Thus, the domain of the obtained composite function are:
Domain (f + g)(x) = [-0.828, 4.828]
Domain (f - g)(x) = [-18.22, 0.22]
Explain about the domain of the function?The range of values that we are permitted to enter into our function is known as the domain of a function.
This pair is the x value in a function also including f(x) .The range of both a function has been the set of values that it function assumes. The values in this setHence, once we input an x value, the function returns. The y values are those.Given functions:
f(x) = 11x - 2x²
g(x) = -7x - 3x² + 4
Then,
addition : (f + g)(x) -
(f + g)(x) = 11x - 2x² -7x - 3x² + 4
Adding the variables with same degree along with sign.
(f + g)(x) = 4x - x² + 4
Graph the function:
Domain (f + g)(x) = [-0.828, 4.828]
Subtraction : (f - g)(x) -
(f - g)(x) = 11x - 2x² - (-7x - 3x² + 4)
Simplifying;
(f - g)(x) = 11x - 2x² + 7x + 3x² - 4
Adding the variables with same degree along with sign.
(f - g)(x) = x² + 18x - 4
Graph the function:
Domain (f - g)(x) = [-18.22, 0.22]
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Translate the sentence into an equation. Twice the difference of a number and 7 is equal to 2. Use the variable y for the unknown number.
Answer:
pls brainliest
Step-by-step explanation:
The difference btw the number and 7= y-7
so twice:2(y-7)=2
2y-14=2
please help me solve this
The speed of both car A and car B are the same which is 0.7 miles per minute
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Let x represent the distance travelled by car A and y represent the distance travelled by car B
Speed of car A = x /20
Car B reaches in 50 minutes, hence:
Speed of car B = y/50
Since both speed are same;
x/20 = y/50
20y = 50x (1)
Car B is 21 miles farther, then:
y - x = 21 (2)
x = 14, miles y = 35 miles
Speed of car A = speed of Car B = 14/20 = 35/50 = 0.7 miles per minute
The speed is 0.7 miles per minute
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please help!!!!!!!!!!!!!!!!!!
Answer:
1x2=2 3x3x1=3
Step-by-step explanation:
Set up a proportion and solve.
Find the cost of 3 scarves if 2 scarves cost $22.80.
Answer:
Proportion: 22.80/2=x/3
x= 34.20
Step-by-step explanation:
First find what the value of one scarf is:
22.80/2=11.40
Then multiple by 3 to get $34.20
Answer:
Proportion : 1 scarf = $11.40
Cost of 3 scarves = $34.20
Step-by-step explanation:
GIVEN: 2 SCARVES = 22.80
LET X = # OF SCARVES
2X=22.80
X=$11.40
$11.40(3) = cost of 3 scarves
$34.20 = cost of 3 scarves
The line that passes through the points (-3,0) and (5,8) is
A.Horizontal
B.Increasing
C. Decreasing
D. Vertical
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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A number cube is rolled. Event A is rolling an odd number, and event B is rolling a factor of 12. What is P(AU B)?
Explanation:
A = set of odd numbers = {1,3,5}
B = set of factors of 12 = {1,2,3,4,6}
A U B = union of set A and set B
A U B = {1,3,5} union {1,2,3,4,6}
A U B = {1,3,5, 1,2,3,4,6}
A U B = {1,2,3,4,5,6}
The set union operation combines two sets into one bigger set. Duplicates are tossed out.
There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.
Therefore, the probability event A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.
Side notes:
A U B can be read out as "event A or event B"; so P(A U B) is "the probability event A happens or B happens or both".A intersect B = {1,3} = values that are in both set A and set B at the same time. These are both odd and a factor of 12.a certain species of tree grows on average of 4.2 cm per week. Write an equation for then sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall
Answer:
h = 200 + 4.2w
Step-by-step explanation:
h = height of tree (cm)
w = weeks
h = 200 + 4.2w
Starting at 200, adding 4.2cm every week
In parallelogram HIJK, the measure of angle H is 45 degrees, segment IK is 20, Segment OH is 15
In the parallelogram HIJK, the measure of angle J and K are 45 degrees and 135 degrees respectively.
What is a parallelogram?You should know that a parallelogram is a quadrilateral whose opposite sides are parallel. The given parameters for the solution are
m<H = 45 degrees
Having said this, the m<K will be:
Produce the line H to P
This implies that <JKP is = 45 degrees ........... corresponding angles
It there means that <HKJ = 180-45 = 135 degrees
Also; <JKP = <IJK ................ corresponding angles
Therefore m<J is 45 degrees.
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The correct question:
In parallelogram HIJK, the measure of angle H is 45∘.
Find the measure of angle J. Explain how you know.
Find the measure of angle K. Explain how you know.
You invested $4000 between two accounts paying 3% and 4% annual interest. If the total interest earned for the year was $130, how much was invested at each rate?
You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.
Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.
To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).
According to the given information, the total interest earned from both investments is $130. So we can set up the equation:
0.03x + 0.04($4000 - x) = $130
Simplifying the equation:
0.03x + 0.04($4000 - x) = $130
0.03x + $160 - 0.04x = $130
-0.01x = $130 - $160
-0.01x = -$30
x = -$30 / -0.01
x = $3000
Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.
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What is the translation from
a) shape X to shape Z?
b) shape Z to shape X?
The translation form of each shape is given as follows:
a) X to Z: (x, y) -> (x + 5, y + 2).
b) Z to X: (x, y) -> (x - 5, y - 2).
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For the composition of translations, we add the coordinates, hence:
-2 + 7 = 5.5 - 3 = 2.Hence the rule from X to Z is given as follows:
(x, y) -> (x + 5, y + 2).
From Z to X, we have the inverse rule, hence:
(x, y) -> (x - 5, y - 2).
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the angle measures of a triangle are 50, 2x, 3x-10. what is the value of x
Answer:
x = 28°
Step-by-step explanation:
Angle sum property of triangle:
Sum of all the three angles of the triangle is 180°.
50 + 2x + 3x - 10 = 180°
2x + 3x + 50 - 10 = 180°
Combine like terms,
5x + 40 = 180°
Subtract 40 from both sides,
5x = 180 - 40
5x = 140°
Divide both sides by 5,
x = 140 ÷ 5
\(\sf \boxed{\bf x = 28^\circ}\)
sara buys 3 gallons of juice. she want to fill 1 pint bottles with juice. how many 1 pint bottles can sara completely fill with 3 gallons of juice
Answer:
So Sara can fill 24 pint bottles completly with 3 gallons of juice.
Step-by-step explanation:
This question can be solved using a rule of three.
Each pint has 0.125 gallons. How many pints are 3 gallons?
1 pint - 0.125 gallons
x pints - 3 gallons
\(0.125x = 3\)
\(x = \frac{3}{0.125}\)
\(x = 24\)
So Sara can fill 24 pint bottles completly with 3 gallons of juice.
If 15% of the customers total is $98,880, then the sum total equals what
The sum total by the given data is equals to $658,880.
We are given that;
Percent=15%
Amount= $98,880
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:
15% = 0.15
To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:
$98,880 / 0.15 = $98,880 x 1/0.15
To multiply by 100, we can move the decimal point two places to the right. This gives us:
$98,880 x 1/0.15 x 100 = $658,880
Therefore, by the percentage the answer will be $658,880.
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Helena is watching a movie ontelevision. She notices that there are9. min of commercials for every hof the movie.What is the unit rate of minutes of commercials per hour of the movie?
Explanation:
\(9\frac{1}{4}\text{minutes of commercial = }\frac{1}{2}\text{hour of Television}\)A unit rate of minutes of commercials per hour of the movie means to find minute of commercial in 1 hour:
\(\begin{gathered} \frac{1}{2}\text{hour = 9}\frac{1}{4}\min \\ 1\text{ hour = x} \\ \text{cross multiply: } \\ x(\frac{1}{2})\text{ = 1(9}\frac{1}{4}) \\ \frac{x}{2\text{ }}=\text{ }\frac{37}{4}\text{ cross multiply} \\ 4x\text{ = 2}\times37 \\ x\text{ = }\frac{74}{4}\text{ = }\frac{37}{2} \\ x\text{ = 18 }\frac{1}{2} \end{gathered}\)The unit rate of minutes of commercials per hour of the movie = 18 1/2 (option D)
Stephen purchased 4 1/2 feet of wire fencing that cost $0.75 per foot. What is the total cost, in dollars, of Stephens fencing?
The total cost, in dollars, of Stephens fencing is $3.38
What is the total feet of wire purchased?
The 4 1/2 feet of wire fencing purchased is the same 4.50 feet since 1/2 is the same as 0.5, based on the price and quantity relationship, the total cost incurred by Stephen is the cost per foot of $0.75 multiplied by the quantity bought purchased, that is 4.5 feet.
total cost=cost per foot*number of feet purchased
cost per foot=$0.75
number of feet purchased=4.5
total cost=$0.75*4.5
total cost=$3.38
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What is the value of x? Enter your answer in the box. x =
Answer:
x = 46
Step-by-step explanation:
Use the triangle angle bisector theorem.
58/63.8 = (x + 4)/55
63.8(x + 4) = 55 * 58
63.8x + 255.2 = 3190
63.8x = 2934.8
x = 46
I need this asap, HURRY
Answer: 6
Step-by-step explanation: To evaluate this problem, the first thing
we want to do is plug in the appropriate values for a, b, and c.
When we do that, we get \(\frac{3(4)}{4(3) - (10)}\).
A good rule of thumb for problems that involve division bars is to simplify what's above the division bar as much as you can and what's below the division bar as much as you can before you do your dividing.
So up top, we simplify 3(4) to get 12.
Down below, we want to multiply before we subtract.
So 4(3) is 12 and we have 12 - 10 which is 2.
So we have 12 / 2 which simplifies to 6.
2) What is the volume of a basketball that has a diameter of 15 inches?
a recipe for kool-aid calls for 4 cups of water for every 6 tablespoons of mix.how many tablespoons of mix should you use if you wanted 6 cups of water. what about 10 cups
for 6 cups of water?
\(\begin{array}{ccll} \stackrel{cups}{water}&\stackrel{tspoons}{mix}\\ \cline{1-2} 4 & 6\\ 6& x \end{array} \implies \cfrac{4}{6}~~=~~\cfrac{6}{x} \\\\\\ \cfrac{ 2 }{ 3 } ~~=~~ \cfrac{ 6 }{ x }\implies 2x=18\implies x=\cfrac{18}{2}\implies x=9\)
how about for 10?
\(\begin{array}{ccll} \stackrel{cups}{water}&\stackrel{tspoons}{mix}\\ \cline{1-2} 4 & 6\\ 10& y \end{array} \implies \cfrac{4}{10}~~=~~\cfrac{6}{y} \\\\\\ \cfrac{ 2 }{ 5 } ~~=~~ \cfrac{ 6 }{ y }\implies 2y=30\implies y=\cfrac{30}{2}\implies y=15\)
answer the question for me
Answer: 1, 2, and 4.
Step-by-step explanation: Each must be wider than the angle than a "L" has.
Brian cut of 25% of a stick which was 1.6 meters long what percent of the stick is remaining
Answer:
The remaining is 75%, the length of the stick would be 1.2
Step-by-step explanation:
According to the information given,
We know that Brian cut off 25% of a stick which was 1.6 meters long
and 1.6 is the 100% of the stick:
It is fairly easy to calculate this, subtract 25 from 100 ( 100 - 25 ), which is equal to 75.
Hence, the answer is 75% and 1.2 for the remaining length of the stick
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1 squared + 1= 2 sqaured - 2
2 sqaured + 2 = 3 squared - 3
3 squared + 3= 4 squared - 4
a) make a conjecture about this pattern. write your conjecture in words
b) generalise your conjecture for this pattern
c) prove that your conjecture is true
Answer:
It would be the letter B :)
How many significant figures are in the number
43.6? 43.6 has [?] significant figures.
Answer:
43.6 has 3 significant figures.
Find the X and Y intercepts for the equation Y= X - 3
Answer:
x- intercept = 3 , y- intercept = - 3
Step-by-step explanation:
y = x - 3
to find the x- intercept let y = 0 ( where line crosses x- axis )
0 = x - 3 ( add 3 to both sides )
3 = x
then x- intercept = 3
to find the y- intercept let x = 0 ( where the line crosses the y- axis )
y = 0 - 3 = - 3
then y- intercept = - 3
Use the graph or table to write a linear function that relates y to x.
Answer:
x+2y=0
Step-by-step explanation:
Answer:
y = -1/4x - 1
Step-by-step explanation:
The equation of a line is y = slope*x + y-intercept
Find the slope by picking two points shown on the graph and doing (y1-y2)/(x1-x2): (4, -2) & (-8, 1) = (-2-1)/(4-(-8) = -3/12 = -1/4 so the slope is 4.
Find the y-intercept by seeing where the line crosses the y-axis: y= -1
So therefore, y = -1/4x - 1
Question 8(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.
How do equations work?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.
Equations can be categorized as identities or conditional equations.
w = (455.95-155.95)/(37.50)
=300/37.50
=8
So, number of weeks = 8
As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.
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Two dozen eggs and a loaf of bread cost K4.94. Half a dozen eggs and two loaves of bread cost K2.32. Find the cost of a dozen eggs.
The cost of a dozen of eggs is $3.
Given two dozen eggs and a loaf of bread cost K4.94 and
Half a dozen of bread cost K2.32
Cost of a dozen of eggs = ?
we know that, 24E ₊ B = 8.50 and
6E ₊ 2B = 6.50
multiply the first equation by 2 and substract
48E ₊ 2B = 17
6E ₊ 2B = 6.50
after solving both equations we get:
42E = 10.50
we are searching for the value of a dozen eggs, which is 12E
multiply 42E = 10.50 by 12/42 = 6/21
and you get
12E = 10.50 × (6/21) \\ 10.50 = 21/2
12E = (21×6)/(2×21)
12E = 3
so a dozen eggs cost 3 dollars.
Hence we get the cost of a dozen of eggs as $3
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Prove or disprove that for all n, there exists a positive integer t such that a set of n elements can be partitioned into a number of subsets where all the subsets have size t or t - 1
The purpose of the SUBSET-SUM issue is to determine whether a subset from a list of integers may add up to a certain value.
A dynamic programming approach that takes repeating, positive, and negative numbers into account. The purpose of the SUBSET-SUM problem is to determine whether a subset of a list of integers may add up to a certain value. As an example, consider the list of numbers [1, 2, 3, 4]. If the target is set to that number, there are two subsets, 3, and 1, 2, 4, that both add up to 7. If the target is equal to 11, there are no solutions.
If there are t integers in the sums list, then there are usually (t -1) subsets that need to be checked to see if there are even any solutions to SUBSET-SUM. This post will look at a technique for using dynamic programming to solve issues more successfully. though, in contrast
Let is SUBSET-SUM (arr, t, sum/2) be the function that returns true if there is a subset of arr [0..t-1] with sum equal to sum/2
The is SUBSET-SUM problem can be divided into two subproblems
is SUBSET-SUM() without considering last element (reducing t to t-1)
is SUBSET-SUM considering the last element (reducing sum/2 by arr[t-1] and t to t-1)
If any of the above subproblems return true, then return true.
is SUBSET-SUM (arr, t, sum/2) = is SUBSET-SUM (arr, t-1, sum/2) || is SUBSET-SUM (arr, t-1, sum/2 – arr[t-1])
Therefore,
The purpose of the SUBSET-SUM issue is to determine whether a subset from a list of integers may add up to a certain value.
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On September 1, 2024, Lindsey Engineering borrows $406,000 cash. The loan is made by FirstLending, under the agreement that Lindsey will repay the principal with four payments of $101,500. Payments are due by October 1 each year, with the first payment being due October 1, 2025 (next year). Interest on the borrowing is 6%, and Lindsey’s year-end is December 31.
By using the annuity formula we conclude that, the payment required to repay the loan is $101,500, which is the same amount for each of the four payments.
What is annuity formula?
The annuity formula is a mathematical formula used to calculate the periodic payment required to pay off a loan or investment with equal payments at fixed intervals over a specified period of time.
To calculate the payments for this loan, we can use the present value of an annuity formula, which gives the payment required to repay a loan with regular payments over a set period of time.
PV = PMT * [1 - \((1 + r/n)^{(-n*t)\)] / (r/n)
where:
PV = present value of the loan (in this case, the amount borrowed, which is $406,000)
PMT = payment amount
r = annual interest rate (6% in this case)
n = number of compounding periods per year (12, since the payments are monthly)
t = number of years over which the loan is repaid (4, since there are four payments)
Using these values, we can solve for PMT:
406,000 = PMT * [1 - \((1 + 0.06/12)^{(-12*4)\)] / (0.06/12)
406,000 = PMT * [1 - \((1 + 0.005)^{(-48)\)] / 0.005
406,000 = PMT * [1 - 0.65125]
PMT = 101,500
Therefore, the payment required to repay the loan is $101,500, which is the same amount for each of the four payments.
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