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3 years ago

Find all the real zeros of the function f(x) = 2x3 - 19x2 + 38x + 24 given that x-4 is a factor.

Mathematics

1 answer:

iris [78.8K]3 years ago

8 0

Answer:

Zeroes: x=4, x=-1/2, and x=6

Step-by-step explanation:

Use Synthetic Division where x-4=0 to find another factor:

4 | 2 -19 +38 +24

___8_-44_-24

2 -11 -6 | 0

So far, your two factors are x-4 and 2x^2-11x-6.

We can actually factor 2x^2-11x-6 into (2x+1)(x-6), so we have three factors which are (x-4), (2x+1), and (x-6)!

By the Zero Product Property, x=4, x=-1/2, and x=6 are your zeroes.

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Now you have

(.15)0.5 lb peanuts = 0.075 lb peanuts
0.5 lb nuts 0.5 lb nuts

for every pound of 75% mixed nuts you add, you get .75 lb peanuts, how many pounds, x, do you need to add to get the ratio 50 to 100?

0.075 lb peanuts + 0.75x lb peanuts = 50 
0.5 lb nuts + x lb nuts 100

cross multiply

(0.075 + .75x) 100 = (0.5 + x) 50
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3 years ago

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3 years ago

Identify the y intercept and asymptote of the graph of the exponential function. y=3^x

nalin [4]

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horizontal asymptote

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3 years ago

will drinks 1.09 liters of juice. richard drinks 0.987 liters of juice. how much more juice does will drink then Richard

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Step-by-step explanation:

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3 years ago

Mrs. Grubb bought some shirts for $4 each and some hats for $12 each. She bought 9 pieces of clothing for $100. Write a system o

Lana71 [14]

Answer:

Mrs. grub bought total number of shirts = 1

Mrs. grub bought total number of hats = 8

Step-by-step explanation:

Let Mrs. grub bought total number of shirts = x

Let Mrs. grub bought total number of hats = y

As given,

Price of 1 shirt = $4

Price of 1 hat = $12

⇒ Price of x shirts = $ 4x

Price of y hats = $ 12y

Given that,

Mrs. Grubb bought total piece of clothes = 9

⇒ x + y = 9 .......(1)

Also given,

She bought all clothing for $100

⇒ 4x + 12 y = 100 ........(2)

Divide equation (2) by 4 we get

x + 3y = 25 .......(3)

Now,

Subtract equation (1) from equation (3) , we get

x + 3y - ( x + y ) = 25 - 9

⇒ x + 3y - x - y = 16

⇒2y = 16

⇒y = $\frac{16}{2}$ = 8

⇒ y = 8

Put value of y in equation (3), we get

x + 3(8) = 25

⇒x + 24 = 25

⇒x = 25 - 24 = 1

⇒x = 1

∴ we get

Mrs. grub bought total number of shirts = x = 1

Mrs. grub bought total number of hats = y = 8

8 0

3 years ago