The graph below represents the number of miles, y, that Jacob can drive his car for every x gallons of gas. Find the rate of change.

The greater triangle and the smaller ones (the two triangles inside the original one, that share the side y) are similar triangles, then we can formulate the following expressions:

• For the larger triangle and the triangle on the left

From this equation, we can solve for z, to get:

Then, z equals 3√5

• Similarly, with the larger triangle and the one on the right:

From this expression, we can solve for x, like this:

Then, x equals 6

• With the triangles on the right and on the left:

Solving for y, we get:

Then, y equals 2√5

Answer:

h = 9 cm

Explanation:

The volume of the solid can be calculated as:

So, we can replace the value of the Volume by 1323 cm³ and B by 147 cm² as:

Then, dividing by 147 into both sides, we get:

Therefore, the height h of the solid is 9 cm.

The answer would be B.

The relationship is proportional. The constant of proportionality is 5.

The fraction of fishes which are guppies in Marcus's aquarium is 2/3

Number of gold fishes in the aquarium = 1/9

Number of angelfish in the aquarium = 5/9

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Let x be the total number of fishes in Marcus's aquarium:

Number of guppies = Total fishes - Number of gold fishes - Number of angelfishes

= x - 1/9 - 5/9

= x - 6/9

x = 6/9 or 2/3

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The linear equation that passes through the two points (0, 360) and (10, 560) is:

y = 20*x + 360

Remember that the slope-intercept form of a linear equation is:

y = a*x + b

Where b is the y-intercept and a is the slope or rate of change.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

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

Here the line must pass through (0, 360) and (10, 560), so the slope is:

[tex]a = \frac{560 - 360}{10 - 0} = 20[/tex]

And because of the point (0, 360) we can see that the y-intercept is 360, then the linear equation is:

y = 20*x + 360

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B. 2/10 = 20%

The total number of weeks shown in the simulation = 10

By observing the simulation, we would see that there is no 0 or 1 in group 2 and group 3. This means that Juan was late everyday of week 2 and week 3

The number of weeks that Juan was late everyday = 2

The estimated probability that Juan will be late evryday of next week = 2/10 = 20%

Given:

a) The radius is​ doubled.

b) The radius is​ tripled.

To find:

The changes to the surface area of a sphere

Explanation:

Let us take the original radius as r.

The surface area of the original sphere is,

a) The new radius will be,

So, the surface area of the sphere with the new radius is,

Therefore, the surface area of a sphere becomes four times the original surface area if the radius is​ doubled.

b) The new radius will be,

So, the surface area of the sphere with the new radius is,

Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is​ tripled.

Alice plans to buy a house. She has $2,000 in her savings account.

She plans to contribute $150 to the account each month.

We know that with each month, n, she deposits $150 and so, each month, her savings account balance increases by $150.

This simply means that after n months, her savings account balance would have increased by:

150 * n = 150n

Her initial balance was $2000, therefore, her balance after n months will be the sum of 150n and the amount that was initially there.

That is:

f(n) = 2000 + 150n

This is the function that describes the relationship between the number of months and her balance.

To be able to determine if the figure is a right triangle.

The given length must satifies the given conditions,

a.) The sum of the two sides must always be lesser than the other side. We get,

Given: a = 14 ; b = 16 ; c = 18

Let's check,

a + b > c ; 14 + 16 > 18 = 30 > 18 Satisfies the criteria

b + c > a ; 16 + 18 > 14 = 34 > 14 Satisfies the criteria

a + c > b ; 14 + 18 > 16 = 32 > 16 Satisfies the criteria

b.) The square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem). We get,

Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.

A lowest denominator to solve the given equation is 10.

What are fractions?

Fraction are ratios in which numerator and denominator are both integers and denominator is not zero.

We are given a equation

[tex]\frac{74}{5}+1\frac{9}{10}[/tex]

Upon solving we get the following

[tex]\frac{74}{5}+\frac{19}{10}[/tex]

If we multiply both numerator and denominator of the first term by 2 we get

[tex]\frac{148}{10}+\frac{19}{10}[/tex]

Hence after this we can add

Hence A lowest denominator to solve the given equation is 10

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Answer:

C

Step-by-step explanation:

HOPE IT HELPS MARK BRAINLEIST PLS

The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.

Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,

At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.

These are the values of outputs, and the ordered pair will be expressed as

{0, 3/2, 3, 6, 15/2}.

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The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.

In order to calculate the radius of the exoplanet's orbit, we would apply  Kepler's Third Law of planetary motion.

Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:

T² = 2π√(r³/GM)

Where:

Making radius (r) the subject of formula, we have:

Radius, r = ∛(GMT²/2π)

Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².

Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds

Substituting the given parameters into the formula, we have;

Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)

Radius, r = 4.71 × 10¹¹ meters.

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Answer: 17x - 39

Step-by-step explanation:

1) Find all sides of the hallway.

P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1

2) Add it together

P= 17x - 39

Recall that to complete the table we have to evaluate the given function at every value of x:

Answer:

Table:

Graph:

Answer: Correct! The answer is 12.

Step-by-step explanation:

1) Draw the triangle.

Drawing a triangle usually helps you see the problem better!
|    \

|        \  13 cm

|           \

|______\

  5 cm

2) Solve the other leg

To find the other leg, we need to use the Pythagorean theorem. Which goes like this

[tex]a^2+b^2=c^2[/tex]

We will then substitute the numbers into the equation

[tex]5^2+b^2=13^2[/tex]

Simplify

[tex]25+b^2=169[/tex]

Set the variable on one side

[tex]b^2=144[/tex]

Get rid of the squared in the b by square rooting both sides.

[tex]b=12[/tex]

The answer is 12.

The value of expression ( – 5q–1)–( – 2q–8) is -3q + 7.

As per the known fact, the similar signs are consequently takes as positive for calculation. So, the two negative signs will be takes as positive. So, rewriting the expression to solve and find its value.

Value of expression = (-5q - 1) + 2q + 8

Rearrange the expression

Value of expression = - 5q + 2q - 1 + 8

Performing addition of numerals written with q and subtraction of constant values

Value of expression = - 3q + 7

Thus, the value of expression mentioned in question is -3q + 7.

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Answer:

Step-by-step explanation:

The difference between two consecutive even integers is 2.

Let the first of the three integers is x, then the following ones are:

x + 2 and x + 4.

The sum of the three is - 78. Express it as equation and solve for x:

The integers are - 28, - 26 and - 24

Okay, here we have this:

Considering the provided set of numbers we are going to organize the numbers from smallest to largest, so we obtain the following:

Remember that 5/6 is approximately 0.83 and 4/5 is 0.8, then:

Considering the number line and that the smaller numbers are further to the left and the larger numbers are further to the right, we are left with the following order from least to greatest: 4/5, 0.82, 5/6.

The numbers that Linda should put on her number line are 5,10,15,20...1000 .

Integers are frequently represented as specifically labelled dots evenly spaced on a line. Despite the fact that the graphic only depicts the integers from -3 to 3, the product contains all real numbers, which continue indefinitely in each direction, as well as numbers that lie between the integers. It is frequently used to help teach simple numerals, particularly with negative numbers.

The numbers are skip counted. so each number differs from the preceding number by 5.

let us take the number counting starts from 0. so the second number will be 5+5=10

The third number 10+5 = 15 and so on and so forth.

Hence it forms an arithmetic sequence of numbers whose first term is 5 and common difference is 5.

A number line is really a picture of a stepped straight line as serves as a visual representation of real numbers in primary mathematics. Every point of a x axis is assumed to coincide to a true figure, and every decimal digits to a point.

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Answer:

P(X = 2) = 43.2%

Step-by-step explanation:

P(X = 2) = 3 * 0.6^2 * (1 - 0.6)^(3 - 2)

P(X = 2) = 54/125

P(X = 2) = 0.432

P(X = 2) = 43.2%

Answer:

78.59$

Step-by-step explanation:

Answer:

melissa spent approximately $491 in total

Answer:

124

Step-by-step explanation:

Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.

[tex]31(4)=124[/tex]

Answer:

  150 km

Step-by-step explanation:

You want to know the number of kilometers each train has traveled when they meet. The first goes 60 km/h and has a half-hour head start. The second goes 75 km/h.

At t hours after 10 am, the distance of the first train from Kanpur will be ...

  distance = speed × time

  distance = 60t

At t hours after 10 am, the distance of the second train from Kanpur will be ...

  distance = 75(t -1/2) . . . . . . the distance is 0 at 10:30 am, 1/2 after 10 am

These distances will be equal when ...

  60t = 75(t -1/2)

The time at which the trains meet will be the solution to the above equation.

  60t = 75t -37.5 . . . . eliminate parentheses

  0 = 15t -37.5 . . . . . . subtract 60t

  0 = t -2.5 . . . . . . . . . divide by 15

  2.5 = t . . . . . . . . . the trains meet 2.5 hours after the first one leaves

The distance traveled by each of the trains is the same at that time. It will be the distance traveled by the first train:

  60t = 60(2.5) = 150 . . . . km

The two trains will be together 150 km from Kanpur.

Considering the given linear function, it is found that:

a)

b) The discrete domain of the function is: {0, 1, 2, 3, 4, 5, 6, 7}.

c) The graph of the function is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the rule given below:

y = mx + b

In which:

The amount of money you have remaining after printing p photographs is  modeled by the following function:

M(p) = 10 - 1.44p.

Hence the coefficients are as follows:

The number of photos printed is a discrete number, as this number cannot assume decimal values, hence the domain is also discrete.

You cannot print a negative value of numbers, neither can M(p) be negative, hence the domain, which is the number of photos you can print, is:

{0, 1, 2, 3, 4, 5, 6, 7}.

Considering the above domain, the graph of the function is given by the image at the end of the answer.

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The coordinates of the other endpoint  of the segment, given its midpoint and one endpoint are (-14, -9)

The Midpoint Formula for a line with endpoints as (x₁, y₁) and (x₂, y₂) is;

((x₁ + x₂)/2, (y₁ + y₂)/2)

We are given the  following;

Midpoint (-15,-6)

End point (-16,-3)

Let x₁ = -16, the x coordinate of the endpoint

Let x₂ = the x coordinate of the unknown endpoint

Let y₁ = -3, the y coordinate of the endpoint

Let y₂ = the y coordinate of the unknown endpoint

Thus, for the x coordinate of the unknown endpoint;

(x1 + x2)/2

(-16 + x₂)/2 = -15

-16 + x₂ = -30

x₂ = -14

For the y coordinate of the unknown endpoint;

(y1 + y2)/2

(-3 + y₂)/2 = -6

-3 + y₂ = -12

y₂ = -12 + 3

y₂ = -9

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