The angle measurements in the diagram are represented by the following expressions.
A= 5x - 15°
B = 2x + 21°
Solve for x and then find the measure of

The Angle Measurements In The Diagram Are Represented By The Following Expressions.A= 5x - 15B = 2x +

Answers

Answer 1

Answer:

45°

Step-by-step explanation:

A and B are Alternate exterior angles and congruent, thus

5x - 15 = 2x + 21 ( subtract 2x from both sides )

3x - 15 = 21 ( add 15 to both sides )

3x = 36 ( divide both sides by 3 )

x = 12

Thus

∠ A = 5x - 15 = 5(12) - 15 = 60 - 15 = 45°

∠ B = 2x + 21 = 2(12) + 21 = 24 + 21 = 45°


Related Questions

what is an equation of the line that passes through the points (4,-6) and (8,-4)​

Answers

Answer:

[tex]y = \frac{1}{2} x - 8[/tex]

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient (also known as slope) and c is the y-intercept (the point through which the line cuts through the y-axis).

[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]

Using the gradient formula above,

[tex]m = \frac{ -4 - ( - 6)}{8 - 4} \\ m = \frac{ - 4 + 6}{4} \\ m = \frac{2}{4} \\ m = \frac{1}{2} [/tex]

Substitute the value of m into the equation:

y= ½x +c

To find the value of c, substitute a pair of coordinates.

When x=4, y= -6,

-6= ½(4) +c

-6= 2 +c

c= -6 -2 (-2 on both sides)

c= -8 (simplify)

Thus, the equation of the line is y= ½x -8.

State if the given functions are inverses. f(x) = 1/x + 3 g(x) = 4/x + 2

Answers

Answer:

  they are not inverses

Step-by-step explanation:

f(1) = 1/1 +3 = 1 +3 = 4

g(4) = 4/4 +2 = 1 +2 = 3 ≠ 1

If the functions were inverses, we would have g(f(1)) = 1, which we do not.

The given functions  are not inverses.

_____

The same would be true if your functions were

  f(x) = 1/(x+3) and g(x) = 4/(x+2)

  f(1) = 1/(1+3) = 1/4

  g(1/4) = 4/(1/4 +2) = 4/(9/4) = 16/9 ≠ 1

Kane is training for a marathone. He started by running 3 miles during every training session. Each week plans to increase the distance of his run by 1/4 mile

Answers

Complete question :

Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the diatance kane runs in a training session after w weeks

Answer:

(11 + w ) / 4

Step-by-step explanation:

Given the following :

Initial miles kane plans to cover per session = 3 miles

Increase in miles covered per session = 1/4 mile per week

Hence, distance covered after w weeks :

Using the sum of an arithmetic progression formula:

Tn = a + (n - 1) d

a = first term = Initial / starting distance = 3 miles

n = nth term = number of weeks = w

d = common difference = constant increase in distance per week = 1/4

Hence, after w weeks :

= 3 + (w - 1) × 1/4

= 3 + (w/4 - 1/4)

= 3 + (w - 1) / 4

Taking L. C. M

(12 + w - 1) / 4

(11 + w ) / 4

The expression that shows the distance Kane runs in a training session after w weeks will be; (11 + w ) / 4

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that the Initial miles kane plans to cover per session = 3 miles

The Increase in miles covered per session = 1/4 mile per week

Using the sum of an arithmetic progression formula to calculate the distance covered after w weeks

Tn = a + (n - 1) d

a = first term = 3 miles

n = nth term = number of weeks = w

d = common difference = the constant increase in distance per week = 1/4

Hence, after w weeks,

= 3 + (w - 1) × 1/4

= 3 + (w/4 - 1/4)

= 3 + (w - 1) / 4

= (12 + w - 1) / 4

= (11 + w ) / 4

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Complete question :

Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance kane runs in a training session after w weeks.

what is the square of 3844​

Answers

Answer:62

Step-by-step explanation:

62^2

Simplify the expression: 2( 5 t + J) + 3( 2t + 4 J )

Answers

Answer:

16t + 14J

Step-by-step explanation:

1) First, you have to multiply the numbers

New Expression: 10t + 2J + 6t + 12J

2) Now, you have to find the like terms and add them together

New Expression: 16t + 14J

Hope this helps!

A yard has a perimeter of 400 feet. If eight times the length of the yard equals seventeen times the​ width, what are its​ dimensions?

Answers

Answer:

Length of the rectangular yard = 136 feet

Width of the rectangular yard = 64 feet

Step-by-step explanation:

Let

Width = 17 × width

Length = 8 × length

8l = 17w

l = 17w/8

Perimeter of a rectangular yard = 2(length + width)

400 = 2(17w/8 + w)

400 = 34w/8 + 2w

400 = 17/4w + 2w

400 = 17w+8w/4

400 = 25w/4

Cross product

1600 = 25w

Divide both sides by 25

w = 1600/25

= 64 feet

Recall,

l = 17w/8

= 17*64 / 8

= 1088/8

= 136 feet

Length of the rectangular yard = 136 feet

Width of the rectangular yard = 64 feet

- If there are 12 inches in a foot, what is 4,096 cubic inches converted to cubic feet? a. 28.44 ft3 c. 2.370 ft b. 341.33 ft3 d. 4.096 ft3​

Answers

Step-by-step explanation:

2.370.

One cubic foot equals 1728 cubic inches. So, to convert from cubic inches to cubic feet you should divide your cubic inches figure by 1728.

I hope it helps!

Write 15 less than twice a number

Answers

Answer:

2x-15

Step-by-step explanation:

2x-15

Point A (-8, 7) and Point B (6,-9) form a line segment on a coordinate plane. What is the midpoint of line segment AB

Answers

Answer:

-1,-1

Step-by-step explanation:

it is the midpint (-1,-1)

Answer:

( -1 , -1 )

Step-by-step explanation:

( -8 + 6 / 2 ) , ( 7 + -9 / 2)

( -2 / 2) , ( -2 / 2)

( -1 , -1 )

9 = -3 + n + 2n what does n equal ?

Answers

Step-by-step explanation:

9=-3+n+2n

9+3=n+2n

12=3n

n=12/3

n=4

[tex]9 = - 3 + n + 2n[/tex]

now let's flip this equation to make things easier

[tex] - 3 + n + 2n = 9[/tex]

now move -3 to the other sidewhen we move -3 to the other side it turns into positive 3

[tex]n + 2n = 9 + 3[/tex]

now add the values on both sidesn + 2n will be equal to 3n and 9 + 3 will be equal to 12

[tex]3n = 12[/tex]

now move 3 to the other sidethe multiplication sign that binded 3 and n together will change into division when moved to the other side

[tex]n = \frac{12}{3} [/tex]

when we divide 12 and 3 we will get 4

[tex]n = 4[/tex]

so final answer is 4

hope that helps !

Sara is 7 years older than Sushil. June is 4 years younger than Sushil. If the total of their ages is 87, how old is the eldest of them?

Answers

Answer:

76

Step-by-step explanation:

Answer:

We have:

a) Sushi+7=Sara

b) June=Suhi-4

c) Sushi+Sara+June=87

3 equations with 3 variables, we can solve it.

we can introduce in a) and b) in  c) and we get: Sushi+Sushi+7+ Sushi-4=87

3 sushi+3=87 which gives:

3 sushi= 87-3=84

sushi=84/3=28

Sara= sushi+7 (from b)= 35

June= sushi-4=24

We can check 24+35+28=87 All good

Step-by-step explanation:


[tex]6 \times x = - 24[/tex]
What is the missing number?​

Answers

The missing number is 4

Convert this rational number
to its decimal form and round
to the nearest thousandth.
1/7

Answers

Answer:

0.143

Step-by-step explanation:

1) convert to decimal form: 0.142857

2) rounding to nearest thousandth (3rd decimal place)

3) number is higher than 5 so it rounds up to 0.143

Solve the equation for the variable.

[tex] - 4v - 9 = 3v + 5[/tex]

v = [?]​

Answers

Answer:

-4v -9 = 3v +5

=) -4v -3v = 5 +9

=) -7v =14

=) v = 14/ -7

V = -2

Write the following standard forms into exponential form 3 x 3 x 3 x 3 and 7 x 7.

Answers

Answer: 3^4, 7^2

Step-by-step explanation:

3 times itself 4 times! Seven times itself 2 times

3*3*3*3 = 3 with power of 4
7*7= 7 with power of 2

What is the domain of the relation? {(−4.5, 0), (−3, 9), (0.9, 0), (4, −7.8), (4, 0), (17, 3)}

{0.9, 4, 17}

{−7.8, 0, 3, 9}

{−4.5, −3, 0.9, 4, 17}

{−4.5, −3}

Answers

Answer:

Domain of the relation is Option (c) : {−4.5, −3, 0.9, 4, 17}

what is the distance between (7, -2) and (3,1) pls help fast

Answers

Answer:

it would be 5

Step-by-step explanation:

Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 460 miles on 20 gallons of gas. What is the car's gas mileage?

Answers

Answer:

23

Step-by-step explanation:

because 460 divided by 20 is 23 so the car gets 23 mpg because 460 represents miles and 20 represents gallons of gas

The car's gas mileage is 23 if the test of a new car results in 460 miles on 20 gallons of gas.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Gas mileage is the number of miles you can drive on a gallon of gasoline.

A test of a new car results in 460 miles on 20 gallons of gas.

Let x be the car's gas mileage.

The value of the x can be found as follows:

x = 460/20

x = 23

20 gallons of gas and 460 miles are represented by the numbers.

Thus, the car's gas mileage is 23 if the test of a new car results in 460 miles on 20 gallons of gas.

Learn more about the fraction here:

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. Rahul has 260 coins of Rs. 1, Rs.2 and Rs.5 altogether. The total value of the money is Rs.309. The number of Rs.2 coins is three times the number of Rs.5 coins. Find the number of coins of each type.

Answers

coin of 5 = 20 coins

coin of 2 = 60 coins

coin of 1 = 80 coins


let the number of coin 5 = Rs.x

so the number of coin 2 = 3x

the number of coin 1 = 160 - 4x

so the amount of rs.5 = 5x

the amount of rs.2 = 6x

a/q

5x + 6x + 160 - 4x = 300

7x = 300 - 160

7x = 140

x = 20

Use the distributive property to find the product

Answers

Answer:

1st one: -24a-6b-36c

2nd one: 14mn-12m

Step-by-step explanation:

1st one: Multiply '-6' w/ '4a', 'b', and '6c'

2nd one: Multiply '2m' w/ '7n' and '-6'

The second one is 14mn - 12m and the first is -24a + -6b + -36c

which graph represents The solution to
6x-2x5X +7

Answers

Answer:

Well where are the options for the graphs?

Find the value of x, if x=3/4
1.2(x)+23=156
2.7(x)-45=383
what is the value of x​

Answers

Answer:

he actually looks like a bu to the back of your head and you have to stilud and I think your deadly weapon is a ps4 controller or an official at the lot

I hope this will help

What effect does decreasing the temperature of a room have on a lifespan of a battery?


Which variable is highlighted in red, bolded tex?

Answers

This question is incomplete. There are options in the question (from reference) and no highlight in the red bolded text in the question.

What effect does decreasing the temperature of a room have on a lifespan of a battery?

Which variable is highlighted in red, bolded tex?  

a . Independent

b . Dependent

c . Control

d . None

But the answer to both the independent and dependent variables will be provided and explained in detail.

Answer:

Independent variable: decrease in temperature

Dependent variable: lifespan of battery

 Step-by-step explanation:

The independent variable in an experiment is defined as the variable that can be changed or manipulated in order to find an outcome while the dependent variable is defined as the variable that is influenced by the changes in the independent variable.

In the given example, a decrease in temperature  is the dependent variable as it is changing and the lifespan of battery  is the dependent variable as it is responding to the independent variable ?9decrease in temperature).

Simplify the expression: 4 + 10x + 5 - 9x

Answers

[tex]\text {Hello! Let's Solve this Equation!}[/tex]

[tex]\text {In order to Simplify this Equation you must subtract}[/tex] [tex]\text { it with the same match as it. Let me show what I mean.}[/tex]

[tex]\text {\underline {Subtract}}[/tex]

[tex]\text {10x-9x=1x=x}[/tex]

[tex]\text {\underline {Add}}[/tex]

[tex]\text {4+5=9}[/tex]

[tex]\text {Your Answer would be:}[/tex]

[tex]\fbox{x+9}[/tex]

[tex]\text {Best of Luck!}[/tex]

Hey there!☺

[tex]Answer:\boxed{x+9}[/tex]

[tex]Explanation:[/tex]

[tex]4+10x+5-9x[/tex]

Let's simplify.

[tex]4+10x+5+-9x[/tex]

Now let's combine like terms.

[tex](10x+-9x)+(4+5)[/tex]

[tex]x+9[/tex]

Hope this helps!

Your car's gas tank is 3/4 full before you leave for your trip. When you stop at the gas station, the tank is only 1/12 full. Show the amount of change as a rational number.

Answers

Answer:

2/3

Step-by-step explanation:

Use the fraction bar interactive to find the difference: One-third minus StartFraction 5 over 6 EndFraction

Answers

Answer:

-1/2

Step-by-step explanation:

Answer:

common denominator

6

1/3 - 5/6 difference

-1/2

Step-by-step explanation:

hope I wasn't to late

have a good day guys

:)


Which option is part of designing a set of experimental procedures?
A. Looking for errors in the collected data
B. Developing a question about a phenomenon
C. Identifying the controlled, manipulated, and responding variables
D. Conducting the experiment

Answers

Answer:

Part of designing a set of experimental procedures is:

C. Identifying the controlled, manipulated, and responding variables

What is the answer to this question?

Answers

Answer:

(-6,300)

Step-by-step explanation:

Answer:

(-6,300)

Step-by-step explanation:

(x,y)

then:

x = -6

y = 300

then:

(-6 , 300)

If m∠2 = 125°, m∠12 = 37° and m∠18 = 102°, find the measure ∠1 = f.m∠7 = k.m∠13 = b.m∠3 = g.m∠8 = l.m∠14 = c.m∠4 = h.m∠9 = m.m∠15 = d.m∠5 = i.m∠10 = n.m∠16 = e.m∠6 = j.m∠11 = o.m∠17 =

Answers

Answer:

Step-by-step explanation:

1). Since, m∠2 + m∠1 = 180° [Supplementary angles]

   125° + m∠1 = 180°

   m∠1 = 180° - 125°

   m∠1 = 55°

2). Since ∠7 ≅ ∠12 [alternate interior angles]

   m∠7 = m∠12 = 37°

3). m∠3 = m∠18 = 102° [Alternate exterior angles]

4). m∠8 + m∠3 + m∠7 = 180°

    m∠8 + 102 + 37 = 180

    m∠8 = 41°

5). m∠14 = (m∠7 + m∠8) [Alternate angles]

    m∠14 = 37 + 41 = 78°

6). m∠4 = 180° - m∠3 [Linear pairs]

             = 180 - 102

             = 78°

7). m∠9 = m∠3 = 102° [Vertical angles]

8). m∠15 = m∠2 [Alternate exterior angles]

               = 125°

9). m∠5 = m∠15 [Corresponding angles]

             = 125°

10). m∠10 + m∠5 = 180° [Sum of interior angles on one side of the transversal]

     m∠10 = 180 - 125

               = 55°

10). m∠16 = m∠10 = 55° [Vertical angles]

11). m∠6 = m∠10 = 55° [Alternate interior angles]

12). m∠11 = m∠15 = 125°

13). m∠17 = m∠14 = 78° [Vertical angles]

The answers are given as follows

Given that

a║b

m∠2 = 125°

m∠12 = 37°

m∠18 = 102°

From the identity of supplementary angles

m∠1 + m∠2= 180°

So m∠1 = 180° - 125° = 55°

m∠7 =m∠12 = 37° (Interior opposite angles )

m∠3 = m∠18=102° (Alternate Exterior angles )

m∠8 = 180° - m∠3 -m∠7  = 180°- 139° = 41°

m∠14 = m∠7+ m∠8= 37° + 41° = 78° ( Alternate opposite angles)  

So m∠13 = 180° -78° = 102° (linear pair)

m∠4= 180° - m∠3  = 180° - 102° = 78°

m∠9 =180° - m∠4 = 180° - 78 = 102° (vertically opposite to m∠3)

m∠15 = m∠2 = 125° (Alternate exterior angles)

m∠5 =m∠15 = 125° (Corresponding Angles )

m∠10 =  180° -125° = 55°

m∠16 = m∠10 =55° ( Vertically Opposite Angles)

m∠6 = m∠10 =55°  (Alternate interior angles)

m∠11 = 180 ° -  m∠6° - m∠7° = 180° - 55° - 37° =  88°

m∠17 = 180° - m∠13 = 180° -102° = 78 °

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Expand The Expression
5 (4a + 5b – 3)

Answers

Answer:

20a + 25b - 15

Step-by-step explanation:

Answer:

 I think is:    

5 ( 4a + 5b - 3 )

= 5 × 4a + 5 × 5b - 5 × 3

= 20a + 25b - 13

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