The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menusto complete the proof.aababClick the arrows to choose an answer from each menu.The expression Choose... represents the area of the figure as the sum of the area of theshaded triangles and the area of the white square.The equivalent expressions Choose...use the length of the figure torepresent the area.Setting two of these area expressions equal to each other and subtracting Choose...from both sides of the equation results in the Pythagorean Theorem, a? + b2 = c?.

The function notation f(-5) has a value of -6

Functions are graphs, ordered pairs, relations, tables and equations that are used to relate independent and dependent variables

The function notation is given as

f(-5)

Also, we have the graphs to be f(x) and g(x)

This is represented by

So, we use the blue curve i.e. f(x)

On the blue curve, we have

f(-5) = -6

Hence, the value of the function is -6

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Gigi, this is the solution to the problem:

This is the information provided to us:

Plan A : $ 6 per month + $ 2 per movie wathced

Plan B : $ 16 per month + $ 1 per movie watched

Step 1: Let's calculate the number of movies that would make the two plans to have an equal monthly payment, as follows:

Let x to represent the number of movies watched by Jonathan

Plan A = Plan B

6 + 2x = 16 + 1x

Like terms:

2x - x = 16 - 6

x = 10

If Jonathan watches 10 movies per month the two plans will have an equal monthly cost

Step 2: Let's graph the functions that represent each plan, this way:

Answer:

-4

Explanation

Given the standard form of a quadratic equation expressed as ax^2 + bx + c = 0

Comparing to the given equation 2x^2+6x+5=0

ax^2 = 2x^2

a = 2

bx = 6x

b = 6

c = 5

Get b^2 - 4ac

Substitute the values of a, b and c into b^2 - 4ac

b^2 - 4ac

= 6^2 - 4(2)(5)

= 36 - 40

= -4

Hence the value of b^2 - 4ac is -4

In the linear graph, the value of x such that f(x) = -3 is -2.

A linear graph is a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.

Therefore, a linear graph is represented in the form of a straight line.

It shows the relationship between variables x and y.

x is the horizontal variables while y is the vertical variables.

Therefore, the graph of the given function is f(x).

Let's use the graph to find x such that f(x) = - 3

f(x)  is the y coordinates of the linear graph.

Let's find x when f(x) = -3

Therefore,

x = - 2

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The volume of a cone is given by

Diameter = 34 in

radius = 34/2 = 17 in

Height = 17in

Answer:

7,680 beetles

Explanation:

The function that gives the beetle population after x weeks is given below:

To determine the beetle population after 56 days, first convert 56 days to weeks.

Thus, the beetle population will be:

There will be 7,680 beetles after 56 days.

If additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.

Given that additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41.

We are required to find the cost after all the rebates and envelopes provided.

The cost can be calculated as under:

Cost=109.99-10.00+0.35+0.41

=$100.75

Hence if additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.

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as this is a vertical line, the slope is undefined

The general equation of line with passing points (a, b) and slope m is :

y = m(x - a) + b

In the given question :

A line goes through the point (2,1)

Passing point (a, b) = (2, 1)

a slope of 2

Slope : m = 2

Substitute these value in the general equation of line :

y = m( x - a ) + b

y = 2 ( x - 2) + 1

y = 2x - 4 + 1

y = 2x - 3

y = 2x - 3

A)

To plot on the graph :

We have one coordinate ( 2, 1)

Find one more coordinate

Substitute x = 1 in the equation os line :

y = 2x - 3

y = 2(1) - 3

y = ( - 1 )

So, (x, y) = ( 1, -1)

Plot the coordinates ( 2, 1) & ( 1, - 1)

y- intercept is the point on the line where x = o

Substitute x = 0 in the given equation of line :

y = 2x - 3

y = 2( 0 ) - 3

y = ( -3 )

Y -intercept : y = ( -3) , (x, y) = ( 0, -3)

In the graph y -intercept is :

The purple point in the graph represent the y -intercept.

B)

The general form of the equation of line in the form of slope intercept form :

y = mx + b

The equation of line y = 2x - 3

On compare with the general equation of slope intercept form we have : m - 2, b = (-3)

So, equation of line in the slope intercept form is : y = 2x - 3

y = 2x - 3

Answer : A) ( x, y) = (0, -3)

B) y = 2x - 3

Farm c is Marc's farm it have 60 % of purple flowers

To find percentage :

In Farm B it shows that 0.6 are purple flowers .

0.6 is 6 of 10 it is 60 %.

And other farms have 11/20 that is 55% in Farm A

For Farm C only 40 %.

Percentage :

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The savings plan balance (future value), after 4 years with an APR of 4% and monthly payments of ​$100, is $5,213.28.

The future value is the compounded amount of monthly payments after four years of monthly savings.

The future value can be computed using an online finance calculator.

N (# of periods) = 48 months (4 x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

PMT (Periodic Payment) = $100

Results:

Future Value (FV) = $5,213.28

Sum of all periodic payments = $4,800 ($100 x 48)

Total Interest = $413.28

Thus, in 4 years, the savings plan will have a future value of $5,213.28.

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We are given the below expression

From the quadratic function generated, we will be solving for x using the general formula

Given,

Total money needed = 225

Money already Marie has = 85

Marie per day Income = 20

Let it take x days for Marie to have enough money to buy the prom dress.

We can say:

Total Money = Money Marie already has + per day income

Using the given information, we can craft an inequality shown below:

This means "85 already have plus 20 per day will need to be atleast 225".

Now, we can do algebra and solve for x. Steps are shown below:

Thus, Marie needs 7 days more to have enough money to buy the prom dress.

The circumference of the circle C = 207.24 inches.

The formula for the circumference of circle is,

Assume the value of pi be 3.14.

Substitute 207.24 for C in the formula to determine the radius of circle.

Thus radius of circle is 33 inches.

The annual payment is $73416.96

[tex]- Total \ cost \ of \ the \ land $=\$ 225 \times 4700$$$=\$ 1057500$$Down payment $=0.25 \times 1057500$$$=\$ 264375$$so, loan amount $=\$ 1057500-264375$$$=\$ 793125$$[/tex]

[tex]Present \ value,\ $P V=P M T\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]$$$P r=793125, r=0.0675 \text {, }$$$t=20$ years, $n=1$$$\therefore \quad P M T=\frac{P v}{\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]}$$$$=\frac{793125}{\left[\frac{1-\left(1+\frac{0.0675}{1}\right)^{-20}}{\left(\frac{0.0675}{1}\right)}\right]}$$$=73416.96$\\So, Annual payment $=\$ 73416.96$[/tex]

A down payment is the first down payment when buying an expensive good/service, such as a car or house. It is usually paid in cash or equivalent at the time of the transaction. Then some kind of loan is needed to finance the rest of the payment. The biggest advantage of a down payment is that it reduces the amount of the loan you need. If you borrow less, you pay less interest.

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The number of toothpicks that the jumbo box hold is 6760.

From the information, there are 250 toothpicks in a regular-size box and jumbo-size box is made by tripling the length, width, and height of the regular box.

Therefore, the number of toothpicks will be illustrated by multiplying the value by the change. This will be:

= 250 × 3 × 3 × 3

= 6750

This was because the dimensions were tripled

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We have the following data set:

2,7,15,3,12,9,15,8,3,10

The range is the difference between the highest and lowest values in the set, to find the range, order the data set from least to greatest.

2,3,3,7,8,9,10,12,15,15

Then,

Mean is represented by the following expression:

Population variance formula looks like this:

Then, substituting:

For the standard deviation:

Answer:mark has 1 liter, lisa has an impossible -1 liter

Step-by-step explanation:

He started at 7 meters away, so if after 2 seconds now he is 3 meters away, then he move:

So he move 4 meters in 2 seconds so to find the rate we divide the meters into the tiem so:

Solution

Step-by-step explanation:

we have:

Part 1) Find the x-intercepts of the parabola and write them as ordered pairs

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

For x=4 and x=-2 the equation is equal to zero

therefore

The x-intercepts are the points (-2,0) and (4,0)

Part 2) Write the equation y=(x-4)(x+2) in standard form

The quadratic equation in standard form is equal to

applying distributive property

where a = 1, b = -2, c = -8

Part 3) With the standard form of the equation from part ll, use the quadratic formula to identify the x-value of the vertex

we know that

the x-value of the vertex is -b/2a

we have

where a = 1, b = -2, c = -8

substitute

x = -b/2a = -2/2(1) = 1

therefore

The x-coordinate of the vertex is 1

Part 4) Substitute the x-value of the vertex from part lll into the original equation to find the y-value of the vertex.

we have

For x=1

substitute and solve for y

therefore

The y-coordinate of the vertex is -9

The coordinate of the vertex is the point (1,-9)

Answer:

A the answer is a

Step-by-step explanation:

it's corn a beautiful thing for me it has the juice

(6) A function is increasing when the y-value increases as the x-value increases.

The domain is the set of allowable x-values

The following graphs increases over their entire domain:

B, E, I, J, N, G

(7) A function is said to be decreasing when the y-value decreases as the x-values increase.

The following graphs decreases over their entire domain:

A, F

1. The decision rule is:

2. The test statistic is: t = 3.42.

At the null hypothesis, it is tested if there is not enough evidence that the mean ticket price has increased from $267, that is:

[tex]H_0: \mu \leq 267[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean ticket price has increased from $267, that is:

[tex]H_1: > 267[/tex]

For the decision rule, we need to consider that:

The critical value for the test is given by:

t* = 2.681.

Hence the rule is:

The test statistic is given by the following equation:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the parameters are defined as follows:

Using a calculator from the given sample, and considering the values tested at the hypothesis, the values of the parameters are:

[tex]\overline{x} = 288.3, \mu = 267, s = 22.46, n = 13[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{288.3 - 267}{\frac{22.46}{\sqrt{13}}}[/tex]

t = 3.42.

The problems asks if the sample gives enough evidence to conclude if the mean ticket price has increased with a significance level of 0.01.

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From the diagram, we can see that CL bisects angle JCN. This means that CL divides the angle JCN into 2 equal halves. It means that

angle JCN = angle JCL + angle LCN

Given that angle JCN = 8r - 2 and angle LCN = 3r + 15, it means that

8r - 2 = angle JCL + 3r + 15

Since angle JCL = angle LCN, then

8r - 2 = 3r + 15 + 3r + 15

8r - 2 = 6r + 30

8r - 6r = 30 + 2

2r = 32

r = 32/2

r = 16

angle JCL = 3r + 15 = 3 * 16 + 15

angle JCL = 48 + 15

angle JCL = 63 degrees

Whole numbers are similar to natural(non-negative, non-fractional). The only difference is that it includes the 0.

In this question, Rio placed -1 as an example of whole number. Since -1 is negative, it is not a whole number, so this the number which Rio placed incorrectly.

A store Mark's down toys by 15% in january. how much does each toy cost during january? use p for price in December

__________________________

P

The student's survey of nine student with regards to the number of first cousins they have gives the standard deviation of the data as the option;

The standard deviation gives a measure of the variability or dispersion of a set of data.

The survey is with regards to a data obtained from a sample of the population (the first nine response),

The standard deviation of a sample is given by the formula;

[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } }} [/tex]

Where;

n = The data count = 9

[tex] \displaystyle{ \bar x = \frac{6+2+7+8+8+8+5+10+10}{9 } = \frac{64}{9} }[/tex]

Which gives;

[tex]\displaystyle{ \sum (x_{i} - \bar x)} [/tex]

(6-64/9)+(2-64/9)+(7-64/9)+(8-64/9)+(8-64/9)+(8-64/9)+(5-64/9)+(10-64/9)+(10-64/9) = 50.888889

Therefore;

[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } } = \sqrt{\frac{50.888889}{8}} \approx 2.52 } [/tex]

The standard deviation of the data is therefore;

2.52 first cousins

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