1. The volume of the pyramid is 320ft³
3. The volume of the pyramid is 2395.83cm³
5. The volume of the pyramid is 1200in³
What is volume of a rectangular pyramid?The volume of a rectangular pyramid can be calculated using the formula:
V = (1/3) * base area * height
Where:
V represents the volume of the pyramidThe base area refers to the area of the base of the pyramidThe height represents the vertical distance from the base to the apex (top) of the pyramid.1. The volume of the pyramid is calculated as;
V = 1/3 * 8 * 12 * 10 = 320ft³
3. The volume of the pyramid is;
V = 1/3 * (25 * 12.5) * 23 = 2395.83cm³
5. The volume of the pyramid is;
V = 1/3 * (15 * 15) * 16 = 1200in³
Learn more on volume of a rectangular pyramid here;
https://brainly.com/question/20620595
#SPJ1
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
Learn more about the triangle here:
brainly.com/question/25813512
#SPJ1
Can someone please help ???
\(\begin{array}{l}\text{Let\ x\ be\ the\ third\ side,\ then,\ by\ Pitagoras}\\\\x^{2} +5^{2} =\left(\sqrt{61}\right)^{2}\\\\\Longrightarrow x^{2} =61-25\\\\\Longrightarrow x=\sqrt{36} =6\end{array}\)
Which of the following is true concerning the expression 6x + 3 + x? 6x and 3 are like terms. B 6x and x are like terms. C The simplified form of the expression is 6x + 3. D The simplified form of the expression is 10x.
Answer:
Time is very precious and we should not waste it in any way. Likewise, we can earn the money we spent but we cannot get back the time we have lost. So, this makes the time more valuable than money. Hence, we should utilize the time in the most possible way.
Step-by-step explanation:
Time is very precious and we should not waste it in any way. Likewise, we can earn the money we spent but we cannot get back the time we have lost. So, this makes the time more valuable than money. Hence, we should utilize the time in the most possible way.
Answer:
9 is the answer because it is the answerr
The right rectangular prism is filled with cubes that have a side length of 1/8 foot.
How many cubes does it take to fill the prism? (please just give me an exact answer.) (I WILL GIVE BRAINLIST) (please just help me)
Answer:
24
Step-by-step explanation:
To find the volume of the cube just cube one of the sides, so 1/8^3 is 1/512
Yes it's the actual volume, it didn't get smaller it's just cubic inches instead of a line.
The rectangle's volume is 1/4*3/8*1/2 which if you change them to have the same denominator it's 2/8*3/8*4/8=3/64
Now convert 3/64 to have a denominator of 512
3/64*8/8= 24/512
24/512 divided by 1/512 is 24
You can fit 24 cubes in the rectangle.
PLEASE HELP
What is the domain of a quadratic functions that opens up or down?
The volume of a right cone is 2325
�
π units
3
3
. If its radius measures 15 units, find its height.
The height of the right cone will be 9.86 units.
What is the volume of a cone?The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.
Given that the volume of the cone is 2325 cubic units and the radius of the cone is 15 units.
The height of the cone will be calculated as:-
Volume = 2325
(1/3)πr²h = 2325
( 1/3 ) x π x 15)² x h = 2325
h = ( 2325 x 3 ) / ( 15 x 15 x π )
h = 9.86 units
Therefore, the height of the right cone will be 9.86 units.
To know more about the volume of the cone follow
https://brainly.com/question/28109167
#SPJ1
Put these numbers in order from least to greatest.
24.269
23.3
23.06
23.7
Answer:
Step-by-step explanation:
23.06, 23.3, 23.7, 24.269
Which is equivalent to 64 1/4
Answer:
4*64=256
256+1=256
there fore 64 1/4 is equivalent to 257/4
What's a negative number greater than?; What does a negative 10 mean?; Is any negative number greater than 0?; How do you write a negative number?
Answer: See explanation
Step-by-step explanation:
Negative numbers are greater than other negative numbers with a higher numerical value, for example negative 1 is greater than negative 3.
Negative 10 means 10 below 0.
There is no negative number that is greater than 0.
You write a negative number by putting a subtraction sign before the number. For example, negative 3 would be -3 (or minus 3 from nothing).
Need help with top problem. Maybe bottom too
1) The area of a circle circumscribed about a square is 307.7 cm².
2.a.) The angle ACB is 39 degrees.°.
2b.) The value of x is 5.42.
How to determine the area of a circle?We shall find the radius to determine the area of a circle.
First, find the side length of the square:
Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.
Next, find the diagonal of the square, using the Pythagorean theorem:
Diagonal = the diameter of the circumscribed circle.
Diagonal² = side length² + side length²
= 14 cm² + 14 cm²
= 196 cm² + 196 cm²
= 392 cm²
Take the square root of both sides:
Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)
Then, the radius of the circle which is half the diagonal:
Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)
Finally, compute the area of the circle using the formula:
Area = π * Radius²
Area = 3.14 * (9.90 cm)²
Area ≈ 307.7 cm² (rounded to two decimal places)
Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².
2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.
Given that arc AB has a measure of 78°, we can find angle ACB as follows:
Angle ACB = 1/2 * arc AB
= 1/2 * 78°
= 39°
Therefore, the angle ACB is 39 degrees.
2b.) To solve for the value of x, we use the information that the angle ADB = (3x - 12)⁴.
Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:
(3x - 12)⁴ = 78
Solve the equation for x, by taking the fourth root of both sides:
∛∛((3x - 12)⁴) = ∛∛78
Simplify,
3x - 12 = ∛(78)
Isolate x by adding 12 to both sides:
3x - 12 + 12 = ∛(78) + 12
3x = ∛(78) + 12
Finally, divide both sides by 3:
x = (∛(78) + 12) / 3
x = (4.27 +12) / 3
x = 5.42
So, x is 5.42
Therefore,
1) The area of the circle is 154 cm².
2a.) Angle ACB is equal to 102°.
2b.) The value of x is 5.42
Learn more about the area of a circle at brainly.com/question/12374325
#SPJ1
Simplify the expression below by following the order of operations and combining like terms. Do not put spaces between characters. If your expression has more than one term put your terms in descending powers of he variable. 6+12b-3*6b The expression simplifies to:
GIven equation:
\(6+12b-3\times6b\)simplyfing the equation,
\(\begin{gathered} =6+12b-3\times6b \\ =6+12b-18b \\ =6-6b \\ =-6b+6 \end{gathered}\)The simplfied equation is -6b+6.
Two shops, Tesco and Asda , sell the same brand of baked beans with the following deals.
Calculate the price per item for each shop.
Write the shop which is the best value for money in the comment box.
Tesco= 2 for £1.14
Asda=5 for £2.80
Answer:
Asda offers a better value
Step-by-step explanation:
1.14 / 2 = 0.57
2.80 / 5 = 0.56
what is the numerical answer?
Answer:
x = 3
Step-by-step explanation:
In a parallelogram the diagonals bisect each other , then
6x + 11 = 5x + 14 ( subtract 5x from both sides )
x + 11 = 14 ( subtract 11 from both sides )
x = 3
I need it done very quick pls help
Can somebody help me, I'm being timed!
Answer:
I think its -- linear postulate
Step-by-step explanation:
(-37)+(-2) please tell quickly
Answer:-39
Step-by-step explanation:
The first thing is to open the bracket.
By doing that, the question becomes -37-2.
note that plus×minus=minus.
Hence,-39 as the final answer
Find g(x) if the indefinite integral of f(x) need little help
Answer:
g(x) = 4x² - x
General Formulas and Concepts:
Algebra II
Functions
Function NotationPiecewise FunctionsCalculus
Integration
IntegralsIntegral NotationIntegration Constant CIntegration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]: \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Step-by-step explanation:
*Note:
Integrating a piecewise function requires you to integrate both parts.
Step 1: Define
Identify.
\(\displaystyle f(x) = \left \{ {{8x - 1 ,\ x \leq 4} \atop {31 ,\ x \geq 4}} \right.\)
\(\displaystyle \int {f(x)} \, dx = \left \{ {{g(x) + C ,\ x \leq 4} \atop {31x + C ,\ x \geq 4}} \right.\)
Step 2: Find function g(x)
We can see that the 2nd part of the piecewise function already has been integrated:
[Integral] Set up: \(\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = \int {31} \, dx ,\ x \geq 4\)[Integral] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31 \int {} \, dx ,\ x \geq 4\)[Integral] Integrate [Integration Rule - Reverse Power Rule]: \(\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31x + C ,\ x \geq 4\)To find function g(x), we simply have the same setup:
[Integral] Set up: \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x - 1} \, dx ,\ x \leq 4\)[Integral] Rewrite [Integration Rule - Addition/Subtraction]: \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x} \, dx - \int {1} \, dx ,\ x \leq 4\)[Integrals] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \int {x} \, dx - \int {} \, dx ,\ x \leq 4\)[Integrals] Integrate [Integration Rule - Reverse Power Rule]: \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \bigg( \frac{x^2}{2} \bigg) - x + C ,\ x \leq 4\)Simplify: \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 4x^2 - x + C ,\ x \leq 4\)Redefine: \(\displaystyle g(x) = 4x^2 - x + C ,\ x \leq 4\)The integration constant C is already included in the answer, so our answer is g(x) = 4x² - x.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration (Applications)
Find rise, run and slope values
From the given graph, the rise, run and slope of this graph are 1, 5, and 1/5 respectively.
Slope of a LineThis is the ratio between the rise and run i.e y-axis and x-axis.
The rise any graph is the change in the y-axis.
Rise\(\delta y = y_2 - y_1\)
The rise in this graph will be
\(\delta y = 1 - 0 = 1\)
RunThe run on any graph is the change in the x-axis.
\(\delta x = x_2 - x_1\)
The run on this graph is
\(\delta x = 5 - 0 = 5\)
Having the values of rise and run, we can find the slope of this graph
\(m = \frac{\delta y}{\delta x} = \frac{1}{5}\)
The rise, run and slope of this graph are 1, 5, and 1/5 respectively.
Learn more on slope here;
https://brainly.com/question/3493733
Find the missing side lengths. Leave your answer as radicals in simplest form.
The values of x and y are in the triangles are (28) x = 90√3 and y = 90 and (29) x = 116 and y = 58
How to determine the missing lengths?Triangle 28
The value of x is calculated using the following cosine function
cos(30) = Adjacent/Hypotenuse
So, we have
cos(30) = x/180
Multiply through by 180
So, we have
x = 180 * cos(30)
Evaluate cos(30)
x = 180 * √3/2
Evaluate the product
x = 90√3
The value of y is calculated using the following sine function
sin(30) = Opposite/Hypotenuse
So, we have
sin(30) = y/180
Multiply through by 180
So, we have
y = 180 * sin(30)
Evaluate sin(30)
y = 180 * 1/2
Evaluate the product
y = 90
Hence, the values of x and y are x = 90√3 and y = 90
Triangle 29
The value of x is calculated using the following sine function
sin(60) = Opposite/Hypotenuse
So, we have
sin(60) = 58√3/x
Multiply through by x
So, we have
x sin(60) = 58√3
This gives
x = 58√3/sin(60)
Evaluate sin(60)
x = 58√3/(√3/2)
Evaluate the quotient
x = 116
The value of y is calculated using the following cosine function
cos(60) = Adjacent/Hypotenuse
So, we have
cos(60) = y/x
cos(60) = y/116
Multiply through by 116
So, we have
y = 116 * cos(60)
Evaluate cos(60)
y = 116 *1/2
Evaluate the product
y = 58
Hence, the values of x and y are x = 116 and y = 58
Read more about right-triangles at
https://brainly.com/question/2437195
#SPJ1
Four sisters are all 2 years apart in age. The
total of their ages is equal to 36 years. How
old is the youngest sister
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The four sisters are all 2 years apart in age. The total of their ages is equal to 36 years.
Let x be the age of the youngest sister. Then the age of other sister will be x + 2, x + 4, and x + 6. Then the equation is given as,
x + x + 2 + x + 4 + x + 6 = 36
4x + 12 = 36
4x = 36 - 12
4x = 24
x = 24 / 4
x = 6
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
Please help!!!! Keep getting answer wrong
Answer:
Your solution is (1, -4)
Step-by-step explanation:
The equations both equal y, so you can set them equal to each other.
y = -4x
y = -3x - 1
-4x = -3x - 1
add 3x to both sides
-x = -1
divide both sides by -1 for x to be positive
x = 1
plug x back in
y = -4(1)
y = -4
y = -3(1) - 1
y = -3 - 1
y = -4
Your solution is (1, -4)
what is equivalent to this complex numberi^15
-i
Explanations:The given complex number is:
\(i^{15}\)Note that:
\(i^2\text{ = -1}\)Also note that:
\(\begin{gathered} i^{15}=i^{14}\times i^{\square} \\ i^{15}=(i^2)^7\times i \\ i^{15}=(-1)^7\times i \\ i^{15}=\text{ -1 }\times i \\ i^{15}=\text{ -i} \end{gathered}\)\(\text{The equivalence of i}^{15}=\text{ -i}\)1) Which number has the
least value?
A. 87.4
B. 7.48
C. 8.74
D. 4.78
PLEASE HELP WILL GIVE BRAINLIEST IF HELPFUL.
log base (2) of (x^2 +5) = (3)
Answer:
x=-√3, √3
Step-by-step explanation:
log base (2) of (x^2 +5) = (3) ==> log base (2) of (x^2 +5) -> 2^(?)=x^2 +5
2^(log base (2) of (x^2 +5)) = 2^(3) ==> important step
2^(log base (2) of (x^2 +5)) = 8
x^2+5 = 8
x^2+5-5=8-5
x^2=3
x=-√3, √3
Can u solve it?
Find x,y,v and u.
Explanation:
Basically, you can do it in many ways. But just, in my opinion, exactly linear algebra was made for such cases.
the optimal way is to do it with Cramer's rule.
First, find the determinant and then find the determinant x, y, v, u.
Afterward, simply divide the determinant of variables by the usual determinant.
eg. \(\frac{Dx_{} }{D}\) and etc.
I think that is the best way to solve it without a hustle of myriad of calculations reducing it to row echelon form and solving with Gaussian elimination.
What is the probability that either event will occur? 17 A 29 B 14 P(A or B)
The probability that either event A or B will occur is 43/60
Getting probability value :Using the parameters given
n(A) = 29
n(B) = 14
Total number of events = 29+17+14 = 60
The probability of each event :
P(A) = 29/60
P(B) = 14/60
P(A or B ) = P(A) + P(B)
P(A or B ) = 29/60 + 14/60
P(A or B ) = 43/60
Therefore, the probability of A or B is 43/60
Learn more on probability: https://brainly.com/question/24756209
#SPJ1
An angle measures 17.4° more than the measure of its complementary angle. What is the measure of each angle?
45 and 27.6 degrees are the two complementary angles.
What are the angles' measurements?The various angles or measurements include:
Measure an acute angle between 0° and 90°.Measure the obtuse angle between 90° and 180°.Right Angle: The measurement is 90 degrees.Straight Angle: The measurement is 180 degrees.Measure the reflex angle from 180° to 360°.Complete or full angle: 360° is the exact measurement.Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.
The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:
x + 17.4 = 90 - x + 17.4
When we simplify and find x, we obtain:
2x = 55.2
x = 27.6
The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.
The two complementary angles are 27.6 and 45 degrees as a result.
To know more about Complementary Angle visit:
https://brainly.com/question/5708372
#SPJ1
Please answer quick and right
Answer:
3.
Step-by-step explanation:
Since it states it needs to be cut into pieces, it's division, so since it's division we do KCF - keep change flip
We keep the first term, then we change the sign to a multiplication sign and flip the numerator and the denominator for the second term, so your equation would be :
6/8 × 4/1
6 times 4 would be 24, then we put 24 over 8, 24/8, - then you just divide 24 by 8 which would be 3. I hope this helps.
Fill in the table using this function rule.
y=-3x-3
X
-2
-1
0
1
y
0
0
0
X
Ś
Answer:
X | y
---------------
-2 | 3
-1 | 0
0 | -3
1 | -6
A trapezoid is 64 m2. The height is 12 cm and one base is 4 cm. What is the length of the missing base?
The length of the missing base is approximately 6.67 cm.
How to calculate the length of trapezoidBy applying the formula for the area of a trapezoid, we will be able to solve for the missing base.
Recall that the formula for the area of a trapezoid is:
A = \(\frac{1}{2} * h * (b_{1} + b_{2})\)
where
A = area
h = height
b₁ and b₂ are the lengths of the parallel bases.
From the question, we are given:
A = 64 m²
h = 12 cm
b₁ = 4 cm.
Plug these values into the formula above to solve the missing base
64 = \(\frac{1}{2} * 12 * (4+ b_{2})\)
Multiplying both sides by 2:
128 = 12(4 + b₂)
Simplifying:
128 = 48 + 12b₂
80 = 12b₂
b₂ = 80/12 = 20/3
b₂ = 6.67
Therefore, the length of the missing base is approximately 6.67 cm.
Learn more about trapezoid here:
https://brainly.com/question/1410008
#SPJ1