Calculate the distance between the points P=(0, 1) and J=(4, -2) in the coordinate plane. Give an exact answer (not a decimal approximation).​

The average rate of change in Greenville's population for this six-year period is 35 person per year

What's the math rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.

Given that:

Greenville population = 4,870

Greenville population after 6 years = 5,080

Difference of population = 5080 - 4870 = 210

Average rate = Population / Years = 210/6 = 35 person per year

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The triangles can be proven congruent using the ASA congruence postulate.

Thus, we can say that triangles ABK and CBK are congruent.

Triangles are congruent, according to the Angle Side Angle Postulate (ASA), if any two angles and their included side are equivalent in the triangle. The side between two angles is considered an included side.

Additionally, you can confirm that your two triangles are congruent by employing the Side Angle Side Postulate (SAS). In this case, we choose a side and its equivalent side on two triangles rather than two angles.

Triangles are said to be congruent according to the SAS Postulate if any pair of corresponding sides and their included angle are also congruent.

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The image of triangle ABC under a dilation whose center is A and scale factor is 4 is as follows.

What is dilation?

Dilation involves changing the size of a shape.

Main body:

Assume point P is the center of origin, then we have the following coordinates of ABC

A= (1,0)

B= (-2,0)

C= (0,2)

The scale factor (k) is given as:

K = 4

So, the dilation rule is represented as:

(x, y) = 4 *(x,y)

Using the above dilation rule, the following coordinates represent the image of triangle ABC

A' =(4,0)

B' =(-8,0)

C' =(0,8)

See attachment for the image of the dilation.

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The equivalent equations of y - 4 = 2/3(x - 1) are y - 4 = 2/3x - 2/3 and y  = 2/3x + 10/3

From the question, we have the following parameters that can be used in our computation:

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

We start by expanding the bracket

So, we have the following representation

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

Next, we add 4 to both sides of the equation

This gives

y - 4 + 4 = 2/3x - 2/3 + 4

Evaluate the like terms

So, we have the following representation

y  = 2/3x + 10/3

Hence, the equivalent equation is y  = 2/3x + 10/3

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Answer:

x=4

Step-by-step explanation:

x=4 because when you have 3x+2=14 Subtract 2 from both sides. Then 3x+2−2=14−23x=12. Divide both sides by 3.3x3=123

The value of x in the figure having 3 angles on a line as shown in the image attached below is 28.

The angle is formed by two rays and a common point.

To calculate the value of x using the diagram attached below:

∠AOC+∠COD+∠BOD = 180° because the sum of all the angles on a line is 180°

On substituting the values from the figure,

∠AOC=3x-7

∠COD=55

∠BOD=x+20

∠AOC+∠COD+∠BOD =3x-7+55+x+20

3x-7+55+x+20=180

4x+68=180

4x=112

x=28

Thus, the value of x is 28 for the figure attached below.

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She should divide both sides by -5 while multiplying the other side by -5. She also did not replace the > symbol with a symbol.

An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

From given question :

-5x-3.5>6.5

-5x > 10

X > -50

Since, we have to solve for x

so, we will isolate x on anyone side

step-1:

Add both sides by 3.5

- 5x - 3.5 + 3.5 > 6.5 + 3.5

- 5x > 10

step-2:

Divide both sides by -5

we know that whenever we divide both sides by negative sign , it's inequality gets revered

so, we get

- 5x / -5 < - 50 / -5

we get

x < 10

so,

She should divide both sides by -5 while she multiplied by -5 on other side

and she also did not change the > symbol to a < symbol

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Answer:

[tex]\boxed{\tt A. \;y = .613x + 4.142}[/tex]

Step-by-step explanation:

Equation: (y-y_1)=y_2-y_1/x_2-x_1 (x-x_1)

Here,

[tex]\tt (x_1,y_1):(-2,2.9)[/tex]

[tex]\tt (x_2,y_2): (-3.5,2)[/tex]

[tex]\tt y-2.9=\cfrac{(2-2.9)}{(-3-5-(-2))} (x-(-2))[/tex]

[tex]\tt y-2.9=\cfrac{-0.9}{-1.5} (x+2)[/tex]

[tex]\tt y-2.9=0.6(x+2)[/tex]

[tex]\tt y-2.9=0.6x+1.2[/tex]

[tex]\tt y=.613x+4.142[/tex]

___________________

Hope this helps you!

Have a nice day!

Answer:

(-8.6)

Step-by-step explanation: If you look at a graph and pinpoint the location of (8,-6) by going up 8 and then going to the left 6. so the point of (8.-6) is in the top left box and if we are reflecting over the x-axis and the y-axis the point will be at the lower right box therefore the answer is (-8.6).

The only option that is not an equivalent of the product of both polynomials is; C: 6x³ + 11x² − 13x + 2

Equations can be classified as either identities or conditioned equations. For each quantity of the variables, an identity is true. Only specific values of the variables make a conditional equation legitimate. The equals sign ("="), which separates two expressions, is a symbol for an equation.

Here,

We are given the expression;

(3x - 2)(2x² + 5x - 1)

The result of expanding the polynomial is;

6x³ + 11x² − 13x + 2

Looking at the given options as seen online, the only one that is not an equivalent of the given product is;

Option C) : 6x³ + 11x² − 13x + 2 is correct

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Answer:

9x-y=10

Step-by-step explanation:

The formula for standard form is Ax + By =C

So, y=9x-10

-1(-9x+y=-10)

9x-y= 10

The mean and the standard deviation of the distributions are

The distribution is given as:

A uniform continuous model

The mean and the standard deviation of this type of model are

Mean = (a + b)/2

Standard deviation = (b−a)/√12

Using the above formulas, we have

a. U(0, 15)

Mean = (0 + 15)/2 = 7.5

Standard deviation = (15−0)/√12 = 4.3301

b. U(90, 230)

Mean = (90 + 230)/2 = 160

Standard deviation = (230 − 90)/√12 = 40.4145

c. U(4, 92)

Mean = (4 + 92)/2 = 48

Standard deviation = (92 - 4)/√12 = 25.4034

Hence, the standard deviation of U(4, 92) is  25.4034

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Answer:

$0.48/pound

Step-by-step explanation:

$5.76 divided by 12

Answer:

350

Step-by-step explanation:

Let "a" represent the number of adult tickets sold and "s" represent the number of student tickets sold. We can set up the following equation to represent the information given:

a + s = 627

s = a - 73

Substituting the second equation into the first equation gives us:

a + (a - 73) = 627

2a - 73 = 627

2a = 700

a = 350

Thus, there were 350 adult tickets sold.

The graph's representation of the inequality system is

y≤3x-2 and y≥-4x+2. So, option a is correct.

One of the basic ideas of social justice theories is the existence of unequal status, rights, and opportunities. In public conversation, it might be confusing because various people often interpret it differently. There are some frequent variants, though. In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. As an illustration, suppose you wish to get a 250 new bicycle. Different types of inequality are indicated by a variety of notations, including:

A less than sign, such as a, denotes that an is greater than b.

Therefore, The  system of inequalities that is represented by the graph is

y≤3x-2 and y≥-4x+2. So, option a is correct.

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The graph that shows the straight line → x - 5y = 27 is plotted and attached.

The general equation of a straight line is -

y = mx + c

where -

[m] is slope of the line.

[c] is the y - intercept of the line.

Given is the equation of the line as -

x - 5y = 27

The given equation of the line is -

x - 5y = 27

Rearranging the equation, we get -

5y = x - 27

y = (1/5)x - (27/5)

y = 0.2x - 5.4

Now, refer to the graph attached. The slope [m] of the equation will be -

m = 0.2 and the [y] - intercept will be y = - 5.4.

Therefore, the graph that shows the linear relation → y = 0.2x - 5.4 is plotted and attached.

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Answer:

The dividend in the synthetic division below is x+2:

     4 | -6 -5 4 -7

     -   --------------

     -   -1 -1 1 -5

     0 | -5 -4 3 -2

     -   --------------

     2 | x+2

In synthetic division, the numbers in the top row represent the coefficients of the polynomial being divided, and the number in the bottom row represents the value of the dividend. In this case, the dividend is x+2 because it is the only number in the bottom row that is not a result of the division operation

a) The coordinates of the midpoints P and Q are given as follows:

b) The two segments are parallel because they have the same slope.

The midpoints between two points is given by the mean of the coordinates of these two points.

Hence the midpoint P of AB has the coordinates given as follows:

The midpoint Q of AC has the coordinates given as follows:

Parallel segments are segments that have the same slope, that is, the same result of the division of the change in y by the change of x of two points in the segment.

The slopes of PQ and BC are given as follows:

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Answer:

500,000 can be written in expanded form in two different ways:

500,000 = 500,000

500,000 = 5 x 100,000 + 0 x 10,000 + 0 x 1,000 + 0 x 100 + 0 x 10 + 0 x 1

In both cases, the expanded form shows the value of each digit in the number. The first way simply lists the number itself, while the second way breaks down the number into its component parts and shows the value of each digit in relation to the place value it holds in the number.

Answer:

Could you give a little more context. I can help.

Answer:hope i helped A. 20% B.45%

A= 40,000/40,000/200000=.2 Or 20%b. 90,000/200000=.45

Step-by-step explanation:

Answer:

18.6

Step-by-step explanation:

Yes , we can drag fields from the field list to an area box in the pivot table fields pane in order to create a pivot table. Hence , true.

The four sections of the pivot table

are located at the bottom of the PivotTable Field List window.

The fields will appear in the corresponding region of the worksheet's pivot table layout when you drag them into these locations.

Only the fields included in the PivotTable Field List can be moved in Excel 2007. If you try to drag the Promo field onto the pivot table in the screen photo below, the cursor displays an X. The drag-and-drop function is broken.

You can alter a setting in the pivot table options if you'd like to drag the pivot fields onto the worksheet layout.

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3x³ + 5x² - 17x - 15

1. Distribute

(x + 3)(3x² - 4x - 5)

x(3x² - 4x - 5) + 3(3x² - 4x - 5)

2. Distribute

x(3x² - 4x - 5) + 3 (3x² - 4x - 5)

3x³ - 4x² - 5x + 3 (3x² -4x - 5)

3. Distribute

3x³ - 4x² - 5x + 3 (3x² -4x - 5)

3x³ - 4x² -5x + 9x² - 12x - 15

4. Combine like terms

3x³ - 4x² -5x + 9x² - 12x - 15

3x³ + 5x² - 5x - 12x - 15

5. Combine like terms

3x³ + 5x² - 5x - 12x - 15

3x³ + 5x² - 17x - 15

3x³ + 5x² - 17x - 15

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.

Given that,

Kristin spends thirty percent of her savings on a watch and sixty percent on a dress.

We have to find what portion of her savings is still available.

We know that,

Kristin spends thirty percent of her savings on a watch.

Sixty percent on a dress.

The money she has a 100%  in that if she spend 30% on watch she get 70% then if she spend 60% on dress she will have 10%

Therefore, Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.

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Answer:

See below

Step-by-step explanation:

From the given parameters, the area of the triangle is 288m².

How to calculate the area of a triangle?

A triangle is a polygon with three angles, three vertices and three sides whose sum of angles is 180⁰

Let the vertices of the triangle be labelled ABC

/AB/=16m

/BC/=45m

<ABC=127⁰

The given information formed an obtuse angled triangle.

Area of the triangle (A) = [tex]\frac{1}{2}[/tex]ACsinB

Substituting the various values in the formula we have;

A=[tex]\frac{1}{2} *16*45*sin127^{0}[/tex]

simplifying the equation to get;

A=8*45*0.7986

A=287.5088

A=288m²

Therefore, the area of the triangle to the nearest whole number is 288m²

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It takes 11.55 years for money to double if invested at 6% compound interest.

What is compound interest?

Calculating the answer exactly:  P⁰°⁰⁶ⁿ=A .

We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.

P⁰°⁰⁶ⁿ = 2P

We divide both sides by  P

e⁰°⁰⁶ⁿ = 2

Using natural logarithm:

0.06 n = ln(2)

n = ln(2)/0.06

n = 11.55 years

Hence, It takes 11.55 years for money to double if invested at 6% compound interest.

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The domain of the inverse function is {5,6}. And as a compound inequality the domain is 5<x<6.

A mathematical statement that expresses the inequality between two inequalities combinedly.

from the graph, we have two inequalities, x>5 and x<6

it can be written as 5<x<6

A function that can be obtained by reversing the primary function is termed as inverse of function. it is denoted by f⁻¹.

The graph shown is got from an inverse function whose domain is {5,6} and ranges are {-2, -4}

The graph also refers the inequalities of x>5 And x<6

compound inequalities of domain 5<x<6

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Answer:

[tex]y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]y=-4x-5[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.

The slope of the given equation is -4.

Therefore, the slope of the perpendicular line is ¹/₄.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point (-2, 3) into the point-slope formula to create the equation of the perpendicular line.

[tex]\implies y-3=\dfrac{1}{4}(x-(-2))[/tex]

[tex]\implies y-3=\dfrac{1}{4}(x+2)[/tex]

[tex]\implies y-3=\dfrac{1}{4}x+\dfrac{1}{2}[/tex]

[tex]\implies y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]

Step-by-step explanation:

A circle with a center of (-1,2) and a radius

of

[tex]2 \sqrt{2} [/tex]