Given is a square pyramid with a base length of 5 centimeters and a height of 6 centimeters.
The volume formula of square pyramid is given by :-
[tex] volume = \frac{1}{3} (base\; area)(height) [/tex]
Base area would be a square of side length equal to 5 centimeters.
Area of square = (side)² = 5 × 5 = 25 squared centimeters.
Now, volume of square pyramid = [tex] \frac{1}{3} (25)(6) [/tex] = 50 cubic centimeters.
So, final answer is 50 cubic centimeters.
10p = 66 what is the value of p
stewart draws a triangle , and each side is 2 1/6 inches long. Judith draws a square , each side is 1 5/8 inches long . which figure has the greater perimeter, the triangle or the square?
Upon calculating, it is found that both Stewart's triangle and Judith's square have the same perimeter of 6 1/2 inches. This shows that despite different shapes, their perimeters can be equal if the lengths of their sides are chosen accordingly.
Explanation:The question is about comparing the perimeters of a triangle drawn by Stewart and a square drawn by Judith. Stewart's triangle has each side measuring 2 1/6 inches long, which when converted to improper fraction becomes 13/6 inches. For the triangle, the perimeter is calculated by multiplying the length of one side by three (since a triangle has three sides). The perimeter of Stewart's triangle is 13/6 * 3 = 39/6 = 6 1/2 inches.
Judith's square has each side measuring 1 5/8 inches long, which is equivalent to 13/8 inches. For the square, the perimeter is the length of one side times four (because a square has four equal sides). Thus, the perimeter of Judith's square is 13/8 * 4 = 52/8 = 6 1/2 inches.
Therefore, both the triangle and the square have the same perimeter of 6 1/2 inches.
Helpppp please anyone. I don't understand
50 POINTS!!! SHOW YOUR WORK AND ANSWER CORRECTLY OR ELSE A MODERATOR WILL HANDLE YOU! Let f (x) = −x^2 − 5x + 36. What is the value of f(-3)? Show your work. Best answer gets brainliest.
consider the following system with a solution (1,3) equation 1 of the system 2x+y=5 equation 2 of the system x-2y=-5 prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution
To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system. Then we will calculate the solution to the modified system of equations and check if the solution is the same.
Explanation:To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system of equations (1,3). Then we will calculate the solution to the modified system of equations in which the first equation is replaced with the sum of the two equations. If the solution to the modified system is also (1,3), then we have shown that the modified system has the same solution.
Original system:
Equation 1: 2x + y = 5
Equation 2: x - 2y = -5
Substitute x = 1 and y = 3 into the original equations to check if it is a solution:
Equation 1: 2(1) + 3 = 5 => 2 + 3 = 5 => 5 = 5 (true)
Equation 2: 1 - 2(3) = -5 => 1 - 6 = -5 => -5 = -5 (true)
Hence, (1,3) is a solution to the original system of equations.
To create the modified system, we will sum equation 1 and a multiple of equation 2:
New equation 1: (2x + y) + k(x - 2y) = 5 + k(-5), where k is a constant
Expanding and simplifying the equation:
(2 + k)x + (1 - 2k)y = 5 - 5k
Let's substitute x = 1 and y = 3 into the modified equation to check if (1,3) is a solution:
(2 + k)(1) + (1 - 2k)(3) = 5 - 5k
2 + k + 3 - 6k = 5 - 5k
3 - 5k = 5 - 5k
3 = 5 (false)
Therefore, the modified system does not have the same solution as the original system, disproving the statement.
Learn more about System of Equations here:https://brainly.com/question/21620502
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Mr. Watkins earns $35 an hour at his new job. During a typical month, he works a total of 160 hours. Mrs. Watkins is a homemaker. After meeting the estimated monthly expenses, how much money will the family have left to spend on other items?
A) $1150
B) $1322
C) $1445
D) $1500
Need help with number 12 please, thanks.
Write the first terms of the sequence. Rule:start at 1/2,add1/3
A human society has 73 dogs and cats to be adopted. the number of cats is 10 more than twice the number of dogs. Write a system of linear equations that represent this situation. How many of each animal is up for adoption?
A linear equation of one variable is expressed in the form of ax + b = 0, where a and b are the two integers, and x is a variable.
In the given question, the linear equation can be represented as:
2x + 10 + x = 73.
The number of dogs is 21, and the number of cats available is 52.
Given that:
Total number of dogs and cats = 73
Let the number of dogs be x.
The number of cats, as given is = 10 + 2x
Now, solving for the equation:
x + 10 + 2x = 73
Solving for the variables:
3x + 10 = 73
3x = 73 -10
3x = 63
x = [tex]\dfrac {63}{3}[/tex]
x = 21
The number of dogs available is 21.
The number of cats available is:
2x + 10
Putting the value of x:
2 (21) + 10
52
Thus, the number of dogs is 21, and the number of cats available is 52.
To know more about linear equations, refer to the following link:
https://brainly.com/question/11897796
n complete two or more sentences, determine the appropriate model for the given data and explain how you made your decision. (1,0), (2,1.5), (5,2.5), (8,3)
dennis wants to buy a card for his wife. dennis calculates the amount of the card as $4.50. the actual price of the card is $4. what is Dennis's percent error?
Final answer:
Dennis's percent error in estimating the price of the card is 12.5%, calculated by taking the difference between his estimate and the actual price, dividing by the actual price, and then multiplying by 100.
Explanation:
Dennis calculated the amount of the card as $4.50, but the actual price is $4.00. To find Dennis's percent error, we'll need to calculate the difference between his estimated price and the actual price, and then divide that by the actual price. Finally, we'll multiply that number by 100 to get the percent error.
Here's how we'll calculate it:
Divide the error by the actual value: $0.50 ÷ $4.00 = 0.125.
Multiply by 100 to convert to a percentage: 0.125 × 100 = 12.5%.
The percent error in Dennis's estimate is 12.5%.
What number could be added to 0.40 mL for the level of precision to be 0.01mL
Answer:
- 0.39
Step-by-step explanation:
Level of precision = 0.01 mL
We need to find a number which could be added to 0.40 mL for the level of precision to be 0.01 mL .
Let x be a number which could be added to 0.40 mL for the level of precision to be 0.01 mL .
[tex]x+0.40=0.01[/tex]
On subtracting 0.40 from both sides , we get
[tex]x+0.40-0.40=0.01-0.40[/tex]
On solving , we get
[tex]x+0=0.01-0.40[/tex]
We know that [tex]x+0=x=0+x[/tex] where 0 is the additive inverse .
So,
[tex]x=0.01-0.40[/tex]
Here , [tex]0.01-0.40=-0.39[/tex]
Therefore ,
[tex]x=0.01-0.40=-0.39[/tex]
Therefore , -0.39 could be added to 0.40 mL for the level of precision to be 0.01mL
Multiply: (−8x − 15)(−12x2 + 12x + 3)
A) 96x3 + 84x2 − 156x − 45
B) 96x3 + 84x2 − 204x − 45
C) 96x3 + 276x2 − 204x − 45
D) 96x3 − 84x2 − 156x − 45
Your friend invites you to go to an indoor skateboard park. You'd like to go, but since you don't have a helmet or knee pads, you'll have to rent them. You'll also need to but a day pass to enter the park.
Write a formula that will help you determine your total cost.
Let's let:
h = helmet rental
k = knee pad rental
p = cost of day pass
c = total cost
HELP What is the area of this figure?
Represent the proportional relationship described with an equation where p equals pepperoni and z equals pizza: eighteen pepperoni for each pizza A) p = 18z B) 18p = z C) p = 18 z D) z = 18 p
Answer:
The answer is A. p=18z I just took the test
Answer:
It is A I got it right on usa test prep
Step-by-step explanation:
The square of a positive number decreased by twice the number is 48. Find the number
The length of a rectangle is 6 inches more than it’s with the perimeter of the rectangle is 24 inches what is the width and length of the rectangle
Water from a leaking faucet is dripping into a cylindrical cup. The height of water in inches, y, after x hours is graphed belowThe water level increases by 1 inch each hour.
A The water level increases by 1 inch each hour.
B The water level increases by 2 inches each hour.
C The water level increases by a factor of 1/2each hour.
D The water level increases by a factor of 2 each hour.
Jones of Boston borrowed $40,000, 90 day, 10% note. After 60 days Jones made an initial payment of $6,000. Assuming the U.S. Rule what is adjusted balance after the first payment. Use 360 days.
Christopher Christopher just found beautiful yarn for 20% off at his favorite yarn store. He can make one scarf from 2/3 of a ball of yarn. If Christopher buys 12 balls of yarn, how many scarves can he make
What is the area of the triangle in this coordinate plane
What shows all like terms in this expression?
4x - 3 + 7x + 1
Answer:
a
Step-by-step explanation:
Jerry started doing sit-ups every day. The first day he did 15 sit-ups. Every day after that he did 4 more sit-ups than he had done the previous day. Today Jerry did 65 sit-ups. Write an equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day. Let n represent the number of days.
Thanks
The first day Jerry did 15 sit-ups:
a0 = 15
The 2nd day he did 4 more sit-ups then the previous:
a1 = a0 + 4
The 3rd day he did 4 more sit-ups then the previous:
a2 = a1 + 4
a2 = a0 + 4 + 4
a2 = a0 + 4*4
the (n+1)-th day he did:
an = a0 + 4n
Today Jerry did 65 sit-ups means we have: an = 65 and we need to find n
a0 + 4n = 65
15 + 4n = 65
Now to solve
subtract 15 from both sides
4n = 50
divide both sides by 4
n = 12.5
But I think this is counting the first day
Not counting the first day would be
4n = 65
n = 16.25
I guess that's the answer :)
Somebody Really Help On These Questions 5 and 6!!!!!!!!!!!!!!!
Last year, at the Great American Pie Festival, over 16,000 slices of pie was eaten. If each piece of pie is 1/8 of and entire pie, how many pies were eaten at the festival?
Answer:
2,000 pies!
Step-by-step explanation:
Why is subtracting an expression similar to distributing -1? Explain.
Subtracting an expression is akin to distributing -1 to each term within the expression. This is because subtraction can be viewed as adding the negation of the expression, which involves multiplying each term by -1. So, each term within the expression gets negated when subtracting.
When you subtract an expression, you can think of it as distributing a negative sign (-1) to each term within the expression. Here's a step-by-step explanation:
Start with the expression you want to subtract from, let's call it A.
When you subtract another expression, let's call it B, from A, you're essentially adding the negation of B to A.
The negation of B is obtained by multiplying each term of B by -1.
Distributing -1 to each term of B results in subtracting each term of B individually from A.
This process aligns with the distributive property, making subtracting an expression akin to distributing -1 to each term within the expression.
when writing an equation of a proportional relationship in the form y equals KX what does K represent
Answer:
k = the constant of proportionality .>. sorry this already kinda answered ;w;'
Oki I have a few but I’m giving a lot of points I just didn’t feel like doing them separate.
Anne wants to draw two adjacent angles on a straight line. She wants one angle to be 24 degrees more than the other angle. Select two correct choices.
A. The measure of the smaller angle is 33 degrees.
B. The measure of the smaller angle is 78 degrees
C. The measure of the larger angle is 57 degrees.
D. The measure of the larger angle is 102 degrees.
A triangle has a side 4.23 meters in length, a 63.2 degree angle, and a 75.9 degree angle. Which of the following statements about the triangle is true. Select all that apply.
A. The triangle is an obtuse triangle.
B. The triangle cannot be equilateral.
C. The triangle must have a third angle measuring 40.9 degrees.
D. The triangle should be isosceles
3. Mika used the proportion y-3 over x equals one third. (Y-3/x= 1/3). When deriving the equation on a line with similar triangles. Which of the statements are correct. Select two that apply.
A. It has a slope of negative one third. (-1/3)
B. It has a slope of one third. (1/3)
C. It has a slope of 3.
D. It has a y intercept of 3.
E. It has a y intercept of one third. (1/3)
F. It has a y intercept of 3.
This is a parallelogram shaped sliding door. It has four sides. (P,Q) (P,S) (S,R) (Q,R) and (Q,P)
More simply... Q is on the top right corner of the parallelogram, R is on the bottom right corner of the parallelogram, S is at the bottom left corner, and P is at the top left corner.
Which two of the statements are true if the door moves two feet to the right.
A. Side PQ would be parallel to SR, and angle R would measure 56 degrees.
B. Side PS would be parallel to side QR and angle S would measure 124 degrees.
C. Side PQ would be parallel to side PS and angle P would measure 56 degrees.
D. Side QR would be parallel to side SR and angle Q would equal to 62 degrees.
Last one!!
A parallelogram has the verifies (-4,2) (-3,5) (2,-2) (3,5)
The parallelogram was rotated 270 degrees counterclockwise about the origin. Which 3 would be the vertex of the origin.
A. (-3,5)
B. (-2,-2)
C. (-2,4)
D. (2,4)
E. (3,-5)
F. ( I’m rlly sry but I forgot this one)
The correct option is (A) (-3,5). The answer covers the relationship between angles in quadrilaterals, properties of triangles, and concepts related to similar triangles and equations.
Angles in quadrilaterals:
In the first scenario, if one angle is 24 degrees more than the other on a straight line, the correct choices are A. The measure of the smaller angle is 33 degrees and D. The measure of the larger angle is 102 degrees.
Triangles:
For the triangle with sides 4.23 meters, the correct statements are A. The triangle is an obtuse triangle and D. The triangle should be isosceles.
Similar Triangles and Equations:
When using the proportion y-3/x=1/3, the correct statements are A. It has a slope of -1/3 and E. It has a y-intercept of 1/3.
Jamal wants to build a square pen for his dog that has an area of 144 ft². What is the length of each side of the pen?
A: 12ft
B: 15ft
C: 36ft
D: 72ft