Given f(x) = x ^ 2 + 2x and g(x) = x - 1 , find (fg)(x)

A) x^3 + 2x^2
B) x^3 + x^2 + 2x
C) x^3 - x^2 - 2x
D) x^3 + x^2 - 2x

To begin with, we can simplify y using the Pythagorean identity:

y = 2 cos²(x) + 3 sin²(x) + 5

y = 2 (cos²(x) + sin²(x)) + sin²(x) + 5

y = 2 + sin²(x) + 5

y = sin²(x) + 7

Next, we can further rewrite this using the half angle identity for sine:

y = (1 - cos(2x))/2 + 7

y = 15/2 - 1/2 cos(2x)

Now, since cos(x) is bounded between -1 and 1, we have

max(y) = 15/2 - 1/2×(-1) = 15/2 + 1/2 = 8

and

min(y) = 15/2 - 1/2×1 = 15/2 - 1/2 = 7

Then the sum of the maximum and minimum is 8 + 7 = 15.

Answer:

1/6

Step-by-step explanation:

It's 1/6 because the only multiple of 5 in a die is 5, so it will be 1/6.

Answer:

500

Step-by-step explanation:

Since we are rounding to the tens place, that is the second value in the number 499. Remember these details when rounding;

Since we have a 9, we round up get and 500.

Best of Luck!

Answer:

499 rounded to the nearest tenth is 500.

Step-by-step explanation:

499 rounded to the nearest tenth is 500 because, every tenths place is + 10

the closest tenth 499 is closest to would be 500.

Hope this helped :)

Answer:

∠ABC measures 85° and ∠DEF measures 95°.

Step-by-step explanation:

We are given that ∠ABC and ∠DEF are supplementary. Then by definition:

[tex]\displaystyle m\angle ABC + m\angle DE F = 180^\circ[/tex]

Substitute:

[tex]\displaystyle \left(9x+4\right) + \left(13x-22\right) = 180[/tex]

Solve for x. Combine like terms:

[tex]22x -18 = 180[/tex]

Add:

[tex]\displaystyle 22x = 198[/tex]

And divide. Hence:

[tex]\displaystyle x = 9[/tex]

To find the measure of ∠ABC, substitute and evaluate:

[tex]\displaystyle \begin{aligned}m\angle ABC &= 9x + 4 \\ &= 9(9) + 4 \\ &= 81 + 4 \\ &= 85^\circ \end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned}m\ngle DE F &= 13x - 22 \\ &= 13(9) - 22 \\ &= 117-22 \\&= 95^\circ \end{aligned}[/tex]

In conclusion, ∠ABC measures 85° and ∠DEF measures 95°.

Answer:

$40.76, if rounded then $40.80.

Step-by-step explanation:

you do 420 times 3.30 divided by 34

Answer:

random number generators return numbers from 0 to 1...

a) generate 25 random numbers if the number x is ≤ .4 he makes the shot

otherwise he misses

a) generate 8 random numbers if the number x is ≤ .752 she makes the shot otherwise it is a miss

otherwise he misses

Step-by-step explanation:

Answer: 186 students

Step-by-step explanation:

7x23+25= 186

Answer:

a) 25%

10%+15% = 25%

b) doesn't have any idea

Answer:

No

Step-by-step explanation:

[5+3x] is an expression that cannot be added because 5 is a natural interger but 3x is an unknown

and therefore it cannot be divided by 2 to get 4

Better example :

if the question will give 4x , then

it should be [5x+3x]/2 = 8x/2 = 4x

it's obvious from the example I gave that 8x can be divided by 2 to give 4x

[tex]\boxed{\sf 1kg=2.205lbs}[/tex]

[tex]\\ \sf\longmapsto 6kg[/tex]

[tex]\\ \sf\longmapsto 6(2.205)[/tex]

[tex]\\ \sf\longmapsto 13.23lbs[/tex]

Answer:

But where is the question???????

Answer:

Hi, there! The correct Answer Is Below

4,540,597 Would Round To 5,000,000

Step-by-step explanation:

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. ...

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.

________________________________________________________

-Darkspirit-

Answer:

Step-by-step explanation:

The hundred thousands digit is 5 so it is 5,000,000.

Answer:

5x-1

Step-by-step explanation:

solution

5x-3+2

or, 5x-1

Answer:

320/420 = 4/3

Step-by-step explanation:

4/7= x /560

Cross multiply

7x = 2240

Divide by 7:

x=320

The school has 320 boys and 240 girls

I hope this helps u:)

Answer:

Problem(1):     [tex]21[/tex]

Problem(2):     Side length = [tex]\frac{1}{4}[/tex]    Area = [tex]\frac{1}{16}[/tex]

Problem(3):     Boys = [tex]320[/tex]     Girls = [tex]240[/tex]

Step-by-step explanation:

(Notes steps are cut from this answer so that it isn't too long)

1. Problem (1)

One is given the following information:

The most logical first step is to solve for the value of (x). One can solve for the numerical value of (x) with the first equation.

[tex]x+\frac{1}{x}=5[/tex]

Multiply the entire equation by (x),

[tex]x^2+1=5x[/tex]

Inverse operations put the equation in the general format of a quadratic equation. The general format of a quadratic equation is as follows,

[tex]ax^2+bx+c=0[/tex]

Put the given equation in this format,

[tex]x^2-5x+1=0[/tex]

Now use the quadratic formula to solve for the value of (x). The quadratic formula uses the coefficients of the terms in a quadratic equation to find the roots of the equation. The quadratic formula is as follows,

[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]

Use the coefficients of the terms in the given quadratic equation in the formal, then simplify to solve for solutions of the given equation,

[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]

Simplify,

[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]

[tex]\frac{5(+-)\sqrt{21}}{2}[/tex]

Now substitute these values into the equation and simplify, even though there are two values of (x), there will only be one solution,

[tex]((\frac{5+\sqrt{21}}{2}-\frac{1}{\frac{5+\sqrt{21}}{2}})^2[/tex]                                      [tex]((\frac{5-\sqrt{21}}{2}-\frac{1}{\frac{5-\sqrt{21}}{2}})^2[/tex]  

[tex](\frac{5+\sqrt{21}}{2}-\frac{2}{5+\sqrt{21}})^2[/tex]                                      [tex](\frac{5-\sqrt{21}}{2}-\frac{2}{5-\sqrt{21}})^2[/tex]

Convert to a common denominator,

[tex](\frac{5+\sqrt{21}}{2}*\frac{5+\sqrt{21}}{5+\sqrt{21}}-\frac{2}{5+\sqrt{21}}*\frac{2}{2})^2[/tex]                   [tex](\frac{5-\sqrt{21}}{2}*\frac{5-\sqrt{21}}{5-\sqrt{21}}-\frac{2}{5-\sqrt{21}}*\frac{2}{2})^2[/tex]

[tex](\frac{(5+\sqrt{21})^2-4}{2(5+\sqrt{21})})^2[/tex]                                           [tex](\frac{(5-\sqrt{21})^2-4}{2(5-\sqrt{21})})^2[/tex]

Simplify,

[tex](\frac{25+10\sqrt{21}+21-4}{10+2\sqrt{21}})^2[/tex]                                     [tex](\frac{25-10\sqrt{21}+21-4}{10-2\sqrt{21}})^2[/tex]

[tex](\frac{42+10\sqrt{21}}{10+2\sqrt{21}})^2[/tex]                                              [tex](\frac{42-10\sqrt{21}}{10-2\sqrt{21}})^2[/tex]

[tex]\frac{1764+840\sqrt{21}+2100}{100+40\sqrt{21}+84}[/tex]                                      [tex]\frac{1764-840\sqrt{21}+2100}{100-40\sqrt{21}+84}[/tex]

[tex]\frac{3864+840\sqrt{21}}{184+40\sqrt{21}}[/tex]                                               [tex]\frac{3864-840\sqrt{21}}{184-40\sqrt{21}}[/tex]

[tex]21[/tex]                                                            

2. Problem (2)

All four sides of a square are congruent (have the same measure), thus dividing the perimeter of a square by (4) will yield the side length of the square,

[tex]Perimeter\ of\ the\ square: 4\\Side\ length: \frac{1}{4}[/tex]

The area is the two-dimensional space that a figure takes up, in the case of a square, the area is the side length times itself:

[tex]A=(\frac{1}{4})^2=\frac{1}{16}[/tex]

3. Problem (3)

Let (x) represent the amount by which the ratio of boys to girls was scaled down. Assuming that these are the only two genders in the school, one can state that the sum ratio coefficients times the scaling value for both boys and girls, will equal the total number of people in the school. Thus, one can form the following equation and solve it with inverse operations and simplification,

[tex]boys + girl = total\ students\\4x + 3x = 560\\7x = 560\\x = 80[/tex]

Now substitute this into the expression for the two genders in this scenario, respectively, to solve for the actual number of students of that gender,

Boys,                         Girls,

[tex]4(x)[/tex]                             [tex]3(x)[/tex]

[tex]4(80)[/tex]                           [tex]3(80)[/tex]

[tex]320[/tex]                              [tex]240[/tex]

Answer:

S = (-8, 0 )

Step-by-step explanation:

Answer:

Step-by-step explanation:

16. Use Euclid Perfect Number formula:

If [tex]2^{n} -1[/tex]a a prime number, then [tex]2^{n-1}(2^{n} -1)[/tex] is a perfect number. 6 is a perfect number when n=2 Let try when n=3

[tex]2^{2} (7)=28[/tex]

So 28 is a perfect number

Answer:

14...

plz mark me brailiest

Answer:

h = 4

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to 2

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = M (h, 3 ) and (x₂, y₂ ) =  N (- 2, - 9 )

m = [tex]\frac{-9-3}{-2-h}[/tex] = [tex]\frac{-12}{-2-h}[/tex] , then

[tex]\frac{-12}{-2-h}[/tex] = 2 ( multiply both sides by - 2 - h )

2(- 2 - h) = - 12 ( divide both sides by 2 )

- 2 - h = - 6 ( add 2 to both sides )

- h = - 4 ( multiply both sides by - 1 )

h = 4

Step-by-step explanation:

The graph is shifted 4 units left.

The graph is shifted 4 units right.

The graph is shifted 4 units up.

The graph is shifted 4 units down.

9514 1404 393

Answer:

  no

Step-by-step explanation:

The expression 2·4 has the value 8.

The expression 8x has the value 8x, which is only equal to 8 when x=1. In general, x may have any value, so the expressions are not equal.

Answer:

89$ for 11 Charities

Step-by-step explanation:

I. If Luis has $979 and he wants to give it to 11 charities right?

  So  [tex]\frac{979}{11}[/tex]

    = 89$

Answer:

x = -3

Step-by-step explanation:

15 = 5/3 (x + 12)

Multiply each side by 3/5 to clear the fraction

3/5 *15 =3/5 *5/3  (x + 12)

9 = x+12

Subtract 12 from each side

9-12 = x+12-12

-3 =x

Answer:

15 = 5/3(x + 12)

Using distributive law

15 = 5x/3 + 20

15 = 5x + 60/3

15 × 3 = 5x + 60

45 = 5x + 60

45 - 60 = 5x

-15 = 5x

-15/5 = x

-3 = x

Answer:

5

Step-by-step explanation:

divide the distance by the rate of speed

5/1=5

Answer:

5 seconds.

Step-by-step explanation:

The round trip distance between the national park and city Y is 593 miles.

Given:

To find :

The round trip distance between the national park and city Y

Solution:

According to the question, the round trip distance between City X and City Y is 647 miles.

Let the distance from City X to City Y = d

Let the distance from City Y to City X = d

[tex]d+d=647 miles\\2d=647 miles\\d=\frac{647miles}{2}=323.5 miles[/tex]

Distance from City X to City Y = 323.5 miles

Distance of City X from national park = 27 miles

From the figure, the distance of the national park from the City Y = d -27 miles:

[tex]= 323.5 miles - 27 miles = 296.5 miles[/tex]

The distance from national park to City Y = 296.5 miles

When we will be going on the round trip between the national park and city Y we will be first traveling 296.5 miles from the national park to the City Y and then 296.5 miles from City Y to the national park.

So, the round trip distance between the national park and city Y:

[tex]296.5 miles + 296.5 miles = 593 miles[/tex]

So the round trip distance between the national park and city Y is 593 miles.

Learn more about- Round trip Distance

brainly.com/question/20691988

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We will find that the ratio of 3 less than k to 2 more than k is:

(k - 3):(k + 2)

The ratio between two numbers A and B can be written as:

A:B

This is the ratio of A to B

and

B:A

Is the ratio of B to A.

Then for the ratio of 3 less than k to 2 more than k we have:

"3 less than k" is: k - 3

"2 more than k" is: k+ 2

Then the ratio is:

(k - 3):(k + 2)

if you want to learn more, you can read:

https://brainly.com/question/13419413