The image provided contains a set of parallel lines, AB and CD, and a transversal line, EF. If angle ∠ a is equal to 135˚, then which of the other angles is equal to 135˚? SELECT ALL THAT APPLY! *
∠ b
∠ h
∠ c
∠ g
∠ e

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You can use Pythagoras theorem as it is a right angle

a^2 + b^2 = c^2

where 'c' is the hypotenuse

Rearrange this to find a side length

c^2 - a^2 = b^2

where 'b' is the missing length

10^2 - 8^2 = b^2

100 - 64 = b^2

b^2 = 36

Square root this to get the answer

b = 6cm

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Answer:

0.27

Step-by-step explanation:

To solve this problem, we will use Set Theory Approach to Probability.

Let U = the Sample Space which consists of all possible tests.

Of course U = {1,2,3 .... ,30}

So, no elements in that.

U = n = 30

Let Q = the event bearing a multiple of 4 No winning ticket, and,

R = the case that has the No. 19 winning ticket

∴

Q  = { 4,  8, 12 , 16 , 20, 24 , 28} ,  and

R  = {19} , so that

Q ∩ R  = ϕ

P(Q ∩R ) = 0

As, n(Q) = 7 , n(R) = 1  , we have,

P (Q) = [tex]\frac{n (A)}{n(U)}[/tex] = [tex]\frac{7}{30}[/tex],  and P (R) = [tex]\frac{1}{30\\}[/tex]

P (Q∪R) = P(Q ) + P(R) − P(A∩B) = [tex]\frac{7}{30}[/tex] +  [tex]\frac{1}{30\\}[/tex] − 0 = [tex]\frac{8\\}{30\\}[/tex]

≅ 0.27 .

Answer:

Step-by-step explanation:

Consider a utlity bill which shows a minimum initial cost plus variable costs dependent upon how many units are sold.

Then:  total cost ≥ (fixed cost) + (unit cost)(number of units sold)  

This involves the "equal to or greater than" concept.

Answer:

the interger would be 15 because you earn 15 so therfore it would be 15.

Step-by-step explanation:

Answer:

b. x = -2

Step-by-step explanation:

x - 8 = -10

x = -10 + 8

x = -2

Answer:

B.)    2 / 15

Step-by-step explanation:

: )

Cute Root: C

Exponential: D

Logarithmic: A

A function assigns the value of each element of one set to the other specific element of another set. The options can be matched with the function as C, D, and A, respectively.

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

The function of different functions is mentioned below.

Hence, the options can be matched with the function as C, D, and A, respectively.

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Answer:

30

Step-by-step explanation:

the area of a parallelogram is its base x height. in this case it will be 6 * 5 = 30

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The area of the parallelogram shaped tapestry is 30 feet².

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides, in which each parallel pair of sides have the same length.

As per the given data:

A tapestry is having a shape of a parallelogram, and we have to find out the area of the parallelogram using the dimensions given.

The base of the parallelogram tapestry (b) = 6 feet

The height of the parallelogram tapestry (h) = 5 feet

The area of a parallelogram is given by the formula:

Area = base × height

By putting the given values in the question:

Area of the tapestry = 6 × 5 feet²

= 30 feet²

Hence, the area of the parallelogram shaped tapestry is 30 feet².

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Answer:

1 infinity

2 one

3 no

4 one

5 infinity

Step-by-step explanation:

Answer: $5

Step-by-step explanation: The interquartile range (IQR) refers to the difference between the upper(75%) quartile and lower(25%) quartile of a distribution. Hence, ensuring that the middle 50% is being captured. With the average given as $60, having a interquartile range capturing the middle 50% as $1 seems so small from a statistical stand point. Similarly, an interquartile range of $100 capturing the middle 50% is also too large and nearly impossible if the average price is $60. However, a price of $5 sit well in between considering the average price of $60

Answer:

[tex] 2 \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] - 2 \frac{1}{3} - ( - 5) = - \frac{(6 + 1)}{3} + 5 \\ \\ = - \frac{7}{3} + 5 \\ \\ = - \frac{7}{3} + \frac{15}{3} \\ \\ = \frac{ - 7 + 15}{3} \\ \\ = \frac{8}{3} \\ \\ = 2 \frac{2}{3} [/tex]

Answer:

Width = 139.445 ft and Length = 1721.11 ft or

Width = 860.555 ft and Length = 278.89 ft

Step-by-step explanation:

If the school has a rectangular shape, we have that its perimeter and area are:

Perimeter = 2*Length + 2*Width

Area = Length * Width

If we just want to cover 3 sides of the school, we can affirm that:

2000 = Length + 2*Width (eq1)

And the area is 240,000 ft2, so:

240000 = Length * Width (eq2)

From (eq1), we have that:

Length = 2000 - 2*Width

Using this value in (eq2), we have:

240000 = (2000 - 2*Width) * Width

240000 = 2000*Width - 2*Width^2

Width^2 - 1000*Width + 120000 = 0

Using Bhaskara's formula, we have:

Delta = 1000^2 - 120000*4 = 520000

sqrt(Delta) = 721.11

Width1 = (1000 + 721.11)/2 = 860.555 ft

Width2 = (1000 - 721.11)/2 = 139.445 ft

If we use Width = 139.445 ft, we will find Length = 1721.11 ft

If we use Width = 860.555 ft, we will find Length = 278.89 ft

Both pairs of dimensions are valid answers, as they would use 2000 feet of gate and the area of the school would be 240,000 ft2

Answer:

c

Step-by-step explanation:

[tex]25\pi + (8*10\pi)+[(35*12)-25\pi]+(35*12)+ 2(15*12)+2(35*15)=\\25\pi +80\pi + (420-25\pi) + 420 + 360 + 1050=\\105\pi-25\pi + 840 +1410=\\80\pi+2250=\\2501.32741229[/tex]

Answer:

4.8 hours

Step-by-step explanation:

First, divide the distance by time to get velocity.

S = D/T

S = 360/4

S = 90 mph

Then, subtract 15 from 90 to get the new speed.

90 - 15 = 75

Lastly divide the distance by the new speed to get time.

T = D/S

T = 360/75

T = 4.8

Therefore, it would take the car 4.8 hours to travel 360 miles at 75 miles per hour.

Answer:

Step-by-step explanation:

total marbles=11+4=15

plastic yellow marbles=4/2=2

P=(plastic marbles)/(total marbles)=2/15

Answer:

2/15

Step-by-step explanation:

11+4 = 15 marbles

Half of the yellow marbles are made of plastic = 2 plastic yellow marbles

P(yellow plastic marbles) = number of yellow plastic marbles / total

                                          =2/15

Answer:

Step-by-step explanation:

Givens

Based on the given information, we can form the following equations.

[tex]b=\frac{1}{2}s[/tex]

Where [tex]b[/tex] is the brush and [tex]s[/tex] is the sketchbook.

[tex]s=\frac{3}{4}p[/tex]

Where [tex]p[/tex] is paint set.

Now, the sum of all three items would give $1.50 of leftover.

[tex]p+b+s=35.25-1.50[/tex]

Replacing expressions, we have

[tex]p+\frac{1}{2}s+\frac{3}{4}p=30.75\\ \frac{7}{4}p +\frac{1}{2}(\frac{3}{4} p)=30.75\\\frac{7}{4}p+\frac{3}{8}p=30.75\\ \frac{56p+12p}{32}=30.75\\ 68p=984\\p=\frac{984}{68}=14.50[/tex]

Then, we use this value to find the other variables

[tex]s=\frac{3}{4}(14.50)=10.88[/tex]

[tex]b=\frac{1}{2}(10.88)=5.44[/tex]

Therefore, the brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.

Answer: paint set costs $18

sketchbook costs $13.5

Brush costs $2.25

Step-by-step explanation:

Let x represent the cost of the paint set.

The sketchbook cost 3/4 the cost of the paint set. It means that the cost of the sketchbook is

3/4 × x = 3x/4

The brush was 1/6 as much as the sketchbook. It means that the cost of the brush is

1/6 × 3x/4 = 3x/24 = x/8

Audrina brought $35.25 to the art supply store. If Audrina had $1.50 leftover after buying these items, it means that the amount spent on the items is

35.25 - 1.5 = 33.75

Therefore,

x + 3x/4 + x/8 = 33.75

Multiplying through by 8, it becomes

8x + 6x + x = 270

15x = 270

x = 270/15

x = 18

The cost of the sketchbook is

(3 × 18)/4 = 13.5

The cost of the brush is

1/8 × 18 = 2.25

Answer:

Is a tangent

Step-by-step explanation:

~ By definition, a tangent to circle is a straight line, presently perpendicular to a radius if one. In this case tangent AB should be perpendicular to the radius. If we were to call the center O, we would say AB should be perpendicular to OA. ~

1. Now let us say at the moment that AB is a tangent. If that is so, it should be that m∠A = 90 degrees ( ° ), provided AB is ⊥ to OA by definition.

2. Now the triangle ABO is a right triangle, and with that is should be that Pythagorean Theorem is applied. This can help us prove if AB is a tangent or not. If Pythagorean Theorem is not applicable it would mean ABO is not a right angle triangle, that AB is not ⊥ to OA, and thus can't be a tangent.

3. Let us say x ⇒ side OA, and that side BO = 9 + 8 + 17:

AB^2 + OA^2  =  BO^2,

15^2 + x^2 = 17^2,

x = 8

4. Now there are two radii present, OA is only one of them. As radii are ≅, OA = other radii, 8 = 8

5. This proves that Pythagorean Theorem is applicable, that ABO is a right triangle, that m∠A = 90°, and that by definition AB is a tangent

* I have already answered this question before *

Answer:

Step-by-step explanation:

Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.

But these things will change direction of the inequality: ...

Don't multiply or divide by a variable (unless you know it is always positive or always negative)

Answer:

C) 32 mpg

This is because to get his miles per gallon,

We divide 634 miles by 19.8 miles to give us 32.0202020....... rounded to 32 mpg

Answer:

240

Step-by-step explanation:

You must multiply 4 by 5, which will give you 20. Then multiply 20 by 12, which will give you the final result of 240.

The trip will take 3 days and 3 hours to complete.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Mr. Tram was planning his trip from Dallas, TX to Detroit, MI.

He knows that the total distance he needs to cover is 1620 km. He usually drives at a speed of 60 km per hour.

That means, the total time,

= 1620/60

= 27 hours.

He is willing to drive up to 8 hours per day.

The trip will take 27/8 = 3 days and 3 hours.

Therefore, the trip will take 27/8 = 3 days and 3 hours.

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Answer:

D

Step-by-step explanation:

only solution C and D are linear function, and they are essentially straight lines. However, C have a x intercept of 5/2, so we rule out option C.

Answer:

Error: +3x should be -3x

x should equal 3

Step-by-step explanation:

In this problem, you have to pay attention how values are transferred from one side to the other. This includes paying attention t the signs.

In 3x + 4 = 8x - 11, you want to try an keep all the values positive

      3x   +   4   =   8x  -   11

    - 3x                - 3x

                  4   =   5x  -   11

                 +11               +11      <--This part of the equation was correct.

                  15  =  5x

                  /5       /5   <--This part of the equation should result in dividing by 5

                  3   =  x

Hope this helps!

Answer:

see below

Step-by-step explanation:

Monica earned twice as much as Samuel

m = 2*s

Divide each side by 2

1/2 m = 1/2 ( 2s)

1/2 m = s

If monica earned 56

1/2 (56) = s

28 =s

Answer:

x = -16

Step-by-step explanation:

[tex]7(x-5) =9x-3 \\7x -35 = 9x - 3\\3- 35 = 9x - 7x\\-32 = 2x\\x = \frac{-32}{2}\\\huge \red{\boxed{x = -16}}[/tex]

Answer:

x = -16

Step-by-step explanation:

We are presented with the equation 7( x - 5 ) = 9x - 3 and we are asked to find the value of x. The first thing to do with equations with brackets is expand them out to make solving the equation easier. Then you want to collect all the 'x' terms to one side and all the numerical values to the other so we can make solving the equation easier.

→ 7( x - 5 ) = 9x - 3

⇒ Expand out the brackets

→ 7x - 35 = 9x - 3

⇒ Minus 9x from both sides to collect the 'x' terms

→ -2x - 35 = -3

⇒ Add -35 to both sides to isolate -2x

→ -2x = 32

⇒ Divide both sides by -2 to isolate x

→ x = -16

Answer:

Its letter B.

Step-by-step explanation:

on edge 2021

The y-intercept of the quadratic function f(x) = (x-6)(x-2) is (0,12).

Given,

f(x) = (x-6)(x-2)

We need to find the y-intercept of this given function f(x).

The point at the y-axis where the function passes through is called the y-intercept.

We take x = 0 for finding y-intercept.

We have,

f(x) = (x-6)(x-2)

Let f(x) = y.

y = (x-6)(x-2)

Put x = 0 in y.

y = (0-6)(0-2)

y = -6 x -2 = 12.

The y-intercept is at 12 on the y-axis and we represent it as (0, 12).

Thus the y-intercept is (0,12).

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Answer:

see below

Step-by-step explanation:

1/2 + 4/6

Get a common denominator of 6

1/2 * 3/3 = 3/6

3/6 + 4/6 = 7/6

We change back to a mixed number

1  1/6

Answer:

7/6 or 1 1/6

Step-by-step explanation:

In this case, you're adding 1/2 plus 4/6.

One strategy you can use to solve this problem is by getting the common denominator.

1/2 is equal to 3/6.

Then you could add 3/6 to 4/6 and you'll get 7/6.

Now depending on the teacher they might want you to have an improper fraction or mixed number.

You can get this mixed number by dividing 7/6 which equals 1 1/6.

Hope this helped :)

Answer:

1. Negative values of b would mean that y can fluctuate between a positive and negative answer depending on what is used for x. In simpler terms, if b < 0, y can be both less than and greater than 0. If b > 0, y can only be greater than 0. This means that only functions where b > 0 can be defined. You would not want to use negative values of b because the answer will not always be a natural number.

2. You cannot consider y = 1^x or y = 0^x to be exponential functions because, while they do utilize an exponent, they do not create exponential growth. 1 multiplied by itself, no matter how many times, will always result in 1. Similarly, 0 multiplied by itself will always result in 0. Therefore, no exponential growth is occurring in either of those equations. (I think this answer is more up to interpretation. I'm sure an argument can be made for those two equations to be considered exponential functions because they have exponents in them. The important thing to recognize here is that no growth occurs with either of them. Therefore, they are different from other "exponential functions").

Answer:

1. If you have a negative base and you try to take the square root of it you get an imaginary number.

2. To get the second point, raising 1 to x will always get you 1 and raising 0 to x will always get you 0.

Step-by-step explanation:

For example if you have the square root of -64, you get +8i and -8i since you're taking the square root. This means that there are no real roots. They're imaginary.

y = 1^x. if we chose the values: 1, 2, 3, 4 to be our x we will always end up with 1 as our answer. If you graph this, you will see a straight horizontal line at y = 1.

This is why it's not an exponential function. It doesn't behave the same way other exponential functions do. You can have a much better understanding if you use a graphing calculator to actually how it looks (try desmos online if you don't have a gc).

Now y = 0^x will also always result in an answer of 0. Take x as 1, 2, 3, 4. 0*0 = 0. 0 * 0 * 0 = 0. I think you get the point. Exponential functions show exponential growth while y = 1^x and y = 0^x are straight horizontal lines, not exponential functions.

Answer:

1.3x-34=136

3x=136+34

3x=170

divide both side by 3

3x/3=170/3

x=56.7 answer

2.3x-34+34=136+34

3x+0=136+34

3x+0=170

3x=170-0

3x=170

divide both side by 3

3x/3=170/3

x=56.7 answer

3.3x=2612+912

3x=3524

divide both side by 3

3x/3=3524/3

x=1174.7 answer

4.3x=3512

divide both side by 3

3x/3=3512/3

x=1170.7 answer

5.(31)31x=3512(31)

31*31x=3512*31

961x=108872

divide both side by 961

961x/961=108872/961

x=113.2903 answer

6.x=10512

the question is still the answer.

Answer:

D) In step 5, he should have multiplied both sides by 1/3

Step-by-step explanation:

============================

Work Shown:

12*sin(2pi/5*x)+10 = 16

12*sin(2pi/5*x) = 16-10

12*sin(2pi/5*x) = 6

sin(2pi/5*x) = 6/12

sin(2pi/5*x) = 0.5

2pi/5*x = arcsin(0.5)

2pi/5*x = pi/6+2pi*n or 2pi/5*x = 5pi/6+2pi*n

2/5*x = 1/6+2*n or 2/5*x = 5/6+2*n

x = (5/2)*(1/6+2*n) or x = (5/2)*(5/6+2*n)

x = 5/12+5n or x = 25/12+5n

these equations form the set of all solutions. The n is any integer.

--------

The two smallest positive solutions occur when n = 0, so,

x = 5/12+5n or x = 25/12+5n

x = 5/12+5*0 or x = 25/12+5*0

x = 5/12 or x = 25/12

--------

Plugging either x value into the expression 12*sin(2pi/5*x)+10 should yield 16, which would confirm the two answers.

Answer:

a

Step-by-step explanation:

12sin(⅖pi x) + 10 = 16

sin(⅖pi x) = 6/12

⅖pi x = sin^-1(½)

⅖pi x = pi/6, pi - pi/6

⅖pi x = pi/6, 5pi/6

x = 5/12, 25/12