Bill is driving on the highway he begins the trip 12 gallons of gas in his car. the car use miles let represent the number of gallons of gas he has left in his tank and let D represent the total distance (in miles) traveled. Write an equation relating G to D and then graph your equation using the axes below.
graph and make a equation to support your awenser

The polynomial function with third degree, zeros of −3, −1, and 4, and a y-intercept of −13 is y = -13/12 (x³ - 13x + 12)

Polynomial function:

polynomial function means a functions of single independent variables, in which variables can occur more than once, raised to an integer power.

Given,

Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.

And we need to construct  a polynomial function with the stated properties and reduce all fractions to lowest terms.

We know that the standard form for the third degree polynomial function is written as,

=> y = K (x + zeros1) (x + zeros2) (x + zeros3)

The third degree, zeros of the function is -3, -1 and -4.

Now, we have to apply it on the general form,

=> y = K (x -3) (x - 1) (x + 4) ----------------------(1)

Here we know the value of y intercept is -13 then the value of x is 0.

So, it can be written as,

=> -13 = K(0 - 3) (0 - 1) (0 + 4)

=> -13 = K (12)

Therefore, the value of K = -13/12

Now, apply the values on the equation (1), then we get,

=> y = -13/12 (x -3) (x - 1) (x + 4)

Therefore, the third degree polynomial function is,

=> y = -13/12 (x³ - 13x + 12)

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The ordered pair of a solution of the inequality are (10, 0) and (0, 5).

The given inequality is x+2y>10.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Graph the inequality by finding the boundary line, then shading the appropriate area.

The solution of the inequality is (10, 0) and (0, 5).

Hence, the ordered pair of a solution of the inequality are (10, 0) and (0, 5).

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The equation of the line is y=-x-4

How to find whether line is perpendicular or not?

Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

The given line is

y=x-1

the slope of it is 1

As the slopes of perpendicular lines are negative reciprocals

So, the slope of the perpendicular line is -1

As the point is(-6,2)

y=mx+b

y=(-1)x+b

2=-1(-6)+b

2=6+b

b=2-6

b=-4

∴The equation of the line that is perpendicular is  y=-x-4

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Step-by-step explanation:

n^2 - n -56 = 0

n^2 -8n +7n-56 = 0

n(n-8) +7(n-8) = 0

(n+7)(n-8) = 0

n = (-7,8)

option B

1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

1 + 2 = 3

As we know, from the definition:

Arithmetic can be defined as, an operation in which we do the addition of numbers, subtraction, multiplication, and division.

For the addition of two numbers:

The two numbers are 1 and 2:

Draw a vertical line 1:  |

Draw two vertical lines 2:  | |

Count the lines:  | | | = 3

Thus, 1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

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Answer:

Angles 2, 3, 6, and 7 will be the same with 41 degrees!

Angles 1, 4, 5, and 8 are the same with 139 degrees!

Step-by-step explanation:

Opposite angles are the same so that makes angles 2, 3, 6, and 7 the same at 41 degrees!

The same rule applies to angles 1, 4, 5, and 8 and we have to subtract!

180 - 41 = 139 degrees!

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Answer:   b

Step-by-step explanation:

We have elaborate below a real-world problem that involves a decimal divided by a decimal.

Since we are given a problem that says that Jake owns a bakery  amd he makes 8.5 boxes of cupcakes in 15.5 hours,  the question is how many cupcakes he makes in 1 hour .So the time taken is 15.5 and the number of cupcakes made in the  15.5 hours is 8.5. So 15 .5hours=8.5 cupcakes, now dividing both sides by 15.5, we get: 1 hour=8.5/15.5 =0.54 = 1 cupcake, therfore, it needs 1 hour  to make 1 cupcake. Here we had two quantities in form of decimals, so there division of expression of decimal dividing a decimal.

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A Linear equation in point slope form using the first point 3/4h , 9 in that can be used to determine the level of chocolate syrup in dispenser after x hours is y = -4x + 12 .

In the question ,

it is given that

in 3/4 hours the the level of chocolate syrup was 9 inch ,

So , the first point is (3/4,9) .

in 5/4 hours the level of chocolate syrup in the dispenser was 7 inch .

So , the second point is (5/4,7)

to find the linear equation we first need to find the slope .

Slope = (7-9)/(5/4-3/4)

= -2/(2/4)

= -4

So , the equation in slope intercept form having point (3/4 , 9) and slope -4 is    .

(y - 9) = -4(x - 3/4)

y - 9 = -4x + 3

y = -4x + 3 + 9

y = -4x + 12

Therefore , The linear equation is y = -4x + 12 .

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The two equations that can be formed by adding or subtracting is

4x−4y = 16 and  2x − 6y = -8 .

the two equations are : x + y = 12 and 3x − 5y = 4

Adding we get :

x + y = 12

3x − 5y = 4

4x -4y = 16

Subtracting we get:

x + y = 12

3x − 5y = 4

-2x + 6y = 8 or 2x - 6y = -8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the unknown parameters variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

It will be regarded as a phrase. In the following section of this article, you will discover the distinction between an equation and an expression.

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The point that represent the origin in the number line is Point W

A number line is a horizontal representation of numbers in parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right

number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p

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Work Shown:

x = number of nickels

y = number of dimes

5x = value of the nickels only (cents)

10y = value of the dimes only (cents)

5x+10y = total value of all the coins = 75 cents

One equation we can form is 5x+10y = 75.

"he has twice as many dimes as nickels" tells us that y = 2x. We can replace every copy of y with 2x and solve for x as shown in the steps below.

5x+10y = 75

5x+10(y) = 75

5x+10(2x) = 75 ... plug in y = 2x

5x+20x = 75

25x = 75

x = 75/25

x = 3

This value leads to y = 2x = 2*3 = 6

Johnny has 3 nickels and 6 dimes.

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

Check:

1 nickel = 5 cents

3 nickels = 3*5 = 15 cents

1 dime = 10 cents

6 dimes = 6*10 = 60 cents

3 nickels + 6 dimes = 15 cents + 60 cents = 75 cents = $0.75

The answers are confirmed.

The relative displacement of the given case is δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

Given;

To get the axial load-related relative displacement of one end of the tapered plate concerning the other end.

Let 'd' be the displacement;

We know,

[tex]w = d1 + \frac{(d2-d1)x}{h} = \frac{d1h+(d2-d1)x}{h}[/tex]

To calculate the relative displacement;

δ = [tex]\int\limits {\frac{p(x)}{A(x)E} } \, dx =p/E \int\limits {\frac{1}{\frac{d1h+(d2-d1)x}{h}t } } \, dx[/tex]

δ = [tex]ph/Et\int\limits^h_0 {\frac{dx}{d1h+(d2-d1)x} } \,[/tex]

δ = [tex]\frac{ph}{Et(d2-d1)}[ln(1+\frac{d2-d1}{d1}) ][/tex]

δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

Therefore, the Relative displacement of the given case is δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

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Answer:

2.9 × 1025

(scientific notation)

= 2.9e25

(scientific e notation)

Step-by-step explanation:

hope this helped

Answer:

Step-by-step explanation:

I believe that f(2) would be 10 and f(-2) would be -5.

As the sample size (n) increases, the number of degrees of freedom increases, and the t-distribution approaches a normal distribution.

What is degrees of freedom ?

The variety of degrees of freedom is the amount of values within the final calculation of a datum that are liberal to vary. Estimates of applied math parameters are often primarily based upon totally different amounts information|of knowledge or data.

Main Body:

Degrees of freedom typically equals the quantity of observations (or items of information) minus the quantity of parameters calculable. once you perform regression, a parameter is calculable for each term within the model, and and every one consumes a degree of freedom. Therefore, as well as excessive terms during a multivariate analysis model reduces the degrees of freedom on the market to estimate the parameters' variability.

Hence the number of degrees of freedom increases,as the sample size (n) increases.

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A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.

Answer:

Step-by-step explanation:

Write the value of x when y is = 7

x = 7

x = -1

x = -4

Answer:

ASA

Step-by-step explanation:

1) the angles are congruent where they intercept in blue

2) the sides that are congruent are between the two congrunet  angles  the blue ones and the given ones

Answer:

Step-by-step explanation:

Since the two vector have opposite directions, their sum will be the difference of magnitudes:

And the direction is the same with the vector with greater magnitude, so it is south.

Answer:

Magnitude = 39 km

Direction = South

Step-by-step explanation:

Formula we use,

→ r + s

Now the required answer will be,

→ r + s

→ 164 + (-125)

→ 164 - 125

→ 39 km

Thus, answer is 39 km due south.

Answer:

Since 1 scoop of ground coffee makes 1 cup of coffee, Andy can make 24 cups of coffee from the jar.

Step-by-step explanation:

Answer:960000000

Step-by-step explanation:

Answer: 960000000

Step-by-step explanation:

960 times 1.0 times 10^6 look it up !!

Answer:

1. -3

2. 6

3.less than

Step-by-step explanation:

The equation of the line that passes through the point and slope (-2, -7) m = 4/5

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The line contains the following point and slope. (-2, -7) m = 4/5

y - y1 = m(x - x1)

y + 7 = 4/5(x + 2)

y = 4x/5 + 8/5 - 7

y = 4x/5 - 27/5

Thus, the equation of the line that passes through the point and slope (-2, -7) m = 4/5

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The product of the radical expression is  - 49 + 13√7. option B is the correct answer

From the question, we have

(7-√7)(-6+√7)

= (7) × (-6) + (-√7) × (√7) + (-√7) × (-6) + (7)(√7)

= -42 - 7 + 6√7 + 7√7

= - 49 + 13√7

The product of the radical expression is  - 49 + 13√7

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Thus the largest length is 15 inches

Size (l) is 14 inches.

Size (w) = 4 inches.

Height is 4 inches (h).

The distance between one bottom corner and the opposite top corner is known as d. Find s, the diagonal across the bottom of the box, first.

[tex]w^2 + l^2 = s^2[/tex]

Replace the prescribed measures.

[tex]4^2 + 14^2 = s^2[/tex]

Simplify.

[tex]16 + 196 = s^2[/tex]

[tex]21^2= s^2[/tex]

To determine d, use the expression for s.

[tex]h^2 + s^2 = d^2[/tex]

Plug in s2 = 212 and h = 4.

4^2 + 21^2 = d^2

Simplify.

16 + 21^2 = d^2

228 = d2

On both sides, take the square root.

√228 = √d2

15.1 ≈ d

Therefore, the part's maximum possible length was 15 inches.

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