1) The dimension of the base of the pool is; (x + 3) and (x + 8)
2) The volume of the pool when x = 3 ft is; 198 ft³
3) If the volume is 100 ft³ of water, the height x is; 2 ft
4) If the maximum capacity of the pool is 520 ft³, the maximum depth is; 5 ft
How to find the volume of a cuboid?We are given that the volume of water in a rectangular, in-ground, swimming pool is; V(x) = x³ + 11x² + 24x
where;
V(x) is the volume in cubic feet when the water is x ft high
1) V(x ) =x³ + 11x³ + 24x
V(x) is the volume in cubic feet when the water is x ft high
Factorizing the polynomial into its' factors gives;
V(x) = x(x² + 11x + 24)
V(x) = x(x + 8)(x + 3)
The water is x ft high and so the dimensions of the base of the pool are (x + 3) and (x + 8)
2) We want to find the volume of the pool when x = 3 ft. Thus;
V(3) = 3(3 + 8)(3 + 3)
V(3) = 3 (11)(6)
V(3) = 198 ft³
3) If the volume is 100 ft³ of water, the height x is calculated as;
x(x + 8)(x + 3) = 100
Solving for x gives us;
x = 2 ft
4) If maximum capacity of the pool is 520 ft³, then the maximum depth is;
x(x + 8)(x + 3) = 520
Solving for x gives us;
x = 5 ft
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Please help!!!
find y and x
Answer:
a) y = 16/x²
b) x = 4/5
Step-by-step explanation:
You want the equation for y in terms of x when y is inversely proportional to the square of x, and y is 16 when x is 1. Further, you want the value of x when y is 25.
(a) RelationThe wording "inversely proportional to the square" means the form of the equation is ...
y = k/x² . . . . . . where k is the constant of proportionality
The value of k can be found from the given (x, y) pair.
k = x²y = (1)²(16) = 16
The equation is ...
y = 16/x²
(b) Value of xSolving for x gives ...
x = √(16/y)
Then the value of x for y = 25 is ...
x = √(16/25)
x = 4/5
Frank wants to earn at least $47 trimming trees. He charges $7 per hour and pays $9 in equipment fees. What are the possible numbers of hours Frank could trim trees?
By setting up the equation and solving and simplifying the equation, the possible number of hours Frank can trim tree is 5.43 hours, round off the hour that will be 6 hours.
What is Algebraic simplification?Algebraic simplification is the process of rewriting an algebraic expression in a simpler form, without changing its value.
What is algebraic expression?An algebraic expression is a combination of numbers, variables, and arithmetic operations that can be evaluated to a specific numerical value.
let the required number of hours be h,
so setting up the equation,
7h + 9 = 47
Then we can subtract 9 from both sides to isolate h:
7h + 9 - 9 = 47 - 9
7h = 38
Dividing both sides by 7 gives us:
7h/7 = 38/7
h = 5.43
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Which expression is equivalent to one and five tenths raised to the fourth power divided by seven tenths raised to the third power, all raised to the sixth power?
0.82
0.810
one and five tenths raised to the tenth power divided by seven tenths raised to the nineth power
one and five tenths raised to the twenty-fourth power divided by seven tenths raised to the eighteenth power
The equivalent expression is 1.5^24/0.7^18
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
one and five tenths raised to the fourth power divided by seven tenths raised to the third power, all raised to the sixth power
Rewrite properly
So, we have
(1.5^4/0.7^3)^6
Open the brackets
So, we have the following representation
(1.5^4/0.7^3)^6 = 1.5^(4 * 6)/0.7^(3*6)
Evaluate the products
(1.5^4/0.7^3)^6 = 1.5^24/0.7^18
Hence, the solution is 1.5^24/0.7^18
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What is the slope of a line perpendicular to the line whose equation is 3x-6y=144 Fully simplify your answer.
Answer:
The slope of the perpendicular line is -2.
Step-by-step explanation:
A perpendicular line has a slope that is the negative inverse of the slope of the reference line. The reference line in this problem is 3x-6y=144.
Let's rearrange this equation to standard slope-intercept form of y=mx+b, where m is the slope and b is the y-intercept (the valuue of y when x=0).
3x-6y=144
-6y=144-3x
-6y=-3x + 144
y = (3/6)x + (144/-6)
y = (1/2)x - 24
This line has a slope of (1/2) and a y-intercept of -24. A line perpendicular to this will have a slope that is the negative inverse of (1/2). This would be -2. The new line will take form:
y = -2x + b
We are not given b, and there is not enough information to calculate one, so let's assume a value of -24, so that it intersects the original line at (0, -24). See the attached graph.
Given that
R
=
8
x
+
4
y
Find
y
when
x
=
8
and
R
=
30
Give your answer as an improper fraction in its simplest form.
Answer: x=8,r=30
Step-by-step explanation:
Can somebody help me look at the picture
Answer:
Seagle =10
Dolphin =2.5
Penguin-flat =0
Shark = -2.5
Clownfish= -7.5
Octpus= -10
Step-by-step explanation:
Answer:
Meters of the seagull: 10 cmMeters of the dolphin: 2 cm Meters of the penguin: 0 cm Meters of the shark: -3 cmMeters of the clownfish: -7 cmMeters of the Octopus: -10 cmStep-by-step explanation:
The distance between each animal and the sea level is already shown in the image.
- for the seagull the vertical line with measurements of 0,5, 10 if you measure how high the seagull it would be 10 cm, how do I measure it? go from 0 to the height of the dolphin and you'll find the answer.
- for the dolphin, look at the vertical line with measurements of 0,5, and 10 how do I measure it? go from 0 to the height of the dolphin and you'll find the answer which would be 2cm.
you keep doing the same thing to the other animals the meters are shown on the image you have to measure from 0 and go up or down depending on where the animal is.
Point H'(4.5, 6.75) is the result of dilating point H(2, 3) using the origin as the center of dilation. What is the scale factor, k, of the transformation
(x,y) → (kx, ky)?
The scale factor of the transformation is 2.25
What is the scale factor of the transformationFrom the question, we have the following parameters that can be used in our computation:
Point H'(4.5, 6.75) is the result of dilating point H(2, 3)
This means that
The scale factor of the transformation = H'/H
Substitute the known values in the above equation, so, we have the following representation
Scale factor = (4.5, 6.75)/(2. 3)
Evaluate
Scale factor = 2.25
Hence, the scale factor is 2.25
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What is the domain of the function shown below?
3
A All real numbers
C All whole numbers
B All integers
D All natural numbers
Answer:
A All real numbers
Step-by-step explanation:
You want to know the domain of a function graphed as a continuous line with negative slope.
DomainThe domain is the horizontal extent of the function, all of the values for which the function is defined.
The graph shows the function is defined not only for all integers (..., -1, 0, 1, ...), but also for all the values between.
The domain is all real numbers.
Write the expression in simplest radical form. Write the expression in simplest radical form. The image is below only answer if ur hood at geometry please!!
Answer:
Step-by-step explanation:
[tex]2\sqrt{35[/tex]
f"(x) = 1/x^3/2, f'(4)=2, f(4)=0
f(x)=?
PLS URGENT
Answer: 6
Step-by-step explanation:
help me with math please
The possible coordinates of point A such that the distance to point B is 10 units are:
(-5, -4) and (-5, 8)
What are the possible coordinates of point A?We know that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)² + (b - d)²)
In this case, we know that:
B = (3, 2)
A = (-5, y)
And the distance is 10 units, then we can write:
10 = √( (3 + 5)² + (2 - y)²)
10² = 8² + (2 - y)²
100 - 64 = (2 - y)²
36 = (2 - y)²
±√36 = 2 - y
±6 = 2 - y
y = 2 ± 6
The two solutions are:
y = 2 + 6 = 8
y = 2 - 6 = -4
Then the possible coordinates are (-5, -4) and (-5, 8).
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Help please! More points will mark as brainiest!
Answer:
384cm^2
Step-by-step explanation:
8x8x6 = 384
Write an equation in point-slope form for the line that passes through each point
with the given slope. Then graph the equation.
(2,-1),m=-3
Answer: y= 3x -5
Step-by-step explanation:
Use the following word problem to answer the following questions.
Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?
1. Provide the mathematical model specific to the word problem(table of values, graph, statement)
2.explain why you chose that type of model
3. what is the answer to the word problem
The length of the rectangular garden is 28 feet.
Statement represents the mathematical solution to the given word problem.
The statement clearly explains the stated circumstance.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
The area of the rectangular garden = 448 square feet.
Also, the length of the garden is 4 feet less than the twice of the width.
Let the width of garden is x feet
Then length of garden = 2x - 4
The area of rectangular garden = 448
x (2x - 4) = 448
x (x - 2) = 224
x = 16
The width of the garden is 16 feet.
The length of the garden = 2x - 4 = 2(16) - 4 = 32 - 4 = 28 feet
The required length of the garden is 28 feet.
The mathematical model to the given word problem is statement.
Statement clarify the given condition clearly.
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Answer question please!
Answer: line and line segment
Step-by-step explanation:
6 Jessica runs for 15 minutes at an average speed of 6 miles per hour.
She then runs for 40 minutes at an average speed of 9 miles per hour.
It takes Amy 45 minutes to run the same total distance that Jessica runs.
Work out Amy's average speed.
Give your answer in miles
per hour.
Answer:
20
Step-by-step explanation:
6*(60/15) = 1.5 (milles)
9*(60/40) = 13.5 (milles)
1.5 + 13.5 = 15 (milles)
15 / (45/60) = 20 (milles per hour)
The speed of Amy is 8.6 mph.
What is speed?Speed is defined as the rate of change of distance with time. It has the dimension of distance by time. Thus, the SI unit of speed is given as the combination of the basic unit of distance and the basic unit of Time. Thus, the SI unit of speed is metre per second.
Given that, Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs.
Calculating the distance covered by Jessica,
15 minutes = 0.25 hours
Speed = distance / time
Distance = speed × time
Distance = 0.25 × 6 = 1.5 mile
And,
40 minutes = 2/3 hours
Distance = 2/3 × 9 = 6 miles
Total distance covered by Jessica = 1.5+6 = 6.5 miles
Since, Amy covers the same distance in 45 minutes,
Therefore, 45 minutes = 3/4 hours
Speed = 6.5/0.75 = 8.6 mph
Hence, The speed of Amy is 8.6 mph.
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Indicate whether (1, 5) is a solution of the given system.
Answer:
To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.
For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.
Substituting these values into the first equation, we get:
5 = 2(1) + 1
5 = 2 + 1
5 = 3
This statement is not true, so (1, 5) is not a solution of this system.
On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.
I hope this helps! Let me know if you have any more questions.
Step-by-step explanation:
find the percent of 25% of 80
Answer: 20
Step-by-step explanation: There are 2 ways to solve this problem. This is one way, it is a shortcut. So if you didn't know, 25% of 100 (the whole thing) is 1/4, so if you divide 80 by 1/4, you should get 20. The 2nd way is to set up a proportion, so it would be 25 over 100 = ? over 80. Now, you would cross multiply the 25 and 80 to get 2000. Then you take the 2000 and divide it by 100 to get 20. I hoped this explanation helped you.
Answer:
20
Step-by-step explanation:
Write 25% as 25/100
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
25/100 of 80 = 25/100 × 80
Therefore, the answer is 20
If you are using a calculator, simply enter 25÷100×80 which will give you 20 as the answer.
The value of y is directly proportional to the value of x. When = 512, y = 128.
What is the value of y when x = 64?
Answer:
Step-by-step explanation:
directly proportional means same
x=y
512=128
64=y
512/64=8
128/8=16
when x=64 then the value of y=16
Answer:
C
Step-by-step explanation:
given y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
to find k use the condition when x = 512, y = 128
128 = 512k ( divide both sides by 512 )
[tex]\frac{128}{512}[/tex] = k , that is k = 0.25
y = 0.25x ← equation of proportion
when x = 64 , then
y = 0.25 × 64 = 16
Richard and Teo have a combined age of 28. Richard is 13 years older than twice Teo’s age. How old are Richard and Thiago?
Answer:
Richard = 23
Teo= 5
Step-by-step explanation:
R + T = 28
R = 2T + 13
(2T+13)+T = 28
3T + 13 = 28
3T = 28 - 13
3T = 15
T = 15/3
T = 5
(Checking your answer)
R + 5 = 28
R = 28 - 5
R = 23
R = 2(5) + 13 = 10 + 13 = 23
Found this on another brainly question
Milton is 1.55 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 27.25 meters. He stands 23.1 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow.
Find the height of the tree to the nearest hundredth of a meter.
The height of the tree that produce a shadow of length 27.25 m is 10.18 m.
What is height?Height is the vertical distance between two points.
To calculate the height of the try, we use the formula of similar angle.
Formula:
d/D = h/H................ Equation 1Where:
d = Distance of Milton from the treeD = Length of the tree's shadowH = Height of the treeh = Height of MiltonFrom the question,
Given:
d = (27.25-23.1) = 4.15 mD = 27.25 mh = 1.55 mSubstitute these values into equation 1 and solve for H
4.15/27.25 = 1.55/HH = (1.55×27.25)/4.15H = 10.18 mHence, the height of the tree is 10.18 m.
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Alvarez says that her family’s move to the United States and the struggle she had in finding her identity as a Dominican and an American had a deep impact on her. Which passage from "Names/Nombres" shows this struggle in finding her identity as a Dominican and an American?
Answer:
the 4rd one
Step-by-step explanation:
Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates. Draw a line segment from point A to the reflecting line, and then draw a line segment from point A' to the reflecting line. What do you notice about the two line segments you drew? Do you think you would see the same characteristic if you drew the line segment connecting B with the reflecting line and then B' with the reflecting line? How do you know?
The two line segments after the reflection over the x-axis are vertical lines, and the same will be true for the third segment.
What are the changes to the triangle?The rule for a reflection over the x-axis is given as follows:
(x,y) -> (x,-y).
Meaning that the x-axis remains constant, while the coordinates of the y-axis are changed.
The vertices of the original triangle will be attributed as follows:
A(1,1), B(4,1) and C(1,5).
Hence the vertices of the reflected triangle will be given as follows:
A'(1,-1), B'(4,-1) and C(1,-5).
Thus the lines are given as follows:
A and A': x = 1.B and B': x = 4.C and C': x = 1.Hence there are three vertical lines.
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What is the image of (-3,-8)(−3,−8) after a dilation by a scale factor of 44 centered at the origin?
The image after a dilation by a scale factor of 4 centered at the origin is (-132,-352).
What is scale factor?Scale factor is a mathematical term that refers to the ratio of two corresponding sides of similar shapes. It is used to compare the size of objects or figures by determining the size of a model in relation to its actual size. For example, if two shapes are similar, then their scale factor will be the same. This is useful in engineering and architecture when building scaled models of structures and machines. Scale factors can also be used to determine the proportions and measurements of an object in relation to similar objects.
This is because a dilation by a scale factor of 4 is the same as multiplying the original coordinates by 4. So, if the original coordinates were (-3,-8), then the new coordinates would be (-12,-32). Then, the coordinates are shifted by the center (the origin), so the new coordinates are (-132,-352).
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there is a line that includes the point (0, 5) and has a slope of 1/9 .what is its equation in slope intercept form?
Answer:
y = 1/9x + 5
Hope this helps!
Step-by-step explanation:
y = mx + b
m = slope
y = [tex]\frac{1}{9} x[/tex] + b
( x, y ) = ( 0, 5 )
(5) = [tex]\frac{1}{9} (0)[/tex] + b
5 = 0 + b
5 = b or b = 5
Putting it all together gets you y = [tex]\frac{1}{9} x[/tex] + 5
3/4x-5=1/2x+2x-10
solve for x
Answer:
x = [tex]\frac{20}{7}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] x - 5= [tex]\frac{1}{2}[/tex] x + 2x - 10
multiply through by 4 ( the LCM of 4 and 2 ) to clear the fractions
3x - 20 = 2x + 8x - 40
3x - 20 = 10x - 40 ( subtract 10x from both sides )
- 7x - 20 = - 40 ( add 20 to both sides )
- 7x = - 20 ( divide both sides by - 7 )
x = [tex]\frac{-20}{-7}[/tex] = [tex]\frac{20}{7}[/tex]
Answer:
[tex]x=\frac{20}{7}[/tex]
Step-by-step explanation:
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
[tex]\frac{1}{2}x+2x-10=\frac{3}{4}x-5[/tex]
Simplify the left side of the equation by combing [tex]\frac{1}{2}[/tex] and [tex]x[/tex].
[tex]\frac{x}{2}+2x-10=\frac{3}{4}x-5[/tex]
To write [tex]2x[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].
[tex]\frac{x}{2}+2x*\frac{2}{2} -10=\frac{3}{4}x-5[/tex]
Simplify terms by combining [tex]2x[/tex] and [tex]\frac{2}{2}[/tex]. Combine the numerators over the common denominator.
[tex]\frac{x+2x*2}{2} -10=\frac{3}{4}x-5[/tex]
Raise x to the power of 1.
[tex]\frac{x^1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]
Factor [tex]x[/tex] out of [tex]x^1[/tex].
[tex]\frac{x*1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]
Factor [tex]x[/tex] out of [tex]x+2x*2[/tex].
[tex]\frac{x*1+x(2*2)}{2} -10=\frac{3}{4}x-5[/tex]
Factor [tex]x[/tex] out of [tex]x*1+x(2*2)[/tex]
[tex]\frac{x(1+2*2)}{2} -10=\frac{3}{4}x-5[/tex]
Multiply 2 by 2.
[tex]\frac{x(1+4)}{2} -10=\frac{3}{4}x-5[/tex]
Add 1 and 4.
[tex]\frac{5x}{2} -10=\frac{3}{4}x-5[/tex]
Combine [tex]\frac{3}{4}[/tex] and [tex]x[/tex].
[tex]\frac{5x}{2} -10=\frac{3x}{4}-5[/tex]
Move all terms containing [tex]x[/tex] to the left side of the equation.
[tex]\frac{7x}{4}-10=-5[/tex]
Move all terms not containing [tex]x[/tex] to the right side of the equation.
[tex]\frac{7x}{4}=5[/tex]
Multiply both sides of the equation by [tex]\frac{4}{7}[/tex]
[tex]\frac{7x}{4}*\frac{4}{7} =5*\frac{4}{7}[/tex]
Simplify both sides of the equation.
[tex]x=\frac{20}{7}[/tex]
2X+3 {2(X+2)+3(X-4)} =10
Answer:
x=2
Step-by-step explanation:
Remove parentheses
collect like terms
move constants to the right
calculate
divide both sides
2. Select all the points of intersection between the graphs of the functions
f(x) = (x + 5)(x 2) and g(x) = (2x + 1)(x
2).
1) The point of intersection is (1, 2) and (-1, 0).
2) The point of intersection is (4, 18).
3) The solutions are 0 and -2.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = x²(x + 1) and g(x) = x + 1
The point of intersection.
f(x) = g(x)
x²(x + 1) = (x + 1)
x² = 1
x = √1
x = ±1
x = 1, f(x) = 2.
(1, 2)
x = -1, f(x) = 0
(-1, 0)
x = 1, g(x) = 2
(1, 2)
x = -1, g(x) = 0
(-1, 0)
This means,
The point of intersection is (1, 2) and (-1, 0).
Now,
f(x) = (x + 5)(x - 2) and g(x) = (2x + 1)(x - 2).
The point of intersection:
f(x) = g(x)
(x + 5)(x - 2) = (2x + 1)(x - 2).
x + 5 = 2x + 1
5 - 1 = 2x - x
4 = x
x = 4
x = 4, f(4) = 9 x 2 = 18
x = 4, g(4) = 9 x 2 = 18
(4, 18)
The point of intersection is (4, 18).
Now,
(x - 3) (x + 5) = -15
The solutions to this equation.
x² + 5x - 3x - 15 = -15
x² + 2x - 15 + 15 = 0
x² + 2x = 0
x(x + 2) = 0
x = 0 and x + 2 = 0
x = 0 and x = -2
The solutions are 0 and -2.
Thus,
1) The point of intersection is (1, 2) and (-1, 0).
2) The point of intersection is (4, 18).
3) The solutions are 0 and -2.
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While shootings baskets at a basketball hoop, you make 36 out of 80 shots. Your friend makes 43.75% of the shots. Between the two of you, who made the higher percentage of shots?
45%
You made a higher percentage of shots.
36/80*100 = 45%
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What is the value of 6 x 3/8?
Answer: 18/8 = 9/4
Step-by-step explanation:
6 can be write as 6/1
6/1 timed 3/8 = 18/8
Simplify by 2 = 9/4