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3 years ago

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The perimeter of a rectangular field is 580 yards. The length is 30 yards more than the width. Find the length and width of the

field (in yards).

1 answer:

aliya0001 [1]3 years ago

6 0

2 L + 2 W = 580

W = L - 30

2( L - 30) + 2 L =580

2L - 60 + 2 L =580

4 L = 640

L = 160

W = 160-30= 130

160 × 2 + 130 × 2 = 580

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will the contents of a cylindrical can of soup with a 1.5-inch radius and a 5-inch height fit into a pan with a 4-inch radius an

Anna007 [38]

Answer:

Answer: The volume of the soup can is less that that of the pan, so the soup will fit in the pan.

Step-by-step explanation:

a. V = s3

V = (7 km)3

V = 7 km × 7 km × 7 km

V = 343 km3

b. V = s3

V = (11 yd.)3

V = 11 yd. × 11 yd. × 11 yd.

V = 1,331 km cu. yd.

a. V = l × w × h

V = 6 m × 2 m × 3 m

V = 36 m3

b. V = l × w × h

V = 5 ft. × 10 ft. × 8 ft.

V = 400 cu. ft.

a. V = πr2h

V = 3.14 × (3 in.)2 × 3 in.

V = 3.14 × 9 sq. in. × 3 in.

V = 84.78 cu. in.

b. V = πr2h

V = 3.14 × (1 m)2 × 4 m

V = 3.14 × 1 m2 × 4 m

V = 12.56 m3

V = s3

V = (2 ft.)3

V = 2 ft. × 2 ft. × 2 ft.

V = 8 cu. ft.

Answer: The capacity of the ice chest is 8 cubic feet.

V = πr2h

V = 3.14 × (1 ft.)2 × 3 ft.

V = 3.14 × 1 sq. ft. × 3 ft.

V = 9.42 cu. ft.

Answer: The volume of the trash can is 9.42 cubic feet.

Closet #1

V = l × w × h

V = 4 ft. × 5 ft. × 8 ft.

V = 160 cu. ft.

Closet #2

V = l × w × h

V = 6 ft. × 3 ft. × 8 ft.

V = 144 cu. ft.

Compare the size of the closets

160 cu. ft. > 144 cu. ft.

Answer: The first closet is larger.

Both the can and the pan are cylindrical shapes. Compare the volumes of the two objects.

Volume of Can

V = πr2h

V = 3.14 × (1.5 in.)2 × 5 in.

V = 3.14 × 2.25 sq. in. × 5 in.

V = 35.325 cu. in.

Volume of Pan

V = πr2h

V = 3.14 × (4 in.)2 × 3 in.

V = 3.14 × 16 sq. in.× 3 in.

V = 150.72 cu. in.

35.325 cu. in. soup can < 150.72 cu. in pan

Answer: The volume of the soup can is less that that of the pan, so the soup will fit in the pan.

3 0

3 years ago

Solve the equation by factoring. 8x^2+10x-7=0<br><br> What is the solution set?

nydimaria [60]

Answer:

$\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}$

Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

<u>When factoring trinomials of the form ax² + bx + c</u>:

multiply the leading coefficient and the last term.
find the product factors that add to give you the coefficient of the middle term.
rewrite the polynomial with those factors replacing the middle term.

1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

4x + 7 = 0
2x - 1 = 0

<u><em>Case 1:</em></u>

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = $\bold{-\dfrac{7}{4}}$

<u><em>Case 2:</em></u>

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = $\bold{\dfrac{1}{2}}$

Solutions:

$\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}$

Learn more about quadratic equations here:

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7 0

2 years ago

Read 2 more answers

How do I do an exponent with a letter variable in it?

WARRIOR [948]

First you transform the expression and then evaluate the power

7 0

3 years ago

I would love some help pls, if anyone could talk me through it, that would be phenomenal I have no clue what’s going on lol

maks197457 [2]

Answer:

B) 7x - 3 = 4

Step-by-step explanation:

3x - 12 = -9

3x = 3

x = 1

A) NOPE

x - 5 = -6

x = -1

B) YES

7x - 3 = 4

7x = 7

x = 1

7 0

3 years ago

What value of x is in the solution set of 9(2x + 1) < 9x – 18

netineya [11]

The answer is: " x < -3 " .
_____________________
Explanation:
_____________________
Given:
______________________
" 9(2x + 1) < 9x – 18 " ;

First , factor out a "9" in the expression on the right-hand side of the inequality:

9x – 18 = 9(x – 2) ;

and rewrite the inequality:
_____________________
9(2x + 1) < 9(x – 2) ;

Now, divide EACH SIDE of the inequality by "9" ;

[9(2x + 1)] / 9 < [9(x – 2)] / 9 ;

to get:

2x + 1 < x – 2 ;

Now, subtract "x" and add "2" to each side of the inequality:

2x + 1 – x + 2 < x – 2 – x + 2 ;

to get:

x + 3 < 0 ;

Subtract "3" from EACH SIDE ;

x + 3 – 3 < 0 – 3 ;

to get:

" x < -3 " .
____________________________________

8 0

3 years ago