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rodikova [14]
3 years ago
6

Twice a number increased by 8 is less than -4

Mathematics
1 answer:
stepladder [879]3 years ago
5 0

Answer:

Twice a number : 2x

increased by : +

8  :  8

is equal to : =

the number : x

increased by :  -

-4  :  -4

The answer is 2x+8 < -4


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A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the vol
k0ka [10]

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

<u>Given the following data:</u>

  • Volume of box = 224 cubic inches.

Translating the word problem into an algebraic expression;

W = 3 + L  ......equation 1

H = 4 + L  ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

Volume = length * width * height  .....equation 3.

Substituting the values into equation, we have;

224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}

Rearranging the polynomial, we have;

L^{3} + 7L^{2} +  12L - 224 = 0

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

(x - 3) = 0\\x = 3

P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9)  + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0

We would try with 4;

P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16)  + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224  - 224 = 0

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: brainly.com/question/10689855

3 0
2 years ago
A
kramer

Step-by-step explanation:

the sum of a number and 2 is no less than the product of 9 and the same number

3 0
2 years ago
Trains Two trains, Train A and Train B. weigh a total of 196 tons. Train A is heavier than Train B. The
aleksklad [387]

Answer:

Train A = 128

Train B = 68

Step-by-step explanation:

We can set up a system of equations for this problem

Let A = # of tons of Train A

Let B = # of tons of Train B

A + B = 196

A = B + 60

Now, we plug in A for the first equation, using substitution

(B+60) + B = 196

2B + 60 = 196

Subtract 60 from both sides

2B = 136

Divide both sides by 2

B = 68

Plug in 68 for B in the 2nd equation

A = 68 + 60

A = 128

Checking work: 128 + 68 = 196 :D hope this helped

5 0
2 years ago
8.2 x 10 ^-5 in standard notation
Mars2501 [29]
8.2*10^-5 can be also written as 0.000082, in standard notation. 
Hope this helps.
5 0
3 years ago
35 is 70 percent of what number? Explain how you got it. Please check out my other questions on my profile and help me with thos
Hunter-Best [27]

Answer:

70% of50

35

70×50/100=35

= 35

Step-by-step explanation:

mark me brainiest

pls and ty

hope this helps!

<u><em>Q</em></u><u>UEEN</u><u><em>O</em></u><u>F</u><u><em>T</em></u><u>ARUS</u>

6 0
2 years ago
Read 2 more answers
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