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4 years ago

Evaluate f[g(x)] when f(x)=7x-5 and g(x)=x+2

Mathematics

1 answer:

Alex4 years ago

5 0

Answer:

7x+9

Step-by-step explanation:

f(x)=7x-5

g(x)=x+2

f[g(x)]= Substitute g(x) in for x in the function f(x)

=7(g(x))-5

= 7( x+2) - 5

Distribute

= 7x+14 - 5

Combine like terms

=7x +9

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Komok [63]

Answer:

Part a) $22.95+0.43x \leq 25$

Part b) The maximum number of candy bars that you can purchase is 4

Part c) The change would be $\$0.33$

Step-by-step explanation:

Part a) Write an equation representing your shopping experience and use x for the number of candy bars

Let

x -----> the number of candy bars

we know that

The inequality that represent this problem is equal to

$2(3.50)+2(2.75)+10.45+0.43x \leq 25$

$22.95+0.43x \leq 25$

Part b) Solve the equation to determine how many candy bars can you purchase?

$22.95+0.43x \leq 25$

Solve for x

Subtract 22.95 both sides

$0.43x \leq 25-22.95$

$0.43x \leq 2.05$

Divide by 0.43 both sides

$x \leq 2.05/0.43$

$x \leq 4.8$

The maximum number of candy bars that you can purchase is 4

Part c) How much change would you have left?

If you purchase 4 candy bars

then

$22.95+0.43(4)=\$24.67$

therefore

$\$25-\$24.67=\$0.33$

4 0

4 years ago

A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 10% are pennies and 42% are

nekit [7.7K]

Answer:

$2.55

Step-by-step explanation:

6 0

4 years ago

one factor of the function f(x) = x^3 -7x^2+14x-8 is (x-4). describe how to find the x intercept and the y intercepts of the gra

Xelga [282]

Answer:

(2 , 0)

(1 , 0)

(4 , 0)

(0, -8)

Step-by-step explanation:

f(x) = x³ -7x² + 14x - 8

The y intercept occurs when x = 0.

This means the first three terms all go to zero an the result is y = -8

As we are given one factor, (x - 4), we know that one zero will occur when this factor is zero

x - 4 = 0

x = 4

taking out the x - 4 term from the quadratic

x³ -7x² + 14x - 8 = (x² ± Cx + 2)(x - 4)

we can see that

2x ± 4Cx = 14x

±4C = 12

C = 12/±4 = ±3

also

±Cx² - 4x² = -7x²

±C - 4 = -7

so C = -3

(x² - 3x + 2)

(x - 2)(x - 1)

x = 2

x = 1

7 0

3 years ago

On your own paper, change 7/8 to a decimal and type in the answer:

Nonamiya [84]

Answer:

.125 is equal to 1/8 so do .125 times 7 and that equals .875

Step-by-step explanation:

.125=1/8

.125x7=.875

6 0

4 years ago

Read 2 more answers

write a quadratic function in vertex form whose graph has the vertex (1,0) and passes through point (2,-17)

kobusy [5.1K]

Answer:

$\displaystyle f(x) = -17(x-1)^2$

Step-by-step explanation:

We want to write a quadratic function in vertex form whose vertex is (1, 0) and passes through the point (2, -17).

Recall that vertex form is given by:

$\displaystyle f(x) = a(x-h)^2 + k$

Where (h, k) is the vertex and a is the leading coefficient.

Since our vertex is at (1, 0), h = 1 and k = 0:

$\displaystyle f(x) = a(x-1)^2$

It passes through the point (2, -17). Hence, when x = 2, y = -17:

$\displaystyle (-17) = a((2)-1)^2$

Solve for a:

$\displaystyle a = -17$

In conclusion, our quadratic function in vertex form is:

$\displaystyle f(x) = -17(x-1)^2$

7 0

3 years ago