Use the graph of f(x) to evaluate the following:

The average rate of change of f from x=0 to x=4 is_____.

Give your answer as an integer or reduced fraction

Answer:

[tex]\large\boxed{(x+y)^2:(x-y)^2=49}[/tex]

Step-by-step explanation:

[tex]3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=\dfrac{y}{3}\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=\dfrac{7y}{3}\qquad(**)\\------------------[/tex]

[tex](x+y)^2:(x-y)^2=\dfrac{(x+y)^2}{(x-y)^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x+y}{x-y}\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(\dfrac{\frac{7y}{3}}{\frac{y}{3}}\right)^2=\left(\dfrac{7y}{3}\cdot\dfrac{3}{y}\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49[/tex]

Answer:

  84 years

Step-by-step explanation:

The future value of an investment is given by ...

  FV = P(1 +r/n)^(nt)

where P is the principal amount, r is the annual rate, and n is the number of times per year interest is compounded. Filling in the given values and solving for t, we get ...

  1000000 = 1334(1 +.08/4)^(4t)

  749.6252 ≈ 1.02^(4t) . . . . divide by 1334 and simplify

  log(749.6252) ≈ 4t·log(1.02) . . . . take logarithms

  t ≈ log(749.6252)/(4·log(1.02)) ≈ 83.57

It will take about 84 years for the account balance to reach $1,000,000.

A function that models the situation is f(x) = 2x + 8.

A graph of the length of Rip van Winkle's beard (in millimeters) as a function of time (in weeks) is shown in the picture below.

In Mathematics, the slope-intercept form of the equation of a straight line refers to the general equation of a linear function and it is represented by this mathematical equation;

y = mx + b

where:

Since Rip van Winkle's beard was 8 millimeters long when he fell asleep, and each passing week it grew 2 additional millimeters, we can logically deduce the following parameters;

slope, m = 2.

initial value or y-intercept, b = 8.

In this context, an equation for the function that relates the length of his beard (in millimeters) to time (in weeks) can be written as follows;

y = mx + b

f(x) = 2x + 8

Answer: [tex]\frac{41}{20}[/tex]

Step-by-step explanation:

The first step is to make the division of the fractions [tex]\frac{9}{16}[/tex] and

[tex]\frac{1}{4}[/tex]. To do this, you can flip the fraction [tex]\frac{1}{4}[/tex] over and multiply the numerators and the denominators of the fractions. Then:

[tex](\frac{\frac{9}{16}}{\frac{1}{4}})-\frac{1}{5}=(\frac{9}{16}*4)-\frac{1}{5}=\frac{36}{16}-\frac{1}{5}[/tex]

Reduce the fraction [tex]\frac{36}{16}[/tex]:

 [tex]=\frac{9}{4}-\frac{1}{5}[/tex]

Now you can make the subtraction:  in this case the Least Common Denominator (LCD) will be the multiplication of the denominators.   Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then subtract the products. Therefore you get:

[tex]=\frac{45-4}{20}=\frac{41}{20}[/tex]

Answer:

x=-19/2  y=-33/2

Step-by-step explanation:

x − y = 7

y = 3x + 12

Substituting the second equation into the first

x − (3x+12) = 7

Distribute the minus sign

x-3x-12 = 7

Combine like terms

-2x-12 =7

Add 12 to each sid

-2x-12+12 =7+12

-2x=19

Divide each side by -2

-2x/-2 = 19/-2

x = -19/2

Now we need to find y

y = 3x+12

y = 3(-19/2) +12

y = -57/2 +24/2

y = -33/2

Answer:

(-19/2, -33/2)

Step-by-step explanation:

Answer:

1934.2

Step-by-step explanation:

3.14*14=43.98 squared=1934.2

Answer:

615.75

Step-by-step explanation:

Use A = πr², letting r = 14, so that:  

A = π(14)²  

≈ 615.75 ft²

Rounding to the nearest hundredth would make the answer 618

Answer:

b. 7/16

Step-by-step explanation:

We can see in the figure that the total dimension parallel to C is 15/16.

The other half dimension with c is 1/2

We will get the dimension C by subtracting 1/2 from 15/16

So,

C = 15/16 - 1/2

= (15-8)/16

=7/16

So the dimension C is 7/16.

Hence option b is correct ..

Answer:

3.5 hours

Step-by-step explanation:

5 x 70 = 350

7 x 65 = 455

350 + 455 = 805

1050 - 805 = 245

245/ 70 = 3.5

They will take an additional 3.5 hours on the third day to reach their destination.

Explanation of the distance covered in the first two days and how much more time it will take on the third day to reach their destination.

The distance covered in the first two days can be calculated using the formula:

Distance = Speed x Time

Therefore, after the first two days, they have covered a total distance of 350 + 455 = 805 miles. They have 1050 - 805 = 245 miles left to travel.

On the third day, at an average speed of 70 mph, they will cover the remaining 245 miles. Therefore, the time it will take for them to reach their friends' home on the third day is:

Time = Distance / Speed = 245 miles / 70 mph = 3.5 hours

They will take an additional 3.5 hours on the third day to reach their destination.

Answer:

parallel

Step-by-step explanation:

If you have two lines and a transversal that form corresponding angles that are congruent. Then the alternate interior angles are congruent and the same-side interior (some people call these consecutive angles) are supplementary.

This has to deal with Parallel Lines Theorem or the Converse of Parallel Lines Theorem.

The lines would be parallel.

Two lines will be parallel.

When two lines are cut by a transversal then the angles formed relatively same position in their respective line at the intersection transversal and two lines are called corresponding angles.

What is converse of corresponding angles theorem?

Converse of corresponding angles theorem states that When two lines are cut by a transversal and the formed corresponding angles are congruent then the two lines will be parallel.

Here given that two lines and transversal are forming corresponding angles which are congruent. So by converse of corresponding angles theorem, the two lines will be parallel to each other.

Therefore two lines will be parallel.

Learn more about corresponding angle

here: https://brainly.com/question/2496440

#SPJ2

Answer:

b < 4.44

Step-by-step explanation:

This is an inequality.

The sign for 'less than' is '< '

Write 9b less than 40 in inequality form.

9b < 40 (Take 9 on the other side of the inequality and divide it by 40)

b < 40/9

b < 4.44

!!

Answer:

1400

Step-by-step explanation:

Nothing can be done further. If I saw the rest of the question, I would be capable of assisting you.

I am joyous to assist you.

Answer:

102 steps/1minute

In seconds it would be 102/60 which can be reduced to 17/10, or 1.7

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x+\dfrac{15}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\==================================[/tex]

[tex]\text{We have}\ y=-4x-1\to m_1=-4\\\\\text{Therefore}\ m_2=-\dfrac{1}{-4}=\dfrac{1}{4}.\\\\\text{The equation of a line perpendicular to}\ y=-4x-1:\\\\y=\dfrac{1}{4}x+b\\\\\text{Put the coordinates of the point (-2, 7) to the equation:}\\\\7=\dfrac{1}{4}(-2)+b\\\\7=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\7\dfrac{1}{2}=b\to b=7\dfrac{1}{2}=\dfrac{7\cdot2+1}{2}=\dfrac{15}{2}\\\\\text{Finally:}\\\\y=\dfrac{1}{4}x+\dfrac{15}{2}[/tex]

Answer:

B

Step-by-step explanation:

First we simplify the equation:

3y − 2x = k (5x − 4) + 6

3y − 2x = 5k x − 4k + 6

3y = (5k + 2) x − 4k + 6

y = (5k + 2)/3 x + (6 − 4k)/3

The line has a positive slope and negative y-intercept.  So:

(5k + 2)/3 > 0

(6 − 4k)/3 < 0

Solving for k in each:

k > -2/5

k > 3/2

k must be greater than -2/5 and 3/2.  Since 3/2 is already greater than -2/5, then k must be greater than 3/2.

If k > 3/2, then it's also true that k > 0.  So the answer is B.

Answer:

24 plushies

Step-by-step explanation:

1 pound = 6 toy plushies

6(4)=24

Answer:

58 m^2.

Step-by-step explanation:

The  area of one of the 5 triangles is:

1/2 * 5.8 * 4 = 11.6 m^2

So the area of the pentagon

= 5 + 11.6

= 58 m^2

Answer:

The area is 58 meters squared.

Step-by-step explanation:

Since the pentagon is conveniently split into 5 separate but equal triangles, we only need to find the area of 1 triangle to find the rest. The area of triangles, as I'm sure you know, is 1/2bh. Using this equation, we get (1/2)x4x5.8. This equals 11.6. This is the area of one of the triangles. There are 5 triangles, so we multiply the area of 1 triangle by 5. 11.6x5= 58 meters squared. Hope this helped. :)

Answer:

OPTION C

Step-by-step explanation:

We know that the toll road is 4 times faster than the side streets.

If 'x' represents the number of minutes she usually spend taking the side streets. The [tex]\frac{1}{4} x[/tex] represents the time she takes taking the toll road.

Also we need to create an equation to represent her total travel time, including wait time. Therefore, the equation is:

[tex]y = \frac{1}{4}x + 30[/tex]

Therefore, the correct solution is the OPTION C.

Answer:

c

Step-by-step explanation:

took the test but give the other guy brainliest he deserves it

EF = 12

KF = 6

LF = 7.8

LK = sqrt(7.8^2-6^2) = 4.98

IJ = LK

Answer with explanation:

→ΔELF ≅ Δ GHJ-------[Given]

→EF=GH----------[CPCT]

→GJ=FL-------[CPCT]

Let , O be the center of the circle.

→ EK=KF--------[Perpendicular from the center to the chord bisects the chord.]

→GI=IH------[Reason same as Above]

→→EK=GI, KF=HI

→→OJ=OL

→OK=KI

→OJ-OK=OL-KI

→LK=IJ

⇒→Δ LKF ≅ Δ JIG-------[SAS]

Now, In Δ LKF, By Pythagorean Theorem

 →(LF)²=(LK)²+(KF)²

→(7.8)²=(LK)²+(6)²

→60.84-36=(LK)²

→24.84=(LK)²

LK=4.98

→→LK=IJ=4.98

Option C:→4.98

Answer:

-28

Step-by-step explanation:

-5(3)^2 - 3 + 20

-5*9 - 3 + 20

-45 -3+ 20

-48+ 20

-28

Hope it helps!

Answer:

m = ±6

Step-by-step explanation:

m^2 -36 =0

Add 36 to each side

m^2-36 +36 = 0+36

m^2 = 36

Take the square root of each side

sqrt(m^2) = ±sqrt(36)

m = ±6

Answer:+6 or -6

Step-by-step explanation:m^2 - 6^2

it becomes difference of two squares,

(m+6) (m-6)=0

m-6=0,m=6

m+6=0,m=-6

Answer:

Option C step 3

Step-by-step explanation:

we have

-14x-2y=24 ------> equation A

14x+8y=-12 -----> equation B

step 1

Solve the system by elimination

Adds equation A and equation B

-14x-2y=24

14x+8y=-12

---------------------

-2y+8y=24-12

6y=12

The step 1 is correct

step 2

Solve for y

Divide by 6 both sides

6y/6=12/6

y=2

The step 2 is correct

step 3

Find the value of x

substitute the value of y in the equation A

-14x-2(2)=24

-14x-4=24

14x=-4-24

14x=-28

x=-2

The step 3 is not correct

therefore

Petro first make a mistake in Step 3

Answer:

Step 3 in the correct answer. Thx. Just to verify with everyone it is step 3.

Step-by-step explanation:

On Edge 2020 got it correct.

Answer:

The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi

Step-by-step explanation:

Given

18.60=2.60b+3

Here 18.60 is the total amount paid, 2.60 is the rate per mile and 3 is the charges for two passengers.

The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi i.e. b represents miles ..

the answer is: the solution b = 6 gives the number of miles the taxi traveled.

i just did the workbook :)

Answer:

Here, the given function,

[tex]f(x) = -x^3 + 3x^2 + x - 3[/tex]

Since, the leading coefficient is negative, and degree is odd,

Thus, the end behaviour of the function is,

[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty[/tex]

[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow \infty[/tex]

Therefore, the graph rises to the left and falls to the right.

Now, when f(x) = 0

[tex]-x^3+3x^2+x-3=0[/tex]

[tex]\implies -(x-3)(x-1)(x+1)=0[/tex]

[tex]\implies x=3, 1, -1[/tex]

That is, graph intercepts the x-axis at (3, 0), (1, 0) and (-1, 0).

When x = 0,

[tex]f(x) = - 3[/tex]

That is, graph intersects the y-axis at ( 0, -3),

Also, for 0 > x > -1 , f(x) is decreasing,

For 2.55 > x > 0, f(x) is increasing,

For 3 > x > 2.55, f(x) is decreasing,

Hence, by the above explanation we can plot the graph of the function ( shown below )

Answer:w

Step-by-step explanation: it should be w i got it on plato

Answer:

[tex]\large\boxed{A:B:C=\dfrac{1}{10A}}[/tex]

Step-by-step explanation:

[tex]A=\dfrac{B}{2}=\dfrac{C}{5}\\\\A=\dfrac{B}{2}\qquad\text{multiply both sides by 2}\\\\2A=B\to\boxed{B=2A}\\\\A=\dfrac{C}{5}\qquad\text{multiply both sides by 5}\\\\5A=C\to C=5A\\\\A:B:C=A:2A:5A=1:2:5A=\dfrac{1}{2}:5A=\dfrac{1}{2}\cdot\dfrac{1}{5A}=\dfrac{1}{10A}[/tex]

Answer:

C. -2x-4

Step-by-step explanation:

-3 - 3x – 1 + x

Combine like terms

-3 -1     -3x +x

-4 -2x

Rearrange the order to put the x term first

-2x-4

c

just got it right on edge

Answer:

1275 USD

Step-by-step explanation:

124.40 Rs -----> 1 USD

158610 Rs -----> x USD

124.40x=158610

×=158610/124.40

x=1275 USD

Answer:

No, that is not the true proportion.

Step-by-step explanation:

40 divided by 8 is 5. 5 multiplied by 4 is 20. Therefore, the true proportion would be 20/40 = 4/8.

Step-by-step explanation:

The formula of a volume of a pyramid:

[tex]V=\dfrac{1}{3}BH[/tex]

B - base area

H - height

H - height of pyramids

Pyramid A:

[tex]B=(10)(2)=200\ m^2[/tex]

[tex]V_A=\dfrac{1}{3}(200)H=\dfrac{200}{3}H\ m^3[/tex]

Pyramid B:

[tex]B=10^2=100\ m^2[/tex]

[tex]V_B=\dfraC{1}{3}(100)H=\dfrac{100}{3}H\ m^3[/tex]

[tex]V_A>V_B\\\\V_A=2V_B[/tex]

The volume of the pyramid A is twice as large as the volume of the pyramid B.

The new height of pyramid B: 2H

The new volume:

[tex]V_{B'}=\dfrac{1}{3}(100)(2H)=\dfrac{200}{3}H\ m^3[/tex]

The volume of the pyramid A is equal to the volume of the pyramid B.

To compare the volumes of the two pyramids, we first need to calculate the volume of each pyramid using the formula for the volume of a pyramid:
\[ V = \frac{1}{3}Bh \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
First, let's calculate the volume of pyramid A:
\[ \text{Area of base of pyramid A} = \text{length} \times \text{width} = 10 \, \text{meters} \times 20 \, \text{meters} = 200 \, \text{square meters} \]
Now, let's call the height of pyramid A (and originally pyramid B) \( h \). Then, the volume of pyramid A is:
\[ V_{\text{A}} = \frac{1}{3} \times 200 \, \text{m}^2 \times h = \frac{200h}{3} \, \text{cubic meters} \]
Next, let's calculate the volume of pyramid B with its original height \( h \):
\[ \text{Area of base of pyramid B} = \text{side} \times \text{side} = 10 \, \text{meters} \times 10 \, \text{meters} = 100 \, \text{square meters} \]
So the original volume of pyramid B is:
\[ V_{\text{B}} = \frac{1}{3} \times 100 \, \text{m}^2 \times h = \frac{100h}{3} \, \text{cubic meters} \]
Now we can compare the volumes of pyramid A and the original volume of pyramid B:
\[ \frac{V_{\text{A}}}{V_{\text{B}}} = \frac{\frac{200h}{3}}{\frac{100h}{3}} = \frac{200}{100} = 2 \]
So, pyramid A has twice the volume of pyramid B.
Now, if the height of pyramid B increases to twice that of pyramid A, its new height is \( 2h \). Therefore, the new volume of pyramid B is:
\[ V_{\text{B new}} = \frac{1}{3} \times 100 \, \text{m}^2 \times 2h = \frac{200h}{3} \, \text{cubic meters} \]
Comparing this new volume of pyramid B to the volume of pyramid A:
\[ \frac{V_{\text{B new}}}{V_{\text{A}}} = \frac{\frac{200h}{3}}{\frac{200h}{3}} = 1 \]
So, the new volume of pyramid B is equal to the volume of pyramid A.
In summary, the volume of pyramid A is twice the volume of pyramid B when their heights are the same. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.

Answer:

y=5/3  or y=1.67

Step-by-step explanation:

In this problem we have  that

(5x+8)=21x ----> given problem

21x-5x=8

16x=8

x=0.5

In the same way

Remember that the slope of a line is a constant

so

20y-2=17y+3

Solve for y

20y-17y=3+2

3y=5

y=5/3  or y=1.67

Answer:

121,6

Step-by-step explanation:

Since the only difference between the triangles are the letters and a few missing numbers, just replace the letters to get your answer. A and D are the same B and E are the same and C and F are the same. So the measurement of angle A is 121 degrees and the length of AB is 6