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3 years ago

Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2

Mathematics

1 answer:

grin007 [14]3 years ago

6 0

Answer:

The answer to your question is: the answer is the second one

Step-by-step explanation:

Data

F(x) = 2x - 1

G(x) = 3x + 2

H(x) = x²

Find H(x + a) - H(x)

H(x + a) = (x+a)² substitution

= x² + 2xa + a² expanding

H(x + a) - H(x) = x² + 2xa + a² - x² simplifying

H(x + a) - H(x) = 2xa + a² or a² + 2ax

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2 years ago

Read 2 more answers

Write the equation of a line perpendicular to 5x – 4y = - 3 that passes through the point (-5,2).

kolezko [41]

Answer: 5y + 4x = - 10

Step-by-step explanation:

Two lines are said to be perpendicular if the product of their gradients = -1.

If the gradient of the first line is $m_{1}$ and the gradient of the second line is $m_{2}$ , if the lines are perpendicular, them

$m_{1}$ x $m_{2}$ = -1 , that is

$m_{1}$ = $\frac{-1}{m_{2} }$

The equation of the line given is 5x - 4y = -3 , we need to write this equation in slope - intercept form in order to find the slope.

The equation in slope -intercept form is given as :

y =mx + c , where m is the slope and c is the y - intercept.

Writing the equation in this form , we have

5x - 4y = + 3

4y = 5x -+3

y = 5x/4 + 3/4

comparing with the equation y = mx + c , then $m_{1}$ = 5/4

Which means that $m_{2}$ = -4/5 and the line passes through the point ( -5 , 2 ).

Using the equation of line in slope - point form to find the equation of the line;

y - $y_{1}$ = m ( x - $y_{1}$ )

y - 2 = -4/5 ( x +5)

5(y - 2 ) = -4 ( x + 5 )

5y - 10 = -4x - 20

5y + 4x = - 10

4 0

3 years ago

In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous we

const2013 [10]

Answer:

1) Increase the sample size

2) Decrease the confidence level

Step-by-step explanation:

The 95% confidence interval built for a sample size of 1100 adult Americans on how much they worked in previous week is:

42.7 to 44.5

We have to provide 2 recommendations on how to decrease the margin of Error. Margin of error is calculated as:

$M.E=z_{\frac{\alpha}{2} } \times \frac{\sigma}{\sqrt{n}}$

Here,

$z_{\frac{\alpha}{2} }$ is the critical z-value which depends on the confidence level. Higher the confidence level, higher will be the value of critical z and vice versa.

$\sigma$ is the population standard deviation, which will be a constant term and n is the sample size. Since n is in the denominator, increasing the value of n will decrease the value of Margin of Error.

Therefore, the 2 recommendations to decrease the Margin of error for the given case are:

Increase the sample size and make it more than 1100
Decrease the confidence level and make it lesser than 95%.

7 0

4 years ago