Answer:
≈ 68.8530
Step-by-step explanation:
You want the area between the curves y = 12 -2x² and y = x² -8.
AreaThe area will be the integral of the difference between the curves, between the points where the curves intersect.
h(x) = (12 -2x²) -(x² -8) = 20 -3x² . . . . . height of a differential of area
The point where the curves intersect has an x-value that makes h(x) = 0. We choose to call the positive value 'a'. The curves also intersect at x=-a.
h(a) = 0
20 -3a² = 0
a² = 20/3
a = √(20/3) = (2/3)√15
So, the integral is ...
[tex]\displaystyle A=\int_{-a}^a{(20-3x^2)}\,dx=\left(20x-\dfrac{3x^3}{3}\right)_{-a}^a\\\\A=2a(20-a^2) = \dfrac{4}{3}\sqrt{15}\cdot\left(20-\dfrac{20}{3}\right)\\\\A=\boxed{\dfrac{160\sqrt{15}}{9}\approx68.8530}[/tex]
The area between the curves is about 68.8530 square units.
5 subtract from 9 as an expression
The statement "5 subtract from 9" as an expression is 9 - 5
How to represent the statement as an expressionFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
5 subtract from 9
Subtraction means minus
So, we have the following representation
5 subtract from 9 = 9 - 5
The question does not require that we solve the expression
So, we leave it at 9 - 5
Hence, the required expression is 9- 5
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6. Sue purchased a car for $18,000 three years ago. If the car depreciates at a rate of 20% per year, the value of the car now is
By writing and evaluating an exponential equation, we can see that the value of the car now is $9,216.
What is the value of the car now?
We know that the initial value of the car is $18.000, and the value depreciates at a rate of 20% per year.
If we define x as the number of years since the car was bought, we can write the value equation as:
V(x) = $18,000*(1 - 20%/100%)^x
V(x) = $18,000*(1 - 0.2)^x
V(x) = $18,000*(0.8)^x
The value of the car after 3 years is what we get if we evaluate the exponential equation in x = 3.
V(3) = $18,000*(0.8)^3
V(3) = $9,216
That is the value of the car now.
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Anil's age is 5 years LESS than Balu's age. Chandu's age is 3 years MORE than Balu's age. If Anil's age is ♦ years, which of the following expressions gives Chandu's age
♦-5-3
♦+5-3
♦-5 +3
♦ +5 + 3
Answer:
+5 + 3 = 8
Step-by-step explanation:
Question 5(Multiple Choice Worth 1 points)
(06.01 LC)
Choose the expression that represents a linear expression.
6 x+6
-6 x²+8 x-9
8 x³+9 x²-10 x+11
7 x⁴-8 x³+9 x²-10 x+11
Answer:
Option a) 6x+6 is correct.
Step-by-step explanation:
Option a) 6x+6 is correct.
The given expression 6x+6 represents a linear expression.
Step-by-step explanation:
Definition: Linear expression is a mathematical statement defining an equality. It is usually a polynomial equation having degree 1. It can be written as linear relationship with variables and a constant.
6x+6 expression represents a linear expression
Because it has degree 1.
Therefore Option a) 6x+6 is correct.
The given expression 6x+6 represents a linear expression.
a) 6x+6
The given expression 6x+6 represents a linear expression.
Definition:
Linear expression is a mathematical statement defining equality. It is usually a polynomial equation having a degree of 1. It can be written as a linear relationship with variables and a constant.
6x+6 expression represents a linear expression.
Because it has degree 1.
Therefore, a) 6x+6 is correct.
The given expression 6x+6 represents a linear expression.
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267 divided by 742
•
________
•
Answer:::
267 divided by 742
is
0.35983827493
rounded off to 0.36
I want to buy a new sofa from the store. I open a savings account with $700
and save up another $50 weekly. I need to save
a minimum of $1,200 to buy the sofa. Write an
inequality to represent this situation.
Answer:
700 + 50x ≥ 1200
where x represents the number of weeks needed to save.
Step-by-step explanation:
Check the picture below.
whatever those savings are on week "x", they have to be at least $1200
700 + 50x ⩾ 1200The graph of a function is shown. What is the function type?
The type of function that is shown in the given graph image is called a; Cubic Function
How to identify the graph function?The vertical line test is a tool in graph functions that is very important when we are trying to determine the function that a specific graph represents. Now, we can further say that the vertical line is typically one that includes all points alongside a specific x-value with the y-value of a point that a vertical line will intersect a graph to represent an output for that particular input x value.
Now, there are different types of graphs and they all depend on the particular type of function that is being graphed. The eight most popular graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each of the types of graphs are usually unique which means that is easy to visually differentiate from the rest.
In this given graph, we can see that the graph shows an image that corresponds to a cubic function because of the classical infinite branches, then the three real roots and then the two extrema values
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23 A commuter train moves from station A to D via B and C in that order, the distance to C via B is 70km and that of B to D via C is 88km. Between stations A and B the travels at an average speed of 48km/h and it takes 15minutes. The average speed of the train between C and D is 45km/h. Find; a) Distance between B and C b) Time taken between C and D c) If the train halts at B for 3 minutes and at C for 4 minutes and average speed for the whole journey is 50km/h. Find its average speed between B and C
The Distance between B to C = 58 km,
distance between C to D = 30 km
Average speed between B to C = 59.79 km/h
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
Given A commuter train moves from station A to D via B and C,
distance from A to C via B = 70 km
distance from B to D via C = 88 km
av. speed of the train from A to B = 48 km/h
av. speed of the train from C to D = 45 km/h
time taken by train to reach B = 15 min = 15/60 = 0.25 hour
distance between A to B = speed x time from A to B
distance between A to B = 48 x 0.25
distance between A to B = 12 km
A. Distance between B to C = distance from A to C - distance between A to B
Distance between B to C = 70 - 12 = 58 km
B. distance between C to D = distance from B to D - Distance between B to C
distance between C to D = 88 - 58 = 30 km
C. let av. speed from B to C is x
total distance covered by train = 12 + 58 + 30 = 100 km
av. speed for journey = 50 km/h
time taken to complete journey = 100/50 = 2 hours
time is taken from A to B = 0.25 hour
time is taken from B to C = 58/x
Time is taken from C to D = 30/45 = 0.66 hour
halt at b = 3 minute and halt at C = 4 minute
total halt = 3 + 4 = 7 minute = 7/60 = 0.12 hour
Total time = time taken from(A to B + B to C + C to D) + total hault
2 = 0.25 + 58/x + 0.66 + 0.12
58/x = 0.97
x = 59.79 km/h
Hence The Distance between B to C = 58 km,
distance between C to D = 30 km
Average speed between B to C = 59.79 km/h
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Solve the system by graphing and write your answer as an ordered pair . y=3x-4 . y=-1/2x+3
This system of equations has been solved graphically and its solution is equal to the ordered pair (2, 2).
What is a graph?In Mathematics, a graph refers to a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection of the lines on the graph;
y = 3x - 4 ........equation 1.
y = -1/2x + 3 ........equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (2, 2).
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The graph of the system of linear equation is attached below with solution of x, y as (2, 2)
What is Graph of system of linear equationA graph of a system of linear equations is a set of lines (or a line in case of a unique solution) on a coordinate plane that represent the solutions of the system. The graph of a system of linear equations can have different types of solutions depending on the number of lines and the relationship between them.
In this problem, we will use a graphing calculator to plot the equation and find the point of intersection which is the solution to the graph.
y = 3x - 4y = -1/2x + 3The point of intersection which shows the solution (x,y) of the system of linear equation is at (2, 2)
Kindly find the attached graph below as solution.
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Which equation represents the relationship shown in the graph?
A coordinate grid is shown with points plotted at left-parenthesis 2 comma 4 right-parenthesis, left-parenthesis 4 comma 8 right-parenthesis, left-parenthesis 6 comma 12 right-parenthesis, and left-parenthesis 8 comma 16 right-parenthesis.
The equation of the proportional relationship is y = 2x.
How to find equation of proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.
Therefore, the proportional relationship can be represented as follows:
y ∝ x
y = kx
where
k = constant of proportionalityusing (2, 4)
y = kx
4 = 2k
k = 4 / 2
k = 2
Therefore, the equation is y = 2x.
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prove that there is a 1-1 correspondence between the set of all positive integers and the set of all rational numbers
A one-to-one correspondence between the set of all positive integers and the set of all rational numbers exists.
By definition, any rational number can be expressed as a fraction a/b, where a and b are integers and b is nonzero. Since any positive integer can be expressed as the fraction a/1, each positive integer can be associated with a rational number a/1.
Thus, there is a one-to-one correspondence between the set of all positive integers and the set of all rational numbers. Furthermore, since any rational number a/b can be expressed as the product of a and b, it can also be associated with the product of two positive integers a and b.
Thus, there is also a one-to-one correspondence between the set of all rational numbers and the set of all positive integers.
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Find the slope of the following graph and choose the correct result.
A : 1/4
B : 1/3
C : 1/5
D : 2/3
Answer:
1/3
Step-by-step explanation:
Slope = Rise/Run
We are rising 1 and running 3 on the graph
Solve the system of equations using elimination: 7x + 4y = -9 and
-5x - 3y = 7.
For the provided functions 7x + 4y = -9 and -5x - 3y = 7, the values of x and y are 1 and -4, respectively.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given the system of equations using elimination: 7x + 4y = -9 and
-5x - 3y = 7.
From equation 2
-5x - 3y = 7
calculate the value of x in the function of y
-5x = 7 + 3y
x = (-7 - 3y)/ 5
Substituting this value in equation 1
7/5(-7 - 3y) + 4y = -9
y = -4
substituting this value in equation 1
7x + 4(-4) = -9
x = 1
Therefore, the values of x and y the given functions 7x + 4y = -9 and
-5x - 3y = 7 are 1 and -4 respectively.
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Question 1 (Multiple Choice Worth 1 points)
A triangle has a perimeter of 9x+6. The first side of the triangle has a length of 5 x and the second side has a length of 3x-7. What a the length of third side of the triangle?
x+13
x-1
5 x-7
17 x-1
The length of third side of the triangle will be A. x + 13.
How to illustrate the perimeter?The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
In this situation, triangle has a perimeter of 9x+6. The first side of the triangle has a length of 5 x and the second side has a length of 3x-7.
The length of third side of the triangle will be:
= 9x + 6 - (3x - 7 + 5x)
= x + 13
The correct option is A.
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Consider a standard deck of 52 playing cards with 4 suits.
If A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck, what is the intersection of A and B?
(Remember that the black cards are spades and clubs.)
A) drawing a 6, a heart, or a diamond
B) drawing a 6, a club, or a spade
C) drawing the 6 of clubs or the 6 of spades
The intersection between A and B in a deck of 52 playing cards is option B, drawing a 6, a club, or a spade.
What is the intersection of two sets?In a standard deck of 52 playing cards with 4 suits
Event A is drawing a 6 from the deck
Event B is drawing a black card from the deck
Therefore A will have 4 possibilities of cards with 6 on them
B will have a total of 26 possibilities of black playing cards with both clubs and spade.
The intersection of A and B will be drawing a 6 or a black card(a club, or a spade) as the common elements in the two sets. Therefore, drawing a 6, a club, or a spade.
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground to the nearest tenth of a foot. y=-16x^2+261x+130
The time that the rocket will hit the ground to the nearest tenth of a foot is 17 secs.
How can the time be calculated?We were given the equation as y=-16x^2+261x+130 , thene we can equate this to zero. as
0=-16x^2+261x+130
from this we can see that this is a quadratic equation, where a= -16, b=261, c =130
Then input into the quadratic formular we have:
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
Then if we input the values we have [tex]x=\frac{-261+-\sqrt{261^{2}-4*-16*130} }{2*-16}[/tex]
Then the value of x are: -0.49 and 16.79
The positive value is the time that the rocket will hit the ground. Therefore, the rocket will hit the ground after 16.79 secs.
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The table below shows some values of a function g(x)
Which function represents the relationship shown in the table?
g(x) = 4x - 1/2
g(x) = -3x - 1/2
g(x) = -1/2x - 1/2
g(x) = 3x - 1/2
The linear function in the table is given as follows:
g(x) = 4x - 1/2.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the output variable y relative to the input variable .b is the intercept, representing the value of y when x = 0.When x increases by 0.5, y increases by 2, hence the slope m is obtained as follows:
m = 2/0.5
m = 4.
When x = 0, y = -0.5, hence the intercept b is given as follows:
b = -1/2.
The function is then defined as follows:
g(x) = 4x - 1/2.
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lim x tends infinity, (2/3)^x = ?
The limit lim x → ∞ (2/3)ˣ = ∞
What are limits?A limit is the value of a function as the independent variable tends to a particular value.
How to find the given limit?Since we have lim x → ∞ (2/3)ˣ, to find this limit, using the fact that lim x → a ㏑f(x) = ㏑[lim x → a ㏑f(x) ]
So, since lim x → ∞ (2/3)ˣ, taking natural logarithm of both sides, we have that
lim x → ∞ (2/3)ˣ
㏑[lim x → ∞ (2/3)ˣ] = lim x → ∞ ㏑(2/3)ˣ
= lim x → ∞ x㏑(2/3)
So, substituting x = ∞ into the equation, we have that
lim x → ∞ x㏑(2/3) = ∞㏑(2/3)
= ∞
So, lim x → ∞ (2/3)ˣ = ∞
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Amanda swims 40 meters per minute. She uses
the inequality below to calculate how many
minutes, m, it takes her to swim at least 1,500
meters.
40m ≥ 1, 500
Which set of numbers makes the inequality true? A. {24, 25, 37.5}
B
{25, 28.5, 37}
C {37, 39, 40.5}
D. (37.5, 42, 43.5}
(37.5, 42, 43.5} is the set of numbers that makes the inequality true
How to determine which set of numbers makes the inequality true?
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
Given that:
Amanda uses the inequality below to calculate how many minutes, m, it takes her to swim at least 1,500 meters.
40m ≥ 1, 500
To determine which set of numbers makes the inequality true, solve for m and check the pick that contains the values greater than or equal to m:
40m ≥ 1, 500
m ≥ 1, 500/40
m ≥ 37.5
Thus, the set of numbers that makes the inequality true is (37.5, 42, 43.5}
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Determine the point estimate of the population mean and margin of error for the confidence interval. The lower bound is 17, upper bound is 25. What is the point estimate of the population mean?
The point estimate of the population mean is 21.
The point estimate of the population mean is the midpoint of the confidence interval.
To find the midpoint, add the lower and upper bounds of the interval and divide by 2. In this case, the lower bound is 17 and the upper bound is 25, so the point estimate of the population mean is (17 + 25) / 2 = 21.
On the other hand, the margin of error is a measure of the precision of the estimate. It is the amount by which the estimate could be off and still be considered accurate. The margin of error is typically expressed as a percentage of the point estimate. In this case, the margin of error would depend on the level of confidence you have in the estimate and the size of the sample you used to generate the interval. Without more information, it is not possible to determine the margin of error.
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4. Chrissy had 4 gallons of gas in her tank when she arrived at the gas
station. She pumped gas into her car at a rate of 3/10 gallon per
second. How many gallons of gas were in the tank after s seconds?
I need Helpp asap please
HELP ME PLEASEEE
Andrew buys 8 pounds of apples for $12.00. He wants to know and use the unit rate of the cost per pound.
True or False: The unit price is $1.45 per pound.
Answer:
False
Step-by-step explanation:
$1.45 * 8= $11.6.
The right unit price would be $1.50
I think
Answer:
false 1.5 is correct
Step-by-step explanation:
so the answer is 8 divided by 12.00 and it is false the answer is 1.5
Stephanie has 6 classes a day. Each class is 52 minutes. She goes to school 5 days a week. How much time does she spend in class? Show two different ways to solve this problem
Time spent in class per week is 6 × 52 × 5 = 1560 minutes.
Time spent in class per day is 6 × 52 = 312 minutes.
How to determine how time does she spend in class?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Since Stephanie has 6 classes a day. Each class is 52 minutes. She goes to school 5 days a week. The time she spend in class can written as:
time in class = 6 × 52 × 5 = 1560 minutes per week
The time can also be written in form of the time spent per day:
time in class = 6 × 52 = 312 minutes per day
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Please answer quickly!!!!
Answer: y int is 8 the slope of the line is -1/2 and the equation of the line is y=-1/2x +8
Step-by-step explanation:
you can get slope by using the the points (6,5) and (8,4) to use y2-y1/x2-x1 and your y int is just where the line intersects the y axis which is 8. 8 then equals b in the equation y=mx+ b and you get m by using the first equation.
4. A bus drives 1 mile west and 4 miles north. Sketch the path of the bus and find the straight line distance and angle from the bus's location to its starting point. (Hint: Use Tan¹ to find the angle whose Tangent is 4/1)
The distance of the straight line is √17 miles and the angle formed is
75.96°.
We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A bus drives 1 mile west and 4 miles north.
Let, The distance the bus travels along the west be adjacent and the distance traveled in the north be the height.
So, By Pythagoras' theorem,
The straight line distance = √(1² + 4²).
= √(1 + 16) miles.
= √17 miles.
Now, We know tan = opposite/adjacent.
tan = 4/1.
tan⁻¹(4/1) = Ф.
Ф = 75.96°.
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If a || b and m∠2 = 71°, what is m∠1?
(4/5) divided by (3/4)
Answer:16/15
1 and 1/15
Step-by-step explanation:
4/5 x 4/3
The population (in millions) of a certain country can be modeled by the exponential equation P=3.5(1.4)x where x represents the amount of decades since 1800. Find P(8)
A. 6.86 million
B. 1,715.18 million
C. 51.65 million
D. 74.83 million
E. 26.52 million
F. 65.92 million
G. 331 million
The value of the function P(8) given that P(x) = 3.5(1.4)ˣ is (c) 51.65 million
How to determine the value of the function P(8)From the question, we have the following parameters that can be used in our computation:
An exponential function
The equation of the exponential function is then given as
P=3.5(1.4)x
Express properly
So, we have
P(x) = 3.5(1.4)ˣ
where x represents the amount of decades since 1800
From the question, we have
x = 8
Substitute the known values in the above equation, so, we have the following representation
P(8) = 3.5(1.4)⁸
Evaluate the expression
P(8) = 51.65261696
Approximate
P(8) = 51.65
Hence, the value of P(8) is (c) 51.65 million
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What is the distance between the points (-3, 8) and (16, 8)?
Distance: 19
Steps:
Distance (d) = √(16 - -3)2 + (8 - 8)2
= √(19)2 + (0)2
= √361
= 19
Jaylen's parents own a chocolate shop, and today he gets to help make the nut truffles. Each truffle starts with one of 2 kinds of nuts and is dipped in one of 6 kinds of chocolate. The truffle is then drizzled with one of 4 sauces. The finishing touch is one of 2 candied garnishes.
How many different nut truffles can they make?
Answer:
96
Step-by-step explanation:
2 x 6=12
12 x 4= 48
48 x 2=96