Answers
The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x
How to evaluate the composite function?The definitions of the functions are given as
f(x) = √4x and g(x) = √16x
Evaluate the square roots in the above equations
This gives
f(x) = 2√x and g(x) = 4√x
To find the composition (f - g)(x), we make use of
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation So, we have the following equation
(f - g)(x) = 2√x - 4√x
Evaluate the like terms
This gives
(f - g)(x) = -2√x
Hence, the value of the composition is (c) (f - g)(x) = -2√x
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Related Questions
Swimming, Manufacturing, and Painting
Problem
Variables to use
Equation
Tyler swims at a constant speed, 5 meters every 4 seconds.
A factory produces 3 bottles of sparkling water for every 8 bottles of plain water.
A certain shade of light blue paint is made by mixing 1 ½ quarts of blue paint with 5 quarts of white paint.
For each of the previous three situations, write an equation to represent the proportional relationship.
Answers
The equations that represent the proportional relationships between the variables are as follows:
Problem Variables to use Equation
1. Tyler swimming Time / Distance D = 1.25t
2. Factory production Total quantity, Q, Q = 3s + 8p
and Sparkling / Plain
3. Paint mixture Blue / White Paints 6q = 1.5b + 5w
What is an equation?An equation models a mathematical statement in which two or more expressions (involving numbers, variables, and operands combined) are equated using the equation symbol (=).
Tyler:Speed = 5 m/4s
= 1.25 m/s (5/4)
Swimming equation: D = 1.25t
Where D = distance and t = time spent.
Given the speed and time, we can find the swimming distance covered by Tyler.
Factory:
Bottles of sparkling water = 3
Bottles of plain water = 8
Ratio = 3:8
Production equation, Q = 3s + 8p
Where Q = total quantity, s = sparkling water, and p = plain water
Paint:Blue paint = 1 ½ quarts
White paint = 5 quarts
Ratio = 1.5:5
Production equation, 6q = 1.5b + 5w
Where 6q = 6 quarts, b = blue paint, and w = white paint
Thus, using the equations, we can use the known variables to find the unknown variables.
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Find the intercepts of the line
Answers
Answer:
x-int=-40
y-int=15
Step-by-step explanation:
we have points 0,15 and -40,0 on the line.
It is as easy as the y-int being 15 and the x-int being -40!
the y-int will always be= (0,#)
the x-int will always be (#,0)
which statement explains why ABC is congruent to A’B’C’?
Answers
The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.
What is congruent triangles?
When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.
Main Body:
First let us find the co-ordinates of both the triangles.
A= (3,5)
B = (-2, 3)
C= (-4,-1)
A' =(10,-5)
B'= (5, -3)
C' =(3,1)
Distance between two points = d=√((x₂ – x₁)² + (y₂ – y₁)²).
In ΔABC
Distance of side AB = √((3 –(-2) )² + (5 –3 )²)
= √5² +2²
= √29
Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)
= √20
Distance of side CA = √((3-(-4) )² + (5-(-1) )²)
= √7² + 6²
= √85
Distance of side A'B' = √((10 -5)² + (-5-(-3))²
= √(5² +2²)
= √29
Distance of side B'C' = √ ((5-3)² + (-3 -1)² )
= √ (2)² +4²
= √20
Distance of side C'A' = √((10-3)² + ( -5-1)²)\
= √(7)² + 6²
= √85
This shows each side of ΔABC is equal to side of ΔA'B'C'.
hence the triangles are congruent.
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adult tickets
A total of 390 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times ti
number of adult tickets sold. How many adult tickets were sold?
Answers
The number of adult tickets were sold is 130 tickets.
Given,
In the question:
Total tickets were sold for the school play is 390 tickets.
The number of student tickets sold was two times number of adult tickets sold.
To find the how many adult tickets were sold?
Now, According to the question:
Based on the given conditions:
Let the number of adult tickets be x.
Formulate the condition:
x × (1 + 2) = 390
x × 3 = 390
Simplify
x = 390/3
x = 130
Hence, The number of adult tickets were sold is 130 tickets.
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A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, what was the change in the altitude of the missile?
Answers
The required change in height of the missile is 16100 feet.
Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.
Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.
here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.
Thus, the required a change in height of the missile is 16100 feet.
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Which points are on the axes 5 units from the origin
Answers
Answer:
E and X
Step-by-step explanation:
look for the 6 then behind it
Answer:
X and E
Step-by-step explanation:
"axes" is the plural of axis. The x-axis is the flat line marked with numbers and arrows at the ends. Its labelled x on the right side.
The y-axis is the up-and-down line marked with numbers and arrows at the ends, labelled y at the top.
The origin is where the two axes cross.
Points J, E, X and P are all on the axes. But X and E are 5 units from the origin (where the lines cross) J and P are 9 units from the origin.
2, 6 and 10 were labelled on the axes, but each tick mark is an evenly spaced amount. So the 5 was unlabelled, but it is understood to be 5. See image.
Peter and Parker work for a cleaning crew. Peter can clean a room in 15 minutes less time than it takes Parker to do the same job. Working together,
they can clean two rooms in 110 minutes. Approximately how long does it take Peter to clean a room by himself?
Answers
how long does it take Peter to clean a room by himself is[tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
What does "rate" mean mathematically?
A rate is a unique ratio where the two words are expressed in several units.
Let Peter take time to clean 1 room be = t
Let Parker take time to clean 1 room be = t+15
Total Time taken by both to clean to room T= 110
Equation for total time taken to clean 2 room by both
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{T}[/tex]
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{110}[/tex]
By taking LCM
[tex]\frac{2t+15}{t^{2}+15} =\frac{1}{55}[/tex]
By cross multiplication in above equation
[tex]110t+825=t^{2} +15t[/tex]
[tex]t^{2}-95t-825=0[/tex]
Hence the answer is [tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
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(-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)
Answers
Solution to the fraction (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9) = -38
How to solve fraction?Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects
To simplify the fraction into a simple form the following steps are followed;
Evaluate (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)
(-7 + 3) x 9 + ⅖ x (-1.1 - 3.9)
Add the numbers
(-4) x 9 + ⅖ x (-1.1 - 3.9)
Evaluate the exponent
(-4) x 9 + ⅖ x (-5)
Multiply the number
-36 + ⅖ x (-5)
-36 -10/5
Subtract the number from each other
-36 -10/5
=-36-2
Answer = -38
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Please help question from 4 through 12 thank you very much
Answers
The answer to the questions from 4 through 12 are below:
4. z³ + 5z² + 5z + - 35. 4d + 6c - 66. 20a - 2b - 17. 40x8. 10x + 16y + 149. a² + 8a - 1010. 15v + 22w11. 10c² + 4c12. z³ - 8z² + 5z + 23What is the perimeter of a rectangle and triangle4. z³ + 5z + 3z² + 1 - 4 - 2z²
= z³ + 5z² + 5z + - 3
5. Perimeter of the square = Addition of all the sides
= (2d - 3) + (3c) + (2d - 3) + (3c)
= 2d - 3 + 3c + 2d - 3 + 3c
= 4d + 6c - 6
6. Perimeter of the triangle = Addition of all the sides
= (4a - 2b) + (9a - 4) + (7a + 3)
= 4a - 2b + 9a - 4 + 7a + 3
= 20a - 2b - 1
7. Perimeter of a square = 4 × side length
= 4 × 10x
= 40x
8. Perimeter of a rectangle = 2(length + width)
= 2{(2x + 7) + (3x + 8y)}
= 2(2x + 7 + 3x + 8y)
= 2(5x + 8y + 7)
= 10x + 16y + 14
Simplify the following
9. 3a + a² + 5(a - 2)
= 3a + a² + 5a - 10
= a² + 8a - 10
10. 8(v + w) + 7(v + 2w)
= 8v + 8w + 7v + 14w
= 15v + 22w
11. 4c² + 6(c + c²) - 2c
= 4c² + 6c + 6c² - 2c
= 10c² + 4c
12. z³ + 5(z + 3) + 4(2 - 2z²)
= z³ + 5z + 15 + 8 - 8z²
= z³ - 8z² + 5z + 23
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4. Two card are down Randomly from well suffled deck of card without Replacement Find the probability by of getting both Face card at two succession tree diagram.
Answers
Answer:
[tex]\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]
Step-by-step explanation:
Two cards are drawn randomly from a well-shuffled deck of cards without replacement. Find the probability of getting both face cards in succession.
In a deck of 52 cards, there are three face cards (J, Q, and K) in each of four suits (clubs, diamonds, hearts, and spades). That means there are 12 face cards in total (J♣, Q♣, K♣, J♦, Q♦, K♦, J♥, Q♥, K♥, J♠, Q♠, K♠).
The probability of drawing a face card the first time, then, is 12 out of 52.
There is now one less face card in the deck, as well as one less card in the deck. Therefore, the probability of drawing a face card a second time is 11 out of 51.
The probability, then, of drawing two face cards in succession is:
[tex]\frac{12}{52}\times{\frac{11}{51}}=\frac{132}{2652}=\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]
What is the equation of the line that passes through the point (4, 6) and has a slope
of o?
Answers
Y is directly promotional to x^2
y = 300 x = 10
Write an equation for y in terms of x
Answers
The proportional equation between y and x^2 is:
y = 3*x^2
How to write the equation?We know that y is directly proportional to x^2, then we can write:
y = k*x^2
Where k is the constant of proportionality.
We also know that when x = 10, the value of y is 300, replacing that in the above equation we get:
300 = k*(10)^2
Now we can solve this for k:
300 = k*100
300/100 = k
3 = k
Then the equation is:
y = 3*x^2
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already answered 1 and 2. i think 3 is "definition of midpoint". is this correct? what are the other two? thank you
Answers
2) I think the statement is wrong
3) def. Of midpoint
4) Reflexive postulate
5) the statement is wrong
Find the area of the following figure:
(Use π=3.14 when finding your final answer. Do not round and Do not enter units!)
Area = _______ mm²
Answers
Answer:
521 mm2
Step-by-step explanation:
Formulas:
area of circle= 3.14 x radius x radius
area of semicircle = 0.5 x 3.14 x radius x radius
diameter of circle= 20mm
radius=0.5x20mm=10mm
area of trapezium= 0.5 x (base+base) x height
Working:
area of semicircle= 0.5 x 3.14 x 10mm x 10mm = 157mm2
area of trapezium = 0.5 x (20mm+32mm) x 14mm = 364mm2
total area of figure= 157mm2 + 364mm2 =521mm2
Find the slope using points: (0, - 3) and (- 4, 2)
Answers
Answer:
-5/4
Step-by-step explanation:
slope
[tex]\frac{y2-y1}{x2-x1}\\\\ \frac{2-(-3)}{-4-0}=\frac{5}{-4}\\ \\slope = \frac{-5}{4}[/tex]
A random sample of 10 subjects have weights with a standard deviation of 10.9508 kg What is the variance of their weights? Be sure to include the appropriate units with the result
Answers
Based on the information given the variance of their weights is 119.9200 kg².
What is variance?
The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: σ².
Main body:
n=sample size=10
Standard deviation=10.9508 kg
Using this formula
Variance=(Standard deviation)²
Let plug in the formula
Variance=(10.9508 kg)²
Variance= 119.9200 kg²
Hence the variance of their weights is 119.9200 kg².
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A small rectangle has a width of 5cm and a length of 7cm. using the same ratio, what will be the length of a bigger rectangle it its width is 90cm?
Answers
We know that for a width of 5 cm we have a length of 7 cm,
Length Width
5 cm ————> 7cm
90 cm ————> x
We multiply in X this data:
5x = 90 * 7
x = 630/5
x = 126 cm
So with all of this we found out that the length of the rectangle with a width of 90 cm is 126 cm.
Jada claims that B'C'D' is a dilation of BCD using A as the center of dilation.
What are someways you can convince Jada that her claim is not true?
Answers
Dilation entails altering a figure's size.
Because the is larger than, Isaiah's assertion is untrue.
What is dilation?A transformation that alters the size of a figure is called a dilation (similarity transformation). It needs a scale factor and a central point. Depending on the value of k, the dilatation is either an enlargement or a reduction.The dilatation is an expansion if | k | > 1The dilation is a decrease if | k | 1.The new image's size in relation to the old image's size is determined by the scale factor's absolute value. The original image and the new image are on the same side of the center when k is positive. They are on opposing sides of the center when k is negative. A dilatation always has its own picture at its center.Although dilation is not a hard transformation, the angles of the figures it dilates remain unchanged.
The aforementioned claim suggests that,
The dimensions of and should be equal.
However, it is evident that;
are not equivalent.
In reality
greater than
Therefore, Isaiah's assertion is false.
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What is the compound interest if $47,000 is invested for 10 years at 8% compounded continuously?
Answers
Need help please someone
Answers
The equation of the linear function is y=8x+(-8).
What do you mean by equation?
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.
According to data in the given question,
We have points (0,-8) and (1,0), thus
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{(0-(-8))}{1-0} \\=8[/tex]
Then
y=8x+b
Points (0,-8) means that when x=0, y=-8 and we use this to find b,
y=8x+b
-8=8(0)+b
-8=0+b
b=-8
So, y=8x+(-8)
Therefore, the equation of the linear function is y=8x+(-8).
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x+13
2x +1
x-8
Find x
Answers
X = 43.5 .............
A footballb team lost the same number of yards on each of 3 consecutive plays.what is the total change in yards from where the team started? Someone pls help I dont understand.
Answers
The total change in yards where the team started is 3x
How to determine the total change in yards?The given parameters in the question are:
Yards per play = unknown
Number of plays = 3 consecutive plays
Represent the yards per play with x
So, we have
Yards per play = x
The total change in yards is the amount of yard per play multiplied by the number of plays
This is represented as
Total change = Yards per play * Number of plays
Substitute the known values in the above equation So, we have the following equation
Total change = x * 3
Evaluate
Total change = 3x
Hence, the total change is 36 yards
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Solve the following inequalities: (i) 5(11 − ) < + 49
Answers
The answer to the inequality is -55 < 49. That is -55 is less than 49.
What is inequality?
This refers to the relationship between two values that are not equal. It can be represented with the following symbols; < less than,> greater than, ≥ greater than or equal to,≤ less than or equal to, and ≠ not equal to.
The given equation States that;
5(11 − ) < + 49
5*11- < + 49
-55 < +49
Therefore, -55 is less than 49.
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here are the first 5 terms of an arithmetic sequence, 2,6,10,14,18... is 86 a term in this sequence, you must give a reason for your answer
Answers
Answer: Yes
Step-by-step explanation:
Because if you keep going it will reach 86, since it's added by 4, so 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86.
Let ()=94+2+2. Compute (5)() .
Answers
Based on the given equation and the given value of (), the value of 5() from the equation is 490
How to solve equation?If
() = 94 + 2 + 2
The equation can be solved by substituting the value of () into 5()
Substituting is the method of inserting the known value of a variable into an equation to solve for the value of the equation.
Then,
Substitute the value of () into (5)()(5)()
= 5(94 + 2 + 2)
= 5(98)
= 490
So therefore, the value of 5() is given by 490.
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Choose the answer.
The difference between 3 times a number and 7 is 5. Write and solve an equation to
determine the number. Select the solution and graph that represents the number.
Answers
5 is the difference between the two numbers 12 and 7.
Given,
In the question;
The difference between 3 times a number and 7 is 5.
Write and solve an equation to determine the number.
Now, According to the question:
Let's assume the unknown number to be x,
so three time the number would be 3x.
The difference between 3 times a number (3x) with 7 is 5, so we can write it as:
3x - 7 = 5
Now we can solve this equation to the find x (the unknown number).
3x = 5 + 7
3x = 12
x = 12/3
x = 4
Therefore 3x= 12
So, 5 is the difference between the two numbers 12 and 7.
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add w and the sum of 9 and 4
Answers
The addition of w, 9 and 4 is (w+13).
According to the question,
We have the following information:
We need to add w, 9 and 4.
We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.
So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.
Now, the whole numbers can be easily added.
So, we have the following expression:
w+9+4
w+13
Hence, the addition of w, 9 and 4 is (w+13).
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A math class has 3 girls and 7 boys in the seventh grade and 4 girls and 4 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys? Write your answer as a fraction in simplest form.
Answers
The probability that the selections are both boys is 7/10
How to determine the probability that the selections are both boys?The given parameters in the question are
Seventh grade
Boys = 7
Girls = 3
Eight grade
Boys = 4
Girls = 4
The probability of selecting a boy is calculated as
P(Boy) = Number of boys/Number of students
So, we have
Seventh grade
Boys = 7
Girls = 3
P(boy) = 7/10
Eight grade
Boys = 4
Girls = 4
P(boy) = 4/8
The probability that the selections are both boys is
P = P(boy) * P(boy)
So, we have
P = 7/10 * 4/8
Evaluate
P = 7/20
Hence, the probability is 7/20
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I need help with this question anyone?
Answers
Answer:
B; 14 cents/1 ounce
Step-by-step explanation:
So you were given the information that there is 140 cents per 10 ounces. Now, we have to get that into a unit rate, which is a number over 1. It would have to be B because the info. was cents/ounces and typically money is over amount.
So you do 140/10
That equals out to 14/1
So it is 14 cents/1 ounce.
Hope this helps!!! :)
Which symbol correctly compares the fractions below?
2/3 ? 6/9
A. >
B. none of these are correct
C. =
D.
Answers
Answer:
C
Step-by-step explanation:
6/9 simplified is 2/3
Hope this helps
