Answer:
V=512^2/3* 19683^1/3*256^1/4 = 6912
Step-by-step explanation:
V= [tex](512^{\frac{2}{3} } ) \times (19683^{\frac{1}{3} } )\times (256^{\frac{1}{4} } )\\[/tex]
As
[tex]2^{9} = 512\\2^{8} = 256\\19683^{\frac{1}{3} } = 27\\[/tex]
putting values in equation
V= [tex]2^{9(^{\frac{2}{3} } )} \times 27 \times 2^{8^({\frac{1}{4}) } } \\[/tex] let it be equation 1
As
[tex]2^9^{\frac{2}{3} } = 2^6 according\,to\,exponential\,rule\\2^8^\frac{1}{4} = 2^2 according\,to\,exponential\,rule\\\\[/tex]
putting values in equation 1
[tex]V= 2^6\times 27\times 2^2[/tex]
According to exponential rule [tex]2^6 \times 2^2 = 2^8[/tex]
V=[tex]2^8 \times 27\\[/tex]
[tex]V=256\times 27\\V=6912[/tex]
So
V= 6912
Keywords: Algebra
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Which table values can be defined by the function y=2x+3
Answer:
beggining poit:3 second point (potentially): 1,5
Step-by-step explanation:
in the y intercept 3 is it so which ever has a 3 as the starting point there could be an option
for the 2x part that is the slope otherwise known as rise over run so what you do is that you turn it to a fraction over or under 1 meaning you rise for 2 and go to the right 1
rise 2
_
run 1
in order to rise 2 you go up 2 from the y intercept(3) and in order to run you go right since its a positive
once you plot those two dots then you draw a line across
GIVEN THE FUNCTION F(X) =3X + 5 AND X SUCH THAT F(X)=38
The value of X is 11.
Step-by-step explanation:
Given,
F(X) = 3X + 5 --------(1)F(X) = 38 ------------(2)Equating eq(1) and (2),
⇒ 3X+5 = 38
⇒ 3X = 38-5
⇒ X = 33/3
⇒ X = 11
Problem PageQuestion
A principal of 3700 is invested at 4.75 %interest, compounded annually. How much will the investment be worth after 5 years?
The investment will be worth $4686.62 after 5 years.
Step-by-step explanation:
Principal, P = 3700
Rate, r = 4.75% = 0.0475
Number of years, t = 5 years
Number of times compounded, n = 5 times
Amount = P(1 + r/n)^nt
⇒ 3700 (1 + 0.0475/5)^25
⇒ 3700 (5.0475/5)^25
⇒ 3700 (1.0095)^25
⇒ 4686.62
∴ Amount = $4686.62
How many cube-shaped boxes with 12-inch edges can fit into a box thatis 4
feet tall, 4 feet long, and 5 feet wide?
Answer:
80
Step-by-step explanation:
First recall that:
1 inch=12 feet
The volume of cube-shaped boxes with 12-inch edges is 1 cm³
The volume of a box that is 4
feet tall, 4 feet long, and 5 feet wide is
given by:
[tex]Volume = lwh[/tex]
We substitute l=4ft, w=5ft and h=4ft
To obtain:
[tex]Volume = 4 \times 4 \times 5 = 80 {ft}^{3} [/tex]
Therefore 80 cube-shaped boxes with 12-inch edges can fit into a box that is 4
feet tall, 4 feet long, and 5 feet wide.
Nat put $550 in an account which pays four percent interest, compounded semiannually. How much will be in the account in three years?
The final answer will be rounding it up to $619.
Step-by-step explanation:
4% = 0.04
1 represents 100%
therefore,
(( 1 + 0.04)^3)x 550
= (1.04^3) x 550
= 1.124864 x 550
= $618.6752
The final answer will be rounding it up to $619.
Explain how you would prove the triangles congruent in order to prove the statements true.
Given data:
QP = PT and RP = SP
Let us first prove ΔQPR and ΔSPT are congruent.
In ΔQPR and ΔSPT,
QP ≅ TP (Given side)
∠QPR ≅ ∠ SPT (Vertically opposite angles are congruent)
RP ≅ SP (Given side)
Therefore, ΔQPR ≅ ΔSPT (by SAS congruence rule)
By corresponding parts of congruence triangles are congruence,
⇒ ∠Q ≅ ∠T
Hence ∠Q ≅ ∠T.
Translate the sentence into a mathematical expression: “Twice x is 5”
Answer:
2x = 5
Step-by-step explanation:
Which numbers are greater?
1.) 3/4 or 70%
2.) 1/2 or o.54
3.) 0.21 or 21%
4.) 2/3 or 66%
Answer:
1. 3/4
2. 54%
3. Both equal
4. Both equal
Step-by-step explanation:
Answer:
1.) 3/4
2.)0.54
3.) Both
4.) 2/3
Which of these statements are correct about a line segment with a length of 12 units in a coordinate plane? Select all that apply.
Correct statements are:
If it is reflected across the y-axis, its length still will be 12 units.
If it is rotated 270° about the origin, its length still will be 12 units.
If it is translated 15 units up, its length still will be 12 units.
Step-by-step explanation:
Whatever it may be rotation, reflection or translation, the size of the line will never change. So length of the line is same as 12 units in the image.
So the wrong statements are
If its reflected across y = -x then the length will no longer be 12 units.
If it is rotated 90° about the origin, then the length will no longer be 12 units.
If it is translated 18 units to the right, then the length will no longer be 12 units.
You can use the fact that reflection, rotation or translation, all three are not modifying the line itself and only its position can change. Whatever be the position, if the line segment itself isn't modified, the length will be same.
Thus, the correct choices are:
Option A: If it is reflected across the y-axis, the length will still be 12 units.Option B: If it is rotated 270° about the origin, its length still will be 12 units.Option E: If it is translated 15 units up, its length still will be 12 units.Rest of the choices are wrong since they blame reflection or rotation or translation to modify the length of that line segment.
Why is the length of a line segment not modified when it is reflected along an axis, rotated or translated by some units in some direction?Suppose you've got a baseball stick. Will it's length change when you take it somewhere else like from your home to playground? No. Will its length change if you hold it upside down? No.
This is the same case with line segment being rotated, reflected, or translated. All these processes do not change the line segment's length and can just move that line segment from one position to other.
Using above conclusion to find the correct options in the given contextSince reflection, rotation, or translation won't affect the length of the line segment,.
Thus, the correct choices are:
Option A: If it is reflected across the y-axis, the length will still be 12 units.Option B: If it is rotated 270° about the origin, its length still will be 12 units.Option E: If it is translated 15 units up, its length still will be 12 units.Rest of the choices are wrong since they blame reflection or rotation or translation to modify the length of that line segment.
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Joseph drives 125 miles in 2 1/2 hours . at that rate , how far does he travel each hour?
If he drives 125 miles in 2 1/2 hours, he will drive 125 ÷ 2 1/2 miles per hour.
125 ÷ 2 1/2 = 50 miles
answer: 50 miles per hour
I need help with pythagoras’ theorem
Answer:
Pythagoras’ theorem is a way to find a side or hypothesis when you have 2 sides.
The formula is: a^2 + b^2 = c^2
a and b are sides
c is the hypothesis
Ex: A triangle has a leg that is 5 inches and a leg that is 7 inches. Find the hypothesis using Pythagoras' theorem.
A leg is another way of saying a side.
5^2 + 7^2 = c^2
25 + 49 = x^2
sqrt(74) = sqrt(x^2)
sqrt(74) inches = hypothesis
Ex: A triangle has a leg that is 9 feet and a hypothesis that is 25 feet. Find the other leg using Pythagoras' theorem.
9^2 + b^2 = 25^2
81 + b^2 - 81 = 625 - 81
sqrt(b^2) = sqrt(544)
b = sqrt(554)
Do you understand more?
Order -9, 5, 6, and -4 from least to greatest.
a. -9, -4, 5, 6 c. -9, -4, 6, 5
b. 6, 5, -4, -9 d. -4, -9, 5, 6
The answer is a. -9, -4, 5, 6.
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Answer:
Option A: -9, -4, 5, 6
Step-by-step explanation:
Since the lowest number is -9, it should go first
Since the 2nd lowest number is -4, it should go second
Since the 3rd lowest number is 5, it should go third
Since the 4th lowest number is 6, it should go fourth
Answer: Option A, -9, -4, 5, 6
Carle is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that has 100 feet
49 pieces of string can be cut from a ball of string that has 100 feet
Solution:
Given that, Carle is cutting pieces of string that are exactly 24 3/8 inches long
Therefore,
[tex]Length\ of\ each\ string = 24\frac{3}{8}\ inches = \frac{8 \times 24 + 3}{8} = \frac{195}{8}\ inches[/tex]
How many pieces can she cut from a ball of string that has 100 feet
Total length of string = 100 feet
Convert feet to inches
1 feet = 12 inch
100 feet = 1200 inch
Therefore, number of pieces that can be cut is given as:
[tex]\text{Number of pieces } = \frac{\text{total length of string}}{\text{length of each string}}[/tex]
Substituting the values we get,
[tex]\text{Number of pieces } = \frac{1200}{\frac{195}{8}}\\\\\text{Number of pieces } = 1200 \times \frac{8}{195}\\\\\text{Number of pieces } = 49.2307 \approx 49[/tex]
Therefore, 49 pieces of string can be cut from a ball of string that has 100 feet
A number to the 9 power divided by the same number to the 6 power equals 27 what is the number
Answer:
3
Step-by-step explanation:
n^9/ n^6 = 27
n^9 - 6 = 27
n^3 = 27
n = ∛27
n = 3
Find the area of the triangle below. Show as much work as possible. Label your answer appropriately.
Answer:
[tex]Area=\frac{5}{12}x^2[/tex]
Step-by-step explanation:
The area of a triangle is given by:
[tex]Area=\frac{1}{2}*base*height[/tex]
From the diagram [tex]base=\frac{5}{6}x,and,height=x[/tex]
We substitute into the formula to get:
[tex]Area=\frac{1}{2}*\frac{5}{6}x*x[/tex]
This implies that:
[tex]Area=\frac{5}{12}x^2[/tex]
Which of the following statements about the relationship between an interior angle of a polygon and its adjacent exterior angle are true? Choose all that apply.
A. They form a linear pair.
B. They are supplementary.
C. They are complementary.
D. They are alternate exterior angles.
9514 1404 393
Answer:
A. They form a linear pair.
B. They are supplementary.
Step-by-step explanation:
An interior angle and its adjacent exterior angle of a polygon are a linear pair. The angles of any linear pair are supplementary.
A 20,000 deposit earns 3.6% interest for 3 years. If no money is deposited or withdrawn how much interest will ever earned at the end of 3 years?
Answer:2,160
Step-by-step explanation:Multiply 20,000 by the percent then multiply the number you get by 3
Out of 25 attempts, a basketball player scored 17 times. One-half of the missed shots are what % of the total shots?
Answer:
%16
Step-by-step explanation:
Step 1: Find the shots missed
25 - 17 = 8
Step 2: Find half of the shots missed
8 / 2 = 4
Step 3: Divide 4 by 25
4/25 = 0.16
Step 4: Convert to Percent
0.16 * 100 = %16
Answer: %16
pls help!
Multiply the following polynomials. 3x3(5x2+4x)
8x6+7x3
15x6+12x4
15x6+12x3
15x5+12x4
8x5+7x4
15x5+12x3
Answer:
78
Step-by-step explanation:
you multiply
Answer:
15x^9+12x^4
b is the answer
Rupert is copying some files from his computer to a compact disc, like the one shown above.
If the diameter of the compact disc is 120 millimeters, what is the approximate area ignoring the center hole? (Use 3.14 for pi.)
A.
376.8 mm2
B.
11,304 mm2
C.
753.6 mm2
D.
45,216 mm2
Option B: [tex]11,304 \mathrm{mm} ^2[/tex] is the area of the compact disc.
Explanation:
The diameter of the compact disc is [tex]120mm[/tex].
To determine the area of the compact disc, let us substitute the values in the area of the circle formula,
[tex]A=\pi r^2[/tex] where [tex]r=\frac{d}{2}[/tex]
Substituting the value of d in [tex]r=\frac{d}{2}[/tex], we get,
[tex]r=\frac{120}{2} =60[/tex]
Thus, [tex]r=60[/tex] and [tex]\pi=3.14[/tex]. Let us substitute these values in [tex]A=\pi r^2[/tex], we get,
[tex]A=3.14\times(60)^2[/tex]
Simplifying, we have,
[tex]A=3.14\times3600[/tex]
Multiplying, we get,
[tex]A=11304mm^2[/tex]
Thus, the area of the compact disc is [tex]11,304 \mathrm{mm} ^2[/tex]
Hence, Option B is the correct answer.
In sixth grade, Manuel reads 35 books this year the books he read increase 40% how many books had he read
Answer: 49 books
Step-by-step explanation:
Number of books read by Manuel this year = 35
Increment in reading rate = 40%
Therefore, we now find 40% of 35 and add it to 35 to know the number of books he had read
Number of books read = 40% of 35
= 40/100 x 35
= 14 books
Total number of books read = 35 + 14
= 49 books
Answer:
Step-by-step explanation:
50
television videl watched 6 times as many hours of television over the weekend as dieen. together they watched a total of 14 hours of television. how many hours of television did each person watch over the weekend?
U Move It charges $16 per hour plus a fueling fee of $25 to rent a truck. Jamarcus needs to rent a truck and can spend no more than $125. Which inequality represents the situation? A 16h + 25 ≤ 125 B 16h + 25 ≥ 125 C 25h + 16 ≤ 125 D 25h + 16 ≥ 125
Answer:
A. 16h+25≤125
Step-by-step explanation:
From the information, the one-time fee is $25.
The rate per hour is $16
Therefore the total cost involved in renting a car is given by:
16h+25
Jamarcus needs to rent a truck and can spend no more than $125.
This implies that:
16h+25≤125
The correct answer is A.
Expression equivalent to (0.28t-0.3)-(0.7t-0.28)?
A. 0.42t+0.58
B. -0.42t-0.02
C. 0.42t-0.02
D. -0.42t+0.58
Please help!
How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 30% antifreeze to get a mixture that is 40% antifreeze?
Answer:
70 gallons
Step-by-step explanation:
x gallon of 50%
x * 0.5 + 70 * 0.3 = (x + 70) * 0.4
0.5x + 21 = 0.4x + 28
0.1x = 7
x = 70
To get a mixture that is 40% antifreeze, we need to mix 70 gallons of 30% antifreeze solution with 40 gallons of 50% antifreeze solution. This conclusion is reached by establishing an equation representing the total amount of antifreeze in the mixture before and after and then solving for the unknown.
Explanation:Your question deals with the concept of a weight ratio in a chemical mixture. Specifically, we're going to solve it using algebra. Let's say you need x gallons of the 50% antifreeze solution. We can work this out by forming an equation based on the information given in the problem:
The total amount of antifreeze in the 70 gallons of 30% solution and x gallons of 50% solution must be equal to the total amount of antifreeze in the (70 + x) gallons of 40% solution.
Therefore, we can write: 0.3 * 70 + 0.5 * x = 0.4 * (70 + x)
Solving the equation above, we find that x equals 40 gallons. So, you would need to mix 40 gallons of a 50% antifreeze solution with 70 gallons of 30% solution to obtain a final solution with a 40% antifreeze concentration.
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Which one is bigger 64 in or 5 ft
64 inches
Step-by-step explanation:
12 inches equals 1 foot so
12*5=60 inches which means it will be bigger than 5 feet.
Which of the following best describes the situation below?
The number of miles a car can run depends on the gallons of gasoline in the
tank.
O
O
O
A. A relation that is not a function
B. A relation that is a function
C. The range of a function
D. The domain of a function
Answer:
c
Step-by-step explanation:
The situation described where the number of miles a car can run depends on the gallons of gasoline in the tank is a relation that is a function. Because for each amount of gas, there is one corresponding maximum distance the car can travel.
Explanation:The situation described illustrates a relation that is a function. In this case, the amount of gasoline (in gallons) in the car's tank is the input or the independent variable (the domain), and the distance the vehicle can travel (the output or dependent variable) is a function of this input. For each amount of gasoline, there is only one corresponding maximum distance the car can travel, so this is a function. Thus, the best answer is B. A relation that is a function.
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If these two figures are similar, what is the measure of the missing angle? 180 90 70 110
Answer:
70
Step-by-step explanation:
Answer:
70
Step-by-step explanation:
please show work read what the question wants in both pictures
Answer:
2) m∠CBD = 60 3) x=15; 95 and 85 4) 12 = x; 98 for both angles
Step-by-step explanation:
2) 2x + 14 + x + 7 = 90 The angles add up to 90 degrees
3x + 21 = 90 Combine like terms
- 21 - 21 Subtract 21 from both sides
3x = 69 Divide both sides by 3
x = 23
Plug 23 in the equation
2(23) + 14
46 + 14
60
3) 2x + 65 + 3x + 40 = 180 The angles add up to 180 degrees
5x + 105 = 180 Combine like terms
- 105 - 105 Subtract 105 from both sides
5x = 75 Divide both sides by 5
x = 15
Plug in 15 into both equations
2(15) + 65 = 95
3(15) + 40 = 85
4) 5x + 38 = 9x - 10
- 5x - 5x Subtract 5x from both sides
38 = 4x - 10
+ 10 + 10 Add 10 to both sides
48 = 4x Divide both sides by 4
12 = x
Plug in 12 into both equations
5(12) + 38 = 98
9(12) - 10 = 98
If the person in the figure wants his shadow to be 3 feet long, how far should he move and in what direction?
See attached photo
Need answer ASAP please help!!
If the person in the figure wants his shadow to be 3 feet long, Then he should move to right for 11/3 feet distance.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In this problem Triangle ADF is similar to Triangle
by AA Similarity Theorem
15/6=(10+ED)/ED
Apply cross multiplication
15ED=6(10+ED)
15ED=60+6ED
Subtract 6 ED from both sides
9ED=60
ED=60/9
ED=20/3 ft.
ED is the length
He should move to the right x feet
x=20/3-3
x=11/3 feet
Hence, he should move to right for 11/3 feet distance.
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