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\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-7 - (-2)~~)^2 + (~~-7 - 3~~)^2} \implies d=\sqrt{(-7 +2)^2 + (-7 -3)^2} \\\\\\ d=\sqrt{( -5 )^2 + ( -10 )^2} \implies d=\sqrt{ 25 + 100 } \implies d=\sqrt{ 125 }\implies d\approx 11.18\)

Exact Distance = \(\boldsymbol{5\sqrt{5}}\) units

Approximate Distance = 11.1803 units

===================================================

Work Shown:

\((x_1,y_1) = (-2,3) \text{ and } (x_2, y_2) = (-7,-7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-(-7))^2 + (3-(-7))^2}\\\\d = \sqrt{(-2+7)^2 + (3+7)^2}\\\\d = \sqrt{(5)^2 + (10)^2}\\\\d = \sqrt{25 + 100}\\\\d = \sqrt{125}\\\\d = \sqrt{25*5}\\\\d = \sqrt{25}*\sqrt{5}\\\\d = 5\sqrt{5}\\\\d \approx 11.1803\\\\\)

The exact distance is \(5\sqrt{5}\) units, which approximates to about 11.1803 units

I used the distance formula. Round the approximate value however your teacher instructs.

A slight alternative is to plot the two points to form a right triangle. The hypotenuse goes from (-2,3) to (-7,-7). Then use the pythagorean theorem.

You can use tools like WolframAlpha or GeoGebra to confirm the answer.

Answer:

Parker will have to pay $31 in a month in which he downloaded 50 songs.

Total amount Parker will pay for s songs = 6 + 0.50s

Step-by-step explanation:

Cost per month = $6

Cost of Offline download = $0.50 per song

A. How much total money would

Parker have to pay in a month in which he downloaded 50 songs?

Total amount Parker will pay = $6 + $0.50(50)

= 6 + 25

= $31

Parker will have to pay $31 in a month in which he downloaded 50 songs.

B. How much would

he have to pay if he downloaded s songs?

Total amount Parker will pay for s songs = $6 + $0.50 * s

= $6 + $0.50s

Total amount Parker will pay for s songs = 6 + 0.50s

Answer:

Solution given:

Let there be a point P(x, y) equidistant from

A(-3, 2) and B(0,4),

so PA = PB,

\(\sqrt{(x+3)²+(y-2)²}=\sqrt{(x-0)²+(y-4)²}\)

squaring both side

\((\sqrt{(x+3)²+(y-2)²})^{2}=(\sqrt{(x-0)²+(y-4)²})²\)

x²+6x+9+y²-4y+4=x²+y²-8y+16

x²+6x+y²-4y-x²-y²+8y=16-4-9

6x-4y+8y=3

6x-4y=3 is a required locus

Actually:

A locus is a curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.

Answer:

y = -2/3x + 5

Step-by-step explanation:

Since the first line is in slope-intercept form, we can also find the equation of the other line in slope-intercept form.  The general equation of the slope-intercept form is y = mx + b, where

Step 1:  Find the slope of the other line:

The slopes of parallel lines always equal each other.  Thus, the slope (m) of the second line is also -2/3.  

Step 2:  Find the y-intercept of the other line:

We can find b, the y-intercept, of the other line by plugging in (3, 3) for x and y and -2/3 for m:

3 = -2/3(3) + b

3 = -2 + b

5 = b

Thus, y = -2/3x + 5 is the equation of the line passing through the point (3, 3) and parallel to the line given by the equation y = -2/3x - 2.

the equation of the line that passes through the point (3,3) and is parallel to the line given by the equation y = –2∕3x – 2 is y = (-2/3)x + 5.

We can determine the slope of the given line by rewriting it in slope-intercept form:y = (-2/3)x - 2The slope of this line is -2/3. Two parallel lines have the same slope, so the slope of the line we are looking for is also -2/3.Since we now have the slope and a point on the line, we can use the point-slope form of an equation to find the equation of the line:y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.y - 3 = (-2/3)(x - 3)Distributing the -2/3:y - 3 = (-2/3)x + 2Adding 3 to both sides:y = (-2/3)x + 5Therefore, the equation of the line that passes through the point (3,3) and is parallel to the line given by the equation y = –2∕3x – 2 is y = (-2/3)x + 5.

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The appropriate conditions for using the one-proportion z-interval procedure are as follows:

A. The procedure is appropriate because the necessary conditions are satisfied.

C. The procedure is not appropriate because n - x is less than 5.

D. The procedure is not appropriate because the sample is not a simple random sample.

Option B is not applicable to the one-proportion z-interval procedure. The condition "x is less than 5" is not a criterion for determining the appropriateness of the procedure.

The one-proportion z-interval procedure is used to estimate the confidence interval for a population proportion when certain conditions are met. The necessary conditions for using this procedure are that the sample is a simple random sample, the number of successes and failures in the sample is at least 5, and the sampling distribution of the sample proportion can be approximated by a normal distribution.

Therefore, options A, C, and D correctly explain the appropriateness of the one-proportion z-interval procedure based on the conditions that need to be satisfied.

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Answer:

x=

y=31

Step-by-step explanation:

hope this helps

Michelle rode an altogether distance of 810 kilometers from her home to school and back, riding her bike.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

We have been given that Michelle lives 2.7 km from school, Last year she made 150 round trips from her home to school and back, riding her bike.

According to the given condition, the required solution would be as:

Total distance rode by her =  150 × 2 × 2.7

Total distance rode by her =  300 × 2.7

Apply the multiplication operation, we get

Total distance rode by her =  810 kilometers

Therefore, Michelle rode an altogether distance of 810 kilometers.

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Answer:

\(y=\frac{4}{5} x-5.\)

Step-by-step explanation:

1) the common form of linear function in slope=interseption form is: y=s*x+i, where 's' and 'i' are slope and interception, unknown numbers;

2) if f(0)=-5, that means i=-5 and the equation is y=s*x-5, where s - unknown number;

3) f(5)=-1 and if to substitute x=5; y= -1 into y=x*s-5, then it is possible to calculate the value of 's': -1=5s-5; ⇒ s=4/5;

4) finally, the required linear function is:

\(y=\frac{4}{5} x-5\).

P.S. note, the suggested way is not the shortest one.

The number of books sold last week by the bookstore owner is 10.Based on the given equation and the profit of $720 from last week, the number of books sold by the bookstore owner is estimated to be 10.

Given the equation p = 8b^2 + 560, where p represents the weekly profit and b represents the number of books sold, we can substitute p = 720 (the profit from last week) into the equation:

720 = 8b^2 + 560

Rearranging the equation, we have:

8b^2 = 720 - 560

8b^2 = 160

Dividing both sides of the equation by 8, we get:

b^2 = 20

Taking the square root of both sides, we find:

b = ±√20

Since b represents the number of books sold, we consider only the positive value, which is approximately 4.47. However, since the number of books sold must be a whole number, the closest integer value is 4.

Therefore, the number of books sold last week by the bookstore owner is 10.Based on the given equation and the profit of $720 from last week, the number of books sold by the bookstore owner is estimated to be 10.

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Consider the following word problem:

"The sum of a number and 5 is 7 less than its double".

To solve the word problem, let n be the number.

Hence, the solution is given by:

Therefore, the required word problem is: "The sum of a number and 5 is 7 less than its double" ; the acceptable answer to the word problem is 12 and any number that is not 12 will not be acceptable.

.

.

Answer: y=4x-5

Y=4x-5

Answer:

Fred's age: 26    Natalie's age: 15

Step-by-step explanation:

    F + N = 41

-)  F + 3N = 71

____________

=> -2N = -30

=> N = 15

F + 15 = 41 => F = 26

The symbols x, y, and z are examples of variables in an instruction like z = x + y.

A variable is a term that signifies anything that can be varied or altered. In programming, variables are utilized to hold values that might be modified and used in later code.

A variable is a name that identifies a memory location where data is stored. It can be changed anytime. Variables are commonly used in mathematical expressions, such as those seen in algebra. For example, x + 150 = 300In this instance, x is the variable. 150 and 300 are constants.

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The two pairs of Adjacent angles in the figure are:

∠1 and ∠3, ∠3 and ∠7.

The correct option is c.

In the given diagram with two intersecting lines and angles ∠1, ∠3, ∠5, and ∠7, the adjacent angle pairs are as follows:

Adjacent angles to ∠1:

∠1 and ∠5

∠1 and ∠3

Adjacent angles to ∠3:

∠3 and ∠1

∠3 and ∠7

Adjacent angles to ∠5:

∠5 and ∠1

∠5 and ∠7

Adjacent angles to ∠7:

∠7 and ∠3

∠7 and ∠5

Adjacent angles are angles that share a common side and a common vertex, where the vertex is the point of intersection between the two lines. In this case, the adjacent angle pairs can be identified based on their relationship to each angle (∠1, ∠3, ∠5, ∠7) and the intersecting lines.

from the given choices,

∠1 and ∠3, ∠3 and ∠7

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Answer:

x = - 3/28

Step-by-step explanation:

Report if wrong

-Stylez-

Answer:

x= -3/28

Step-by-step explanation:

Multiply both sides of the equation by 42

-28x+18=21

-28x=21-18

-28x=3

x= -3/28

Answer: 'Percent (%)' means 'out of one hundred':

p% = p 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100.

8% = 8/100 = 8 ÷ 100 = 0.08.

100% = 100/100 = 100 ÷ 100 = 1.

Step-by-step explanation:

To calculate percentage decrease:

First: work out the difference (decrease) between the two numbers you are comparing. Then: divide the decrease by the original number and multiply the answer by 100. If your answer is a negative number, then this is a percentage increase.

The mean and standard deviation obtained from simulations may differ from the true mean

standard deviation of a negative binomial distribution with parameters $r=0.6$ and $p=10$. However, with a large number of simulations, the mean and standard deviation from the simulations should approach the true mean and standard deviation of the distribution.

In general, the mean of a negative binomial distribution with parameters $r$ and $p$ is $r \cdot (1-p)/p$, and the standard deviation is $\sqrt{r \cdot (1-p)/p^2}$.

These formulas can be used to calculate the true mean and standard deviation of a $nb(0.6,\ 10)$ distribution.

Comparing the simulated mean and standard deviation to the true values can help assess the accuracy of the simulation results.

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A. The number of red balls he had was 8  at the beginning.

Duke's starting red ball total can be found by setting up a system of equations. First, let x represent the number of red balls and y represent the number of blue balls.

After 5 days, the equation is x-15=y+10. This equation states that after 5 days, the number of red balls (x) minus 15 will equal the number of blue balls (y) plus 10. After 9 days, the equation is x-27=2y+20.

This equation states that after 9 days, the number of red balls (x) minus 27 will equal twice the number of blue balls (y) plus 20. To solve for x, both equations can be set equal to each other and solved. This results in x=8. Therefore, Duke had 8 red balls at the beginning.

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Answer:

4800

Step-by-step explanation:

If a question is asking for the "sum" of numbers, this just means we have to add them altogether.

975+983+923+913+985 = 4779

To find the hundredth place, we use our place value. 4 is in the thousands column, and 7 is in the hundreds. Once we find the hundreds, we need the number to the right of it (7).

7 > 5 so we round up. 7 becomes 8.

4800.

80+x+45=180 (sum of angles on a straight line)

x=180-80-45

x=55.

9. Answer:

30

10. Answer:

2

11. Answer:

4

12. Answer:

4

13. Answer:

-1

Tip:

Use photomath, its an app

Answer:

a) 4

b) 10

Thank you and please rate me as brainliest as it will help me to level up

The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)

We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).

Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)

Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...

(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.

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Step-by-step explanation:

7x-8y = - 5     arrange to   y = mx+ b  form    m is the slope of this line

8y = 7x+5

y = 7/8 x = 5/8     <======   m, slope = 7/8  

           perpendicular slope =  - 1/m  =  - 8/7

Now use point ( -7,3)   slope (-8/7)  form:

  y-3   = - 8/7 ( x - - 7)     simplify

   y = -8/7 x  + 5          re-arrange ,   add  8/7 x to both sides of the equation

   8/7 x  + y = 5                 multiply through by 7 to get integer values

      8x + 7y =  - 35  

A. The basis for the subspace of vectors whose components are equal in R4 is {(1, 1, 1, 1)}.

B. The basis for the subspace of vectors whose components add to zero in R4 is {(1, -1, 0, 0), (1, 0, -1, 0), (1, 0, 0, -1)}.

C. The basis for the subspace of vectors perpendicular to (1, 1, 0, 0) and (1, 0, 1, 1) in R4 is {(1, -1, 1, 0), (-1, 0, 1, -1)}.

D. The basis for the column space of U (in R2) is determined by the non-zero columns of U. The nullspace of U (in R5) is the set of vectors that satisfy the equation Ux = 0, where x is a vector. The basis for the column space and nullspace of U depends on the specific matrix U given in the problem. Without the matrix U, it is not possible to determine the basis for these subspaces.

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She rewrites the given equation in the following way as: (x + 10)² = 82.

An equation is a mathematical statement that shows the equality between two expressions. It contains one or more variables, which represent unknown values, and may involve mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. The goal of an equation is to find the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, physics, engineering, and other sciences to model and solve various real-world problems.

Here,

We can complete the square as follows:

x² + 20x + 18 = 0

x² + 20x = -18

(x + 10)² - 100 = -18 (adding and subtracting 100 to the left-hand side)

(x + 10)² = 82

Taking the square root of both sides, we get:

x + 10 = ±√(82)

x = -10 ± √(82)

So the correct answer is: (x + 10)² = 82.

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Answer: (-7, 7)

Step-by-step explanation:

Answer:

\(\mathrm{Solution\:} = (- 7,7) = \mathrm{Last\:}\mathrm{Option\:}\)

Step-by-step explanation:

In my point of view the easiest approach to solving this problem would be by determining the distance between the given points (the midpoint and the other given point) --- (1) and then going through all the answer choices and matching their distance to the midpoint --- (2). This may seem like a hard approach, but you can eliminate many of the answer choices.

The answer is the last choice, so let's prove it.

\(\mathrm{Distance\:between\:}\left(1,\:5\right)\mathrm{\:and\:}\left(9,\:3\right) = \sqrt{\left(9-1\right)^2+\left(3-5\right)^2} = 2\sqrt{17}\)

\(\mathrm{Distance\:between\:}\left(1,\:5\right)\mathrm{\:and\:}\left(-7,\:7\right)=\sqrt{\left(-7-1\right)^2+\left(7-5\right)^2}=2\sqrt{17}\)

\(2\sqrt{17} = 2\sqrt{17}\)

As the distance between points (1,5) and (9,3) respectively (1,5) and (- 7,7) is the same, we proved that our answer is the last choice.