Find the measure of each exterior angle of a regular pentagon​

Answer:

1. [tex]-5x+3y+44=0[/tex]

2. [tex]2x+y-2=0[/tex]

3. [tex]2x+y-4=0[/tex]

Step-by-step explanation:

Standard form of a line is [tex]Ax+By+C=0[/tex].

If a line passing through two points then the equation of line is

[tex]y-y_1=m(x-x_1)[/tex]

where, m is slope, i.e.,[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex].

1.

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

[tex]y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)[/tex]

[tex]y+3=\dfrac{-5}{-3}(x-7)[/tex]

[tex]y+3=\dfrac{5}{3}(x-7)[/tex]

[tex]3(y+3)=5(x-7)[/tex]

[tex]3y+9=5x-35[/tex]

[tex]-5x+3y+9+35=0[/tex]

[tex]-5x+3y+44=0[/tex]

Therefore, the required equation is [tex]-5x+3y+44=0[/tex].

2.

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to [tex]2 x + y =-5[/tex].

Slope of the line : [tex]m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2[/tex]

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

[tex]y-2=-2(x-0)[/tex]

[tex]y-2=-2x[/tex]

[tex]2x+y-2=0[/tex]

Therefore, the required equation is [tex]2x+y-2=0[/tex].

3.

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to [tex]2x + y =-5[/tex].

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

[tex]y-0=-2(x-2)[/tex]

[tex]y=-2x+4[/tex]

[tex]2x+y-4=0[/tex]

Therefore, the required equation is [tex]2x+y-4=0[/tex].

Answer:

A.64/50

Step-by-step explanation:

8/10*8/5

64/50

The least simplified form of the equation is 32/25

The simplified form of expression is option (D) 64/50 is the correct answer.

Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.

For the given situation,

The expression is (8/10)(8/5)

The simplified form of expression is

⇒ [tex](\frac{8}{10} )(\frac{8}{5} )[/tex]

⇒ [tex]\frac{64}{50}[/tex]

Hence we can conclude that the simplified form of expression is option (D) 64/50 is the correct answer.

Learn more about simplification of an expression here

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Answer:

a) What is her average speed in mph?

= 65 mph

b) How many miles does Matthew drive?

=310 miles

Step-by-step explanation:

The average speed in meters per hour (mph) of Helen is 65 miles per hour

Given:

Total distance = 195 miles

Time taken = 3 hours

= 195 miles ÷ 3 hours

= 65 miles per hour

If Matthew drives at an average speed of 62 mph for 5 hours.

Total distance between traveled = Average speed × Time taken

= 62 mph × 5 hours

= 310 Miles

Therefore the total miles Helen traveled in 5 hours at the rate of 62 mph is 310 miles

Read more:

https://brainly.com/question/8406966

Answer:

x = 0   ,   x = -2

Step-by-step explanation:

The function given to us is:

f(x) = 3/2x - 5

g(x) = x² + 2x

We have to find the input x, for which the output of the function g(x) becomes 0.

It means that there is no use for the function f(x) in this question, so discard it

Substitute g(x) = 0 into the given equation of g(x):

g(x) = x² + 2x

0 = x² + 2x

Take x common from both the terms:

x(x+2) = 0

Thus, the values of x can be written as:

x = 0     ,     x + 2 = 0

x = 0     ,     x = -2

Answer:

Lowest value:  24

Highest value:  84

Spread:  60

Center value: mean = 52.11

median = 53

Step-by-step explanation:

Given data

35. 42, 65, 59,84.62.46. 52,24

let arrange is from smallest to largest

24, 35, 42, 46, 52, 59, 62, 65,84

Thus,

Lowest value = 24

Highest values = 84

Spread is the range of data

range is difference of highest and lowest value

spread = 84-24 = 60

Center value is mean and/or mean of data

mean = sum of data/ no. of data

no. of data = 9

mean = 24+ 35+ 42+ 46+ 52+ 59+ 62+ 65+84/9 = 469/9 = 52.11

median is the middle term when data is arranged in ascending order.

median is (n+1)/2 th term when no. of data is odd

median is (9+1)/2th term = 5th term

5 th term is 52

thus, median is 52.

Thus, solution is

Lowest value:  24

Highest value:  84

Spread:  60

Center value: mean = 52.11

median = 53

Answer:

  a)  P(1/2, 1/2)

Step-by-step explanation:

If the point does not lie on a coordinate axis, then the sum of the coordinates must be greater than 1. (This is a consequence of the triangle inequality and the fact that the hypotenuse of the right triangle is 1.)

This fact lets you readily identify (1/2, 1/2) as not being on the unit circle.

Answer:

Volume ≈ 138.3

Step-by-step explanation:

[tex]V = \pi r^2 h\\h = 11in\\d = 4in \\r = d/2 = 4/2 = 2\\\\V= \frac{22}{7} \times 2^2 \times 11\\V = \frac{22}{7} \times 4 \times 11\\V = 22/7 \times 44\\\\V = 968/7\\\\V = 138.2857[/tex]

Answer:138.2

Step-by-step explanation: n(2)^2(11) = 138.2300768 = 138.2

Answer:

the ratio is 1:3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

You can look them up in the graphs.

f(2) means "where is the blue graph when x=2?", and you can see it is at y=0.

Answer:

1500

Step-by-step explanation:

Let the length of the perpendicular dropped from the right angle to the hypotenuse be h units.

Now by geometric mean property:

[tex]h = \sqrt{1600 \times 900} \\ h = 40 \times 30 \\ h = 1200 \: units \\ Next \: by \: Pythagoras \: Theorem: \\ {x}^{2} = {h}^{2} + {900}^{2} \\ {x}^{2} = {1200}^{2} + {900}^{2} \\ {x}^{2} = 1440000 + 810000 \\ {x}^{2} = 2,250,000 \\ x = \sqrt{2,250,000} \\ \huge \red{ \boxed{x = 1500\: units }}[/tex]

Answer:

1500

Step-by-step explanation:

Use the right triangle altitude theorem.

x/900 = 2500/x

x^2 = 900 * 2500

x = sqrt(900 * 2500)

x = 30 * 50

x = 1500

Answer:

In the given question, it is given that A ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.

The ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet.

And we have to find the value of tan B.

And tangent of any angle is equal to the ratio of vertical by horizontal. That is

tan B= 8/15

Step-by-step explanation:

Answer:

250 kg of 17% and 150 kg of 25%

Step-by-step explanation:

For answering this, we do it by proportions.

take the difference

17%  ===  20% === 25%

         3              5

Then ratio

17% :25% = 5:3

For 400 kg,

17% = 5/(5+3)  * 400 = 250 kg

25% = 3/(5+3) * 400 = 150 kg.

Above is a mental method, no calculation or pencil need.

I will edit to give an algebraic method.

Algebraic method:

Given:

17% rods and 25% rods.

Need to make 400 kg of 20% rods.

Let  

A=weight of 17% rods

B=weight of 25% rods

to make 20% rods, we need  

( 0.17A + 0.25B ) / (A+B) = 0.20  ............(1)

But we know that  

A+B=400 .............(2)

substitute

B=400-A in (1)

( 0.17A + 0.25 (400-A) ) / 400 = 0.20

Cross multiply and simplify

(0.17-0.25)A +100 = 80

-0.08A = -20

A = -20 / (-0.08)

A = 250 ...........(3)  (17% rods)

substitute (3) in (2)

B = 400-250 = 150   (25% rods)

Same answer as mental calculations

Even simpler albebra, same answer!

Given:

17% rods and 25% rods.

Need to make 400 kg of 20% rods.

Let  

W=weight of 25% rods

400-W = weight of 17% rods

To make 20% purity rods, we need to have 400*0.2=80 kg of pure metal, which is

0.25W + 0.17(400-W) = 80

Expand and simplify

0.25W + 68 - 0.17W = 80

0.08W = 80-68 = 12

W = 12/0.08 = 150  (25% rods)

400-W = 250 kg (17% rods)

Answer:

245432

Step-by-step explanation:

Angela uses  cup of strawberries to make  of a liter of smoothie. What is the unit rate in cups of strawberries per liter of smoothie?

Answer:

C   x<-2 or x>_ 4

Step-by-step explanation:

Dont get corona!

Answer:

Step-by-step explanation:

d= distance

t= time

The independent variable is t, time. The distance the car travels depends on the time in hours spent travelling. The dependent variable is d, distance. Here is a table with 5 coordinate pairs that can be used.

(T)        (D)

1           30

2          60

3          90

4         120

5         150

These are the coordinate pairs for the function. When we use division and determine the rate of change, we can determine that the average rate of speed (MPH) is 30 MPH.

Answer:

This is an extremely easy question. Your correct answer is 1/7,200 or 0.01389%

Step-by-step explanation:

Since you have to choose the three numbers and one super ball to be able to win the lottery, your chances of getting 3 white numbers is 1/10 x 1/9 x 1/8 = 1/720

The chances of getting the super ball is 1/10

And the chances of winning the jackpot is 1/720 x 1/10 = 1/7,200 = 0.01389%

Answer:

95 meters

Step-by-step explanation:

The perimeter of the scale garden is 6 + 8 + 3 + 5 + 3 + 13 = 38 (you can find the missing side lengths by doing 6 - 3 and 13 - 8). Since 1 cm is 2.5 meters, 38 cm is 38 * 2.5 = 95 meters.

Answer:

44 units length

Step-by-step explanation:

The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally. Therefore:

20/10 = x/22

20/10*22 = x

44 = x

Answer:

This equation is false

Step-by-step explanation:

Well,

-11b + 7 = 4 - 11b + 7 = 40

combine like terms

-11b + 7 = -11b + 3 = 40

Communicative property

-3 to both sides

-11b + 4 = -11b = 40

-4 to both sides

-11b = -11b = 36

+11b to both sides

0 = 36

0 is not equal to 36 meaning that this equation is false.

Thus,

the equation given is false.

Hope this helps :)

Answer:

b= -3

Step-by-step explanation:

So uh it was not -11b+7 = 40−11b+7=40

it was -11b+7 = 40 the equasion was probably just copy pasted twice.

Sorry im  late i just got this question on khan acadamey

hope this helps

Answer:

c = -6

d = -1

Step-by-step explanation:

In the picture attached, the question is shown.

Shape A is composed of the points:

(3, 2)

(5, 2)

(3, 5)

Reflection across the x-axis transforms point (x, y) into (x, -y). Applying this transformation to shape A:

(3, 2) → (3, -2)

(5, 2) → (5, -2)

(3, 5) → (3, -5)

Translation (c, d) transforms (x, y) into (x+c, y+d). The point (3, -2) in the pre-image (before translation) corresponds to point (-3,-3) in the image (after translation). Therefore:

(3, -2) → (3+c, -2+d) → (-3,-3)

3+c = -3

c = -3 -3 = -6

-2+d = -3

d = -3+2 = -1

Answer:

Part A: 7/10

Part B: 1/2

Part C: look below*

Step-by-step explanation:

Part A:

The probablity is a 7/10 because in the previous record the gerbil went left 7 out of the 10 times

Part B:

Theoretically the gerbil has a 1/2 of going either left or right since there are two options.

Part C:

The experimental probabilty does not equal the theoretical probability because during the trial the gerbil went left 7/10 and theoretically the gerbil would go left 5/10 times.

Answer: 9 yards

Step-by-step explanation:

The proportion x/15 = 12 / 20 ||| X * 20 = 20X ||| 12 x 15 = 180 ||| 180 / 20 = 9

Answer:

.7

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Just did the test and -6 was the right answer.

Answer:

A: d= every time she walks the dog

   b= every time she babysits

B: 8d+12b

Brainlyest pls

Answer:

A: d= every time she walks the dog b= every time she babysits

B: 12b+8d

Step-by-step explanation:

I just did it.

Answer:

sample.

Step-by-step explanation:

It is given that a department store wants to know what motivated customers to visit their store on that particular day.

We need to fill the blank.

Since 80 percent of the customers are male, researchers have decided to collect a ____ by ensuring that 8 out of every 10  survey participants are male.

For survey, researchers need small part of whole data, i.e., sample.

So, the required answer is "sample".

Since 80 percent of the customers are male, researchers have decided to collect a sample by ensuring that 8 out of every 10  survey participants are male.

Since 80 percent of the customers are male, researchers have decided to collect an erroneous sample by ensuring that 8 out of every 10 survey participants are male. This is a sampling error.

A sampling error can arise when the said sample is not representative of the entire population as is in the case of the example above.

To eliminate the statistical error, the sample must be collected in such a way that the probability of every member of the population being included in the sample is equal to 1.

Learn more about sampling errors at:
https://brainly.com/question/5137866

Answer:

B. a^2x

Step-by-step explanation:

squaring a^x gives. (a^x)²

by applying the rules of indices, ^2 multiplies x therefore making it a^2x

Answer: 3.2

Step-by-step explanation:

Answer:

1.5 miles

Step-by-step explanation:

Step 1: Convert 6 miles per hour to miles per minutes

6 mph = 0.1 mpm

Step 2: Multiply 15 and 0.1 mph

15(1/10) = 1.5

Answer:

c

Step-by-step explanation:

The statement i.e. true is that when the baby gained the weight so the price of the phone should be increased.

Since the  correlation coefficient should be 0.87 that shows between the baby's weight and the price of a smartphone.

So here it shows the healthy and positive relationship between the weight and the price.

Therefore, the option c is correct.

learn more about correlation here: https://brainly.com/question/1564293

Answer:

x=65

Step-by-step explanation:

h²=25*(169-25)=25*144=3600

x²=h²+25²=3600+625=4225

x=√4225

x=65

Answer:

1/10 or ( 0.1 )

Step-by-step explanation:

no. of even no.s greater than 80 = 10

Total no.of numbers = 100

So P(no. of even no.s greater than 80) = 10/100 = 1/10

Answer:

There are 10 even numbers greater than 80.

So Probability of getting an even numbers greater than 80 is 10/100 (1/10)

Hope it helps you. Please mark Brainliest :)

Have a nice day PPLS!!!!!!!