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ElenaW [278]
3 years ago
14

What is the equation of the line that contains the point (3,-1) and has the same slope as the the line y=1/3x+5

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0

Answer:

<em>y = 1/3x - 2</em>

Step-by-step explanation:

Line y = 1/3x + 5 has slope 1/3, so the line we are looking for also has slope 1/3.

y = 1/3x + b

We know a point, so we plug in the values of x and y, and we solve for b.

y = 1/3x + b

-1 = (1/3)(3) + b

-1 = 1 + b

b = -2

Now that we know b, the equation is:

y = 1/3x - 2

You might be interested in
Simplify the following polynomial expression. (5x^4 - 9x^3 + 7x - 1) + (-8x^4 + 4x^2 - 3x + 2) - ( -4x^3 + 5x - 1)( 2x - 7)
Lady bird [3.3K]

Answer: 5x^{4}-37x^{3}-6x^{2} +41x-6


Step-by-step explanation:

1. You must apply the Distributive property.  You need to remember the product property of exponents: If you multiply powers with the same base, you must add the exponents. Them you have:

=5x^{4}-9x^{3}+7x-1-8x^{4}+4x^{2}-3x+2-(8x^{4}+28x^{3}+10x^{2}-35x-2x+7)\\=5x^{4}-9x^{3}+7x-1-8x^{4}+4x^{2}-3x+2-8x^{4}-28x^{3}-10x^{2}+35x+2x-7

2. Now, you must add the like terms. Then, you obtain the following result:

=5x^{4}-37x^{3}-6x^{2} +41x-6



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Explain why a rotation of 90 degrees around any point zero never maps a line to a line parallel to itself
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Answer:

Since zero is on the origin (0,0) a 90 degree rotation will intercept the origin no matter what so, it can't be parallel.

Step-by-step explanation:

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Brand name producers of aspirin claim that one advantage of their aspirin over generic aspirin is that brand name aspirin is muc
11Alexandr11 [23.1K]

Answer:

Step-by-step explanation:

The claim here is that the brand name aspirin is more consistent in the amount of active ingredient used than the generic aspirin.

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean amount of active ingredients in brand name aspirin and μ2 be the mean amount of active ingredients in generic name aspirin

The random variable is μ1 - μ2 = difference in the mean amount of active ingredients between the brand name and generic aspirin

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 ≥ μ2 H0 : μ1 - μ2 ≥ 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

This is a left tailed test

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 325.01

x2 = 323.47

s1 = 10.12

s2 = 11.43

n1 = 200

n2 = 180

t = (325.01 - 323.47)/√(10.12²/200 + 11.43²/180)

t = 1.24

1.237877

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [10.12²/200 + 11.43²/180]²/[(1/200 - 1)(10.12²/200)² + (1/180 - 1)(11.43²/180)²] = 1.53233946713/0.00537245359

df = 285

We would determine the probability value from the t test calculator. It becomes

p value = 0.108

Since alpha, 0.025 < than the p value, 0.108, then we would fail to reject the null hypothesis. Therefore, at 2.5% level of significance, these data support the brand name producers claim

5 0
3 years ago
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