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3 years ago

Please show me the work thank you

Mathematics

2 answers:

KiRa [710]3 years ago

6 0

Answer: B. x < 25

Remember: when multiplying or dividing negatives, flip the inequality sign.

3(x + 3) > 4(x - 4) Distributive Property
3x + 9 > 4x - 16 Subtract 4x from both sides
-x + 9 > -16 Subtract 9 from both sides
-x > -25 Divide by -1 to both sides and flip the sign
x < 25 Answer!

lianna [129]3 years ago

6 0

3(x + 3) > 4(x - 4)

To solve this problem, first, we distribute.

3x + 9 > 4x - 16

Then, we can simplify this inequality.

9 > x - 16
0 > x - 25
x < 25

The answer is B.

Hope this helped!

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You are given g(x)=4x^2 + 2x and

Strike441 [17]

Answer:

324

Step-by-step explanation:

Given:

$g(x)=4x^2+2x\\ \\f(x)=\int\limits^x_0 {g(t)} \, dt$

Find:

$f(6)$

First, find f(x):

$f(x)\\ \\=\int\limits^x_0 {g(t)} \, dt\\ \\=\int\limits^x_0 {(4t^2+2t)} \, dt\\ \\=\left(4\cdot \dfrac{t^3}{3}+2\cdot \dfrac{t^2}{2}\right)\big|\limits^x_0\\ \\=\left(\dfrac{4t^3}{3}+t^2\right)\big|\limits^x_0\\ \\= \left(\dfrac{4x^3}{3}+x^2\right)-\left(\dfrac{4\cdot 0^3}{3}+0^2\right)\\ \\=\dfrac{4x^3}{3}+x^2$

Now,

$f(6)\\ \\=\dfrac{4\cdot 6^3}{3}+6^2\\ \\=288+36\\ \\=324$

4 0

3 years ago

An investment made in the stock market decreased at a rate of 2.2% per year for 10 years. What is the current value of

never [62]

Answer:

$800,500 (nearest dollar)

Step-by-step explanation:

The given scenario can be modeled as an exponential equation.

General form of an exponential function:

$f(x)=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

The initial value (a) is the value of the investment.

Therefore, a = 1,000,000.

If the investment decreases by 2.2% each year, then it will be 97.8% of the previous year.

Therefore, b = 97.8% = 0.978.

Substitute these values into the formula to create a general equation for the scenario:

$f(x)=1000000(0.978)^x$

(where x is the time, in years).

To find the value of the investment after 10 years, substitute x = 10 into the formula:

$\implies f(10)=1000000(0.978)^{10}=800500.1586$

Therefore, the value of the investment after 10 years is $800,500 (nearest dollar).

Learn more about exponential functions here:

brainly.com/question/27949445

brainly.com/question/27955470

3 0

1 year ago

Solve for u. u+1/4=-4/5

DedPeter [7]

Answer:

u = (-21)/20

Step-by-step explanation:

Solve for u:

u + 1/4 = (-4)/5

Put each term in u + 1/4 over the common denominator 4: u + 1/4 = (4 u)/4 + 1/4:

(4 u)/4 + 1/4 = -4/5

(4 u)/4 + 1/4 = (4 u + 1)/4:

1/4 (4 u + 1) = -4/5

Multiply both sides of (4 u + 1)/4 = (-4)/5 by 4:

(4 (4 u + 1))/4 = (-4)/5×4

4×(-4)/5 = (4 (-4))/5:

(4 (4 u + 1))/4 = (-4×4)/5

(4 (4 u + 1))/4 = 4/4×(4 u + 1) = 4 u + 1:

4 u + 1 = (-4×4)/5

4 (-4) = -16:

4 u + 1 = (-16)/5

Subtract 1 from both sides:

4 u + (1 - 1) = (-16)/5 - 1

1 - 1 = 0:

4 u = (-16)/5 - 1

Put (-16)/5 - 1 over the common denominator 5. (-16)/5 - 1 = (-16)/5 - 5/5:

4 u = (-16)/5 - 5/5

-16/5 - 5/5 = (-16 - 5)/5:

4 u = (-16 - 5)/5

-16 - 5 = -21:

4 u = (-21)/5

Divide both sides by 4:

u = ((-21)/4)/5

5×4 = 20:

Answer: u = (-21)/20

3 0

3 years ago

Cole paid $24 for 2 calculators and a pack of pens. Kai paid $45 for 3 calculators and 2 packs of pens. They both paid $6 for ea

s344n2d4d5 [400]

$12 for one of the calculators

3 0

3 years ago

Read 2 more answers

denis-greek [22]

Answer:

Part a) $AB=15\ cm$

Part b) $AB=11.1\ cm$

Part c) $AB=3/5\ cm$

Part d) $AB=3s\ cm$

Step-by-step explanation:

see the attached figure to better understand the question

we know that

To find the length of the image after a dilation, multiply the length of the pre-image by the scale factor

Part a) we have

The scale factor is 5

The length of the pre-image is 3 cm

therefore

The length of the image AB after dilation is

$3(5)=15\ cm$

Part b) we have

The scale factor is 3.7

The length of the pre-image is 3 cm

therefore

The length of the image AB after dilation is

$3(3.7)=11.1\ cm$

Part c) we have

The scale factor is 1/5

The length of the pre-image is 3 cm

therefore

The length of the image AB after dilation is

$3(1/5)=3/5\ cm$

Part d) we have

The scale factor is s

The length of the pre-image is 3 cm

therefore

The length of the image AB after dilation is

$3(s)=3s\ cm$

7 0

3 years ago