The function operation ( f + g )( x ) in the functions f( x ) = x² + 2x and g( x ) = 4x² - 3 is 5x² + 2x - 3.
What is the function operation ( f + g )( x ) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = x² + 2xg( x ) = 4x² - 3( f + g )( x ) = ?First, replace the function designators in f + g with actual functions.
( f + g )( x ) = ( f )(x) + ( g )( x )
( f + g )( x ) = ( x² + 2x ) + ( 4x² - 3 )
Remove the parenthesis
( f + g )( x ) = x² + 2x + 4x² - 3
Collect and add like terms
( f + g )( x ) = x² + 4x² + 2x - 3
( f + g )( x ) = 5x² + 2x - 3
Therefore, the function operation ( f + g )( x ) is 5x² + 2x - 3.
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WILL GIVE BRAINLY IF WRITE PLS HEP ASAP
Three students are participating in a walkathon. The data for each student is shown. Student A: the equation y = 14x represents the amount of money raised (y) for walking (x) miles
Student B:$42 is raised after walking 3 miles.
Student C: miles walked 6 and 9 money raised $72 and $108
Answer choses
Student A
Student B
Student C
All three students raised the same amount of money after walking 8 miles.
The student that raised the least amount based on the information is student C.
How to illustrate the information?For student A, the equation illustrated is y = 14x and this represents the amount of money raised (y) for walking (x) miles.
For student B, $42 is raised after walking 3 miles. The amount raised per mile will be:
= $42 / 3
= $14 per mile
For C, The miles walked 6 and 9 and the money raised $72 and $108. This shows that the amount is:
= $72 / 6
= $12 per mile.
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Three students are participating in a walkathon. The data for each student is shown. Student A: the equation y = 14x represents the amount of money raised (y) for walking (x) miles
Student B:$42 is raised after walking 3 miles.
Student C: miles walked 6 and 9 money raised $72 and $108
Who raised the least amount
Answer:
The student that raised the least amount based on the information is student C.
Step-by-step explanation:
10y-2y + 30 = 8y - 15 + 5
Answer:
No Solution
Step-by-step explanation:
a one way train ticket in the city costs $1.95. A monthly pass costs $50. For what numbers of rides should you buy the monthly pass?
For 26 rides in a month, a monthly pass should be made, while for rides less than 26 using a one-way ticket will be a cost-effective method
Cost of one way train ticket = $.195
Cost of monthly pass = $50
Monthly pass: It is a prepaid fare card good for one month of limitless travel. This saves cost and time in terms of commuting costs and time of getting the tickets issues
Let x represent the number of rides one takes
Formulating the equation we get:
Cost of one-way ticket*Number of rides = Cost of a monthly pass
= 1.95*x = 50
x = 25.64 or 26 rides
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Select the EXAMPLE(S) that demonstrate financial honesty.
1.Cooper includes all truthful information when he completes an application for a checking account.
2. Brianna writes a check knowing that she has the funds in her checking account to cover it.
3. Allison makes a large purchase with store credit without knowing how she will pay for it.
4. Greg discloses all the fees in the sales contracts for the products he sells in his store
(multiple choice) help please
Answer: 1, 2, and 4
Step-by-step explanation:
1. Cooper included ALL truthful information.
2. Brianna KNOWS she has the funds.
3. Allison makes a large purchase WITHOUT knowing how she will pay.
4. Greg discloses ALL fees.
Point Q has coordinates (5,6). If you rotate Q 90° about the origin, (0,0), what are the coordinates of Q′
The coordinates of the image after 90° about the origin is (6, -5)
What is a 90 degrees rotation?A 90 degrees rotation denoted by R(90, 0) is a rotation that has the same effect as the 270 degrees counterclockwise of a figure.
How to determine the image of the rotation?The coordinate of the point is given as
(5, 6)
The rotation is given as 90° about the origin
So, we have
(x, y) => (y, -x)
Substitute (5, 6) in (x, y) => (y, -x)
So, we have
(5, 6) => (6, -5)
Hence, the coordinates of the image is (6, -5)
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A pile of sand has a weight of 65 kg.
Some of the sand is put into a small sack.
The rest of the sand is put into a large sack.
The sand in the large sack weighs 15 kg more than the sand in the small sack.
What is the weight of the sand in the small sack?
Answer:
25 kg
Step-by-step explanation:
The sum of the weights of the small and large sacks is 65 kg. The larger sack weighs 15 kg more. You want the weight of the smaller sack.
SetupLet w represent the weight of the sand in the small sack. Then (w+15) is the weight of the sand in the larger sack. The total weight is 65 kg, so we have ...
w +(w+15) = 65
SolutionSubtracting 15 from both sides gives ...
2w = 50
w = 25
The weight of the sand in the small sack is 25 kg.
Determine the unknown angle in the triangle pictured below:
Find the circumference and area of the figure if each unit on the graph measures 1 centimeter Round answers to the nearest tenth, if necessary
A(2,3)
B(4,1)
Circumference of the circle = 17.8 units
Area of the circle = 25.1 square unit
What is circumference of circle ?An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle."
Formula to get the circumference of a circle = 2πr
Where r = radius of the circle
Radius of the given circle = Distance between the points A(2, 3) and B(4, 1)
r = [tex]\sqrt{(2-4)^{2} +(3-1)^{2} }[/tex]
r = 2√2units
Therefore, circumference = 2π(2√2)
= 17.77
≈ 17.8 units
Area of the circle = πr²
= π(2√2)²
= 8π
= 25.13
≈ 25.1 square unit
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George found that he blinked 85 times in 15 minutes. At this rate, how many seconds passed during the 51 blinks?
what congruence short cut do I use
By ASA or SAS the triangles can be proves congruent.
What is Congruence of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.
As, from the given figure we can find some equal parts.
First we have two triangles named KOE and LOB
Now, in both triangles
EO = OB ( given)
<KOE =< LOB (Vertically opposite angle)
Now, we have one side and one angle congruent.
There are two possibilities now either we have another pair of side to make SAS Congruence or we have another angle congruent to make ASA congruence.
So, either KO = OL or
<LBO = <OKE.
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Do number 12 and 13 please thank you!!
12. The statement ' x+3 = 9' is true sometimes.
How is this explained?
Let x= 6,
6 + 3 = 9 (true)
Let x= 5 ,
5 + 3 = 8 (not true)
13. Option c. The statement 'multiplicative inverse of a number is less than the original number' is true for all numbers greater than 1.
How is this explained?
Let us consider some numbers,
a) 1
The multiplicative inverse of 1 = 1
Thus, multiplicative inverse of this number is not less than the original number.
b) 2 (greater than 1)
The multiplicative inverse of 2 = 1/2
multiplicative inverse of this number is less than the original number.
c) 8/7 (greater than 1)
The multiplicative inverse of 8/7 = 7/8
Here, multiplicative inverse of this number is less than the original number.
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Yvonne is training for the marathon. She calculates to see whether she can cover 9 miles in 10 minutes. But she completes the distance in 8 minutes. What is the percent error in Yvonne's calculation?
The relative error exists multiplied by 100 to estimate the percent error. The percent error in Yvonne's calculation exists 11% error.
What is meant by percent error?The difference between the estimated value and the actual value in relation to the actual value is known as the percent error. To calculate the percent error, the relative error is multiplied by 100.
Percent error calculates the difference between an estimate and a correct value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual value. It is also referred to as % error and percentage error.
%error = (calculated value - experimental value) / calculated × 100%
%error = (10 - 9)/9 × 100%
= 1/9 × 100%
= 11.11111 ≈ 11% error
Therefore, the percent error in Yvonne's calculation exists 11% error.
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Differentiate the function, f(x) = ln (2x + 4) with respect to x?
Answer:
f'(x) = [tex]\frac{1}{x+2}[/tex]
Step-by-step explanation:
using the chain rule to differentiate
f(x) = g(h(x)) , then
f'(x) = g'(x) × h'(x)
f(x) = ln(2x + 4) , then
f'(x) = [tex]\frac{1}{2x+4}[/tex] × [tex]\frac{d}{dx}[/tex] (2x + 4)
= [tex]\frac{1}{2x+4}[/tex] × 2
= [tex]\frac{2}{2x+4}[/tex]
= [tex]\frac{1}{x+2}[/tex]
Micah is planning a road trip. He estimates that he will drive a total of of 7 hours. He wants to stop for gas after ⅓ of the total time has passed. How long will he drive before he stops for gas? Express your answer as a mixed number.
Answer:
After 2 1/3 hours.
Step-by-step explanation:
For this you have to calculate how much hours is 1/3 of 7 hours. The word 'of' implies a multiplication function.
1/3 * 7 = 7/3 = 2 1/3
The square root of a certain number is approximately 9.2371. The certain number is between what 2 integers
The number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.
What is an integer ?
Integer is the collection of whole numbers and negative numbers. It does not include the fractional part.
It is given that square root of a decimal number is 9.2371 and we have to find out that the number lies between which 2 integers.
We know that the integer 9 is less than 9.2371 , so the square of 9 will be :
9² = 81
And
The square of next integer 10 is equal to 100.
The square of 9.2371 will be equal to :
= (9.2371)²
= 85.32
So , the number is 85.32 and it lies between 2 integers which are 81 and 100.
Therefore , the number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.
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Eugene is deciding between two payment plans when purchasing a new car. If Eugene chooses payment plan A, he will pay $429.47 a month for 36 months for the car. If Eugene chooses payment plan B, he will pay $340.89 a month for 48 months for the car. How much money will Eugene save on the car overall if he chooses payment plan A?
Eugene will save $901.8 on the car overall if he chooses payment plan A.
Eugene has to buy a new car, and there are two payment plans from which he has to decide which to opt for.The two plans are, namely, plan A and plan B.In plan A, he has to pay an amount of $429.47 a month for 36 months for the car.In plan B, he has to pay an amount of $340.89 a month for 48 months for the car.The total amount to be paid if he chooses plan A is 36*429.47 = $15,460.92.The total amount to be paid if he chooses plan B is 48*340.89 = $16,362.72.We can see that plan A is better than plan B.The amount saved by Eugene by selecting plan A is represented in the equation below:$16,362.72 - $15,460.92 = $901.8To learn more about equations, visit :
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X-3 is a factor of x³+ax²–2x+3
Answer:X-3 is a factor of x³+ax²–2x+3
Step-by-step explanation:X-3 is a factor of x³+ax²–2x+3
p(x)=x
3
−ax
2
+2x+a−1
⇒ p(a)=(a)
3
−a(a)
2
+2(a)+a−1
⇒ 0=a
+2a+a−1=0
⇒ 3a−1=0
⇒ 3a=1 a=
3
1
Ian is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $1.25 per mile driven. How much would a taxi ride cost if Ian is riding for 2 miles? How much would a taxi ride cost that is mm miles long?
It would cost him $ 5 to cover a distance of 2 miles.
Amount charged by the taxi driver which is mandatory to be paid is $ 2.50
Additional amount charged by the driver is $1.25
Since Ian is driving 2 miles thus we can write it as follows :
2.50 + (1.25 × 2) = 2.50 + 2.5
= $5
The additional charges are basically the amount which is charged by the driver to cover a particular distance and thus this distance changes as the distance changes.
However the mandatory fees is constant and it never changes.
It would cost him $ 5 to cover a distance of 2 miles.
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Solve this problem!!! PLEASE HELP WILL GIVE BRAINLIEST
Answer:
1.264×10^-5
Step-by-step explanation:
If you are allowed to use a calculator, it will totally do this question for you. Check mode for Sci Not or use the ^ or EE button.
If no calculator allowed, factor out the 10^-6 and add the numbers. Change back to Scientific Notation and fix the first number. It has to have one digit to the left of the decimal. Adjust the exponent to account for changing 12.64 to 1.264 See image.
Pls help!
if you have to work it out pls work it out my teacher will be mad if no work!
Answer:
1st one: 50%, 0.5, 1/2
2nd one: 25%, 0.25, 1/4
3rd one: 18%, 0.18, 9/50
4th one: 10%, 0.1, 1/10
5th one: 20%, 0.2, 1/5
Step-by-step explanation:
Hope this helps!
Which function produces a range of {−11,−5,1,4,10} given a domain of {−2,0,1,3,5}?
theres a pic to help u understand more
Answer:
f(x) = -3x + 4
Step-by-step explanation:
Plug domain into each function and see if it matches any values in the range.
a fruit salad contains pineapples, apples. bananas, and oranges. It contains twice as many bananas as apples, 10 times as many oranges as pineapples, and the same number of apples as oranges. Jeff made this fruit salad using 1 pineapple. How many of each of the other fruits did he use
Using algebraic expression, if Jeff made the fruit salad using one pineapple, then he use 10 oranges, 10 apples and 20 bananas
Number of pineapples = 1 pineapple
Number oranges equal to the 10 times the number of pineapples
We have to multiply number of pineapples by 10
Number of oranges = 1×10
= 10 oranges
Number of oranges equal to the number of apples
Number of apples = 10 apples
Number of bananas equal to the twice the number of apples
Number of bananas = 2×10
= 20 bananas
Hence, using algebraic expression, if Jeff made the fruit salad using one pineapple, then he use 10 oranges, 10 apples and 20 bananas
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Pls help me how did I get the question wrong
Answer:
see explanation
Step-by-step explanation:
the equation of a line (linear equation) has slope- intercept form
y = mx + c ( m is the slope (gradient)) and c the y- intercept )
y = 12 + 2x or y = 2x + 12 ← is in slope- intercept form
with gradient m = 2
--------------------------------------------------------
the only graphs in linear form are
y = [tex]\frac{1}{2}[/tex] x and y = 12 - x
the other 2 have an x² term which indicates they are quadratic
a population of watermelons in a farmer’s field has unknown population mean weight , but the population standard deviation weight is known to be about
95% confidence interval for the true population mean watermelon weight. is (69.94, 72.06)
Confidence Interval formula = Mean ± z × Standard deviation/√n
Mean = 71 ounces
Standard deviation = 2.8 ounces
z score = 95% confidence interval = 1.96
Confidence Interval = 71 ± 1.96 × 2.8/√27
= 71 ± 1.96 × 0.5388602512
= 71 ± 1.0561660924
71 - 1.0561660924
= 69.943833908 ounces
Approximately = 69.94 ounces
71 + 1.0561660924
= 72.0561660924 ounces
Approximately = 72.06 ounces
95% Confidence Interval = (69.94, 72.06).
the complete question is
You measure 27 watermelons' weights, and find they have a mean weight of 71 ounces. Assume the population standard deviation is 2.8 ounces. Based on this, construct a 95% confidence interval for the true population mean watermelon weight.
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can someone help me with this
Answer: Slope intercept from is y= 4/13x-5/13
Step-by-step explanation:
I need help with this question
The proportional relationship modeled by Table A is graphed on the image given at the end of the answer.
Direct proportional relationshipA direct proportional relationship is defined when the output variable y is calculated with the multiplication of the input variable x and the constant of proportionality r as follows:
y = rx.
The meaning of this is that a proportional relationship is only represented when the division of y by x for all pairs of points (x,y) are the same.
Hence, the proportional relationship in this problem is represented by table A, as:
r = 10/5 = 8/4 = 6/3 = 2/1.
Hence the equation is:
y = 2x.
For table B, a proportional relationship is not shown, as:
3/1 is different of 4/2.
The graph containing the points listed on table A are given at the end of the answer.
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Help please
I don’t understand
1) Let the value of yellow circles = x
Let the value of green butterflies = y
Consider the left string,
3x + y = 15 ----(1)
Consider the right string,
x + 2y = 15 ----(2)
Let us solve the linear equations
(1) *2 => 6x+ 2y = 30 ---(3)
(3) - (2) => 6x+ 2y = 30 - ( x + 2y = 15)
=> 5x = 15
=> x = 3
Substituting x in (1)
3(3) + y = 15
y = 15- 9
y = 6
The value of yellow circles = 3
The value of green butterflies = 6
2) Let the yellow circles = c
Let the green butterflies = b
The linear equations that could be formed are:
a) Left string equation:
3c+b = 15
b) Right string equation:
2b +c = 15
c) Equation of both strings:
4c +3b = 30
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Which could be the first step in solving the equation represented by the model below? XX X X Add 4 negative unit tiles to both sides. Add 4 negative unit tiles to the left side, and add 6 negative unit tiles to the right side. Add 4 positive unit tiles to both sides. Add 6 negative unit tiles to the left side, and add 4 negative unit tiles to the right side.
The most appropriate choice for linear equation will be given by -
First option is the correct option
Adding 4 units negative tiles to both sides.
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expression by an equal to sign.
A one degree equation is called linear equation.
Here,
The equation is 3x + 4 = 2x + 6
For the second option,
If we have to add 4 units negative tiles to left side, we will also have to add 4 units negative tiles to right side.
Second option is wrong
For the third option
We have to add four units negative tiles to both sides, not 4 units positive tiles.
For the fourth option
Adding 6 units negative tiles to left side and 4 units negative tiles to right side will not eliminate any of 6 or 4.
So the first option is correct.
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Complete Question
The diagram has been attached below
A ticket to see your favorite baseball team costs 37.26$. That price decreases by 0.28$ for every game lost during the regular season. What equation could you use to find the cost C of a ticket after L losses? Represent the total change in the cost of a ticket after the team loses 37 games. What is the price of a ticket after the team loses 37 games?
Equation: (C Stands for Cost and L stands for losses)
37.26 C-0.28 L
The total change in the cost of a ticket is dollars.
The equation that represents the given situation is required.The cost of the ticket after L losses is a. Initial cost of the ticket = $49.64Price decrease per game lost = $0.41Number of games lost = LMoney lost after L losses is So, the cost of the ticket after L losses would be the initial cost of the ticket minus the money lost after L losses.The cost of the ticket after L losses is a.