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3 years ago

14

Which choice is equivalent to the expression below?

2 answers:

Natalija [7]3 years ago

8 0

Answer:

C. 4√7 - 4x√7

Step-by-step explanation:

4√7 - 3x√7 - x√7

combine like terms

4√7 - 4x√7

Andre45 [30]3 years ago

7 0

<u>Answer:</u>

C. $4\sqrt{7} -4x\sqrt{7}$ is correct

<u>Steps</u><u>:</u>

$4\sqrt{7} -3\sqrt{7}x-x\sqrt{7} \\\\4\sqrt{7} -3\sqrt{7} x-\sqrt{7} x\\\\4\sqrt{7} +(-3\sqrt{7} x-\sqrt{7} x)\\\\4\sqrt{7} -4\sqrt{7} x$

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You must design a closed rectangular box of width w, length l and height h, whose volume is 504 cm3. The sides of the box cost 3

Charra [1.4K]

Answer:

Dimensions will be

Length = 7.23 cm

Width = 7.23 cm

Height = 9.64 cm

Step-by-step explanation:

A closed box has length = l cm

width of the box = w cm

height of the box = h cm

Volume of the rectangular box = lwh

504 = lwh

$h=\frac{504}{lw}$

Sides which involve length and width and height, cost = 3 cents per cm²

Top and bottom of the box costs = 4 cents per cm²

Cost of the sides $C_{s}$ = 3[2(l + w)h] = 6(l + w)h

$C_{s}$ = 3[2(l + w)h]

$C_{s}=6(l+w)(\frac{504}{lw} )$

Cost of the top and the bottom $C_{(t,p)}$ = 4(2lw) = 8lw

Total cost of the box C = $3024\frac{(l+w)}{lw}$ + 8lw

= $3024[\frac{1}{l}+\frac{1}{w}]$ + 8lw

To minimize the cost of the sides

$\frac{dC}{dl}=3024(-l^{-2}+0)+8w=0$

$\frac{3024}{l^{2}}=8w$

$\frac{378}{l^{2}}=w$ ---------(1)

$\frac{dC}{dw}=3024(-w^{-2})+8l=0$

$\frac{3024}{w^{2}}=8l$

$\frac{378}{w^{2}}=l$

$w^{2}=\frac{378}{l}$ -------(2)

Now place the value of w from equation (1) to equation (2)

$(\frac{378}{l^{2}})^{2}=\frac{378}{l}$

$\frac{(378)^{2} }{l^{4}}=\frac{378}{l}$

l³ = 378

l = ∛378 = 7.23 cm

From equation (2)

$w^{2}=\frac{378}{7.23}$

$w^{2}=52.28$

w = 7.23 cm

As lwh = 504 cm³

(7.23)²h = 504

$h=\frac{504}{(7.23)^{2}}$

h = 9.64 cm

6 0

3 years ago

good morning fellow brainsters please help me i’m tired and i just drank a four loko... can’t think. will give 15 points

borishaifa [10]

Answer:

7. $x=3$

8. l=11cm and w=7 cm

9. $x-5\ge12$

10. $\frac{x}{3}\le15$

Step-by-step explanation:

Question 7.

The given expression is:

$12-3(2x+1)=7x-3(7+x)$

Expand the parenthesis using the distributive property:

$12-6x-3=7x-21-3x$

Group similar terms:

$-6x-7x+3x=-21+3-12$

Simplify

$-10x=-30$

Divide both sides by -10

$x=3$

Question 8:

Let the width of the rectangle be; $w$

The length of the rectangle is $l=w+4$

The perimeter is given as: $P=2(l+w)$

Given that the perimeter P=36, then:

$36=2[(w+4)+w)]$

$\implies 36=2(2w+4)$

Divide both sides by 2:

$\implies 18=2w+4$

Subtract 4 from both sides:

$\implies 18-4=2w$

$\implies 14=2w$

$\implies w=7$

The dimensions of the rectangle is: w=7 cm and l=7+4=11cm

Question 9

Let the number be x.

"5 fewer than the number" is written as $x-5$

"5 fewer than a number is at least 12" becomes

$x-5\ge12$

Question 10:

Let the number be x.

The quotient of a number and 3 is written as:

$\frac{x}{3}$

The quotient of a number and 3 is no more than 15 is written as;

$\frac{x}{3}\le15$

4 0

3 years ago

Ms. Jenkins stocks a pond with fish. For every 6 bluegill fish, she puts in 1 rock bass fish. Does this ratio mean that Ms. Jenk

snow_tiger [21]

Answer:

Ms. Jenkins puts <u>for every 6</u> bluegill fish <u>one</u> rock bass fish so she puts the number multiple of 7

6 0

3 years ago

A bunch of friends went to the snack shake for lunch. The first family ordered 4 hamburger and 4 orders of fries for 9$. The sec

nexus9112 [7]

Answer:

$1.50 for hamburgers, and $0.75 for fries.

Hope this helps you! Have an amazing day :)

8 0

3 years ago

Plz help fast will mark brainliest

Semenov [28]

Answer: -270

Step-by-step explanation:

First, simplify the exponent

$-6*(25+20)$

Then, distribute

$-150+-120$

Then, subtract(add a negative)

$-270$

Hope it helps <3 :)

6 0

2 years ago

Read 2 more answers