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3 years ago

What is the area of the shaded region on the graph shown?

Mathematics

1 answer:

Sindrei [870]3 years ago

5 0

Answer:

As Doris Day said: Good morning to you

Answer 27/2

Step-by-step explanation:

$f(x)=-x^3+5x\\F(x)=-\dfrac{x^4}{4} +\dfrac{5x^2}{2} \\F(2)=\dfrac{-16}{4}+\dfrac{20}{2} =6\\\\F(-1)=\dfrac{-1}{4} +\frac{5}{2} =\dfrac{9}{4} \\g(x)=\dfrac{3x^2}{2}+\dfrac{x}{2}-5\\\\G(x)=\dfrac{x^3}{2} +x^2-5x\\\\G(2)=4+1-10=-5\\\\G(-1)=\dfrac{-1}{2} +\dfrac{1}{4} +5=\dfrac{19}{4} \\\\\int\limits^2_{-1} {(f(x)-g(x))} \, dx =F(2)-G(2)-(F(-1)-G(-1))\\\\=11+\dfrac{5}{2} =\dfrac{27}{2}$

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4 lbs 7 oz; oz conversions ratios thing

bogdanovich [222]

Answer:

4 lb 7 oz = 71 oz

Step-by-step explanation:

Do you need to convert 4 lb 7 oz into oz?

If so, do the following.

Obviously, 7 oz is already in oz, so all you need to do is convert 4 lb into oz and then add 7 oz.

1 lb = 16 oz

For every lb, there are 16 oz. To convert lb to oz, multiply the number of lb by 16.

4 lb = 4 * 16 oz = 64 oz

4 lb 7 oz = 4 lb + 7 oz = 64 oz + 7 oz = 71 oz

4 0

3 years ago

(8/9)^-2 without an exponent

Ganezh [65]

Answer:

81/64 or 1 17/64

Step-by-step explanation:

A negative exponent means to flip the fraction

(8/9) ^-2

(9/8)^2

81/64

Changing this to a mixed number

1 17/64

8 0

3 years ago

1. Maryann is tracking the change in her vertical jump over 6 months. Use the table to write a linear function that models her j

ArbitrLikvidat [17]

Answer:

Part 1) Option A. f of x equals one half times x plus 16

Part 2) Option A. x = 5

Part 3) Option C. x − 4y = −9

Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.

Step-by-step explanation:

Part 1)

Let

x -----> the number of months

y ----> vertical jump in inches

step 1

Find the slope

we have the points

(0,16) and (2,17)

$m=(17-16)/(2-0)=\frac{1}{2}$

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=\frac{1}{2}$

$b=16$ -----> the point (0,16) is the y-intercept

substitute

$y=\frac{1}{2}x+16$

convert to function notation

f(x)=y

$f(x)=\frac{1}{2}x+16$

Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?

step 1

Find the slope

we have the points

(5, 0) and (5, −2)

$m=(-2-0)/(5-5)=\frac{-2}{0}$

the slope is undefined

This is a vertical line (parallel to the y-axis)

therefore

The equation is

x=5

Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)

step 1

Find the slope

we have the points

(−1, 2) and (3, 1)

$m=(1-2)/(3+1)=-\frac{1}{4}$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-\frac{1}{4}$

$point\ (3, 1)$

substitute

$y-1=-\frac{1}{4}(x-5)$

Convert to standard form

Multiply by 4 both sides to remove the fraction

$4y-4=-(x-5)$

$4y-4=-x+5$

$x-4y=-4-5$

$x-4y=-9$

Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario

we know that

The independent variable is the variable whose change isn’t affected by any other variable (An example the age and time)

The dependent variable it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))

Let

x ----> the number of rides

y ----> the total cost in dollars

In this problem

The independent variable or input is the number of rides

The dependent variable or output is the total cost

5 0

3 years ago

Hurry Please). The function f (x) models the value of goods that are imported into the United states, where x is the number of y

nata0808 [166]

Answer:

Answer 1: 15

Answer 2: 11.55

Answer 3: 1985

Step-by-step explanation:

your welcome (*_*)

8 0

3 years ago

4) Which number would divide the numerator and the denominator of the first

pav-90 [236]

Answer:

2/2

Step-by-step explanation:

I think so, because 14/2 = 7 and 18/2 = 9

6 0

2 years ago