The values for 4f(x)+2 g(x) = 2x²- 2x + 24
What are the domain of the function 4f(x)+2 g(x) ?Given : f(x)=2x+5
g(x)=x²-3x+2
Solution:
4f(x) = 8x+20
2g(x) = 2x²-6x+4
4f(x) + 2g(x) = 8x+20 + 2x²-6x+4
4f(x) + 2g(x) = 2x²- 2x + 24
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What would happen to a monthly payment if the interest rate increased?
OA. The payment would go up.
B. The payment would go down.
OC. The payment would remain the same.
OD. None of the above
Confused on this entire problem i apoligize
The linear function f(x) with a slope of -8 and that f(1) = 2 is f(x) = 10 -8x
Equation of a lineFrom the question, we are find a linear function with slope of -8 and that f(1) = 2
If f(1) = 2, then the line passes through the point (1, 2)
Using the point-slope form of the equation of a straight line
y - y₁ = m(x - x₁)
Where m is the slope
Then,
y - 2 = -8(x - 1)
Simplify
y - 2 = -8x + 8
y = -8x + 8 + 2
y = -8x + 10
∴ f(x) = -8x + 10
f(x) = 10 - 8x
Hence, the linear function is f(x) = 10 -8x
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Write each expression in simplest form. (x¹/₄ / y⁻³/₄)¹²
The given expression can be written in its simplest form by solving the exponents.
There are two types of exponent rules that will be applied to the expression. First, we will solve the negative exponent then we will multiply the exponents.
According to the negative exponent rule: x^-n=1/x^n.
Hence, applying the rule to the base term in the denominator, 1/y^⁻³/₄= y^³/₄
Therefore, x^¹/₄ / y^⁻³/₄= x^¹/₄ y^³/₄
According to the multiplication of exponent rule: (x^n)^m=x^nm
Hence, applying the rule to the expression,
(x^¹/₄ y^³/₄)^12=x^¹/₄*12 y^³/₄*12
Multiplying the powers and simplifying,
x^¹/₄*12 y^³/₄*12=x^3y^9
The simplest form of the expression (x^¹/₄/y^⁻³/₄)^12 is x^3y^9.
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The Brandywine Dance Team is buying equipment and T-shirts. The equipment costs $356 and the T-shirts cost $12 each. The team spent a total of $644
The number of T-shirts bought by the Brandywine Dance Team is 24.
How is the number of T-shirts determined?The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.
First, the cost of the equipment is subtracted from the total cost spent by the team. The remainder refers to the cost of the T-shirts. Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.
Data and Calculations:The total amount spent = $644
The cost of the equipment = $356
The remainder after the equipment = $288 ($644 - $356)
Unit cost of T-shirts = $12
The number of T-shirts bought = 24 ($288/$12)
Thus, the Brandywine Dance Team bought 24 T-shirts.
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Question Completion:How many T-shirts were purchased by the Team?
x/a=y/b solve for x please help my homework is due today
i need all 3 im confused on them
Answer:
1. 5/12 in exact form and 0.416 in decimal form
2. 26/3 in exact form and 8.6 in decimal form and 8 2/3 in mixed number form.
On each "6" there's a - on top!
WITHOUT GRAPHING identify the coordinates of A(-3, 7), B(4, 9), and C(0, -2) after the following transformations. 1. Translation 2 units up and 7 units right.
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
What is transformation?Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.
Dilation is a transformation that affects the size of a figure.
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
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Which angles are vertical to each other?
At the local movie theatre, there are 115 boys, 92 girls, and 28 adults.
a. Write the ratio of the number of boys to the number of girls.
115:92
b. Write the same ratio using another form (: vs. to ).
115 to 92
c. Write the ratio of the number of boys to the number of adults.
115:28
d. Write the same ratio using another form.
115 to 28
A. The ratio of the number of boys to the number of girls is; 115:92
B. The same ratio using another form is; 115 to 92
C. The ratio of the number of boys to the number of adults is; 115:28
D. The same ratio using another form is; 115 to 28
What is the Ratio?We are told that there are 115 boys, 92 girls, and 28 adults. Thus;
Number of boys = 115
Number of girls = 92
Number of Adults = 28
Now, we want to find some ratios and they are;
A) The ratio of boys to the number of girls = 115 : 92
B) Now, when we have a ratio of a:b, in words, it simply means a to b. Thus, our ratio of boys to girls here can be expressed as;
115 to 92
C) The ratio of the number of boys to the number of adults is;
115:28
D) Similar to answer B above, the ratio of the number of boys to the number of adults can also be expressed as; 115 to 28
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The data show the traveler spending in billions of dollars for a recent year for a sample of the states. find the range, variance, standard deviation for the data. 20.1, 33.5,21.7,58.4,23.2,110.8,30.9,24.0,74.8,60.0
We know that the measures of dispersion tend to see how numbers are scattered around the mean. In this case, we are asked to find three of the measures of dispersion which are; range, variance and standard deviation.
We first have to arrange the data in the proper order as follows;
20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8
It is now easier for us to find the range of the data set as the difference between the largest and the smallest value; 110.8 – 20.1 = 90.7
The mean of the dataset is = 20.1 + 21.7+ 23.2 + 24.0 + 30.9 + 33.5 + 58.4 + 60.0 + 74.8 + 110.8/10
= 45.74
Now;
Variance = (20.1 - 45.74)^2 + (21.7 - 45.74)^2 + (23.2 - 45.74)^2 + (24.0 - 45.74)^2 + (30.9 - 45.74)^2 + (33.5 - 45.74)^2 + (58.4 - 45.74)^2 + (60.0 - 45.74)^2 + (74.8 - 45.74)^2 + (110.8 - 45.74)^2/10
= 657.4 + 577.9 + 508.1 + 472.6 + 220.2 +149.8 + 160.3 + 203.3 + 844.5 + 4233/10
= 802.71
Standard deviation = √variance = √802.71
= 8.96
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Find the domain and range. Graph each relation.
1. {(0, 0), (1, -1),(2, -4).(3,-9),(4, -16)}
The domain of the relation: {0, 1, 2, 3, and 4}
The range of the relation: {0, -1, -4, -9, -16}
The graph for the relation is in the attachment.
What is the Domain is a Relation?A domain of a relation can be defined as the set of x-values or inputs of a relation.
What is the Range of a Relation?The set of all output or y-values that correspond to the x-values in a set of ordered pairs.
Given the relation, {(0, 0), (1, -1),(2, -4), (3,-9), (4, -16)}
The domain of the relation is: {0, 1, 2, 3, and 4} (these are all the input of the relation)
The range of the relation is: {0, -1, -4, -9, -16} (these are all the output of the relation)
The graph for the relation is in the attachment.
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The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $ 1200 . The party must have 13 adult chaperones.
b. The class wants to promote the event by giving away 30 spots to students in a drawing. How does the model change? Now how many paying students must attend so the cost for each is no more than $ 7.50 ?
The function model will be -
Divide the cost by the number of pupils to split it, and you'll get the function C=1200 / n.
How many pupils must enroll in order for the price per pupil to not exceed $7.50?1200/N ≤ 7.50
1200 / 7.50 ≤ N
N ≥ 1200/7.5
N ≥ 160
To keep the price per kid to no more than $7.50, there must be more than 160 participants.
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If f(x) is given as an equation and g(x) is given as a table, how i can tell they are inverses
Answer: f(x) and g(x) both represent y of the equations
Step-by-step explanation: f(x) and g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.
To get to work each morning, Emily takes a horse 10.9810.9810, point, 98 kilometers and a bike 4.064.064, point, 06 kilometers.
Answer: Emily's in total journey is 15.045 kilometers.
Step-by-step explanation:
Given data,
Emily traveled a certain distance on a horse = 10.98 kilometers
Emily traveled a certain distance on a bike = 4.06 kilometers
The overall distance traveled by Emily on her horse and bike needs to be determined.
For "Total Distance" , we will use addition operation:
So, Total distance covered by Emily's journey is given by equal to
Emily traveled a certain distance on a horse + Emily traveled a certain distance on a bike
Let us assume,
Total distance covered by Emily's journey is represented by 'x'
Then we can write,
x = 10.981 kilometers + 4.064 kilometers
x = 15.045 kilometers
Therefore, Emily's in total journey is 15.045 kilometers.
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Which system of equations is represented by the matrix below?
[4 0 5
2 -117
47576777...................
Let g(x)=3 x+2 and f(x)=x-2 / 3 . Find each value.
(g⁰g)(1)
Value for (g⁰g)(1) = 17
What is the domain of the function (g⁰g)(1)?Now, (g⁰g)(x) = g[g(x)]
let g(x) = 3x + 2
(g⁰g)(x) = g(3x + 2)
(g⁰g)(1) = g(5)
(g⁰g)(1) = 3(5) + 2
(g⁰g)(1) = 17
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The graph below describes the journey of a train between two cities.
a) Work out the
acceleration, in km/h²,
in the first 15 mins
b) Work out the distance
between the two cities.
c) Work out the average
speed of the train during
the journey.
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
According to the given question:
Each block of horizontal is 1/8 hr = 7.5 min
Each block of vertical is 10 km/hr
Time Velocity (km/hr)
0 Min ( 0 hr) 0
15 Min (1/4 hr) 50
45 Min (3/4 hr) 50
60 MIn ( 1 hr) 100
90 Min ( 3/2 hr) 100
120 Min ( 2hr) 0
The acceleration in first 15 minutes = (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)
= 200 km/h²
The distance between the two cities =
= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)
= 25/4 + 25 + 75/4 + 50 + 25
= 125
Distance between two cities = 125 km
Average Speed of train during the journey = 125/2 = 62.5 km/hr
Therefore,
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
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A survey finds that 110 people ate breakfast and 30 people skipped breakfast. Of those who ate
breakfast, 10 people felt tired. Of those who skipped breakfast, 10 people felt tired. Make a
two-way table that shows the conditional relative frequencies based on the breakfast totals.
Here is the two-way table :
Felt tired Did not feel tired Total
Ate breakfast 0.0714 0.7142 0.7857
Did not eat breakfast 0.0714 0.1428 0.2143
Total 0.1428 0.8572 1
What is the two way table?A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns. A conditional relative frequency is the ratio of the frequency of a class to the total frequency.
People who ate breakfast and did not feel tired = 110 - 10 = 100
People who did not breakfast and did not feel tired = 30 - 10 = 20
Felt tired Did not feel tired Total
Ate breakfast 10 100 110
Did not eat breakfast 10 20 30
Total 20 130 140
Felt tired Did not feel tired Total
Ate breakfast 10 / 140 100 / 140 110 / 140
Did not eat breakfast 10 / 140 20 / 140 30 / 140
Total 20 / 140 130 / 140 140 / 140
Felt tired Did not feel tired Total
Ate breakfast 0.0714 0.7142 0.7857
Did not eat breakfast 0.0714 0.1428 0.2143
Total 0.1428 0.8572 1
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Find the inverse of each function. Is the inverse a function?
f(x)=2x² /5 +1
Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f-1 or F-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the function provided the output for.We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex]. ....(1)
Let y = f(x)
[tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]x=f^{-1}(y)[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]
We can check that this is really an inverse function or not
Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex] equation (1) , we get
[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]
As LHS = RHS which means inverse function is correct .
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If a person walks
mile in 1 hour, how far does that person walk
in 1 3/4 hours at that rate?
7/4 miles distance does that person walk.
What is distance?
The length or width between two objects, points, lines, etc. remoteness is the state or fact of something or someone being physically distant from another. A straight line in space It would take too long to walk seven miles in one hour. a distance; a space: The ship was encircled by a sizable body of water.We can use a ratio to solve
1 mile x miles
----------------= ---------------
1 hour 1 3/4 hours
Changing to improper fractions
1 mile x miles
----------------= ---------------
1 hour 7/4 hours
Using cross products
1 * 7/4 = 1 * x
7/4 = x
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About how much farther did she bike on Wednesday than Thursday?
the answer is 71 miles far
(Use the following statement to answer questions 10-16.)
“If a number is greater than -500, then the number is greater than 500.”
Determine the truth value of the conditional statement. Explain.
The truth value of the conditional statement is false
How to determine the truth value of the conditional statement?The conditional statement is given as
“If a number is greater than -500, then the number is greater than 500.”
The above conditional statement is false
This is so because
Not all numbers greater than -500 are greater than 500
Take for instance 499 is greater than -500, but less than 500
Hence, the truth value of the conditional statement is false
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ashley drove 605 miles in 11 hours at the same rate how long would it take her to drive 495 miles
Answer:
9 hours
Step-by-step explanation:
605 miles/11 hours = 55miles/hour
495 miles (time) = 495 / 55 =9
So, 9 hours
PLSSSPLSS PLS HELP ME WILL GET BRIANLIEST
Kim has a part-time job assembling bicycles for a local store. each day, she earns $20 plus $15 for each bike assembled. kim's boss daily goal is to assemble no more than 6 bicycles a day. if x represents the number of bikes assembled, the total amount she earns can be represented by . what is the range for the function for this situation?
The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.
The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).
The total amount she earns can be represented by
y = 15x + 20
where y is her daily earnings and x is the number of bikes she assembles
If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).
domain : {x| 0 ≤ x ≤ 6}
where x is a whole number
Substituting the minimum and maximum value of x in the function.
y = 15(0) + 20 when x = 0
y = 20
y = 15(6) + 20 when x = 6
y = 110
range : $20 ≤ y ≤ $110
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Work out the following, giving your answers in their simplest form:
a) 4/7 / (1 3/4)
b) 5 3/5 / (2 2/3)
The simplest form of the following are -
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.
We have been given that
a) 4/7 / (1 3/4)
Rewrite as -
= (4/7) / (1× 3/4)
= (4/7) / (7/4)
= (4/7) × (4/7)
= 16/49
b) 5 3/5 / (2 2/3)
Rewrite as -
= (5× 3/5) / (2× 2/3)
= (5× 3/5) / (8/3)
= (28/5) / (8/3)
= (28/5) × (3/8)
= 7/5 × 3/2
= 21/10
= 2.1
Thus , the following are in order of simplicity:
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
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I need some help with these it's hard for me can some help asap
Answer:
C and B
Step-by-step explanation:
Evaluate g(5) then substitute the value obtained into f(x)
g(5) = [tex]\sqrt{5-1}[/tex] = [tex]\sqrt{4}[/tex] = 2 , then
f(2) = 3(2) + 1 = 6 + 1 = 7
-----------------------------------------------------------------------------
f(x) = [tex]\frac{x^2+3}{(x-4)(x+8)}[/tex]
the denominator of f(x) cannot be zero as this would make f(x) undefined.
equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
(x - 4)(x + 8) = 0
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 8 = 0 ⇒ x = - 8
the vertical asymptotes are x = 4 and x = - 8
Devon has 4 3/4 bags of soil to put in hs flower bed each bag will cover 15 ft2 how many squares will he be able to cover
Devon will be able to cover 71.25 ft² of flower bed.
The number of bags of soil Devon has = [tex]4\frac{3}{4}[/tex]
Converting mixed fraction to fraction
Number of bags of soil = (4×4+3)/4
Performing multiplication and addition in numerator to find the number of bags of soil with Devon
Number of bags of soil = 19/4
Now, it is stated that area covered by 1 bag = 15 ft²
So, 19/4 bags will cover area = 15×(19/4)
Performing multiplication and division to find the area covered by the bags of soil
Area covered by bags of soil Devon has = 71.25 ft²
Hence, the area covered by bags of soil Devon has is 71.25 ft²
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The complete question is -
Devon has 4 3/4 bags of soil to put in his flower bed. Each bag will cover 15 ft2. How many square feet will he be able to cover?
Elena has $225 in her bank account. She takes out $20 each week for w weeks. After w weeks she has d dollars left in her bank account.
Write an equation that represents the amount of money left in her bank account after w weeks.
Answer:
y20=225x or y225+x20 ir can be
what is 2169 rounded to the nearest hundred
Answer: 2169 rounded to the nearest hundred is 2200
Step-by-step explanation: Since 6 in the tenth place is greater than 5 the number in the hundred place which is 1 goes up to 2. That is how you get 2200