The volume of an oblique pyramid with a square base is V units3 and the height is h units.
Which expression represents the area of the base of the pyramid?
A)3v/h units
B)(3V – h) units
C)(V – 3h) units
D)V/3H units
Answers
V = (1/3) * (Ab) * (h)
Where,
Ab: base area
h: height
Clearing the area of the base we have:
Ab = (3 * V) / (h)
Answer:
An expression that represents the area of the base of the pyramid is:
A) 3v / h units
Answer: A. 3V/ h units^2
Step-by-step explanation:
Related Questions
Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 3 possible answers.
Answers
Hope this helped!
The probability of selecting correct options is 1/3.
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P[E] = n[E]/n[S]
Given are first 2 questions on a multiple choice test such that each of the question has 3 possible answers.
Now, there are two questions, with three possible answers, this means that we have total of 6 elements in a sample space. Let [A] represent the event of selecting correct options. Then there could be only 2 possible answers from the given six. Therefore, the probability of the event [A] would be :
P[A] = n[A]/n[S]
P[A] = 2/6
P[A] = 1/3
Therefore, the probability of selecting correct options is 1/3.
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Suppose you have five books in your bookbag. three books are novels
Answers
we know that
The probability on the first day is 3/5 since there are 3 novels out of 5 and when you take a book out at random, all of them have a equal chance of being picked. Since you returned the book to the bag, the next day too, we have the same probability.
Probability of a novel being grabbed both days is the product of the two probabilities-----> (3/5)*(3/5)----> 9/25
the answer is
9/25
A model of the is 2.9 ft tall and 1.2 ft wide. The Eiffel Tower is actually 410 ft wide. What is the actual height of the Eiffel Tower?
Answers
Answer:
its B)990.8 ftStep-by-step explanation:
On a digital clock, the colon (two dots between the hour and minutes) blinks every second. In 2 hours and 20 minutes, how many times will it blink?
Answers
120+20=140
140·60=8400
8400
See Picture
The colon will blink 8400 times in 2 hours and 20 minutes.
How many times will the colon blink?Since the colon blinks every second. And we know that there are 60 minutes in an hour and there are 60 seconds in a minute.
Thus, we can say:
1 minutes = 60 seconds
1 hour = 60 minutes = 3600 seconds
Note: 60 minute = (60 * 60) seconds = 3600 seconds
Thus, in 2 hours and 20 minutes, we have:
2 hours + 20 minutes = (2 * 3600) + (20 * 60)
= 7200 + 1200
= 8400 second
Therefore, the colon will blink 8400 times in 2 hours and 20 minutes.
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Drag and drop the correct expression to complete the derivation of the formula.
Answers
In the second fill in the blank you put: third option
In the third fill in the blank you put: second option
Math help please!!!!! If AO = 21 and BC = 14, what is AB?
Answers
Given is a circle O with tangent AB and secant OB.
Given is OA = 21 units and BC = 14 units.
From the diagram, OB = OC + BC.
OC and OA, both are radius, so OC = OA = 21 units.
Now OB = 21 + 14 = 35 units.
In right triangle ΔOAB, using Pythagorean theorem;
OA² + AB² = OB²
⇒ (21)² + AB² = (35)²
⇒ 441 + AB² = 1225
⇒ AB² = 1225 - 441 = 784 square units
⇒ AB = [tex]\sqrt{784} =28[/tex]
⇒ AB = 28 units.
Hence, final answer is AB = 28 units.
What are the dimensions of a rectangle that has a perimeter of 26 in the area of 36?
Answers
Katherine invested $140.she earned a simple interest of 4% per year on the initial investment. If no money was added or removed from the investment what was the amount of interst katherine received at the end of two years?
Answers
Interest for 2 years = $5.60 x 2 = $11.20
Total amount at the end of 2 years = $11.20 + $140 = $151.20
Answer: $151.20
Tell whether the ratios form a proportion: 1/9, 6/54
Answers
Final answer:
To find out if the ratios 1/9 and 6/54 form a proportion, calculate their cross-products. Since both cross-products are equal (54 = 54), they do form a proportion.
Explanation:
The question asks if two given ratios form a proportion. To determine whether ratios form a proportion, you can compare the cross-products of the ratios. If the cross-products are equal, the ratios do form a proportion. For the given ratios 1/9 and 6/54, we will calculate the cross-products:
For the first ratio, 1 times 54 equals 54.
For the second ratio, 9 times 6 equals 54.
Since both cross-products are equal (54 = 54), the ratios 1/9 and 6/54 do indeed form a proportion.
To write a proportion by setting two ratios equal to one another with the unit 'meters', an example would be 1/20 = 1/5.5. When working with unit scales or unit rates, such as in map readings or speed, you compare two measurements where one of the ratios is typically a value of 1, like the example provided 55 miles per hour, which is written as 55/1 miles/hour.
Stephen recently purchased a camper. The value of the camper after t years is given by the following expression.
22475(0.81)^t
Which of the following best describes the expression?
A.) the product of the initial value of the camper and its growth factor raised to the number of months since it was purchased
B.) the product of the initial value of the camper and its decay factor raised to the number of months since it was purchased
C.) the product of the initial value of the camper and its growth factor raised to the number of years since it was purchased
D.) the product of the initial value of the camper and its decay factor raised to the number of years since it was purchased
Answers
Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter. area: 36 square feet
Answers
A perimeter of 24 feet is achieved in this optimal scenario.
For an area of 36 square feet, we can factor this into pairs: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). Since we are looking for the minimum perimeter, the closest factors will yield the smallest perimeter, which in this case is the pair (6, 6). Therefore, a rectangle with the dimensions 6 feet by 6 feet will not only satisfy the area requirement of 36 square feet but will also have the minimum perimeter, which is 24 feet.
The perimeter (P) of a rectangle is calculated by the formula P = 2(l + w), where 'l' is the length and 'w' is the width. Given our dimensions, P = 2(6 + 6) = 24 feet. The square shape of the rectangle, which is a special case where the length and width are equal, is what minimizes the perimeter for a given area.
The rectangle with an area of 36 square feet that has minimal perimeter is actually a square with dimensions of 6 feet by 6 feet.
To find the length and width of a rectangle with an area of 36 square feet that has the minimum perimeter, we need to follow these steps:
Assume the length is l and the width is w. The area equation becomes: l × w = 36 sq ftExpress one variable in terms of the other: l = 36 / wUse the perimeter formula: P = 2l + 2w. Substitute l = 36 / w into this formula: P = 2(36 / w) + 2wTo find the minimum perimeter, take the derivative of P with respect to w and set it to zero: P'(w) = -72/w² + 2 = 0Solve for w: 2 = 72/w² gives w² = 36, so w = 6 ftThen, find l using l = 36 / w, giving l = 6 ftThus, the dimensions that yield the minimum perimeter are 6 feet by 6 feet. This results in a square having the smallest possible perimeter for the given area.
1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals negative 4 x
2.) Which kind of function best models the data in the table? Use differences or ratios.
x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2
3.) Solve the system of equations algebraically. Show all of your steps.
y equals x squared plus two x; y equals three x plus twenty
PLEASE HELP!
Answers
To solve the given quadratic equation, we simplified and factored it, yielding solutions x = 0 and x = 17. For the data in the table, an exponential function is suggested by the consistent ratio between y-values. Algebraically solving the system of equations results in two solutions: (5, 35) and (-4, 8).
Formula to Solve the Equation
To solve the equation x squared minus 21 x equals negative 4 x, you'll first want to rewrite it in standard form. Moving all the terms to one side gives us [tex]x^2 - 21x + 4x = 0[/tex], which simplifies to [tex]x^2 - 17x = 0[/tex]. To find the solutions, we can factor out an x, giving us x(x - 17) = 0. This yields two solutions: x = 0 and x = 17.
Model the Data in the Table
Looking at the data given, we see that each y-value seems to be a multiple of the previous y-value. This suggests an exponential function might be a better fit than a linear one. To confirm, you can divide each y-value by the previous y-value and observe if the ratios are consistent. Calculating the ratios between consecutive y-values in the table, we see that the ratio is consistently around 4, confirming that an exponential model is appropriate.
Solve the System of Equations Algebraically
To solve the system [tex]y = x^2 + 2x[/tex]and y = 3x + 20, set the right sides of the equations equal to each other:[tex]x^2 + 2x = 3x + 20[/tex]. Bringing all terms to one side gives us the quadratic equation[tex]x^2 - x - 20 = 0[/tex]. Factoring the quadratic equation we get (x - 5)(x + 4) = 0, which gives us two solutions for x: x = 5 or x = -4. Substituting these back into either original equation provides the related y-values, thus giving us two solutions for the system: (5, 35) and (-4, 8).
What is the standard form for the quadratic function?
g(x)=(x−6)2−5
g(x)=x2−12x+31
g(x)=x2−31
g(x)=x2+12x−41
g(x)=x2−41
Answers
[tex] a{x}^{2} + bx + c = 0[/tex]
multiple answers above fit this description.
Answer:
A) g(x)=x2−12x+31
Suppose that in a large company, 30% of the computers are infected by adware. if 6 computers are randomly selected and tested, what is the probability that 2 of the computers are infected by adware?
Answers
The expression 100 + 20m gives the volume of water in Eduardo’s pool (in liters) after Eduardo spends mmm minutes filling his pool. What is the volume of water in Eduardo’s pool after he fills it for 5.25 minutes?
Answers
Answer:
205 cubic units
Step-by-step explanation:
Given : The expression 100 + 20m gives the volume of water in Eduardo’s pool (in liters) after Eduardo spends m minutes filling his pool.
To Find: What is the volume of water in Eduardo’s pool after he fills it for 5.25 minutes?
Solution:
Expression: Volume of water in pool after m minutes= 100 + 20m
Volume of water in pool after m minutes = 100 + 20m
Where m is the number of minutes spent in filling pool.
Now we are supposed to find the volume of water in Eduardo’s pool after he fills it for 5.25 minutes
Substitute m = 5.25
Volume of water in pool after m minutes= 100 + 20(5.25)
=205
Thus the volume of water in Eduardo’s pool after he fills it for 5.25 minutes is 205 cubic units.
If f(x) = 4x and g(x) = 2x – 1, what is g(f(–2))?
A-17
B-13
C-8
D-5
Answers
so f(-2) = 4*-2 = -8
and
g((f(-2)) = g(-8) = -16-1 = -17
Its A
Heather has to solve this system of equations using elimination. What should be her first step?
Answers
The elimination method is used for solving linear systems of equations.It is way of solving a linear system of equations.In the elimination method we either add or subtract the equations to get an equation in one variable.The main concept behind elimination method is to create terms with opposite coefficients because they cancel each other when added.
When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
When Heather has to solve this system of equations using elimination her first step will be to make the coefficients of x or y the same so that one of the variable is eliminated on addition or subtraction of the equations.
you have a coupon for 10% off a dvd that cost $15. if a tax of 8% is charged on the orginal amount, what will you pay for the DVD
Answers
10% coupon = 10% x $15 = 0.10 x 15 = $1.50
Price after discount = $15 - $1.50 = $13.50
8% Tax = 8% x $15 = 0.08 x 15 = $1.20
Final Price = $15 - $1.50 + $1.20 = $14.70
Answer: $14.70
please help!!! will give brainiest if correct
Answers
need help with algebra 2! but I need the work show
Answers
[tex] \sqrt{7x} \sqrt{x}- \sqrt{7x}*7 \sqrt{7} \\ \\ = \sqrt{7} \sqrt{ x^{2} }-7 \sqrt{x} \sqrt{ 7^{2} } \\ \\ =x \sqrt{7} -7*7 \sqrt{x} \\ \\ \\ =x \sqrt{7} -49 \sqrt{x} [/tex]
Someone who knows math more than I do, can you please answer this question for me, I'd appreciate it so much <3
A right triangle has one angle that measures 28o. The adjacent leg measures 32.6 cm and the hypotenuse measures 35 cm.
What is the approximate area of the triangle? Round to the nearest tenth.
Area of a triangle = 1/2 bh
Answers
x = sqrt(35^2 - 32.6^2) = 12.74 cm
Since this is a right triangle, the base and height are simply the two sides that are perpendicular to each other.
Then the approximate area is (1/2)(leg 1)(leg 2) = (1/2)(32.6)(12.74) = 207.6 cm^2.
An umbrella you bought is shaped like a regular octagonal pyramid with a side length of four feet and a slant height of five feet. Estimate the amount of fabric that the umbrella has.
Answers
The estimated amount of fabric that the umbrella has is approximately [tex]\(112 + 32\sqrt{2}\)[/tex] square feet.
To estimate the amount of fabric that the umbrella has, we first need to find the total surface area of the regular octagonal pyramid.
A regular octagonal pyramid consists of 8 congruent isosceles triangles as its lateral faces and a regular octagon as its base.
Given:
- Side length of the octagon (s) = 4 feet
- Slant height of the pyramid (l) = 5 feet
First, let's calculate the area of one of the lateral faces (isosceles triangle) using the formula for the area of a triangle:
[tex]\[ \text{Area of one lateral face} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
In this case, the base of the triangle is the side of the octagon, s=4 feet, and the height is the slant height of the pyramid, l=5 feet. Therefore:
[tex]\[ \text{Area of one lateral face} = \frac{1}{2} \times 4 \times 5 = 10 \text{ square feet} \][/tex]
Since there are 8 congruent lateral faces on the octagonal pyramid, the total area of the lateral faces is:
[tex]\[ \text{Total area of lateral faces} = 8 \times 10 = 80 \text{ square feet} \][/tex]
Now, let's calculate the area of the base (regular octagon). The formula for the area of a regular octagon is:
[tex]\[ \text{Area of octagon} = 2 \times (1 + \sqrt{2}) \times s^2 \]\[ \text{Area of octagon} = 2 \times (1 + \sqrt{2}) \times 4^2 \]\[ \text{Area of octagon} \approx 2 \times (1 + \sqrt{2}) \times 16 \]\[ \text{Area of octagon} \approx 32 \times (1 + \sqrt{2}) \][/tex]
Now, we can calculate the total surface area of the regular octagonal pyramid by adding the area of the lateral faces and the area of the base:
[tex]\[ \text{Total surface area} = \text{Area of lateral faces} + \text{Area of octagon} \]\[ \text{Total surface area} = 80 + 32 \times (1 + \sqrt{2}) \]\[ \text{Total surface area} \approx 80 + 32 \times (1 + \sqrt{2}) \]\[ \text{Total surface area} \approx 80 + 32 + 32\sqrt{2} \]\[ \text{Total surface area} \approx 112 + 32\sqrt{2} \][/tex]
Find the mean, median, and mode
15, 3, 11, 15, 1, 14, 7, 2, 1, 1, 2
A. mean = 6.5, median = 8, mode =1
B. mean = 6, median = 3, mode = 1
C. mean = 6, median = 3, mode = 8
D. mean = 6.5, median = 3, mode = 1
Answers
median=3
mode=1
so the answer is d
I know its right for sure :)
i need this ASAP
Why is it not wise to sell your house when house prices decline or level off
Answers
Answer:
Because in one way or another, you would lose money.
Step-by-step explanation:
Sometimes, it is a good idea to underprice a house when selling it, specially when there is a hot market to start a bidding war. If this is not the case, when the prices go down, it means that the seller must adjust his prices to the market; meaning that the lower the prices are, the lower the underpricing should be, so the seller would lose money.
The doorway into a room is 4 feet wide and 8 feet high. what is the length of the longest rectangular panel that can be taken through this doorway diagonally
Answers
Perhaps you want to know the diagonal length of the opening. The Pythagorean theorem tells you it is
√((4 ft)² +(8 ft)²) = 4√5 ft ≈ 8.944 ft
This is a Pythagorean theorem problem. You need only apply a^2 + b^2 = c^2 to get the answer.
Formula
a^2 + b^2 = c^2
Givens
a = 4
b = 8
Sub and solve
a^2 + b^2 = c^2
4^2 + 8^2 = c^2
16 + 64 = c^2
80 = c^2
c = sqrt(80)
c = sqrt(2 * 2 * 2 * 2 * 5) out 4 twos 2 can be taken outside the brackets.
c = 4*sqrt(5) is the longest piece that can be taken through the door.
c = 8 feet + 0.944 of a foot
c = 8 feet + 11.33 inches.
What is the correct evaluation of 15-x, when x is equal to -5?
Answers
Use the unit circle to find the value of each trigonometric function at the angle indicated
Answers
-1
-inf
1
0
0
repectively
Answer:
Step-by-step explanation:
We have to find the values of the given trigonometric ratios at the angle indicated. Thus,
(A) The given trigonometric function is:
[tex]cos270^{\circ}[/tex]
Since, the function lies in Quadrant III, therefore the value of the function will be negative.
Also, [tex]cos270^{\circ}=-(0)=0[/tex]
(B) The given trigonometric function is:
[tex]sin270^{\circ}[/tex]
Since, the function lies in Quadrant III, therefore the value of the function will be negative.
Also, [tex]sin270^{\circ}=-1[/tex]
(C) The given trigonometric function is:
[tex]tan270^{\circ}[/tex]
Since, the function lies in Quadrant III, therefore the value of the function will be negative.
Also, [tex]tan270^{\circ}=undefined[/tex]
(D) The given function is:
[tex]cos0^{\circ}[/tex]
Since, the function lies in Quadrant I, therefore the value of the function will be positive.
Also, [tex]cos0^{\circ}=1[/tex]
(E) The given function is:
[tex]sin0^{\circ}[/tex]
Since, the function lies in Quadrant I, therefore the value of the function will be positive.
Also, [tex]sin0^{\circ}=0[/tex]
(F) The given function is:
[tex]tan0^{\circ}[/tex]
Since, the function lies in Quadrant I, therefore the value of the function will be positive.
Also, [tex]tan0^{\circ}=0[/tex]
The cost of parking in a garage, in dollars, can be modeled by a step function whose graph is shown. How much does it cost to park for 3 hours and 45 minutes?
$3
$4
$6
$10
Answers
3 hours 45 minutes=3 hours 0.75 hours
3 hours 45 minutes = 3.75 hours
3 hours < 3.75 hours < 4 hours →Cost=$6
Answer: Third option $6
Answer:
the cost is [tex]\$6[/tex]
Step-by-step explanation:
observing the graph
we know that
For the interval of x------> [tex](0,1][/tex] -----> the cost is [tex]\$0[/tex]
For the interval of x------> [tex](1,3][/tex] -----> the cost is [tex]\$4[/tex]
For the interval of x------> [tex](3,4][/tex] -----> the cost is [tex]\$6[/tex]
For the interval of x------> [tex](4,infinite)[/tex] -----> the cost is [tex]\$10[/tex]
In this problem we have
[tex]3[/tex] hours and [tex]45[/tex] minutes
therefore
the value of x belong to the interval [tex](3,4][/tex]
the cost is [tex]\$6[/tex]
A bathtub can be filled in 8 min. it takes 12 min for the bathtub to drain. if the faucet is turned on but the drain is also left open, how long will it take to fill the tub?
Answers
time taken to drain the bathtub is 12 min
fraction of bathtub filled in 1 hour=1/8
fraction of bathtub drained in 1 hour=1/12
fraction that will be filled in a minute given that both taps are opened at he same time:
1/8-1/12
=1/24
thus time taken for the bathtub to be filled is 24 min
It will take 24 minutes to fill the tub when both the faucet is running and the drain is open. The calculation is done using rates and subtraction.
Explanation:This problem can be approached with the concept of rates. The rate at which the bathtub fills is 1 tub per 8 minutes or 1/8 tubs/min. Similarly, the rate at which it drains is 1 tub per 12 minutes or 1/12 tubs/min. When the faucet is running and the drain is open, the net rate is the fill rate minus the drain rate.
So, (1/8 - 1/12) tubs/minute = 1/24 tubs/minute. Thus, it will take 24 minutes to fill the bathtub with both the faucet running and the drain open.
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A TV has a listed price of $ 899.99 before tax. If the sales tax rate is 7.25 % , find the total cost of the TV with sales tax included.