Answer:
B
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x + 8 - 4x - 3 ← collect like terms
= - 3x + 5
Answer:
[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]
Step-by-step explanation:
Given functions:f(x) = x + 8g(x) = -4x - 3Solution:Add both functions
(f + g)(x) = x + 8 + (-4x - 3)
(f + g)(x) = x + 8 - 4x - 3
(f + g)(x) = x - 4x + 8 - 3
(f + g)(x) = -3x + 5
[tex]\rule[225]{225}{2}[/tex]
what is the slope of the line through the points (-2,-1) and (8,-3)
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
You are choosing between two different cell phone plans. The first plan charges a rate of
21 cents per minute. The second plan charges a monthly fee of $44.95 plus 11 cents per
minute. How many minutes would you have to use in a month in order for the second
plan to be preferable?
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.
The perimeter of a standard-sized rectangular rug is 24 ft. The length is 2ft longer than the width. Find the dimensions.
The length and width of the rectangle are equal to: 7 ft and 5 ft, respectively
QuadrilateralsThere 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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Select the correct answer. The table represents a proportional relationship. x y 11 2 22 4 33 6 The graph represents another proportional relationship. Which equation represents the lower unit rate of these two relationships? A. B. C. D. Reset Next
The equation which represents the lower unit rate of these two relationships is y = 2x/11.
How to determine the equation?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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can someone please help me
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
1
√
x
If
y
=
3
when
x
=
36
find,
y
when
x
=
9
Answer:
3y= 36×9x
3y=324x
y=324÷3
y=108 ans
Which is the graph of f(x) = √x?
Look at the attached image.
One number is 6 more than twice another. If their sum is 51, find the numbers.
Which of the following systems of equations represents the word problem?
y = 2x + 6 and y = x + 51
y = 2x + 6 and x + y = 51
y = 2(x + 6) and x + y = 51
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
The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g.
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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1
..S
4 in.
Find h.
10 in.
h = √[?] in.
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
The volume of a can of Pepsi is 0.33liter. There are 12 cans in 1 carton
What is the volume of 5 cartons of Pepsi?
Answer:
19 liters 800 milliliters
Step-by-step explanation:
0.33 * 12 * 5 = 19.8 liters
If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x)= 155-(x/10):
a. find an expression for the total revenue from the sale of x thousand candy bars.
b. find the value of x that leads to maximum revenue
c. find the maximum revenue
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.
What is the maximum revenue?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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A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/25 for red, 1/20 for green, 1/15 for purple, and 1/10 for black. What is the probability of pulling a green or red card, written as a reduced fraction?
Probability helps us to know the chances of an event occurring. The probability of pulling a green or red card is 9 / 100.
What is Probability?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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A line passes through (-9,-6) and has an undefined slope. Write an equation of the line satisfying the given conditions.
A. x= -9
B. y= -9
C. y= -6
D. x= -6
The equation of the line is x = -9 , Option is the correct answer
What is the equation of a line ?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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A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many committees can be formed if no person can serve on more than one committee?
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.
f is an even function, g is an even function. a=
Answer:
a=6 it's even
Step-by-step explanation:
please mark me as brainlest
Answer:
A= 4
B= 3
i got it right.
Find the value of x for which m||n
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
express 2.603603603 . . . as a rational number
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]
Greg has a piece of string that is 3 1/3 yards long. If he cuts off 3/4 yard, how many yards of the string
will be left?
Explain the steps you would take to find the quotient of
1
3
÷ 4
3
A fire fighter sees a woman trapped in the building 81 feet up from the bottom floor. If the firetruck is parked 41 feet away from the bottom of the building, at what angle of elevation, to the nearest degree, shut the fire fighter extend the ladder to reach the woman?
please help
0.06/1.71
Answer:
0.04
Step-by-step explanation:
0.03508772
Find the sum of the first six terms in the sequence {1, 5, 9, 13, …}
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]
Which expressions are equivalent to the given equation. Logarithmic form
The expression that is equivalent to the given logarithm equation is log₄ 1 / 4 + log₄ x²
How to solve logarithm?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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What's x ? find the indicated side of the right triangle
-------------------------------------------------------------------------------------------------------------
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
[tex]\textsf{sin(30) = }\frac{\textsf{opposite}}{\textsf{hypotenuse}}[/tex][tex]\textsf{sin(30) = }\frac{\textsf{3}}{\textsf{x}}[/tex]Multiply both sides by x
[tex]\textsf{sin(30) * x = }\frac{\textsf{3}}{\textsf{x}}\textsf{ * x}[/tex][tex]\textsf{sin(30) * x = 3}[/tex]Divide both sides by sin(30)
[tex]\textsf{sin(30) * x}*\frac{1}{\textsf{sin(30)}}\textsf{ = 3}}*\frac{1}{\textsf{sin(30)}}[/tex][tex]\textsf{x = 3}}*\frac{1}{\textsf{sin(30)}}[/tex]Simplify
[tex]\textsf{x = 3}}*\frac{1}{\textsf{0.5}}[/tex][tex]\textsf{x = 6}[/tex]Therefore, the value of the unknown variable x is 6 units.
An electrical resistor is rated at 4500 ohms ± 3%. Express this tolerance in ohms and state the
actual range of resistance.
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.
How to determine the tolerance in ohms and state the actual range of resistance.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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(3/7 * (- 5/8)) + (1/3 * 5/6) + |- 1/2 - 1/5|
Answer:
Exact Form:
1789/2520
Decimal Form:
0.70992063
6. Divide:
6x²+7x-2/3x-1
using Long Division.
Step-by-step explanation:
3x-1) 6x^2 + 7x -2 ( 2x+3
-6x^2 -2x
+
0 + 9x -2
- 9x -3
+
1
Which expression is equivalent to...
Answer:
A is correct yes
Step-by-step explanation:
ndnanndnqnjed
Please answer all 3 questions I will give brainliest if I can if ur right!
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
