All categories

3 years ago

21:20

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

6 0

Answer:

Step-by-step explanation:

Given the quadratic equation 6x² + 24x + 7 = 0, the following steps must be followed when finding the roots using the completing the square method.

Step 1: Subtract 7 from both sides

6x² + 24x + 7 - 7= 0 -7

6x² + 24x = -7

Step 2: divide through by the coefficient of x²

6x²/6 + 24x/6 = -7/6

x² + 4x = -7/6

Step 3: Add half of the coefficient of x (i.e 4/2 = 2) to both sides of the equation to complete the square of the equation x² + 4x.

x² + 4x + 2= -7/6 + 2

(x+2)² = -7/6 + 2

(x+2)² = 5/6

Step 4: taking the square root of both sides

√(x+2)² = √5/6

x+2 = ±√5/6

x = -2±√5/6

x = -2+√5/6 and -2-√5/6

Based on the conclusion above, it can be seen that Yvonne made the first error in step 2. Yvonne suppose to divide through by the coefficient of x² (i.e 6)

You might be interested in

F(x)=( x^4 + 5x^3 - 2x^2 + 5x - 3) d(x)=( x^2 + 1) Divide f(x) by d(x)

VLD [36.1K]

f '(x) = [(-40x +11)(7x - 9) - 7(-4x +3)(5x + 1)]/(7x - 9)2
= [(-280x2 + 360x + 77x - 99) - 7(-20x2 - 4x + 15x + 3)]/(7x - 9)2
= [(-280x2 + 437x - 99) + (140x2 + 28x - 105x - 21)]/(7x - 9)2
= (-140x2 +360x - 120)/(7x - 9)2

i think thats how you would solve it
hope this helps tho:)

4 0

4 years ago

The lines given by the equations y=4x and y=0.25x are

d1i1m1o1n [39]

They are not parallel because the slopes are different (slope of 4 and slope of 0.25)

Neither are they perpendicular. If they were then m1*m2 ( the product of their slopes) would be -1 ). The product of these slopes = 4*0.25 = 1)

So choice A is the correct one.

6 0

3 years ago

A machine, when working properly, produces 5% or less defective items. Whenever the machine produces significantly greater than

vovikov84 [41]

Answer:

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

Step-by-step explanation:

A machine, when working properly, produces 5% or less defective items.

This means that the null hypothesis is:

$H_0: p \leq 0.05$

Test if the percentage of defective items produced by this machine is greater than 5%.

This means that the alternate hypothesis is:

$H_a: p > 0.05$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.05 is tested at the null hypothesis:

This means that $\mu = 0.05, \sigma = \sqrt{0.05*0.95}$

A random sample of 300 items taken from the production line contained 27 defective items.

This means that $n = 300, X = \frac{27}{300} = 0.09$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}$

$z = 3.18$

Pvalue of the test:

Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.

Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993

1 - 0.9993 = 0.0007

5 0

3 years ago

HElp ME PKLEASEPLESSSS ASAP ASAP SASPSKPSks

Ivanshal [37]

Answer:

The y intercept means shawn ran 4 laps at week zero

Step-by-step explanation:

3 0

3 years ago

The measure of an angle is 61°. What is the measure of its supplementary angle?

MrMuchimi

Answer:

119°

Step-by-step explanation:

if sum of two angles=180,then they are supplementary.

61+x=180

x=180-61=119

5 0

3 years ago