9, 21

5. The given equation is presented as follows;

[tex]\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}[/tex]

5 × (x + 2) = 3 × (x + 7)

5·x + 10 = 3·x + 21

5·x - 3·x  = 21 - 10

2·x = 11

[tex]\displaystyle x = \mathbf{ \frac{11}{2}}[/tex]

The correct option is; [tex]\displaystyle \underline{(E) \ \frac{11}{2}}[/tex]

6. The width to length ratio is [tex]\displaystyle \mathbf{\frac{2.5}{7.0}}[/tex]

The simplified ratio is therefore;

[tex]\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}[/tex]

The correct option is (E) [tex]\displaystyle \underline{(E) \ \frac{5}{14}}[/tex]

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

Therefore;

[tex]\overline{BC}[/tex]:[tex]\overline{EF}[/tex] = 3:1

Which gives;

[tex]\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}[/tex]

[tex]\overline{BC}[/tex] = 18

Therefore;

[tex]\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}[/tex]

18 × 1 = 3 × [tex]\overline{EF}[/tex]

[tex]\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6[/tex]

[tex]\overline{EF}[/tex] = 6

By Pythagorean theorem, we have;

[tex]\overline{DF}[/tex]² = [tex]\mathbf{\overline{DE}}[/tex]² + [tex]\mathbf{\overline{EF}}[/tex]²

Which gives;

[tex]\overline{DF}[/tex]² = 3² + 6² = 45

[tex]\overline{DF}[/tex] = √(45) = 3·√5

Using the given ratio, we have;

[tex]\overline{AC}[/tex] = 3 × [tex]\mathbf{\overline{DF}}[/tex]

Which gives;

[tex]\overline{AC}[/tex] = 3 × 3·√5 = 9·√5

[tex]\overline{AC}[/tex] = 9·√5

The correct option is; (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√5

8. EF = 1, AB = 2

CD = 2, CE = 4

Therefore;

[tex]\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}[/tex]

[tex]\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}[/tex]

Which gives;

[tex]\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}[/tex]

(C) The values are equal

9. AC = 6, BE = 8

DF = 3, BD = 6

Column A

[tex]\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}[/tex]

Column B

[tex]\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}[/tex]

[tex]\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}[/tex]

Therefore;

Column A is greater than column B

(A) The value in column A is greater

Learn more about ratios here:

https://brainly.com/question/2774839

Part C
Does this curved line represent a function? If not, at what points does it fall the vertical line test?

Use the associative property to simplify the expression.
43 +30 + 70
O A. 43 + 10(3 + 7) = 43 + 10(10) = 143
O B. 43+ (30 + 70) = 43 + 100 = 143
O C. 43 + 30 + 70 = 73 + 70 = 143
O D. 43 + 70 + 30 = 113 + 30 = 143

blank % of $10 = $5


thank u for anyone who helps!!

Bones or no bones day?

find k where y varies directly as x, and the following are true.
y = 2 when x = 16

if shan has rupees 4800 left after spending 40% of his salary how much did he have in the beginning ​

please help me with math !!

the diagram shows two parallel lines OP and RQ. Straight line PQ is parallel to the y-axis and O is the origin.

a) Find the equation of the straight line PQ.
b) Find the equation of the straight line RQ.
c) Find the x-intercept of the straight line RQ.​

y-4 = 6(x + 7)
What’s the y-intercept of the equation?
Please explain it to me

A retailer plans to sell two models of earbuds at costs of $250 and 5400.
The $250 model yields a profit of $45 and the $400 model yields a profit of
$50. The retailer estimates that the total monthly demand will not exceed
250 units. Find the number of units each model that should be stocked in
order to maximize profit, given that the retailer is not investing more than
$70,000 in inventory

David hikes 2 1/4 miles in 1/2 an hour. At his rate, how long will it take him to walk 18 miles

Find the surface area of a cylinder with radius 8m and height 5 m

help pls please hmmm​

initial value on this table

A trucking company uses matrix A, shown below, to represent the driving time in hours for 6 trucking routes. A=[4686810]The driving time matrix is based on an average speed of 60 miles per hour. This means that the matrix 60A represents the driving distances in miles for these 6 trucking routes. Which of these is the matrix 60A?

Which angle do ΔEBC and ΔADC share?

Tire King is having a sale where customers can buy 4 new tires for $ 319.96 . What is the unit price of the tires?

Item 4
What is the expanded form of this number?

570.086


(5×100)+(7×10)+(8×110)+(6×1100)

(5×100)+(7×10)+(8×1100)+(6×1100)

(5×100)+(7×10)+(8×1100)+(6×11,000)

(5×100)+(7×10)+(8×110)+(6×11,000)

the three altitudes of a triangle intersect at the:

FURNITURE A modern table is constructed with four legs made
of concrete cubes with cube-shaped notches.
a. Define one or more variables and write an expression that
represents the volume of one table leg.

b. Marisol determined that she will use 12,636 cubic inches of
concrete to construct the four table legs. If the sides of the
notches are 40% of the sides of the legs, how long are the sides of the legs?

6√21 ×√28
please show work :D

Type the correct answer in each box. Use numerals instead of words.

What type of triangle is this?
5
7
8
acute
obtuse

a piece of string 44 centermerters long.Many cuts of a piece that is 15 centermeaters long .how much string is left?

Help me please on question one and two

Solve for the variable 2y<14 A) y<12 B) y>-7 C) y>7 D) y<7

Complete the tables of values.
Q1) y = x2 - 2x + 4
x -1 0 1 2 3
y

I need answer please the answer is not translation​

∠A and \angle B∠B are vertical angles. If m\angle A=(2x-10)^{\circ}∠A=(2x−10) ∘ and m\angle B=(x+8)^{\circ}∠B=(x+8) ∘ , then find the measure of \angle A∠A.

The base of a pyramid has n sides.
Write an expression for the number of vertices of the pyramid.

In the equation, y=3x+2, is the point (2,8) a solution the equation?

1: Yes, the point is solution
2: No, the point is not a solution