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3 years ago

Write the equation in slope intercept form: slope = -4; Y-intercept = (0,2)

Mathematics

2 answers:

tatuchka [14]3 years ago

7 0

Answer:

y=-4x+2

Step-by-step explanation:

The slope intercept form is: y=mx+b

Then

y=-4x+b

y=2 and x=0 at the intercept

thus

2=-4(0)+b

b=2

y=-4x+2

Svetradugi [14.3K]3 years ago

7 0

Slope intercept form(ula):
y=mx+b

Slope= m= -4
Y-int= b= 2

Answer:
y= -4x+2

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You are choosing between two health clubs. Club A offers membership for a fee of $ 19plus a monthly fee of $ 21.â€ƒâ€ƒClub B off

11111nata11111 [884]

Answer:

For 2 months

Step-by-step explanation:

Let after x months the cost of each health club is same,

Now, In club A,

Membership fees = $ 19,

Monthly fees = $ 21,

So, the total fees for x months = membership fees + total monthly fees for x months

= 19 + 21x

In Club B,

Membership fees = $ 23,

Monthly fees = $ 20,

So, the total fees for x months = membership fees + total monthly fees for x months

= 23 + 20x

Thus, we can write,

19 + 21x = 23 + 20x

21x - 20x = 23 - 21

x = 2

Hence, for 2 months the total cost of each health club would be same.

8 0

3 years ago

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

Find the sum of the following infinite geometric series, if it exists. 2 + 6 + 18 + 54 +… Does not exist 23,567 25,982 29,034

Sladkaya [172]

Option A: The sum for the infinite geometric series does not exist

Explanation:

The given series is $2+6+18+54+.......$

We need to determine the sum for the infinite geometric series.

<u>Common ratio:</u>

The common difference for the given infinite series is given by

$r=\frac{6}{2}=3$

Thus, the common difference is $r=3$

<u>Sum of the infinite series:</u>

The sum of the infinite series can be determined using the formula,

$S_{\infty}=\frac{a}{1-r}$ where $0$

Since, the value of r is 3 and the value of r does not lie in the limit $0$

Hence, the sum for the given infinite geometric series does not exist.

Therefore, Option A is the correct answer.

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3 years ago

Write the first four terms in the following sequences. A(n+1)=12 A(n) for n≥1 and A(1)=4 .

ycow [4]

Answer:Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8

3 0

3 years ago

How does supply and demand affect consumers?

mezya [45]

Supply and demand affects prices which affects consumers want and likelihood of buying a product

5 0

2 years ago