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Anni [7]
3 years ago
13

Can anyone explain how to factor quadratics? i have a whole page of stuff like the picture.

Mathematics
1 answer:
finlep [7]3 years ago
3 0

Answer:

7) (s + 2)(s + 5)

   s = -2, -5

8) (x + 7)(x + 4)

   x = -7, -4

9) (d - 3)(d + 9)

    d = 3, -9

Step-by-step explanation:

To start you will want to try and look for two numbers that multiply to equal a*c and have a sum equal to b. So with number 7, a=1 b=7 and c=10. We need to find two numbers that multiply to equal 1*10 and add to equal 7. so the numbers 5 & 2 work perfectly. 5*2 = 10 and 5+2 = 7. so now we will split up the 7s into 5s+2s.

s^2 + 5s + 2s + 10

The next step would be to group each side together. Using parentheses will help keep us organized.

(s^2 + 5s)(2s + 10)

So now it's time to factor something out of each side. You are going to work on one side at a time and find something that the two have in common. so starting with (s^2 + 5s), we can see that the s^2 and the 5s both have an s in common, so we can go ahead and factor that out.

s(s + 5)

Now with the (2s + 10), we can see that you can easily divide a 2 from both sides.

2(s + 5)

So now if we reassemble to two parts we would have something that looks like this.

s(s + 5) + 2(s + 5)

So now, the numbers/variables that we factored out, s & 2, would be put together in their own parentheses and the two (s + 5)s can be combined into their own set of parentheses. This would look something like this:

(s + 2)(s + 5)

Now this is your fully factored form, if you wanted to take it a step further and solve the equation you could take each side and set it equal to 0 and solve for your s.

s + 2 = 0

s = -2

&

s + 5 = 0

s = -5

7) s^2 + 7s + 10

   s^2 + 5s + 2s + 10

   (s^2 + 5s) + (2s + 10)

   s(s + 5) + 2(s + 5)

   (s + 2)(s + 5)

   s = -2, -5

8) x^2 + 11x + 28

   x^2 + 4x + 7x + 28

   (x^2 + 4x) + (7x +28)

   x(x + 4) + 7(x + 4)

   (x + 7)(x + 4)

   x = -7, -4

9) d^2 + 6d - 27

    d^2 + 9d - 3d - 27

    (d^2 + 9d) + (-3d - 27)

    d(d + 9) + -3(d + 9)

    (d + -3)(d + 9)

    (d - 3)(d + 9)

    d = 3, -9

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Answer:

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Step-by-step explanation:

130/6.5 = 20

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3 years ago
Consider the following hypothesis test: H0: LaTeX: \mu_1-\mu_2=0μ 1 − μ 2 = 0 Ha: LaTeX: \mu_1-\mu_2\ne0μ 1 − μ 2 ≠ 0 The follow
Pavel [41]

Answer:

z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53

Step-by-step explanation:

Data given and notation

\bar X_{1}=104 represent the mean for the sample 1

\bar X_{2}=106 represent the mean for the sample 2

\sigma_{1} =8.4 represent the population standard deviation for the sample 1

\sigma_{2}=7.6 represent the population standard deviation for the sample 2

n_{1}=80 sample size for the group 1

n_{2}=70 sample size for the group 2

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0:\mu_{1}-\mu_{2} =0

H1:\mu_{1} -\mu_{2} \neq 0

If we analyze the size for the samples both are greater than 30 and we know the population deviations so for this case is better apply a z test to compare means, and the statistic is given by:

z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

And with this we can replace in formula (1) like this:

z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53

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The formula F=9/5c changes a temperature reading from the Celsius scale C to the Fahrenheit scale F. What is the temperature mea
pogonyaev

Answer:  The correct formula for converting C to F is:

F = (9/5)C + 32

30°C = 86°F

Step-by-step explanation:

F = (9/5)C + 32

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2 years ago
What its the exact and estimate of -3.7 +(-6.8) and i need work
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Exact:

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6 0
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Read 2 more answers
a rectangular lawn has an area of a^3 - 125. use the difference of cubes to find out the dimensions of the rectangle.
ANEK [815]

The area of a rectangle is the product of its dimensions

The dimensions of the rectangle are: \mathbf{Length = a -5} and \mathbf{Width = a^2 + 5a + 25}

The area is given as:

\mathbf{Area = a^3 - 125}

Express 125 as 5^3

\mathbf{Area = a^3 - 5^3}

Apply difference of cubes

\mathbf{Area = (a - 5)(a^2 + 5a + 5^2)}

\mathbf{Area = (a - 5)(a^2 + 5a + 25)}

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\mathbf{Area = Length \times Width}

So, by comparison:

\mathbf{Length = a -5}

\mathbf{Width = a^2 + 5a + 25}

Read more about areas at:

brainly.com/question/3518080

6 0
2 years ago
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