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3 years ago

A box has a volume given by the trinomial x^3 5x^2 -24x What are the possible dimensions of the box?

2 answers:

vladimir2022 [97]3 years ago

8 0

Volume is legnth times width times height so 3 dimentions
thee teacher probabl y wants you to factor the trinomial into 3 factors so
x^3+5x^2-24x
first factor out x
x(x^2+5x-24)
then factor
find what 2 numbers multiply to get -24 and add to get 5
the numbers are -3 and 8
x^2+5x-24 factors to
(x-3)(x+8)
the factored form is
(x)(x-3)(x+8)=volume
no dimention can be ≤0 so therefor
x≤0

x-3≤0
add 3
x≤3

x+8≤0
subtract 8
x≤-8

so the values for x is x<3

so if you had the volume, let's say 42 then
x^3+5x^2-24x=42
subtract 42 from both sides
x^3+5x^2-24x-42=0
factor and set each to zero to find the dimentions

hoa [83]3 years ago

6 0

Answer:

116

Step-by-step explanation:

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Convert 0.875 inch to a fraction in simplest form. Click to select the correct answer.

inna [77]

This isnt the simplist but 875/1000 . Thats 875 over 1000.

8 0

3 years ago

What is the P(T,H,T,H) on 4 flips of a coin? i need help

Katen [24]

Answer:

1/16

Step-by-step explanation:

Each coin flip is an independent event so the probabilities are independent

P(T,H,T,H) = P(T) P(H) P(T) P(H)

= 1/2 * 1/2 * 1/2 * 1/2

= 1/16

5 0

3 years ago

−8.5x + 0.36 = −3.04

erma4kov [3.2K]

X= 0.4

-8.5x=-3.4
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4 0

2 years ago

An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the i

Natasha_Volkova [10]

Answer:

The amount invested in the mutual fund that earned 5% was $1,000

The amount invested in the mutual fund that earned 3% was $1,800

Step-by-step explanation:

Let

x ----> the amount invested in the mutual fund that earned 5%

y ----> the amount invested in the mutual fund that earned 3%

we know that

$x+y=2,800$ ----> $y=2,800-x$ ----> equation A

$5\%=5/100=0.05$

$3\%=3/100=0.03$

$0.05x+0.03y=104$ ----> equation B

Solve the system by substitution

substitute equation A in equation B

$0.05x+0.03(2,800-x)=104$

Solve for x

$0.05x+84-0.03x=104$

$0.05x-0.03x=104-84$

$0.02x=20$

$x=\$1,000$

Find the value of y

$y=2,800-x$

$y=2,800-1,000=\$1,800$

therefore

The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800

5 0

3 years ago

Suppose that you are conducting a survey on how many students have blue eyes in each first period classroom at Garfield Middle s

rusak2 [61]

Answer:

The correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean

Explanation:

To calculate how many standard deviations a particular value in a group is from the mean, you can use the z-score:

$z-score=(x-\mu )/\sigma$

Where:

$z-score$ is the number of standard deviations the value of x is from the mean

$\mu$ is the mean

$\sigma$ is the standard deviation

Substitute in the formula:

$z-score=(10-6)/2=4/2=2$

Which means that the number of blue-eyed students in Mr. Garcia's class is 2 standard deviations above the mean.

Above the mean is the same that to the right of the mean, because the in the normal standard probability graph the central value is Z = 0 (the z-score of the mean value is 0), the positive values are to the right of the central value, and the negative values are to the left of the central value.

Therefore, the correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean,

4 0

3 years ago