Find the equation of a line, in slope-intercept form of a line that passes through the point (-5, -1) and is parallel to -2x+4y=8. ​

the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

We have two points p=(-7,-2) and E=(1,-9)

then the distance between PE is

d=√(1+7)²+(-9+2)²

d= √(64+49)

d=√113

the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

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Answer:

m^2+5m+25/4

perfect square trinomial^^

ANS : 12 3 321

Refer the attachment for your reference !!

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

Answer:

edcafgb

Step-by-step explanation:

-2 1/2 = -5/2 < -2 < -1.75 < -1 < 1.75 < 9/4

*-2 1/2 and -5/2 are the same.

To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

The inequality on the graph is the third option:

(2/5)*x - 3/2 ≥ y

Let's analyse the graph if the inequality.

We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:

y ≤ linear equation.

We know that the symbol "≤" must be used because of the solid line.

We also can see that when x = 0, y takes a velue between -1 and -2.

With that in mind the correct option is the third one:

(4/5)*x - 2y ≥ 3

Isolating y we get:

(4/5)*x - 3 ≥ 2y

(2/5)*x - 3/2 ≥ y

Changing the order:

y ≤ (2/5)*x - 3/2

That is the graphed inequality.

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Based on the given argument, it is concluded that my friend's reasoning was incorrect.

This refers to the type of function that represents one line on a linear plane in cartesian mathematics.

With this in mind and from the claim of my friend that a line always represents a function, my friend is incorrect because If the line was vertical, then it could not pass through and as such, cannot represent a function.

Therefore, the answer to the question is that my friend is incorrect in his claim about lines and functions.

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The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

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There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

Answer:

D. 1.95 units clockwise

Step-by-step explanation:

I calculated it logically

Answer:

Yes, it is

Step-by-step explanation:

Given

The attached image

Required

Is AB a tangent to the circle

From the attached circle, we can see that AP is the radius of the circle P.

And by definition, a tangent touches the circle at only one point.

Since AB touches the circle at only point A, then AB is a tangent.

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Explanation:

1/2 is at the simplest form

8/16 need to be divide to the simplest form to determine if they would be the same

dividing the numerator and denominator by 2:

8/2 divided by 16/2

= 4 divided by 8

dividing the numerator and denominator by 2:

4/2 divided by 8/2

2 divided by 4

2/4 = 1/2

they are proportional

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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Answer:

~ 15 %

Step-by-step explanation:

116.4   - 98.3 = 18.1

  18.1 / 17.5 = 1.034  SD ABOVE the mean

         this is a z-score of .8485   meaning 84.85 % have a score LESS than 116.4     so    15.15 % have a score higher

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Given

225 is 25 % of a number

Answer

let number be x

Answer:

0.43ᵣ = 0.1 + 0.33ᵣ = 1/10 + 1/3 = 3/30 + 10/30 = 13/30

The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

x = 0.43333......

Multiply the equation by 10 on both sides, then we have

10x = 10 × 0.43333......

10x = 4.33333......                        ...1

Multiply the equation by 100 on both sides, then we have

100x = 100 × 0.43333......

100x = 43.33333......                     ...2

Subtract equation 1 from equation 2, then we have

100x - 10x = 43.3333.... - 4.3333.....

90x = 39

x = 39 / 90

x = 13 / 30

The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.

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Answer:

18

Step-by-step explanation:

Change 3 into a fraction.

Which gives you 3/1

multiply 3/1 by the inverse of 1/6

3/1x1/6

Then you get 1 :)

Answer:

False. The product of two negative integers is a positive integer.

The formula to find time from distance is time = distance/speed

As a general rule, the formula of speed is

Speed = Distance/Time

Multiply both sides by Time

Time * Speed = Distance

Divide both sides by Speed

he formula to find time from distance

Hence, the formula to find time from distance is time = distance/speed

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Answer:

Total length of the rim = 232.36 cm (Approx.)

Total length of the rim and spokes = 296 cm (Approx.)

Step-by-step explanation:

Given:

Number of spokes = 8

Length of spokes = 37 cm

Radius of wheel = Length of spokes = 37 cm

Find:

Total length of the rim and spokes

Computation:

Total length of the rim = 2πr

Total length of the rim = 2(3.14)(37)

Total length of the rim = 232.36 cm (Approx.)

Total length of spokes = 8 x 37

Total length of the rim and spokes = 296 cm (Approx.)

Complete Question

A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test this claim, he selects random cities in the state the senator represents and compares the approval ratings before the decision to the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where each difference is calculated by subtracting the percent approval rating before the decision from the percent approval rating after the decision. Assume that the ratings are normally distributed. Using a test statistic oft -3.935, the significance level Q=0.05, and the corresponding p-value less than 0.01, draw a conclusion for the appropriate hypothesis test, where the null hypothesis is \(H_o. :  \mu_d= 0\) and the alternative hypothesis is  \(H. : \mu_d < 0\)

a. Reject the null hypothesis.

b. Fail to reject the null hypothesis.

c. The conclusion of the hypothesis test is that there is sufficient evidence to suggest that there was a drop in approval ratings in cities after the decision to support the bill.

d. The conclusion of the hypothesis test is that there is insufficient evidence to suggest that there was a drop in approval ratings in cities after the decision to support the bill.

Answer:

The correct option is  a and  c

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  8  

    The  test statistics is t =  -3.935

    The level of significance is  \(\alpha =  0.05\)

    The  p-value  is \(p-value  =  0.01\)

From the data given we see that the \(p-value  <  \alpha\) hence

The decision rule is  

  Reject null hypothesis

The conclusion

There is sufficient evidence to suggest that there was a drop in approval ratings in cities after the decision to support the bill.

Answer:

7.21

Step-by-step explanation:

use pythagoream theroem

To find out how many miles Jodi's car traveled per gallon of gas, you can divide the total number of miles traveled by the number of gallons of gas used. In this case, you would divide 420 miles by 12 gallons to get 35 miles per gallon. Here's the calculation:

420 miles / 12 gallons = 35 miles per gallon

This means that Jodi's car traveled 35 miles for every gallon of gas it used.

Answer:

Jodis car travelled 35 miles per gallon of gas.

Step-by-step explanation:

Jodis car travelled 420 per 12 gallons of gas.

We want to find how much it travelled per 1 gallon of gas. To find miles per 1 gallon given miles 12 gallons we must divide both the miles and the gas by 12:

Jodis car travelled 420 milres per 12 gallons of gas.

>Jodis car travelled \(\frac{420}{12}\) per \(\frac{12}{12}\) gallons of gas.

>Jodis car travelled 35 miles per 1 gallon of gas.

Answer:

\(45\)°, \(55\)°, and \(80\)°

Step-by-step explanation:

Dilations preserve angle measures, regardless of the scale factor. Therefore, the angle measures of the image will be the same of that of the pre-image, so our answer is still \(45\)°, \(55\)°, and \(80\)°. Hope this helps!