All categories

2 years ago

Which of the following is the y-intercept of:

Mathematics

2 answers:

Varvara68 [4.7K]2 years ago

6 0

Answer:

the y-intercept is the point (0, -4) on the plane

Step-by-step explanation:

In order to find the y-intercept, write the equation in "slope intercept form" solving for "y":

$2\,y=x-8\\y=\frac{x-8}{2} \\y=\frac{x}{2} -\frac{8}{2} \\y=\frac{x}{2} -4$

Recall now that the y-intercept is the value at which the line crosses the y-axis (when x = 0), therefore:

$y=\frac{x}{2} -4\\y=\frac{0}{2} -4\\y=-4$

So the y-intercept is the point (0, -4) on the plane.

Wewaii [24]2 years ago

4 0

$(0,-4)$ fits the linear equation perfectly.

Hope this helps.

You might be interested in

The expression 3xy-(2x+4xy) is equivalent to

Goryan [66]

There are no answer options so I will just simplify the expression:
3xy-(2x+4xy)
3xy-2x-4xy
-2x-xy

3 0

2 years ago

What percent is represented by the shaded area?<br>T

Fudgin [204]

There ain’t even T on the graph show the whole graph and maybe we can help you answer the question Karen

6 0

3 years ago

How to solve this problem 15 = 5x

Lostsunrise [7]

Answer:

x = 3 (see below)

Step-by-step explanation:

To solve for x, you need to isolate the variable to one side of the equation. To do that, you need to use reverse operations. For example, the reverse operation of subtraction is addition.

In this case, we have:

15 = 5x

5x is the same thing as 5 (x) or 5 times x. This means the reverse operation is division. So, we need to divide both sides of the equation by 5:

15 = 5x

----- ----

5 5

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

3 = x

x = 3

4 0

2 years ago

5-2 ????=7-5 ???? which value of x is the solution to the above equation?

saw5 [17]

5-2x=7-5x
-2x+5x=7-5
3x=2
X=2/3

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago