Help please, it’s for average rate of change.

Answer:

The car uses less gas

They use the same amount of gas after [tex]\frac{640}{7}[/tex] miles

Step-by-step explanation:

Given

The table represents the car mileage

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

First, calculate the car's slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

From the table, we have:

[tex](x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)[/tex]

So, we have:

[tex]m = \frac{10.5 - 13.5}{180 - 60}[/tex]

[tex]m = \frac{-3}{120}[/tex]

[tex]m = -\frac{1}{40}[/tex]

Calculate the equation using:

[tex]y = -\frac{1}{40}(x - 60)+13.5[/tex]

[tex]y = -\frac{1}{40}x + 1.5+13.5[/tex]

[tex]y = -\frac{1}{40}x + 15[/tex]

[tex]m = -\frac{1}{40}[/tex] implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

By comparison to: [tex]y = mx + b[/tex]

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

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

[tex]1/40 < 1/5[/tex]

This means that the car uses less gas

Solving (b): Distance traveled for them to use the same amount of gas.

We have:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

[tex]y = -\frac{1}{40}x + 15[/tex] --- The car

Equate both

[tex]-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15[/tex]

Collect like terms

[tex]\frac{1}{40}x -\frac{1}{5}x =-31 + 15[/tex]

[tex]\frac{1}{40}x -\frac{1}{5}x =-16[/tex]

Take LCM

[tex]\frac{x - 8x}{40} = -16[/tex]

[tex]\frac{- 7x}{40} = -16[/tex]

Solve for -7x

[tex]-7x = -640[/tex]

Solve for x

[tex]x = \frac{640}{7}[/tex]

Answer:

D

Step-by-step explanation:

you just add it all up 10+6+8

Answer:

volume of the prism=8×6×10

=480 in²

Answer:

12

Step-by-step explanation:

Just substitute 3 for n and solve.

Solve the expression [tex]2+(3-1)5\\[/tex]

Use PEMDAS and solve.

(3-1) = 2 so it becomes 2 + (2)5

Then multiply 2 and 5 to get 10.

Then add 2 so you get 12.

[tex]a_{3}[/tex]=12

Answer:

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted.

hope this helps

have a good day :)

Step-by-step explanation:

Replace f(x) to 5x-3 and g(x) to 3x-3 then subtract f(x) by g(x).

[tex] \large{f(x) - g(x) = (5x - 3) - (3x - 3)}[/tex]

Cancel the brackets, remember that multiplying or expanding the negative symbol will switch the sign. From plus to minus and minus to plus.

[tex] \large{ f(x) - g(x)= 5x - 3 - 3x + 3 }[/tex]

Combine like terms.

[tex] \large{f(x) - g(x) = 2x + 0 \longrightarrow \boxed{2x}}[/tex]

Answer

Answer:

5x-3-(3x-3)

5x-3-3x+3

5x-3x

2x

Answer:

18

Step-by-step explanation:

make 11 1/4 into improper fraction > 45/4

multiply by 2 so it has same denominator > 90/8

90/8 divided by 5/8 = 18

Answer:

18 binder clips

Step-by-step explanation:

The question basically asks, how many 5/8 inch binder clips can you add to get 11 1/4 inches.

To get the answer, you simply divide 5/8 by 11 1/4.

To divide first convert 11 1/4 to an improper fraction. To get an improper fraction you multiply the denominator by the whole number and then add the numerator. Here it would be (11*4)+1= 45 so 11 1/4 as a mixed fraction would be 45/4.

Now you can divide.

[tex]\frac{45}{4} / \frac{5}{8}[/tex]

To divide, use the chant, "keep, change, flip". Keep the 45/4, change the division to multiplication, and flip the 5/8.

You would get this:

[tex]\frac{45}{4} *\frac{8}{5}[/tex]

There are multiple ways to solve now. You can just multiply the numerator and then the denominators to get 360/20 and simplify to get 18 OR you can cross multiply and change the 45 to 9 because 45/5 is 9 and change the 8 to 2 because 8/4 is 2 and then multiply 9 by 2 to also get 18.

I hope it helps!

Answer:

In simple terms, a bar chart is used in summarizing categorical data, where a histogram uses a bar of different heights, it is similar to the bar chart in many terms but the histogram groups the numbers into the ranges while representing the data.

bar chart is a graph in the form of boxes of different heights, with each box representing a different value or category of data, and the heights representing frequencies.

but,

Histogram is graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency.

Answer:

equation: y = 4x-12

slope: 4

y-intercept: -12

Step-by-step explanation:

3 points across an x-axis is +1 x-axis difference and +4 y-axis away from origin, so you have to subtract 3 by 1 andsubtract y by 4. until x is 0, you get -12 on y-axis

Answer:

5 and 3 is vertical. 4 and 6 are vertical. 2 and 1 are supplementary angles.

9514 1404 393

Answer:

  k = 2/15

Step-by-step explanation:

We can solve the given equation for k:

  k = s/p . . . . . . divide the given equation by p on both sides

Using the first values from the table (15 pounds, 2 scoops), we have ...

  k = 2/15

The value of k is 2/15.

Answer:

A) P ( chicken is small ) = 0.3085,  P ( chicken is medium ) = 0.6621

   P (chicken is large ) = 0.0294

B) C = 3.9233

C) 0.1404

Step-by-step explanation:

A) Probabilities

i) P ( chicken is small )

 P( w ≤ 3.5 ) = Fw ( 3 .5 )

                    = F ( 3.5 - 3.8 / 0.6 )

                    = F ( -0.5 ) = 1 - F( 0.5 ) [∵ F(-x) 1 - F(x) ]

                    = 1 - 0.6915 ( from Table )

                    = 0.3085

ii) P ( chicken is medium )

  P ( 3.5 < w < 4.9 )

  P ( w < 4.9 ) - P ( w < 3.5 )

= Fw ( 4.9 ) - Fw ( 3.5 )

= F ( 4.9 - 3.8 / 0.6 ) - 0.3085

= 0.9706 - 0.3085 = 0.6621  

iii) P (chicken is large )

= P ( w > 4.9 )

= 1 - P ( w < 4.9 )

= 1 - Fw ( 4.9 ) = 1 - 0.9706 = 0.0294

B) Find c

Given:  P( w < c ) = 0.6

Fw ( c ) = 0.6

F ( c - 3.8 / 0.6 ) = 0.6

c - 3.8 / 0.6 = 0.2055 ( from table )

∴C = 3.9233

C) P ( 3 out of 5 = small )

P ( 3 of 5 = small ) = 0.1404

attached below is a detailed solution

Answer:

The answer is option A.

:)))))))

Answer:

ST = 15

Step-by-step explanation:

Given:

QR = 3x

LM = x + 9

ST = 6x - 3

Required:

ST

Solution:

First, we need to find the value of x by creating an equation.

Based on the trapezoid mid-segment theorem, we have the following equation:

LM = ½(QR + ST)

Substitute

x + 9 = ½(3x + 6x - 3)

x + 9 = ½(9x - 3)

Multiply both sides by 2

2(x + 9) = 9x - 3

2x + 18 = 9x - 3

Collect like terms

2x - 9x = -18 - 3

-7x = -21

Divide both sides by -7

x = -21/-7

x = 3

Find ST:

ST = 6x - 3

Plug in the value of x

ST = 6(3) - 3 = 18 - 3

ST = 15

Answer:

3

Step-by-step explanation:

-48/16 = 48/16

-48/16 = -3/1 = -3

Cindy and Javier would be ln(x) and x^(1/2) as they will grow somewhat fast at first and then die out.

While Alison would be 1/(1+e^-x) representing an s curve showing a lot of growth and later evening out.

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3x = 81, 5x - 3 = 625, 62y - 7 = 121, etc are some examples of exponential equations.

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3x = 81, 5x - 3 = 625, 62y - 7 = 121, etc are some examples of exponential equations.

Learn more about exponential equations here: brainly.com/question/2883200

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Cindy and Javier would be ln(x) and x^(1/2) as they will grow somewhat fast at first and then die out.

While Alison would be 1/(1+e^-x) representing an s curve showing a lot of growth and later evening out.

What is an exponential equation?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3x = 81, 5x - 3 = 625, 62y - 7 = 121, etc are some examples of exponential equations.

What is an example of an exponential equation?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3x = 81, 5x - 3 = 625, 62y - 7 = 121, etc are some examples of exponential equations.

Answer:

x=1

y=-1

Step-by-step explanation:

Answer:

x = 1

y = -1

Step-by-step explanation:

[tex]x = 2x - 1 \\ 1 = 2x - x \\ 1 = x \\ x = 1 \\ [/tex]

[tex]y = 3y + 2 \\ - 2 = 3y - y \\ - 2 = 2y \\ \frac{ - 2}{2} = y \\ - 1 = y \\ y = - 1 \\ [/tex]

serian 144 apretones de manos en total

Answer:

66

Step-by-step explanation:

hope it helps :)

Answer:

C

Step-by-step explanation:

Try it.

Answer:Its B or C

Step-by-step explanation:I expain it so A is wrong ebcause 3 times 20 is 60 and since x is 14 that measn 14 times 3 is 42 so 60 minus 42 is not 44 but 18.C is wrong becasue 2 times 14 is 28 and 2 times 3 is 6 so if u subract you get 22 and D is worng because 14 minus 3 isnt 22.

Answer:

60 square meters

Step-by-step explanation:

Answer:

x = 111

Step-by-step explanation:

180- 82 -29 is 69 and 180-69 is x which x is equal to 111

Answer:

111°

Step-by-step explanation:

By exterior angle theorem:

[tex]x = 82 \degree + 29 \degree \\ = 111 \degree[/tex]

Answer:

h(t) = -16t2 + 186t + 43

at the ground h = 0

hence;  -16t2 + 186t + 43 = 0  

solving this quadratic equation using the quadratic formula ; a = -16, b = 186, c = 43 ; x = (-b +-(b2 - 4ac)1/2)/2a

gives t = 11.8 seconds to the nearest tenth (note that the negative root has no practical significance)

Step-by-step explanation:

9514 1404 393

Answer:

  a) MBE; b) EBY; c) MBY; d) MBE; e) YME; f) XEW; g) EBM, EBY; h) EBY, EBM

Step-by-step explanation:

There are many choices here. We'll use choices that make as much use as possible of the same points and segments.

a) ∠MBE is an acute angle

b) ∠EBY is an obtuse angle

c) ∠MBY is a straight angle

d) ∠MBE is an angle with vertex B

e) ∠YME is an angle with side MY

f) ∠XEW is another name for ∠BER

g) ∠EBM and ∠EBY are adjacent angles

h) ∠EBY and ∠EBM are supplementary angles

__

Additional comments

An acute angle measures less than 90°; an obtuse angle measures more than 90°. A straight angle measures exactly 180°. A linear pair is a pair of adjacent angles that together measure 180°. That is, they are supplementary and combine to make a straight angle. (Supplementary angles only need to have a sum that is 180°. They do not need to be a linear pair. However, in a figure like this, where angle measures are not marked, angles are guaranteed to be supplementary only if they are a linear pair.)

Let x,y be the two numbers.

Given that one number is 8 greater than another.

Let x be the smaller number ans y be the greater number.

That is y=x+8. Let this be the first equation.

And also given that product of the two numbers is 84.

That is x × y = 84, let us plugin y=x+8 here.

x × (x+8) = 84

x²+ 8x -84 = 0.

x²+12x-4x-84 = 0

x(x+12)-4(x+12) =0

(x-4)(x+12)=0

That is x= 4 or -12.

Hence two positive numbers corresponding to given conditions are 4,12.

And two negative numbers corresponding to given conditions are -12,-4.

Step-by-step explanation:

hope it may help you!!

please mark as brainlist please (´;︵;`)

Answer:

Exponent form

[tex] {6}^{5} [/tex]

Answer:

6^5

Step-by-step explanation:

6 x 6 x 6 x 6 x 6

There are 5 6's multiplied together

The base is 6 and the power is 5

6^5

Answer:

D x is all real numbers

R y ≥ -3

Step-by-step explanation:

The domain is the values that x can take

The domain is all real numbers

The range is the values that y can take

The range is y is greater than or equal to -3

Answer:

There was a 45% increase in furniture sales.

Furniture sales rose by 9 percentage points.

Step-by-step explanation:

absolute difference = new - old

29-20= 9 percentage points

absolute difference / initial value = 9/20 = .45 * 100 = 45%

Two statements which are true about furniture sales are  [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and  [tex](f)[/tex]  Furniture sales rose by [tex]9[/tex] percentage points.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage [tex]=\frac{Obtained\ number}{Total\ number}\ * 100[/tex]

We have,

Sales of furniture in [tex]2015=20\%[/tex]

Sales of furniture in [tex]2016=29\%[/tex],

So,

Change in Percentage [tex]=29-20=9\%[/tex]

i.e.

Sales rise by [tex]9\%[/tex] points,

And,

Increase in Percentage [tex]=\frac{9}{20}\ *100=45\%[/tex]

Hence, we can say that Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.

To know more about Percentage click here

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Answer:

x=7

Step-by-step explanation:

Alternate interior angles so they are congruent. So, 13x+5=12x+12. Subtract 12x and get x+5=12. Subtract 5 and you get x=7