Finding the Slope of a Line from a Table What is the slope of the linear function represented in the table?
-7
-1/7
1/7
7​

Answer:

Correct option: F.

Step-by-step explanation:

The slope of a line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

To show the slope of PR is equal to the slope of RT, we'll use the extreme points of each segment.

For PR, use P=(-7,7) R=(-4,3). Now calculate the slope

[tex]\displaystyle m=\frac{3-7}{-4-(-7)}[/tex]

For RT, use R=(-4,3) (2,-5). Calculate the second slope:

[tex]\displaystyle m=\frac{-5-3}{2-(-4)}[/tex]

If both slopes are equal, then:

[tex]\displaystyle m=\frac{3-7}{-4-(-7)}=\frac{-5-3}{2-(-4)}[/tex]

Correct option: F.

Answer:

The answer is below

Step-by-step explanation:

The height of tank = 12 m = 1200 cm, the diameter of the tank = 8 meters, hence the radius of the tank = 8/2 = 4 m = 400 cm

Let h represent the water level = 8 m = 800 cm. The radius (r) of the water level at a height of 8 m is:

r/h = radius of tank/ height of tank

r/h = 400/1200

r = h/3

[tex]\frac{change\ in\ volume}{change\ in \ time}=water\ in-water\ out\\ \\\frac{dV}{dt=} water\ in-water\ out\\\\V=\frac{1}{3}\pi r^2h\\ \\r=\frac{1}{3}h \\\\V=\frac{1}{3}\pi (\frac{1}{3}h )^2h\\\\V=\frac{1}{9} \pi h^3\\\\\frac{dV}{dt} =\frac{1}{3} \pi h^2\frac{dh}{dt}\\\\\frac{dh}{dt}=2\ cm/min,h=8\ m=800\ cm\\\\[/tex]

[tex]\frac{dV}{dt} =\frac{1}{3} \pi (800)^2(2)=426666.7\ cm^3/min\\\\\frac{dV}{dt=} water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-20000\ cm/min\\ \\water\ in=426666.7\ cm^3/min+20000\ cm/min\\\\water\ in=446666.7 \ cm^3/min[/tex]

Answer:$15 = 100 x rate x (2/52)

The 2/52 represents 2 weeks out of 52 weeks in a year

So 15/100 = rate x (2/52)

.15 = rate x (2/52)

If you divide by (2/52) on both sides, you get: 3.9 = rate

Don't be fooled by this answer, because it is not in percent form. In order to get it into percent form you need to multiply by 100. So the percent of interest paid on the loan is 390%.

In a lot of these problems you can predict around the percentage before you even do the problem. In this problem, you can tell that the percentage is going to be high because the loan has accrued $15 interest in just two weeks (15% in just two weeks!)

So if there is 15% interest in two weeks, you know it is going to be a very high annual percentage.

I am very confident that this is the answer, if you can check the answer with your online homework I would do so and send me a message to let me know. Also, if you need more clarification I am happy to message you more without a charge. Let me know!!$15 = 100 x rate x (2/52)

The 2/52 represents 2 weeks out of 52 weeks in a year

So 15/100 = rate x (2/52)

.15 = rate x (2/52)

If you divide by (2/52) on both sides, you get: 3.9 = rate

Don't be fooled by this answer, because it is not in percent form. In order to get it into percent form you need to multiply by 100. So the percent of interest paid on the loan is 390%.

In a lot of these problems you can predict around the percentage before you even do the problem. In this problem, you can tell that the percentage is going to be high because the loan has accrued $15 interest in just two weeks (15% in just two weeks!)

So if there is 15% interest in two weeks, you know it is going to be a very high annual percentage.

I am very confident that this is the answer, if you can check the answer with your online homework I would do so and send me a message to let me know. Also, if you need more clarification I am happy to message you more without a charge. Let me know!!

Step-by-step explanation:

Answer:

In step by step explanation

Step-by-step explanation:

a) Normal distribution N( 0, 1 )

If the sample size is equal n = 16 we have to use t-student distribution since     n < 30.

In the case n = 36 we should use normal distribution (z tables)

b) We can´t use the  standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 in the first case n < 30 .

We can calculate that  probability in the case of the second sample

Answer: She must wash at least 13 cars

Therefore, Grace must wash at least 13 cars in order to have $65 in spending money

Answer:

The equation in standard form:

2x-y-10=0

9514 1404 393

Answer:

  $20,020

Step-by-step explanation:

The future value formula is helpful.

  FV = P(1 +r)^t

  $80,000 = P(1.08^18) = 3.9960195P

  P = $80,000/3.9960195 = $20,019.92

They should invest about $20,020 now.

Step-by-step explanation:

Given that the first number is

5,555 and

the second number is 4,444

the product of 5,555 and4,444= 24686420

to the nearest thousand 5,555= 6000

to the nearest thousand 4,444= 5000

Therefore the product of 6000 and 5000 is

=6000x5000

=30000000

Answer:

D

Step-by-step explanation:

Here, we want to state if it is unusual or not get a sandwich in 12 minutes given the mean time and the standard deviation.

The answer here is that it is unusual.

The reason why it is unusual is because, two standard deviations above the mean in this case will be 5 + 3 + 3 = 11

Looking at the value given which is 12, we can see that this value is actually greater than the value which is 2 standard deviations above the mean.

What we are saying here is that 12 is greater than two standard deviation above the mean which is valued at 11

Answer: 5 because it has 5 space left

Answer:

5

Step-by-step explanation:

i did this on i-ready and got it right Good luck!

Answer: 16 - C

Step-by-step explanation:

So basicly, what it is asking is to solve this problem. I would like to call it a puzzle because there is a missing part that we have to find. Let's get this started!

Here is the equaiton: 2 x (8 - C)

First, we will multiply 8 by 2.

8 x 2 = 16

Now the equation is: 16 - C

We don't know what C is, so this equation is as done as we can do it.

Answer:

195 tickets

Step-by-step explanation:

If the dance teacher spent the whole budget, then that means you can just divide the budget by the cost of tickets:

5,460 / 28, which is 195 tickets.

Answer: x = 13/2

Step-by-step explanation:

Distribute: 4(x - 2) = 18

4x - 8 = 18

Add 8 to both sides

4x - 8 + 8 = 18 + 8

Simplify:

4x = 26

Divide both sides of the equation by the same term

4x = 26

4x/4 and 26/4

Cancel term that are both in the numerator and denominator

Divide the numbers

X = 13/2

Answer:

Step-by-step explanation:

(A) The population is the 2,668 people who were tracked from early childhood to adulthood.

(B) The sample comprised all 13-year olds within the population. Since the members of the population started out as kids (and later became adults), the sample was inclusive of all 2,668 individuals but only at the age of 13. That is where the focus was; at the age of 13.

The study then proceeded to divide them into two groups - the experimental group (13 year olds who were frequent targets of bullies) and the non-experimental group (13 year olds who were not frequent targets of bullies).

(C) The variables in this study are:

- 13 year olds who were frequent targets of bullies

- 13 year olds who were not frequent targets of bullies

- Adults (from the same population who were once 13 year olds) with depression

- Adults (from the same population who were once 13 year olds) without depression.

NOTE HOWEVER that the degree of bullying each teenager faced and the magnitude of depression each adult faced, can be gotten from the above variables; when they assume a figure or number which can be high, low or medium.

Answer: From R:(c, d), draw line segment RA perpendicular to the x-axis. Let O denote the origin (0,0).

area ΔPQR = area trapezoid OPRA- area ΔQAR - area ΔOPQ

=

2

1

c(a+d) -

2

1

d(c−b)-

2

1

ab=

2

1

(ac+bd−ab).

If c area ΔPQR = area trapezoid OPRA + area Δ QAR - areaΔOPQ=

2

1

c(a+d)

2

1

d(b−c)−

2

1

ab=

2

1

(ac+bd−ab).

Step-by-step explanation: done

Answer:

24,840,000

Step-by-step explanation:

Round up of numbers includes rounding them up to a given place value.

We are asked to round 24,837,618 to the ten thousands place.

The ten thousands place is the place where the number 3 in the number is located.

The number after 3 = 7 is a number above 5. Hence, we add 1 to 3, making it 4

Therefore, 24,837,618 to the ten thousands place is 24,840,000

Answer:

32

Step-by-step explanation:

Answer:

The correct option will be:   c.  8 pieces of wood.Step-by-step

Answer: 43 should be divided into 0.37 to find “x”.

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

I got it right

Answer:

b

Step-by-step explanation:

Answer:

That would take you 7 hours to get to your location.

Answer:

-42.75 meters

Step-by-step explanation:

Answer:

Joe scored higher by 1600

Step-by-step explanation:

Given

[tex]Simon = 4 * 10^2[/tex]

[tex]Joe = 2 * 10^3[/tex]

Solving (a): Which is higher?

First, we need to convert both numbers to whole numbers

[tex]Simon = 4 * 100[/tex]

[tex]Simon = 400[/tex]

[tex]Joe = 2 * 10^3[/tex]

[tex]Joe = 2 * 1000[/tex]

[tex]Joe = 2000[/tex]

2000 is greater than 400;

Hence, Joe score higher

Solving (b): By how much?

We simply calculate the difference

[tex]Difference = Joe - Simon[/tex]

[tex]Difference = 2000 - 400[/tex]

[tex]Difference = 1600[/tex]

Answer:

A = a^2.....the Area (A) of a square = a^2...where a = one side

79 = a^2...now take the sqrt of both sides, this eliminates the ^2

sqrt 79 = a

8.888 rounded = 8.89 = a......so one side = 8.89 ft

Step-by-step explanation:

Answer:

16-22

Step-by-step explanation:

Answer:

i agree with the other person

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

Using GCF:

The factors of 24 are; 1, 2, 3, 4, 6, 8, 12, 24

Factors of 28 are; 1, 2, 4, 7, 14, 28

The highest greatest common factor is 4.

Now, 4 × 6 gives 24

While 4 × 7 gives 28.

Thus, our original equation is now;

4(6 + 7)

Using distributive property, let's add the number in the bracket first to get;

4(13).

Now,we multiply out to get 52.

Answer:4(7+6)

Step-by-step explanation: i passed the quiz with an 100%

Answer:

[tex]y=-2^{(x+2)}+1[/tex]

Step-by-step explanation:

Equation of the parent function of the graph attached is,

y = [tex]2^{x}[/tex]

Let the equation of the transformed function function shown in the graph be,

y = a(2ˣ) + b

Now we will find the values of a and b by substituting the points lying on the curve.

For (-2, 0),

0 = a(2⁻²) + b

[tex]\frac{a}{4}+b=0[/tex] ------(1)

For (0, -3),

-3 = a(2⁰) + b

a + b = -3 --------(2)

Subtract equation (1) from equation (2),

(a + b) - ([tex]\frac{a}{4}+b[/tex]) = 0 + 3

[tex]\frac{3a}{4}=3[/tex]

a = -4

From equation (2),

-4 + b = -3

b = 1

Therefore, equation of the transformed function will be,

[tex]y=-4(2^x)+1[/tex]

[tex]y=-2^{2}(2^x)+1[/tex]

[tex]y=-2^{(x+2)}+1[/tex]

Graph transformation is the process by which an existing graph is modified to produce a variation of the proceeding graph.

Equation of transformed graph is, [tex]y=-2^{x+2}+1[/tex]

Here,  equation of original graph is given, [tex]y=2^{x}[/tex]

Let us consider, equation of transformed graph is,  [tex]y=m(2^{x} )+n[/tex]

Since, given graph passing through points (-2,0) and (0,-3)

Substituting above points into equation.

We get two equation,

                                      m +4n = 0

                                     m + n = -3

After solving, we get   m= -4 and  n = 1

So, equation becomes  [tex]y=-2^{x+2}+1[/tex]

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