Jacob spent 24% of his allowance last week. What fraction of his allowance did Jacob spend? Write the answer in simplest form.

Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

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Answer:

A) (x-4)(x+16)

Step-by-step explanation:

\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

Answer:

5 units is the answer.

Step-by-step explanation:

\(d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(8-8)^2 + (9-4)^2}\\\\d=\sqrt{(0\\)^2+(5)^2} \\\\d=\sqrt{25} \\\\d=5 \\\\\)

∴ d = 5 units

Explanation:

x is the number of years since 1988

x = 0 represents the year 1988

x = 1 is the year 1988+1 = 1989

x = 2 is the year 1988+2 = 1990

etc

x = 32 is the year 1988+32 = 2020

Answer: 65 degrees

( Im probally wrong and how is this college math?????)

Step-by-step explanation:

Answer:

12 multiple choice and 8 True/False

Step-by-step explanation:

To do this we set up a system of equations. Let x represent the True/Fale questions and y represent the multiple-choice questions. Here is a system we can use:

x + y = 20

2x + 7y = 100

We can solve this by using elimination. To do this we multiply one equation by a number, and add them together. If we multiply the first equation by -2, the "x"s will, when added together, cancel out so we can solve for y.

-2(x + y = 20)

-2x - 2y = -40

Now add them together

5y = 60

Solve for y.

y = 12

This means there are 12 multiple choice questions. 20 - 12 is 8 True/False questions.

Hope this helps and have a great day! :D

Answer:

8 True/False and 12 Multiple Choice

Step-by-step explanation:

x+y=20  ...1

2x+7y=100   ...2

Now you can multiply 2 on 1

2x+2y=40

2x+7y=100

Subtract:

-5y=-60

Divide -5 on both sides:

y=12

Substitute y with 12

x+12=20

Subtract 12 on both sides:

x=8

So there are 8 True/False and 12 Multiple Choice

Hope this Helps!

Answer helped by: azailiaskoglund

Answer:

C

Step-by-step explanation:

Answer:

5/18, 13/18

Step-by-step explanation:

The basic probability of anything is Specific Outcome / Total Outcomes

The specific outcome here is pulling a purple marble. We see there are 5 purple marbles therefore there are 5 ways to get them. The total outcomes are the total number of marbles which is 18. Therefore, the answer is 5/18

The complement of a probability is 1 minus the original probability, so, it would be 1 - 5/18 here getting us 13/18 as the answer.

Answer:

96.

Step-by-step explanation:

Divide the silver beads by 85=96

Then divide the black beads by 30=96.

Total necklaces that can be made: 96

Answer: f(0)=3/2, f(4)=7/2

Answer:

b and e

Step-by-step explanation:

Answer:

A. mBC = 71

B. mAB = 142

C. AD = 30

D. BD = 30

E. YD = 16

F. DC = 18

Step-by-step explanation:

A. mBC = mAC = 71

B. mAB = mBC + mAC = 71 + 71 = 142

C. AD = AB/2 = 60/2 = 30

D. BD = AD = 30

E. YA^2 = YD^2 + AD^2

YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256

YD = √256 = 16

F. DC + YD = YC

DC = YC - YD = 34 - 16 = 18

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

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Darlene is extruding a polygon of five sides. The end result will be a pentagonal prism.

Extrusion represents a 3D modeling technique that involves extending a two-dimensional shape into a three-dimensional object by pulling it along a given path. In this particular case, Darlene is applying extrusion to a polygon comprising of five sides, thereby stretching out the two-dimensional figure along a trajectory to yield a novel 3D construct.

It is worthy of mention that the structure obtained following the process solely depends on the pathway employed by Darlene in carrying out the extrusion procedure. Should she choose a direct line, the resulting creation will be a prism having five sides i.e. pentagonal prism.

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The graph that would best show the data collected from measuring the volume of a balloon at varying temperatures is a scatter plot graph.

The frequency table is used to show how often a certain result is given. For example, if we roll a dice 100 times we can use this table to display how often each number came up, which can look like:

10 times

30 times

25 times

20 times

5 times

10 times

A bar graph is often used to compare groups or track changes over time. For example, we can measure how many cars pass by certain points in an hour and use a bar graph to display how many cars passed by each place during that hour by representing each place with its own bar, whose height will tell us the number of cars. This would not be the graph we use because we are comparing changes in a single balloon, not in groups of balloons.

The first option is a circle graph, which is used when one thing contains varying percentages within it. The circle graph can display how much of the total is comprised by each sub-division. This is not the kind of graph we are looking to use because it would be incapable of displaying varying values for the same variable.

The graph that would best show the data collected from measuring the volume of a balloon at varying temperatures is a scatter plot graph because this kind of graph can represent two different variables and is used to compare the relationship between them, in this case, the volume of the balloon and the temperature.

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complete question:

Which type of graph would best show the data collected from measuring the volume of a balloon at varying temperatures?

circle graph

frequency table

bar graph

scatter plot

5. 6. 11. 17. 28. 45 . 73

5 &6 are given,

Then,

5+6=11

6+11=17

11+17=28

17+28=45

So,

28+45=73

Answer:

73

Step-by-step explanation:

We are adding the two numbers before

5+6 = 11

6+11 = 17

11+17 = 28

17+28 = 45

28+45 =73

To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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Answer:

(3, -2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

3y = -2x

y = x - 5

Step 2: Solve for x

Substitution

Step 3: Solve for y

Answer:

y = -2

x = 3

Step-by-step explanation:

First plug in the y= x-5 equation into the 3y = -2x so that it looks like this:

3(x-5)=-2x

Second after distributing the 3 to the x and -5 you will have an equation that looks like this: 3x -15 = -2x

Then you have keep the x's on one side so you add 2x to both sides and add 15 as well so now you have: 5x = 15

Divide both sides by 5 and get x = 3

To find y, you plug x=3 in in to the y = x-5 and get that y = -2

Answer:

can you take a better pick

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Step-by-step explanation:

Given that the mean of the numbers is 12

\(mean = \frac{sum \: \: of \: observations}{total \: number \: of \: observations} \)

so here

let's that one as x and another one as 2x since it is given that one is twice the other

Therefore we get

\(mean = \frac{13 + x + 4 + 16 + 6 + 2x}{6} \)

Given mean = 12

\(12 = \frac{39 + 3x}{6} \)

\(72 = 39 + 3x\)

\(3x = 33\)

\(x = 11\)

Hence it's 11 and 22

Answer:

Step-by-step explanation:

¼ + ⅔ = 11/12

1 - 11/12 = 1/12

He has 1/12 of £264 = £22 left

Answer:

Step-by-step explanation:

Solution:

A four-digit number 4ab5 is divisible by 55. Then the value of b - a is 1.

Answer:

1) Classroom 2

2) Classroom 3

3) Classroom 2

4) Classroom 4

Answer: Multiply the length, the width, and the height.

You can multiply them in any order to get the same different result. The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W

Step-by-step explanation:

Answer:

Step-by-step explanation:

so first you need to find the slope

you can draw the line on a graph and use a protractor

final answer=46 degrees

Answer:-5/-19

the answer is -5/-19 and can not be simplify

The Future Value Annuity Factor (FVAF) is 11.6853 for an interest rate of 10 percentage and a number of periods of 10 years. It is determined by consulting a time value of money table..

Find the interest rate and the number of periods

Interest Rate = 10%

Number of Periods (T) = 10 years

Consult a time value of money table

Find T = 10 and 10 percent

Calculate the Future Value Annuity Factor (FVAF)

FVAF = 11.6853

The Future Value Annuity Factor (FVAF) is a mathematical formula used to determine the future value of a series of equal payments or receipts at a certain rate of return. To calculate the FVAF, first you need to find the interest rate and the number of periods, also known as 'T'. In this example, the interest rate is 10% and the number of periods is 10 years. Next, you need to consult a time value of money table to find the appropriate FVAF value. To do this, read down the rows to find T = 10 and across the columns to find 10 percent. The resulting FVAF value is 11.6853. This indicates that each period's payment or receipt will be worth 11.6853 times its present amount when it is received 10 years in the future.

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The complete question is

To find the future value annuity factor from a time value of money table, read down the rows to find T = 10 and across the columns to find 10 percent and number of periods.

Answer:

I'm certainly late, but it took me a while to figure this one out so I want to leave an answer.

A=-5 B=2 C=19 D=-2

Step-by-step explanation:

I looked back at the video and actually tried to pay attention and the way to figure these problems out is set up all of the degrees of x in an equation. So, take all of the coefficients that are attached to an x^3, and set them up equal to each other. This makes -5=A, which is the first answer. Repeat for x^2 and you have B=2. For x, it becomes 9=2A+C. A is equal to -5 (from the x^3), so you can substitute and get c=19. Repeat for the x^0 term (the constants), and you get 2=2B+D. Plug in the value for B, 2, and get 2=4+D, which then becomes D=-2. That's how you get the answer and I hope this helps somebody.

The values are A=-5, B=2, C=19 and D=-2

Partial fractions are the fractions used for the decomposition of a rational expression. When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction. Hence, basically, it is the reverse of the addition of rational expressions.

Given:(-5x³+2x²+9x+2) / x²+2 =(Ax + B)/x²+2 + (Cx + d)/x²+2 .......(1)

First, we have to perform the long division as follows

The long division gives

(-5x³+2x²+9x+2 )/ x²+2= ( -5x+2)+ (19x-2)/ x²+2

Now, we have to find the partial fraction for  (19x-2)/ x²+2

But, as denominator cannot be factored, So no partial fraction can be calculated.

Thus, (-5x³+2x²+9x+2 )/ x²+2=  ( -5x+2)+ (19x-2)/ x²+2

Comparing it with equation (1), we get

Hence, A=-5, B=2, C=19 and D= -2

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