The composite function (f o g)(x) is found by substituting g(x) into the f(x) expression. Upon simplification, (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1) is: 1/(x² + 2x + 1) + 6/(x+1) + 5.
Explanation:To find the composite function (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1), we substitute g(x) into f(x). That is, wherever you see 'x' in f(x), replace it with what g(x) is equal to.
Start with f(g(x)) = f(1/(x+1)). In f(x), replace x with 1/(x+1), which gives us: (1/(x+1))² + 6*(1/(x+1)) + 5. This is the composite function (f o g)(x).
To simplify further: the first term '(1/(x+1))²' becomes '1/(x² + 2x + 1)', the second term '6*(1/(x+1))' becomes '6/(x+1)', and the third term is just '+5'. So the composite function (f o g)(x) simplifies to: 1/(x² + 2x + 1) + 6/(x+1) + 5.
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Which of the following matrix addition problems are possible?
Answer:
Option A
Step-by-step explanation:
When adding two matrices, they should be of the same sizes.
Option A:
Matrix [tex]\left[\begin{array}{c}2&3\end{array}\right][/tex] has 2 rows and 1 column.
Matrix [tex]\left[\begin{array}{c}3&4\end{array}\right][/tex] has 2 rows and 1 column too.
So, these matrices can be added.
The result will be
[tex]\left[\begin{array}{c}2+3&3+4\end{array}\right]=\left[\begin{array}{c}5&7\end{array}\right][/tex]
Answer:
A
Step-by-step explanation:
E2020
missy sold between seven and 12 glasses of lemonade every hour at her lemonade stand. If she sold lemonade for two hours how many glasses could she have sold?
Answer:
"she could have sold between 14 and 24 glasses"
Step-by-step explanation:
7 to 12 glasses sold per hour
Min 7 glasses and Max 12 glasses
If she sold for 2 hours, her minimum would be:
7 * 2 = 14 glasses
and her max would be:
12 * 2 = 24 glasses
Hence,
she could have sold between 14 and 24 glasses
A retailer who sells fashion boots estimates that by selling them for x dollars each, he will be able to sell 70−x boots each week. Use the quadratic function R(x)=−x2+70x to find the revenue received when the average selling price of a pair of fashion boots is x. Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.
Answer: $35 is the selling price and $1225 is the maximum revenue.
Step-by-step explanation:
Since we have given that
[tex]R(x)=-x^2+70x[/tex]
We need to find the maximum revenue.
So, We will first derivative it w.r.t. x.
So, it becomes,
[tex]R'(x)=-2x+70[/tex]
Now, we will find critical points.
So, R'(x) = 0
So, it becomes,
[tex]-2x+70=0\\\\-2x=-70\\\\x=\dfrac{70}{2}=35[/tex]
Now, to check whether it yields maximum revenue or not.
So, second derivative w.r.t. x, we get that
R''(x) = -2<0
So, At $35, it yields maximum revenue.
Amount of maximum revenue would be
[tex]R(35)=-(35)^2+70\times 35=-1225+2450=\$1225[/tex]
Hence, $35 is the selling price and $1225 is the maximum revenue.
1. If f(x) = log2 (x) and g(x) is the image of f(x) after a
translation five units to the left, which equation
represents g(x)?
1. g(x) = log 3 (x + 5)
2. g(x) = log 3 (x) + 5
3. g(x) = log 3 (x - 5)
4. g(x) = log 3 (x) - 5
Hi! The correct answer is 2. g(x) = log3 (x) + 5. Message me if you need further help.
The transformation of a function may involve any change. The correct option is 2. The value will be g(x) = log₂(x+5).
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k \times f(x)
Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)
As we know to shift a function towards the left horizontally, we need to add the number of units to the value of x. Therefore, the function of g(x) will be written as,
g(x) = log₂(x+5)
Hence, the correct option is 2. The value will be g(x) = log₂(x+5).
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Explain what these ratios all have in common: 8:5,16:10,24:15 . Create a diagram to support your answer please and thank you
Answer:
Step-by-step explanation:
8:5, 16:10, 24:15
these can be written as 8/5, 16/10, 24/15
8/5
16/10 reduces to 8/5
24/15 reduces to 8/5
so basically, they are all the same ratio in simplest form
How much greater is the probability that a motorcyclist will die in a motor vehicle crash compared to the occupants of a car?
10 times greater
20 times greater
35 times greater
Answer:
My personal opinion to this question would be 20 times greater.
Step-by-step explanation:
This is because in a car, there is more safety as there is airbags for the driver and the passenger seat also if the people sitting on the back, lean forward from the crash, they would most probably hit their head on the headrest.
Triangle ABC has vertices at A(-3,4)B(4,-2)C(8,3).The triangle is translated 4 units down and 3 units left . Which rule represents the translation? After the translation, what are the coordinates of vertex C
Answer:
see explanation
Step-by-step explanation:
A translation of 4 units down means subtract 4 from the y- coordinate of the original point and a translation of 3 units left means subtract 3 from the original x- coordinate, thus translation rule is
(x, y ) → (x - 3, y - 4 )
Thus
C(8, 3 ) → C'(8 - 3, 3 - 4 ) → C'(5, - 1 )
17 divided by 768 in long Division
Answer:
45 remainder 3.
Step-by-step explanation:
Simplify the square root of 30/20
Answer:
√6/2
Step-by-step explanation:
7.08 × 26
Estimate and then find the exact answer.
Answer:
184.08
Step-by-step explanation:
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 24 cubic feet. A total of 23 boxes of paper were shipped with a combined volume of 426 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
x+y=23 and 10x+24y=426 can be used to determine the number of small and large boxes shipped where x represents the number of small boxes and y represent the number of large boxes.
Step-by-step explanation:
Given,
Volume of small box = 10 cubic feet
Volume of large box = 24 cubic feet
Total boxes shipped = 23
Combined volume = 426 cubic feet
Let,
x represent the number of small boxes.
y represent the number of large boxes.
x+y=23
10x+24y=426
x+y=23 and 10x+24y=426 can be used to determine the number of small and large boxes shipped where x represents the number of small boxes and y represent the number of large boxes.
Keywords: linear equation, addition
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-6+3(2-4(-3)+6)+(-5)
Answer:
43
Step-by-step explanation:
Remove parenthesis.
−6+3(2−4⋅−3+6)−5
Multiply −4 by−3.
−6+3(2+12+6)−5
Add 2 and 12.
−6+3(14+6)−5
Add 14 and 6.
-6+3(20)-5
Multiply 3 by 20.
-6+60-5
Add -6+60.
54-5
Subtract 54 and 5.
43
The cost of pumpkin seeds is proportional to their weight. A 24-ounce bag of pumpkin seeds costs $6.00. What is the unit rate for the pumpkin seeds?
$0.24 per ounce
$0.25 per ounce
$0.40 per ounce
$0.60 per ounce
Answer:
$0.25 per ounce
Step-by-step explanation:
Look at this and now tell me if my deleted answer was right
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Unit rate has to do with comparison or the proportionality of an item to its unit value or unit of measure.
The unit rate for the pumpkin seeds is $0.25 per ounce.
Based on this question, unit rate is the cost of 1-ounce of pumpkin seeds
From the question:
24-ounce of pumpkin seeds = $6.00
1- ounce of pumpkin seeds = ?
Cross Multiply
1 - ounce × $6.00 / 24-ounce
= $0.25
Therefore, unit rate for pumpkin seeds is $0.25 per ounce.
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graph a line with a slope of -5 that contains the point -3,-4
Answer:
The equation of the line is 5x + y + 19 = 0
Step-by-step explanation:
The equation of the line with slope 'm' and given a point (x₁, y₁) passing through it we use the Slope - one - point form which is given by:
y - y₁ = m(x - x₁)
The point given is: (-3, -4) and the slope is -5.
We get the equation of the line to be:
y - (-4) = -5(x - (-3))
⇒ y + 4 = -5(x + 3)
⇒ y + 4 = -5x - 15
⇒ 5x + y + 19 = 0. is the required equation of the line.
plz someone help me 7(2m−1)−35m=65(4−3m)
Solve for m.
Enter your answer in the space provided. Enter only your answer.
Answer:
Step-by-step explanation:
1. m = -1/5
2. c = -9.75
3. q = 0
Answer:
m = 89/56 = 1 33/56
(Can be simplified to 1.58)
PLZ HELP I REALLY NEED IT
Answer:
Angle = 64 Degrees
Supplement of Angle = 116 Degrees
Step-by-step explanation:
Let the angle be "x"
We know
The complement of the angle is "90 - x"
and
The supplement of the angle is "180 - x"
From the statement given, we can write:
supplement is 12 LESS THAN twice the angle
The equation would be:
180 - x = 2x - 12
Now, we solve this for x:
[tex]180 - x = 2x - 12\\180+12=2x+x\\192=3x\\x-\frac{192}{3}\\x=64[/tex]
The angle is 64 degrees
The supplement of the angle is 180 - 64 = 116 degrees
Convert Зcis 180° to rectangular form.
А. -3
в. -3i
с. з
D. Зі.
Answer:
-3
Step-by-step explanation:
[tex]3 cis(180^\circ)[/tex] means [tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
What is the [tex]x[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is -1.
What is the [tex]y[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is 0.
So this implies [tex]\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0[/tex].
[tex]3 cis(180^\circ)[/tex]
[tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
[tex]3(-1+i (0))[/tex]
[tex]3(-1+0)[/tex]
[tex]3(-1)[/tex]
[tex]-3[/tex]
Use the diagram to complete the table by matching the Theorem with the angle relationship.
Answer:
The Table with Correct reasons are as follows.
Step-by-step explanation:
The Table with Correct reasons are as follows
Answer Angle Relationship
c. Corresponding Angles ∠ 1 ≅ ∠ 5
d. Same Side Interior ∠ 4 + ∠ 5 = 180
a. Alternate Exterior Angles ∠ 3 ≅ ∠ 6
b. Alternate Interior Angles ∠ 4 ≅ ∠ 5
c. Corresponding Angles ∠ 2 ≅ ∠ 6
83%
18)
Suppose two parallel lines are cut by a transversal. Which angles MUST be supplementary?
vertical angles
corresponding angles
alternate exterior angles
alternate interior angles
At a farm ,Justin picks 3 bushels of fruits, the bushel weigh 8 1/4 pounds,6 1/2 pounds, and 6 5/8 pounds. What is the average weight per bushel
Answer:
7.125
Step-by-step explanation:
The average weight per bushel of fruits that Justin picked is calculated as the sum of all weights divided by the number of bushels, which comes out to be 7.125 pounds per bushel.
To calculate the average weight per bushel when Justin picks 3 bushels of fruits weighing 8 1/4 pounds, 6 1/2 pounds, and 6 5/8 pounds, we need to add up the weights of the bushels and then divide by the number of bushels. Here are the steps:
First, convert all fractions to decimals or common denominators for easier addition:
8 1/4 = 8.25 pounds
6 1/2 = 6.5 pounds
6 5/8 = 6.625 pounds
Add up the weights of the three bushels:
8.25 + 6.5 + 6.625 = 21.375 pounds
Finally, divide the total weight by the number of bushels to find the average:
21.375 pounds \/ 3 bushels = 7.125 pounds per bushel
The average weight per bushel that Justin picks is 7.125 pounds.
What is Blaine's driving rate in miles per hour
Sorry, but I don't see any information for me to use to answer that question.
Round 22,451 with 10
Answer:
22,450
Step-by-step explanation:
the ones place is below 5 so you keep the number
Answer:
22,450
Step-by-step explanation:
22,451 rounded to the nearest 10 is 22,450, as 1 rounds down to 0.
:)
y equals 4x to the 3rd power minus 3 plus 2x to the second power
simplify c + 6 < -20
Answer:
Step-by-step explanation:
c + 6 < -20
Subtract 6 from both side
c +6 -6 < -20-6
c < -26
So value of c should be less than -26. Value of c = { - ∞ ...... -28, - 27 }
Eg:
If c = -27
-27 + 6 = - 21 . -21 is less than -20
Which pair of ratios does not
form a true proportion?
A) 6:16 and 21:56
B) 2 to 10 and 15 to 75 C) 9/11=27/15
D) y = 5x
Answer:
C
Step-by-step explanation:
Write the expression: the sum of the quantity h and 3 divided by 6.
A) h/6 + 3
B) h/3 + 6
C) h+3/6
D) 6/h+3
The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6 so option (C) is correct.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
The sum of the quantity h and 3 = h + 3
It is divided by 6 so, (h + 3)/6
Hence "The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6".
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What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?
Answer:
z = x^3 +1
Step-by-step explanation:
Noting the squared term, it makes sense to substitute for that term:
z = x^3 +1
gives ...
16z^2 -22z -3 = 0 . . . . the quadratic you want
_____
Solutions derived from that substitution
Factoring gives ...
16z^2 -24z +2z -3 = 0
8z(2z -3) +1(2z -3) = 0
(8z +1)(2z -3) = 0
z = -1/8 or 3/2
Then we can find x:
x^3 +1 = -1/8
x^3 = -9/8 . . . . . subtract 1
x = (-1/2)∛9 . . . . . one of the real solutions
__
x^3 +1 = 3/2
x^3 = 1/2 = 4/8 . . . . . . subtract 1
x = (1/2)∛4 . . . . . . the other real solution
The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.
Answer:
x^3 +1
Step-by-step explanation:
Aiden has three 20$ bills and two 10$ bills he wants to save a total of 95$ how much more money does he need what bills could they be
Answer:
$15.00
A $10.00 and a $5.00 dollar bill
Step-by-step explanation:
Answer:$80
Step-by-step explanation:
3 times 20=60
2 times 10=20
either 1, $10 and 1, $5, or 3, $5 or 15, $1
What is the most efficient way to solve the equation?
5j = 40
Answer: j = 8
Step-by-step explanation: To solve for j in this equation, we want to get j by itself on the left side of the equation. Since j is being multiplied by 5, to get j by itself, we need to divide by 5 on the left side of the equation. Since we divided by 5 on the left side, we must also divide by 5 on the right side.
On the left side, notice that the 5's cancel out so we are simply left with j. On the right side, we have 40 divided by 5 which gives us 8 so we have j = 8.
Finally, remember to check your answer by substituting an 8 back into the original equation. So we have 5 (8) = 40 which is a true statement so our answer checks. Remember to show all your work when solving equations.
The Answer is :J=8 =)
plz hurry!!!! thank you!!!!
Step-by-step explanation:
Since SP=TR, the differnce of PR and ST 24-15 divided by 2 is the length of PD (4.5)
Try to understand the rest from the attached picture