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3 years ago

The first three steps of completing the square to solve the quadratic equation x² + 4x - 6 = 0, are

Mathematics

1 answer:

slavikrds [6]3 years ago

8 0

Answer:

The next 3 steps are

Step 4: $(x+2)=\pm \sqrt{10}$

Step 5: $x=-2\pm \sqrt{10}$

Step 6: $x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}$

Step-by-step explanation:

Given:

Quadratic Equation is

x² + 4x - 6 = 0

To Find:

x = ?

Solution:

Step 1: x2 + 4x = 6

Step 2: x2 + 4x + 4 = 6 + 4

Step 3: (x + 2)2 = 10

Step 4: $(x+2)=\pm \sqrt{10}$

Step 5: $x=-2\pm \sqrt{10}$

Step 6: $x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}$

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--12 + 8x < -44 i need help

tigry1 [53]

The answer to this problem is x<-4

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2 years ago

If 3x+2=5/9, what is the value of −3x+8?<br><br>Group of answer choices

allsm [11]

Answer:

= 4

Step-by-step explanation:

first lets find the value of x in 3x+2=5/9

3x+2=5/9

3x = $\frac{5}{9}$ -2

3x = $\frac{3}{9}$

3x = $\frac{1}{2}$

x = $\frac{1}{2 * 3\\ }$

x = $\frac{1}{6}$

$\frac{1}{6}$ can also be written as $6^{-1}$

−3x+8

-3 ( $\frac{1}{6}$ ) +8

$\frac{-3}{6}$ +8

= 4

3 0

2 years ago

G is between E and H, and F is the midpoint of EG. If FG=2 and FH=8, find EH.

kykrilka [37]

Answer:

EH = 10

Step-by-step explanation:

Because F is a midpoint, that means that FG and EF are congruent to each other. So, since FG = 2, that means that EF also equals 2. Because FH also includes FG, you can take the 2 from the FG, and then take that 2 away from 8. Now you know that GH = 6. All that is left is to add all 3 of the units together (2+2+6=10).

8 0

3 years ago

4(2b-b) what is the answer?

Burka [1]

4b because you distribute the 4 to get 8b - 4b so that equals 4b

6 0

3 years ago

Read 2 more answers

An automobile manufacturer claims that its van has a 31.3 miles/gallon (MPG) rating. An independent testing firm has been contra

Yuliya22 [10]

Answer:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

$z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82$

$p_v =2*P(z$

If we compare the p value and the significance level given $\alpha=0.02$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is NOT significantly different from 31.3 at 2% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=31.1$ represent the sample mean

$\sigma=1.3$ represent the population standard deviation for the sample

$n=140$ sample size

$\mu_o =31.3$ represent the value that we want to test

$\alpha=0.02$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We can assume that we conduct a hypothesis in order to check if the true mean is equal to 31.3 , the system of hypothesis would be:

Null hypothesis: $\mu =31.3$

Alternative hypothesis: $\mu \neq 31.3$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82$

P-value

Since is a two-sided test the p value would be:

$p_v =2*P(z$

Conclusion

5 0

2 years ago