Answers
The image by rotation of the triangle ABC with vertices A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) is represented by vertices A'(x, y) = (- 9, - 8), B'(x, y) = (- 4, - 5) and C'(x, y) = (- 1, - 7). The transformation rule is R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ).
How to find the transformation rule and image of a given figure
In this problem we have the case of triangle set on a Cartesian plane and that must be rotated 90° clockwise, the image can be found by using the following transformation rule:
R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.
θ - Angle of rotation, in degrees.
If we know that A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) and θ = - 90°, then the image of the triangle is:
A'(x, y) = (8 · cos (- 90°) - (- 9) · sin (- 90°), 8 · sin (- 90°) + (- 9) · cos (- 90°))
A'(x, y) = (- 9, - 8)
B'(x, y) = (5 · cos (- 90°) - (- 4) · sin (- 90°), 5 · sin (- 90°) + (- 4) · cos (- 90°))
B'(x, y) = (- 4, - 5)
C'(x, y) = (7 · cos (- 90°) - (- 1) · sin (- 90°), 7 · sin (- 90°) + (- 1) · cos (- 90°))
C'(x, y) = (- 1, - 7)
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Related Questions
Substitutions this equation
8x-y=-6
2x-3y=4
Answers
Make y the subject of the first equation
8x + 6 = y
Substitute for y in the second equation
2x - 3(8x + 6) = 4
2x -24x - 18 = 4
-22x = 4 + 18 = 22
x = 22/-22 = -1
y = 8 x -1 + 6
y = -8 + 6
y = -2
Sketch a cone with diameter of 16 feet and height of 10 feet, then find the volume. If needed, round to the nearest hundredth.
Answers
The volume is 2679.46ft^3.
What is volume?
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
We know that
The volume of the cone is equal to
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
where
r is the radius of the circular base of the cone [tex]$\mathrm{h}$[/tex] is the height of the cone
we have
[tex]$$\begin{aligned}& r=16 f t \\& h=10 f \mathrm{t}\end{aligned}$$[/tex]
assume
[tex]\pi=3.14[/tex]
substitute the values
[tex]$$\begin{aligned}& V=\frac{1}{3}(3.14)(16)^2(10) \\& V=2679.46 f t^3\end{aligned}$$[/tex]
The drawing in the attached figure
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Simplify (m^6n)^3.
mn^21
m^9n^3
m^18n
m^18n^3
Answers
After solving the given expression, the value obtained is [tex](m^1^8^n)[/tex]. Hence, option C is correct.
What is Simplification?To streamline a phrase, one must use many techniques to make it shorter and simpler. The actions needed to reduce things are carried out in a predetermined sequence known as BODMAS.
Minimize a fraction to its simplest form to make it simpler. A fraction is said to be in its simplest form if both its numerator and denominator only include the integer.
As per the given information in the question,
The expression is,
[tex](m^6^n)^3[/tex]
= [tex](m^1^8^n)[/tex]
Therefore, option C is correct.
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Find the slope Y intercept in the equation for the data in the table and in the graph
Answers
Answer:
slope 6
y intercept 4
y = 6x + 4
Step-by-step explanation:
The slope is the change in y over the change in x.
Look at he two points (0,4) and (1,10)
The y started at 4 and went up to 10. That is a distance of 6.
AT the same time, the x changes from 0 tp 1 (0,4) (1,10). That is a distance of 1.
6/1 = 6
The y intercept is where the line crosses the y axis. It crosses at (0,4). 4 is the y intercept
y = mx + b Put the slope is for m and the y intercept for b
y = 6x + 4
An interior designer is designing a room. Her options include 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures. How many
different room designs can be created from these options?
Answer
Answers
The total number of different room designs is 1296.
What is the fundamental principle of counting?According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.
Given that, there are 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures.
As per the basic principle of counting, the total number of different room designs is:
6 × 4 × 6 × 3 × 3
= 1296
Hence, the total number of different room designs is 1296.
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The classroom outside bag had 5 frisbees in it. If 25% of the outside toys are frisbees, then how many total toys are in the bag?
Answers
The Christmas lights on the tree and the lights on the porch blink at a consistent rate. The tree lights blink every 4 seconds which the porch lights blink every 6 seconds after how many second will they blink together
Answers
Answer:
The tree lights and the porch lights will blink together every 12 seconds.
Step-by-step explanation:
In order to determine when the two sets of lights will blink together, you must find the least common multiple (LCM) of the time periods for each set of lights. The LCM of 4 and 6 is 12, which means that the tree lights and the porch lights will both blink again after 12 seconds have passed. Therefore, they will blink together every 12 seconds.
help meeeeeeeeeee pleaseee
Answers
The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.
What is barometric air pressure?In essence, atmospheric pressure is the force that the weight of the air above a particular point on the Earth's surface exerts at that location.
In other words, the weight of the air molecules as a whole determines the atmospheric pressure, which is produced by the air that surrounds the Earth.
Lower pressure is felt by air molecules at higher altitudes because there are fewer molecules pressing down on them from above, while higher pressure is felt by air molecules at lower altitudes because they are closer together and are under more pressure from molecules piled on top of them.
F(x) is the pressure in inches of mercury
It is given pressure 28 inches of mercury
Put F(x) equal to 28
F(x) = 0.48㏑(x+2) +27
28 = 0.48㏑(x+2) + 27
28-27= 0.48㏑(x+2)
1= 0.48㏑(x+2)
1/0.48= ㏑(x+2)
25/12= ㏑(x+2)
x+2= [tex]e^{\frac{25}{12} }[/tex]
x+2=8.03119
x=8.03119-2
x= 6.03119
x = 6(round off)
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which inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) on the boundary?
Answers
The second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
Given that, the zeros of the quadratic function are -7 and 1 and include the point (2,27/2).
Substitute x = 1 into the given inequality to check whether any of them becomes less than 0 or not:
From the first inequality:
y < -3/2 + 9 + 21/2
y < 18
From the second inequality:
y < 3/2 + 9 -21/2
y < 0
Since the inequality is less than 0, it is also less than the quadratic function at x = 1.
Similarly, checking the third inequality also gives y < 0, but the fourth doesn't.
Now, from the second and the third inequality, check which one is less than 27/2 for x = 2:
From the second inequality:
y < 6 + 18 -21/2
y < 27/2
From the third inequality:
y < -6-9+21/2
y < -27/2
Since the second inequality, y < (3/2)x² + 9x -21/2, is less than 0 at x =1 and less than 27/2 at x=2, it is also less than the quadratic function whose zeros are -7 and 1 and includes the point (2,27/2).
Hence, the second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
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Answer:
it’s B took the test
Step-by-step explanation:
Force An 8.0-pound weight is lying on a sit up bench at the gym. If the bench is
inclined at an angle of 15°, there are three forces acting on the weight, as shown
in Figure 12. Find the magnitude of N and the magnitude of F.
Answers
Answer: 7
Step-by-step explanation: 7+2
Solve for a
2x-2=-3x+13
X =
Answers
To solve for x, we need to isolate x on one side of the equation. To do this, we can first move all the terms that do not contain x to the right side of the equation by adding 3x and 2 to both sides:
2x - 2 + 3x + 2 = -3x + 13 + 3x + 2
5x = -3x + 15
8x = 15
Dividing both sides by 8, we get:
x = 15/8
= 1.875
Therefore, the value of x is approximately 1.875.
The value of x in equation 2x-2= -3x+13 is 3
To solve this equation we need to find the value of x so that all x terms should be one side and all constants should be at ones side:
2x+3x=13+2
5x=15
Now divide both side with 5 then, we get:
5x/5=15/5
x=3
Therefore, the value of x is 3
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Find the domain and solve 2*4^(sqrt(5x^2-8x)+1)+4=33*2^(sqrt5x^2-8x)
Answers
To find the domain of the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we need to consider the values of x for which the expression is defined.
First, we need to consider the square root term, sqrt(5x^2-8x). The square root of a number is only defined for nonnegative values, so we need to find the values of x for which 5x^2-8x is nonnegative. We can do this by setting 5x^2-8x equal to 0 and solving for x:
5x^2-8x=0
5x(x-8)=0
We can see that x=0 and x=8 are the solutions to this equation. Since the square root of a negative number is not defined, the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is only defined for x values that are greater than or equal to 0 and less than or equal to 8. This means that the domain of the expression is x ∈ [0, 8].
To solve the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we can start by isolating one of the exponential terms on one side of the equation. Let's isolate the term 2^(sqrt(5x^2-8x)):
24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x))
22^(2sqrt(5x^2-8x)+1)=332^(sqrt(5x^2-8x))
2^(2sqrt(5x^2-8x)+1)=16.52^(sqrt(5x^2-8x))
2sqrt(5x^2-8x)+1=4.5+sqrt(5x^2-8x)
sqrt(5x^2-8x)=3.5
5x^2-8x=12.25
5x^2-8x-12.25=0
We can use the quadratic formula to solve this equation for x:
x = (-(-8) ± sqrt((-8)^2 - 45(-12.25))) / (2*5)
x = (8 ± sqrt(64 + 97)) / 10
x = (8 ± sqrt(161)) / 10
x = (8 ± sqrt(289)) / 10
x = (8 ± 17) / 10
x = -9/10 or 25/10
Since x must be greater than or equal to 0 and less than or equal to 8, the only solution that is within the domain of the expression is x=25/10, or x=2.5.
Therefore, the solution to the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is x=2.5.
what do you mean by domain of a function?
The domain of a function is the set of all input values for which the function is defined. In other words, it is the set of all values that can be plugged into the function as an argument, or input, and produce a valid output
For example, consider the function f(x) = x^2. The domain of this function is all real numbers, since the function is defined for any value of x. However, some functions may not be defined for certain values of x. For example, the function g(x) = 1/x is not defined for x=0 because division by zero is not allowed. In this case, the domain of the function g(x) would be all real numbers except for x=0.
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determine the sum of all the multiples of the first integer from the last problem or the second integer from the last problem - below 1000
Answers
The total of all multiples of either the first or second integer from the previous issue that are below 1000 will be 233168.
What is multiples of integer?Manifold is the fundamental definition of multiplicity. A multiple in mathematics refers to the outcome of multiplying two numbers together. In mathematics, multiples are the results of multiplying an integer by a given number. A number that is produced by multiplying a given integer by a natural number is referred to as a multiple of that number. The factors of 20, for instance, are 1, 2, 4, 5, 10, and 20. The multiples of 20 include, for instance, 20, 40, 60, 80, 100, etc.
Here,
The statement of the problem is to sum the multiples of 3 and 5 below 1000, not up to and equal 1000.
The equation is attached in image,
166833+99500−33165=233168
The sum of all the multiples of the first integer from the last problem or the second integer from the last problem - below 1000 will be 233168.
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Old Faithful in Yellowstone National Park has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is normally distributed with a standard deviation of 21.25 minutes. What is the probability that a randomly selected sample of 35 time intervals between eruptions has a mean longer than 95 minutes?
Answers
The probability that the randomly selected time interval is longer than 95 minutes while solving for the mean time of the eruptions is 0.3192.
How to solve for the probability of a ramdom sample?mean of x = 85 minutes
σ = 21.25 minutes
x ~ N(σ², μ)
p(x < 95)
1-p(x≤95)
1 - p(z≤0.47)
Using the z table here
1-0.6808 = 0.3192
Probability of x > 95 = 0.3192
b. n = 20
from central limit theorem
1 - p (z < 2.1045)
1-0.99826 = 0.0174
1 - p (z < 2.58)
1-0.9951
= 0.0049
. What we can observe from these results is that as the sample increase is increasing from 1, 20 to 30, the probability keeps decreasing.e. The probability is very small so one has to be doubtful if they are a really the population mean or if it has to be more than that.
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Question Divide. 27÷655 Enter your answer by filling in the boxes. R
100 points and FREE BRAINLYEST IF YOU ANSWER WRONG I WILL ASK A ADIMIN TO DELETE YOUR ANSWER
Answers
Answer: 24. The remainder is 7
Step-by-step explanation:
A pre-paid phone company charges $17.75 as a monthly access fee and $0.13 per minute of calling time.
What will the monthly cost be if you make 176 minutes of calls this month?
Answers
Answer:
$40.63
Step-by-step explanation:
If the phone company charges $17.75 already, and each minute costs $0.13, then we can do an equation that looks something like this:
17.75 + (0.13 × 176) = total price
We need to figure out how much 0.13 multiplied by 176 is.
0.13 × 176 = 22.88
Now that we figured out that 0.13 multiplied by 176 is equal to 22.88, we need to add the monthly access fee.
22.88 + 17.75 = 40.63
The monthly cost will be $40.63.
The pattern below has been created by placing toothpicks together a) Find an expression for the total number of toothpicks in any set up b) How many toothpicks should there be in the 45th set up? Show your work.
Answers
For 45th set up 140 toothpicks are required.
What is Arithmetic Progression?A progression of numbers in which the difference between any two succeeding numbers is always a fixed amount is known as arithmetic progression (AP). It also goes by the name Arithmetic Sequence.
given:
For First Figure, 8 toothpicks are used
For Second Figure, 11 toothpicks are used
For Third Figure, 14 toothpicks are used
So, we get the series 8, 11, 14, ...
Now, for n= 45
Using Arithmetic Progression
[tex]a_{45} = a+ (45- 1) d[/tex]
= 8 + 44(3)
= 140
Hence, for 45th set up 140 toothpicks are required.
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Sue and her brother wanted to buy 25 pieces of candy for their family's stockings. They chose to buy Kit Kats and Skittles. After shopping they spent $ 20.70. Skittles
cost 80 cents each and kit kats cost 90 cents each. How many of each candy did they get at the store? Let s-skittles and k=kit kats.
Which systems of equations represents this situation?
Answers
Answer:
18 Skittles and 7 Kit Kats
Linear system of equations in two variables
Step-by-step explanation:
We a linear system of two equations which can be solved simultaneously
Total pieces of candy equation
s + k = 25 [1]
Total cost equation
0.8s + 0.9k = 20.70 [2]
Multiply [1] by 0.80
0.80s + 0.80k = 20 [3]
Subtract [3] from [2]
0.80s + 0.90k = 20.70
[tex]-[/tex]
0.80s + 0.80k = 20
[tex]\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots[/tex]
0.1k = 0.70
k = 0.70/0.10 = 7
In [1]
[tex]s + 7 = 25\\\\s = 25-7\\\\s = 18\\\\[/tex]
Answer: 18 Skittles and 7 Kit Kats
AB of rhombus ABCD passes through the point (6, 6) and is perpendicular to the graph of y=3/4x-11. CD is parallel to AB and passes through the point (-6, 10). Select the equation in slope-intercept form of the line that includes CD.
A. y=4/3x+2
B. y=-4/3x+2
C. y=-3/4x+2
D. y=3/4x+2
Answers
Answer: [tex]y=-\frac{4}{3}x+2[/tex]
Step-by-step explanation:
The slope of [tex]AB[/tex] is [tex]-4/3[/tex]. Thus, the slope of [tex]CD[/tex] is also [tex]-4/3[/tex].
Thus, the equation of [tex]CD[/tex] can be found as follows:
[tex]y-10=-\frac{4}{3}(x+6)\\\\y-10=-\frac{4}{3}x-8\\\\y=-\frac{4}{3}x+2[/tex]
Use the following function rule to find f(11).
f(x)=12|x+8|
f(11)=____
Answers
Answer:
f(11) = 228
Step-by-step explanation:
10. You are ordering shirts for the math club at your school. Short-sleeved shirts cost $ 8 each. Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts. The equation 8 x+20 y=200 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts. Graph the equation. Interpret the intercepts.
x-intercept:_____
y-intercept:_____
Answers
The x - intercept is (25, 0) and the y - intercept is (0, 10).
What is intercepts?
The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.
Put y = 0 and work out x to find the x-intercept.
Set x = 0 and work out y to find the y-intercept.
Given: You are ordering shirts for the math club at your school.
Short-sleeved shirts cost $ 8 each.
Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts.
The equation 8 x+20 y=200 models the total cost,
where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
To find the x - intercept plug y = 0 in the above equation.
⇒ 8x + 20(0) = 200
8x = 200
x = 25
So, the point becomes, (25, 0).
To find y - intercept plug x = 0 in the above equation.
⇒ 8(0) + 20y = 200
20y = 200
y = 10
So the point becomes, (0, 10).
Hence, the x - intercept is (25, 0) and the y - intercept is (0, 10).
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hi!! if someone could help me out and find the answer for number 17 i would appreciate it sm:) 100 points im just trying to get some of my work done by tomorrow
Answers
Answer: y=−2x+16
Step-by-step explanation:
[tex]\frac{1}{10} +\frac{7}{10}[/tex]
Answers
Answer given in the screenshot below. ↓
How much simple interest is made on an investment of $800 for 7 years at 6%
Answers
Answer:
$1,136
Step-by-step explanation:
The simple interest equation is A = P(1 + rt)P is the original amount invested (in this case, it is $800)r is the interest rate (in this case, it is 0.06 or 6%)t is the years (in this case, it is 7 years)
From here, we can just plug in the values into the equation to get 800(1 + 0.06 x 7) = $1136
Which is a strict inequality?
A. y>4
B. y≤4x+2
C. y≥x
D. y=−8x+3
Answers
The option that is a strict inequality is A. y>4
How can you tell if an inequality is strict?It should be noted that inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.
Inequalities involving < or ">" are considered "strict inequalities," whereas those involving "" or "" are not. If you "switch" the two sides of an inequality, you must then reverse the inequality symbol's direction. For example, because 4 5 is true, it follows that 5 > 4.
In conclusion, the correct option is A.
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The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 274 people entered the park, and the admission fees collected totaled 836.00 dollars. How many adults were admitted?
a. 209
b.170
c.104
Answers
Therefore in this question the solution of particular equation is 108 children and 175 adults in the amusement park on that particular day.
What is Equation ?When two expressions' values are set to be equal by a mathematical statement, that statement is known as an equation. To put it another way, it is a mathematical expression that means "this is equivalent to that." An equal sign, a mathematical expression, and a mathematical expression can all be seen on the left side of the symbol. The right ride of the equation frequently contains zero.
Let's first configure our system by giving x and y meaningful definitions. Let x be the total number of kids and y be the total number of adults.
Children cost $1.50, while adults cost $4.00. The number of kids, x, is multiplied by 1.5 to determine how much money a group of kids will cost. The 1.5x symbol stands for this. We will use 4y for adults, who must pay $4 to enter. On the specified day, $862 in total revenue was earned. We must add 1.5x and 4y to get at this sum.
1.5x + 4y = 862 equation required
Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.
x + y = 283
System of equations:
1.5x + 4y = 862
x + y = 283
Thus,
x + y = 283
y = 283 - x
Substitute y = 283 - x
862=1.5x + 4 (283 - x)
1.5x + 1132 - 4x = 862
1132 - 2.5x = 862
-2.5x = -270
x = 108
Substitute x =108 back into y = 283 - x
y = 283 - 108 = 175
Therefore there were 108 children and 175 adults in the amusement park on that particular day.
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opinions: y= -3x + 5, y = - 1/5x + 3, y= 1/3x + 1/5, y=1/3x + 5, y= 3x + 1/5
Answers
The required matches for the given equation of line are explain below.
Explain general equation of line.The general equation of a straight line is y = mx + c, where m is the inclination, and y = c is the worth where the line cuts the y-hub. This number c is known as the block on the y-pivot. The condition of a straight line with slope m and block c on the y-hub is y = mx + c.
According to question:We will find the graph, by using general form of equation
y = -3x + 5
Its y-intercept is 5,and angle is negative,So graph(3) is matches
similarly,
y = - 1/5x + 3
Its y-intercept is 3,So graph(1) is matches
y=1/3x + 5
Its y-intercept is 5,and angle is Positive,So graph(4) is matches
y= 3x + 1/5
Its y-intercept is 1/5,and angle is more than one,So graph(2) is matches
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Which of the following statements is TRUE?
a. If f(x) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) d, then the function f(x) · g(x) attains its global maximum at x = attains its global maximum on [a, b] at x = c · ·d. b. The critical points of f' (x) are same as the critical points of f(x) c. The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint. d. All of the statements are false. e. Every local maximum a global maximum
Answers
The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.
What is a critical value of a function?The critical value is the value of x for which the double derivative of the function f(x) becomes zero.
When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either
a maxima or a minima.
Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.
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PLEASE HELPED I"M TIMED I WILL GIVE BRAINLIST
Answers
Answer:
Below
Step-by-step explanation:
Angle 2 or angle HFE
Vertex is F
GF and FE are the sides of angle 1
Which equation represents the volume of the box
Answers
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
What is volume?The volume of any object is the capacity. How much it can hold.
What is the formula of volume?The formula of volume is a product of length, breadth and height.
Volume = L × B × H
Given:
The perimeter of the square base of side s plus height h = 250cm
as per the given question,
The perimeter of the square base of side s plus height h = 250cm
2( s + s ) + h = 250
2 (2s) + h = 250
4s + h = 250
We can express h in the terms of s as,
h= 250 - 4s
Volume = length X breadth X height
Volume = s × s × h
V = s² × h
V = s² × (250 - 4s)
V = 250s² - 4s³
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
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