Final answer:
To find the volume of a regular hexahedron with a face diagonal of 8√2 inches, we first calculate the side length of the cube and then use it to determine the volume, resulting in a volume of 512 cubic inches.
Explanation:
The question asks to find the volume of a regular hexahedron (which is a cube), given the diagonal of one of its faces is 8√2 inches. Since we know the face of a hexahedron is a square, we can use the Pythagorean theorem to find the side of the square. The diagonal (d) of a square relates to its side (s) by the formula d = s√2. Therefore, we can solve for s: s = d / √2 = (8√2) / √2 = 8 inches. Now that we have the length of the side of the cube, we can compute the volume (V) using the formula V = s3. Substituting s = 8 inches, we calculate the volume as V = 83 = 512 cubic inches.
$29,000;$4 decrease find the new amount given the original amount and the percent of change.
What is the area of ABC below? If necessary, round your answer to two decimal places.
The answer I got from apex was- 106.26
what is the value?
5x+3=4x ?? bit confused
please help me I really need it.
Answer:
(x, y, z) = (-5, -1, 0) (x, y, z) = (-8, -7, 5)Step-by-step explanation:
1. A graphing calculator or equation-solving web site can tell you the solution is (-5, -1, 0).
As is sometimes the case with multiple-choice questions, you can choose the "consensus answer".
For x, -5 appears in 3 of 4 answer choices.
For y, -1 appears in 3 of 4 answer choices.
For z, 0 appears in 3 of 4 answer choices.
Thus, the "consensus" is that the answer is (-5, -1, 0). Choosing this one to check can shorten the work of checking the answer choices.
-5 +5(-1) +4(0) = -10 . . . first equation can use this answer2(-5) -(-1) +5(0) = -9 . . . second equation can use this answer2(-5) -10(-1) -5(0) = 0 . . . third equation can use this answerSo, by "guess and check" we have determined the solution to be (-5, -1, 0).
__
2. First of all, you can substitute the given value of z into the other two equations. Then you have ...
2x -y +5 = -4-2x +3y -5 = -10The first of these equations can be solved for y:
y = 2x +9
and this can be substituted for y in the second of these equations:
-2x +3(2x +9) -5 = -10
4x +22 = -10
4x = -32
x = -8
and ...
y = 2(-8) +9 = -7
So this solution, too, is the "consensus solution," ...
(x, y, z) = (-8, -7, 5)
Use the function described below to answer questions 1 - 4.
Yvonne invested $4,000 in a savings account which pays 3.5% interest compounded annually. Use the formula A = P(1 + r)t, where P is the principal, r is the interest rate, and t is the time in years.
1. Approximately, how much money will Yvonne have in 4 years? Round to the nearest cent.
2. Approximately, how much money will Yvonne have in 8 years? Round to the nearest cent.
3. Approximately, how many years will it take for Yvonne to double her money? Write the number of years only.
4 Alex buys a top of the line computer. He did not realize that the computer would lose value so fast. If his computer cost $1800.00 and it depreciates at a rate of 45% each year, in how many years will it be worth less than 1/3 of what he paid for it?
whats x?
16x - 4x = -48
If possible, can you show your steps
0.00014s in scientific notation? ...?
Describe the kernel and range of (a) the orthogonal projection on the xz -plane (b) the orthogonal projection on the yz-plane (c) the orthogonal projection on the plane defined by the equation y=x ...?
A college writing seminar increased its size by 50% from the first to the second day. If the total number of students in the seminar on the second day was 15 how many students were in the class on the first day
What is 35/10 convert into a decimal?
You drive your car for 3 hours at an average speed at 30 km per hour. how far did you go?
two consecutive odd negative integers have a product of 483, find the integers ...?
if (3x^2)+7=0 then (x-1/3)^2
52.063 divided into 9.2 rounded to the nearest hundredth
Answer:
The answer is 5.66
Step-by-step explanation:
52.063 divided by 9.2 is 5.65902173913. Then you round of to the nearest hundredth which is two decimal places to the right (so it's 5). Then you round it off one value higher since 9 is above 5. Therefore the final answer is 5.66
4x-6=10x-3
?? i am bad at math lol
The price of a pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these shoes? A.) $2.84 B.) $3.16 C.) $4.50
Mark has a baking tray with 24 muffins and the muffin are arranged in 4 equal rows how many are there in each row
How does the graph of g(x) 1/x+4-6 compare to the graph of the parent function f(x) 1/x
g(x) is shifted 4 units right and 6 units up from f(x).
g(x) is shifted 4 units right and 6 units down from f(x).
g(x) is shifted 4 units left and 6 units up from f(x).
g(x) is shifted 4 units left and 6 units down from f(x).
Answer:
Option 4- Graph of g(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
Given : Graph of [tex]g(x)=\frac{1}{x+4}-6[/tex]
To find : How does the graph of g(x) compare to the graph of the parent function [tex]f(x)=\frac{1}{x}[/tex]
Solution :
The graph f(x) is being translated to form the graph g(x).
In graph [tex]g(x)=\frac{1}{x+4}-6[/tex] there is
Translation of 4 unit left and 6 unit downward.
In graph f(x) if we shift the graph with 4 unit left it form
f(x)→f(x+b) , the function is shifted towards left with b unit.
So, [tex]f(x)=\frac{1}{x+4}[/tex]
In graph f(x) if we shift the graph with 6 unit downward it form
f(x)→f(x)-a , the function is shifted downward with a unit.
So, [tex]f(x)=\frac{1}{x+4}-6[/tex]
Therefore, Option 4 is correct.
Graph of g(x) is shifted 4 units left and 6 units down from f(x).
A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a_______
.When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, _______vertex
of ∆A″B″C″ will have the same coordinates as B′.
Answer:The first one is a Reflection
The second one is B
Step-by-step explanation:
A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
5 units
10 units
12.5 units
The diameter of the cylinder with a volume of 175 cubic units and a height of 7 units is 5 units.
To calculate the diameter of a cylinder, we first need to find the radius using the formula for the volume of a cylinder, V = πr²h. Given that the volume is 175 cubic units and the height is 7 units, the radius comes out to be 5 units. Since the diameter is twice the radius, the diameter of the cylinder is 5 units.
In the fall, you go to the local nursery and purchase a package of 10 rose plants. The clerk informs you that on average you can expect 5% of the plants to not live through the winter. Assume that the plants are a random sample.
a) Use the binomial formula to determine the probability that one or more of the plants will not survive the winter.
b) What is the probability that all the plants will survive? Write how the binomial formula is used to calculate the probability.
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
[tex]-2x^2+4x=-1[/tex]. Now we factor out the -2:
[tex]-2(x^2-2x)=-1[/tex]. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
[tex]-2(x^2-2x+1)=-1-2[/tex]. Simplifying gives us this:
[tex]-2(x^2-2x+1)=-3[/tex]
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
[tex]-2(x-1)^2+3=y[/tex]
From this form,
[tex]y=-a(x-h)^2+k[/tex]
you can determine the coordinates of the vertex to be (1, 3)
Answer:
(1,3)
Step-by-step explanation:
Heather has $500 in her savings account. she withdraws $20 per week for gas. write an equation heather can use to see how many weeks it will take her to have a balance of $220.
Bill makes four payments a year of $128.25 for life insurance; four payments of $161.82 for real estate taxes; twenty-four payments of $37.46 for health insurance; and six payments of $221.65 for auto insurance. What is the total of his annual fixed expenses for these items?
To calculate the total annual fixed expenses, we multiply the number of yearly payments by the amount of each payment for the different insurances and taxes, and then add these products together to find that the annual fixed expenses total $3,388.74.
The student has asked to calculate the total of his annual fixed expenses for life insurance, real estate taxes, health insurance, and auto insurance. To determine this, we will multiply the amount of each payment by the number of times the payment is made annually and then sum these amounts to get the total yearly expense:
Life Insurance: 4 payments of $128.25
Real Estate Taxes: 4 payments of $161.82
Health Insurance: 24 payments of $37.46
Auto Insurance: 6 payments of $221.65
Now, we calculate each:
Life Insurance: 4 imes $128.25 = $513.00
Real Estate Taxes: 4 imes $161.82 = $647.28
Health Insurance: 24 imes $37.46 = $898.56
Auto Insurance: 6 imes $221.65 = $1,329.90
Adding these amounts gives us the total annual fixed expenses:
$513.00 (Life Insurance) + $647.28 (Real Estate Taxes) + $898.56 (Health Insurance) + $1,329.90 (Auto Insurance) = $3,388.74 as the annual fixed expenses.
Write the distribution of 7×6=
Lauren bought 6 yellow roses, 10 orange roses, and 12 pink roses to make a bouquet. What is the ratio of the number of yellow roses to the total number of roses in Lauren’s bouquet?
Denver is called the mile-high city because it is at an altitude of 1 mile. how many feet is the
A student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d = days, r = raffle tickets, and h = hours, what function can he use to calculate his earnings?
Answer: C. [tex]T=15d+\frac{r}{4}+2h[/tex]
Step-by-step explanation:
Let d = days, r = raffle tickets, and h = hours.
Given: A student earns in a day = $15
Then his earning in d days =$15d
Also, he earns for each riffle = $0.25
Then his earning in for r riffles =$0.25r
And , he earns for each hour he works at the game = $2
Then his earning for h hours = $2h
Then the function he can use to calculate his earnings is given by :_
[tex]T=15d+0.25r+2h\\\\\Rightarrow\ T=15d+\frac{1}{4}r+2h[/tex]
Explain how you use the bar model to solve 14-7 equal seven
A 13 foot ladder is leaning against a wall. If the point where the ladder meets the wall is 12 feet above the ground, how far from the base of the wall is the the ladder?
A) 1 foot
B) 2 feet
C) 5 feet
D) 22 feet