The graph shows the distance, d, in miles, that Joe can drive his car using g gallons of gasoline. What is the rate of change in this situation?


30 miles per gallon of gasoline


35 miles per gallon of gasoline



20 miles per gallon of gasoline


25 miles per gallon of gasoline
pllllllllzzzzzz help!

the equation t² = 3 x + 1 will be written as x = t² / 3 - 1 / 3 with the subject as x.

We are given an equation:

t² = 3 x + 1

We need to solve it so that the subject becomes x.

For this, we will first subtract 1 from both the sides:

t² - 1 = 3 x + 1 - 1

3 x = t² - 1

Now, we will divide both the sides by 3

3 x / 3 = (t² - 1) / 3

x = t² / 3 - 1 / 3

So, the subject is being made as x now.

Therefore, we get that, the equation t² = 3 x + 1 will be written as x = t² / 3 - 1 / 3 with the subject as x.

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Answer:

b

Step-by-step explanation:

Answer:

Q = { (x,y) : (0,0), (1,2), (2,16), (3, 54), (4, 128), (5,250) } is cubic

R= { (x,y) : (2,3), (4,4), (6,5), (8,6) } is linear

S = { (x,y), : (1,3), (2,9), (3,17), (4,27), (5, 39), (6,53) } is quadratic

Equation of the linear relation is

y = 0.5x + 2

Step-by-step explanation:

A linear equation has the form y = mx + b where m is the slope and b is the y-intercept. Slope is a constant and growth of function is determined by x value

A quadratic equation has the general form y = ax² + bx + c where a b and c are constants. Growth of the function is mostly determined by the square of x

A cubic equation has the general form y = ax³ + bx² + cx + d where a, b and c are constants. The growth of the function is mostly determined by the cube of x value

Looking at the three relations

#1 is obviously cubic since the value of y appears to be determined by the cube of the value of x. Specifically, when x = 0, y = 0/. When x =1, y = 2 but when x =2, y =16 and 16 is 2x³ = 2(2³) = 2 x 8

Looking at x =3, 2(3³) = 2(27) = 54

So this is a cubic function

#2 is obviously a linear function When x increases by 2, y increases by 1 so it is a linear growth

#3 In this equation we can see that the y value appears to be controlled by the square of x. The specific equation is y = x² + 3x -1

For the linear equation, find the slope from the first two points

m = (4-3)/(4-2) = 1/2 = 0.5

So the equation is y = 0.5x + b

To find b, use the coordinates of any point. Let's choose (4,4)

At x = 4, y = 4 so

4 = (0.5)4 + b = 2+b yielding b = 2

So the equation is y = 0.5x + 2

Relation Q is not linear, relation R is linear with the equation y = (1/2)x + 2, and relation S is not linear.

1: Q = { (0,0), (1,2), (2,16), (3,54), (4,128), (5,250) }

To determine if this relation is linear, quadratic, or cubic,

Examine the differences between the y-values.

Calculate the differences for the given data:

Difference in y-values:

(2-0) = 2

(16-2) = 14

(54-16) = 38

(128-54) = 74

(250-128) = 122

Looking at the differences,

we can see that they are not constant.

In a linear relation, the differences between the y-values would be constant.

Therefore, we can conclude that this relation is not linear.

2: R = { (2,3), (4,4), (6,5), (8,6) }

Similar to the previous relation, let's calculate the differences:

Difference in y-values:

(4-3) = 1

(6-4) = 2

(8-6) = 2

In this case, the differences between the y-values are constant

(both are 2). This indicates a linear relation.

To find the equation, we can use the slope-intercept form (y = mx + b). Let's choose any two points from the relation, for example, (2,3) and (4,4):

Slope (m) = (4-3) / (4-2) = 1/2

m = 1/2

Now, let's plug in the values of one point (2,3) and the slope into the equation:

y = mx + b

3 = (1/2) x 2 + b

3 = 1 + b

b = 2

Therefore, the equation for this linear relation is y = (1/2)x + 2.

3: S = { (1,3), (2,9), (3,17), (4,27), (5,39), (6,53) }

Again, calculate the differences:

Difference in y-values:

(9-3) = 6

(17-9) = 8

(27-17) = 10

(39-27) = 12

(53-39) = 14

The differences between the y-values are not constant, indicating that this relation is not linear.

Hence,

Relation Q is not linear.

Relation R is linear, with the equation y = (1/2)x + 2.

Relation S is not linear.

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Answer:

[tex]\sqrt{3}[/tex], 2, 1

Step-by-step explanation:

sin30=a/h=1/2

a=length of opposite side a =1

h=length of hypotenuse h=2

tan30=a/b=1/√3

a=length of opposite side a =1

b=length of adjacent side a =[tex]\sqrt{3}[/tex]

hope this helps

Answer:

i dont really know

Step-by-step explanation:

Answer:

f(3) = -17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = -5x - 2

f(3) is x = 3

Step 2: Evaluate

Graph of the equation is attached in the following image .

Input is x = - 3 , - 2 , - 1 , 0 , 1 , 2 , 3

Output is y = 1 , 0 , - 1 , - 2 , - 1 , 0 , 1  

Since , the given function is a modulus function , graph will be V - shaped .

Modulus Function : A function f ( x ) = | x | is a modulus function , it takes positive value as an output . If x is negative , then - x is the output . It takes the absolute value of a function .

Hence , graph of the equation is attached in the following image .

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Answer:2-4

Step-by-step explanation:

Answer:

2-4

Step-by-step explanation:

now please answer my question

Answer:

95%

Step-by-step explanation:

19÷20×100=95

Hope it's right

Answer:

[tex]95\ percent[/tex]

Step-by-step explanation:

[tex]We\ know\ that:\\Percentage = Ratio*100\\Or,\\Percentage=\frac{Observation}{Total}*100\\Here,\\No. of\ answers\ Amiya\ gets\ correct=19\\Total\ no.\ of\ answers\ in\ the\ test=20\\Hence,\\Percentage\ of\ answers\ Amiya\ gets\ correct= \frac{19}{20}*100\\=19*5\\=95\ percent\\[/tex]

Answer: Yes

Step-by-step explanation:

Answer:

Its graph is a parabola, and many horizontal lines cut the parabola twice. The function f(x)=x 3, on the other hand, IS one-to-one. If two real numbers have the same cube, they are equal. The horizontal line test is also easy to apply.

Step-by-step explanation:

Answer:

second in first 1 in last and last is 4

Step-by-step explanation:

Answer:

(2x + 3)(x - 7)

Step-by-step explanation:

Given

2x² - 11x - 21

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 21 = - 42 and sum = - 11

The factors are - 14 and + 3

Use these factors to split the x- term

2x² - 14x + 3x - 21 ( factor the first/second and third/fourth terms )

= 2x(x - 7) + 3(x - 7) ← factor out (x - 7) from each term

= (2x + 3)(x - 7) ← in factored form

Answer:

3x=15 the x is 5

10+5=15

10 quarters

5 dimes

Step-by-step explanation:

Answer:

[tex]8 + \frac{1}{2} x = - 12 \\ 16 + x = - 24 \\ x = - 24 - 16 \\ x - 40[/tex]

Can you mark as BREINLEST

[tex]So distance from a) xy plane = |-5| = 5 b) yz plane = |4| = 4c) xz plane = |7| = 7d) x-axis = √[(7)^2+(-5)^2] = √[49+25]=√[74] = 8.6023e) y-axis =√[(-5)^2+(4)^2] = √[25+16] =√[41] = 6.4031f) z-axis = √[(4)^2+(7)^2] = √[16+49] = √[65] = 8.0622[/tex]

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates that are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length. An axis is a line that is used to sketch, measure, rotate, etc. a curve or a figure. The Cartesian axes in the plane or in space, which are often mutually perpendicular, are the most frequently seen axes. Axes, pronounced "ax-ees," is the plural form of "axis." The phrase is also used to describe a line that passes across a group of aircraft. The line on a graph that passes 0 horizontally (left to right).

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Answer:

b= 50

Step-by-step explanation:

the entire angle equals 80 degrees and a portion of it equals 30. therefore the portion that equals b = 50 because 30+50=80 hope this helps.

Answer:

432 ft^2

Step-by-step explanation:

Answer:

432

Step-by-step explanation:

Lets plug it into the formula

b1 should be the horizontal line on the bottom horizontal line and b2 should be the top horizontal line

so we get b1 = 28 and b2 = 20

according to the formula we should add b1 and b2, getting us 48.

divide 48 by 2: we get 24

24 times h, or the hieght, or 18 is 432

so the answer is 432

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Answer:

D. m = -15/1

Step-by-step explanation:

Slope Formula-

m = (y2-y1)/(x2-x1)

Using two random points-

(-1, 13) (0,-2)

-1 = x1

13 = y1

0 = x2

-2 = y2

m = (-2 - 13)/(0-(-1))

m = -15/1

Answer: False

Step-by-step explanation:

If t<-3, and t>2, that means that all values less than 3, and all values greater than 2 are true.

In the inequality -3<t<2, only values between -3 and 2 are true, so this means they are not equivalent.

Step-by-step explanation:

t>-3 or t<2

THE STATEMENT ABOVE CONTRADICTS THE GIVEN STATEMENT THEREFORE IT IS FALSE

Answer: 10

Step-by-step explanation:

You just add them together-

Step-by-step explanation:

using Pythagoras theorem :

hyp²= opp² + adj²

x²= 7² + 3²

x² = 49 + 9

x² = 58

take the root of both sides

x = √58

x = 7.62

Answer: 0 and -5

Step-by-step explanation:

Answer:

-5 and 0 make the inequality true.

Step-by-step explanation:

-5 and 0 are less than 1, making 1 and 5 greater than one (so 1 and 5 don't apply to this situation)

Answer: 4 dollars/ lbs

Step-by-step explanation:

Tom paid 16 dollars for 4 lbs

16/4=4 dollars/ lbs

Answer:

$4

Step-by-step explanation:

$16 for 4 pounds so divide 16 by 4 to find how much was one pound:

16/4 = 4

I pound cost $4

100ml

Step-by-step explanation:

l think so

Answer:

$5.22

Step-by-step explanation:

you would subtract so 5.60-.38=$5.22

Answer:

$5.22

Step-by-step explanation:

$5.22-0.38

ĺlllllllllllllllllllllll

Given:

[tex]\ln(y-8)=-2x+\ln C[/tex]

To find:

y as a function of x.

Solution:

We have,

[tex]\ln(y-8)=-2x+\ln C[/tex]

It can be written as

[tex]\ln(y-8)=\ln e^{-2x}+\ln C[/tex]           [tex][\because \ln e^x=x][/tex]

[tex]\ln(y-8)=\ln (Ce^{-2x})[/tex]           [tex][\because \ln (ab)=\ln a+\ln b][/tex]

On comparing both sides, we get

[tex]y-8=Ce^{-2x}[/tex]

Adding 8 on both sides, we get

[tex]y=Ce^{-2x}+8[/tex]

Therefore, the equation function is [tex]y=Ce^{-2x}+8[/tex].

Answer:

x ≈ 16.5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use trig to find the missing side length.

Step 2: Identify Variables

POV from the angle measure

Angle = 38°

Adjacent Leg = x

Hypotenuse = 21

Step 3: Solve for x

Answer:

1)B

Step-by-step explanation:

Answer:

The slope is -5/4 and the y-intercept is 5 so the answer is A

Step-by-step explanation:

Answer:

I think the answer is A sorry if it is wrong

Step-by-step explanation: