Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Given that [tex]g(x) = \frac{x + 1}{x - 2}[/tex] and h(x) = 4 - x
Now, if y = f(x) and y = g(x) then the composite function (f∘g)(x) is given by f[g(x)].
Hence, (g∘h)(x) = [tex]g[h(x)] = \frac{(4 - x) + 1}{(4 - x) - 2} = \frac{5 - x}{2 - x}[/tex] .......... (1)
Now, from equation (1) we get,
(g∘h)(x) = [tex] \frac{5 - x}{2 - x}[/tex]
⇒ (g∘h)(- 3) = [tex]\frac{5 - ( - 3)}{2 - ( - 3)} = \frac{8}{5}[/tex] (Answer)
Answer:
The answer is 8/5
Step-by-step explanation:
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 =)
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
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.
:)
round 98 inches to the nearest foot
Answer 8.17
Step-by-step explanation:
1.divide 98 by twelve, since there are 12 inches in a foot
98 \ 12
2.then round to the nearest tenth. 8.16 is rounded to 8.17
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.
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
-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
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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How do I simplify -3(x-4)
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)
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
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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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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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.
On Friday and Saturday, there were a total of 200 cars in the parking lot of a movie theater. On Friday, 120 cars were in the parking lot.
A. What percent of the total number of cars were in the parking lot on Friday?
Show your work.
B. What percent of the total number of cars were in the parking lot on Saturday?
Show your work.
Answer:
(A) 40%
(B) 60%
Step-by-step explanation:
Given:
Total number of cars = 200
Cars in parking lot on Friday = 120
Total number of cars = Total cars on Friday + Total cars on Saturday.
⇒ 200 = 120 + Total cars on Saturday.
⇒ Total cars on Saturday = 200 - 120 = 80
So, 80 cars were in parking lot on Saturday.
(A)
Percentage of cars in parking lot on Friday is given as:
[tex]=\frac{\textrm{Cars in parking lot on Friday}}{\textrm{Total cars parked}}\times 100\\\\=\frac{120}{200}\times 100\\\\=\frac{120}{2}=60\%[/tex]
Therefore, 60% of the cars were in the parking lot on Friday.
(B)
Now, since 60% of the cars were parked on Friday, the remaining percent will be on Saturday.
Therefore, percentage of cars in parking lot on Saturday = 100% - 60% = 40%. This can be verified with the same formula used in part (A).
[tex]=\frac{\textrm{Cars in parking lot on Saturday}}{\textrm{Total cars parked}}\times 100\\\\=\frac{80}{200}\times 100\\\\=\frac{80}{2}=40\%[/tex]
Jake owns twice as many DVDs as Louis.Bo has sixty fewer DVDs than five times Louis’s collection. If Jake and Bo have the same amount of DVDs how DVDs are in Louis’s collection?
There are 20 number of DVD's in Louis collection
Solution:
Let "J" be the number of DVD's with Jake
Let "B" be the number of DVD's with Bo
Let "L" be the number of DVD's with Louis
Given that Jake owns twice as many DVDs as Louis
So we can say,
number of DVD's with Jake = 2(number of DVD's with Loius)
J = 2L ------ eqn 1
Given that Bo has sixty fewer DVDs than five times Louis’s collection
So we can say,
number of DVD's with Bo = 5 times number of DVD's with Louis - 60
B = 5L - 60 ---- eqn 2
Given that Jake and Bo have the same amount of DVDs
number of DVD's with Jake = number of DVD's with Bo
J = B ---- eqn 3
Let us solve eqn 1, 2, 3 to find value of "L"
From eqn 1 and eqn 3,
2L = B ----- eqn 4
Substitute eqn 4 in eqn 2
2L = 5L - 60
2L - 5L = -60
-3L = -60
L = 20Thus there are 20 number of DVD's in Louis collection
Louis has 30 DVDs in his collection.
Let's denote the number of DVDs Louis has as L. According to the problem, Jake owns twice as many DVDs as Louis, so Jake has 2L DVDs. Bo has sixty fewer DVDs than five times Louis's collection, which means Bo has 5L - 60 DVDs.
Since Jake and Bo have the same amount of DVDs, we can set their quantities equal to each other:
2L = 5L - 60
Now, let's solve for L:
5L - 2L = 60
3L = 60
L = 60 / 3
L = 20
Louis has 20 DVDs in his collection.
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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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
17 divided by 768 in long Division
Answer:
45 remainder 3.
Step-by-step explanation:
Suppose an iphone loses 63% of its value each year. Write a function that represents the value of the phone after x years.
Answer:
The function which represent the phone value after x years f = i [tex](0.37)^{x}[/tex]
Step-by-step explanation:
Given as :
The rate of depreciation of i-phone value each year = r = 63%
The initial value of i-phone = $ i
The final value of i-phone = $ f
The time period for depreciation = x year
Now, According to question
The final value of i-phone = The initial value of i-phone × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, $ f = $ i × [tex](1-\dfrac{\textrm r}{100})^{\textrm time}[/tex]
Or, $ f = $ i × [tex](1-\dfrac{\textrm 63}{100})^{\textrm x}[/tex]
Or, $ f = $ i × [tex](0.37)^{x}[/tex]
So, The function which represent the phone value after x years = f = i [tex](0.37)^{x}[/tex]
Hence, The function which represent the phone value after x years f = i [tex](0.37)^{x}[/tex] Answer
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.
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
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:
a juice company produced 8064 cartons of juice in 21 days each day they produced the same the same number of carton and delivered those carton 216 area of coffee shops the cart the cartons were delivered in cases of six cartons per case and each coffee shop received an equal number of cases in each delivery. how many cases were delivered to each coffee shop each day
Answer:
The each coffee shops receives 4 cases of juice everyday.
Step-by-step explanation:
The juice company produced 8064 cartons of juice in 21 days each day they produced the same number of cartons.
Therefore, each day the company produces [tex]\frac{8064}{21} = 384[/tex] cartons.
The juice company delivers those cartons in 16 areas of coffee shops.
So, each coffee shop receives [tex]\frac{384}{16} = 24[/tex] cartons of juice.
Now, the cartons were delivered in cases of six cartons per case and each coffee shop received an equal number of cases in each delivery.
Hence, each coffee shops receives [tex]\frac{24}{6} = 4[/tex] cases of juice everyday. (Answer)
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.
Can somebody please help me with this problem??? I can't figure it out...
We can use the Pythagorean theorem to solve. (a² + b² = c²)
Fill in with what we know → 6² + b² = 11²
Simplify → 36 + b² = 121
Subtract 36 to both sides → 36 - 36 + b² = 121 - 36
Simplify → b² = 85
Take the root of both sides → √b² = √85
Simplify → b = 9.2195...
Round if necessary → 9.2195 = 9.22
Hence, b equals 9.2195.. (unrounded) or 9.22 (rounded).
Best of Luck!
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.
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