A) 35° B) 55° C) 70° D) 145° In the figure above, lines and m are parallel and lines s and t are parallel. If the measure of 21 is 35°, what is the measure of Z2?​

The correct answer is [b] ΔHGF and ΔABC.

In geometry, the two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

In geometry, the two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into the one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. This indicates that either object may be precisely aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are congruent. The paper may be turned over.

Triangles with two pairs of congruent sides and an included congruent angle are said to be congruent by ASA.

According to the graph, sides TU, FG, and BC are congruent, as well as sides TV, HG, and AB. Additionally, it shows that angles G and B are congruent as well as angles U, F, and C. Triangle TUV is eliminated because ASA cannot find another triangle that is equivalent to angle U of triangle TUV using the information provided.

The only triangles left are FGH and ABC. These triangles are congruent by ASA since it is clear that angles G and B are included angles.

To know more about graph visit: https://brainly.com/question/17267403

#SPJ9

The height of a the given shape which has a volume of 7/8, length of 5/8, width of 7/9 is 9/5

Volume = Length × width × height

7/8 = 5/8 × 7/9 × x

7/8 = 35/72x

x = 7/8 ÷ 35/72

= 7/8 × 72/35

= 9/5

So therefore, the height of the given shape is 9/5

Read more on volume:

https://brainly.com/question/1972490

#SPJ1

Answer: (8,-4), (6,-2), (5,-1)

Answer:

the percentage change is a 60% change.

Step-by-step explanation:

A change from 5 to 2 represents a negative change (decrease) of -60%

Use the formula found below on this webpage to find the percent change by replacing the given values:

Percent change = New - Old

|Old|

× 100%

Percent change = 2 - 5

|5|

× 100% =

-3

5

× 100 = -60% (decrease)

Where: 5 is the old value and 2 is the new value. In this case we have a negative change (decrease) of -60 percent because the new value is smaller than the old value.

Using algebraic identities, we found that for B=2 and B= -2 , the trinomial x² + Bx +1  makes a perfect square.

Algebraic identities are the identities which aids in solving products or powers of algebraic expressions. Most common identities are :

(a+ b)² = a² + 2ab + b²

(a- b)² = a² - 2ab + b²

a² -b² = (a+ b) (a- b), where a and b can be variable or constants or algebraic expressions.

Let the perfect square of the trinomial be (x +a)²

x² + Bx +1 = (x+ a)² = x² + 2xa + a² (using identity (a+ b)² = a² + 2ab + b²)

⇒ x² + Bx +1  = x² + 2xa + a²

⇒ Bx = 2xa , a² =1

⇒B = 2a , a =± 1

if a =1 ⇒ B = 2

If a = -1 , B = -2

For B = 2 , x² + Bx +1  = x² + 2(1)x +1² = (x+1)² ( ∵(a+ b)² = a² + 2ab + b²)

For B = -2 , x² + Bx +1  = x² -2x + (-1)² = x² -2x +1 = ( x-1)²  (∵(a- b)² = a² -2ab  

                                                                                                                 + b²)

Thus, the given trinomial x² + Bx +1  is perfect square when B =2 or -2

Also, Learn more about the identities of algebraic expression from the link below:

https://brainly.com/question/26838190

#SPJ1

Answer:

=(3x - 2y( (4x - 3y)

Step-by-step explanation:

We have,

12x2 – 17xy + 6y2

The coefficient of x2 is 12

The coefficient of x is -17y

Constant term is 6y2

So, we express the middle term -17xy as -9xy – 8xy

12x2 -17xy+ 6y2 = 12x2 – 9xy – 8xy + 6y2

= 3x (4x – 3y) – 2y (4x – 3y)

= (3x – 2y) (4x – 3y)

The starting point is 1,365 miles .

Given :

→ initial time of plane = 1.7 hours

→ initial speed = 140 mph

→ final time of plane = 9.6 hours

→ final speed = same = 140 mph

The initial displacement of the plane is :

distance = speed × time

= 1.7 × 140

= 238 miles

The final displacement of the plane is :
distance = 9.6 × 140

= 1,344 miles

The angles between initial and final displacement is :

100° - 10 ° = 90 °

The distance of the plane from its starting point is calculated as follows

d = [tex]\sqrt{238^{2}+ 1344^{2} }[/tex]

d  = [tex]\sqrt{56644 + 1806336}[/tex]

   = [tex]\sqrt{1862980}[/tex]

    = 1364.9 miles ≈ 1,365 miles

To know more distance visit:

https://brainly.com/question/26264531

#SPJ9

Answer:

54.4 %

Explanation:

The percent change in net sales can be calculated as:

Where the final number is the net sales in quarter 2 and the initial number is the net sales in quarter 1. Replacing the values by 170 and 110, we get:

Therefore, the answer is:

percent change = 54.5 %

26 = (110 - x)/2

52 = 110 - x

x = 110 - 52

x = 58°

-6x-11=19/+11 <=>

<=> -6x=30/:(-6) <=>

<=> x=-5

Answer:

-1/4

Explanation:

To write the decimal -0.25 as a fraction we need to multiply and divide by 100 as follows:

We multiply by 100 because there are 2 digits after the decimal point.

Then, we need to simplify the fraction, so we can divide the numerator and the denominator by 25 as:

So, the fraction in its simplest form is -1/4

Answer:

Step-by-step explanation:

If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour

The equation is

w = 0.75f

Where w is the number of cups waters needed for f cups of flour.

Here w is is dependent variable and f is the independent variable

We can see that w is proportional to the f, the 0.75 is the constant.

w = 0.75f

Move the f to left hand side of the equation

w/f = 0.75

Hence, If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour

Learn more about proportional here

brainly.com/question/12917806

#SPJ1

The probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

For the given question;

The data for the vehicles registered in the united states is given as-

The formula for the z score is-

z = (x - μ)/(σ/√n)

Put the values.

√n = √36 = 6

For x = 98 months

z = (98 - 96)/(15/6)

z = 0.8

p(z < 0.8) = 0.7881

For x = 100 months

z = (100 - 96)/(15/6)

z = 1.6

p(z < 1.6) = 0.9452

P(0.8<x<1.6) = 0.9452 - 0.7881

P(0.8<x<1.6) = 0.1571

Thus, the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

To know more about the z-score, here

brainly.com/question/15333077

#SPJ4

Step-by-step explanation:

the y-intercept (b) is the easiest :

it is the y-value, when x = 0 : -3

the slope (m) is the ratio (y coordinate difference / x coordinate difference) when going from 1 point to another.

so, we need to identify 2 points in the line.

one we have already with b : (0, -3)

another is the x-axis intercept, which is clearly (4, 0)

the difference is not important, but we need to use the same for both (x and y).

I prefer to go from left to right, so from (0, -3) to (4, 0) :

x changes by +4 (from 0 to 4)

y changes by +3 (from -3 to 0)

the slope is +3/+4 = 3/4

The monomial in standard form is 6x¹¹y¹⁸.

The given expression is

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]

We to write the expression as a monomial in standard form

Monomial is an expression having a single term. It can be represented as kxⁿ, where k is any integer often known as the coefficient, x represents the variable/s in the given expression and n denotes the power.

In the expression

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]

we first need to multiply the powers

using the formula

(mn)ˣ = mˣnˣ

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}\\(-3x^3y^{2.3}) .(-\frac{2}{3}x^{2.4} y^{3.4} )\\(-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\[/tex]

Now, we need to multiply both the terms

The following formula is used

xᵃ . xᵇ = xᵃ+ᵇ

[tex](-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\\\-3(-\frac{2}{3})x^{3+8} y^{6+12} \\\\6x^{11}y^{18}[/tex]

Therefore the monomial in standard form is 6x¹¹y¹⁸.

To learn more about monomial refer here

https://brainly.com/question/102541

#SPJ1

Substitution method - the points are (-6, -11/2),(-4,-3), (-8/5,0), (0,2) and (4,7)

what is the substitution method?

To solve many simultaneous linear equations, use the substitution method in algebra. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.

we are given the equation,

5x - 4y = -8

case I

when x = -6

5(-6) - 4y  = -8

-30 - 4y = -8

-4y = -8 + 30

-4y = 22

y = -(22/4)

y = -11/2

(x,y) = (-6, -11/2)

case II

when y = -3

5x - 4(-3) = -8

5x + 12 = -8

5x = -8 -12

5x = -20

x = -20/5

x = -4

(x,y) = (-4,-3)

case III

when y = 0

5x - 4y = -8

5x - 4(0) = -8

5x = -8

x = -8/5

(x,y) = (-8/5,0)

case III

when x = 0

5(0) - 4y = -8

0 - 4y = - 8

y= 8/4

y = 2

(x,y) = (0,2)

case IV

when x = 4

5(4) - 4y = -8

20 - 4y = -8

-4y = -8-20

-4y = -28

y = 28/4

y = 7

(x,y) = (4,7)

for more information on the substitution method visit:
https://brainly.com/question/22340165
#SPJ13

The three responses that can show a number of friends Wes could divide his tokens among evenly include:

25 tokens each for 2 friends.

5 tokens each for 5 friends.

10 tokens for 5 friends.

From the information, Wes wants to treat his friends to some arcade games. He has 50 game tokens.

It should be noted that this information simply wants you to illustrate the factors of 50.

Therefore, the factors are 2, 5, 10, 25 and 50.

Therefore, 25 for 2 friends will be 50. Same with 5 for 10 friends. In this case, it should be noted that 25 × 2 = 50 and 5 × 10 = 50. This gives the original value and shows how he can divide the game tokens equally.

Learn more about factor on

brainly.com/question/25829061

#SPJ1

The problems in the test are 16.

In the given case a student missed four problems on a test.

The test happened to be a mathematics test and the student scored a total percentage of 75%.

It is mentioned that every question has of same score values.

To find out how many problems were actually on the test we need to solve the problem by following the steps.  

Let,

Questions not attempted ( x ) = 4

Percentage gained ( y ) = 75%

The percentage lost is 25%

The total questions in the test are;

         → A = (100/25) * 4

            A = 16

Therefore, the questions in the test are 16.

To learn more about Percentage click here:

brainly.com/question/28269290

#SPJ4

Answer: 9 square inches

Step-by-step explanation:

a computer randomly selects 800 names from a list of all registered voters. Then option C  is correct  that is Simple random sampling

A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.

the complete question is

Identify the sampling method as simple random​ sampling, systematic​ sampling, convenience​ sampling, or stratified sampling. A computer randomly selects 800 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.

Choose the correct sampling technique below.

A. Systematic sampling

B. Convenience sampling

C. Simple random sampling

D. Stratified sampling

learn more about of sample method here

https://brainly.com/question/15836453

#SPJ4

According to a government study among adults the percent of the adults spend more than $2,775 per year on reading and entertainment is

Given data form the question

the mean amount spent per year on reading and entertainment is $1,875

standard deviation of $640

what percent of the adults spend more than $2,775 per year on reading and entertainment

Definition of variables

mean sample, μ = $1,875

standard deviation, σ =  $640

measure X = $2,775

For normal distribution, the z-score of a measure X with mean μ and standard deviation σ  is given by as follows:

Z = ( X - μ ) / σ

Z = (2775 - 1875) / 640

Z = 1.40625 gives p-value of 0.0798250014

This is equivalents to 7.98%

Learn more about normally distributed variable at:

https://brainly.com/question/28948351

#SPJ1

The shortest side is 22 meters in the mentioned quadrilateral.

Let us assume the length of first side be x. So, the other three sides of length will be (x + 1), (x + 2) and (x + 3). The perimeter is sum of all sides of the quadrilateral.

Keep the values in the formula of perimeter -

94 = x + x + 1 + x + 2 + x + 3

Performing addition on Right Hand Side of the equation

94 = 4x + 6

Shifting 6 to other side of the equation

4x = 94 - 6

Performing subtraction on Right Hand Side of the equation

4x = 88

Shifting 4 to Right Hand Side of the equation

x = 88 ÷ 4

Performing division

x = 22

Thus, the shortest side of quadrilateral is 22 meters long.

Learn more about quadrilateral -

https://brainly.com/question/23935806

#SPJ9

Answer: [tex]\frac{\sqrt{x}^3 }{3}[/tex]

Step-by-step explanation:

Step 1: Insert f(x) in for the x in g(x). This will give you [tex]\sqrt{x^3}[/tex]

Step 2: Insert [tex]\sqrt{x^3}[/tex] into the x in h(x) giving you [tex]\frac{\sqrt{x}^3 }{3}[/tex]

Answer: 6

Step-by-step explanation:

1. add (0.5 + 4.5) which equals 5, so now you have 2 x 5^2.

2. evaluate the power (5^2) which equals 25 and you end up with 2 x 25 which equals 50.

3. now you have 300 divided by 50.

300 divided by 50 is 6.

The value of the expression 300 divided by 2(0.5 +4.5)²is 6

Simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.

Given an expression, 300 divided by 2(0.5 +4.5)²

300/2(0.5 +4.5)²

= 300/2x5²

= 300/2x25

= 300/50

= 6

Hence, The value of the expression 300 divided by 2(0.5 +4.5)²is 6

For more references on simplification, click;

https://brainly.com/question/2804192

#SPJ2

The relationship has no relation to continental drift theory, as it is a relation between distance and time, not distance and elevation.

The continental drift theory states that the world's tectonic plates are in constant motion over time.

This is supported by the fact that some millions of years ago, there was only one continent, named Pangea, and now we have the continents as we know. These continents are also moving a small amount a year.

In this problem, the elevation decreases and the distance increases, however, the continental drift theory should have the distance increasing or decreasing over time, hence the graph relationship has no relation to the continental drift theory.

More can be learned about continental drift theory at https://brainly.com/question/14691551

#SPJ1

Answer:

Step-by-step explanation:

2038

Answer:

p > -10/3

Step-by-step explanation:

-4<6+3p

-10<3p

p>-10/3

:]

Answer: p > 10/-3

Step-by-step explanation:

1) Remove the whole numbers next to the variable

Add 10 on both sides.

-3p < 10

2) Set x by itself

Divide -3 on both sides. Dividing -3 will flip the operator sign. (Dividing/Multiplying negative number flips the sign)

p > 10/-3

The missing entries are (a) $686, (b) $635, (c) $1035, (d) $1010, (e) $938.88 and (f) $447.37.

Debit card is a card owned by a person for which the money used for transaction will be withdrawn or added into the account of the holder immediately.

Given is a table showing the transactions of Gino with his debit card.

He has an initial deposit amount of $778.19.

New balance in the account will be the difference of previous balance and the payment amount.

He paid $92.19 for baseball bat.

a = $778.19 - 92.19 = $686

He paid $51.00 for gas.

b = $686 - $51 = $635

He deposited $400.

c = $635 + $400 = $1035

He paid $25 for gas.

d = $1035 - $25 = $1010

He paid $71.12 for dinner at Spooner's on the beach.

e = $1010 - $71.12 = $938.88

He paid $491.51 for the books for all semester.

f = $938.88 - $491.51 = $447.37

Hence the missing entries are found.

Learn more about Debit Card here :

https://brainly.com/question/27934503

#SPJ2