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3 years ago

What is the value of x? −3/4(12−8x)=5x+15−7x

Mathematics

1 answer:

AnnyKZ [126]3 years ago

7 0

Answer:

x = 3

Step-by-step explanation:

step 1: distribute -3/4 among 12 and 8x to get: -36/4 + 6x

step 2: combine 'like terms' on right side to get -2x + 15

-9 + 6x = -2x + 15

-9 + 8x = 15

8x = 24

x = 3

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Four friends shared 1/2 of one carton of orange juice and 1/4 of another carton of apple juice. What fraction of each carton of

Natalka [10]

Answer:

$\dfrac{1}{16}$

$\dfrac{1}{32}$

$\dfrac{3}{32}$

Step-by-step explanation:

So in the first carton of orange juice 4 friends shared the juice.

This can be shown as:

$\dfrac{(\dfrac{1}{2})}{4}$

$\dfrac{(\dfrac{1}{2})}{4}=\dfrac{1}{16}$

The 4 friends got 1/16 of the carton each in the first carton of OJ.

Next for the second carton, it can be shown as:

$\dfrac{(\dfrac{1}{4})}{4}$

$\dfrac{(\dfrac{1}{2})}{4}=\dfrac{1}{32}$

The 4 friends got 1/32 of the carton each in the first carton of OJ.

Now to see how much they got in total each, we simply add 1/16 to 1/32

$Total OJ each = \dfrac{1}{16}+\dfrac{1}{32}$

$Total OJ each = \dfrac{3}{32}$

Each friend got a total of $\dfrac{3}{32}$ each from both cartons of OJ.

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3 years ago

Just part a I’ve done b. Photo provided.

Rasek [7]

Answer:

Step-by-step explanation:

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Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-24

Zanzabum

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

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