a parking garage charges the rates in the table below. what is the rate of change? don’t forget your units.
f(x)=x+a/x+b such that f(f(1))=0 and f(2)=-3 then the values of a and b respectively
The values of a and b are 8 and - 9.
Given that:
f(x) = x + a/x + b ........ (1)
f(1) = 0, f(2) = - 3
Putting the value of x = 1 in equation (1). We get,
f(1) = 1 + a/1 + b
f(1) = 1 + a + b ....... (2)
Putting the value of x = 2 in equation (1). We get,
f(2) = 2 + a/2 + b
f(2) = (4 + a + 2b)/2 ........ (3)
Putting the value of f(1) = 0 in equation (2). We get,
a + b = - 1 ......... (4)
Putting the value of f(2) = -3 in equation (3). We get,
=> -3 = (4 + a + 2b)/2
=> -6 = (4 + a + 2b)
=> a + 2b = - 10 ......... (5)
To find the value of a and b we have to solve equations (4) and (5) by elimination method.
So, for that subtract equation (4) from (5).
We got the value of b = - 9.
Then put the value of b in equation (4).
We got the value of a = 8.
Checking the value of a and b satisfies the value of the function's output and input.
Hence, the values of a and b are 8 and - 9 respectively.
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To rent a taxi in Philadelphia, the taxi service charges a flat rate of
$35.80 and an additional $5.60 per mile driven. Write an equation
in slope-intercept form where x represents the distance of the trip,
and y represents the amount the taxi service would charge to drive
that distance.
Please I need help badly
Answer:
y = 5.60x + 35.80
Step-by-step explanation:
trust
solve the equation. justify each step
2(-x - 5) = 12
2(-x - 5) = 12
Step 1 : Expand the bracket.
=> -2x - 10 = 12
Step 2 :Add both side by 10.
=> -2x - 10 + 10 = 12 + 10
=> -2x = 22
Step 3 : Divide both side by -2.
=> -2x : (-2) = 22 : (-2)
=> x = -11
Therefore, x = -11.
Answer:
x = - 11
Step-by-step explanation:
2(- x - 5) = 12 ( divide both sides by 2 )
- x - 5 = 6 ( add 5 to both sides )
- x = 11 ( multiply both sides by - 1 )
x = - 11
8. The length of a rectangle is 3 feet longer than the width. If the width is x feet, how long is the rectangle?
Answer:
Let the width be x feet. As length is 3 feet longer, it is x+3 feet. As perimeter is twice of te sum of length and width, it is 2×(x+3+x)=2×(2x+3)=4x+6 feet.
Step-by-step explanation:
Mr. C is buying some Hot Cheetos for our school hangout. He can buy an 18 ounce bag for $4.50 or he can buy a 40 ounce bag of the same Cheetos for $8.80. Which bag of Hot Cheetos offers the lowest price ounce?
Answer:
Step-by-step explanation: You want to figure out how much it costs per ounce. You’ll divide $4.50/18 ounces to get $0.25 per ounce for the 18 ounce bag and $8.80/40 ounces to get $0.22 per ounce for the 40 ounce bag. The 40 ounce bag is cheaper per ounce.
X
y
1
9
2
7
3₂
3
6
4
7
1 -2
a. Graph the points above as a scatter plot.
b. Calculate the correlation coefficient.
8
-5
10
-8
10
X is top y is bottom
The correlation coefficient of points is a negative correlation.
The given coordinates are (1, 9), (2, 7), (3, 6), (4, 1), (7, -2),(8, -5) and (10, -8).
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
• A scatter plot with increasing values of both variables can be said to have a positive correlation.
• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.
The given coordinate points are plotted on graph.
From the graph (scatter plot) we can see that, the points have a negative correlation.
Therefore, the correlation coefficient of points is a negative correlation.
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a determined gardener has 100 ft of deer-resistant fence. she wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 600 ft2. what range of values (in ft) is possible for the length of her garden? (enter your answer using interval notation.)
The range of values for the rectangle length is 20 ≤ y ≤ 30 .
What is a rectangle made of?
With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Rectangles are two-dimensional shapes, and as such, they have length and width as their defining characteristics.The garden is to be rectangular shape.
Let x = width
Let y = length
Set the equations for perimeter and area.
2(x + y) = 100 -----> perimeter
x + y = 50 ------> perimeter
xy = 600 ----> area
We have two equations to work with.
x + y = 50 eq1
xy = 600 eq2
Substitute eq1 into eq2. We can get eq2 in terms of x.
x(50 - x) = 600
-x2 + 50x = 600
-x2 + 50x - 600 = 0
Divide both sides of the equation by -1, so that we have a positive x2. The goal is to try to use FOIL to factor.
x2 - 50x + 600 = 0
(x - 30)(x - 20) = 0
x = 30 and x = 20
Next, we plug in these values of x into eq1 to solve for y.
y = 50 - x and y = 50 - x
y = 50 - 30 y = 50 - 20
y = 20 y = 30
Based on this, the range of values for the length is
20 ≤ y ≤ 30
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One year, the population of a city was 325,000. Several years later it was 263,250. Find the percent decrease.
The percentage decrease of the population of a city is 19%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the population of a city was 325,000 and several years later it was 263,250.
The percentage decrease will be:
= Decrease in population / Original population × 100
= (325000 - 263250) / 325000 × 100
= 61750 / 325000 × 100
= 19%
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The maximum height covered is 32m and the time taken to reach maximum height is 1.25 seconds
What is rate of change?A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change = change in y / change in x. Rates of change can be positive or negative.
h(t) = -16[tex]t^{2}[/tex] +40t + 7
at maximum height the rate of change of h(t) with respect to t is zero.
so [tex]\frac{dh(t)}{dt}[/tex] = 0
but [tex]\frac{dh(t)}{dt}[/tex] = -32t + 40
so,
-32t + 40 = 0
32t = 40
t = 40/32
t = 1.25
to find h(t), we substitute t = 1.25 into the equation above
h(t) = -16[tex](1.25)^{2}[/tex] + 40(1.25) + 7
h(t) = 32m
In conclusion, the maximum height reached is 32m and the time taken to reach maximum height is 1.25 seconds
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The sides of a triangle are in the ratio of 3:4:5. A man jogged around it 5 times and cover a distance of 3000m What are the sides of the triangle?
The sides of the triangle are 150m, 200m and 250m.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Given: The sides of a triangle are in the ratio of 3:4:5. A man jogged around it 5 times and cover a distance of 3000m.
As man jogged around triangle 5 times and cover a distance of 3000m.
So, the distance for one round is 3000/5 = 600m.
The covered distance is nothing but the perimeter of the triangle.
So, the perimeter of the triangle is 600m.
Let, 3x, 4x, 5x are the sides of the triangle.
⇒ 3x + 4x + 5x = 600
12 x = 600
x = 50
Therefore,
3x = 3(50) = 150
4x = 4(50) = 200
5x = 5(50) = 250
Hence, the sides of the triangle are, 150m, 200m and 250m.
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Jerald i having drain iue at hi home and decide to call a plumber. The plumber charge $35 to come to hi houe and $60 for every hour they work. If the plumber charge Jerald a total of $305, how many hour did the plumber work?
Write and olve an equation to determine the number of hour worked by the plumber
The calculation for the plumber's total number of hours worked is 190 = 35 + 50x, where the result is 3.1 hours.
A linear equation is what?
It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
It follows that:
Jerald chooses to call a plumber after discovering a problem with his home's drains.
The plumber bills him $35 to visit his home and $50 per hour of work.
Suppose there are x hours in a day:
190 = 35 + 50x
50x = 155
x=3.1 hours
As a result, the answer to the question of how many hours the plumber worked is 190 = 35 + 50x, which is 3.1 hours.
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Find measure vzw pls helppppp
VZW=64
Step-by-step explanation:
Since the lines are straight the angles are equal. 2x+32=3x+16
Solve this for x.
32=x+16
16=x
Put the value for x (16) in to one of the angle equations
2(16) + 32 = 32 + 32 = 64
What is the value of negative 7 divided by 5?
Answer:
-7/5 or -1.4
Step-by-step explanation:
Given f(x) = -11x² + 5, what is the value of f(4)?
Answer: f(4) = -171
Step-by-step explanation:
To answer this question, we will solve the function for 4. In other words, we will input 4 into the function and simplify. Don't forget the order of PEMDAS when simplifying.
Given:
f(x) = -11x² + 5
Input of 4:
f(4) = -11(4)² + 5
Raise to the power of 2:
f(4) = -11(16) + 5
Multiply:
f(4) = -176 + 5
Add:
f(4) = -171
A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 50 meters and a standard deviation 100 meters. What is the probability that the measured distance will be smaller than the true distance?.
The likelihood that the measured distance will be shorter than the actual distance is equal to 0.3085.
In this case, the chance that the measured distance will be less than the true distance will be determined using the z-score formula. The z score is a normal score that adheres to a normal distribution with a mean and standard deviation of 0 and 1, respectively.
Given that,
Mean, μ = 50
Standard deviation, σ = 100
Less than 0% of the time, the overestimation is likely.
Consequently, the necessary probability is P (X ≤ 0)
Now,
P (X ≤ 0) = P [(X − μ) / σ ≤ (0 − μ) / σ]
P (X ≤ 0) = P [Z ≤ (0 − 50) / 100]
P (X ≤ 0) = P [Z ≤ − 0.5]
Excel formula for the probability mentioned above:
=NORMDIST(-0.5,0,1,1)
P (X ≤ 0) = 0.3085
0.3085 is the likelihood that the measured distance will be shorter than the actual distance.
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Write the equation of the line in fully simplified slope-intercept form.
go
9
876
8
5
10 %
4
321
-12-11-10-9-8-7-6-5-4-3-2-1
-1
-2
2 3 750 0
-3
-4
-5
-6
5999 2
-7
-8
-9
-11
-12
1 2 3 4 5 6 7 8 9 10 11 12
The equation of the line in fully simplified slope - intercept form is 5x + y = 8 .
In the question ,
a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .
to find the equation , we need minimum two points ,
So , from the graph
we can see that
when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 8 ,
the first point is (0 [tex],[/tex] 8) .
when x [tex]=[/tex] 2 , the value of y [tex]=[/tex] -2 ,
the second point is (2 [tex],[/tex] -2) .
the slope can be calculated by
slope = (-2-8)/(2-0)
= -10/2
= -5
So , the equation of the line passing through point (2,-2) with slope -5 , in the slope intercept form is
(y -(-2)) = -5(x-2)
y + 2 = -5x + 10
Simplifying further , we get
5x + y = 10 - 2
5x + y = 8
Therefore , The equation line in fully simplified slope - intercept form is 5x + y = 8 .
The given question is incomplete , the complete question is
Write the equation of the line in fully simplified slope-intercept form, the line graph is shown below .
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WORTH 15 POINTS!
what is the cycle? please list in order.
tysm
The cycle in order is D, E, F, B, C then A.
Define life cycle.
An organism goes through a series of shape changes in a biological life cycle before reverting to its original state. The notion contrasts with those of life history, development, and ontogeny in that it emphasizes renewal. Life cycles are common to all animals and plants.
The stages, which frequently entail beginning as a seed, egg, or live birth, then growing up and reproducing, are best shown visually using diagrams. Life cycles keep repeating themselves.
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Find the total amount given the original price and tax rate. Round to the nearest cent if necessary. $31.69, 6%
The total amount given the original price and tax rate is $33.59
How to determine the total amount?From the question, we have the following parameters:
Original price = $31.69
Sales tax rate = 6%
In order to determine the total sales amount, we make use of the following total sales equation
Total sales = original price + original price * sales tax rate
Substitute the known values in the above equation
So, we have the following equation
Total sales = 31.69 + 31.69 * 6%
Evaluate
Total sales = 33.59
Hence, the total amount is $33.59
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A local candy shop sells boxes of chocolate for $3.75 each. If a customer purchases six or more boxes, the cost is only $3.25 per box, plus the customer has an additional $5 fee per order. C(x) represents the total cost and x represents the number of boxes, which can be modeled by the function below.
A piecewise function c of x in two pieces. The function is defined by part 1, which is 3 point 75 times x for x greater than 6, and part 2, which is 3 point 25 times x plus 5 for x is greater than or equal to 6.
Predict the cost of an order with 6 boxes.
$14.50
$22.50
$24.50
$27.50
Answer:
$24.50
Step-by-step explanation:
In order to predict the cost of an order with 6 boxes, x has to be equal to 6.
So we have to use the function 3.25x + 5 for [tex]x\geq 6[/tex].
Then, plug in 6 for x and solve.
3.25(6) + 5 = 19.50 + 5 = 24.50
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The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
As we know that the perimeter of rectangle
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
From the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.
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−0.25 + 316 + 2112? what is the answer to this and how did i solve it?
Answer:
Step-by-step explanation:
2427
Segment RS is reflected over the line y = x and then translated by (x+3, y + 4). The resulting segment
RS" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
The original coordinates are R= (-6,-6) and S = (-4,0)
What is translation?
Translation in mathematics is a property in which we shift each coordinate on a line by a constant value.
We are given that we originally had a segment RS which is reflected over the line y = x and then translated by (x+3, y+4) after this the segment we get the coordinates are R'' (-1,4) and S( -3,-2)
We are asked to find the coordinates of R and S
To find the coordinates we first reverse the process we subtract 3 from both x coordinate and 4 from both y coordinate
Hence we get,
R' = (-1,4)-(3,4)
R' = (-4,0)
And
S' = (-3,-2)-(3,4)
S' = (-6,-6)
Now to find the original coordinates we reverse the coordinates
Hence we get,
R= (-6,-6) and S = (-4,0)
Therefore the coordinates are R= (-6,-6) and S = (-4,0)
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2. Write 420 as a product of prime numbers.
Answer:
As a product of prime numbers:
420 = 2 × 2 × 3 × 5 × 7
Find the Area of the figure below, composed of a parallelogram and two semicircles. Round to the nearest tenth place.
Answer:
550.4 square units.
Step-by-step explanation:
This problem is easier than it seems.
To find the area of the parallelogram, multiply 11 and 32 to get 352 sq. units
The two semicircles must be equal because the sides of a parallelogram must be equal.
So if you add the semicircles together, you get a circle.
So we're really finding parallelogram+circle.
The area of a circle is [tex]\pi[/tex]x[tex]r^{2}[/tex], and the circle's radius is 8 because the radius is half of the diameter.
[tex]\pi[/tex]≈3.1 because you're rounding to the nearest tenth.
3.1x64=198.4 sq. units
198.4+352=550.4 square units.
help plss!!!
Based on the tables showing the price of buying different amounts of two brands of sugar. Suman determined that Sweet Sugar was the better buy based on price alone. How much money per pound will Suman save if he buys the Sweet Sugar brand?
Answer: b
Step-by-step explanation:
Answer:
He will save 1 cent per pound if he buys the Sweet Sugar brand
the robots are powered coffee alone. They use 2 bags of coffee each day. how long will 1/4 of a bag last them?
Answer:
3 hours
Step-by-step explanation:
The robots are powered coffee alone. They use 2 bags of coffee each day. how long will 1/4 of a bag last them?
1/4 = 0.25
0.25 / 2 = 1/8 or 0.125
0.125 * 24 hours = 3 hours
Simplify each expression. select the correct answer from the dropâ€""down menu. −6(3i)(−2i) = 2(3 − i)(−2 4i) = 2i(4 − 5i) =
By simplifying each expression:
−6(3i) (−2i) = -36
2(3 − i)(−2 + 4i) = -4+28i
2i(4 − 5i) = 10+8i
Simplifying each expression step by step:
1. −6(3i)(−2i) = -6 (-6i²)
= 36 (-1)
= -36
2. 2(3 − i)(−2 + 4i)
= 2 x (-6+12i+2i-4i²)
= -12 +24i +4i - 8i²
= -12 - 8i² +28i
=-12 - 8 (-1) + 28i
= -4+28i
3. 2i(4 − 5i)
= 8i - 10i²
= 8i -10(-1)
= 10+8i
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Solve the equation for y
Answer:
y = [tex]\frac{2}{3}[/tex] x - 6
Step-by-step explanation:
y - [tex]\frac{2}{3}[/tex] x = - 6 ( isolate y by adding [tex]\frac{2}{3}[/tex] x to both sides )
y = [tex]\frac{2}{3}[/tex] x - 6
1/4(12k-4) ''simplify''
Using the distributive property, the simplified form of the expression 1/4(12k-4) is 3k-1.
In the given question we have to simplify the given expression.
The given expression is 1/4(12k-4).
To simplify the given expression we use the distributive property.
According to property; a(b+c) = ab+bc
Now simplifying the expression;
1/4(12k-4) = 1/4*12k-1/4*4
1/4(12k-4) = 3k-1
Hence, the simplified form of the expression 1/4(12k-4) is 3k-1.
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