Question 8 of 15
Triangle ABC with vertices A(-1, 2), B(-1, -2), and C(-4,-2) is dilated by a scale factor of 2 to form triangle A'B'C'.
у
A
C
4321
-4-3-2-10 이 1234
1
OHN 3 +
B
+2+
-3+
Submit Test
-4-
What is the length, in units, of side A'B'?
units
2223 Math Grade 8 IA1
X

The equation of the line is x + 3y = 2

Linear equations are equations that have constant average rates of change.

The given parameters are

Slope, m = -1/3

Points (x, y) = (1, 1/3)

A linear equation is represented as

y = slope * (x - x₁) + y₁

Where

(x₁, y₁) = (1, 1/3)

Substitute (x₁, y₁) = (1, 1/3) and Slope, m = -1/3 in the equation y = slope * (x - x₁) + y₁

So, we have

y = -1/3* (x - 1) + 1/3

Multiply through by 4

So, we have

3y = -(x - 1) + 1

Remove the brackets

3y = -x + 1 + 1

So, we have

x + 3y = 2

Hence. the linear equation is x + 3y = 2

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(a)

The angle R of triangle PQR is congruent to the angle U of triangle STU. So

(b)

The angle H of triangle GHJ is congruent to angle Q of triangle PQR and angle Q of triangle PQR is congruent to angle T of triangle STU, which means

So,

(c)

The side QR of triangle PQR is congruent to the side TU of triangle STU. So

(d)

The side JG of triangle GHj is congruent to side RP of triangle PQR and side RP of triangle PQR is congruent to side US of triangle STU. So

Given

To obtain the minimum value of y, we first take the derivative of y

The derivative of y is:

Equating

gives the minimum value we require.

Doing that, we have:

So that

Therefore, the minimum value is x = 3

Using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.

As given,

let us assign the unknown quantity (number of weeks) a variable x.

Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.

Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.

For Jacob and Diego to tie in the race, their volunteer hours should be equal.

Solution of the  system of equation is given by:

6x = 5x+50

=> 6x-5x = 50

=> x = 50

Therefore, using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.

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The plot of the points on a coordinate plane is added as an attachment

The coordinate of the point on a coordinate plane is given as

Point = (-3 1/2, -1 1/4)

As a general rule, we express the above coordinate as follows:

(x, y) = (-3 1/2, -1 1/4)

The next step is to remove the bracket

So, we have the coordinates into x and y coordinates

This is represented as

x = -3 1/2 and y = -1 1/4

The interpretation of the above equations is:

Next, we plot the points

See attachment for the plot of the points on a coordinate plane

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The value of x for the given parallel line d || e is x = 20.

From the given question;

The lines d || e.

Thus, both sum of both angles will be 180 by linear pair.

2x - 3 + 7x + 3 = 180

Solving;

9x = 180

x = 20

Thus, the value of x obtained for the given parallel lines is 20.

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The 2 events are independent​ because the outcome of the first draw doesn't affect the outcome of the second.

ANSWER

independent​

Answer:

Positive Slope, the graph interprets how much it costs to rent a canol per hour.

Step-by-step explanation:

The length of this rectangular painting is equal to 1/4 yard.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Making L the subject of formula, we have:

L = A/W

Given the following data:

Width of rectangular painting = 2/3 yard.

Area of rectangular painting = 1/6 square yard.

Substituting the given parameters into the formula, we have;

L = 1/6/(2/3)

L = 1/6 × 3/2

L = 3/12

Length, L = 1/4 yard.

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Answer:

y (y + x)

Step-by-step explanation:

Simplify the following:

y^2 + x y

Factor y out of y^2 + x y:

Answer: y (y + x)

Answer:

650,000÷10^3 = 650

40,000÷10^4 = 4

7,000÷10^2=70

Step-by-step explanation:

The radius, area, and circumference of the given bicycle wheels are:

So, the Diameter of the bicycle wheel = is 22 inches

Circumference of a bicycle wheel:

Area of bicycle wheel = πr²

Therefore, the radius, area, and circumference of the given bicycle wheels are:

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The water level compared to normal at the end of April is 23 13/42 inches below normal.

From the information, the water level in a lake was 22 inches below normal at the beginning of March and rhe water level decreased by 3 1/6 inches in March and increased by 1 6/7 inches in April.

The water level compared to normal at the end of April will be:

= -22 - 3 1/6 + 1 6/7

= - 22 - 3 7/42 + 1 36/42

= -22 - 1 13/42

= -23 13/42

There, it is 23 13/42 below normal.

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The most appropriate choice for right rectangular prism will be given by

a) Dimension of the prism = [tex]\frac{4}{3}[/tex] ft [tex]\times[/tex] [tex]1[/tex] ft [tex]\times[/tex] 1 ft

b) There are 36 unit cubes

c) Volume of prism = [tex]\frac{4}{3}[/tex] [tex]ft^3[/tex]

What is a right rectangular prism?

A geometrical figure which has 6 faces, 12 edges and 8 vertices is called a right rectangular prism.

If l is the length, b is the breadth and h is the height of right rectangular prism, volume will be l [tex]\times[/tex] b [tex]\times[/tex] h .

a)  The right rectangular prism is filled with [tex]\frac{1}{3}[/tex] ft of unit cubes

   Length of right circular prism = [tex]4 \times \frac{1}{3} = \frac{4}{3}[/tex]  ft

   Breadth of right circular prism = [tex]3 \times \frac{1}{3} = 1[/tex] ft

   Height of right circular prism = [tex]3 \times \frac{1}{3} = 1[/tex] ft

   Dimension of the prism = [tex]\frac{4}{3}[/tex] ft [tex]\times[/tex] [tex]1[/tex] ft [tex]\times[/tex] 1 ft

b) Number of unit cubes = [tex]4 \times 3 \times 3[/tex]

                                         = 36 ft

c) Total volume = [tex]\frac{4}{3} \times 1 \times 1[/tex]

                          = [tex]\frac{4}{3}[/tex] [tex]ft^3[/tex]

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Complete Question

The diagram has been attached here

It should be noted that translating the phrase into an algebraic expression the sum of b and 9 will be b + 9.

It should be noted that an algebraic expression in mathematics simply refers to the expression which is made up of constants and variables.

From the information given, we want to translate the sum of b and 9 into an expression. This will be:

= b + 9

Therefore, the expression is b + 9.

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Answer:

Types of Polygons

3 sides - Triangle.

4 sides - Quadrilateral.

5 sides - Pentagon.

6 sides - Hexagon.

7 sides - Heptagon.

8 sides - Octagon.

9 sides - Nonagon.

10 sides - Decagon.

the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.

Let the total number of students be x

Mathematics = 1 / 2 x

natural philosophy = 1 / 4 x

Silence = 1 / 7 x

Remaining = 3

So, we get the equation as:

x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3

(28 x - 14 x - 7 x - 4 x) / 28 = 3

3 x / 28

x = (3 × 28) / 3

x = 28

Number of students in class = 28.

Therefore, the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.

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A fraction which is not equivalent to 12/20 is: D. 2/3

A fraction simply refers to a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

Next, we would evaluate the given fractions as follows:

Dividing the fraction by 2, we have:

12/20 = 6/10

Dividing the fraction by 3, we have:

12/20 = 4/5

Dividing the fraction by 4, we have:

12/20 = 3/5

Multiplying the fraction by 2, we have:

12/20 = 24/40

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Answer:

18.25%

Step-by-step explanation:

730/4000 = 0.1825

The total cost of renting the car for 6 days and driving 350 miles is $358.75 .

What is renting car?
An organisation known as a car rental, hire car, or car hire agency lends out cars to the general public for brief periods of time, typically from a few hours to a few weeks. Usually situated close to airports or busy city centres, it is frequently structured with a number of local branches that let customers return vehicles to multiple locations. A website that allows online reservations is sometimes added on top of this.
Car rental businesses generally cater to customers who need a short-term vehicle, such as those who don't own their own car, tourists who are out of town, or owners of damaged or totaled vehicles who are awaiting repairs or insurance settlement.

The cost of renting the car is $35 for each day .
And for each mile the car is driven we have to pay 42.5 cents .
Therefore 6 days the rent is = $35 x 6
= $210

And for 350 miles we have to pay = 350 x 42.5 cents
= 14875 cents = $148.75
In total $ 358.75

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Answer: 18

Step-by-step explanation:

n=number

-5=n/6 - 8

-5*6=6(n/6 - 8)

-30=n - 48

48-30=n-48+48

n=18

The number of phone calls that Karen can be said to have received in these evenings are: 30 , 80 , and 20 calls

Wr have x, y , z as the number of phone calls that have been received

Such that

x + y + z = 130

On the second day she received 4 calls more than the 3rd day

y = 4z

On the first evening she had 10 more calls than the last

x = 10 + z

We have to substitute the equations in the first equation

10 + z + 4z  + z = 130

10 + 6z = 130

6z = 120

divide through by 6

z = 20

Then x = 10 + 20

x = 30

y = 4z

= 4 x 20 = 80

Therefore on the first day the phone call was 30 minutes, the second day was 80  and the third was 20

To check, 20 + 30 + 80 = 130. the solution is correct

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The number that will produce the greatest number of rectangular arrangements is 6.

From the information, when forming a marching band the leader wants the number so the greatest number of arrangements can be made and she has to choose between 18 and up to 42 members.

It should be noted that the question simony relate to the highest common factor of the values that are given. This will be illustrated as:

18 = 1, 2, 3, 6, 9 and 18

42 = 1, 2, 3, 6, 7, 14 and 42

Therefore, the highest common factor is 6 and this is the greatest number.

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Given,

The measurements of interior angles of a triangle are given:

60°, 65° and 55°

We have to find the corresponding exterior angles:

We know that exterior and interior angles are supplementary.

That is, the sum of the exterior and interior angle is 180°

So here,

180° - 60° = 120°

180° - 65° = 115°

180° - 55° = 125°

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Using the comparison test, we have that [tex]\frac{2}{\sqrt[3]{n}}[/tex] is divergent, as the given sequence [tex]a_n = \frac{1}{n}[/tex] is divergent and [tex]\frac{1}{n} \leq \frac{2}{\sqrt[3]{n}}[/tex] for all values of n ≥ 1.

Suppose that we have two series, defined by [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex], considering that [tex]a_n, b_n \geq 0[/tex] for all n and [tex]a_n \leq b_n[/tex] for all n, then:

For this problem, the sequences are given as follows:

[tex]a_n = \frac{1}{n}, b_n = \frac{2}{\sqrt[3]{n}}[/tex]

Then we have to compare when one of the sequences is greater than another, as we do from the graph at the end of the answer.

From the graph, we have that [tex]\frac{1}{n} \leq \frac{2}{\sqrt[3]{n}}[/tex] for all values of n ≥ 1, and since [tex]\frac{1}{n}[/tex] is divergent, as stated in the problem, then [tex]\frac{2}{\sqrt[3]{n}}[/tex] is also divergent.

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Answer:

Step-by-step explanation:

1)

f(x) = m*x + b

x = 0

5 =m*0 + b

b = 5

2)

2 = m*2 + 5

2*m = - 3

m = - 3/2

3)

f(x) = - 3/2*x + 5

The maximum height the ball reaches is 80 feet

The ball stayed in the air for 1 second

A function can be defined as a law, rule or expression that shows the relationship between two known variables:

Given the function:

h(t) = -16t² + 96

Where;

To determine the maximum height in feet that the ball reached, we have to substitute the value of t as

We have:

h(1) = -16(1)² + 96

expand the bracket

h = -16 + 96

Add the values

h = 80 feet

The time it took the ball to stay in the air would be 1 second, this is so because the ball reached it maximum height as t = 1 sec

Hence, the maximum height is 80 feet

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Given:

Number line is given.

D is point locateed in 2.6 on the number line.

D is in 2.6

Answer:

the answer is B

Step-by-step explanation: