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valentinak56 [21]
3 years ago
8

A car starts a journey with a full tank of gas. The equation y=16 - 0.05x relates the number of gallons of gas, y, left in the t

ank to the number of miles the car has traveled, x.
A. What are the x- and y-intercepts of the graph of this equation?

B. What does x-intercept represent in the context of this problem?

C. What does y-intercept represent in the context of this problem?
Mathematics
1 answer:
mr_godi [17]3 years ago
4 0

A.  The y-intercept is y = −0.05 x + 16 and the x-intercept is x = −20y + 320

B. The x-intercept represents the number of miles the car has traveled.

C. The y-intercept represents the number of gas in gallons.

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Factor Completely : 3x^3 -12x
Thepotemich [5.8K]
The answer you're looking for will be,
ANSWER:    3x(x + 2)(x - 2)

You're welcome.

STEPS:
#1.
Factor out common term 3x.
7 0
3 years ago
A cylinder has a diameter of 8 inches and a volume of 1287 cubic inches. What is the height of
fredd [130]

Answer:

25.62

Step-by-step explanation:

the answer is rounded and pi was 3.14 to solve this

8 0
3 years ago
explain the benefits of each of the three forms of quadratic equations, standard form, vertex form, and factored form. What do t
mamaluj [8]

Answer:

Summary:

Standard form allow us to quickly find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Step-by-step explanation:

The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.

Standard Form:

The standard form of a quadratic is:

ax^2+bx+c

There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.

The leading coefficient a will tell us if the parabola curves upwards or downwards.

And the constant c will give us the y-intercept.

Vertex Form:

The vertex form of a quadratic is:

a(x-h)^2+k

There are also two details that can be conveyed by a quadratic in vertex form:  (1) the vertex, and (2) the leading coefficient.

The leading coefficient is given by a. Again, this tells us the orientation of the parabola.

And the vertex is given by (h, k).

Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.

Factored Form:

The factored form of a quadratic is:

a(x-p)(x-q)

Where p and q are the zeros/roots/solutions of the quadratic.

Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.

The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.

Summary:

Therefore, each form of a quadratic equation has its own benefits.

Standard form allow us to find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Hence, depending on the question, each form can be useful in its own way.

4 0
3 years ago
Simplify into one fraction<br><br> 8x-2/x-8-2/x-8
Elis [28]
\frac{8x-2}{x-8} - \frac{2}{x-8}

The fractions already have a common denominator of x-8, so all wee need to do is combine the numerators:

\frac{8x-2-2}{x-8}

\frac{8x-4}{x-8}
3 0
3 years ago
Find the 62nd term of the arithmetic sequence<br> 15, 13, 11, ...
Annette [7]

Answer:

a_{62}=-107

Step-by-step explanation:

This is an arithmetic sequence:

a_n=a_1+(n-1)d

where d is the common difference and n is the index of any given term.

The common difference of the given sequence is -2:

13-15=-2\\11-13=-2

Using the first term and the common difference, you can write the equation for this sequence:

a_n=15+(n-1)(-2)

And using that equation, you can find the 62nd term:

a_{62}=15+(62-1)(-2)\\a_{62}=15+(61)(-2)\\a_{62}=15-122\\a_{62}=-107

7 0
2 years ago
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