What rule describes the translation that was applied to triangle JKM to create triangle J’K’M’, Initial directions with the pic below.

The simple interest charged by the lender on Alonzo is $ 126 and the amount paid after 6 years is $ 826.

Principal amount of loan = $ 700

Time period = 6 years

Interest rate = 3 %

The simple interest is charged by the lender:

The interest will be:

SI = p × r × t / 100

Substitute the values, we get that:

SI = 700 × 3 × 6 / 100

SI = 7 × 3 × 6

SI = $ 126

The amount paid by Alonzo after 6 years will be:

Amount = $ 700 + $ 126

A = $ 826

Therefore, the simple interest charged by the lender on Alonzo is $ 126 and the amount paid after 6 years is $ 826.

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To multiply the matixes, we'll look at their elements

In order to get AB, we simply use the following formula

In this case

Since both matrixes have 4 elements. Thus

In order to know the rate of pay, we need to divide the value of the paycheck ($624.65) by the total hours Alex worked (32.5 hours):

$624.65/(32.5 hours) = $624.65/(32.50 hours) = $62465/(3250 hours)

Now, to solve this division, we can do as follows:

Therefore, the rate of pay is

$19.22/hour

1) Gathering the data

$78 20% off

2) To find the final price Jerry has paid just multiply

78----20%

3) So, the expression used was 78 x (0.8) and Jerry has paid $62.4 for the table

EXPLANATION

Minimum

The first Quartile is the value separating the lower quarter and higher three - quarters of the data set.

The first quartile is computed by taking the median of the lower half of a sorted set.

Arranging terms in ascending order

40, 42 , 46, 48, 51, 55, 58, 66, 67, 68, 69

Here, we can see that:

Minimum = 40

Maximum = 69

Q2=55 (median)

Taking the lower half of the ascending set:

Counting the number of terms in the data set:

{40, 42 , 46, 48, 51, 55, 58, 66, 67, 68, 69}

{1, 2 , 3, 4, 5, 6, 7, 8, 9, 10, 11}

The number of terms in the data set is:

11

Since the number of terms is odd, take the elements below the middle one, that is, the lower 5 elements.

40, 42 , 46, 48, 51

Median of 40, 42 , 46, 48, 51:

The number of terms in the data set is 5.

Since the number of terms is odd, the median is the middle element of the sorted set.

Q1: 46

------------------------------------

Q3:

Since the number of terms is odd, take the elements above the middle one, that is, the upper 5 elements.

58, 66, 67, 68, 69

The number of terms in the data set is

5

Since the number of terms is odd, the median is the middle element of the sorted set.

Q3=67

------------------------------------------------------------------------------------

Interquartile Range:

The interquartile range is the difference of the first and third quartiles

We have that:

Q1=46

Q3=67

Computing the difference between 67 and 46:

67-46= 21

Interquartile Range=21

-------------------------------

Answers:

Minimum = 40

Q1=46

Q2=55 (median)

Q3=67

Maximum = 69

Interquartile Range=21

The given equation is

We have to find a new line perpendicular to the given line and must pass through P(-5,7).

First, we use the definition of perpendicularity for two lines.

Where one of the slopes is equal to -1 because the coefficient of x in the given equation is -1. Let's find the other slope.

This means the new perpendicular line has a slope of 1.

Now, we use the slope we found, the point P, and the point-slope formula, to find the equation.

The point-slope formula is

where m is the slope of a line passing through the point (x₁, y₁).

Also, the slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is

In this problem, the line passes through points (4, -3) and (-2, 5). Thus, we have:

x₁ = 4

y₁ = -3

x₂ = -2

y₂ = 5

Then, the slope is

And the equation in point-slope form is

Now, we need to rewrite this equation in slope-intercept form. The slope-intercept equation of a line with slope m and y-intercept b is

Thus, we need to isolate y on the left side of the equation to obtain the slope-intercept form, as follows:

Therefore, the slope-intercept form of that linear equation is

Answer:

slope = -3.5

Explanation:

The points we have are:

We have to label the coordinates as follows:

And now we use the formula to calculate the slope between the points:

We substitute the known values:

And solve the operations to find the slope "m" between the points:

Answer: slope = -3.5

Hello!

First, the temperature is -6.2ºC, and Jesse wants to raise it until be positive.

If we add 6.2ºC, we will obtain a temperature equal to 0ºC, right? So, to the temperature be positive you can choose any temperature greater than 6.2º.

For example, I'll choose 15ºC.

We will write the current temperature plus the temperature that we will add, then we obtain the new temperature, look:

-6.2ºC + 15ºC = 8.8ºC

Let r and v be the number of socks ina regular pack and value pack, respectively. Since the store gave 6 regular packs and 5 value packs which contained 163 pair of socks, we can write

Similarly, since the store donated 6 regular packs and 4 value pack which add 146 pair of socks, we can write

Then, we have the following system of equations:

Solving by elimilation method.

By multiplying equation (b) by -1, we have an equivalent system of equations:

Then, by adding both equations, we have

Now, in order to obtain the number of socks in a regular pack, we must substitute the last result into equation (a). It yields,

which gives

By subtracting 85 to both sides, we have

Then, r is given by

Therefore, the answer is: There are 13 pairs of socks in each regular pack and 17 pairs in each value pack.

Answer:

He must make $7,500 in sale

Step-by-step explanation:

Let's say:

s = amount make in sales per week

P1 = weekly salary of Plan 1

P2 = weekly salary of Plan 2

P1 and P2 can be expressed using the fixed amount plus the commission.

P1 = 600 + 0.02s

P2 = 0 + 0.1s

P2 = 0.1s

If both plans result in the same salary:

P1 = P2

600 + 0.02s = 0.1s

0.1s - 0.02s = 600

0.08s = 600

s = 600/0.08

s = $7,500

First, we divide the first equation by -6

Then, we combine this equation with the second one

Now, we use the x-value to find y

Answer:

(1,3)

Explanation:

Given the system of equations:

To solve the system using the elimination method, multiply the first equation by 3.

Next, substitute x=1 into any of the equations to solve for y.

The solution to the system of equations is (x,y)=(1, 3).

let,

lenght (l)=11.4 , and width (b)=7.4

so,

area=84.36

Answer:

Explanation:

Here, we want to check if the given line is linear or not

From the image shown, the line connects two points on the axes

This connection is in the form of a line segment

Thus, we can confirm that the line is linear

Given:

Given the system of equations:

Required: Solution of the system using Cramer's rule

Explanation:

The system of equations can be rewritten as

Write down the augmented matrix.

Calculate the main determinant.

Substitute the c-column with RHS and find the determinant.

Substitute the p-column with RHS and find the determinant.

Substitute the w-column with RHS and find the determinant.

Permutations

Suppose there are only two people in the meeting. Person A gives a card to person B and vice-versa. Two cards were given.

Now we have 3 people. Person A gives two cards. Person B gives two cards. Person C gives two cards. Total = 6 cards given.

Each people gives a card to everyone else (except themselves, of course) and it's done by everyone in the meeting, thus for 130 people:

130 x 129 = 16,770 cards were given

Rewrite one side(or both) by combining like terms

Explanation:

Equation A: 5 = -2(x - 1)

Equation B: 5 = -20 +2

To get Equation B from Equation A, we equate the right sides of both equations since equating the left side give the same answer.

Left side: 5 = 5

Right side: -2(x - 1) = -20 +2

Then we solve:

-2x + 2 = -18

-2x = -18-2

-2x = -20

x = -20/-2

x = 10

To get Equation B from Equation A, we make x = 10

Rewrite one side(or both) by combining like terms

The value of -|-34| is -34

-|-34|

Apply absolute rule: |-a|=a,  a>0 =-34

The absolute value (or modulus)| x |  of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5. A number's absolute value can be conceived of as its distance from zero along the real number line.

Absolute values for real numbers occur in a wide range of mathematical contexts. Absolute values, for example, are defined for complex numbers, quaternions, ordered rings, fields, and vector spaces. In numerous mathematical and physical contexts, the absolute value is intimately related to the concepts of magnitude, distance, and norm.

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The equation of the tangent line may be identified using the first derivative of the function which gives us its slope.

The tangent line passes through (/4, -√2/2) so we can solve for the y-intercept, b.

So the equation of the tangent line is:

We have:

- There are 8 choices for awarding first prize.

- Then there are 7 choices for awarding second prize.

- And there are 6 choices for awarding third prize.

Therefore, there are:

Answer: 336 ways

Answer:

C

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 9, 4 ) and (x₂, y₂ ) = (3, - 12 )

d = [tex]\sqrt{(3-(-9))^2+(-12-4)^2}[/tex]

   = [tex]\sqrt{(3+9)^2+(-16)^2}[/tex]

   = [tex]\sqrt{12^2+256}[/tex]

   = [tex]\sqrt{144+256}[/tex]

   = [tex]\sqrt{400}[/tex]

   = 20 units

The rule for a dilation with center at (0,0) and scale factor k is:

Find the transformed vertices A'. B', C' and D' using this rule:

Similarly, the coordinates of B', C' and D' wil be:

Plot A', B', C' and D' along with A, B, C and D:

Calculating the unit rate for Tree 2 we have the following

When simplified the unit rate is

This is 2.5 inches per week. Compared to Tree 1,

For a)

Before

Rachel : Timothy

12 : 13

After

Rachel : Timothy

3 : 1

In order to have the same amount for Rachel

12: 4

Timothy

13units -4 units =9 units

9units=$27

1 unit=27/9

1unit = $3

For Rachel

Rachel saved $36

b)

Total units at first =12+13=25

If 1units is $3

25 units is 3x25

25 units is $75

They saved together 75

ANSWER

Rachel saved $36

They saved together 75

If the line is perpendicular to:

the we know that the slope will be the negative reciproc of the slope so the new slope is:

So the equation is:

So we can replace the coordinate (-2,-4) and solve for b so:

So the final equation is:

We have two points and we need to calculate the distance between them.

The points are P1(-4,3) and P2(3,2).

We can apply the following formula for the distance between points:

The answe is 5 times the square root of 2:

We can solve this question using cross multiplication,

If the number of students who sleep 6 hours a day increases by, this means we'll have a total of 6 students who sleep 6 hours a day.

We want the ratio to be same: 15%

Then we can write:

6 students are the 15%, then N students are the 100%

Now solve for N:

The answer is 40 students are expected.

This is a reasonable answer, given that if the number of students who sleep 6 hours doubles, for the rate to remain the same, the total of students must double.

In order to determine the correct expression for the length of the side, consider that the distance in between two points (x1,y1) and (x2,y2) is given by the following formula:

d = √((x2 - x1)² + (y2 - y1)²)

if (x1,y1) = (5,5) and (x2,y2) = (7,-3) you have for d:

d = √((7 - 5)²+(5 - (-3))²)