mile
long. You walk 3 laps around the lake in the morning
and 2 laps in the evening. Your friend walks the same
1
total distance as you on a 1--mile track. How many
2
laps does your friend walk?

The value of x when r(x) = -4 is 20/3.

Given, the function is r(x) = ₋2/3x ₊ 4

substitute r(x) = ₋4 in the value of r(x)

r(₋4) = ₋2/3(₋4) ₊ 4

r(₋4) = 8/3 ₊ 4

r(₋4) = 8 ₊ 12/3

r(₋4) = 20/3

hence we get the value as 20/3

Learn more about Function here:

brainly.com/question/20240210

#SPJ9

Inverse of the give function F(x) = ( x + 4 )³ - 1 is F⁻¹(x) = [√( x + 1 ) ] - 4.

Given is a function of x, F(x) = ( x + 4 )³ - 1

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = ( x + 4 )³ - 1 becomes y = ( x + 4 )³ - 1

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = ( x + 4 )³ - 1, we get

x = ( y + 4 )³ - 1

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x = ( y + 4 )³ - 1

=> x + 1 = ( y + 4 )³

=>  (y + 4 )³ = x + 1

=> y + 4 = √( x + 1 )

=> y = √( x + 1 ) - 4

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = √( x + 1 ) - 4 becomes F⁻¹(x) = √( x + 1 ) - 4

Therefore, we get the inverse of the give function F(x) = ( x + 4 )³ - 1 as F⁻¹(x) = [√( x + 1 ) ] - 4.

Learn more about Inverse of a Function here:

https://brainly.com/question/2541698?referrer=searchResults

#SPJ9

A parabola's maximum value is the y-coordinate of its vertex when it opens downward.

Therefore, a parabola's maximum value is the y-coordinate of its vertex when it opens downward.

Know more about a parabola here:

https://brainly.com/question/4061870

#SPJ4

Answer:

[tex]48\sqrt 6[/tex]

Step-by-step explanation:

[tex]2\sqrt{8}=2(2\sqrt{2})=4\sqrt{2} \\ \\ 6\sqrt{12}=6(2\sqrt{3})=12\sqrt{3} \\ \\ (4\sqrt 2)(12\sqrt 3)=48\sqrt 6[/tex]

A quadrilateral has four sides that are each an even number of meters long (in meters).Considering a 46 meter of perimeter, the value of the longest side length out of the four sides is 12.

Given that,

A quadrilateral has four sides that are each an even number of meters long (in meters).

Considering a 46 meter of perimeter.

We know that even numbers differ by 2 and are multiples of 2.

Thus, due to the four sides of quadrilaterals.

let those sides' lengths be

2x,2x+2,2x+4 and 2x+6

The perimeter of a quadrilateral's boundary as a whole is its perimeter. An irregular or regular four-sided polygon is referred to as a quadrilateral. A regular quadrilateral has sides that are all the same length and angles that are all the same measure; an irregular quadrilateral does not have equal sides and angles.

Perimeter of a quadrilaterals is

perimeter=sum of the 4 sides.

36=sum of the 4 sides.

Which we have taken 2x,2x+2,2x+4 and 2x+6.

2x+2x+2+2x+4+2x+6=36

8x+12=36

8x=36-12

8x=24

x=[tex]\frac{24}{8}[/tex]

x=3.

Now, we can find the sides by the x value which is 3.

1st side=2x=2[tex]\times[/tex]3=6

2st side=2x+2=2[tex]\times[/tex]3+2=8

3st side=2x+4=2[tex]\times[/tex]3+4=10

4st side=2x+6=2[tex]\times[/tex]3+6=12

Therefore, the value of the longest side length out of the four sides is 12.

To learn more about quadrilateral visit: https://brainly.com/question/12131358

#SPJ1

Answer:13

Step-by-step explanation:

x+x+1+x+2+x+3=46

4x+6=46

-6 -6

4x=40

4x/4=40/4

x=10

Longest side: x+3

=10+3

=13

Answer:

D

Step-by-step explanation:

hope this works for you :)

Answer:

36 × 12 = 432

hopefully this helps :)

Answer:

QR = 3

Step-by-step explanation:

given Q is the midpoint of PR , then

PQ = QR , that is

3x = x + 2 ( subtract x from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Then

QR = x + 2 = 1 + 2 = 3

Answer:

QR = 3

Step-by-step explanation:

since Q is the midpoint, then PQ is the same as QR. so we equate the two as follows:

3x = x+2

then find x as shown below.

3x-x = 2 ( I grouped the like terms)

2x = 2. now divide by 2 to find x

x= 1,

since QR is x+2, now substitute x for 1

1+2 =QR

3 is the answer.

.thanks

Answer:

[tex]y=\frac{ac}{a-b-c}[/tex]

Step-by-step explanation:

[tex]y(a-b)=c(y+a) \\ \\ y(a-b)=cy+ac \\ \\ y(a-b)-cy=ac \\ \\ y(a-b-c)=ac \\ \\ y=\frac{ac}{a-b-c}[/tex]

Only the third statement (c)"To square a number multiply the number by itself" is true.

The square of any number is defined as the product of the number and itself .

Let us consider a number a , then the square of a is denoted by a² and  a² = a × a .

Let us take each statement and verify if they are true or false.

a)"To square a number, multiply the number by 2"

this is false as to square we have to multiply the number with itself.

example: 3²=9 but 3 × 2 = 6

b)The second statement is also false because square-root of a number is different than dividing a number by 2.

Example: √16=4 but 16÷2=8

c) "To square a number, multiply the number by itself."

This statement is true .

d) a perfect square is defined as a number whose square-root is an integer (both odd and even)

9 is a perfect square and √9=3 which is odd

Therefore the fourth statement is also false.

Hence only statement (c) is correct .

To learn more about the square of a number visit:

https://brainly.com/question/17749819

#SPJ9

[tex]~~~~~~~~~~~~\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[/tex]

Exact Distance = [tex]\boldsymbol{5\sqrt{5}}[/tex] units

Approximate Distance = 11.1803 units

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

Work Shown:

[tex](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\\\\[/tex]

The exact distance is [tex]5\sqrt{5}[/tex] 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.

The rationalization the denominator of the given expression is [tex]\frac{5\sqrt{6}x^3 }{2\sqrt{y} }[/tex] .

We have given an expression [tex]\frac{5\sqrt{3}x^3 }{\sqrt{2y} }[/tex] .

The denominator of the expression is [tex]\sqrt{2y}[/tex] .

Multiply the fraction in the numerator and denominator by [tex]\sqrt{2y}[/tex] , we get

         [tex]\frac{5\sqrt{3}x^3\times\sqrt{2y} }{\sqrt{2y} \times\sqrt{2y} }=\frac{5\sqrt{6}x^3\sqrt{y} }{2y}[/tex]

Learn more about rationalization here :

https://brainly.com/question/1622425

#SPJ4

The value of x for the equation 3ˣ = 27 is 3.

A linear equation with one variable is one that has just one variable. It has the formula Ax + B = 0, with A and B being any two real integers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

One method for expressing a linear equation is in the slope-intercept form (the equation of a line). Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). Using y=mx+b to graph a line is often simple.

The equation is -

3ˣ = 27

It can be expressed as -

3ˣ = 3³

x= 3

To learn more about linear equations from given link

https://brainly.com/question/2030026

#SPJ4

In M = rp+c, the equation illustrated shows that the value for p is p = (M - c)/r.

It should be noted that in Mathematics, an equation is used to illustrate or show the relationship that can be found with the variables that are expressed.

In this case, it should be noted that the given equation is illustrated as:

M = rp + c

Subtract c from both sides

M - c = rp + c - c

M - c = rp

Divide through by r

(M - c) / r = rp/r

p = (M - c)/r

Learn more about equations on:

brainly.com/question/13763238

#SPJ1

Step-by-step explanation:

supplementary angles mean that they are together 180°.

so,

a + (a - 51) = 180

2a - 51 = 180

2a = 231

a = 115.5°

its supplement is 180 - 115.5 = 64.5°

The measure of the angle's supplement is 64.5 degrees.

Let's denote the measure of the angle as "a" degrees. The supplement of an angle is the angle that, when added to the given angle, results in a total of 180 degrees (because the sum of angles in a straight line is 180 degrees).

According to the problem, the measure of the angle's supplement is 51 degrees less than the measure of the angle. Mathematically, we can express this as:

Supplement angle = Angle - 51

Since the sum of the angle and its supplement is 180 degrees, we can write the equation:

Angle + Supplement angle = 180

Substitute the expression for the supplement angle:

a + (a - 51) = 180

Combine like terms:

2a - 51 = 180

Now, solve for "a":

2a = 180 + 51

2a = 231

a = 231 / 2

a = 115.5

So, the measure of the angle "a" is 115.5 degrees.

Now, to find the supplement angle:

Supplement angle = a - 51 = 115.5 - 51 = 64.5

Therefore, the measure of the angle's supplement is 64.5 degrees.

To know more about angle's:

https://brainly.com/question/30147425

#SPJ3

Answer:

1225

Step-by-step explanation: i did the tesr b

We will get [tex]\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex] after simplifying the given expression

log 33,000- log 99+ log 30.

So,

Then,

[tex]\left\{\begin{array}{l}\log \cdot 33 \\000-\log \cdot 99+\log \cdot 30\end{array}\right.\\\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex]

Therefore, we will get [tex]\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex] after simplifying the given expression log 33,000- log 99+ log 30.

Know more about expressions here:

brainly.com/question/723406

#SPJ4

The total length of the strips will be 6L. Then the total length of the ribbon should have been 6L + 6/8.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Shayla cuts six ribbon pieces to create hair bows. She completes it, only to discover that each strip is 1/8 inch too short.

Let L be the length of the strips of ribbon. Then the total length of the strips will be

⇒ 6L

The total length of the ribbon should have been

⇒ 6(L + 1/8)

⇒ 6L + 6/8

The total length of the ribbon should have been 6L + 6/8.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Answer:

7, 5

Step-by-step explanation:

Change the denominator to make the end result 0. Anything with a 0 denominator results in it being undefined.

The expression (10-t)/(t-7) is undefined when t=7.

The expression 10/(3t-15) is undefined when t=5.

To find the values of t for which the expressions are undefined, we need to look for any values of t that make the denominators equal to zero.

we know that dividing by zero is undefined.

For the expression (10-t)/(t-7),  the denominator is t-7.

So, this expression is undefined when t-7=0

To find the value of t that makes t−7=0, solve the equation:

t-7=0

t=7

So, the expression (10-t)/(t-7) is undefined when t=7.

For the expression 10/(3t-15), the denominator is t-7.

So, this expression is undefined when 3t-15=0

To find the value of t that makes 3t-15=0, solve the equation:

3t-15=0

Add 15 on both sides:

3t=15

Divide both sides by 3:

t=5

So, the expression 10/(3t-15) is undefined when t=5.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ3

Answer:

4 is 4 2/3

Step-by-step explanation:

3 can only go in 14 4 times with 2 leftover

Answer:

b = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] = [tex]\frac{b}{2}[/tex] ( cross- multiply )

8b = 6 ( divide both sides by 8 )

b = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

b=3/4

Step-by-step explanation:

3/8=b/2

First you will need to cross multiply because apparently that's how we do things. To cross multiply, you would just have to take the bottom of the fraction from the LHS (left hand side) and times it with the top part of the fraction in RHS (right hand side). You do the same thing to the other side (take the top part of LHS and multiply it with the bottom of RHS). Make sure to keep the = sign in the middle.

8 x b = 3 x 2 (8 x b= 8b)

8b=6

Then, you would have to make the b on the LHS alone so you would have to divide the RHS by 8. (To move from one side to another, you would have to change it to the opposite of the sign like if it's -9, then to the other side it would be +9 and if it's x8 then the other side would be /8 and vice versa).

b=6/8

You will have to simplify unless the question asks you not to but I'll do it anyways. 2 goes into 6 and 8 as a common factor and so the answer should look like this:

b=3/4

If you have any further questions please ask me!

The number of pairs of parallel sides the rotated figure have is 2

Parallel sides or lengths are line segments or lines in the same plane that extend on both sides without intersecting

The shape is given as:

Shape = Rhombus

Rotation= 90 degrees counterclockwise rotation about the vertex G

The rotation transformation is a rigid transformation

This means that when a shape is rotated by 90 degrees counterclockwise about a vertex (in this case, the vertex G), the image of the rotation would have the same properties as the preimage

A rhombus has 2 pairs of parallel sides

This means that the number of pairs of parallel sides the rotated figure have will also be 2 (same as the original shape)

Hence, the number of pairs of parallel sides the rotated figure have is 2

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Answer:

  -4 ≤ y ≤ 2

Step-by-step explanation:

You want the range of the graph shown.

The range of a relation is the set of output values of the relation, the vertical extent of its graph.

The graph shown extends continuously from an absolute minimum of y=-4 to an absolute maximum of y=2.

The range is -4 ≤ y ≤ 2.

Answer:

2x + 15y + 2,960

Step-by-step explanation:

Single Rides are $2 each, represented by x

All day passes are $15 each represented by y

Combined they equal the total revenue; 2,960.

Answer in decimal form = -26.25

Answer as an improper fraction = -105/4

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

Work Shown:

1/2 = 0.5

Replace every copy of x with 0.5 in the f(x) function.

f(x) = x-8

f(0.5) = 0.5-8

f(0.5) = -7.5

Repeat the same idea for the g(x) function

g(x) = x+3

g(0.5) = 0.5+3

g(0.5) = 3.5

Then multiply the results

f(0.5)*g(0.5) = (-7.5)*(3.5) = -26.25

Then optionally convert to an improper fraction following the steps shown below.

-26.25 = -(26.25)

-26.25 = -(26+0.25)

-26.25 = -(26+1/4)

-26.25 = -(26*(4/4)+1/4)

-26.25 = -(104/4+1/4)

-26.25 = -105/4

Answer:

x = 4

Step-by-step explanation:

[tex]\frac{x}{7}[/tex] = [tex]\frac{28}{49}[/tex] ( cross- multiply )

49x = 7 × 28 = 196 ( divide both sides by 49 )

x = 4

The recursive equation here is; a_n = 3n - 1

Formula for the nth term of an arithmetic sequence is;

an = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

We are given that;

First term; a = 2

Second term; a2 = 5

Common difference; d = 3

Thus, recursive equation here is;

a_n = 2 + 3(n - 1)

a_n = 2 + 3n - 3

a_n = 3n - 1

Read more about arithmetic sequence at; https://brainly.com/question/7882626

#SPJ1

Answer:

74

Step-by-step explanation:

[tex]5(2(10)-5)-1 \\ \\ =5(20-5)-1 \\ \\ =5(15)-1 \\ \\ =75-1 \\ \\ =74[/tex]