The width of the base of the rectangular pyramid is 6 inches, which is found by rearranging and simplifying the formula for the volume of a pyramid using the given values for the pyramid's volume, height, and length.
Explanation:The student has asked about finding the width of the base of a rectangular pyramid with a known volume, height, and base length. To find the width (w), we use the formula for the volume of a pyramid: V = (1/3) × base area × height. The base area is the product of the base length (l) and width (w), so we can rewrite the equation as V = (1/3) × l × w × h, where
V is the volume of the pyramid,l is the length of the base,w is the width of the base,h is the height of the pyramid.Given that V = 1512 in³, h = 12 in, and l = 21 in, the equation becomes 1512 = (1/3) × 21 × w × 12. Simplifying, we find w = 1512 / (1/3 × 21 × 12), which calculates to 6 in. Hence, the width of the base of the pyramid is 6 inches.
A sphere has a diameter of 0.926 inch what is the volume of the sphere use 3.14 for Pie
Answer:
The volume of the sphere is [tex]0.415\ \text{inch}^3[/tex].
Step-by-step explanation:
The diameter of a sphere is 0.926 inch. It is required to find the volume of the sphere. The formula used to find the volume of sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Since, r is radius, r = d/2 = 0.463 inch
So,
[tex]V=\dfrac{4}{3}\times 3.14\times (0.463)^3\\\\V=0.415\ \text{inch}^3[/tex]
So, the volume of the sphere is [tex]0.415\ \text{inch}^3[/tex].
Javon is helping his dad build a tree house. He has a piece of trim that is 19 feet long. How many pieces can Javon cut that are 1 yard long? How much of a yard will he have left over?
Workout this equation
X(x+2)(x+4)
Answer:
x^3 <-- exponent, x to the power of three
Explanation:
x(x+2)(x+4)
=(x(x+2))(x+4)
=(x(x+2))(x)+(x(x+2))(4)
=x^3+2x^2+4x^2+8x
=x^3+6x^2+8x
Step-by-step explanation:
x(x+2)(x+4)
first get rid of the bracket
x square +2x+x+4
x^2 + 3x + 4
What is the y-intercept when f(0) = 5^1?
Answer:
(0,5)
Step-by-step explanation:
5^1=5, meaning that the y coordinate y-intercept is 5. Therefore, the y intercept is (0,5). Hope this helps!
Convert
102.48
°
to radian measure.
Round your answer to the nearest hundredth.
Answer:
1.79 radians to the nearest hundredth.
Step-by-step explanation:
To covert, we multiply degrees by π/180
so radians = 102.48 * π/180
= 1.7886 radians.
Write a formula for r in terms of θ based on the image below.
The angle in the figure is a central angle in radians.
Answer:
7pi/theta
Step-by-step explanation:
Arc length = r × theta
7pi = r × theta
r = 7pi/theta
Answer:
7pi/theta
Step-by-step explanation:
hope it helps <3
what is q + 166 = 300?
what is 14.2 = t − 5.4?
Answer:
For the first one q is 134
And the second one is t is 8.8
Step-by-step explanation:
That is true cause 134 +166 = 300
and, 14.2 = 8.8 - 5.4.
Please Mark brainliest!
For the equations given, the value of q is found to be 134 after subtracting 166 from both sides, and the value of t is calculated as 19.6 by adding 5.4 to both sides.
To solve the first equation, q + 166 = 300, we need to isolate the variable q by subtracting 166 from both sides of the equation:
q + 166 - 166 = 300 - 166
q = 134
So, the value of q is 134.
For the second equation, 14.2 = t - 5.4, we need to isolate the variable t by adding 5.4 to both sides of the equation:
14.2 + 5.4 = t - 5.4 + 5.4
t = 19.6
Thus, the value of t is 19.6.
Can someone please answer this it’s due today and i’ll mark brainliest
Answer:
Step-by-step explanation:
9-2=7
Answer=7
What is the simplified form of
Answer:
Step-by-step explanation:
[tex]\sqrt{64x^{16}} =\sqrt{8^{2}*x^{8*2}}\\\\ =\sqrt{8^{2}*(x^{8})^{*2}}\\\\=8x^{8}[/tex]
Can you help me work out the circumference of this circle? If so, give your answer in terms of Pi
The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.
Explanation:The circumference of a circle can be found using the formula C = 2πr, where C represents the circumference and r is the radius of the circle.
For example, if the radius of the circle is 5cm, the circumference would be C = 2π(5) = 10π cm. It is important to note that the circumference is always given in terms of π, which represents the mathematical constant.
Therefore, the circumference of a circle can be calculated by multiplying the radius by 2π.
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Jessica records the number of winners at the Dunk-a-Teacher booth at the town fair as shown in the table. If there are 750 contestants on Monday, how many should Jessica expect to dunk a teacher?
Answer:
do you need help
Step-by-step explanation:
Answer:
Between 75 and 98.
Step-by-step explanation:
Let's first have a look at the previous data available:
Friday, 27 dunk teachers out of 215 participants (12.5%)
Saturday: 54 dunk teachers out of 417 participants (12.9%)
Sunday: 39 dunk teachers out of 368 participants (10.6%)
So, based on the previous 3 days, she can expect between 10% and 13% will dunk a teacher.
If she has 750 contestants on Monday, the number of winners should then be in the range of 75 (10% of 750) and 98 (13% of 750).
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Step-by-step explanation:
PLEASE HELP ME FOR BRAINLIEST
Answer:
x = 3.873 units
or x = [tex]\sqrt{15}[/tex] units
Step-by-step explanation:
Hypotenuse = 4 , x = height of this isosceles triangle.
base is 2,
so Use Pythagorean Theorem.
x^2 + 1^2 = 4^2
x^2 = 4^2 - 1^2
x^2 = 16 - 1 = 15
x = root(15) =
Fido’s domain is limited by a 10-foot long leash that is tethered to the corner of his expansive 7 by 5-foot dog mansion. How much outdoor territory can Fido mark?
9514 1404 393
Answer:
83.5π ft² ≈ 262.3 square feet
Step-by-step explanation:
Fido's area is 3/4 of a 10' radius circle plus 1/4 each of a 3' radius and 5' radius circle.
A = (3/4)(π(10 ft)²) +(1/4)(π)((3 ft)² +(5 ft)²)
= (75π +34/4π) ft² = 83.5π ft² ≈ 262.3 square feet
Answer:
approximately 262.3 square feet
Step-by-step explanation:
Determine the volume of each right prism
A- area of base = 6cm2, height = 4cm
B- Area of base = 20cm, height =2cm
C- Height = 10cm, area of base = 15cm
Answer:
his page is about surface area of prism. ... Base is triangular so either use 1) Area = ½ x base x height or if the height is ... 1) The base of a triangular prism is ΔABC, where AB = 3 cm, BC = 4 cm and ∠B = 90. If the height of the prism is 10 cm. ... by Pythagorean theorem in ΔABC, C 2 = a 2 + b 2 = 3 2 + 4 2 = 9 + 16. C 2 = 25
Step-by-step explanation:
Evaluate. 5(-6) = _______
Answer:
-30
Step-by-step explanation:
-6*5=-30
The value of the x is -30 or the value of the number expression is -30 after performing the arithmetic operation the answer is -30.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that;
The number expression is:
= 5(-6)
Let x be the value of the expression;
x = 5(-6)
After performing the arithmetic operation:
x = -30
Thus, the value of the x is -30 or the value of the number expression is -30 after performing the arithmetic operation the answer is -30.
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Sharon hits a golf ball off the ground. The function h represents the height of the golf ball, in feet, t seconds after it is hit. h(t) = -16(t − 3)2 + 144 Which of the following statements describes this situation correctly?
The statement which best describes the situation correctly is that the golf ball is on the ground at 0 and 6 seconds.
Given that:
Sharon hits a golf ball off the ground.
The function h represents the height of the golf ball, in feet, t seconds after it is hit.
h(t) = -16(t - 3)² + 144, which is a quadratic function.
Since the options contain the time when the ball hits the ground, it is required to find the time when the ball hits the ground.
When the ball is on the ground, the height is 0.
So, h(t) = 0
-16(t - 3)² + 144 = 0
-16(t - 3)² = -144
Divide both sides by -16.
(t - 3)² = 9
Take the square root on both sides.
t - 3 = ±√9
t - 3 = ±3
So, t = 3 + 3 and t = -3 + 3
So, t = 6 and t = 0
Hence, the ball hits the ground when t = 0 and t = 6, which is option B.
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The complete question is given below.
Given the figure. Find AC.
(10) COS(40°) = AC
10/cos(40°) = AC
10/sin(40°) = AC
(10) sin(40%) =
Image is missing, so i have attached it.
Answer:
AC = 10sin 40°
Step-by-step explanation:
From the diagram attached, using terms in trigonometric ratio, AC is the opposite side, BC is the adjacent side and AB is the hypotenuse.
Thus, since we want to find AC;
We know that in trigonometric ratios; opposite/hypotenuse = sin θ
In the diagram, θ = 40° and AB = 10
Thus,
AC/10 = sin 40°
Multiply both sides by 10 to get;
AC = 10sin 40°
For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?
Answer:
k = 21
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
Inverse Variation: xy = k
x = 7
y = 3
Step 2: Solve for k
Substitute: 7(3) = kMultiply: 21 = kRewrite: k = 21Is h=11 a solution of the equation 1=h/11
Answer:
Yes
Step-by-step explanation:
1/1=1
So 11/11 =1
By substituting 11 for h you get it fits
please help me!!!!!!!!
Answer:
C
Step-by-step explanation:
Using the sine ratio in the right triangle
sin17° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{25}[/tex]
Multiply both sides by 25
25 × sin17° = x, thus
x ≈ 7.3 → C
What’s 0 divided by 0
Answer:
YOU CANNOT DIVIDE BY 0
Step-by-step explanation:
Answer:
Undefined. You cannot divide zero by zero.
Find the area of the figure?
Answer:
14 m
Step-by-step explanation:
For the triangle, you use the formula A=1/2bh. So in this case it's 3×4×1/2. 3×4 is 12, times 1/2 is 6 m. Now for the rectangle it's just 2×4 which is 8. 8+6 is 14. Hope this helps! If you are still confused please comment!
11x+14y=13
11x+10y=25
Add or subtract.
7z2 − 2z4 − 2z2 − 5z4
To solve the given polynomial addition and subtraction question, combine like terms. The z4 terms combined are -7z4 and the z2 terms are 5z2, resulting in the simplified expression 5z2 - 7z4.
Explanation:To add or subtract the polynomials 7z2 − 2z4 − 2z2 − 5z4, you'll want to combine like terms. Like terms are terms that have the same variables raised to the same power.
Here, z2 and z4 are like terms, so you can combine them separately.
Starting with the z4 terms:
-2z4 and -5z4 combine to give you -7z4. They both have the same variable z raised to the fourth power, so you just add the coefficients, keeping the exponent the same.
Then, combine the z2 terms:
7z2 and -2z2 combine to give you 5z2.
Similarly, these terms have the same variable z raised to the second power.
Now, putting it all together, you get:
5z2 − 7z4
This is the simplified version of the polynomial after combining like terms.
Jordan is using centimeter cubes to build a model. She makes a rectangular prism that is 25 cubes long, 6 cubes tall, and 16 cubes wide. What is the volume of Jordan's model?
Answer:
2,400 cm3
Step-by-step explanation:
If the dimensions of the rectangular prism are 25 cubes, 6 cubes and 16 cubes, and each cube has 1 centimeters, the dimensions in centimeters are:
25 cm, 6 cm and 16 cm.
Then, to find the volume of the rectangular prism, we just need to multiply all three dimensions:
Volume = 25 * 6 * 16 = 2,400 cm3.
FP!!!!!!!!!!!!!!!!!!!!
(10 x 6 ) + 20
Answer:
80
Step-by-step explanation:
Following the order of operations (PEMDAS), you would first multiply 10 by 6 to get 60. You would then add 20 to the product to get your answer.
(10 · 6) + 20
60 + 20 = 80
look at the attached picture
hope it will help you
A wave has a frequency of 900Hz and a wavelength of 200m at what speed is this wave traveling
Answer:
180000 m/s
Step-by-step explanation:
The frequency of the wave is 900 Hz.
The wavelength of the wave is 200 m.
The speed of a wave is given as the product of wavelength and frequency. That is:
v = λf
where λ = wavelength
f = frequency
The speed of the wave is therefore:
v = 200 * 900 = 180000 m/s
The speed of the wave is 180000 m/s.
1) An object exerts a force of 30 lb on an area of 5 square inches. What is the pressure the object
exerts on the surface?
Answer:
Pressure = 6psi
Step-by-step explanation:
The formula for finding pressure is
Pressure = Force ÷ Area
Substitute your values into the equation and solve for Pressure
Pressure = 30 ÷ 5
Pressure = 6psi
bob got a raise, and his hourly wage increased from 12 to 15. what is the percent increase?
25%
12x0.25=3
12+3=$15
Using percentages we know that the percentage increase is 1.25%.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.So, the percentage increase:
Formula: Original price + amount increases/original priceThe amount increased: 15 - 12 = $3Now, calculate as follows:
Original price + amount increases/original price12 + 3/1215/121.25%
Therefore, using percentages we know that the percentage increase is 1.25%.
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The length of a rectangle is 7 inches longer than it is wide. If the area is 20 square inches, what are the dimensions of the rectangle?
Area of a rectangle is length x width.
Let the width = x
The length would be x +7. ( 7 inches longer than the width)
Area = 20
Set up the formula:
20 = x * x+7
Simplify the right side:
20 = x^2 + 7x
Subtract 29 from both sides:
X^2 + 7x -20 = 0
Solve using the quadratic equation
X = -b + sqrt(b^2 -4ac) / 2a
X = -7 + sqrt(7^2-4(1)(-20) / 2(1) (exact answer)
X = 2.178908 ( as a decimal)
The width is 2.178907 inches (round as needed)
The length would be 9.178907 inches ( round as needed.)
Depending on how you round, when you multiply them together you get approximately 20 square inches.
Step-by-step explanation:
Step 1: Find the dimensions
l = 7 + w
Area = 20
Find width
[tex]A = l * w[/tex]
[tex]20 = (7 + w)(w)[/tex]
[tex]20 - 20 = 7w + w^2 - 20[/tex]
[tex]w^2 + 7w - 20 = 0[/tex]
[tex]w=\frac{-(7)\pm\sqrt{(7)^2-5(1)(-20)}}{2(1)}[/tex]
[tex]w = 2.17890...[/tex]
Find length
[tex]l = 7 + w[/tex]
[tex]l = 7 + 2.17890...[/tex]
[tex]l = 9.17890...[/tex]
Answer: [tex]Width = 2.17890..., Length = 9.17890...[/tex]