Pam takes her truck in for basic service. The service agent says a few extra repairs are also needed, so Pam adds the cost of those repairs in her head, rounding to the nearest $10. The costs are as follows: Wheel alignment: $110 Transmission fluid flush: $75 Cabin air filter: $23 What is her total estimate for the repairs?

By definitions of collinearity and line segment, the length of the line segment KL is equal to 25 units.

In this problem we find four points that are collinear, that is, that lie in the same line. Therefore, there are three consecutive line segments: IJ, JK and KL, whose ratios are known. From the statement, we derive the following formula for KL:

KL = (5 / 12) · IL

KL = (5 / 12) · 60

KL = 25

The length of the line segment KL is equal to 25 units.

To learn more on collinear lines: https://brainly.com/question/2108998

#SPJ1

Answer:

y = 4x + 5

Step-by-step explanation:

-4x + y = 5

-4x + 4x + y = 5 + 4x

y = 5 + 4x

Hope this helps! :)

Answer:

[-10, 2]

Step-by-step explanation:

The domain is the set of x values.

Step-by-step explanation:

464

first u will multiply 16 with 29

after u get that number that will be your answer

Answer:

  29

× 16

54

120

90

+ 200

= 464

The result function of  (fog)(x) in the given functions is 3x² - 1.

Given the functions in the questions;

Set up the composite result function and simplify.

(fog)(x) = f(g(x) = f(x²)

Evaluate f(x²) by substituting in the value of g into f

fx(x) = 3x - 1

f(x²) = 3(x²) - 1

Now, simplify

f(x²) = 3(x²) - 1

f(x²) = 3x² - 1

Therefore the result function of  (fog)(x) in the given functions is 3x² - 1.

Learn more about composite function here: https://brainly.com/question/20379727

#SPJ1

The labeled graph showing ABCDE, A'B'C'D'E', and the line of reflection x = -2 is shown. Also, m∠ A = m∠ A'.

In the question, we are given that the polygon ABCDE is reflected across the line x = - 2.

We are asked to graph and label the image A'B'C'D'E'. Also, we are asked if m∠ A = m∠ A'.

When the polygon ABCDE is reflected across the line x = - 2, all the coordinates on it are reflected across the line x = -2.

The reflection of any point with coordinates (x, y) on reflection across the line x = a, results in a point with coordinates (-x + 2a, y).

The coordinates of the vertices of the given polygon are:

A (-4, 4), B (-3, 3), C (-3, 2), D (-5, 1), and E (-5, 3).

Reflecting these points across the line x = - 2, we get:

A (-4, 4) → A' ( -(-4) + 2(-2), 4) = A' (0, 4).

B (-3, 3) → B' ( -(-3) + 2(-2), 3) = B' (-1, 3).

C (-3, 2) → C' ( -(-3) + 2(-2), 2) = C' (-1, 2).

D ( -5, 1) → D' ( -(-5) + 2(-2), 1) = D' (1, 1).

E (-5, 3) → E' ( -(-5) + 2(-2), 3) = E' (1, 3).

Plotting ABCDE, A'B'C'D'E', and the line x = -2 has been shown on the graph.

The angles m∠ A and m∠ A' are equal since ABCDE is reflected to make A'B'C'D'E' which makes the two figures congruent. And in congruent figures, the corresponding angles are equal.

Learn more about reflection at

https://brainly.com/question/2551977

#SPJ9

Answer:

  24

Step-by-step explanation:

You want the value of the product ...

  (√14 + √10i)(√14 - √10i)

The factoring of the difference of squares is ...

  a² -b² = (a +b)(a -b)

Here, we have a=√14 and b=√10i. The product of the sum and difference of these values is ...

  (√14 + √10i)(√14 - √10i) = (√14)² -(√10i)²

  = 14 -(10(-1)) = 24

The product is 24.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{8}~,~\stackrel{y_1}{14})\qquad P(\stackrel{x_2}{-21}~,~\stackrel{y_2}{-39})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NP=\sqrt{(~~-21 - 8~~)^2 + (~~-39 - 14~~)^2} \implies NP=\sqrt{( -29 )^2 + ( -53 )^2} \\\\\\ NP=\sqrt{ 841 + 2809 } \implies NP=\sqrt{ 3650 }\implies NP\approx 60.42[/tex]

Answer:

3-x

Step-by-step explanation:

Based on the statement given, the completion of the statement is 7 divided by 1/8 = 56.

The statement is asking for the number that would divide 7 such that the result of this division would be 56.

Assuming the number is x, the formula would be:
7/x = 56

Here, x would be the mystery number that would divide 7 to give 56.

Solving for x is:

7/x = 56

7 = 56x

x = 7/ 56

x = 1/8

In conclusion, when 7 is divided by 1/8, it gives 56.

Find out more on divisions at https://brainly.com/question/28031660

#SPJ1

The vertices of the rectangle are:

P'(4,12)

Q'(12,12)

R'(12,8)

S'(4,8)

Given,the vertices of the rectangle are:

P(5,15), Q(15,15), R(15,10) and S(5,10)

also k= 4/5 to find the new vertices, that is:

P' = P×k

P' = P × 4/5

P' = (5×4/5 , 15×4/5)

P' = (4,12)

similarly:

Q' = Q×k

Q' = Q × 4/5

Q' = (15×4/5 , 15×4/5)

Q' = (12,12)

R' = R×k

R' = R × 4/5

R' = (15×4/5 , 10×4/5)

R' = (12,8)

S' = S×k

S' = S × 4/5

S' = (5×4/5 , 10×4/5)

S' = (4,8)

Hence we get the required points, for which we plot the graph.

Learn more about Transformations here:

brainly.com/question/2387958

#SPJ1

a. S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

a. S, R, and Q are on a straight line. Therefore:

S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

Learn more about collinear points on:

https://brainly.com/question/13127256

#SPJ1

Answer:3

Step-by-step explanation:bc

The bakery is short on half a bag of flour.This problem can be solved using fractions . So, first loaf of bread requires 2bags of flour and a quarter which can be written as  2[tex]\frac{1}{4}[/tex]second loaf of bread also requires the same amount which is 2[tex]\frac{1}{4}[/tex]

the third loaf of bread requires one bag and two third of another bag which can be written as 1[tex]\frac{2}{3}[/tex]

And the final loaf of bread requires half bag of flour which is [tex]\frac{1}{2}[/tex]

the total requirement of flour for making the four loaves of bread is

             = 2[tex]\frac{1}{4}[/tex] + 2[tex]\frac{1}{4}[/tex]+ 1[tex]\frac{2}{3}[/tex]+[tex]\frac{1}{2}[/tex]

              =[tex]\frac{9}{4}[/tex]  +[tex]\frac{9}{4}[/tex] + [tex]\frac{5}{3}[/tex] +       [tex]\frac{1}{2}[/tex]

              = [tex]\frac{27}{12}[/tex]+      [tex]\frac{27}{12}[/tex] +[tex]\frac{20}{12}[/tex] +[tex]\frac{6}{12}[/tex]

            = [tex]\frac{80}{12}[/tex]

To work out how much flour the bakery will have left after making these loaves we need to reduce the total requirement with total flour we have = 6 -[tex]\frac{80}{12}[/tex]

                                       =[tex]\frac{72}{12}[/tex] -  [tex]\frac{80}{12}[/tex]

                                     =- [tex]\frac{6}{12}[/tex] or- [tex]\frac{1}{2}[/tex]

therefore the bakery is short on half a bag of flour

To know more about fractions - https://brainly.com/question/10354322

#SPJ9

Answer:

x= 8

Step-by-step explanation:

Vertical lines have undefined slopes, with an equation of x= ____. This is because when using the slope formula, the denominator would be a zero. The coordinates of points that lie on a vertical line have the same y-coordinate, but different x-coordinate value.

Given that the line passes through (8, 6), the line has an equation of x= 8.

To learn more about the equations of vertical and horizontal lines, check out: https://brainly.com/question/28305863

(C) The perimeter of the ΔABC is 9 + √41 units.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.

The vertices of the triangle on the girds are A( - 1, 5 ), B( 4, 5 ), and C( - 1, 1 ).

The distance formula for the length of a line segment is given as:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore,

[tex]AB=\sqrt{(4-(-1))^2+(5-5)^2}=\sqrt{(4+1)^2+0}=5[/tex]

[tex]BC=\sqrt{(-1-4)^2+(1-5)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{25+16}\\BC=\sqrt{41}[/tex]

[tex]AC=\sqrt{(-1-(-1))^2+(1-5)^2}=\sqrt{(-1+1)^2+(-4)^2}\\AC=\sqrt{0+16}=4[/tex]

Hence, the length of the sides of the triangle are [tex]5,\sqrt{41},4[/tex] units.

Now, the perimeter of a triangle is the sum of all three sides of the triangle.

Therefore, the perimeter of the triangle ABC is:

P = AB + BC + AC

P = 5 + √41 + 4

P = 9 + √41 units

Therefore, the perimeter of ABC is 9 + √41 units.

Learn more about perimeter here:

https://brainly.com/question/27255543

#SPJ1

The complete question is mentioned below:

Triangle ABC is shown on the grid.

What is the perimeter of triangle ABC?

(A) 9 + √21 units

(B) 9 + √29 units

(C) 9 + √41 units

(D) 9 + √61 units

Answer:

3

Step-by-step explanation:

-4|3| -1 = -13

-12 -1 = -13

-13 = -13

Answer:

3

Step-by-step explanation:

-4|3| -1 = -13

-12 -1 = -13

-13 = -13

we need the table to answer the question

Answer:

8 students

c>=A+B

b=2a

24<=C

The given quadrilateral is not a parallelogram.

According to the statement

We have to find that the whether the quadrilateral is a parallelogram or not.

So, For this purpose, we know that the

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

From the given information:

The coordinates of the vertices of quadrilateral ABCD are A(-6,-1), B(-5,2), C(-1.-5), and D(0.-2).

Then

To show that the diagonals are bisect each other, we have to find the midpoint of both diagonals and if the midpoint is same then they bisect each other.

So,

Midpoint of AC = Midpoint of BD

Midpoint of A(-6,-1),C(-1.-5)  = Midpoint of B(-5,2),D(0.-2)

( -6-1/2 , -1-5/2) = (-5+0/2 , 2-2/0)

( -7/2 , -6/2) = (-5/2 , 0/2)

And these midpoints are not same then they do not bisect each other and then it is not a parallelogram.

So, The given quadrilateral is not a parallelogram.

Learn more about parallelogram here

https://brainly.com/question/1509864

#SPJ1

The diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter

The diameter of a shape (usually a round shape) is a line that divides the shape to equal parts

The diameters are given as:

Diameter of a gold atom = approximately 144 trillionths of a meter

Diameter of an oxygen atom = approximately 0.074 billionths meter

Using a calculator, we convert the above numbers to scientific numbers

So, we have

Diameter of a gold atom = approximately 1.44 x 10^-10 meter

Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter

The number with the higher exponent is greater than the other number

Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom

In (a), we have

Diameter of a gold atom = approximately 1.44 x 10^-10 meter

Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter

Calculate the difference

d = 1.44 x 10^-10 - 7.4 x 10^-11

Evaluate the difference

d = 7 x 10^-11

Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter

Read more about scientific numbers at

https://brainly.com/question/5756316

#SPJ1

Answer:

Since the quantity started at 90 and then changed to 160, there was clearly an increase in its value.

Step-by-step explanation:

There are 2322432 coupons generated .

According to the question we have been given that the code contains one digit followed by four letters . That is it can be assumed as

                         code = D L L L L   where D and L represent the digits and letters.

Now total digits we have is  = 7

       total number of letters we have = 24

So we have to choose the first digit from these 7 digits. Thus there are 7 ways in which we can choose as they are repeated.

Also there are 24 ways to select the 4 letters after the digits as the letters are being repeated, that is ways =   24⁴

Therefore the number of coupons that can be generated from the combination are :

                                7*24⁴ = 7*331776

                                          = 2322432

Hence the number of coupons generated are 2322432.

learn more about permutation here : https://brainly.com/question/12468032

#SPJ9

Answer:

2.2 hours or

2 hours and 12 minutes they will meet.

Step-by-step explanation:

Givens

Mary's speed = 51 mph

Friend's speed = 66 mph

Mary will be on the road for t hours

Her Friend will be on the road t - 0.5. Why minus? Because she was on the road 1/2 hour less than Mary was. Any time you see More or Less in a question, pay attention. usually it is the key to the question.

Equation

d_Mary = d_friend

d = rate * time

Solution

51 * t = 66*(t - 0.5)                 Remove the brackets.

51*t = 66*t - 66*0.5

51*t = 66*t - 33                    Subtract 66t from both sides. Be careful

51t - 66t = - 33                     Combine

- 15t = - 33                            Divide by - 15

t = - 33/-15

t = 2.2 hours or 2 hours and 12 minutues

Answer:

675,745.92

Step-by-step explanation:

(9.6 × 103) × (6.7 × 102)

(988.8) × (683.4)

= 675,745.92

I hope this helps!

We get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.

We are given that the red line is perpendicular to the green line.

Also, we are given that the slope of the red line is - 5 / 2

m₁ = - 5 / 2

Now, we need to find the slope of green line.

Let the slope of the green line be m₂

We know that, when the lines are perpendicular, then the relationship between their slopes is given by:

m₁ ×  m₂ = - 1

Substituting the values, we get that:

- 5 / 2 × m₂ = - 1

m₂ = - 1 × - 2 / 5

m₂ = 2 / 5

Therefore, we get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.

Learn more about perpendicular here:

https://brainly.com/question/1202004

#SPJ9

Based on the area of Marcellus's lawn, the number of pounds of fertilizer needed for Marcellus's lawn is 4 ¹/₅ pounds

In order to fertilize an area of 2 acres, the number of pounds of fertilizer needed is 10 ¹/₂ pounds.

The area of Marcellus's lawn is only 4/5 of an acre however so to find the pounds of fertilizer needed, use direct proportion:

2 acres : 10 ¹/₂ pounds

4/5 acres : x

2x = 8.4

x = 8.4 / 2

x = 4.2 pounds

= 4 ¹/₅ pounds

Find out more on acres and fertilizer at https://brainly.com/question/25278761

#SPJ1

The four sides of the quadrilateral are 9 m,10 m, 11 m and 12 m.

What is a quadrilateral?

A quadrilateral is a four-sided polygon with four angles and four vertices. The term "quadrilateral" comes from the Latin words "quadri," which means "four," and "latus," which means "side."

Let the four sides of the quadrilateral be (x-2), (x-1), x, (x+1).

Then, perimeter = (x-2) + (x-1) + x + (x+1)

i.e., x - 2 + x - 1 + x + x + 1 = 42

i.e., 4x - 2 = 42

i.e., 4x = 42 + 2

i.e., 4x = 44

i.e., x = 11

Hence, the four sides of the quadrilateral are 9 meters, 10 meters, 11 meters and 12 meters.

To know more about quadrilaterals, click on the link

https://brainly.com/question/12672291

#SPJ1

The change in rainfall between the rainfall last year and the average (or mean) annual rainfall is 22 inches

The given parameters are

Average annual rainfall = 51 inches

Last year = 29 inches

The change in rainfall between the rainfall last year and the average (or mean) annual rainfall is calculated as

Change = |Annual rainfall - Last year|

This gives

Change = |51 - 29|

Evaluate

Change = 22

Hence, the change in rainfall between the rainfall last year and the average (or mean) annual rainfall is 22 inches

Read more about net change at:

https://brainly.com/question/1153322

#SPJ1