If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).
A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5

Answer:

1. 30 ft

2. sqrt(2164) yd

3: 12 cm

Step-by-step explanation:

For all three questions I'll be using the Pythagorean Theorem which states that a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the base and height

Question 1:

40^2 + d^2 = 50^2

1600 + d^2 = 2500

d^2 = 900

d = 30

Question 2:

42^2 + 20^2 = c^2

2,164 = c^2

c = sqrt(2164)

Question 3:

5^2 + a^2 = 13^2

25 + a^2 = 169

a^2 = 144

a = 12

Probability helps us to know the chances of an event occurring. The probability of pulling a green or red card is 9 / 100.

Probability helps us to know the chances of an event occurring.

P =  [tex]\dfrac{Desired \ outcomes}{Posiible \ outcomes}[/tex]

The probabilities of different color cards being pulled are 1/25 for red, 1/20 for green, 1/15 for purple, and 1/10 for black Therefore, the probability of pulling  a green or red card is,

Probability = 1/20 + 1/25

                 = (5 + 4) /100

                 = 9 / 100

Hence, the probability of pulling a green or red card is  9 / 100.

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Answer:

3y= 36×9x

3y=324x

y=324÷3

y=108 ans

Answer:

at least 450 minutes

Step-by-step explanation:

Find an expression for the cost of each plan as a function of the number of minutes. Set the expressions equal to each other, and solve for the number of minutes.

Let x = number of minutes.

First plan:

cost (in dollars) = 0.21x

Second plan:

cost (in dollars) = 0.11x + 44.95

Set the expressions equal:

0.21x = 0.11x + 44.95

Subtract 0.11x from both sides.

0.1x = 44.95

Divide both sides by 0.1

x = 44.95/0.1

x = 449.5

Since you cannot have a fraction of a minute, the answer is 450 minutes.

Answer:

√96

Step-by-step explanation:

halve the diameter to set up the pythagorean theorem

2²+b²=10²

4+b²=100

-4 on each side

b²=96

square root each side

b=√96

it could the be further simplified to 4√6

Answer:

66

Step-by-step explanation:

The sequence you provided seems to be arithmetic as it increases as 4 each term. Assuming 1 is the first term the equation would be [tex]a_{n}=1 + 4(n-1)[/tex]. You could just take the first 6 terms and add them together since you already have 4 values calculated and you could calculate the other 2 by adding 4. This would give you

(1 + 5 + 9 + 13 + 17 + 21) = 66

But there's an easier way to do it. You could use the formula [tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]. You can calculate [tex]S_6[/tex] by plugging in those values. You would need to calculate [tex]a_6[/tex] before hand, but you can calculate that using the formula I defined above. Which in general is [tex]a_n = a_1 + d(n-1)[/tex] where d is like the slope, or how much it changes each term. So if you calculate [tex]a_6[/tex] you'll get [tex]1+4(6-1) = 1+4(5) = 21[/tex]. Now plug this into the series formula above and you get [tex]S_6 = \frac{6(1+21)}{2}=\frac{6(22)}{2}=\frac{132}{2}=66[/tex] which is exactly what you get if you add the first 6 terms as shown above when you do it manually.

[tex]\text{First let's find two more terms, because we have only six. We can do that by}\\\text{adding 4:: 13+4=17; 17+4=21}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now we just add the terms: 1+5+9+13+17+21}[/tex]

[tex]\rule{300}{1.7}\\\text{66}[/tex]

Answer:

Step-by-step explanation:

Using slope m = y_2-y_1/x_2-x_1 to find the solution slope that passes through those two-point.

Point-slope form into y-intercept form.

Answer:

For finding slope

we have the formula

m = y2 - y1/ x2 - x1

x1 = (-2)

x2. = ( 8)

y1. = (-1)

y2 =(-3)

putting the value of this in the formula we get,

m = (-3)-(-1)/8-(-2)

m = (-3+1)/8 + 2.

m = (-2)/10

m = (-1)/5.

m = (-1)/5

Answer:

A is correct yes

Step-by-step explanation:

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Answer:

Exact Form:

1789/2520

Decimal Form:

0.70992063

Part 1

f(2) represents the value of y when x=2, which is 3

Part 2

We need to find the value of x that makes y=2, which is -1

The statement "The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g" is FALSE.

Domain is the values of x in the function represented by y=f(x), for which y exists.

THe given statement is "The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g".

Now we assume the [tex]g(x)=x+2[/tex] and [tex]f(x)=\frac{1}{x-6}[/tex]

So here since g(x) is a polynomial function so it exists for all real x.

[tex]f(x)=\frac{1}{x-6}[/tex]  does not exists when [tex]x=6[/tex], so the domain of f(x) is given by all real x except 6.

Now,

[tex](fg)(x)=f(g(x))=f(x+2)=\frac{1}{(x+2)-6}=\frac{1}{x-4}[/tex]

So now (fg)(x) does not exists when x=4, the domain of (fg)(x) consists of all real value of x except 4.

But domain of both f(x) and g(x) consists of the value x=4.

Hence the statement is not TRUE universarily.

Thus the given statement about the composition of function is FALSE.

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Look at the attached image.

The length and width of the rectangle are equal to: 7 ft and 5 ft, respectively

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.

For this question, the length is 2ft longer than the width - L=2+W. Thus,

24=2*(2+W)+2W

24=4+2W+2W

24-4=4W

20=4W

W=5 ft

If W=5, L will be 2+5=7 ft.

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Answer:

1,260

Step-by-step explanation:

[tex]\implies C(9,4)*C(5,3)*C(2,2)[/tex]

[tex]\implies 9!/4!(9-4)!*5!/3!(5-3)!*2!/2!(2-2)![/tex]

[tex]\implies 9!/4!5!*5/3!2! *2!0![/tex]

[tex]\implies (9 * 8 * 7 * 6 / 4 * 3 * 2 * 1) * (5 * 4 / 2 * 1) * 1[/tex]

[tex]\implies 1260[/tex]

Therefore, 1,260 committees can be formed.

Answer:

Range =  4365-4635

Step-by-step explanation:

4500 * 3/100 = 135

4500 + 135  = 4635

4500 - 135  = 4365

Range =  4365-4635

The actual range of resistance is from 4365 ohms to 4635 ohms.

To express the tolerance in ohms, we need to calculate 3% of the rated resistance, which is 4500 ohms.

Tolerance in ohms = 3% of 4500 ohms

Tolerance in ohms = 0.03 * 4500

Tolerance in ohms = 135 ohms

The actual range of resistance can be found by adding and subtracting the tolerance from the rated resistance:

Lower limit = Rated resistance - Tolerance

Lower limit = 4500 ohms - 135 ohms

Lower limit = 4365 ohms

Upper limit = Rated resistance + Tolerance

Upper limit = 4500 ohms + 135 ohms

Upper limit = 4635 ohms

So, the actual range of resistance is from 4365 ohms to 4635 ohms.

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The expression that is equivalent to the given logarithm equation is log₄ 1 / 4  + log₄ x²

log₄ (1 / 4 x²)

Using logarithm law, the logarithm can be express as follows;

using logarithm law,

Therefore, the expression that is equivalent to the given logarithm equation is as follows:

using addition law for logarithm,

log₄ (1 / 4 x²) = log₄ 1 / 4  + log₄ x²

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The equation of the line is x = -9 , Option  is the correct answer

The equation of a line is given by y = mx+c

where m is the slope and c is the intercept

It is given that

A line passes through (-9,-6) and has an undefined slope.

undefined slope means it is a vertical line at -9

Therefore the equation of the line is x = -9 , Option  is the correct answer

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Step-by-step explanation:

3x-1) 6x^2 + 7x -2 ( 2x+3

-6x^2 -2x

+

0 + 9x -2

- 9x -3

+

1

Answer:

a=6 it's even

Step-by-step explanation:

please mark me as brainlest

Answer:

A= 4

B= 3

i got it right.

Answer:

19 liters 800 milliliters

Step-by-step explanation:

0.33 * 12 * 5 = 19.8 liters

Answer:

0.04

Step-by-step explanation:

0.03508772

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{x = 6}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{The image provided with 2 angles and one side}[/tex]

Find:  [tex]\textsf{Solve for the unknown side of x}[/tex]

Solution:  In order to determine the length of x we need to use some trigonometric functions.  Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees.  We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin.  Plug in the values and solve for the unknown.

Plug in the values

Multiply both sides by x

Divide both sides by sin(30)

Simplify

Therefore, the value of the unknown variable x is 6 units.

Answer:

y = 2x + 6 and y + x = 51

Step-by-step explanation:

the first number is y

the second number is X

" 6 is more than" implying +

"6 is more than twice another" implying y = 6 + 2 multiples by the second number "X"

their sum is equal to 51

add first and the second number

that is

y+x = 51

so we have

y = 6+2x and y +x = 51

Answer:

x = 61

Step-by-step explanation:

Alternate exterior angles must be congruent for the lines to be parallel.

3x - 43 = 2x + 18

x = 61

The equation which represents the lower unit rate of these two relationships is y = 2x/11.

In order to determine the equation which represents the lower unit rate of these two relationships, we would find the slope of the given points.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given parameters into the formula, we have;

[tex]Slope = \frac{6\;-\;4}{33\;-\;22}\\\\Slope = \frac{2}{11}[/tex]

Slope = 2/11.

From the standard equation, we have:

y = mx + c

y = 2x/11 + 0

y = 2x/11.

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The expression for the total revenue from x thousand sales is 155,000x - 100x².

The value of x is 775 cents and the maximum revenue is $60,062,500.

First, come up with an expression for total revenue from x thousand sales:

= (155  - x /10 ) × x × 1,000 units

= 155,000x - 100x²

The value of x would then be:

Derive the function from the total revenue function to give:

0 = 155,000 - 200x

x = 775 cents

The maximum revenue is therefore:

= 155,000(775) - 100(775)²

= $60,062,500

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Answer:

[tex] \frac{289}{111} [/tex]

Step-by-step explanation:

[tex]2 + \frac{603}{1000 - 1} = 2 \frac{603}{999} = 2 \frac{67}{111} = \frac{289}{111} [/tex]