Select the vector along which a translation of the plane would map point A to its image T(A).

Given:

Line a is parallel to line b.

As shown:

m∠1 = m∠5 ; the corresponding angles are congruent

m∠2 = m∠2 ; the corresponding angles are congruent

So, the answer will be option 2

Explanation

For the given data, we will have the following:

We are given grouped data, from which we will obtain the mean and standard deviation

Thus, we will have

From the above,

We have the mean to be approximately 44.68.

For the standard deviation

We will have

Thus, we have the standard deviation to be 10.22

f(x)=x ^2

Translate 8.5 units to the left

f(x)= (x + 8.5 )^2

vertical Stretch of a factor of 3

f(x)= 3 (x + 8.5 )^2

7 units down

f(x)= 3 (x + 8.5 )^2 - 7

Jenny's age is 20 years, Lynn is 14 years and Kim is 23 years.

Let's take Jenny as J, Kim as K and, Lynn as L.

From the given statement we get the equation.

As the sum of the age of the three sisters is 57. So we have an equation,

J + K + L = 57 ........(i)

Jenny is 6 years older than Lynn. So the next equation is,

J = 6 + L .......(ii)

Kim is 5 years less than twice her age Lynn. So the equation is,

K = 2L -5 .........(iii)

Putting equations (ii) and (iii) in equation (i)

6 +L + 2L - 5 + L = 57

4L = 56

L = 14

Put the value of L in equations (ii) and (iii)

J = 6 + 14

 = 20

K = 2(14) -5

   = 28 - 5

   = 23

Therefore the age of Jenny is 20 years, Lynn is 14 years and Kim is 23 years.

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We will find the quotient and remainder as follows:

The quotient is 749 and the remainder is 2.

Answer:

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Answer:

16

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors. Hope this helps! <3

Answer:

7 day

Step-by-step explanation:

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Answer: 8 days

Step-by-step explanation:

1) Set up an equation. Let x be the day

3,500 >= 2(816) + x(100+95)

The 816 is just two times (Plane ticket back and forth) so it doesn't go into the x. 100 and 95 do as it is one day.

2) Solve the equation

3,500 >= 2(816) + x(100+95)

1868 >= 195x

9.57 >= x

3) Rounding

Since the x has to be less than 9.57, our next option is 8

whenever you have an equation with one variable on both sides, you might end up with one of the following case:

1. You might end up with an inconsistent equation, therefore there is not solution. Example

x = x+3. If you subtract x on both sides, you get 0=3 which is impossible.

2. You might end up having infinite solutions. Example:

x+6 = x+6. If you subtract x on both sides you get 6 =6 which is true regardless of the value of x.

3. You might end up having only one solution. Example:

3x +2 = x +5

If you subtract x on both sides and subtract 2 on both sides, you get

2x = 3.

then if you divide by two on both sides, you find

x = 3/2. So this equation has one unique solution.

Answer:

B

Step-by-step explanation:

Because i used a calculator

Answer:

C 700

Step-by-step explanation:

7271 is close to 7000

12 is close to 10

So 7000/10 = 700

Answer: 126°

Step-by-step explanation:

Step-by-step explanation: Since every triangle has 180 interior degrees, we can say 2x + 3x + 90° = 180°. Subtract 90° from each side and we get

2x + 3x = 90°

5x = 90°

x = 18°

Plug in x for Angle 2, giving us Angle 2 = 54°

Angle 1 and angle 2 must add up to 180°

Subtract 54° from 180° and we get 126°

We have to write the facts..

It's a little bit easy to understand if you put that numbers in a table.. like this

Now, they ask you an integer that represents a change per hour, and they say you that assume a constant change... then we complement the table with different values per hour until arrive at midnight..

now, you can see that you have two points.. with two coordinates, and you can find a line equation assuming that you have a constant change like this case...

that you place in the cartesian axes.. like this..

You know that you put x values in the horizontal line and y values in the vertical line..

for example, we're gonna place the point (2,1) that means that 2 in x axe and 1 in y axe..

The linear equation parallel to y = 3x - 2 that passes through the point (4, 6) is:

y = 3*x - 6

Here we want to find a linear equation parallel to:

y = 3x - 2

Now, a general linear equation is:

y = m*x + b

Where m is the slope and b is the y-intercept.

Remember that two lines are parallel if and only if the lines have the same slope and different y-intercept.

So our linear equation will be something like:

y = 3*x + c

Now we also want our line to pass through the point (4, 6), then we can replace these values:

6 = 3*4 + c

6 = 12 + c

6 - 12 = c

-6 = c

So the linear equation is:

y = 3*x - 6

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Solution

Total numbers of Doctors = 7

Number of female doctors = 4

Number of male doctors = 3

The probability that the patient is assigned to a female doctor is given as

To express as a percentage

Students takes both French and Spanish is 5 members

Student takes just Spanish = 14 members

Student takes just French = 13 members

Given :

Total numbers of students in class = 35

how many members take spanish = 19

how many members take french = 18

students take neither = 3

To find :

A) Both French and Spanish

B) Just Spanish

C) Just French

Solution :

from venn diagram

a+b+c+d = 35 → 1

b+c = 19 → 2

c+d = 18 → 3

a = 3 → 4

Substract equation 1 and equation 2

a+b+c+d-b-c=35-19

a+d=16 → 5

substract a=3 in the eqution 5

3+d=16

d=13

put d=13 in equation 3

c+d=18

c+13=18

c=5

Students takes both French and Spanish is 5 members

Student takes just Spanish = 14 members

Student takes just French = 13 members

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We go from degrees to radians:

Now, the length of arc CE is:

Where CD = 6 units. Using the angle in radians:

Answer:

B

Step-by-step explanation:

the treaty for defeated Germany was Article 231, commonly known as the "War Guilt Clause," which forced the German nation to accept complete responsibility for initiating World War I. Germany was required to make enormous reparation payments

the given equation is,

and

now the expression is,

2y + z

put the values,

thus, the correct answer is option C

0. From the given graph, the cumulative frequency value indicates the number of students, we have 100 total number of students .

• so,Median is half of the students = 100/2 = 50

the value of test score that corresponds with 50 = 55 test score

• This means that the median , 50 students scored 55 % in the exa,m.

2. Finding the lower quartile Q1 :

since we have 100 students , 100/4 = 25, so Q1 = 25

the value that corresponds with cumulative frequency of 25 = 45

• This means that 25 students scores 45 %

3. Finding the Interquartile range :

IQR = Upper Quartile -Lower Quartile

Upper quartile = Q3 = 75 students : 60 %

and lower quartile = 45%

So,

IQR = 60-45

= 15

• This means that 15 students got 35 %

The percent of change from Week 1 to Week 2 is 10%.

The percent of change from Week 2 to Week 3 is  6.8%

Percentage is the ratio of an amount that is expressed as a number out of 100. Percentage is a measure of frequency. The sign that is used to represent percentage is %.

The percent of change from Week 1 to Week 2 = (number of sit ups in week 2 / number of sit ups in week 1) - 1

(44 / 40) - 1 = 0.1 = 10%

The percent of change from Week 2 to Week 3 = (number of sit ups in week 3 / number of sit ups in week 2) - 1

(47 / 44) - 1 = 0.068 = 6.8%

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The given function is expressed as

y = (6x + 12)/2

In order to determine the inverse of the given function, we would substitute x for y and y for x. Then we would solve for y. It becomes

x = (6y + 12)/2

x = 3y + 6

3y = x - 6

y = (x - 6)/3

y = x/3 - 2

The inverse is

y = x/3 - 2

We are asked to evaluate cot 120,

Equation of 'm'

(y - 6) = - ³/₅ (x - 2)     [point-slope form]

y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

Equation of 'q'

(y - 6) = ⁵/₃ (x - 2)         [point-slope form]

y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

To find the equation for both 'm' and 'q' requires a bit of work. Because neither  'm' nor 'q' has two points to find the slopes of the line, we have to get creative.

The Line 'n' has two points [ (4, 4) & (1, -1) ], and as such we can find the slope of that line. The line 'n' is parallel with 'q' and perpendicular with m.

For finding the slope of 'n'

The slope of the 'n'    =  (y₂ - y₁) ÷ (x₂ - x₁)      

=  (4 - (- 1)) ÷ (4 - 1)  

=  5 ÷ 3

=  ⁵/₃

To estimate the slope of 'q' and 'm'

When two lines exists parallel, they contain the exact slope.

Since 'n' and 'q' exists parallel,

then the slope of q = ⁵/₃

When two lines exists perpendicular, the product of their slopes exists -1. This means that the slopes exists negative-reciprocals of each other.  

Since 'n' and 'm' exists perpendicular

then the slope of m = - ³/₅

Write the equation for 'q' and 'm'

We can now utilize the point-slope form (y - y₁) = m(x - x₁)) to write the equation for the lines

For both 'q' and 'm' let (x₁, y₁) be (2, 6)

Equation of 'm'

(y - 6) = - ³/₅ (x - 2)     [point-slope form]

y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

Equation of 'q'

(y - 6) = ⁵/₃ (x - 2)         [point-slope form]

y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

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Answer:

32,700

Step-by-step explanation:

By definition, the Rate of change is also called "Slope".

The slope of a line can be found dividing the difference between the y-coordinates of two points, by the difference between the x-coordinate of those points:

In this case you know that:

Knowing the following point on the line:

You can set up the following (substituting the slope and the coordinates of those point into the formula)

Now you can solve for "a":

The answer is: Third option.

The expression given as -8+19+8 has a value of 19

From the question, the expression is given as

-8+19+8

Rewrite the expression properly

This is rewritten as follows

-8 + 19 + 8

Collect the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 8 - 8 + 19

Evaluate the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 0 + 19

Finally. we add 0 and 19

So, we have the following equation

-8 + 19 + 8 =  19

Hence, the valye of the expression is 19

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The obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

In mathematics, the addition, subtraction, division, and multiplication of built-in expressions can also be used to specify arithmetic operations.

The expression which is given in the question is below

⇒ -8 + 19 + 8

Rearrange similar terms in the above expression,

⇒ 8 - 8 + 19

Apply the subtraction operation,

⇒ 0 + 19

Apply the addition operation to get the answer,

⇒ 19

Hence, the obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

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Conversion of Degrees Celsius to Degrees Fehrenheit.

Substitute 12 for t in eqn(1), we get

When t =24,

C(24) = 0 , ( does not exist since the graph did not touch the graph)

Hence, the correct answer are:

t =12, C(12) = 104 degrees Fehrenheit, and

t =24, C(24) = 32 degrees Fehrenheit

The values of x and y will be 100° and 10° when two parallel lines are being cut by a transversal line.

According to the question,

We have a figure where two parallel lines are being cut by a transversal line.

Now, we know that the angles formed on a straight line is 180° and vertically opposite angles are equal.

The sum of consecutive interior angles is 180°.

Now, we will use these three statements in finding the values of x and y.

Now, adding (2x-70)° and (5y)° will give 180° because the angles made are on a straight line.

(2x-70)°+(5y)° = 180°

2x+5y = (180+70)°

2x+5y = 250° .... (1)

Now, (x+30)° will be the interior angle consecutive to 5y° because they are vertically opposite angles.

So, we have:

(x+30)°+5y° = 180°

x+5y = (180-30)°

x+5y = 150°

5y = 150-x

Now, putting this value of 5y in equation 1:

2x+5y = 250

2x+150-x = 250

x+150 = 250

x = (250-150)°

x = 100°

Now, we will find the value of y:

5y = 150-x

5y = 150-100

5y = 50

y = 50/5

y = 10°

(Note that the values of x and y will be in ° because angles are measured in degree.)

Hence, the value of x is 100° and the value of y is 10°.

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Given:-

57 students in a physics course earned A.

79 students course earned B.

102 students course earned C.

94 students course earned D.

53 students failed the course.

To find:-

How many degrees would be used to indicate the region A.

Total number of students is,

Now we find the degrees to indicate the region A. we get,

So the required soluion is 53.29 degrees.