When parallel lines are cut by a transversal, why are same-side interior angles supplementary? Use the fact that a line parallel to the transversal can be drawn to form a parallelogram in your answer.
A because the sum of the measures of a pair of same-side interior angles is equal to one-fourth the number of degrees in a parallelogram

B because the sum of the measures of a pair of same-side interior angles is equal to one-half the number of degrees in a parallelogram

C because the sum of the measures of a pair of same-side interior angles is equal to the number of degrees in a parallelogram

D because the sum of the measures of a pair of same-side interior angles is equal to twice the number of degrees in a parallelogram

Answer:

The son is now 20. The father is now 60

Step-by-step explanation:

The son was 10, ten years ago. Five times that was 50 years, the age of the father. Now they have both aged 10 years, and the son is 20 and the father is 60. Add them together, and it makes 80.

CAN EXPLAIN FURTHER

appreciate brainliest but it doesn't matter

Answer:

20 years old

Step-by-step explanation:

10 → Ten years ago

50 → The father was five times as old as his son.

Current Ages

20 → Son

60 → Father

[tex]20 + 60 = 80[/tex]

I am joyous to assist you anytime.

Answer:

x=17

Step-by-step explanation:

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

In the triangle ABC

m∠A+m∠B+m∠C=180°

substitute the values and solve for m∠C

4x+49°+m∠C=180°

m∠C=180°-49°-4x

m∠C=131°-4x

In the triangle EDC

m∠E+m∠D+m∠C=180°

we have

m∠E=x

m∠D=100°

m∠C=131°-4x -----> by vertical angles

substitute the values

[tex]x+100\°+(131\°-4x)=180\°\\-3x+231\°=180\°\\3x=231\°-180\°\\3x=51\°\\x=17[/tex]

The value of x for the given geometric problem is determined to be 17 by using the concept that the sum of the internal angles of a triangle is equal to 180 degrees.

We are looking to find the value of x where two triangles are involved.

First, according to the laws of geometry, the sum of the internal angles of a triangle must be equal to 180 degrees.

So, in triangle ABC, m∠A+m∠B+m∠C=180°.

If we have m∠A = 4x and m∠B = 49°, then by substituting these values, m∠C becomes 180° - (49° + 4x) i.e 131° - 4x.

In the triangle EDC, the summation m∠E + m∠D + m∠C also equals 180°.

If m∠E=x, m∠D=100°, and m∠C=131°-4x, we can form an equation of x + 100 + 131 - 4x = 180 which simplifies to 231 - 3x = 180. Solving this equation gives x = 17.

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Answer: May you please have answer choices. Please forgive me if I am being rude but I am not.

Answer:

Yes, the total price is proportional to the pounds of oranges she purchased.

Step-by-step explanation:

The price of oranges is $0.78 per pound.

So, the price $0.78 corresponds to one pound, in a way, that is called direct proportionality.

This means that the price will increase or decrease in a constant ratio, depending on the amount of pounds purchased.

For example:

If she buys 1 pound of oranges she will pay $0.78. Ratio is 0.78 (0.78/1)

If she buys 2 pounds of oranges she will pay $1.56. Ratio is 0.78 (1.56/2)

If she buys 2.5 pounds of oranges she will pay $1.95. Ratio is 0.78 (1.95/2.5)

If she buys 3 pounds of oranges she will pay $2.34. Ratio is 0.78(2.34/3)

We can see that ratio is constant, then we can say that the total price she pays is proportional to the pounds of oranged purchased.

Answer:

a

Step-by-step explanation:

a. x=4, y=2

plug it in:

4+20=6 true

b. x=3, y=3

3+3=6

3=3+2

3=5 not equal

c. x=2,y=4

2+4=6

2=4+2

2=6 not true

d. x=6, y=4

6+4=6 not true

6=4+2

Answer:

D

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ), thus

C(1, 2 ) → C'(2, - 1 ) → D

The image after the rotation is C' (2, -1), the correct option is D.

Here we have the point (1, 2), and we have a rotation of 90° clockwise.

Notice that our point is on the first quadrant, then a rotation of 90° will leave us in the fourth quadrant.

The change that we will have is a permutation of the values, and the y-value must become negative, then the transformation gives:

(1, 2) ---> (2, -1)

The correct option is D.

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Answer:

I think the answer is j > 1

To find out the total cost after using a coupon, you first add the prices of the items - $1.29 for chips and $0.89 for a drink, totalling $2.18. Then subtract the value of the coupon, $0.75, from this amount. The final cost would be $1.43.

The first step in solving this problem is to add the prices of the bag of chips and the drink. According to the prices given, the chips cost $1.29 and the drink costs $0.89.

By adding these together, you will get the total cost before using the coupon. The sum of $1.29 and $0.89 equals $2.18. This is the total cost without any discounts.

Next, you need to take into account the coupon for $0.75 off the total price. Subtracting this from the initial cost, we get: $2.18 - $0.75 = $1.43.

So, the final cost of the bag of chips and the drink after using the 75 cents coupon would be $1.43.

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Adam is carrying a total of 15.4 pounds of books to the classroom, calculated by multiplying the weight of one book (3.85 pounds) by the number of books (4).

The subject of this question is Mathematics, and it is appropriate for a middle school grade level. The student has asked about the total weight Adam is carrying when he transports four books to the classroom, with each book weighing 3.85 pounds.

To find the total weight of the books Adam is carrying, we multiply the weight of one book by the number of books:

Therefore, Adam is carrying approximately 15.4 pounds of books to the classroom.

Answer:

a.  13xyz + 9 + 2xyz + 3

13xyz+2xyz+ 9+3 ( combine like terms)

15xyz+12

b. 6ab + (–2ab) + 4 + 6

6ab-2ab+4+6

4ab+10

Answer:

a. 13xyz + 9 + 2xyz + 3

Combine the coefficents of the like monomials.

(13 + 2 = 15)

15xyz + 9 + 3

Add the constants (9 + 3 = 12).

Answer: 15xyz + 12

b. 6ab + (–2ab) + 4 + 6

Combine the coefficents of the like monomials.

[6 + (–2) = 4]

4ab + 4 + 6

Add the constants (4 + 6 = 10).

Answer: 4ab + 10

Step-by-step explanation:

straight from Penn

Answer:

Its 24

Step-by-step explanation:

Answer:

P = 52.5

Step-by-step explanation:

P = ( L + L ) + ( W + W )

P = ( 12.25 + 12.25 ) + ( 14 + 14 )

P = 24.5 + 28

P = 52.5

Hello!

because of the way Clinton's yard is measured, it must be a rectangle.

here is the equation to find the perimeter of a rectangle:

L2 + W2 = P

12.25 * 2 = 24.5

14 * 2 = 28

24.5 + 28 = 52.5

your answer is: The perimeter of Clinton's yard is 52.5 Meters

I hope this helps, and have a nice day!

Answer:

Part 1) The equation is [tex]h=42y[/tex]

Part 2) The number of hats Paula can knit is 42 per yard of yarn

Part 3) see the procedure

Part 4) For 378 yards of yarn Paula can knit 9 hats

Step-by-step explanation:

Let

h -----> the number of hats

y ----> the amount of yarn in yards  

k ---> constant of proportionality

Part 1) Write an equation to represent the relationship between the numbers of yards of yarn Paula has and the number of hats she can knit

we know that

A relationship between two variables, h, and y, represent a proportional variation if it can be expressed in the form [tex]h/y=k[/tex] or [tex]h=ky[/tex]

we have

[tex]k=42[/tex]

substitute

[tex]h=42y[/tex]

Part 2) What does the constant if proportionality 42, represent in this problem?

The constant of proportionality represent the slope of the linear equation

The value of the slope is [tex]42\ \frac{hats}{yd}[/tex]

That means that the number of hats Paula can knit is 42 per yard of yarn

Part 3) Complete the table showing the yards of yarn and the number of hats Paula can knit

we have

[tex]h=42y[/tex]

Part a) For y=0 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(0)=0\ hats[/tex]

Part b) For h=3 hats Find the value of y

substitute in the linear equation the value of h and solve for y

[tex]3=42y[/tex]

[tex]y=3/42\ yd[/tex]  ----> [tex]y=1/14\ yd[/tex]

Part c) For y=210 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(210)=8,820\ hats[/tex]

Part d) For y=378 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(378)=15,876\ hats[/tex]

Part 3) For h=11 hats Find the value of y

substitute in the linear equation the value of h and solve for y

[tex]11=42y[/tex]

[tex]y=11/42\ yd[/tex]  

Part 4) Interpret the meaning of the point (378,9)

we have that

y=378 yd

h=9 hats

That means -----> For 378 yards of yarn Paula can knit 9 hats

Answer:

yes

Step-by-step explanation:

yes thank you this is helping me a lot

Answer:

See below.

Step-by-step explanation:

There is an infinite number of values of x that make each answer true. The problem is asking "for which value" with value in the singular, so I thought it was asking to choose one answer from several, and only one was correct.

1a.

Any number between 8 and 9 is correct.

Examples: 8.1, 8.01, 8.2, 8.3, 8.4, 8.9, 8.95, etc.

As I wrote above, there is an infinite number of correct answers.

1b.

Examples: 8.91, 8.92, 8.93, 8.99, 8.905, 8.97, etc.

Answer:

Assuming that inequalities are a valid answer for this question:

1a. 8 < x < 9

1b. 8.9 < x < 9.1

Step-by-step explanation:

Really, there's no exact answer. For example, on 1a, it could be 8.1, 8.11, 8.2, 8.99999, etc. Inequalities are used to denote the fact that the x value can be anywhere between two values. In 1a, x is between 8 and 9, and in 2a, x is between 8.9 and 9.1.

Final answer:

To find the ratio of nonwinners in group A to nonwinners in group B, subtract the number of winners from the total number of people in each group. The ratio of nonwinners in group A to nonwinners in group B is therefore 156:319.

Explanation:

To find the ratio of nonwinners in group A to nonwinners in group B, we need to determine the number of winners in each group and subtract that from the total number of people in each group to find the nonwinners.

In group A, three-fifths of the 390 people will win fuel cards, which is equal to (3/5) * 390 = 234 people winning cards. So, the number of nonwinners in group A is 390 - 234 = 156.

In group B, the same number of fuel cards will be given out, but there are 553 people in that group. So, the number of nonwinners in group B is 553 - 234 = 319.

The ratio of nonwinners in group A to nonwinners in group B is therefore 156:319.

Answer:

the last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

the last one

The correct answer is B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Yes, they have a proportional relationship.

The table shows sequences, where x-values increase +3, and y-values increase +5, that is, while x increases 3 unites, y increases 5 units, this ratio between variables can be described as the slope:

[tex]m=\frac{13-(-2)}{12-3} =\frac{15}{9}=\frac{5}{3}[/tex]

This fraction or ratio is referring to what we said in words, while y increases 5 units, x increases 3 units. We observe that is a positive ration, this means that magnitudes are both increasing.

Therefore, the right answer is the first one A.

[tex]\bf \underset{\leftarrow \qquad \textit{\large 7x-10}\qquad \to }{\stackrel{4x-29}{\boxed{B}\rule[0.35em]{10em}{0.25pt}} C\stackrel{5x-9}{\rule[0.35em]{17em}{0.25pt}\boxed{D}}} \\\\\\ BD=BC+CD\implies 7x-10=(4x-29)+(5x-9) \\\\\\ 7x-10=9x-38\implies 7x+28=9x\implies 28=2x \\\\\\ \cfrac{28}{2}=x\implies 14=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{BC}{4(14)-29\implies 27}~\hfill \stackrel{CD}{5(14)-9\implies 61}~\hfill \stackrel{BD}{7(14)-10\implies 88}[/tex]

Answer:

mean = 5

Step-by-step explanation:

"mean" is another term for "average"

to find the mean, you have to add all the integers up, and divide by the number of integers there are.

So you have to combine all the numbers together

-26 +39 -10 -16 +12 +31 = 30

Now you have to divide by 6, since there are 6 integers that you combined to get 30

30/6 = 5

the mean = 5

Hope this helps!

If you have any questions, feel free to ask :)

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this firm use the method of completing the square

Factor out - 1 from each term

y = - (x² - 9x + 12)[tex]\frac{33}{4}[/tex]

To complete the square

add/subtract (half the coefficient of the x- term )² to x² - 9x

y = - (x² + 2( - [tex]\frac{9}{2}[/tex])x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 12 )

  = - ( (x - [tex]\frac{9}{2}[/tex])² - [tex]\frac{33}{4}[/tex] )

y = - (x - [tex]\frac{9}{2}[/tex] )² + [tex]\frac{33}{4}[/tex] ← in vertex form

Answer:

470

Step-by-step explanation:

1000 x 0.53 = 530

1000 - 530 = 470

Answer:

14.14

Step-by-step explanation:

10[tex]10^{2} +10^{2} =x^{2}[/tex]

Simplifying gives you:

10\sqrt{2} ≈ 14.14213562...

The length of the path through Chi's flower garden is approximately 14.14 feet, rounded to two decimal places.

We have,

To find the length of the path through the flower garden, you can use the Pythagorean theorem since the path forms a right-angled triangle inside the square garden.

The garden is a square with a side length of 10 feet.

The path goes from one corner of the square to the opposite corner, forming the hypotenuse of a right-angled triangle.

The other two sides of the triangle are the sides of the square, which are also 10 feet each.

Using the Pythagorean theorem, you can find the length of the hypotenuse (the path):

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse (the path), and a and b are the lengths of the other two sides (which are both 10 feet in this case).

[tex]c^2 = 10^2 + 10^2[/tex]

c² = 100 + 100

c² = 200

Now, take the square root of both sides to find the length of the path (c):

c = √200 ≈ 14.14 feet

Thus,

The length of the path through Chi's flower garden is approximately 14.14 feet, rounded to two decimal places.

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Answer:

g(3)=9-7=2

f(2)=5×2-4=10-4=6

Answer:

Step-by-step explanation:

f(x)=5x-4 g(x)=3x-7

g(3) = 3(3)-7=2

f(g(3))=f(2) =5(2)-4 = 6

Answer:

8 hours

Step-by-step explanation:

81 - 17 = 64

64/8 = 8

A: 8 hours

A function assigns the value of each element of one set to the other specific element of another set. The number of hours for which Emily rents the bike is 8.

A function assigns the value of each element of one set to the other specific element of another set.

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given that Molly's Bikes rents bikes for $17 plus $8 per hour. Therefore, for x number of hours the function to calculate the total rent can be written as,

Total rent, f(x) = $17 + $8(x)

Now, if Emily paid $81 to rent a bike. The number of hours can be calculated as,

f(x) = $17 + $8(x)

$81 = $17 + $8(x)

$81 - $17 = $8(x)

$64 = $8(x)

x = $64 / 8x

x = 8

Hence, the number of hours for which Emily rents the bike is 8.

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Answer:

they are multiplicative inverses because to find the inverse of a number you change it from positive to negative or vice versa, and you have to change it to it's inverse. to do this you have to put it in fraction form if it isn't already (so 5 would be 5/1) and flip it (5/1 flipped would be 1/5)

Step-by-step explanation:

They are reciprocals, that is why they are multiplicative inverse.

If we have a number, then reciprocal of that number is called multiplicative inverse of the number.

Example : If m be a number then 1/m is its multiplicative number.

Here the number be -5.

Reciprocal of this number is -1/5

We know that reciprocal of a number is called multiplicative inverse.

So, -5 & -1/5 are multiplicative inverse of each other.

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Answer:

x

Step-by-step explanation:

7x+18−6(x+1)−12

start out with distributive property

7x+18+(-6x)+(-6)+(-12)

then add the common things together

x+0

answer is just x, or infine answers, you could put in anything for x

Answer:

7

Step-by-step explanation:

12+9=21

21 divided by 3 is 7

Answer:

q = 3.636363636 repeating

Step-by-step explanation:

  - 4q + 9 = 7q - 31

   + 4q      + 4q

     9 = 11q - 31

  + 31         + 31

      40 = 11q

      [tex]\frac{40}{11} = \frac{11q}{11}[/tex]

Answer:

[tex]\large\boxed{q=\dfrac{40}{11}}[/tex]

Step-by-step explanation:

[tex]-4q+9=7q-31\qquad\text{subtract 9 from both sides}\\\\-4q+9-9=7q-31-9\\\\-4q=7q-40\qquad\text{subtract }\ 7q\ \text{from both sides}\\\\-4q-7q=7q-7q-40\\\\-11q=-40\qquad\text{divide both sides by -11}\\\\\dfrac{-11q}{-11}=\dfrac{-40}{-11}\\\\q=\dfrac{40}{11}[/tex]