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vichka [17]
3 years ago
6

Simplify the numerical expression: (15÷3)×2+10

Mathematics
1 answer:
Nostrana [21]3 years ago
4 0

Answer:

20.

Step-by-step explanation:

Using order of operations (PEMDAS):

(15 / 3)*2 + 10

= 5*2 + 10

= 20.

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1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a
ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

1.

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

2.

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

3.

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

4.

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

g(4) = -2*4 - 1 = -9

7 0
3 years ago
Select the correct answer. what is the solution set of y = x2 2x 7 and y = x 7? a. {(0, 7), (-1, 6)} b. {(0, 7), (-7, 0)} c. {(0
Kaylis [27]

Answer:

a. {(0, 7), (-1, 6)}

Step-by-step explanation:

y = x^{2} +2x+7\\y=x+7

subtract the equations

y = x^{2} +2x+7 \\-       \ \ \ \ \  y=x+7\\y - y =x^{2} +2x+7-(x+7)\\0=x^{2} +x\\x = 0 \ and \ x= -1

for y = x^{2} +2x+7, substitute x = 0

y = (0)^{2} +2(0)+7\\y = 0 +0+7\\y=7

for y = x^{2} +2x+7, substitute x = 0

y = (-1)^{2} +2(-1)+7\\y = 1 -2+7\\y=6

6 0
1 year ago
FCD=x+41, BCF=x+78, BCD=95. Find x
Lorico [155]
You'll set the two expressions equal to 95.
So 2x+119=95
Then 2x=-24
Finally x=-12
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3 years ago
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3 years ago
A jeweler works with two kinds of metals, the first contains
Darina [25.2K]

Answer:

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Step-by-step explanation:

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