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3 years ago

Simplify the expression (2x² + 9) (x² - 7)

Mathematics

2 answers:

Natali5045456 [20]3 years ago

7 0

Answer:

2 $x^{4}$ - 5x² - 63

Step-by-step explanation:

Given

(2x² + 9)(x² - 7)

Each term in the second factor is multiplied by each term in the first factor, that is

2x² (x² - 7) + 9(x² - 7) ← distribute both parenthesis

= 2 $x^{4}$ - 14x² + 9x² - 63 ← collect like terms

= 2 $x^{4}$ - 5x² - 63

Mashutka [201]3 years ago

6 0

Answer:

$\boxed {2x^{4} - 5x^{2} - 63}$

Step-by-step explanation:

Solve the following expression:

$(2x^{2} + 9) (x^{2} - 7)$

-Use Distributive Property:

$(2x^{2} + 9) (x^{2} - 7)$

$2x^{4} - 14x^{2} + 9x^{2} - 63$

-Combine like terms:

$2x^{4} - 14x^{2} + 9x^{2} - 63$

$\boxed {2x^{4} - 5x^{2} - 63}$

Therefore, the final answer is $2x^{4} - 5x^{2} - 63$ .

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Primitive function for: 1. f(x)=4e2x+e−x, sådan att F(0)=2

Free_Kalibri [48]

The primitive function for $f(x) = 4e^{2x} + e^{-x}$ is given by it's indefinite integral.

To calculate it, recall:

$\frac{d}{dx}e^{ax}=ae^{ax}$

$\int c f(x)dx = c\int f(x)dx$

Let's begin

$\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\$

$F(x) = 2e^{2x}-e^{-x} +c$

To find the costant, we just need to use the fact that $F(0)=2$

$F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3$

Therefore,

$\boxed{F(x) = 2e^{2x} - e^{-x} -3 }$

6 0

3 years ago

A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before t

aleksklad [387]

Answer:

We cannot say that the mean wake time are different before and after the treatment, with 98% certainty. So the zopiclone doesn't appear to be effective.

Step-by-step explanation:

The goal of this analysis is to determine if the mean wake time before the treatment is statistically significant. The question informed us the mean wake time before and after the treatment, the number of subjects and the standard deviation of the sample after treatment. So using the formula, we can calculate the confidence interval as following:

$IC[\mu ; 98\%] = \overline{y} \pm t_{0.99,n-1}\sqrt{\frac{Var(y)}{n}}$

Knowing that $t_{0.99,15} = 2.602$ :

$IC[\mu ; 98\%] = 98.9 \pm 2.602\frac{42.3}{4} \Rightarrow 98.9 \pm 27.516$

$IC[\mu ; 98\%] = [71.387 ; 126,416]$

Note that $102.8 \in [71.384 ; 126.416]$ so we cannot say, with 98% confidence, that the mean wake time before treatment is different than the mean wake time after treatment. So the zopiclone doesn't appear to be effective.

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3 years ago

Joe Hernandez has inherited $25,000 and wishes to purchase an annuity that will provide him with a steady income over the next 1

mote1985 [20]

Answer:

p=2982

Step-by-step explanation:

Rate of interest = 6 % p.a

No of year = 12

P.V = $ 25000

Installments (p) = ?

We know the formula of P.V annuity

P.V = P[ 1-(1+r)-n/r]

25000 = P[1-(1+0.06)-12/0.06]

P = 2982 will withdraw annuity

8 0

3 years ago

Read 2 more answers

100 points whats 9 times 3 plus 3 divided by 2

Dmitrij [34]

Answer:

Step-by-step explanation:

28.5

5 0

3 years ago

Read 2 more answers

Step 2 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries

aivan3 [116]

The synthetic division's representation of the dividend is 2x3 + 10x2 + x + 5.

Given that

An L shape is created when two lines intersect vertically and horizontally.

The shape has entries in two rows.

Entries in row 1 are 2, 10, 1, and 5.

Blank, -10, and 0 are the entries in row 2.

A simplified method of dividing a polynomial with another polynomial equation of degree one is known as synthetic division.

On the exterior, to the left of the form, is entry number 5.

The entry stands for the divisor's zero.

If the variable is x, then this entry to the variable is;

2x³+10x²+x+5

The dividend is thus represented by synthetic division as

2x³+10x²+x+5

The Question is incomplete And complete question is given below!!

What dividend is represented by the synthetic division below? A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0. Negative 10 x squared minus 5 2 x cubed 10 x squared x 5 2 x squared 1 2 x cubed x.

Learn more about Synthetic division here

brainly.com/question/27979968

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1 year ago

Simplify the expression (2x² + 9) (x² - 7)​

Simplify the expression (2x² + 9) (x² - 7)