Answer:
3 ft, 144 ft³Step-by-step explanation:
Find the width as below
l² + w² + h² = d², where l- length, w- width, h- height, d- the distance between top and bottom cornersSubstitute the values and solve for w
4² + w² + 12² = 13²w² + 160 = 169w² = 9w = 3 feetNow find the volume
V = lwhV = 4*3*12 = 144 ft³Answer:
width = 3ft
volume = 144 ft³
Step-by-step explanation:
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
The diagonal of the base of the aquarium, its height, and the length from the top corner to the opposite bottom corner forms a right triangle. As we know two of the lengths, we can use Pythagoras Theorem to calculate the unknown length (diagonal of base).
Given:
a = height of aquarium = 12 ftb = diagonal of basec = top corner to opposite corner = 13 ft[tex]\implies \sf 12^2+b^2=13^2[/tex]
[tex]\implies \sf b=\sqrt{13^2-12^2}[/tex]
[tex]\implies \sf b=5[/tex]
Now we know the length of the diagonal of the base, we can again use Pythagoras Theorem to find the width of the aquarium.
Given:
a = length of aquarium = 4 ftb = width of aquarium c = diagonal of base = 5 ft[tex]\sf \implies 4^2+b^2=5^2[/tex]
[tex]\sf \implies b=\sqrt{5^2-4^2}[/tex]
[tex]\sf \implies b=3[/tex]
Therefore, the width of the aquarium is 3 ft.
As the aquarium is modeled as a rectangular prism:
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf width \times length \times height\\ \implies \textsf{Volume of aquarium} & = \sf 3\:ft \times 4\:ft \times 12\:ft\\& = \sf 144 \:\:ft^3\end{aligned}[/tex]
You want to save for retirement. assuming you are now 25 years old and you want to retire at age 50, you have 25 years to watch your investment grow. you decide to invest in the stock market, which has earned about 13% per year over the past 80 years and is expected to continue at this rate. you decide to invest $1,000 today. required: how much do you expect to have in 25 years?
Answer:
4250
Step-by-step explanation:
0.13 = 13%
1000×0.13=130
130×25= 3250 + 1000 = 4250
What I did:
You have to turn the percent to a decimal first
Then multiply the decimal by the first investment amount (1000)
then multiply that by the years that you have before retirement
You add that amount plus the 1000 you have started with
y=4x+3 system of equations
Step-by-step explanation:
y=4x + 3
it should have another one
What is the value of x^2+y^2 given the following system?
x+y=10
x-y=8
Answer:
I hope this helps, you can ask any questions for clarification
28x+1=32x-1 solve for x
Answer:
x = 1/2
Step-by-step explanation:
28x + 1 = 32x - 1 <== subtract 28x from both sides
-28x -28x
1 = 4x - 1 <== add 1 to both sides
+ 1 + 1
2 = 4x <== divide both sides by 4 to isolate the variable
/4 /4
1/2 = x
Hope this helps!
[tex] \Large{\boxed{\sf x = \dfrac{1}{2} }} [/tex]
[tex] \\ [/tex]
Explanation:Given equation:
[tex] \sf 28x + 1 = 32x - 1 [/tex]
[tex] \\ [/tex]
Subtract 28x from each side :
[tex] \sf 28x + 1 - 28x = 32x - 1 - 28x \\ \\ \sf 1 = 4x - 1 [/tex]
[tex] \\ [/tex]
Add 1 to both sides:
[tex] \sf 1 + 1 = 4x \\ \\ \sf 2 = 4x [/tex]
[tex] \\ [/tex]
Divide both sides by 4:
[tex] \sf \dfrac{2}{4} = \dfrac{4x}{4} \\ \\ \\ \boxed{\boxed{\sf x = \dfrac{1}{2} }} [/tex]
[tex] \\ \\ [/tex]
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A closet is in the shape of a rectangular prism. It is 214feet long, 3 feet wide, and 4 feet tall.
What is the volume of the closet?
I got these three exercises that I gotta do and I need help. It’s in Hebrew but it would mean a lot if someone could help!
Answer:
i dont lnow the language sorry
For the diagram at right, write and solve an equation to find x
Answer:
x = 24
Step-by-step explanation:
The formula for determining the sum of interior angles is:
[tex](n-2) * 180[/tex]
[tex]4 * 180 = 720[/tex]
Therefore to determine an equation for x, we must add up all the interior angle equations and set them equal to 720.
[tex](2x+3) +(3x+12) + (7x+14) + (9x+2) + (4x+8) + (3x+9) = 720\\28x + 48 = 720\\28x = 672\\x = 24[/tex]
The equation and answer above shows how to find x, which equals 24.
A pet store has 4 tanks of fish. Each tank has 32 fish. How many fish does the store have?
Answer:
128
Step-by-step explanation:
32 × 4 = 128
Each tank has 32, and there are four, so 32 times 4.
The store has 128 fish in the tank.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that pet store has 4 tanks of fish. Each tank has 32 fish.
Therefore,
Total fish = Number of fish that a tank can hold x Number of tanks
32 × 4 = 128
Hence, we get 32 for each tank, and there are four,
Thus, 32 times 4.
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what is the constant of proportionality of the below
Answer:
Proportionality constant k
When two variables are directly or indirectly proportional to each other, then their relationship can be described as y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.
Answer: Proportionality constant k
Step-by-step explanation:
below?
Paul is making grey paint. He mixes black and white paint in the ratio 1:3. He makes 35 litres of grey paint. How much white paint does he use?
Which property of addition is shown below?
If x = a + bi and y = –a – bi, x + y = 0.
commutative property
identity property
associative property
inverse property
Answer: D
Step-by-step explanation:
Noah is making grilled cheese sandwiches for friends. He has 24 ounces of cheese. He plans to split the cheese evenly between 6 sandwiches.
Write an equation to determine how many ounces of cheese, ccc, Noah can use on each sandwich.
Answer:
24 / 6 = ccc
Step-by-step explanation:
There is 24 oz of cheese total that will be split evenly (divided) into 6 parts.
Each part will equal one sandwich worth of cheese (ccc) on the other side of the equation.
This one is very simple to solve, you could just calculate 24/6 to get your answer. But I'll go through it using typical algebra you would use for a less simple equation.
To solve:
Multiply by 6 to cancel the division by 6 on the left side
24 = 6ccc
Divide by 6 to isolate ccc again
4 = ccc
So each sandwich would get 4oz of cheese.
What is the domain and range of the following graph
Answer:
Step-by-step explanation:
Domain is x-values the graph can have
x = [-3,22]
range is the y values the graph includes
range-= [-3,+2]
Radius ob measures x units. which expression represents the circumference of the smaller circle with radius oa? (startfraction pi over 3 endfraction)x units (startfraction 2 pi over 3 endfraction)x units 2πx units 6πx units
The circumference of the smaller circle is C = 2*pi*x/3.
We have given that radius ob measures x units
What is the formula for the circumference of the circle ?circumference of the circle is given by,
[tex]C = 2\times \pi \times R[/tex]
where pi = 3.14
R= radius
we have two circles, A and B, where B is the larger circle and A is the smaller circle.
We know that,The circumference of B is 3 times the circumference of A.
The radius of circle B is OB = x
The radius of circle A is OA
We want to find an expression of OA.
The circumference of circle B is given by
[tex]C(B) = 2\times \piOB = 2\times pi\times x[/tex]
The circumference of circle A is given by
[tex]C(A) = 2\times\pi\times OA[/tex]
we know that the circumference of circle B is 3 times the circumference of circle A,
[tex]C(B) = 3\times C(A)[/tex]
replacing the equations for the circumferences
[tex]2\times\pi\times x = 3\times (2\times pi\times OA)[/tex]
We have divide both sides by [tex]2\pi[/tex]we get:
[tex]x = 3\times OA[/tex]
Now we want to solve this for OA, then we need to isolate it,
[tex]x/3 = OA[/tex]
We can conclude that the radius of the smaller circle is equal to x/3.
Then the circumference of circle A is
[tex]C(A) = 2\times pi\times x/3[/tex]
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Answer:
c
Step-by-step explanation:
17=3x-4
Find the value of x
Answer:
x=7
Step-by-step explanation:
I need help on this one
X/3+7=12
Help :)
I need to write more to send it so…
Answer:
15
Step-by-step explanation:
To solve you have to get x by itself on one side.
x/3+7=12
First, you move the seven over.
x/3+7-7=12-7
Simplify.
x/3=5
Now to get x by itself you can multiply both sides by 3.
x/3*3=5*3
Simplify.
x=15
Answer:
x = 15
Step-by-step explanation:
x/3 + 3⋅7/3 = 12
x+3⋅7/3=12
x+21/3
X=15
Josh studied for his
science test from
3:45 p.m. until
5:30 p.m each day for
three days. how long
did he study in all?
he studied for 495 minutes. 165 minutes a day.
Answer: He studied for 315 minutes. Because he studied for 1hr and 45 mins (105 mins). Then you multiply this by 3 because it's been three days.
Hope this helps!
Please help The diagram below shows a square prism. The plane ABC is inside the
prism, and M is the midpoint of the base diagonal BC. MD. = square root 18
b Hence find, correct to the nearest degree, the angle that the plane ABC
makes with the base of the prism. Diagram is attached below.
Answer:
43°
Step-by-step explanation:
Triangle ADM is a right triangle with legs AD=4 cm and DM=√18 cm. The angle at M is the angle of interest. It can be found using the inverse tangent function.
Tan = Opposite/Adjacent
tan(∠AMD) = AD/MD = 4/√18
∠AMD = arctan(4/√18) ≈ 43.31°
The angle the plane makes is about 43°.
Answer:
the measure of the angle that the plane ABC makes with the base of the prism = 43 degree (to the nearest degree)
Step-by-step explanation:
We notice that the plane ABC and the base of the prism intersect along the line BC
And as the plane (ADM) is perpendicular to the line BC
then the angle between the plane ABC and the base of the prism is the angle AMD
Let θ be the measure of the angle AMD
[tex]\begin{aligned}\tan (\theta) &=\frac{A D}{M D} \\&=\frac{4}{\sqrt{18}}\end{aligned}[/tex]
[tex]\begin{aligned}\Rightarrow \theta &=\tan ^{-1}\left(\frac{4}{\sqrt{18}}\right) \\&=43,31385 \ldots\end{aligned}[/tex]
Solve for x and y
7y - 5x = 45
x = 8 – 2y
Answer:
Hope the pictures will help you.
The solution to the system of equations is x = -2 and y = 5.
What is the solution to the system of equations?Given the parameters:
7y - 5x = 45
x = 8 - 2y
To solve the system of equations, substitute the expression for x from the second equation into the first equation.
7y - 5x = 45
Plug in x = 8 - 2y:
7y - 5( 8 - 2y) = 45
7y - 40 + 10y = 45
Collect and add like terms:
7y + 10y = 45 + 40
17y = 85
y = 85/17
y = 5
Plug the value of y into the second equation and solve for x:
x = 8 - 2y
Plug in y = 5:
x = 8 - 2( 5 )
x = 8 - 10
x = -2
Therefore, the value of x is -2 and y is 5.
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How long does this lease last?
write an equation for the nth term of the arithmetic sequence -7, -2, 3, 8
Answer:
n=5
Step-by-step explanation:
So I'm not sure how to write the equation, but i do know that each term has five added from the previous one, hope that help a little bit!
Is it possible to rewrite any proof that uses the AAS Congruence Theorem as a proof that uses the ASA Congruence Theorem? Explain your reasoning.
Answer: Yes
Step-by-step explanation:
If you were to use AAS, you could prove the third pair of angles congruent by using the fact that the sum of the measures of the angles of a triangle is 180 degrees, and since you have two of the angles, you can solve for the third pair of angles, which would be congruent.
anybody know if your suppose to use the pie symbol or the numbers when doing math
Answer:
Depends on the question or if it specifically says to.
Step-by-step explanation:
For finding the volume of cylinders and spheres use the pi symbol or just say "use 3.14 for pi"
2. A traffic study was conducted on a busy street. In 15-minute intervals from 6:30 a.m. to 8:00
a.m., the number of vehicles that passed a certain point in one minute was recorded in the table
below. Write an equation for the curve of best fit, then approximate the number of cars that passed
the point at 9:15 a.m.
The line of best fit of the traffic study is a line through a scatterplot of data points which shows the relationship between the points.
How to illustrate the equation?Your information is incomplete as the table isn't given. Therefore, an overview will be given.
The least square methods is used by statisticians to arrive at the geometric equation for the line. A straight line will simply result from a simple regression of two or more independent variables.
A regression that has to do with multiple related variables lead to a curved line. The line of best fit is an important output of regression analysis.
A regression that has two independent variables will have a formula with:
y = c + b1x1 + b2x2
where,
c = constant
b1 = first regression coefficient
x1 = first independent variable
b2 = second regression coefficient
x2 = second independent variable.
In conclusion, the line of best fit expresses the relationship in a scatterplot of the data points.
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question in pic below ;))))
Answer:
The first table
Step-by-step explanation:
If you create a fraction x/y, you will see all of the answers reduce down to -1/4. The other tables don't reduce to the same values.
the phases in algebra are
Answer:
rhetorical stage, syncopated stage, symbolic stage
Step-by-step explanation:
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.15x2 − 6x + 400
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
The function of the production cost is a quadratic function, and the maximum production cost of the company is $340
How to determine the maximum production cost of the company?The function of the production cost is given as:
f(x) = 0.15x² - 6x + 400
Differentiate the function
f'(x) = 0.3x - 6
Set the function to 0
0.3x - 6 = 0
Add 6 to both sides
0.3x = 6
Divide both sides by 0.3
x = 20
Substitute x = 20 in f(x) = 0.15x² - 6x + 400
f(20) = 0.15 * 20² - 6 *20 + 400
Evaluate
f(20) = 340
Hence, the maximum production cost of the company is $340
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the volume inside a rectangular storage room is 2,025 cubic feet. the room is 9 feet high. find the the area of the floor.
Answer:
(Sorry if this answer is not correct, if it is or is not, please tell me in the comments!)
232.777778 feet squared (feel free to round the answer)
Step-by-step explanation:
The formula on how to find the volume is:
(the area of the floor) x (the height of the room) = 2025 cubic feet
We already know the height, so we need to plug it in.
(the area of the floor) x 9 feet = 2095 cubic feet
To get the area of the floor, we need to divide 2095 by 9.
So, the area of the floor is exactly 232.777778 feet squared.
Answer:
225 ft²
Step-by-step explanation:
Formula
Volume = Base Area x HeightVolume = 2,025 ft³Height = 9 ftSolving :
Base Area = Volume / HeightBase Area = 2,025 / 9Base Area = 225 ft²What is the Pythagorean Theorem used for?
Answer:
Pythagorean Theorem used for finding the missing side length for a triangle the formula is a^2 + b^2 = c^2
a= base
b= height
c= the diagonal side a.k.a. hypotenuse
Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation: