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3 years ago

The sum of a whole number and twice its square is 21. Find the whole number

1 answer:

6 0

SOLUTION:

Let whole number = x

x + 2x^2 = 21

2x^2 + x - 21 = 0

2x^2 + 7x - 6x - 21 = 0

x ( 2x + 7 ) - 3 ( 2x + 7 ) = 0

( 2x + 7 ) ( x - 3 ) = 0

2x + 7 = 0

2x = - 7

x = - 7 / 2

OR

x - 3 = 0

x = 3

ANSWER:

Therefore, as 3 is a whole number while - 7 / 2 isn't a whole number, the whole number must be 3.

Hope this helps! :)
Have a lovely day! <3

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3 years ago

The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesse

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<h3>The value of the larger number, x, is 57.</h3><h3>The value of the smaller number, y, is equal to 42.</h3>

x - y = 15

2x + 8 = 3y - 4

We can quickly get a temporary value for x by altering the original equation.

x - y = 15

Add y to both sides.

x = 15 + y

Now that we have a value of x, we can find the exact value of y.

2(15 + y) + 8 = 3y - 4

Distributive property.

30 + 2y + 8 = 3y - 4

Combine like terms.

38 + 2y = 3y - 4

Subtract 2y from both sides.

38 = y - 4

Add 4 to both sides.

y = 42

Now that we know the exact value of y, we can plug it back into the original equation.

x - 42 = 15

Add 42 to both sides.

x = 57

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2 years ago

Dawn works at the sponge factory and puts sponges in bags. She gets paid $0.12 for every sponge. If she got a paycheck for $864.

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Answer:

A.) 7,200

Step-by-step explanation:

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2 years ago

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How do you do this?

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U just need to add row by row
I'll do the first 1: 1+1=2
1+2=3
1+3=4
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3 years ago

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Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.

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So,

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The percent chance of there actually being oil is 45%. We can convert this into fraction form and simplify it.

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$\frac{3*3*5}{2*2*5*5}--\ \textgreater \ \frac{3*3}{2*2*5}$

$\frac{3*3}{2*2*5}--\ \textgreater \ \frac{9}{20}$

That is the simplified fraction form.

The kit has an 80% accuracy rate. Since we are assuming that the land has oil, we need the probability that the kit predicts no oil.

The probability that the kit detects no oil will be the chance that the kit is not accurate, which is 20% (100 - 80 = 20). We can also convert this into fraction form and simplify it.

20% --> $\frac{20}{100}$

$\frac{20}{100}--\ \textgreater \ \frac{2}{10}$

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That is the probability of the kit not being accurate (not predicting any oil).

To find the compound probability of there being oil and the kit not predicting any oil, we simply multiply both fractions together.

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