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2 years ago

F(x) = x² + 5x-1 is shifted 3 units right. The result is g(x). What is g(x)?

Mathematics

1 answer:

CaHeK987 [17]2 years ago

3 0

Answer:

Step-by-step explanation:

When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)

Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)

Given f(x) is shifted 3 units right,

the new function, g(x) becomes:

$g(x) = {(x - 3)}^{2} + 5(x - 3) - 1$

Therefore the answer is D in this case.

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irina1246 [14]

Answer:

Sinx = 5/13

cosy = 5/13

cosy = sinx ; they both share a proportional relationship

Step-by-step explanation:

From the attached triangle, since the triangle is right angled, we can use trigonometric functions where ;

sinx° = opposite / hypotenuse

From Pythagoras ;

Hypotenuse = √(opposite² + adjacent²)

Hypotenus = √(12² + 5²)

Hypotenus = 13

Sin x° = opposite / hypotenus = 5 / 13

Sin x° = 5/13

Cos y = adjacent / hypotenus = 5 / 13

Hence,

sinx = cosy

Therefore, they both share a proportional relationship.

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Step-by-step explanation:

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2 years ago

70% of the students applying to a university are accepted. Assume the requirements for a binomial experiment are satisfied for 1

marshall27 [118]

Answer:

a) 0.3826

b) 0.9894

Step-by-step explanation:

We are given the following information:

We treat students accepted at university as a success.

P(students accepted at university) = 70% = 0.70

Then the number of students accepted at university follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

a) P( 8 or more will be accepted)

$P(x \geq 8) = P(x = 8) + P(x = 9) + P(X=10)\\\\= \binom{10}{8}(0.7)^8(1-0.7)^2 + \binom{10}{9}(0.7)^9(1-0.7)^1+ \binom{10}{10}(0.7)^{10}(1-0.7)^0\\\\= 0.2334 + 0.1210 + 0.0282\\= 0.3826$

b) P(4 or more will be accepted)

$P(x \geq 4) =1 - P(x = 0) - P(x = 1) - P(X=2)-P(x=3)\\\\=1 - ( \binom{10}{0}(0.7)^0(1-0.7)^{10} + \binom{10}{1}(0.7)^1(1-0.7)^9+ \binom{10}{2}(0.7)^{2}(1-0.7)^8+ \binom{10}{3}(0.7)^{3}(1-0.7)^7 )\\\\= 1 - 0.0106\\= 0.9894$

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