2. Find the midpoint of AB
given A(-3, 8) and B(-7, -6).

The correct option is E. √26.

The distance between the points A and B is √26.

Algebraic representation that gives the distances between two points based on of those coordinates (see coordinate system). The distance formulas for points throughout rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.

Now, as per the given question;

The coordinates of the points A and B are  (-2,4) and (3,3).

The formula of distance formula is written as for the points A and B ia-

AB² = (x₂ - x₁)² + (y₂ - y₁)²

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

The coordinates of A and B are-

(x₁,y₁) = (-2,4)  and (x₂,y₂) = (3,3).

Substituting the values in the formula;

AB = √[(3 + 2)² + (3 - 4)²]

AB = √[(5)² + (-1)²]

AB = √[25 + 1]

AB  = √26

Therefore, the distance between the coordinates A and B is found to be √26.

To know more about the distance formula, here

https://brainly.com/question/661229

#SPJ4

Answer:

x = 0

Step-by-step explanation:

You are solving for x

[tex]\frac{x}{5}[/tex] + 2 = 2  Subtract 2 from both sides of the equation

[tex]\frac{x}{5}[/tex] = 0  Multiply both sides by

[tex]\frac{x}{5}[/tex]  [tex](\frac{5}{1})[/tex] =  0 [tex]\frac{5}{1}[/tex]

x = 0

The given sequence 100,117,134,151,168, ........... is in AP. The next three terms are 185, 202, 219..

The difference between two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd emerge across a few fundamental words in AP that have been labeled as:

The AP can also be described in terms of common differences, as shown below.

Now, the given sequence is; 100,117,134,151,168, ...........

The series comprises of five given terms.

Let the initial term be 'a₁' = 100.

The second term be 'a₂' = 117.

The third term be 'a₃' = 134.

And, the fourth term is 'a₄' = 151.

The AP must have the equal common difference. So,

d = a₃ - a₂

Substitute the values.

d = 134 - 117

d = 17

Thus, the computed common difference is 17.

or d = a₄ - a₃ (Substitute the values)

d = 151 - 134

d = 17

Since, a₃ - a₂ = a₄ - a₃

Thus, we can get to know that the given sequence is in AP.

Now, the 6th term is estimated as; a₆ = a₅ + d = 168 + 17

a₆ = 185

Similarly, the 7th term will be; a₇ = a₆ + d = 185 + 17

a₇ = 202

And, the 8th term will be calculated as; a₈ = a₈ + d = 202 + 17

a₈ = 219.

Therefore, it can be said that the given sequence is in AP next three terms be 185, 202, 219.

To know more about the arithmetic progression, here

https://brainly.com/question/16954227

#SPJ4

The amount that she would earn in one year at her part time job is 1440

Note that a function is an expression, rule or law that shows the relationship between a dependent and an independent variable.

Given the expression as;

12(100+20)

To determine the amount, we need to use the BODMAS rule by solving the bracket, we have

Amount = 12(100+20)

Amount = 12(120)

Expand the bracket

Amount = 1440

Thus, the amount that she would earn in one year at her part time job is 1440

Learn more about functions here:

https://brainly.com/question/17043948

#SPJ1

The advanced trail is 4.32 times as long as the beginner's trail.

A decimal is a number that is made up of integers and non-integers. The whole numbers are separated from numbers that are not whole number by a decimal point. An example of a decimal is 1.2.

Let:

The equation that represents the length of the medium trail: 1.2 x b = 1.2b

The equation that represents the length of the advanced trail: 3.6 x 1.2b = 4.32b

To learn more about decimals, please check: https://brainly.com/question/15287678

#SPJ1

Answer:

7.2

Step-by-step explanation:

7.4-0.2=7.2

Answer:

1 hour has 3600 seconds

to get how many dollars Jack earns we have to do this

3600 sec x $0.02 = $72

40 weeks x $72 = $2880

Answer:

$149,760

Step-by-step explanation:

As:

⇒ 1 hour = 60 × 60 seconds = 3600 seconds

As:

⇒ 52 × 40 = 2080 hours per year

Therefore, the number of seconds Jack works per year is:

⇒ 2080 × 3600 = 7,488,000 seconds

If Jack earns $0.02 per second, then the number of dollars per year he earns is:

⇒ $0.02 × 7,488,000 = $149,760

The ninth and tenth term of the given arithmetic sequence are: -18 and -21.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Now,

Given: 6, 3, 0, -3, ....; it is a decreasing AP.

Here, a = 6 (initial term) and d = -3 (common difference)

Thus, in the formula: [tex]a_n[/tex] = a + (n - 1) d, substituting these values:

=>  [tex]a_n[/tex] = 6 + (n - 1)(-3)

For ninth term, n = 9

Thus,  [tex]a_n[/tex] = [tex]a_9[/tex] = 6 + (9 - 1)(-3)

=> [tex]a_9[/tex] = 6 + (8)(-3)

=> [tex]a_9[/tex] = 6 -24

=> [tex]a_9[/tex] = -18

Similarly, for the tenth term, n = 10

Thus, [tex]a_n=a_{10}[/tex] = 6 + (10 -1) (-3)

=> [tex]a_{10}[/tex] = 6 + (9) (-3)

=> [tex]a_{10}[/tex] = 6 - 27

=> [tex]a_{10}[/tex] = -21

Hence, The ninth and tenth term of the given arithmetic sequence are: -18 and -21.

To learn more about arithmetic sequences, refer to the link: https://brainly.com/question/6561461

#SPJ4

Answer:

Step-by-step explanation:

Answer: x=-3/4

Step-by-step explanation:

12-x=15+3x

12-x+x=15+3x+x

12=15+4x

12-15=15-15+4x          ==> isolate the variable x.

-3=4x

4x/4=-3/4

x=-3/4

Answer:

The first one would be -11x + 3

The second on would be 29x + 3

Step-by-step explanation:

For the first equation you add -2 to 5 so you have 9x+3-20x. Then you add the 9x to -20x which will leave you with -11x+3.

For the second equation you add the -2 to 5 and have 9x+3+20x. You add 9x to 20x which will leave you with. 29x+3

Answer: Large Box: 18.75 kilograms

Small Box: 15.75 kilograms

Step-by-step explanation:

l=large box. s=small box

5l+3s=141

7l+9s=273

(5l+3s=141)*3

15l+9s=423    ==> subtract this equation

7l+9s=273   ==> subtract this equation

8l=150 ==> subtract the two above equations

l=150/8

l=18.75

5(18.75)+3s=141

93.75+3s=141

93.75+3s=141.00

3s=47.25

s=15.75

Large Box: 18.75 kilograms

Small Box: 15.75 kilograms

The formula to find the sum of an arithmetic sequence: Sn = n/2[2a + (n - 1)d], where a is the first term, n is the number of terms and d is the common difference.

1) Let's substitute the values into the formula.

S17 = 17/2[2(11) + (17 - 1)6]

S17 = 17/2[22 + (16)6]

S17 = 17/2[22 + 96]

S17 = 17/2[118]

S17 = 17/2 × 118

S17 = 1003

Therefore, the sum of the first 17 terms of this arithmetic sequence is 1003.

To know more about "Common difference"

Refer this link:

https://brainly.com/question/19601308

#SPJ4

Answer:

B. 4/5

Glad to help :)

By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is  (4 , 2 , -3).

Given:

x - y + z = -1     (equation 1)

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.

Subtracting equations 1 and 3 will eliminate the variable y.

2x - y + 2z = 0     (equation 3)

 x - y + z = -1   (equation 1)

x        + z = 1     (equation 4)

Adding equations 2 and 3 will eliminate the variable y.

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

3x      + 5z = -3     (equation 5)

Multiply equation 4 by -5 and add with equation 5.

x + z = 1     (equation 4)

⇒ -5x - 5z = -5

+    3x + 5z = -3     (equation 5)

-2x             = -8

x = 4

Substitute the value of x to either equation 4 or 5 and solve for z.

x + z = 1     (equation 4)

4 + z = 1

z = 1 - 4

z = -3

Finally, substitute the value of x and z to any of the first three equations, and solve for y.

x - y + z = -1     (equation 1)

4 - y + (-3) = -1

-y = -1 - 4 + 3

-y = -2

y = 2

Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.

x - y + z = -1     (equation 1)

4 - 2 + (-3) = -1

-1 = -1

x + y + 3z = -3     (equation 2)

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

-3 = -3

2x - y + 2z = 0     (equation 3)

2(4) - 2 + 2(-3) = 0

0 = 0

Hence, the solution of the system of equations is (4 , 2 , -3).

Learn more about solving systems of equations by elimination here: brainly.com/question/28405823

#SPJ4

Answer: Since the radius of the circle is perpendicular to AB, AB is tangent to the circle.

Step-by-step explanation:

Answer:

perpendicular and tangent

Step-by-step explanation:

1)The neighborhood park is 60m by 50 m. The park is reduced in size by 321m2 as a portion of it is ripped up to create a uniform-width sidewalk around it. What quadratic equation best captures the circumstances?

2)A rectangle's length is 1 m less than twice its width. The rectangle has a 120 m2 area. What quadratic equation best describes the circumstances?

Answer for the first question is the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].

Answer for the second question is The quadratic equation is [tex]x^{2} -x-120=0[/tex].

1)Let 'x' stand in for the sidewalk's width.

The area of the park is: [tex]A_{1} =60\times50[/tex]

The reduced area of the park measures

60-2x by 50-2x with area of [tex]A_{2} =(60-2x)(50-2x)[/tex]

[tex]A_{1} -A_{2} =321[/tex]

[tex]60\times50-(60-2x)(50-2x)=321[/tex]

[tex]3000-(60-2x)(50-2x)=321\\3000-(3000-120x-100x+4x^{2} )=321\\220x-4x^{2} =321\\4x^{2} -220x+321=0\\[/tex]

Therefore, the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].

2) Given that,

Width=x.

length=2x-1

Area=120[tex]m^{2}[/tex]

We know area=length[tex]\times[/tex]width

120=x(x-1)

[tex]x^{2} -x=120\\x^{2} -x-120=0[/tex]

Therefore, The quadratic equation is [tex]x^{2} -x-120=0[/tex].

To learn more about quadratic equation visit: https://brainly.com/question/17177510

#SPJ9

Answer: In geometry, when you translate an object, it means that you have turned that object in a different direction. Hence a translated angle is an angle that has been turned in a different direction.

From the first option in part A, it is clear from the image that the angle didn't change. It moves 7 units from the positive to the negative part of the x-axis.

From Part B, the angles also do not change. Note that when an angle is rotated or translated, it does not modify the angles.

From Part C, what we have is the reflection of the angles. This means that both angles are equal because they are a reflection of each other.

From Part D, the two sets of parallel lines will remain parallel to each other also long as they are both translated as the same time.

From part E, although in each set of parallel lines, the two sets of lines remain equidistant to each other, the parallel line that is at an angle to the Y-axis will not intersect that which is at an angle to the x-axis if they are extended infinitely.

Step-by-step explanation: hope this helps alittle

The distance between the given parallel lines is 4 units

In the given statement is :

The equations of the pair of each parallel lines is:

y=-0.75 x-1

3 x+4 y=20

To find the distance between each pair of parallel lines.

Two lines a₁x +b₁y + c₁=0   and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.

As we know that distance between the parallel lines (d) is given as:-

d = [tex]\frac{c_{2}-c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]

Parallel lines equation as:

y=-0.75 x-1...(1)

3 x+4 y=20....(2)

Divide by -3 in equation (2)

Now, The equations is

-0.75x -y -1 =0

-0.75x -y +4 =0

Here,

a = -0.75 , b = -1, c1 = -1 , c2 = 4

Therefore, putting the values

[tex]d =\frac{4-(-1)}{\sqrt{(-0.75^{2} )+(-1)^{2} } } \\\\d=\frac{5}{\sqrt{0.5625+1} }\\ \\d = \frac{5}{\sqrt{1.5625} }[/tex]

d = 4 units

Hence, The distance between the given parallel lines is 4 units

Learn more about Parallel lines at:

https://brainly.com/question/2235918

#SPJ4

An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.

If the expression be (-3)(-9) then the value of (-3)(-9) is 27.

Let (-3)(-9) be the given expression

We know the rule , (-) × (-) = (+)

(-3) × (-9) = +27

Therefore, the value of (-3)(-9) is 27.

To learn more about simplifying expressions, refer to:

https://brainly.com/question/723406

#SPJ4

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

They are congruent triangles.

What do you mean by congruent?

In the triangle JKL, the sides can be calculated as following:

J(2;5); K(1;1)

            => JK = [tex]\sqrt{( ( 1 - 2 )^{2} + ( 1 - 5 )^{2} } = \sqrt{( -1 )^{2} + ( -4)^{2} } \\= \sqrt{ 1 + 16 } = \sqrt{17}[/tex]

J(2;5); L(5;2)

            JL = [tex]\sqrt{( 5 - 2 )^{2} + ( 2 - 5 )^{2} } = \sqrt{3^{2} + ( -3)^{2} } \\[/tex]

                 = [tex]\sqrt{ 9 + 9 } = \sqrt{18} = 3\sqrt{2}[/tex]

K(1;1); L(5;2)

            =>  KL = [tex]\sqrt{ ( 5 - 1 )^{2} + ( 2 - 1 )^{2} } = \sqrt{4^{2} + 1^{2} } = \sqrt{ 1 + 16} = \sqrt{17}[/tex]

In the triangle QNP, the sides can be calculate as following:

Q(-4;4); N(-3;0)

            => QN  = [tex]\sqrt{[ -3 - ( -4)^{2} ] + ( 0-4)^{2} } = \sqrt{1^{2} + 16 } = \sqrt{17}[/tex]

Q (-4;4); P(-7;1)

  => QP =  [tex]\sqrt{ [ -7 - ( -4 )^{2} + ( 1 - 4 )^{2} } = \sqrt{( -3)^{2} + ( -3)^{2} } = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}[/tex]

N(-3;0); P(-7;1)

      =>  NP = [tex]\sqrt{[-7 -( -3)]^{2} + ( 1 - 0 )^{2} } = \sqrt{ - 4^{2} + 1 } = \sqrt{ 16 + 1} = \sqrt{ 17}[/tex]

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles

Learn more about congruent

brainly.com/question/12413243

#SPJ4

Answer:

See proof below

Step-by-step explanation:

[tex]4cos^2(x) +4sin(x) = 5\\\\\sf Divide\; both \; sides\; by\; 4\\== > cos^2(x) + sin(x) = \dfrac{5}{4} .................(1)\\\\cos^2(x) + sin^2(x) = 1\\\\cos^2(x) = 1- sin^2(x) \\\\\textsf {Substituting into equation (1) }\\1-sin^2(x) + sin(x) = \dfrac{5}{4}\\\\\\sf Subtract\; 1\; from\; both \; sides\\\mathsf{-\sin^2(x) + \sin(x) = \dfrac{5}{4} - 1}\\\\ \dfrac{5}{4} - 1 = \dfrac{5}{4} - \dfrac{4}{4} = \dfrac{1}{4}\\[/tex]

[tex]\sf {-\sin^2(x) + \sin(x) = \dfrac{1}{4}\\[/tex]

[tex]\sf Subtract\; \dfrac{1}{4}\;from\;both\;sides\\[/tex]
[tex]{-\sin^2(x) + \sin(x) - \dfrac{1}{4} = 0\\\\[/tex]

Multiply throughout by -1
[tex]\sf \sin^2(x) - \sin(x) + \dfrac{1}{4} = 0\\\\[/tex]

Let u = sin(x). Substituting we get
[tex]\sf u^2 - u + \dfrac{1}{4} = 0[/tex]

This is a quadratic equation which can be solved using sum of squars

Note that

[tex]\sf (u - \dfrac{1}{2})^2 = u^2 -2\cdot \dfrac{1}{4}u + (\dfrac{1}{2})^2 \\= \sf u^2 - u + \dfrac{1}{4} = 0[/tex]

So
[tex]\sf (u - \dfrac{1}{2})^2 = 0\\Solution\; is \;u = \dfrac{1}{2}\\\\Substituting\sin(x) \;for\;u \;gives\\sin(x) = \dfrac{1}{2}[/tex]

PROVED

Answer:

Step-by-step explanation:

In all three pictures, the data are correctly matching except this one..

~~

Answer:

Step-by-step explanation:

Answer:

A: D:(-6,6)

B: D:(-7,5]

C: Not a function D: -5

D: Not a function D:(-4,4)

E: Not a function D:(0,∞)

F:  D:[0,∞)

G: D:[-3,5)

H: D:(-4,2)

I: D:[-3,4]

J: Not a function D:(-3.-4)

K: D:(-∞,∞)

L: D:(-∞,∞)

Number of songs that will be downloaded in 2020 = 2600 million

Given that in 2004, 200 million songs were downloaded and in 2006, 500 million songs were downloaded from the internet.

When we graph this trend, these data corresponds to the points (4,200) and (6, 500).

Also it will be a straight line. So its slope can be found.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150

This means that there is an increase of 150 million songs downloads pe year.

Also 2020-2006 = 14 years

So the number of songs downloaded in 2020 = Number of songs downloaded in 2006 + 14 x 150 = 500 + 14 x 150

                                                     = 500 +2100

                                                     = 2600 million

So 2600 million songs will be downloaded legally from the internet by 2020.

Learn more about slope at https://brainly.com/question/16949303

#SPJ4

If a red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds, then the number of times the red and blue string of holiday lights will blink in one minute is equal to 20 and 15 respectively.

The number of times each string of holiday lights will blink can be determined by using division.

As we have to calculate the number of times they blink in one minute, we can convert one minute into seconds.

One minute = 60 seconds

Now, the number of times each string of light blinks can be calculated by dividing the total seconds by the seconds after which the light blinks

For the red string of holiday lights :

The number of times the light will blink in one minute = 60 ÷ 3 = 20

For the blue string of holiday lights :

The number of times the light will blink in one minute = 60 ÷ 4 = 15

Hence the red string of holiday lights will blink 20 times and the blue string of holiday lights will blink 15 times in one minute.

To learn more about division, click here:

https://brainly.com/question/28119824

#SPJ4

Answer:

See below

Step-by-step explanation:

-1.887 x10^2   would be one answer

- 18.87 x 10^1    could be another

Answer:

Step-by-step explanation: Wowee! That's pretty hard.

Scientific Notation:

-1.887 × 102

E-Notation:

-1.887e2

Engineering Notation:

-188.7 × 100

Real Number:

-188.7

Hope this helps!

[tex]format \: \: y = mx + c[/tex]

[tex]m = \frac{5 - 0}{10 - 0} = \frac{5}{10} = \frac{1}{2} [/tex]

[tex]c = 0 \: since \: the \: line \: passes \: through \: the \: origin \\ [/tex]

[tex](d) \: \: \: y = \frac{x}{2} [/tex]

The equation that we need to solve and the solution is:

A = 11.7mi/3 = 3.9 mi

We conclude that he needs to ride an average of 3.9 miles per day.

Here we know that Carter wants to ride his bicycle 28.7 miles this week, and he has already ridden 17 miles, so the distance left is:

D = 28.7 mi - 17mi = 11.7mi

Now, if he has 3 days to complete that distance, then the average distance that he needs to travel each day is given by the quotient:

A = 11.7mi/3 = 3.9 mi

So that is the equation that we need to solve and the solution, we conclude that he needs to ride an average of 3.9 miles per day.

learn more about quotients:

https://brainly.com/question/629998

#SPJ1

The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

R = x^2/y

Where

y = 3.8 x 10^5

x = 5.9 x 10^4

Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y

So, we have

R = (5.9 x 10^4)^2/3.8 x 10^5

Evaluate the exponent in the above equation

So, we have

R = 34.81 x 10^8/3.8 x 10^5

Evaluate the quotient in the above equation

So, we have

R = 9.16052631579 x 10^3

Approximate the above expression

So, we have

R = 9.2 x 10^3

Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

Read more about scientific notation at

brainly.com/question/27862246

#SPJ1

Step-by-step explanation:

let this number is x