Write an equation of the line that passes through the given point and is perpendicular to the given line. (-8, 4) ; y = 7​

The circumference of the given circle is 17.8 cm and the area of the given circle is 25.1 [tex]cm^2[/tex]

What is area and circumference of circle?

Circumference of circle is the length of the boundary of the circle

If the radius of the circle is r, then the circumference of the circle is [tex]2\pi r[/tex]

Area of the circle is the total space taken by the circle

If the radius of the circle is r, then the area of the circle is [tex]\pi r^2[/tex]

Center of the circle = (2, 3)

Point on a circle = (4, 1 )

Radius of the circle =

[tex]\sqrt{(4-2)^2 + (1 - 3)^2}\\\sqrt{2^2 + (-2)^2}\\\sqrt{4 + 4}\\\sqrt{8}[/tex]

Circumference of circle = [tex]2 \pi \sqrt{8}[/tex]

                                       = [tex]2 \times 3.14 \times 2 \times \sqrt{2}[/tex]

                                       = [tex]2 \times 3.14 \times 2 \times 1.414[/tex]

                                       = 17.8 cm

Area of circle = [tex]\pi \times \sqrt{8} \times \sqrt{8}\\[/tex]

                       = [tex]3.14 \times 8[/tex]

                       = 25.1 [tex]cm^2[/tex]

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Complete Question

The figure has been attached here

Find the perimeter or circumference and area of each figure if each unit on the graph measures 1 cm. Round answers to the nearest tenth, if necessary.

Answer: c≈26.91

Step-by-step explanation: c=a2+b2=202+182≈26.90725

Hello..!

We use the Pythagorean formula:

[tex] \sf \red{c {}^{2} } = \blue{ a {}^{2} + b {}^{2} }[/tex]

We know that once we have the formula we extract the Raised data:

[tex] \sf \red{c {}^{2}} = \blue{(20cm) {}^{2} + (18cm) {}^{2} }[/tex]

Having the Raised data, we will add as a power and we know that:

[tex] \sf \red{20 {}^{2} } = \orange{400}[/tex]

[tex] \sf \red{18 {}^{2}} = \orange{324}[/tex]

So, to solve a power we must multiply squared and then get our result, in this case I added and then increased it by 0

[tex] \sf \red{c {}^{2} }= \blue{400cm {}^{2} + 324cm {}^{2} }[/tex]

We have the results, once that is done we will add.

[tex] \sf \red{400 + 324 }= \blue{724}[/tex]

So, we have the result we just have to put it like this:

[tex] \sf\red{c {}^{2} } = \blue{724cm {}^{2} }[/tex]

Once we have our result, we must take the square root, then the (square "²") automatically disappears.

[tex] \sf \red{c =} \green{ \sqrt{724cm} }[/tex]

[tex] \sf \red{c }= \orange{ 26.90cm}[/tex]

So, our result of our problem is: [tex] \orange{ \sf \longmapsto} \sf \blue{ \: 26.90cm}[/tex]

The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)

The list of options represents the given parameter

All ordered pairs are relations but not all ordered pair are functions

For an ordered pair to be a function, the following must be true:

The y values on the ordered pair must have  different x values

Using the above as a guide,

This means that the ordered pair in option (b) represents a function

Hence, the ordered pair that is a function is (b)

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Answer:

Use the Intermediate Value Theorem to prove that every cubic function has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.

Answer:

[tex]2x^{2} +17x+21[/tex]

Step-by-step explanation:

multiply the 2x by x and 7 and then multiply 3 by x and 7. you will get 2[tex]x^{2}[/tex]+14x+3x+21. combine like terms so add 14x to 3x and thats the only like trerms in the equation. so 2x^2+17x+21

The required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct.

Given that,
To determine the equation that has the solution x = all real numbers.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Equation 1
5(3-x)+7x = 3x + 15 - x
15 - 5x + 7x = 3x +15 - x
2x = 2x
Since it implies the variable x solution as all real numbers,
While all other equation has a distinct unique solution,

Thus, the required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct

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Answer:

65 good sir.

Step-by-step explanation:

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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The solution to the expression is -180

From the question, we have the following parameters that can be used in our computation:

(-6)(15)(-2)(-1)

Remove the brackets in the expression

So, we have the following product expression

(-6)(15)(-2)(-1) = -6 * 15 * -2 * -1

Evaluate the products using a calculator

This gives

(-6)(15)(-2)(-1) = -180

Hence, the solution is -180

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Probability that the sample mean would differ from the true mean by more than 162 dollars if a sample of 71 persons is randomly selected is 50%

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation 805 , the zscore of a measure X is given by:

Z = (X - μ)/σ

s = σ/√n

In this problem, we have that:

μ = 21053, n = 71, σ = 805

s = 805/√71 = 95.53

Eiher it differs by 162 or less dollars, or it differs by more than 162 dollars. The sum of the probabilities of these events is decimal 1. So

Probability it differs by 160 or less dollars.

pvalue of Z when X = 21053 + 162 = 21215 subtracted by the pvalue of Z when X = 21053 - 162 = 20891.

X = 21215

Z = (X-μ)/σ

Z = (21215-21053)/95.53

Z = 1.69

has a pvalue of 0.091

X = 21568

Z = (X-μ)/σ

Z = (21215-21053)/95.53

Z = 1.69

has a pvalue of 0.041

0.091 -  0.041 = 0.05098

p + 0.50 = 1

p = 0.50

Thus, Probability that the sample mean would differ from the true mean by more than 162 dollars if a sample of 71 persons is randomly selected is 50%

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Answer is : 5a + 4b

Using corresponding and alternating angle theorem. The values of the angles in the figure are m∠1 = 47, m∠2 = 133, m∠3 = 139, m∠4 = 41, m∠5 = 139 degrees respectively.

The corresponding angle postulate states that the corresponding angles are congruent if the transversal intersects two parallel lines. In other words, if a transversal intersects two parallel lines, the corresponding angles will be always equal.

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

a. m∠1 = m∠7

Reason : Corresponding angles are equal

m∠1 = 47°

b. m∠2 = 180 - m∠1

Reason: Angles on a straight line

m∠2 = 180 - 47

m∠2 = 133°

c. m∠3 = m∠16

Reason : alternating angles are equal

m∠ = 139°

d. m∠4 = 180 - m∠3

Reason : Angles on a straight line

m∠4 = 41°

e. m∠5 = 180 - m∠4

Reason: Angles on a straight line

m∠5 = 139°

n. m∠17 = 180 - m∠6

m∠17 = 41°

f. m∠ 6 = m∠15

m∠15 = m∠17

Reason : Opposite angles are equal

m∠ 6 = m∠ 17

Reason : Alternating angles are equal

m∠ 6 = 41°

g. m∠8 = m∠1

m∠ 8 = 47°

h. m∠ 9 = m∠2

m∠9 = 133°

m. m∠15 = m∠ 17

m ∠ 15 = 41°

o. m∠ 18 = 360 - (m∠15 + m∠16  m∠ 17)

m∠18 = 360 - (41 + 139 + 41)

m∠18 = 139°

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Answer: range 14 IQR 12

Step-by-step explanation:

took the exam got it right

The slope of the line  passing through the points ( -8,8) and ( 2,8) is 0.

What is slope?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols y and x stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is given by m = change in y/change in x = y/x. where'm' denotes a line's slope

Here the given points are,

[tex](x_1,y_1)=(-8,8)\\(x_2,y_2)=(2,8)[/tex]

Now using slope formula ,

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

=> slope m= [tex]\frac{8-8}{2+8}[/tex]

=> slope m = 0

Hence slope of the given points is 0.

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The x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.

In the given question we have to find the x- and y-intercepts of the graph of x +6y= 10.

The given equation is x +6y= 10.

To find the x intercept we have to put y=o and to find the y intercept we have to put x=0.

Firstly finding the x intercept by putting y=0 in the equation.

x +6×0= 10

x+0=10

x=10

Now finding the y intercept by putting x=0 in the equation.

0 +6y= 10

6y = 10

Divide by 6 on both side

6/6 y =10/6

y=5/3

Hence, the x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.

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Answer:

Table B

Step-by-step explanation:

To determine whether or not something is linear, we find the slope between two different coordinates and see if that slope remains consistent throughout the data. To find the slope between two points, use the equation (y2-y1)/(x2-x1)

Table A -->  (-1-5)/(3-2) = -6/1 = -6

Now we have to see if the slope remains consistent in "Table A" by finding the slope using two other coordinates:

(6-3)/(5-4) = 3/1 = 3

We see that the slope is not consistent in Table A, so we repeat the same steps with the other Tables to find one with a consistent slope.

Table B --> (0- -3)/(5-3) = 3/2

                  (6-3)/(9-7) = 3/2

Table B's data creates a consistent slope, so Table B represents a linear function.

C:

3500(0.93)^d

Exponential functions have the form a·b^x, where:

   a is the initial amount

   b is the percent remaining after each time period

a = 3500, since that's the original volume.

Since 7% is lost each day, 93% remains, so b=0.93.

If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

In the question ,

it is given that

the when the object is dropped from height h then the velocity with which it hits the ground is given by the formula

v = √(19.6×h)

to find the height it was dropped , and it hits the ground with velocity 25.7 meter per second ,

we substitute v = 25.7 in the equation v = √(19.6×h) ,

we get ,

25.7 = √(19.6×h)

squaring both the sides , we get

19.6 × h = 25.7²

19.6 × h = 660.49

h = 660.49/19.6

h = 33.698

h ≈ 33.7

Therefore ,If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

The given question is incomplete , the complete question is

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v = √(19.6×h) . If an object hits the ground with a velocity of 25.7 meters per second, from what height was it dropped?

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Answer:Smallest + Middle + Largest = 53

M= S + 2

L = 2S

Substitute M= S +2 and L = 2S into S + M + L =53

S + S + 2 + 2S = 53

4S + 2 = 53

4S/4 = 51/4

S = 12.75

M = 12.75 + 2

M = 14.75

L = 2 (12.75)

L = 25.5

Step-by-step explanation:

The amount of money in the account in 35 years to the nearest cent is $1629.25.

The compound interest formula is expressed as;

A = P(1 + r/n)^(n*t)

Where A is accrued amount, P is principal, r is rate,  and t is time.

Given that;

Plug the given values into the compound interest formula and solve for A.

A = P(1 + r/n)^(n*t)

A = $100( 1 + 0.08/12)^( 12 × 35)

A = $100( 1 + 0.08/12)⁴²⁰

A = $1629.25

Therefore, the accrued amount is $1,629.25.

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The balance after one year if you deposit one $25 envelope each month, all year is  $306.97.

Given,

you make an initial deposit of $300 into an account that pays 5% APR at the beginning of the year and then you divide up the remaining $300 into 12 envelopes each with $25.

we are asked to find the balance after one year for the initial deposit of $300, if you also deposit one $25 envelope each month, all year, into the account that pays 5% APR with monthly compounding = ?

The balance after 1 year can be determined using this formula:

Amount deposited monthly x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

r = interest rate = 5% /12 = 0.417%

n = number of years = 1 x 12 = 12

Annuity factor = 1.004167^12 - 1 / 0.00417 = 12.279082

Balance = 12.279082 x 25 = $306.97

Hence we get the required answer.

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The integrals in this problem are given as follows:

a) 18 units².

b) 18π units².

c) (18π + 4.5) units².

d) (9π + 9) units².

To obtain the integrals in this problem, we need to have knowledge of the meaning of the integrals, which is that they represent the area of the function over the interval.

For item a, the area is obtained as follows:

Hence the integral is of 18 units².

For item b, the figure is a semicircle of radius 6, hence the area is given as follows:

A = 0.5πr² = 18π units².

For item c, the area is composed as follows:

Hence the area is of:

A = (18π + 4.5) units².

For item d, the area is given as follows:

Hence the area is of:

A = (9π + 9) units².

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The formula for the arithmetic sequence that contains a(8) = 12 and a(16) = 22 is a(n) = 13 / 4 + (5 / 4) · (n - 1).

In this problem we must derive the formula behind the arithmetic series. Arithmetic series are sets of numbers generated by expression of the form:

a(n) = a' + r · (n - 1)

Where:

If we know that a(8) = 12 and a(16) = 22, then the formula for the arithmetic formula is:

12 = a' + 7 · r

22 = a' + 15 · r

Now we find a system of two linear equations with two variables, whose solution is found by using numerical methods:

(a', r) = (13 / 4, 5 / 4)

Then, the formula for the arithmetic sequence is a(n) = 13 / 4 + (5 / 4) · (n - 1).

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Answer:

false

Step-by-step explanation:

x+2<-9

x<-9-2

x<-12

Her monthly payment is $88.64

The total of her monthly payments is $2,127.39

The finance charge is $127.39

Given, Melissa wants to check the accuracy of the finance charge on her promissory note.

She has a $2,000, two-year loan at a APR of 6%.

As, she has a $2,000 loan for two year at a APR of 6%.

Then, the total amount she has to pay is $2,127.39

(a) So, the monthly payments be

$2,127.39/24 = $88.64

(b) Now, she has to pay monthly payments for 24 months

So, the total of her monthly payments is $2,127.39.

(c) the finance charge she has to pay is,

$2,127.39 - $2,000 = $127.39

Hence, her monthly payment is $88.64

the total of her monthly payments is $2,127.39

the finance charge is $127.39

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A circle graph is attached.

A circle graph, also known as a pie chart, is used to visualize information and data. A circle graph is commonly used to show the results of an investigation in a proportional manner. The arcs of a circle graph are proportional to the percentage of the population who answered a specific question.

Given data

Top-selling US kids magazine as of 2002

Seventeen      2.352

Ym                      2.242

Teen              1.729

Teen people      1.625

Boys              1.280

First, we have to add up the dataset

Total = 2.352 + 2.242 + 1.729 + 1.625 + 1.280

= 9.228

The proportion of each magazine is then calculated.

This is calculated by dividing each magazine's frequency by the total frequency.

Mathematically, the formula is represented as:

Proportion = issue sold/ Total magazines sold

So we have

Seventeen= 2.352/9.228

= 25.5%

Seventeen= 2.242/9.228

= 24.3%

Seventeen= 1.729/9.228

= 18.7%

Seventeen= 1.625/9.228

= 17.6%

Seventeen= 1.280/9.228

= 13.9%

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As per the given sales tax, the total cost of the bicycle is $1056.194

Sales tax:

Sales tax is defined as the amount of money, calculated as a percentage, that is added to the cost of a product or service when purchased by a consumer at a retail location.

Given,

DeShawn buys a bicycle that costs $129.95. The sales-tax rate in his city is 712%.

Here we need to find the total cost of the bicycle.

Let us consider the 712% is applied as the tax for $129.95.

So, the amount of tax is calculated as,

=> 712% of 129.95

=>  712/100 x 129.95

=> 7.12 x 129.95

=> 926.244

Therefore, the total amount is obtained by adding the tax amount plus the cost of bicycle,

Then,

=>  129.95 + 926.244

=> 1056.194.

Therefore, the total cost of the bicycle is $1056.194.

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Answer:

3 hours and 44 minutes

Answer:

isosceles triangle

Step-by-step explanation:

first by using corresponding angle theorem:

<A=<C

<A=50°

then by using exterior angle theorem:

<A+<C=<B(the outer angle)

50°+<C=<B,<B=180°-80°(angle B lies in a staight line)

<B=100°

50°+<C=100°

<C=50°