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3 years ago

7

Geometry What is the value of x?

1 answer:

denis23 [38]3 years ago

8 0

Answer:

x = 17 1/3

Step-by-step explanation:

Corresponding segments are proportional.

(3x)/(4x) = (3x +7)/(5x -8)

3(5x -8) = 4(3x +7) . . . . . . . . multiply by 4(5x-8)

15x -24 = 12x +28 . . . . . . eliminate parentheses

3x = 52 . . . . . . . . . . add 24-12x

x = 17 1/3 . . . . . . . . . divide by 3

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3 Calculate the missing values <br>3:5 -> 30 :<br><br>

RoseWind [281]

Answer:

3:5 = 30:50 because it is ratio 3 x 10 = 30 5 x 10 = 50

4 0

3 years ago

out of of are 40 students, 15 are on the student council. what percent of the students are NOT on the student council?

saw5 [17]

40-15=25 students not on student council

25/40 = .625 decimal

multiply by 100 to get percent

62.5% of students are not on student council

Estimating:

15 rounds to 20 and 40 rounds to 50

40% are in student council and that leaves roughly 60% not in student council.

6 0

3 years ago

The width of a rectangle is 9 in. shorter than its length. The area of the rectangle is 252 in². What is the length of the recta

erastovalidia [21]

Answer:

the length of the rectangle is, 21 in.

Step-by-step explanation:

Area of the rectangle(A) is given by:

$A=lw$ .....[1]

where,

l is the length of the rectangle

w is the width of the rectangle.

As per the statement:

The width of a rectangle is 9 in. shorter than its length.

⇒ $w = l-9$

It is also given that:

The area of the rectangle is 252 in².

⇒A = 252 in².

Substitute in [1] we have;

$252 = l(l-9)$

⇒ $252 = l^2-9l$

⇒ $l^2-9l -252 = 0$

Factorize this equation:

Split the middle term;

⇒ $l^2-21l+12l-252=0$

⇒ $l(l-21)+12(l-21)=0$

⇒ $(l-21)(l+12)=0$

By zero product property we have;

$l-21 =0$ and $l+12 =0$

⇒ $l = 21$ and $l = -12$

Since, length cannot be in negative

⇒ $l = 21 in.$

Therefore, the length of the rectangle is, 21 inches.

4 0

3 years ago

Given the rectangle abcd shown below has a total area of 72. E is in the midpoint of bc and f is the midpoint of dc. What is the

scoray [572]

Refer to the attached image.

Given the rectangle ABCD of length 'l' and height 'h'.

Therefore, CD=AB = 'l' and BC = AD = 'h'

We have to determine the area of triangle AEF.

Area of triangle AEF = Area of rectangle ABCD - Area of triangle ADF - Area of triangle ECF - Area of triangle ABE

Area of triangle ADF = $\frac{1}{2}bh$

= $\frac{1}{2}(DF \times AD)$

= $\frac{1}{2}(\frac{l}{2} \times h)$

$=\frac{lh}{4}$

Area of triangle ECF = $\frac{1}{2}bh$

= $\frac{1}{2}(CF \times CE)$

= $\frac{1}{2}(\frac{l}{2} \times \frac{h}{2})$

$=\frac{lh}{8}$

Area of triangle ABE = $\frac{1}{2}bh$

= $\frac{1}{2}(AB \times BE)$

= $\frac{1}{2}(l \times \frac{h}{2})$

$=\frac{lh}{4}$

Now, area of triangle AEF =

Area of rectangle ABCD - Area of triangle ADF - Area of triangle ECF - Area of triangle ABE

= $72 - (\frac{lh}{4} + \frac{lh}{8} + \frac{lh}{4})$

= $72 - (\frac{2lh+lh+2lh}{8})$

= $72 - (\frac{5lh}{8})$

= $72 - (\frac{5 \times 72}{8})$

$=\frac{72 \times 8 - (5 \times 72)}{8}$

= 27 units

Therefore, the area of triangle AEF is 27 units.

8 0

3 years ago

Percentages: Decrease 253 by 42%

Mariana [72]

146.74 because 42% of 253 is 106.26, and take that away from 253 = 146.74

4 0

3 years ago