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3 years ago

8

Show the sample space of the following ice cream choices: You have vanilla, chocolate, or strawberry ice cream and you can have

either hot fudge or caramel as a topping.

1 answer:

77julia77 [94]3 years ago

7 0

Is this like the chicken feet problems?

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What is the height, width, and length

Novosadov [1.4K]

so, let's say the length is "L".

width = 2 shorter than L = L - 2.

height = 9 more than twice L = 2L + 9.

check the picture below.

keeping in mind that the volume of a <u>rectangular prism</u> is simply the product of its length, width and height, and since we know the volume has to be 45.

$\bf 45=(L)(L-2)(2L+9)\implies 45=(L)(2L^2+5L-18) \\\\\\ 45=2L^3+5L^2-18L\implies 0=2L^3+5L^2-18L-45 \\\\\\ \stackrel{\textit{now let's do some grouping}}{0=(2L^3+5L^2)-(18L+45)}\implies \stackrel{\textit{common factor}}{0=L^2(2L+5)-9(2L+5)}$

$\bf \stackrel{\textit{again common factor}}{0=\underline{(2L+5)}(L^2-9)}\implies \stackrel{\textit{difference of squares}}{0=(2L+5)\stackrel{\downarrow }{(L^2-3^2)}} \\\\\\ 0=(2L+5)(L-3)(L+3)\implies L= \begin{cases} -\cfrac{5}{2}\\[1em] \boxed{3}\\ -3 \end{cases}$

from those 3 factors, we get those solutions/zeros.

we can't use -5/2, or -3, because the length can't be a negative value, so L = 3.

that means the width = 3 + 2, and the height = 2(3) +9.

8 0

3 years ago

Look at the triangle: A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is

mezya [45]

Answer:

tan x degrees is opposite over adjacent, making it 8 over 6 and your answer 8 divided by 6

8 0

3 years ago

Read 2 more answers

1. 81 1/2 x 27 1/3 <br><br> 2. 32x = 729

stepan [7]

Answer:

1.

Step-by-step explanation:

1. 1.811/2=3.622 271/3=813

3.622*813=2,944.686

this is number one

2. 32x=729

divide both sides by 32

32x=729/32=

22.78125 approximate=22.8 or 23

3 0

2 years ago

-1/2 w - 3/5 = 1\5 w <br> w=

Scorpion4ik [409]

Answer:

cucuchchcuchcucucchfhfuc uchczchcj h. fzchchch vzvzvhvhvuvzvz z <em>vvzvzc</em><em> </em><em>fudge</em>

5 0

3 years ago

What is the product in lowest terms?

Alisiya [41]

-5/12 × 8/13

First, we need to start out by applying the multiplication rule towards fractions. If you haven't learned or don't remember the rules, you can always look up fraction rules. The rule is: a/b × c/d = ac/bd. Basically, we are combining the numerators and both of the denominators.
$- \frac{5 \times 8}{12 \times 13}$

Second, let's now multiply what we have in the fraction. (5 × 8 = 40) and (12 × 13 = 156). Doing so will create a new fraction for us to use.
$-\frac{40}{156}$

Third, now obviously, we can simplify the fraction we just got into lower terms. To do that, we have to collect the greatest common factor (GCF) of both the numerator and denominator and list their factors to find the common factor that is the greatest.

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

Out of the listed factors, which of those are the common ones? 1, 2, and 4 are the common factors. Since we are looking for the greatest common factor, it would be 4 since that is the higher number out of the commons. The GCF is 4.

Fourth, we can now divide our numerator (40) and our denominator (156) by the GCF we just found out, which was 4.
$40 \div 4 = 10 \\ 156 \div 4 = 39$

Fifth, our last step is to create our new simplified fraction. All we have to do is take our new numerator and denominator to see the fraction.

Answer in fraction form: $\fbox {-10/39}$
Answer in decimal form: $\fbox {-0.2564}$

4 0

2 years ago