Answer:
The area enclosed by two curves can be found by subtracting the area between one curve and the x-axis from the area between the other curve and the x-axis.
Let's call the x-value where the two curves intersect as X. At X, both y values are equal to 0. Hence, the equation for X is
-x^2 + c = x^2 - c
Solving for x, we get
2x^2 = 2c
x^2 = c
The area between y = -x^2 + c and the x-axis is equal to the area between y = x^2 - c and the x-axis, so the total area is double that, or 2c.
Setting 2c equal to 56, we have:
2c = 56
c = 28
So the value of c for which the area enclosed by the curves y = −x^2 + c and y = x^2 − c is equal to 56 is 28.
point charges of 10.4 nc and 43.9 nc are placed 0.500 m apart. what is the electric field halfway between them? indicate direction by a positive or a negative value. keep in mind that a positive vector is one directed to the right and a negative vector is one directed to the left. your answer should be a positive or a negative number with two decimal places, do not include the unit. hint: 1 nc
The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.
The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.
The electric field because of a point charge q is written as [tex]E=\frac{kq}{r^2}[/tex]
Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,
[tex]\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}[/tex]
The required answer is -4824 N/C.
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The output is seven less than the input
The function rule describes the connection between the input or domain and the output or range and we know that the required function rule is x=y-7.
What do we mean by function rule?The relationship between the input or domain and the output or range is known as the function rule.
If and only if there is a single value in the range for each domain value, then a relation is a function.
Consequently, the expression f (x) = 3 x + 1 can be used to represent the function rule y = 3 x + 1.
Function notation is the name for this method of expressing a function rule.
We can read the function notation above as A function exists that is "expressed in terms of the variable" in such a way that it equals 3 x + 1 or of equals 3 x + 1.
So, Y is the result, and x is the input.
According to the provided information, the output is 7 less than the input.
Since the output is y and the input is x, y is therefore 7 less than x.
Since y is 7 less than x, you may express that as an equation, giving you x = y -7.
Therefore, the function rule describes the connection between the input or domain and the output or range and we know that the required function rule is x=y-7.
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Complete question:
Write a function rule for "The output is 7 less than the input." Let x be the input and let y be the output.
Which equation best represents the relationship
The equation that best represents the relationship is 7x - 4y = -20
How to determine the equation of the tableFrom the question, we have the following parameters that can be used in our computation:
x y
5 13.75
10 22.50
15 31.25
In the above table, we can see that
As x increases by 5
y increases by 8.75
So, the slope is
m = 8.75/5 = 1.75
A linear equation is represented as
y = mx + c
so, we have
y = 1.75x + c
Using the ordered pair, we have
1.75 * 5 + c = 13.75
Evaluate
c = 5
So, we have
y = 1.75x + 5
Express as
4y = 7x + 20
This gives
7x - 4y = -20
Hence, the relaionship is 7x - 4y = -20
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24
x+y+z=9
2₂75y +72=5₂
22² +y=z=0
Using Gaussian elimination method
x=-224/229, y=296/229, Gaussian elimination approach is z=118/229.
Explain about the Gaussian elimination method?The row reduction strategy for solving linear equation systems in mathematics is also referred to as the Gaussian elimination method. A series of procedures are carried out on the corresponding coefficients matrix to create it.
Gaussian elimination is the name of this process, which entails the gradual removal of the variables. Sample 1 Make this system work: The variable x is removed from the second equation by multiplying the first equation by 3, then adding the result. This last formula, 5 y = 5, suggests y = 1 right away.
Systems of linear equations are resolved using the Gaussian elimination (also known as row reduction) approach. It bears the name of Carl Friedrich Gauss, a well-known German mathematician who discussed this approach but did not create it.
-5x-7y-4z=-6
6x+2y+3z=-2
-x+2y-7z=0
(Multiply with -5 and add the result to the first equation; multiply with 6 and add the result to the second equation)
-x+2y-7z=0
-17y+31z=-6.....(mult with 14) (mult with 14)
the sum of 14y-39z=-2 (mult with -17)
-x+2y-7z=0
We have z=118/229 since -229z=-118.
14y-39*(118/229)=-2, thus y=296/229 follows.
-x+2*(296/229)-7*(118/229)=0, hence x=-234/229 is the result.
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Cargo is tied with rope on the roof of a 45-foot tall car. The car travels down a road at 40 mi/h and hits a concrete barrier and the rope snaps, allowing the cargo to propel forward. Find the time it
takes for the cargo to hit the groupd and the horizontal distance the cargo travels. Let y represent height in feet, let x represent horizontal distance in feet, and let rrepresent time in seconds.
Equation 1:7-1611²+ 45
Equation 27-0047x²+45
Answer:5.29 seconds to hit ground 30.86 feet in air
Step-by-step explanation:
The first equation, y = 7.16t^2 - 40t + 45, represents the vertical position of the cargo as a function of time.
The second equation, y = -0.047x^2 + 45, represents the height of the cargo as a function of horizontal distance traveled.
To find the time it takes for the cargo to hit the ground, we need to find when y = 0 in the first equation.
Setting y = 0, we have:
0 = 7.16t^2 - 40t + 45
Solving for t, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
where a = 7.16, b = -40, and c = 45.
t = (40 ± √(40^2 - 4 * 7.16 * 45)) / (2 * 7.16)
t = (40 ± √(1600 - 322.2)) / (2 * 7.16)
t = (40 ± √1277.8) / (2 * 7.16)
t = (40 ± 35.62) / 14.32
t = (75.62 / 14.32, 4.38 / 14.32)
Since t must be positive, t = (75.62 / 14.32) = 5.29 s
Now that we have the time it takes for the cargo to hit the ground, we can use that time in the second equation to find the horizontal distance the cargo traveled.
x = √((45 - 0) / -0.047)
x = √(45 / -0.047)
x = √(45 * -21.28) = √(957) = 30.86 ft
So, it takes the cargo 5.29 seconds to hit the ground, and it travels 30.86 feet horizontally.
Aaron used the scaled picture on his jigsaw puzzle box as a guide for putting the puzzle together. Both the picture and the scale used to make it are shown below. According to the scale, what will the length of the finished puzzle be, in inches? A. inch B. inch C. 16 inches D. 32 inches
What was the principal investment
James needs to invest $83226.33 as his principal in order to achieve this goal.
How to Work Out How Much
An asset or item purchased with the intention of generating income or appreciation is referred to as an investment. The term "appreciation" describes a rise in an asset's value over time. When a person buys a product as an investment, they don't intend to use it right away; instead, they plan to use it to make money later on.
Here is the basic interest calculation formula:
I, or simple interest, is equal to PRT/100.
Where:
P represents the primary amount.
R represents the rate.
The letter T represents time.
Modify the values.
2496.79 = P × 1 × 3/ 100
Multiplying by two
3 P = 249679
Create "P" as the formula's
P = 249679/ 3
Count through
P = $ 83226.33
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You deposit $10000 into a standard simple interest savings account. You deposit $12000 into a higher yield account whose interest rate is triple the basic account. In one year, you make $460 in interest. What were the interest rates for each account?
ANSWER THESE⬇️⬇️
Focus on the question at the end of the situation. What is unknown about the situation? Define variables to represent these unknowns.
What are the TWO situations that are being described in the problem? Write an equation that represents each.
The interest rate for the basic account is 10% and the interest rate for the higher yield account is 30%.
What were the interest rates for each account?Let the basic account interest rate be r, then the higher yield account interest rate is 3r.
The interest earned in the basic account is r * $10000 = $1000r.The interest earned in the higher yield account is 3r * $12000 = $3600r.The total interest earned ($460) is
$1000r + $3600r = $460
$460 = $4600r
Dividing both sides by $4600:
r = 0.1
This gives
r - 10%
So, the interest rate for the basic account is 10%
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Line r passes through points (10, 8) and (1, 4). Line s passes through points (10, 9) and (1,
5). Are line r and line s parallel or perpendicular?
Lines r and s have the same slope of 4/9, therefore, they are parallel.
What are Parallel and Perpendicular Lines?To determine if two lines are parallel or perpendicular, you can use the slope formula. If the slopes of the two lines are equal, the lines are parallel. If the product of the slopes of the two lines is -1, the lines are perpendicular.
The slope formula is: m = (y2 - y1) / (x2 - x1)
For line r:
m = (4 - 8) / (1 - 10) = -4 / -9 = 4/9
For line s:
m = (5 - 9) / (1 - 10) = -4 / -9 = 4/9
Since the slopes of the two lines are equal, they are parallel.
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 Select the equation that has Infinite Solutions.
O a
Ob
C
d
5× =4×+1
2 - 2x = -2(x - 1)
2x + 7 = 2x - 7
5x+4=5(×+4)
The equation that has infinite number of solutions is A: 5x = 4x + 1.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
When certain requirements are met, an equation can have an unlimited number of solutions. In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited. The two lines are actually in the same line if they share the same slope and y-intercept.
The first equation is 5x = 4x + 1.
Solve the equation -
5x - 4x = 1
x = 1
The x value is obtained as 1 which means the line is made parallel to the y-axis at point x = 1.
Therefore, this line has infinite number of solutions.
The second equation is 2 - 2x = -2(x - 1).
Solve the equation -
2 - 2x = -2x + 1
-2x + 2x = 1 - 2
0 = -1
This equation doesn't exist.
Therefore, there are no solutions for the equation.
The third equation is 2x + 7 = 2x - 7.
Solve the equation -
2x - 2x = -7 + 7
0 = 0
This equation doesn't exist.
Therefore, there are no solutions for the equation.
The fourth equation is 5x + 4 = 5(x + 4).
Solve the equation -
5x + 4 = 5x + 4
5x - 5x = 4 - 4
0 = 0
This equation doesn't exist.
Therefore, there are no solutions for the equation.
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TAKE IT TO THE BANK
Ricky just watched his favorite pool player, Montana Mike, make a double bank shot in a trick-shot competition. Montana bounced a ball off two rails (sides) of the table and sank it in the corner pocket. “That doesn’t look too hard,” Ricky says, “I just need to know where to put the ball and in which direction to hit it.”
Your teacher will provide you with a model.A diagram of Montana’s shot is shown at right. The playing area of a tournament pool table is inches by inches. Along its rails, a pool table is marked with a diamond every inches. Montana started the shot with the ball against the top rail and the ball hit the bottom rail three diamonds from the right rail.
Your Task: Figure out where on the top rail Ricky needs to place his ball and where he needs to aim to repeat Montana Mike’s bank shot. Write instructions that tell Ricky how to use the diamonds on the table to place his ball correctly, and at what angle from the rail to hit the ball. Explore using the Lesson 6.2.1 Resource Page.
Ricky should place the ball along 2nd diamond of top rail from right.
Aim should be towards the 2nd diamond of right rail.
What is Distance angle?Distance-angle commonly refers to the horizontal distance of an angle that reaches a certain height, which in turn forms a triangle.
Given,
In the Diagram,
Shot of Montana Mike is shown,
Montana started the shot with the ball against the top rail and the ball hit the bottom rail three diamonds from the right rail.
By the figure,
To repeat Montana shot,
Ball should be along 2nd diamond of the top rail from the right rail.Aim should be towards 2nd diamond of the right rail.Hence, the shot will be repeated by Ricky if ball is placed along the 2nd diamond of top rail from right and aim towards 2nd diamond of right rail.
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I don’t know how to figure this question out:(
The population of the nation as per the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.
What is canadian population?Canada is larger than the United States, making it the second-largest country in the world. However, despite this vast territory for a relatively small population, more than 90 percent of Canadians live within 150 miles of the US border.
The population of the country as per the provisional figures of Census 2011 is 1210.19 million of which 623.72 million (51.54%) are males and 586.46 million (48.46%) are females. The provisional figures of Census 2011 were released in New Delhi today by Union Home Secretary Shri G.K.Pillai and RGI Shri C. Chandramouli.
Canada contains the world's seventh-largest Indian diaspora. The highest concentrations of Indian Canadians are found in the provinces of Ontario and British Columbia, followed by growing communities in Alberta and Quebec as well, with the majority of them being foreign-born.
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PLEASE HELP ME!
Going into the final exam, which will count as two tests, Sharon has test scores of 77, 84, 72,65, and 96. What score does Sharon need on the final in order to have an average score of 80 ?
Answer:
Sharon needs to receive a score of 43 on the final to have an average score of 80.
Step-by-step explanation:
First, let's understand what is being told to us. We are being asked to find the score Sharon needs on the final, or x. Since the final is worth 2 tests, the final is equal to twice the score she receives, or 2x. Next, we need the average of all the tests, including the final, to be equal to 80. It's important to also note that we will be taking the average of 6 scores. Now, let's use all of our information to write an equation to solve:
( 77 + 84 + 72 + 65 + 96 + 2x ) / 6 = 80. [Combine like terms]
( 394 + 2x ) / 6 = 80 [Multiply by 6]
394 + 2x = 480 [Subtract 394 from both sides'
2x = 86 [Divide both sides by 2]
x = 43
So, Sharon needs to receive a score of 43 on the final to have an average score of 80.
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in this line of circles
Answer:
11
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.
Currently, there is 1 red circle and 3 blue circles, making the ratio 1: 3.
Adding 1 red circle would make the ratio 2: 3.Adding 8 circles would make the ratio 9: 3.Adding 11 red circles would make the ratio 12: 3.The ratio 12:3 can be simplified to get 4:1.
12 ÷ 3 = 43 ÷ 3 = 1Therefore, you will need to add 11 red circles to get the ratio 4: 1.
How many 11/2 ounce doses of medication are there in a 24 ounce bottle?
Answer:
There are only 4, 11/2 ounce of medication in a 24 ounce bottle
Step-by-step explanation:
11/2 = 5.5, 24/5.5=4.4
Karissa purchased a set of LED lights online that normally sells for $90 but was marked down to $67.60 what is the discount rate karissa received
The discount rate Karissa received is 12% discount.
What is discount rate?In a discounted cash flow (DCF) analysis, the interest rate used to calculate the present value of future cash flows is known as the discount rate. This aids in determining if the present-day capital outlay required to fund a project or investment will be greater than the value of the projected future cash flows from that project or investment.
The WACC and adjusted present value are the two main formulas for calculating the discount rate (APV).
WACC = E/V x Ce + D/V x Cd x (1-T) is the formula for the WACC discount, and
APV = NPV + PV of the impact of financing is the formula for the APV discount.
Take the change in price
65 - 57.20 =7.80
And divide by the original price
7.80/65=.12
Change to percent form
12%
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A marinade for chicken uses 3 parts lime juice for every 5 parts of orange juice. If the marinade uses 1/5 cup of lime juice how much oj should be used?
Answer:
You should use [tex]\frac{1}{3}[/tex] orange juice.
Step-by-step explanation:
Set up a proportion
[tex]\frac{3}{5}[/tex] = [tex]\frac{\frac{1}{5} }{x}[/tex]
This is lime juice to orange juice. Cross multiply and solve for x.
3x = [tex]\frac{5}{1 }[/tex] x [tex]\frac{1}{5}[/tex]
3x = 1 Divide both sides by 3
x = [tex]\frac{1}{3}[/tex]
Answer: 1/3 cup of oj
Step-by-step explanation:
You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents per minute. The second plan charges a monthly fee of $29.95 plus 9 cents per minute.
Let
be the number of minutes you talk and
and
be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans.
c1=
c2=
If you talk for ____ minutes the two plans will cost the same. (round your number to one decimal place)
Equation for charges of first plan
C₁ = 24.t
Equation for charges of second plan
C₂ = 9t + 2995
If we talk for _199.7__ minutes the two plans will cost the same.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given,
First plan charges rate of 24 cents per minute
C₁ = 24.t
C₁ is the charge of first plan
t is the number of minutes
Second plan charges $29.95 plus 9 cents per minute.
C₂ = 9t + $29.95
1 dollar = 100 cents
C₂ = 9t + 2995
Where C₂ is the charge of first plan
t is the number of minutes.
Let after x minutes the cost of both plans will be same
C₁ = C₂
24x = 9x + 2995
24x - 9x = 2995
15x = 2995
x = 2995/15
x = 199.667 ≈ 199.7 minutes
Hence, C₁ = 24.t and C₂ = 9t + 2995 are the equations for the charges of first plan and second plan respectively.
After talking 199.7 minutes the cost of two plans will be same.
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The ABC Cell Phone Company offers a plan that includes a flat rate fee of $29 per month plus a$0.12 charge per minute. Write an equation to find C, the total monthly cost for m minutes. Then solve the equation for m = 50.
Answer:
Step-by-step explanation:
The cost has two parts; a fixed cost of $29 and a variable cost of $0.12 per minute. So, the total monthly cost for 50 minutes is $35.
In a recent NBA basketball game, the Hornets were trying to earn a playoff spot with a win over LeBron James and the Cavaliers! In the first quarter, the Cavaliers scored 25 points and the Hornets scored 20 points. In the second quarter, the Hornets scored 25 points, and the Cavaliers scored 20. What was the score for each team after the second quarter? Would it have changed if the Hornets scored 25 in the first quarter and 20 in the second? Why or why not?
Answer:
After the second quarter, the Cavaliers' score would be 25 points and the Hornets' score would be 45 points. The score for each team would not have changed if the Hornets scored 25 points in the first quarter and 20 points in the second quarter because the total number of points scored by each team would still be the same. The order in which the points were scored does not affect the final score of the game.
a number y multiplied by -4 is no more than -2/3 write this word sentecne as an inequality
The word sentence as an inequality is -4y ≤ -2/3
What is an inequality?An inequality can be defined as a mathematical relation that makes a non-comparison between two expressions, equations or numbers.
It is also important to note that algebraic expressions can be defined as expressions that are composed of terms, coefficients, variables, constants and factors.
The signs in an inequality are;
< represents less than> represents greater than≤ represents greater than or equal to≥ represents less than or equal toFrom the information given, we have that
The variable is y
The fraction is -4
This can be represented as;
y × -4 ≤ -2/3
multiply the values
-4y ≤ -2/3
Hence, the expression is -4y ≤ -2/3
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A new bank customer with $4500 wants to open a money market account. The bank is offering a simple interest rate of 1.9%. a. How much interest will the customer earn in 20 years? b. What will the account balance be after 20 years?
Answer:
see below
Step-by-step explanation:
$4500
simple interest 1.9% per year
20 years = 20*1.9%=38%
4500*(1+38%) = 6210
Suppose we are using a Riemann sum with right rectangles to approximate ∫ 05 f(x) dx for some function f(x). Which of the following sums would you expect to give the best approximation? There is not enough information to tell. O a rectangle approximation with Δx=20
O a rectangle approximation with Δx=2
O a rectangle approximation with Δx=0.02
O a rectangle approximation with Δx=0.2
The approximation is: A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.
To calculate the approximate integral using a Riemann sum with right rectangles, we need to calculate the area of each rectangle and then add them all together. The area of each rectangle is given by the formula A = f(x) * Δx, where f(x) is the value of the function at a given x and Δx is the width of the rectangle.
For a rectangle approximation with Δx=20:
Calculate the x-coordinates of the right endpoints of the rectangles:
x1 = 0, x2 = 20, x3 = 40, x4 = 60.Calculate the values of f(x) at each x-coordinate:
f(x1) = f(0), f(x2) = f(20), f(x3) = f(40), f(x4) = f(60).Calculate the area of each rectangle using the formula A = f(x) * Δx, where
Δx = 20: A1 = f(0) * 20, A2 = f(20) * 20, A3 = f(40) * 20, A4 = f(60) * 20.Add up the areas of all the rectangles to get the approximate integral:
∫0 5 f(x) dx ≈ A1 + A2 + A3 + A4.For a rectangle approximation with Δx=2:
Calculate the x-coordinates of the right endpoints of the rectangles:
x1 = 0, x2 = 2, x3 = 4, x4 = 6.Calculate the values of f(x) at each x-coordinate:
f(x1) = f(0), f(x2) = f(2), f(x3) = f(4), f(x4) = f(6).Calculate the area of each rectangle using the formula A = f(x) * Δx, where
Δx = 2: A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.Add up the areas of all the rectangles to get the approximate integral:
∫0 5 f(x) dx ≈ A1 + A2 + A3 + A4, where:
A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.
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Evaluating Composite Functions Use the graphs of f and g to evaluate each expression. If the result is undefined, explain why.(a) (f ∘ g)(3)(b) g(f(2))(c) g(f(5))(d) (f ∘ g)(−3)(e) (g ∘ f)(−1)(f) f(g(−1))
Composite Functions for : f [ g (x) ] = 3 g(x) + 7 will be f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8
Common functions typically have a subset of the real numbers as their domain. Any integer from the domain may be used to replace a variable.
The domain of a composite function is determined by another function, not by a collection of numbers. We refer to it as "a result of another function. Example:
If: . f (x) = 3x + 7 . f [g(x)] must be found and simplified. g(x) = 5x - 5. Due to the fact that the domain of this function is a function of another function, f (x) is a simple function or just a function.
Let's make the example I gave previously simpler.
G (x) signifies in f "Replace x with g (x) in the function f (x). The Composite function f [g (x)]
we have : f [ g (x) ] = 3 g(x) + 7 . but . g( x) = 5x - 5
replace x in f[ g(x ) ] . by. 5x - 5 and simplify
f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8 **
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The question seems to be wrong
Evaluating Composite Functions for : f [ g (x) ] = 3 g(x) + 7
3x – 2 < 4
A. x < 2
B. x < -3
C. x < -2
D. x < 6
Answer: A. x < 2
Step-by-step explanation:
We will isolate the variable with inverse operations.
Given:
3x – 2 < 4
Add 2 to both sides of the equation:
3x < 6
Divide both sides of the equation by 3:
x < 2
A. x < 2
Isosceles triangle: hypotenuse is 20, what are the side lengths?
Answer: [tex]10\sqrt{2}[/tex]
Step-by-step explanation:
Angles in an isosceles right triangle are: 90, 45, 45.
The ratio of the sides are: [tex]1:1:\sqrt{2}[/tex]
Side of 90° = 20
Side of 45° = [tex]\frac{20}{\sqrt{2} }[/tex]
[tex]\frac{20}{\sqrt{2} } =[/tex] [tex]\frac{20\sqrt{2} }{\sqrt{2} ^{2} } = \frac{20\sqrt{2} }{2} = 10\sqrt{2}[/tex]
Use the vertex (h,k) and a point on the graph (x,y) to find the general form of the equation of the quadratic function.
(h,k)=(−3,3) , (x,y)=(2,10)
Answer:
y = 7/25x² +42/25x +5 13/25
Step-by-step explanation:
You want the general form of the equation for the quadratic function that has (-3, 3) as its vertex and (2, 10) as a point on the graph.
Vertex formThe vertex form equation is ...
y = a(x -h)² +k
where (h, k) is the vertex and 'a' is a vertical scale factor.
For the given vertex, this becomes ...
y = a(x +3)² +3
We want to find 'a' such that the point (x, y) =(2, 10) satisfies the equation:
10 = a(2 +3)² +3
7/25 = a . . . . . . subtract 3, divide by 25
General formThe expanded equation is ...
y = 7/25(x +3)² +3 = 7/25(x² +6x +9) +3
y = 7/25x² +42/25x +5 13/25
General form of the equation of the quadratic function:
y = (7/25)x² + (42/25)x + 138/25
What is quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Given
vertex (h,k) = (−3,3)
Point (x,y) = (2,10)
Standard Form Equation for a Parabola:
a(x-h)² = y-k
for vertex (h,k)
(h,k) = (−3,3)
a(x - -3)² = y - 3
a(x + 3)² = y - 3 ______(1)
(x,y)=(2,10)
a(2+3)² = 10 - 3
25a = 7
a = 7/25
Substituting value of a in equation 1
(7/25)(x+3)² = y - 3
(7/25) (x² + 9 + 6x) = y - 3
7x² + 63 + 42x = 25y - 75
7x² + 63 + 75 + 42x = 25y
7x² + 42x + 138 = 25y
⇒ y = (7/25)x² + (42/25)x + 138/25
Hence, y = (7/25)x² + (42/25)x + 138/25 is the general form of the equation of the quadratic function.
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Two cyclists start at the same point and travel in opposite directions. One cyclist travels 6 mih faster than the other. If the two cyclists are 60 miles apart after 2 hours, what is the rate of each cyclist?
Answer:
12 and 18
Step-by-step explanation:
60 miles in 2 hours, so that means together the cyclists are traveling at 30mph,
one is traveling at 6mph more so 30mph-6mph =24
24/2=12
so the slower one is going at 12mph and the other at 18mph
help me please my mom can't even figure it out
Answer:
I think it's [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5} * \frac{3}{1} = \frac{4}{1} *\frac{3}{5}[/tex]
= [tex]\frac{12}{5}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4}{5}\times 3}[/tex]
[tex]\mathsf{= \dfrac{4}{5}\times \dfrac{3}{1}}[/tex]
[tex]\mathsf{= \dfrac{4\times3}{5\times1}}[/tex]
[tex]\mathsf{= \dfrac{12}{5}}[/tex]
[tex]\mathsf{= 2\dfrac{2}{5}}[/tex]
[tex]\star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\ \star[/tex]
[tex]\mathsf{4\times\dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{4}{1}\times\dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{4\times3}{1\times5}}[/tex]
[tex]\mathsf{= \dfrac{12}{5}}[/tex]
[tex]\mathsf{= 2\dfrac{2}{5}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{12}{5}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Learning about sukutes. Noel began to notice them all around him. He noticed that the windshield wiper on a car divides the windshield into two sukutes. Look at the picture and calculate the unknown sukute? Fast Help
Draw a line connecting the two perpendicular lines, creating a triangle. Calculate the two remaining unknown sukutes, subtract 62 from 180 to get 118 degrees, and divide this by two to get 59 degrees.
What are perpendicular lines?
Perpendicular lines are described in geometry as line segments that join or overlap at right angles. The word 'perpendicular' comes from the Latin word 'perpendicularis,' which means a plumb line. If two lines AB and CD are parallel, we may express them as AB and CD. The sign indicates that the lines are perpendicular.
Step 1: Draw a line from the center of the windshield to the left side of the windshield. This line should be 90 degrees.
Step 2: Draw another line perpendicular to the first line, going from the center of the windshield to the right side of the windshield. This line should also be 90 degrees.
Step 3: Draw a line connecting the two perpendicular lines, creating a triangle. This line should be 62 degrees.
Step 4: Calculate the two remaining unknown sukutes. To do this, subtract 62 from 180 to get 118 degrees. Then divide this by two to get the two remaining unknown sukutes, which should both be 59 degrees.
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