Mathematics High School

The price of a community pool membership has a one-time sign-up fee and a monthly fee. The price can be modeled by the function y = 20x + 50, where x is the number of months.

What is the slope, and what does it represent?

Answers

Answer 1
the slope in this equation is 20. This represents the monthly fee. Every month u go, u pay 20 bucks
Answer 2

Answer:

The answer is 20 and it represents the monthly fee.

Step-by-step explanation:


Related Questions

Find the total area of the prism in ( _+_√_ )

Answers

First find the hypotenuse of the right triangle bases.
a^2 + b^2 = c^2
4^2 + 6^2 = c^2
16 + 36 = c^2
52 = c^2
2√13 = c

Triangle bases:
A = (1/2) * b * h * 2
A = (1/2) * 4 * 6 * 2
A = 24 ft^2

Front Rectangle:                 Left side Rectangle             Back Side Rectangle
A = 8 * 2√13 = 16√13  ft^2      A = 4 * 4 = 32 ft^2           A = 6 * 8 = 48 ft^2

24 + 32 + 48 + 16√13 =        Total area = 104 + 16√13 ft^2

The transformation from f to g represents a __________ stretch. f(x) = Square root of x. and g(x) = 6Square root of x.

Answers

The answer is vertical.
Answer:

The transformation from f to g represents a Vertical stretch.

Step-by-step explanation:

We are given a parent function f(x) as:

                      [tex]f(x)=\sqrt{x}[/tex]

and the transformed function g(x) as:

        [tex]g(x)=6\sqrt{x}[/tex]

We know that any function transformation of the type:

      f(x) → a f(x)

represents either a vertical stretch stretch or compression depending on the value of a.

If   0<a<1 then the transformation is a vertical compression and if a>1 then the transformation is a vertical stretch.

Here we have a=6>1

Hence, the transformation is a VERTICAL STRETCH.

traveling at 65 miles per hour how many minutes rounded to the nearest whole number does it takes to drive 125 miles from san digit to malibu

Answers

divide total miles by speed

125/65 = 1.923 hours

there are 60 minutes per hour

multiply 1.923*60 = 115.384 minutes

 rounded off to nearest whole number = 115 minutes

A) side-side-side triangle similarity postulate
B) angle-angle triangle similarity postulate
C) angle-side-angle triangle similarity postulate
D) hypotenuse-lag triangle similarity postulate

Answers

The question tells you that  the 3 corresponding angles are equal.

For similarity you only have to know that 2 corresponding angles are equal.
The answer is B.) Angle-Angle Triangle Similarity Postulate, however the extra pair of congruent angles were unnecessary since the Angle-Angle Similarity Postulate only needs two pairs of angles to be congruent in order to be true.

The sum of two rational numbers will always be

Answers

that would always be rational

A basket contains 11 pieces of fruit: 4 apples, 5 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?

Answers

Final answer:

The probability that Jonas will get an orange and Beth will get an apple is 20/121.

Explanation:

To find the probability that Jonas will get an orange and Beth will get an apple, we need to find the probability of Jonas getting an orange and then multiply it by the probability of Beth getting an apple.

The probability of Jonas getting an orange is the number of oranges in the basket (5) divided by the total number of fruits (11):

P(orange for Jonas) = 5/11

The probability of Beth getting an apple is the number of apples in the basket (4) divided by the total number of fruits (11):

P(apple for Beth) = 4/11

To find the combined probability, we multiply these two probabilities together:

P(orange and apple) = P(orange for Jonas) * P(apple for Beth) = (5/11) * (4/11) = 20/121

Solve the equation ,and check the solution.

r - 3 r
____ = __
10 13 Check:



Answers

Things are a bit cluttered. 
I'm assuming the equation should be (r-3)/10 = r/13.

Use parenthesis to indicate what is being divided. In this case all of "r-3" is over 10. 

If my assumption above holds up, then we can solve for r like so
(r-3)/10 = r/13
13(r-3) = 10r ... cross multiply
13r-39 = 10r
13r-39-13r = 10r-13r ... subtract 13r from both sides
-39 = -3r
-3r = -39
-3r/(-3) = -39/(-3) ... divide both sides by -3
r = 13

The value of r is r = 13

-----------------------

Check:

Replace every copy of "r" with "13" to get
(r-3)/10 = r/13
(13-3)/10 = 13/13
10/10 = 13/13
1 = 1 ... equation is true; answer has been confirmed

Final answer:

To solve the equation, we cross multiply to eliminate the fractions and solve for r. The solution is r = 13. We can check the solution by substituting it back into the original equation.

Explanation:

To solve the equation (r - 3) / 10 = r / 13, we can cross multiply to eliminate the fractions. This gives us 13(r - 3) = 10r. Distributing, we get 13r - 39 = 10r. We can then solve for r by subtracting 10r from both sides and adding 39 to both sides. This gives us 3r = 39. Dividing both sides by 3, we find that r = 13.

To check the solution, we substitute r = 13 back into the original equation. The left side becomes (13 - 3) / 10 = 10 / 10 = 1, and the right side becomes 13 / 13 = 1. Since both sides are equal to 1, we can confirm that the solution r = 13 is correct.

Learn more about Solving equations here:

https://brainly.com/question/14410653

#SPJ12

Use complete sentences to describe the range of the sine function.

Answers

The Range of a function is the set of all values that that function can take.

Given the sine function f(x)=sinx,

This function is the function which calculates the sine of the values of x.

According to the definition of the sine of an angle x in the unit circle, 

[tex]-1 \leq sinx \leq 1[/tex],

so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.

This means that the values that the sine function takes are any values between -1 and 1, inclusive.

This determines the Range of the sine function. 

So the Range of the sine function is [-1, 1]

(Solve for r) 0.5r − 3.8 = 5.66

Answers

0.5r - 3.8 = 5.66....add 3.8 to both sides
0.5r = 5.66 + 3.8
0.5r = 9.46...divide both sides by 0.5
r = 9.46 / 0.5
r = 18.92 <==
0.5r = 5.66 + 3.8
0.5r = 9.46
r = 9.46 ÷ 0.5
r = 18.92
r = 18/23/25

Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is ____ cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be _____ times the original volume.

options for the first blank are: 20.22, 35.08, 50.07, or 100.11

options for the second blank are: 2, 4, 6 or 8

Answers

The total volume of the flask will be 50.06 [tex]\rm inches ^3[/tex] and if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.

Given :

Flask can be modeled as a combination of a sphere and a cylinder.

The volume of Sphere is given by the:

[tex]V_s = \dfrac{4}{3}\pi r^3[/tex]

Given - diameter of sphere = 4.5 inches. Therefore, radius is 2.25 inches.

Now, the volume of sphere of radius 2.25 inches will be:

[tex]V_s = \dfrac{4}{3}\times \pi\times (2.25)^3[/tex]

[tex]\rm V_s = 47.71\; inches^3[/tex]

The volume of Cylinder is given by the:

[tex]V_c = \pi r^2h[/tex]

Given - diameter of cylinder = 1 inches then radius is 0.5 inches and height is 3 inches.

Now, the volume of cylinder of radius 0.5 inches and height 3 inches will be:

[tex]V_c = \pi\times (0.5)^2 \times 3[/tex]

[tex]\rm V_c = 2.35\; inches^3[/tex]

Therefore the total volume of the flask will be = 47.71 + 2.35 = 50.06 [tex]\rm inches ^3[/tex].

Now, if both the sphere and the cylinder are dilated by a scale factor of 2 than:

Radius of sphere = [tex]2.25\times 2[/tex] = 4.5 inches

Radius of cylinder = [tex]0.5\times 2[/tex] = 1 inch

Height of cylinder = [tex]3\times 2[/tex] = 6 inches

Now, the volume of sphere when radius is 4.5 inches will be:

[tex]V_s' = \dfrac{4}{3}\times \pi \times (4.5)^3[/tex]

[tex]\rm V_s' = 381.70\; inches ^3[/tex]

And the volume of cylinder when radius is 1 inch and height is 6 inches will be:

[tex]V_c' = \pi \times (1)^2\times 6[/tex]

[tex]\rm V_c'=18.85\;inches^3[/tex]

Therefore the total volume of the flask after dilation by a scale factor of 2 will be = 381.70 + 18.85 = 400.55 [tex]\rm inches ^3[/tex].

Now, divide volume with dilation by theorginal volume of the flask.

[tex]\dfrac{400.55}{50.06}=8[/tex]

Therefore, if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.

For more information, refer the link given below:

https://brainly.com/question/15861918

What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?

Answers

find inersection first

both equal y so
2x-5=-x+1
3x-5=1
3x=6
x=2
sub back

y=2x-5
y=2(2)-5
y=4-5
y=-1
intersection is (2,-1)

paralell to a line is having same slope
y=mx+b, m is slope
given
y=1/2x+4
slope is 1/2
so
y=1/2x+b
find b
given the point (2,-1) that it must pass through
(x,y) so x=2 and y=-1
-1=1/2(2)+b
-1=1+b
-2=b

the equation is y=1/2x-2
y = 2x - 5
y = -x + 1

2x - 5 = -x + 1
2x + x = 1 + 5
3x = 6
x = 6/3
x = 2

y = -x + 1
y = -2 + 1
y = -1

solution is (2,-1)...point of intersection between the 2 lines given.

y = 1/2x + 4....slope here is 1/2. A parallel line will have the same slope.

y = mx + b
slope(m) = 1/2
(2,-1)...x = 2 and y = -1
sub and find b
-1 = 1/2(2) + b
-1 = 1 + b
-1  -1 = b
-2 = b

so ur parallel equation is : y = 1/2x - 2 <==

Line BC has an equation of a line y = 2x + 3, and line EF has an equation of a line y = negative one over 2 x + 4. These two equations represent

Answers

They represent that the 2 lines are perpendicular because, the slopes of two perpendicular lines are always negative reciprocals of one another.

Answer:

Perpendicular lines.

Step-by-step explanation:

We have been given that line BC has an equation of a line [tex]y=2x+3[/tex] and line EF has an equation of a line [tex]y=-\frac{1}{2}x+4[/tex]. We are asked to determine what these both equations represent.

We know that slope of two perpendicular lines is negative reciprocal of each other. This means the product of slope of both lines is equal to [tex]-1[/tex].

Let us find the product of slopes of both lines.

[tex]2\times \frac{-1}{2}[/tex]

Upon cancelling 2 with 2 we will get,

[tex]=-1[/tex]

Therefore, the given two equations represent equations of two perpendicular lines.

(07.05 MC)

An equation is shown below:

4x + 2(x – 3) = 4x + 2x – 11

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points

Answers

4x + 2(x - 3) = 4x + 2x - 11
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
6x - 6x = -11 + 6
0 = -5...incorrect......this has no solution...0 solutions

one property used was the distributive property :2(x - 3) = 2x - 6

Answer:

-6 = -11

Distributive Property

Step-by-step explanation:

A.

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 4x + 2x - 11

6x - 6 = 6x - 11

-6 = -11

since -6 is not equal to -11, so there's no solution

B. Distributive property

A rectangle is 42 square feet. what percent of the area of the rectangle is a square with side lengths of 6 feet?

Answers

area = L x w

42 = 6 x w

w=42/6 = 7

rectangle is 6 x 7

square would be 6 x 6 = 36 square feet

36/42 = 0.857 = 85.7% ( Round answer if needed)

SOMEBODY HELP ME WITH THESE PLEASE! I really need the help like NOW PLS!

Answers

93. [tex]g(n) = n - 4[/tex]
[tex]f(n) = 2n^2 - 5n[/tex]

then [tex]g(n) +f(n) = (n-4) + (2n^2 - 5n)[/tex]
                                [tex]= n - 4 + 2n^2 - 5n[/tex]
                                [tex]= 2n^2 -5n + n - 4[/tex]
                                [tex]= 2n^2 - 4n -4[/tex]


95. [tex]f(n) = -n+3[/tex]
      [tex]g(n) = n^3 + 3n[/tex]
Then [tex]f(n) . g(n) = (-n+3) . (n^3 + 3n)[/tex]
                                 [tex]= -n^4 + 3n^3 - 3n^2 + 9n [/tex]
 

97. [tex]f(x) = 3x+1[/tex]
[tex]g(x) = 2x[/tex]
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
[tex]f(g(x)) = 3*(2x) + 1[/tex]
                  [tex]= 6x + 1[/tex]


99. [tex]f(n) = n - 3[/tex]
[tex]g(n) = 2n^2 - 3n[/tex]

[tex]g(-7) = 2*(-7)^2 - 3 * (-7) = 2* 49 + 21 = 98 + 21 = 119[/tex]
[tex]f(g(-7)) = 119 - 3 = 116[/tex]

Answer:

97.

For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).

                 

99.

Step-by-step explanation:

I don't get it I got a different answer then these

Answers

You should first change the denominator into same number, which is 18

So you multiply the first fraction of both numerator and denominator by 3, and the second by 2:

3(g-2) / 18 - 2(g+3) / 18 = (3g - 6 - 2g - 6) / 18 = (g-12)/18
      3(g-2) - 2(g+3)
=  ---------------------
             18

      3g - 6 -2g - 6
=  ---------------------
             18

       g - 12
=  -----------
         18

this is what i got

1. is acute. 2. is isosceles. 3. is right. Which two statements contradict each other?

Answers

Answer:

the answer is 2 and 3

Step-by-step explanation:

I took the test

(02.02 MC)

Line segment RS is shown on a coordinate grid:
The line segment is rotated 270 degrees counterclockwise about the origin to form R'S'. Which statement describes R'S'?
R'S' is parallel to RS.
R'S' is half the length of RS
. R'S' is twice the length of RS.
R'S' is equal in length to RS.

Answers

R'S' is equal in length to RS.

length doesnt change, it was just rotated.
I think it's R'S' is equal in length to RS.

(25 Points)Enter numbers to write 4.23×10^3 in standard notation.

Answers

10^3 = 1000, i.e. three 0's after the "1"

So the answer will be 4230

A rectangular prism with a square base has a lateral area of 192 square yards and a surface area of 264 square yards. What is the length of a base edge?

Answers

A rectangular prism is like a cardboard shoe box. It has two equal bases, one on the top and the other on the bottom. It also has 4 lateral faces to close the figure. The surface area of the prism is the area of all its faces: the 4 side faces and the 2 bases. On the other hand, lateral surface area only accounts for the 4 lateral faces. Therefore, we can conclude that the total surface area is equal to the lateral surface area plus the areas of the two bases.

TSA = LSA + 2s²

Since the base is said to be the square, its area is equal to s² where s is the base edge. Because there are 2 bases, that's why it's 2s².

264 = 192 + 2s²
s² = (264-192)/2
s = √36
s = 6 yards

 

The sum of four consecutive whole numbers is 54, what are the four numbers

Answers

Let the four consecutive numbers be x, x+1, x+2, and x+3.

The sum of the four numbers is 54, therefore
x + (x+1) + (x+2) + (x+3) = 54
4x + 6 = 54
4x = 54 - 6 = 48
x = 12

Answer:
The four numbers are 12, 13, 14, and 15

Write an equation for the line that is parallel to the given line and that passes through the given point.

y = 1/2 – 8; (–6, –17)

A.) y = 2x – 14

B.) y = 1/5x + 5/2

C.) y = -2x + 14

D.) y = 1/2x – 14

Answers

I honestly think that the answer is d

Jean has 5 different colors of markers: red, blue, green, orange, and purple. Two colors are used to make a sign. How many different combinations are possible? List them.

Answers

We need to find the number of possible combinations of r objects from a set of n objects. 
Jean has 5 different colors which means that n=5 and 2 colors are used to make a sign, which means r=2.
The number of combinations can be calculated with the formula: 
C=n!/((n-r)!r!)
C=5!/(5-2)!*2!
C=5*4*3!/3!*2*1
C=20/2=10
The possible combinations are:
1.red blue
2.red green
3.red orange
4.red purple
5. blue green
6. blue orange
7. blue purple
8. green orange
9. green purple
10. orange purple

what is the period of the sinusoid given by y=-4sin( [tex] \frac{2π}{3} [/tex] x) ?

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\\\ f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\ f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}} \end{array} \\\\ -------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ [/tex]

[tex]\bf \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]

with that template in mind, let's see

[tex]\bf \begin{array}{llll} y=&-4sin(&\frac{2\pi }{3}x)\\ &A&B \end{array}\qquad period\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{2\pi }{3}}\implies \cfrac{\frac{2\pi }{1}}{\frac{2\pi }{3}} \\\\\\ \cfrac{2\pi }{1}\cdot \cfrac{3}{2\pi }\implies 3[/tex]

Answer:

The answer is 3 for A P E X

Step-by-step explanation:

How could the relationship of the data be classified?

scatter plot with points loosely scattered going down to the right

A positive correlation
A causation
A negative correlation
No correlation

Answers

It would be C. A negative correlation. Think of it as a line. If a line goes to the right and is dipped downward just a little bit, it would have a negative slope.

Answer: A negative correlation


Step-by-step explanation:

If the points in the scatter plot scattered going down to the right, it shows that there are inverse relationship between the quantities.

With the increase of one quantity or variable there is decrease in the other quantity or variable.

Therefore, if in the scatter plot with points loosely scattered going down to the right , then the relationship of the data be classified as a negative correlation.



Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

Part A: Find (f + g)(x). Show your work. (3 points)

Part B: Find (f ⋅ g)(x). Show your work. (3 points)

Part C: Find f[g(x)]. Show your work. (4 points)

Answers

A:

(f+g)(x)=f(x)+g(x)

(f+g)(x)=4x-5+3x+9

(f+g)(x)=7x+4

B:

(f•g)(x)=f(x)•g(x)

(f•g)(x)=(4x-5)(3x+9)

(f•g)(x)=12x^2-15x+36x-45

(f•g)(x)=12x^2+21x-45

C:

(f○g)(x)=f(g(x))

(f○g)(x)=4(3x+9)-5

(f○g)(x)=12x+36-5

(f○g)(x)=12x+31


let n be the first 3 of consecutive even integers. what is the sum of those integers?

Answers

assuming you meant that n is the first of the 3 even integers

even integers are 2 apart

so the 3 integers are n,n+2,n+4
the sum is n+n+2+n+4=3n+6

the sum is 3n+6

Two 6-sided dice are rolled. what is the probability the sum of the two numbers on the die will be 4?

Answers

1+3=4. 2+2=4. 3+1=4.
3/6 or 1/2 if only addition
5-1=4. 6-2=4.
2/6 or 1/3 if only subtraction
if both 5/6

Answer:

[tex]\frac{1}{12}[/tex].

Step-by-step explanation:

Given : Two 6-sided dice are rolled.

To find : what is the probability the sum of the two numbers on the die will be 4.

Solution : We have given

Two 6-sided dice are rolled.

Dice have number { 1,2,3,4,5,6}  { 1,2,3,4,5,6} .

[tex]Probability =\frac{outcome\ happn}{total\ outcome}[/tex].

sum of the two numbers on the die will be 4.

Case (1) : first dice rolled 3 and second dice rolled 1.

{3,1}

3 +1 = 4 .

Case (2) : first dice rolled 1 and second dice rolled 3 .

{1,3}

1 + 3 = 4 .

Case (3) : first dice rolled 2 and second dice rolled 2.

{2,2}

2 + 2 = 4.

Then there are 3 possible outcomes where the sum of the two dice is equal to 4.

The number of total possible outcomes = 36.

[tex]Probability =\frac{3}{36}[/tex].

[tex]Probability =\frac{1}{12}[/tex].

Probability of getting sum of two dice is [tex]\frac{1}{12}[/tex].

Therefore,  [tex]\frac{1}{12}[/tex].

A rectangular garden has length twice as great as its width. A second rectangular garden has the same width as the first garden and length that is 4 meters greater than the length of the first garden. The second garden has area of 70 square meters. What is the width of the two gardens?

Answers

The widht of the two gardens is 5metres by each

What are the roots of the function y = 4x2 + 2x – 30? To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of .
Next, factor the trinomial completely. The equation becomes .
Use the zero product property and set each factor equal to zero and solve. The roots of the function are .

Answers

4x² + 2x - 30 = 0

factor out the GCF:
2(2x² + x - 15) = 0

factor the trinomial completely:
2x² + x - 15 = 0
2x² + 6x - 5x - 15 = 0
2x(x + 3) - 5(x + 3) = 0
(2x - 5)(x + 3) = 0

use the zero product property and set each factor equal to zero and solve:
2x - 5 = 0     or     x + 3 = 0
2x = 5                   x = -3
x = 2.5

The roots of the function are x=-3,  x=2.5

The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2

Roots of a quadratic equation

The given quadratic equation is:

[tex]y=4x^2+2x-30[/tex]

Set y = 0

[tex]4x^2+2x-30=0[/tex]

Factor the trinomial completely

[tex]4x^2-10x+12x-30=0\\\\2x(2x-5)+6(2x-5)=0\\\\(2x-5)(2x+6)=0[/tex]

Set each factor to zero and solve

2x  -  5  =  0

2x  =  5

x  =  5/2

2x  +  6  =  0

2x  =  -6

x  =  -6/2

x  =  -3

The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2

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