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IceJOKER [234]
3 years ago
14

Complete the square for 5x^2+10x-16. first one to answer gets brainiest

Mathematics
1 answer:
ella [17]3 years ago
5 0

Answer: x= -1 <u>+</u> √(21/5)

Step-by-step explanation:

The given equation can be written as 5x^2+10x-16=0

keep the x terms on one side and constant on another side

5x^2+ 10x = 16.

Now, to make a complete square like (x+a)^2 = x^2+2xa+a^2.

Divide the given equation by 5 on both sides,

The equation now becomes x^2+2x = 16/5.

The middle term is 2xa=2x

By solving for term "a" in above equation, a= 1

The entire equation of complete square should be x^2+2x+1, which is equal to (x+1)^2

Here, in the equation given in question, +1 is missing to make a complete square.

In order to add 1 we have to simultaneously minus 1 to keep the values in the equation unchanged.

Thus, x^2+2x+1-1 =16/5.

Again moving the constant -1 to other side, we have

x^2+2x+1 =16/5+1

After simplification,

(x+1)^2= 21/5

Taking square root on both sides,

(x+1)= <u>+</u> √(21/5)

The answer is x= -1 <u>+</u> √(21/5)

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Step by step please ASAP
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Answer:

-2x^2 - 2

Step-by-step explanation:

(6x^2 + 3) - (5 + 8x^2)

-2x^2 + 3 - 5

-2x^2 - 2

3 0
3 years ago
What number should be placed in the box to help complete the division calculation?
Anarel [89]
344 should be placed in the box
3 0
3 years ago
This is due in 15 minutes pls help me lol thx
GaryK [48]

Answer:

ITS A

Step-by-step explanation:

PLZ GIVE BRAINLEIST

7 0
3 years ago
Read 2 more answers
What is the slope of the line through (1, -1) and (5. – 7)?
Vladimir [108]

Answer:

-3/2

Step-by-step explanation:

Given two points, we can find the slope by

m = (y2-y1)/(x2-x1)

    = (-7 - -1)/ (5-1)

    = (-7+1)/(5-1)

    = -6/4

    = -3/2

6 0
3 years ago
Read 2 more answers
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
Vadim26 [7]

Answer:

We conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.

Step-by-step explanation:

We are given that a particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000.

From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles.

<u><em>Let </em></u>\mu<u><em> = average miles for deluxe tires</em></u>

So, Null Hypothesis, H_0 : \mu \geq 50,000 miles   {means that deluxe tire averages at least 50,000 miles before it needs to be replaced}

Alternate Hypothesis, H_A : \mu < 50,000 miles    {means that deluxe tire averages less than 50,000 miles before it needs to be replaced}

The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about population standard deviation;

                                  T.S.  = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean lifespan = 46,500 miles

            \sigma = population standard deviation = 8000 miles

            n = sample of tires = 28

So, <u><em>test statistics</em></u>  =  \frac{46,500-50,000}{\frac{8000}{\sqrt{28} } }

                               =  -2.315

The value of the test statistics is -2.315.

Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is less than the critical value of z as -2.315 < -1.6449, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.

4 0
3 years ago
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