Answer:
There are 17 natural numbers divisible.
There are 17 natural numbers between 150 and 300 that are divisible by 9.
To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.
The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).
Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):
Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1
Number of multiples of 9 = (297 - 153) / 9 + 1
Number of multiples of 9 = 144 / 9 + 1
Number of multiples of 9 = 16 + 1
Number of multiples of 9 = 17
So, there are 17 natural numbers between 150 and 300 that are divisible by 9.
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Drag each length to the correct location on the triangle. each length can be used more than once, but not all lengths will be used. what are the missing side lengths for the triangle? 10 5
Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
What is Trigonometry Ratios?Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
According to the given information:Reference angle (∅) = 60
Adjacent = 4√3
Opposite = ?
Apply TOA:tan 60 = opp/adj
tan 60 = Opp/4√3
√3 = opp/4√3
Opposite = √3 × 4√3
Opposite = 12
Find the other missing side:Reference angle (∅) = 60
Adjacent = 4√3
Hypotenuse = ?
Apply CAH:cos 60 = adj/hyp
cos 60 = 4√3/hyp
hyp = 4√3/cos 60
hyp = 4√3/1/2
hyp = 4√3 × 2
hyp = 8√3
Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
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I need help cancelling units. please help
Hello and Good Morning/Afternoon:
Let's take this problem step by step:
Let's write out the equation we would hypothetically use to convert 410 kilometers to meters:
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}[/tex]
Let's see if there are any errors:
there are 1000 meters in 1 kilometerwhen converting kilometer --> meter⇒ we want to get rid of the kilometer symbol
⇒ which is done in this problem
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}=\frac{410 kilometers}{1 kilometers}*1000 meters = 410000meters[/tex]
Thus the answer is true
Answer: True
Hope that helps!
kelvin pumped 15.2 gallons of gas into his car. if he paid 59.13 for the total amount of gas, what was the rate per gallon that kelvin paid
Answer:
3.89
Step-by-step explanation:
if 15.2 gallons cost 59.13.What about 1
then we just divide 59.13 by 15.2 to get the cost of 1 gallon
Let x be a discrete random variable. if pr(x<9) = 1/6, and pr(x>9) = 1/3, then what is pr(x=9)?
Answer: 1/2
Step-by-step explanation:
The probabilities must add to 1, so:
[tex]P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}[/tex]
In 2010 and 2012, gallup asked the same 50 people how many hours had they worked at a job in the past 7 days. Is there a difference in the population mean amount of hours worked at a job between 2010 and 2012? would this be an example of independent or dependent samples?.
The given case of Gallup asking the same 50 people how many hours had they worked at a job in the past 7 days. is an example of dependent sample.
What is dependent sample?The measured values in relation in a dependent sample (also called a paired sample).
Some characteristics of dependent sample are-
It is a dependent sample, for instance, if a sample of patients who have knee reconstruction is selected, and each patient is questioned during the procedure. The reason for this is that the identical person was questioned twice.If, for instance, you wish to examine if a new category of baseball bat really does have an impact on notable features and the same individuals play once from the old bat and once with new bat, you also have a dependent sample. Since each player utilized both bats, there are two measured values for each player, all measured values are likewise accessible in pairs.A variation is preselected based on the format wherein you insert your data. A series is typically a respondent and, more broadly, a case. Metric values in a sequence are therefore originally regarded as dependent.To know more about dependent sample, here
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5. Betty claims the solution to the equation 4x - 5(x - 5) = 7x + 13 is x = 1.5. She shows her steps below to
justify her solution.
Given
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
4x5(x-5) = 7x + 13
4x5x + 25 = 7x + 13
-x+ 25 = 7x + 13
25 = 8x + 13
12 = 8x
1.5 = x
Select the all correct justifications for the given steps.
Step 1: Distributive Property
Step 2: Combining Like Terms
Step 3: Addition Property of Equality
Step 4: Subtraction Property of Equality
Step 5: Associative Property of Equality
Answer:
See attached image
Step-by-step explanation:
Every step holds except for step 5
In mathematics, it deals with numbers of operations according to the statements.
Here,
Step 1 is the result of the distribution of -5 while opening the parenthesis, So, Step 1 holds the distributive property.
Step 2, states adding like terms across each side, so combining as terms hold,
Step 3, Addition over the equal sign. So it also holds
Step 4, subtraction of 12 over the equal sign. So subtraction of the terms also holds.
Step 5, does not hold because the number 12 gets divided by 8 it is not an associative property.
Thus, Every step holds except for step 5.
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3.
Determine how much this home would cost to replace: 2,600 square feet at $86.00 per square foot
Answer: $
Answer: $223,600
Step-by-step explanation:
Since it is $86 per square foot and you're replacing the 2,600 square foot house you would just take 2,600 × 86 and get 223,600 dollars.
Use the laplace transform to solve the given initial-value problem. y'' − 6y' 13y = 0, y(0) = 0, y'(0) = −5
Answer:
Laplace transforms turn a Differential equation into an algebraic, so we can solve easier.
y'= pY-y(0)
y"=p²Y - py(0)- y'(0)
Substituting these in differential equation :
p²Y -py (0) -y' (0)-6(pY-y(0)) + 13Y
Substituting in the initial conditions given , fact out Y, and get:
Y( p²-6p+13) = -3
Y=-3/ p²-6p+13
now looking this up in a table to Laplace transformation we get:
y=-3/2.e³т sin(2t)
for the last one, find the Laplace of t∧2 . which is 2/p³
pY - y(0)+ 5Y= 2/p³
Y= 2/p³(p+5)
Taking partial fractions:
Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³
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Answer:
The integral transform that converts a function of a real variable to a function of a complex variable is called Laplace transform. first we need to substitute y' and y" in differential equation then finding Laplace transformation and at last taking partial fractions.
Given: y'= pY-y(0)
y"=p²Y - py(0)- y'(0)
Putting y' and y" in differential equation :
p²Y -py (0) -y' (0)-6(pY-y(0)) + 13Y
Substituting in the initial conditions given , fact out Y, and get:
Y( p²-6p+13) = -3
Y=-3/ p²-6p+13
by Laplace transform we get:
y=-3/2.e³т sin(2t)
for the last one, find the Laplace transform of t∧2 . which is 2/p³
pY - y(0)+ 5Y= 2/p³
Y= 2/p³(p+5)
Taking partial fractions:
Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³
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A local school needs to paint the floor of its theater room, where the length of the floor, x, is at least 12 feet. The width of the floor is 4 feet less than the length. It will have a stage and a closet, and the remaining area of the floor will be painted. The dimensions are shown in the diagram:
rectangle with length of x ft and width of x minus 4 ft, right triangle inside labeled stage with height of x minus 4 ft and base of 8 ft, rectangle inside labeled closet with length of 8 ft and width of 4 ft, the rest of the rectangle is labeled floor
Let A represent the painted area, in square feet, of the floor. Choose the correct equation to solve for area (A).
The correct equation that shows the area of painted area is
A=[tex]x^{2} -8x-16[/tex].
Given that the length of the floor,x,is atleast 12 feet.The width of the floor is 4 feet less than the length.There is a right angle of height x-4 and base 8 feet. The rectangle inside has length of 8 feet and width be 4 feet.
We are required to find the painted area of the theater room in square feet.
To find the painted area of the theater the following steps must be followed:
1) Find the area of the theater room.
length =x
Breadth=x-4
Area=x(x-4)
=[tex]x^{2} -4x[/tex]
2) Area of the right triangle.
Height=x-4
Base=8
Area=1/2 *8*(x-4)
=4(x-4)
=4x-16
3) Find the area of the rectangle inside labeled closet.
Length=8
Width=4
Area=8*4
=32
Area=Area of theater room-Area of of right triangle-Area of closet.
=[tex]x^{2} -4x[/tex]-4x+16-32
=[tex]x^{2} -8x-16[/tex]
Hence the correct equation that shows the area of painted area is
A=[tex]x^{2} -8x-16[/tex].
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Answer:
A = x(x − 4) − 0.5(8)(x − 4) − 3(7)
Work:
x = length, making the width (x-4)
The stage closet will be (x-4)(8)(1/2)
The rectangle is 7(3)
which makes the painted area x(x-4) - 4(x-4)
thus giving us
x(x − 4) − 0.5(8)(x − 4) − 3(7)
Step-by-step explanation:
hope this helps :)
Please answer quickly! It would be great if you could include the question # and the answer in the answer section, and then explain it below. Thank you in advance!
Answer:
[tex]\textsf{19.} \quad S_{20}=1490[/tex]
33. None of these are correct.
Step-by-step explanation:
Question 19General form of an arithmetic sequence:
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven values:
[tex]a_n[/tex] = 27n = 20d = -5Substitute the given values into the formula and solve for a:
[tex]\implies 27=a+(20-1)(-5)[/tex]
[tex]\implies 27=a+(19)(-5)[/tex]
[tex]\implies 27=a-95[/tex]
[tex]\implies a=27+95[/tex]
[tex]\implies a=122[/tex]
Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]
where:
a is the first term.d is the common difference.Given values:
a = 122n = 20d = -5Substitute the given values into the formula and solve:
[tex]\implies S_{20}=\dfrac{1}{2}(20)[2(122)+(20-1)(-5)][/tex]
[tex]\implies S_{20}=10[244-95][/tex]
[tex]\implies S_{20}=10[149][/tex]
[tex]\implies S_{20}=1490[/tex]
Question 33Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
where:
a is the first termr is the common ratioGiven values:
a₁ = 1458r = ¹/₃Substitute the given values into the formula and solve:
[tex]\implies S_6=\dfrac{1458\left(1-\frac{1}{3}^6\right)}{1-\frac{1}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456}{\frac{2}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456 \cdot 3}{2}[/tex]
[tex]\implies S_6=2184[/tex]
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each side of a 4ft x 6ft rectangular flower bed was lengthened by the same amount. the area of the new flower bed is twice the area of the old one. Find the new dimensions.
The new dimensions of the flower bed are 4√2 and 6√2
How to determine the new dimensions?The dimensions of the initial rectangular flower bed are given as:
Length = 4ft
Width = 6 ft
The area of the new flower bed is twice the area of the old one.
This means that
New Area = Old Area * 2
Substitute the dimensions of the old area in the above equation
New Area = 4 * 6 * 2
Express 2 as √2 * √2
This gives
New Area = 4 * 6 * √2 * √2
Rewrite the above equation as:
New Area = 4√2 * 6√2
The area of a rectangle is
Area = Length * Width
This means that:
Length = 4√2 ft
Width = 6√2 ft
Hence, the new dimensions of the flower bed are 4√2 and 6√2
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Answer: 6x8
Step-by-step explanation:
(4+x)(6+x)=2*24
x^2+10x+24=48
subtract 48 on both sides
x^2+10x-24=0
Solve using the quadratic formula
-10±√(100+96)÷2
simplifies to
-(10±14)÷2 = 2, -12
-12 doesn't work though because the sides can't be negative.
So x=2
To check, add both sides by 2:
2(4x6)=6x8=48
Question 9 of 25 a bookstore costs $105 a day to keep open, and it spends $12 for each book that it sells. if each book sells for $15, what is the break-even point for this bookstore?
The store will break even after selling 35 books.
What is the break-even point?The break-even point is the moment at which total cost and total revenue are equal, implying that your small firm has no loss or benefit. In other words, you've reached the point where the costs of production equal the revenues for a product.To find what is the break-even point for this bookstore:
Given:
The cost required per day to keep the store open = $105Amount spent on each book = $12Let, n be the number of books.
Total costs = 12n + 105
The selling price of each book = $15
Total revenue = 15n
For breaking even, costs = revenue.
12n + 105 = 15n105 = 15n - 12n105 = 3n3n = 105Dividing both sides by 3:3n/3 = 105/3n = 35Therefore, the store will break even after selling 35 books.
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Distribute to create an equivalent
expression with the fewest symbols
possible.
2(3 – 8y)
=
Answer:
6 - 16y
Step-by-step explanation:
2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y
Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.A) 3 sec2(θ) − 4 = 0B) cot(θ) + 1 = 0
The solution of the assumed equation is
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
Assuming the equation is
csc^2(θ) = 2cot(θ) + 4
and not
Assuming the equation to be:
csc^2(θ) = cot^2(θ) + 1
Solving these equations usually begins with algebra and/or trigonometry. ID for transforming equations to have one or more equations of the form:
trigfunction(expression) = number
It is not always easy to understand how to perform the desired transformation. If it's not obvious, first use the trigonometric identity to reduce the number of different arguments or functions in the equation. In this expression, all arguments are θ. Therefore, there is no need to reduce the number of arguments. But he has two different functions, csc and cot.
csc^2(θ) = cot^2(θ) + 1
Substituting the right side of this equation into the left side of the equation, we get: :
cot^2 (θ) + 1 = 2 cot(θ) + 4
Now that we have only one function cot and one argument θ, we are ready to find the form we need. Subtracting the entire right-hand side from both sides gives:
cot^2(θ) - 2cot(θ) - 3 = 0
The left-hand side factorizes:
(cot(θ)-3)(cot (θ) ) + 1 ) = 0
Using the properties of the zero product,
cot(θ) = 3 or cot(θ) = -1
These two equations are now in the desired form.
The next step is to write the general solution for each equation. The general solution represents all solutions of the equation.
cot(θ) = 3
Note that 3 is not a specific angle value for cot. That's why you need a calculator. Your computer probably doesn't have the crib button, so you'll need to switch it to tan
Since tan is the reciprocal of cot, if cot = 3...
tan(θ) = 1/3
Inverse tan tan^-1(1/3) can be used to find the reference angle. You should get a reference angle of 18.43494882 degrees. Using this reference angle and cot (and tan) being positive in the 1st and 3rd quadrants, we get the general solutions
θ = 18.43494882 + 360k
and
θ = 180 + 18.43494882 + 360k
.
θ = 198.43494882 + 360k
where
cot(θ) = -1
-1 should be recognized as a special angle value for cot. So you don't need a calculator. This reference angle is 45 degrees. Using this reference angle, cot is negative in the 2nd and 4th quadrants, so
θ = 180 - 45 + 360k
and
θ = -45 + 360k (or 360 - 45 + 360k) the general solution for
must get. to:
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
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Determine what type of model best fits the given situation: the membership of the local pta increases by 3 members a day for each day during the month of september.
Type of model best fits the given situation linear. Since it has a constant of +3 everyday.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.linear type of model best fits the given situation.the membership of the local pta increases by 3 members a day for each day during the month of September.
Since it has a constant of +3 everyday.
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how do i find x? pls tell me with working
Answer:
35
Step-by-step explanation:
Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.
Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.
Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.
In the following expression, both AAA and BBB are variables that can take positive values.
A+\dfrac{2}{B}A+
B
2
A, plus, start fraction, 2, divided by, B, end fraction
Which of these actions will cause the expression's value to increase?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Keeping AAA constant and increasing BBB
(Choice B)
B
Keeping AAA constant and decreasing BBB
(Choice C)
C
Increasing AAA and keeping BBB constant
(Choice D)
D
Decreasing AAA and keeping BBB constant
The value to increase is keeping A constant and decreasing the value of B
What are fractions?Fractions are written as a ratio of two integers. For instance a.b is a fraction where a and b are integers.
In the fraction a/b, the numerator is and the denominator is b. If the value of the denominator is decreasing the fraction will increase but if the value of the denominator is increasing the fraction will decrease.
Given the expression A + 2/B, the higher the value of B provided such that that A is constant, the higher the expression. Hence the expression that will cause the value to increase is keeping A constant and decreasing the value of B
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Which expression is equivalent to?
Answer: [tex]\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{\frac{16}[81}} \sqrt[4]{\frac{x^{11}y^{8}}{x^{7}y^{6}}}\\\\=\frac{2}{3} \sqrt[4]{x^{4}y^{2}}\\\\=\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
The area of the trapezoid is 40 square units.
A trapezoid is shown. The lengths of the bases are 6 and 10, and the height of the altitude is h.
What is the height of the trapezoid?
3 units
5 units
10 units
12 units
The altitude of the trapezoid, based on the given parameters is 5 units
How to determine the height of the trapezoid?From the question, we have the following parameters about the trapezoid
Base length 1 of the trapezoid = 6
Base length 2 of the trapezoid = 10
Area of the trapezoid = 40
Altitude of the trapezoid = h
The area of the trapezoid is calculated using
Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid
Substitute the given parameters in the above formula
40 = 0.5 * (6 + 10) * h
Evaluate the sum of 6 ad 10 (do not approximate)
40 = 0.5 * (16) * h
Evaluate the product of 0.5 and 16 (do not approximate)
40 = 8 * h
Divide both sides by 8 (do not approximate)
h = 5
Hence, the altitude of the trapezoid, based on the given parameters is 5 units
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Answer:
5 units
Step-by-step explanation:
Which function has exactly one zero?
Answer:
Step-by-step explanation:
Answer:
i think no 3 hasexactly one 0
how many days will he cut the last section?
Solving a linear equation, we will see that after 9 days he cuts the last section.
how many days will he cut the last section?We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.
So, the length as a function on the number of days, is:
L(x) = 20m - 2m*x
Here we just need to solve:
L(x) = 2m
Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).
Solving that, we get:
20m - 2m*x = 2m
20m - 2m = 2m*x
18m/2m = x = 9
After 9 days he cuts the last section.
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If a diameter intersects a chord of a circle at a perpendicular, what conclusion can be made?
If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.
What is the relation between the chord and diameter of a circle?The segments of a circle whose endpoints are on its perimeter are called chords.A circle's diameter is the chord that passes across its center.The circle's longest chord equals its diameter.Any line that is perpendicular to a chord on the circle cuts it in half and goes through the center.The solution to the problem:
A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.
Therefore, the chord is bisected.
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The points (2,5) , (3,3) and (k,1) all lie on a straight line
(a) find the value of k
(b) find the equation of the line
Answer:
(a) k = 4
(b) y = - 2x + 9
Step-by-step explanation:
x2-x1, y2-y1
= 3-2, 3-5
= 1,-2
3,3 + 1,-2 = (4,1)
x=4
Luigi is navigating a maze. He gets to a junction and has 3 directions he can go in. For each of these choices, he eventually gets to another junction where he has 6 choices of direction.
How many different possible paths are there?
Helppp!! pleasee i put a ss!
Answer:
-20
Step-by-step explanation:
He went back 20 and not forward 20. Everyone would want a penalty if you got to go forward.
Which of the following is true with respect to the following functions:
The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"
What is the explanation for the above?Lets examine f(x) = 3x + 14Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.
Let us examine h(x) = 3ˣ + 1This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:
y = 0
Let us look at F'(x) = Log₃ (x = 1).
This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0
Let us take a look at g(x) = X⁴ + 3x² - 14Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.
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What are the x-intercept and vertex of this quadratic function? Write each feature as an ordered pair: (a,b). The x-intercept of function g is The vertex of function g is
The x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0) and the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)
How to determine the x-intercept?The function is given as:
g(x) = -5(x - 3)^2
Set g(x) to 0, to determine the x-intercept.
-5(x - 3)^2 = 0
Divide through by -5
(x - 3)^2 = 0
Take the square root of both sides
x - 3 = 0
Add 3 to both sides
x = 3
Hence, the x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0)
How to determine the vertex?The function is given as:
g(x) = -5(x - 3)^2
A quadratic function is represented as:
g(x) = a(x - h)^2 + k
Where, the vertex is
Vertex = (h, k)
By comparing g(x) = a(x - h)^2 + k and g(x) = -5(x - 3)^2, we have
(h, k) = (3, 0)
Hence, the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)
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In order for you to use the goodnees-of-fit test, the test of independence, or the test of homogeneity, the expected frequencies for each cell needs to be at least:____.
The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
According to the statement
we have to find the condition of the expected values in the case of testing of goodness-of-fit test.
So, For this purpose we know that the
The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.
So, The main condition of the expected value for the goodness of fit test is
For each category, the expected frequency is at least 5.
Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.
So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
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The function f(x) represents the time it takes a boat to travel upstream. the function g(x) represents the time it takes a boat to travel downstream. given f(x) = 3x − 10 and g(x) = 12x 8, solve for (f g)(x) to determine the total roundtrip time. (f g)(x) = 15x − 2 (f g)(x) = 9x − 2 (f g)(x) = 15x 2 (f g)(x) = 9x 2
The (f + g)(x) = 15x - 2 is represent the total round trip time.
According to the statement
we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.
And we have to find the total round trip time.
So, For this purpose, the given information is:
f(x) = 3x − 10 and g(x) = 12x + 8
And
The total round trip time is represented by the term (f + g)(x)
We know that the
(f + g)(x) = f(x) + g(x)
Substitute the given values in it
So, (f + g)(x) = f(x) + g(x)
(f + g)(x) = (3x - 10) + (12x + 8)
(f + g)(x) = 15x - 2
Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.
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PLEASE HELP!!
Part C
What is the difference of the x-coordinate of point A and the x-coordinate of point B?
The difference of the x-coordinate of point A and the x-coordinate of point B is 0
Coordinates of a pointThe coordinate of a point on an xy-plane is written in the form (x, y). The given figures are circles A and B where the circle A is greater than circle B.
The position of the dots in both sides are positioned at the centre and as such the coordinate point at the centre of both circle will be the origin (0, 0)
According to the question, we are to find the difference of the x-coordinate of point A and the x-coordinate of point B
x-coordinate of pint A = 0
x-coordinate of point B = 0
Take the difference
Difference = 0 - 0
Difference = 0
Hence the difference of the x-coordinate of point A and the x-coordinate of point B is 0
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