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3 years ago

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(−3x − 6)(3x2 − 6x + 3)????

2 answers:

scoundrel [369]3 years ago

6 0

Answer:

-216

Step-by-step explanation:

(−3x − 6)(3x2 − 6x + 3)

=(18)(6 − 6x + 3)

=(18)(6 − 18)

=(18)(− 12)

= -216

Monica [59]3 years ago

6 0

Answer:

-9 • (x + 2) • (x - 1)2

Step-by-step explanation:

(-3x-6)(3x2-6x+3)

Final result :

-9 • (x + 2) • (x - 1)2

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(-3x - 6) • ((3x2 - 6x) + 3)

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

-3x - 6 = -3 • (x + 2)

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

(3x2 - 6x + 3) = 3 • (x2 - 2x + 1)

Trying to factor by splitting the middle term

4.2 Factoring x2 - 2x + 1

The first term is, x2 its coefficient is 1 .

The middle term is, -2x its coefficient is -2 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1

Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -2 .

-1 + -1 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and -1

x2 - 1x - 1x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-1)

Add up the last 2 terms, pulling out common factors :

1 • (x-1)

Step-5 : Add up the four terms of step 4 :

(x-1) • (x-1)

Which is the desired factorization

Multiplying Exponential Expressions :

4.3 Multiply (x-1) by (x-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x-1) and the exponents are :

1 , as (x-1) is the same number as (x-1)1

and 1 , as (x-1) is the same number as (x-1)1

The product is therefore, (x-1)(1+1) = (x-1)2

Final result :

-9 • (x + 2) • (x - 1)2

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can i get some help? i tried figuring it out myself already but i must have done something wrong. please help!

zaharov [31]

First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.

N will represent nickels

D will represent dimes

N + D = 30

---The problem tells us that there are 30 total coins

0.05N + 0.10D = 2.95

---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95

Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.

N + D = 30

N = 30 - D

Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.

0.05(30 - D) + 0.10D = 2.95

1.5 - 0.05D + 0.10D = 2.95

1.5 + 0.05D = 2.95

0.05D = 1.45

D = 29

Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.

N = 30 - D

N = 30 - 29

N = 1

Therefore, there are 29 dimes and 1 nickel.

Hope this helps!

5 0

3 years ago

Number of specific terms in x^5+y^5

Airida [17]

Answer:

There are two terms.

3 0

4 years ago

A store charges 8% tax on every dollar spent. The table shows the tax amount for several different purchases. How much tax would

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3 years ago

Read 2 more answers

Find the diagonal of the rectangular solid

earnstyle [38]

There are four (4) diagonals: 3 face diagonals and one space diagonal. We assume you are interested in the space diagonal.

The face diagonal of the 3×4 face has length
d₃₄ = √((3 ft)² +(4 ft)²) = √(25 ft²) = 5 ft

Taking the 5 ft edge and the 5 ft face diagonal as sides of the triangle with the space diagonal as its hypotenuse, we find the length of the space diagonal to be
d = √((5 ft)² +(5 ft)²)
d = 5√2 ft

The space diagonal of the rectangular solid is 5√2 ft ≈ 7.07 ft.

4 0

4 years ago

The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in in

Grace [21]

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

P.Q. = $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, s = sample standard deviation = $\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }$ = 5.063

$\sigma$ = population standard deviation

n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

<u>So, 90% confidence interval for the population standard deviation, </u> $\sigma$ <u> is ;</u>

P(11.59 < $\chi^{2}__2_1$ < 32.67) = 0.90 {As the critical value of chi at 21 degrees

of freedom are 11.59 & 32.67}

P(11.59 < $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ < 32.67) = 0.90

P( $\frac{ 11.59}{(n-1) \times s^{2}}$ < $\frac{1}{\sigma^{2} }$ < $\frac{ 32.67}{(n-1) \times s^{2}}$ ) = 0.90

P( $\frac{(n-1) \times s^{2} }{32.67 }$ < $\sigma^{2}$ < $\frac{(n-1) \times s^{2} }{11.59 }$ ) = 0.90

<u>90% confidence interval for</u> $\sigma^{2}$ = [ $\frac{(n-1) \times s^{2} }{32.67 }$ , $\frac{(n-1) \times s^{2} }{11.59 }$ ]

= [ $\frac{21 \times 5.063^{2} }{32.67 }$ , $\frac{21 \times 5.063^{2} }{11.59 }$ ]

= [16.48 , 46.45]

<u>90% confidence interval for</u> $\sigma$ = [ $\sqrt{16.48}$ , $\sqrt{46.45}$ ]

= [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

5 0

3 years ago