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3 years ago

Factor by grouping. 4x^3 − 16x^2 + 12 − 3x

1 answer:

5 0

He first thing that we would really want to consider is that we would definitely want to group this up because it would make things a lot more easier.

$(((4 * (x^3)) - 2^4x^2) + 12) - 3x \\ \\ as \ we \ simplify \ this . . . \\ \\ ((2^2x^3 - 2^4x^2) + 12) - 3x \\ \\ Factoring: \ \boxed{4x^3-16x^2-3x+12 } \\ \\ Factoring: \ 4x^2-3 \\ \\$

Your answer: $\boxed{\bf{ (4x^2 - 3) *(x - 4)}}$

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7. The cost of renting the party room for 10 people is $117.50. The cost of renting the room is $151.25 for 15 people. Write an

Viktor [21]

Answer:

C = 6.75n + 50

Step-by-step explanation:

The equation for the cost of renting the party room can be written in the form;

C= mn+k ......i

Where C = cost

n = number of people

Substituting the 2 cases into the equation we have,

Case 1

117.5 = 10m + k ......1

Case 2

151.25 = 15m + k .....2

Subtracting eqn 1 from 2 we have

151.25 - 117.50 = 15m - 10m

5m = 33.75

m = 33.75/5 = 6.75

Substituting m = 6.75 into eqn 1, we have

117.50 = 10(6.75) + k

k = 117.5 - 67.50

k = 50

Therefore, rewriting the eqn i, we have

C = 6.75n + 50

5 0

3 years ago

5 less than a product of 4 and a number is equal to 6

DIA [1.3K]

Answer:

4x-5=6 is the equation.

Step-by-step explanation:

What you do is look at the product part. That means multiplying.

Less than means subtraction.

Equals to means equals of course so the equation is

4x-5=6.

3 0

3 years ago

Read 2 more answers

What is 5X minus Y equals 6+ negative 2X plus Y=8

vova2212 [387]

Answer:

For the given expression: $X = (\frac{10}{3}) , Y = (\frac{26}{3})$

Step-by-step explanation:

Here, the given expression in statement form is given as:

5 X minus Y equals 6 + negative 2 X plus Y = 8

Now, converting the given statement mathematically, we get:

5X - Y = 6 + (-2X) + Y = 8

Now, considering first and the last terms,we get:

5 X - Y = 8 .... (1)

and , considering second and the last terms,we get:

6 + (-2X) + Y = 8 or, -2X + Y = 2 ......... (2)

Adding (1) and (2) , we get:

5 X - Y - 2 X + Y = 8 + 2

or, 3 X = 10

or, X = 10/3 = 3.34

Now, 5X - Y = 8

or, $5(\frac{10}{3}) - Y = 8\\ \implies Y = \frac{50}{3} - 8 = \frac{50 - 24}{3} = \frac{26}{3} \\\implies Y = \frac{26}{3}$

Hence, for the given expression:

$X = (\frac{10}{3}) , Y = (\frac{26}{3})$

3 0

3 years ago

Please select the best answer from the choices provided

Ira Lisetskai [31]

<u>Answer:</u>

The correct answer option is c. $\frac{1}{9a^2}$ .

<u>Step-by-step explanation:</u>

We are given an expression $(27a^{-3})^{-\frac{2}{3} }$ and we are supposed to simplify it.

We can also write $(27a^{-3})^{-\frac{2}{3} }$ as $(\frac{3^3}{a^3} )^{-\frac{2}{3} }$ .

We know the power rule (a^m)^n=a^{mn} which means that to raise a power to a power you need to multiply the exponents.

So multiplying the exponents to get:

$\frac{3^{(3.-\frac{2}{3})} }{a^{(3.\frac{2}{3})} }\\\\\frac{3^{-2}}{a^2}\\ \\\frac{1}{3^2a^2} \\\\\frac{1}{9a^2}$

Therefore, the correct answer option is c. $\frac{1}{9a^2}$ .

4 0

3 years ago

An ANOVA procedure is used for data that were obtained from four sample groups each comprised of five observations. The degrees

jeyben [28]

Answer:

(3,16)

Step-by-step explanation:

The degrees of freedom of the critical value F are (k-1,n-k).

We are given that there are four sample group, so,

k=4.

Also, we are given that the each four groups contains five observations, so,

n=4*5

n=20

The critical value F has degree of freedom

(k-1,n-k)

(4-1,20-4)

(3,16).

Thus, the degrees of freedom for the critical value of F are (3,16).

6 0

3 years ago