Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days.
After day 1, Lin reaches page 70, which matches the point (1,70) She made it on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) She made it on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.

Sketch a line showing Lin's original plan on the axes.Click on the graph and select edit to complete the graph. Once done, hit save and close to see your completed graph.
What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?


What does the slope mean in this situation? How do the slopes of the two lines compare?

1) vertical angles theorem

2) transitive property of congruence

Answer:

your picture is blank if you can fix it i will be glad to help you

Step-by-step explanation:

Answer:

First option

Step-by-step explanation:

The line corresponds to the f(x).

Hope this helps

Answer:

x= 10 y=14 : 10 3 point, 14 5 point

Step-by-step explanation:

Write your equation down vertically,

3x + 5y = 100

 x + y   =  24

Next find multiply bottom equation by one number from the tops opposite,

3x + 5y = 100

(-3)x +(-3)y = (-3)24

3x + 5y = 100

-3x - 3y= -72

Add the two functions to isolate y

2y= 28 y=14

Plug y back into original and solve

3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 x=10

The simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.

1) 4 2/7 - 2 1/3

First we convert the mixed fraction 4 2/7 and 2 1/3 into an improper fraction.

4 2/7 = (7×4 + 2 )/7 = 30/7

2 1/3 = (3×2 + 1 )/3 = 7/3

Hence,

30/7 - 7/3

( 30×3 - 7×7  )/21

( 90 - 49  )/21

41/21

2) 4.5 - 2 5/8

First we convert both 4.5 and 2 5/8 into an improper fraction.

4.5 = 4 5/10 = (4×10 + 5)/10 = 45/10 = 9/2

2 5/8 = (2×8 + 5 )/8 = 21/8

Hence,

9/2 - 21/8

(9×8 - 21×2  )/16

(72 - 42  )/16

30/16

15/8

3) 5 2/8 - 15%

First we convert both 5 2/8 and 15% into an improper and proper fraction respectively.

5 2/8 = (5×8 + 2)/8 = 42/8 = 21/4

15% = 15/100 = 3/20

Hence

21/4 - 3/20

(21×20 - 3×4  )/80

(420 - 12  )/80

408/80

51/10

Therefore, the simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.

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Answer: x=5.6 or 5 3/5

Step-by-step explanation:

Cross multiplication is when you have two fractions (ratios) that are equivalent and you can multiply the numerator of the first one by the denominator of the second one, and the denominator of the first one by the numerator of the first one. The answers to these two are equivalent.

So, 5x/8 = 7/2

10x=56

x=5.6

x= 5 3/5

Answer:

{x  = -1 + √13  ,  x  = -1 - √13}

Step-by-step explanation:

Completing the square:

f(x) = x² + 2x - 12

     = x² + 2x + 1 - 1 - 12

     = (x² + 2x + 1) - 1 - 12

     = (x + 1)² - 13

Solving:

f(x) = 0

⇔ (x + 1)² - 13 = 0

⇔ (x + 1)² = 13

⇔ x + 1 = √13  or  x + 1 = -√13

⇔ x  = -1 + √13  or  x  = -1 - √13

Answer:

$142.5

Step-by-step explanation:

225-60=165

165/2=82.5

82.5+60=142.5

Quarts of detergent 1208

First, we convert each unit to its pint equivalent.

1 gallon =eight US Pint

114 gallons =114 X eight =912 Pint

34 gallon =34 X 8 =272 Pint

further, 1 quart =2 Pint

12 quart = 12 X 2 Pint =24 Pint

including the three values

912+272+24=1208 Pint

therefore, Meredith will want 1,208 Pint boxes.

The unitary technique is a way of solving trouble by way of first finding the fee of a single unit, and then finding the essential value with the aid of multiplying the unmarried unit price.

The system of the unitary technique is to locate the fee of an unmarried unit after which multiply the fee of a single unit to a wide variety of devices to get the vital fee.

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Answer:

x- axis , quadrant 2 , quadrant 3

Step-by-step explanation:

(9.5, 0 ) ← is located on the x- axis

(- 4, 7 ) ← is located in Quadrant II

(- 1, - 8 ) ← is located in Quadrant III

Answer:

C is correct

Step-by-step explanation:

I'm not sure what the substituting part has to do anything, but here is how I got the answer

4(x+x+7)-2x+8-4

4(2x+7)-2x+4

8x+28-2x+4

6x+32

Factor and you get

2(3x+16), which is answer choice C

You can check that the answer is right by plugging in x=1 and x=2 into the original equation and the answer choice, which may be what that is asking.

The derivative and domain of the function f(x) = x²-2x³  is :[tex](-\infty, \infty)[/tex].

The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.

Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.

Calculation for the derivative:

Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).

[tex]\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}[/tex]

       [tex]\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}[/tex]

       [tex]=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}[/tex]

Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.

      [tex]\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}[/tex]

f and f' are polynomials, so their domains are all real numbers.

Therefore,  for f(x) = x²-2x³      domain of f and f' :[tex](-\infty, \infty)[/tex].

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The complete question is -

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.

Answer: y=-(1)/(3)x-3

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It can be proved that Circles X and Y are similar.

We were told that circle Y have a  radius of s

And X have the  Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y  by making a division on the  radii of both circles.

Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are similar

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Answer: A

Step-by-step explanation:

[tex]P(x) Q(x)=R(x)\\\\(x+1)Q(x)=2x^3 + 2x^2 - 3x-3\\\\Q(x)=\frac{2x^3 + 2x^2 - 3x-3}{x+1}\\\\Q(x)=\frac{2x^2 (x+1)-3(x+1)}{x+1}\\\\Q(x)=2x^2 - 3[/tex]

These districts are best characterized as Proportional Representation districts.

What is Proportional Representation?

There are numerous types of proportional representation systems, but they all have two things in common. They start by using districts with multiple members.

Proportional Representation, abbreviated as PR, uses significantly bigger districts that elect multiple members at once, such as five or ten, rather than electing one member of the legislature in each local district. Second, the percentage of votes a party receives in these districts with several members determines which candidates gain the seats.

The Proportional Representation system of America overcomes the wide ranging drawbacks of single-district voting system like not representing the  large number of voters, discrimination against third parties, etc.

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The distance between the bottom of the lighthouse and the boat is 77.6m.

The lighthouse and the boat would form a right triangle. The height would be the height of the lighthouse. The  distance between the top of the lighthouse and boat would be the hypotenuse. The  distance between the bottom of the lighthouse and the boat would be the base.

In order to determine the required distance, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

125²  = 98²  + b²

b² = 125²  - 98²

b = √(25²  - 98² )

b = 77.6m

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USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].

To find how many dollars would each receive:

Avogadro's number of pennies is divided equally among 261 million people.

Avogadro's number is [tex]6.022[/tex] × [tex]10^{23}[/tex].

To find the number of pennies each person will receive, we divide [tex]6.022[/tex] × [tex]10^{23}[/tex] by 261 million.

Pennies per person = [tex]\frac{6.022 * 10^{23} }{261 million} = \frac{6.022 * 10^{23} }{261 * 10^{6} } = 2.31 * 10^{15}[/tex]

This is equal to the number of cents each person receives.

To convert pennies into dollars, 1 USD = 100 pennies, divide [tex]2.31 * 10^{15}[/tex] by [tex]100[/tex].

USD per person = [tex]\frac{2.31 * 10^{15} }{100} = $2.31 * 10^{13}[/tex]

Therefore, USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].

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The question you are looking for is here:

If Avogadro's number of pennies is divided equally among the 261 million men, women, and children in the United States, how many dollars would each receive?

Answer:

The 3rd answer down

Step-by-step explanation:

If I broke apart the initial answer, I would see that x is equal to or greater than 8 and x is less than 9.5

There are 430 non square numbers that lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].

Given two numbers [tex]215^{2}[/tex] and [tex]216^{2}[/tex] and we are require to find non square numbers that lie between them.

Numbers can be consecutive numbers or non consecutive numbers. In our question we will find the consecutive numbers.

Square numbers are those numbers whos square is in a proper number means decimal should not be there.

First number=[tex]215^{2}[/tex]

Second number=[tex]216^{2}[/tex]

First we have to find the exact value of numbers by finding the square of these numbers.

First number=215*215=46225

Second number=216*216=46656

Numbers that  lie between them=(46656-46225)-1

=431-1

=430

Hence 430 numbers lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].

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The interval in which 99.7% of the sample means fall within 3 standard deviations of the mean is 19,306 to 21,694.

According to the central limit theorem,

Sample mean = Population mean = μ

Sample standard deviation = (Population standard deviation)/√n = σ/√n

where n is at least 30.

It is given that,

The overall population mean = 20,500

Population standard deviation σ = 2180

Sample size n = 30

Since n = 30, the central limit theorem can be applied.

According to the Empirical rule(68-95-99), 99.7% of the sample means fall within the 3 standard deviations of the mean.

So, the interval is calculated by

Sample mean = Population mean = μ = 20500

Standard deviation(sample) = σ/√n

⇒ S = 2180/√30 =398.011 ≅ 398

Thus,

The lower bound  = 20500 - 3 × 398 = 19,306

The upper bound = 20500 + 3 × 398 = 21,694

Therefore, the required interval is from 19,306 to 21,694.

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The citizens of a state may only register to vote after proving to have submitted their census survey is a "false" statement.

In order to create statistics that define populations and their characteristics, such as age, education, housing, and income, the U.S. Census Bureau compiles data from households.

The purpose of census survey are-

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The complete question is-

The citizens of a state may only register to vote after proving to have submitted their census survey.(True/False)

By the definition of inverse functions, we will get:

[tex]arcsin(-1) = -pi/2[/tex]

The function arcsin(x) is the inverse of the sine function, such that, if:

[tex]sin(x) = y\\\\arcsin(y) = x[/tex]

Now, we know that:

[tex]sin( -pi/2) = -1[/tex]

Where pi = 3.14

Then, using the above rule:

[tex]arcsin(-1) = -pi/2[/tex]

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Answer:

our answer is X=2 or X= -1

Answer: C. {-1,2}
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If two cans hold 750ml ,then their voLume is 0.3 liters less than 1.8 liters.

Given volume of two cans being 750 ml each.

We are required to calculate the quantity in liters of how much the volume of two cans less than 1.8 liters.

Volume is the quantity of substance a container can hold in its capacity.

So volume of cone means quantity of liquid cone can hold if fully filled.

Volume of first cone=750 ml

Volume of second cone=750 ml

Total volume=750+750

=1500 ml

1 liter= 1000 ml

so 1500 ml will be equal to 1500/1000

=1.5 liter

We are required to do comparison with 1.8 liters.

Difference =1.8-1.5

=0.3 liters.

Hence two cans have 0.3 liters less than 1.8 liters.

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Answer:

answer is 121/9

Step-by-step explanation:

13.4444444444 (decimal form)

121/9 (improper fraction form)

13 4/9 (mixed fraction form)

To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use z-test procedure.

What is a Z-test?

A statistical method of testing a hypothesis is the z-test where either:

Additional prerequisites for using the z-test include the following:

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Answer:

Option B: 3

Step-by-step explanation:

#1: Substitute in 6 for [tex]y[/tex] and 3 for [tex]x[/tex]: [tex]13=(3)(6)-5[/tex]

#2: Multiply 3 and 6: [tex]13=18-5[/tex]

#3: Evaluate the equation: [tex]13=18-5[/tex] → [tex]13=13[/tex]

#4: Check if the solution is equal: [tex]13=13[/tex] ✓

[tex]x[/tex] is equal to 3 (Option B).