A swimming pool holds 528 cubic feet of water. It measures 11 feet by 8 feet. How deep is the swimming pool?
Answers
Answer:
6 feet
Step-by-step explanation:
Related Questions
40=3x+x^2
How do I find the answer to this
Answers
Answer:
x = -8, x = 5
Step-by-step explanation:
This can be solved using Factorization method:
\( 40 = 3x + {x}^{2} \\ \\ \implies \: {x}^{2} + 3x - 40 = 0 \\ \\ \implies \: {x}^{2} + 8x - 5x- 40 = 0 \\ \\ \implies \: x({x} + 8) - 5(x + 8) = 0 \\ \\ \implies \: ({x} + 8) (x - 5) = 0 \\ \\ \implies \: ({x} + 8) = 0 \: \: or \: \: (x - 5) = 0 \\ \\ \implies \: x = - 8 \: \: or \: \: x = 5 \\ \\ x = - 8, \: \: 5\)
calculate either the missing angle or side stated. Give your answer correct to 1 decimal place
Answers
Answer:
a = 7.3 cm
Step-by-step explanation:
In this exercise, the hypotenuse and an angle are known. We have to find "a", which is the adjacent side to 56°.
So, we can use the formula for cosine:
\(\cos \alpha=\frac{adjacent}{\text{hypotenuse}}\)Substituting the values, we have:
\(\begin{gathered} 0.56=\frac{a}{\text{1}3} \\ a=0.56\cdot13 \\ a=7.3 \end{gathered}\)Answer: "a" is the side length and its measure is 7.3 cm.
To find the missing angle:
The sum of the angles in a triangle is 180°. Let's say β is the missing angle,
180 = 90 + 56+ β
β = 180 - 90 - 56
β = 34°
An Olympic diver is competing for a metal. His height in meters above the water can be modeled by the function
f (x)= -4.9x^2+9.8x+14.7f(x)=−4.9x +9.8x+14.7
where is is the time in seconds after he begins the dive.
After how many seconds does he reach the water?
What domain makes sense for this scenario?
Answers
Answer:
-4.9x²+75x=-4.9x+50x+38
75x=50x+38
25x=38
x=1.52
1.52 -4.9(1.52)²+75(1.52)=102.67904≈102.7 meters
Double check: -4.9(1.52)²+50(1.52)+38=102.67904≈102.7. Yes.
102.7 meter.
Step-by-step explanation:
Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team members who do not wear glasses, 30 percent of them are in the 10th grade.
To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade?
14%
17%
55%
67%
Answers
Answer: 14%
Step-by-step explanation: To find the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade, we divide the number of members who meet both criteria (14) by the total number of members (100) and multiply by 100 to get a percentage. Therefore, the probability is approximately 14%.
- Lizzy ˚ʚ♡ɞ˚
The value of 3 cubed plus 4 squared
Answers
Answer: 31
Step-by-step explanation:
A line passes through -8,5 and has a slope of 3/4 write the equation in slope intercept form
Answers
The equation of the line in slope-intercept form is y = (3/4)x.
To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,
where m is the slope and b is the y-intercept.
Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).
First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Using (-8, 5) as the point and 3/4 as the slope, we have:
5 - 5 = (3/4)(-8 - x)
0 = (3/4)(-8 - x)
0 = (-3/4)(8 + x)
0 = -6 - (3/4)x
Next, we can solve for x:
(3/4)x = -6
x = -6 \(\times\) (4/3)
x = -8
Now that we have the value of x, we can substitute it back into the equation to find the value of b:
0 = -6 - (3/4)(-8)
0 = -6 + 6
0 = 0
So, the value of b is 0.
Finally, we can write the equation of the line in slope-intercept form:
y = (3/4)x + 0
y = (3/4)x.
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Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?
A. a reflection over the x -axis
B. a rotation 90° clockwise about the origin
C. a rotation 180° counterclockwise about the origin
D. a translation 10 units to the left and 10 units down
Answers
A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.
What is a rotation?In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Coordinates of point X (0, 4) → Coordinates of point Y = (0, -4)
Coordinates of point X (1, 3) → Coordinates of point Y = (-1, -3)
In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.
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Two side of a triangle have the following measures. Find the range of possible measures for the third side.
8, 9
_______ < x < _______
Answers
Answer:
8<x<9
Step-by-step explanation
Which table represent a linear function. Picture attached and I will mark brainly
Answers
Answer:
Bottom right
Step-by-step explanation:
A linear function is a function that if ploted would be represented by a straight line. The only function out of the following 4 that follows this statement is the bottom right option.
Calculate the surface area
Answers
To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:
Length = 8 cmWidth = 3 cmHeight = 6 cmRefer to the attachment below.
Three pairs of facesThere are three pairs of faces on a rectangular prism:
Two faces (top & bottom) with dimensions: Length × Width (8 cm × 3 cm).Two faces (front & back) with dimensions: Length × Height (8 cm × 6 cm).Two faces (left & right) with dimensions: Width × Height (3 cm × 6 cm).Finding the areaArea of Length × Width faces8 cm × 3 cm = 24 cm²
Since there are two of these faces, the total area is:
2 × 24 = 48 cm²
Area of Length × Height faces8 cm × 6 cm = 48 cm²
Since there are two of these faces, the total area is:
2 × 48 = 96 cm²
Area of Width × Height faces3 cm × 6 cm = 18 cm²
Since there are two of these faces, the total area is:
2 × 18 = 36 cm²
Adding the areas of the facesNow, add up the areas of all six faces:
Surface Area = 48 + 96 + 36 = 180 cm²
AnswerSo, the surface area of the rectangular prism is 180 cm².
________________________________________________________
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What is the measure of angle 1?
Answers
Answer:
50°
Step-by-step explanation:
Place the midpoint of the protractor on the VERTEX of the angle.
Line up one side of the angle with the zero line of the protractor (where you see the number 0).
Read the degrees where the other side crosses the number scale.
I need help with 25. 26. And 27 plz I don’t know how
Answers
Answer:
25. 8ft
26. 3m
27. 7cm
Step-by-step explanation:
Because it says each is an area of a sqare the square root will give you the side length
b. Write
√x
as a single radical in simplest form.
5√x
Answers
Answer:
(tenth root of x to the third power)
see image
Step-by-step explanation:
To do this problem you need to know how to convert radicals to an expression with a fraction exponent(and back to radicals again), ALSO exponent rules for division ALSO subtracting fractions.
Square root x can be written as x^ 1/2
fifth root x can be written as x^ 1/5
When you are dividing expressions with the same base, exponent rules say to SUBTRACT the exponents.
1/2 - 1/5 change to common denominator
5/10 - 2/10
= 3/10
x^1/2 / x^1/5 =
x^ (1/2 - 1/5) =
x^ (5/10-2/10) =
x^ 3/10
Then change back to a radical. Remember "down and out" or "roots are down" and "up, up, up" or "exponents are up"
the number down below goes out (outside) the radical. And the number up top is up and exponents are up, up, up
see image.
x^3/10 =
tenth root (x^3)
see image.
Henry's savings account has an APR of 3.65%, calculates interest daily, and
pays interest at the end of the month. If during the month of November, his
balance was $300 for the first 10 days of the month, $1200 for the next 10
days of the month, and $800 for the last 10 days of the month, how much
total interest did Henry earn in November?
Answers
First, we need to calculate the daily interest rate:
Daily interest rate = APR / 365 = 0.0365 / 365 = 0.0001
For the first 10 days, the interest earned on $300 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 300 x 0.0001 x 10 = $0.30
For the next 10 days, the interest earned on $1200 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 1200 x 0.0001 x 10 = $1.20
For the last 10 days, the interest earned on $800 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 800 x 0.0001 x 10 = $0.80
Therefore, the total interest earned by Henry in November is:
Total interest = $0.30 + $1.20 + $0.80 = $2.30
Therefore, Henry earned $2.30 interest in November.
There are 145 students at a small school and 41 of them are freshman. What fraction of the students are freshman
Answers
Answer: 41/145
Step-by-step explanation:
Freshmen/Total students = 41/145
For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number. 34,19
Answers
The two factors are 2 and 17.
What are Factors?The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
Given:
The numbers are 34 and 19.
Now, the factor of 34 = 2, 17
Now, multiply the factor, 17 x 2 = 34
and, the addition = 17 + 2 = 19 which is the second number.
Hence, the number are 2 and 17.
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A certain company’s charges for tiling a rectangular room include the cost of the material used and a flat rate for installation. The length of a certain room is 2 feet more than its width, and the company’s charges, in dollars, for tiling the room are 12.5x(x+2) + 400.
Match each part of this expression with what it represents in this context.
Available Responses:
the width, in feet, of the room
the length, in feet, of the room
the area, in square feet, of the room
the cost, in dollars, for tile per square foot
the amount of materials needed to cover the room's floor
the flat rate, in dollars, the company charges for installation
12.5 represents ______
x(x+2) represents _______
400 represents _______
Answers
Answer:
12.5- the cost, in dollars, for tile per square foot
x(x+2)- the area, in square feet, of the room
400- the flat rate, in dollars, the company charges for installation
The length and width of the rectangular room is L = x feet , W = ( x + 2 ) feet
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangular room be A
Now , the length of the room L = x feet
And , length of a certain room is 2 feet more than its width
The width of the room W = ( x + 2 ) feet
The total charge for tiling the room C = 12.5 x ( x + 2 ) + 400
Now , the area of the rectangular room A = x ( x + 2 ) feet²
So , the width, in feet, of the room = ( x + 2 ) feet
The length, in feet, of the room = x feet
The area, in square feet, of the room = x ( x + 2 ) feet²
The cost, in dollars, for tile per square foot = $ 12.50
The amount of materials needed to cover the room's floor = 12.5 x ( x + 2 )
The flat rate, in dollars, the company charges for installation = $ 400
Hence , the expressions are solved and the area of rectangle is x ( x + 2 ) feet²
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if x + y equals to 10 and x - 2 y equals 8 what is the value of 3 y
Answers
We have this first condition given:
\(x+y=\text{ 10 (1)}\)And the second one:
\(x-2y=\text{ 8 (2)}\)If we solve for x from equation (1) we got:
\(x=\text{ 10}-y\text{ (3)}\)And if we solve for x from equation (2) we got:
\(x=\text{ 8+2y (4)}\)Now we can set equal equations (3) and (4)
\(10-y=\text{ 8+2y}\)And solving for y we got:
\(18=\text{ 3y }\rightarrow\text{ y= }\frac{18}{3}=\text{ 6}\)Final answer:
\(y=\text{ 3}\cdot6\text{ = 18}\)Find the total income produced by a continuous income stream in the first 15 years if the rate of flow is given by the following function, where t is time in years.
Answers
The total income produced by a continuous income stream in the first 15 years is $45,000.
What is continuous income stream?
We can see the money flowing into the account continuously rather than in a lot of discrete payments if the deposits are made often enough and the intervals between deposits are short compared to the account's overall lifespan. This scenario will be referred to as a constant revenue stream.
Given function is
f(t) = 3000
Now integrate both side of the function and the lower limit is t = 0 and upper limit is t = 15.
\(= \int^{15}_{0}3000 dt\)
\(=3000[t]_0^{15}\)
= 3000 [ 15 - 0]
=45000
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What is 6 1/4% of 95?
What is 3/10% of 115?
Answers
1.) 95/16
2.) 69/200
A 9-pack of popsicles costs $4.23. What is the unit price?
Answers
Answer:
Unit price is $0.47
Step-by-step explanation:
4.23÷9= .47
Sound is measured in decibels, using the formula d=10log(p/p0) where p is the intensity of the sound and p0 is the weakest sound the human ear can hear. A horn has a decibel warning of 20. how many times more intense is this horn compared to the weakest sound heard to the human ear?
Answers
Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.
What is the equation for the sound in decibels?The equation is given by:
\(d = 10\log{\frac{p}{p_0}}\)
In which:
d is the intensity of the sound in decibels.p is the intensity of the sound.\(p_0\) is the weakest sound that the human ear can hear.In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:
\(d = 10\log{\frac{p}{p_0}}\)
\(20 = 10\log{\frac{p}{p_0}}\)
\(\log{\frac{p}{p_0}} = 2\)
The logarithm is inverse of the function \(10^x\), hence we apply the function to both sides to find the ratio.
\(\frac{p}{p_0} = 10^2\)
\(\frac{p}{p_0} = 100\)
Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.
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It takes an older computer twice as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 12 minutes to send out the email. How long will it take the older computer to send out the email on its own? Do not do any rounding.
Answers
The older computer takes 8 minutes to send out the email on its own.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Let , the older computer works at the rate of x.
According to the condition,
then the rate of work of newer computer is x/2.
And the combined work of both the computer = x/2 + x = 3x/2
It means that 3x = 12
then x = 4
Hence, x =8of the job per minute.
It means the older computer will make the entire job in 84 minutes.
Therefore, the older computer takes 8 minutes to send out the email on its own.
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What are the points of the image of the line in Q4 after the dilation?
Answers
Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)
How is this so ?To rotate a point 90 degrees clockwise about a given point,we can follow these steps -
Translate the coordinates of the given point so that the center of rotation is at the origin. In this case,we subtract the coordinates of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).
Perform the rotation by swapping the x and y coordinates and changing the sign of the new x coordinate. In this case,we swap the x and y coordinates of (-5, 3) to get (3, -5).
Translate the coordinates back to their original position by adding the coordinates of the center (0,1) to the result from step 2. In this case, we add (0,1) to (3, -5) to get (3, -4).
Therefore, the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).
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Write a fraction that is equivalent to 3/5 that has a denominator of 20.
5
15
20
20
12
12
20
3
20
Answers
Answer:
12/20
Step-by-step explanation:
\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)
The answer is:
12/20In-depth-explanation:
The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.
We need to multiply both the numerator and the denominator by 4, so we do this:
\(\sf{\dfrac{3\times4}{5\times4}}\)
\(\sf{\dfrac{12}{20}}\)
Hence, the answer is 12/20.How many ml are needed to prepare 750 mg from 1:250
Answers
187, 500 ml are needed to prepare 750 mg from 1:250.
We have to find amount in ml to prepare 750 mg from 1:250.
let the amount needed in ml be x.
Using proportion
1/750 = 250 / x
x= 750 . 250
x= 187, 500 ml
Thus, to prepare 750 mg 187,500 ml is needed.
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f(x) = x^2 and g(x)=x^2 +1
find (g/f)(x)
Answers
((x^2)/(x^2))+(1/(x^2))=1+(1/(x^2))
multiply three 1,5. -5,6. 0,0
Answers
Answer:
0
Step-by-step explanation:
=1/2 × -5,6 × 0
=-8,4×0
=0
PLSSSSSS HELPPPPPPPPP
Answers
Answer:
y = 2x
Step-by-step explanation:
the answer is rise over run, the rise is 4 the run is 2 4/2 is 2. Slope is 2. Y intercept is zero. y = 2x
Please answer
Picture attached
Answers
Answer:
1) a) ∠MOS = 62
b) ∠MLP = 31
Step-by-step explanation:
1)
a) Chord MS creates an angle of ∠MTS = 31 at a point on the circle
∠MOS is the angle created by chord MS at the centre
Therefore,
∠MOS = 2*∠MTS
= 2*31
=62
∠MOS = 62
b) Since PM = MS, the angle created by these chords are the same
∠MLP = ∠MTS
∠MLP = 31
2) Prove that ON = MS/2
Since MS = MP,
we need to prove that ON = MP/2
We have OL = OM = radius
OL + OM = ML
ML = 2*OL -eq(1)
Since ON bisects LP,
LN = NP
LP = LN + NP
LP = 2*LN -eq(2)
Consider ΔMLP and ΔOLN
\(\frac{ML}{OL} = \frac{2*OL}{OL} =2\;\;(from\;eq(1))\\\\\frac{LP}{LN} = \frac{2*LN}{LN} =2\;\;(from\;eq(2))\\\\\implies \frac{ML}{OL} = \frac{LP}{LN}\)
Also ∠MLP = ∠OLN = 31
By SAS property, ΔMLP and ΔOLN are similar
\(\implies \frac{ML}{OL} = \frac{LP}{LN} = \frac{MP}{ON}\\\\\implies \frac{MP}{ON} = 2\\\\\implies \frac{MP}{2} = ON\)
Answer:
1)a)62
1)b)31
Step-by-step explanation:
1)a)
∠MTS = 31
Also, 2* ∠MTS = ∠MOS
∠MOS = 2*31 = 62
b) MS = MP
so ∠MTS = ∠MLP
∠MLP = 31
2)NL = PL/2
OL = ML/2
in triangle LMP and LON,
∠MLP = ∠OLN
by SAS, the triangles are similar
ML/OL = MP/ON
ML/(ML/2) = MP/ON
MP/ON = 2
ON = MP/2