After multiplying 0, 3 times and following the laws of exponents, the value yielded is 0.
What is the law of exponents?
There are varied exponent laws in mathematics. Numerous fine problems that involve repeated addition operations can be answered using all of the exponentiation principles. The principles of exponents make addition and division processes simpler and make it easier to answer issues. The six significant rules of exponents will be covered in this composition along with multitudinous worked-out exemplifications.When multiplying a number by itself constantly, exponents are employed to illustrate this. For the case, 73 can be used to represent 7 x 7 x 7. The exponent, in this case, is" 3," denoting how numerous times the number 7 has been multiplied. Then, the number that's actually being multiplied is 7, which serves as the base.
Given that,
[tex]0^3[/tex] , Expanding it following laws of exponents,
We get,
0*0*0=3
Therefore, [tex]0^3=0[/tex].
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A cylinder has a height of 5 feet and a diameter of 2 feet. Which measurement is closest to the volume of the
cylinder in cubic feet?
62.8 ft³
15.7 ft3
78.5 ft3³
157.1 ft3
The measurement that is closest to the volume of the cylinder in cubic feet is: 15.7 Feet. (Option B)
Recall that volume is
V = πr²h
Given:
h = 5 feet
r = 2/2 = 1
Hence
V = 5 x 1 x 22/7
= 15.7142857143
Hence, the cylinders volume in cubic feet is given as:
[tex]$\approx$[/tex] 15.7 ft
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Answer: 15.7 ft3
Step-by-step explanation:
Could someone help me? The problems (see image attached) are about whether or not a decimal can be written as a question and why or why not.
Answer:
yes it can be bc it is repeating
what following is (are)the solution to(x-3)=7x-4
Answer:
Step-by-step explanation:
The X is equal to 1/6.
Meaning that the X is 1/6.
Answer:
x = 1/6
Step-by-step explanation:
(x - 3) = 7x - 4
x = 7x -1
-6x = -1
-x = -1/6
x = 1/6
Use the Segment Addition Postulate to solve the problem below.
Point E is the midpoint of line segment YT.
line segment YT = 14
line segment YE = 3x + 1
What is the value of x?
Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.
What is the numerical value of x?A midpoint is simply a point that divides a segment into two equal halves.
Given the data in the question;
Point E is the midpoint of line segment YTLine segment YT = 14Line segment YE = 3x + 1Numerical value of x = ?Point E is the midpoint of line segment YT, YT is divided into two equal halves. Hence, Two times Line segment YE equals to YT.
2( Line segment YE ) = Line segment YT
Plug in the given values and solve for x.
2( Line segment YE ) = Line segment YT
2( 3x + 1 ) = 14
Expand using distributive property
2 × 3x + 2 × 1 = 14
6x + 2 = 14
Collect like terms
6x = 14 - 2
6x = 12
6x/6 = 12/6
x = 12/6
x = 2
Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.
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Find the sum of all multiple 3 between 5 and 64
Answer:
The multiple of 3 between 5 and 64 are 6+9+12+15+18+21+24+27+30+33+36+39+42+ 45+48+51+54+57+60+63
=690
An engineer is estimating the weight of a steel beam. the actual weight of the beam is 286 pounds. the engineer's estimate is 300 pounds.
find the absolute error and the percent error of the engineer's estimate. if necessary, round your answers to the nearest tenth.
The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .
Absolute Error is defined as the difference between The Actual value and the estimated value .
Percent Error is defined as the difference between The Actual value and the estimated value in comparison to actual value expressed in percent .
[tex]Percent Error=\frac{|Estimated Value-Actual value|}{Actual Value} *100[/tex]
Given that the Estimated value =300 pounds
Actual Value=286 pounds
Absolute Error=300-286=14 pounds
Percent Error=[tex]\frac{|300-286|}{286} *100[/tex]
=[tex]\frac{14}{286} *100=4.89[/tex]%
Therefore , The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .
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Add:
4⁄6 + 2⁄4 + 3⁄5 =
Answer:
Step-by-step explanation:
[tex]\frac{4}{6} + \frac{2}{4} + \frac{3}{5} = \frac{80}{120} + \frac{60}{120} + \frac{72}{120} = \frac{212}{120}[/tex]
simplest form : [tex]\frac{53}{30}[/tex]
I need help is -2x=3/8 a literal equation?
The equation -2x=3/8 is not a literal equation.
What is a literal equation?A literal equation can be defined as an equation which primarily of letters.
It is an equation made up of several variables or letters.
Examples of literal equations are;
V = dts = ut + 1/2 at^2Area = πr²D = m/ vWe can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.
Given the equation;
-2x=3/8
We can see that there is only one variable to be worked out and hence, is not a literal equation.
Thus, the equation -2x=3/8 is not a literal equation.
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If the radius of a circle is 16 inches find the diameter area and circumference
diamater:
[tex]d=2r \\\\d=2 \cdot 16 \\\\d=32[/tex]
circumference:
[tex]C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48[/tex]
Hope that I helped you!
Brian invests £2300 into his bank account.
He receives 10% per year simple interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.
Line RQ bisects line DE at S. If DS = 10 + 3x and ES = -2 + 6x, what is DE
The equation for DE is [tex]8+9x[/tex]
According to the question statement, Line RQ bisects line DE at S. If DS = 10 + 3x and ES = -2 + 6x. We are supposed to find DE.
For solving this we need to know about Linear Equations and Bisector of a line.
Given that, DS = 10 + 3x and ES = -2 + 6x.
S is mid point of line DE as RQ bisects it.
So DS = SE
And DE = DS + SE
Hence, DE = [tex]10 + 3x + (-2 + 6x)[/tex]
DE = [tex]10 + 3x -2 + 6x[/tex]
DE = [tex]10 -2 +3x+6x[/tex]
DE = [tex]8+9x[/tex]
Hence equation of DE is 8+9x.
Linear Equation: The equation whose graph is always a straight line.Bisector of a line: The line or a point which divides it in two equal portions i.e., bisects it.To learn more about linear equations, click the link given below
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A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece . find the leg of each piece
One of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
Here,
A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece .
We have to find the leg of each piece.
What is Length, Width and height?
The length, width and height of an object are the different dimensions in linear units. length is the longest side of a shape, width is the shorter side, and height is the vertical dimension of the shape.
Now,
If you're going to cut the 72 inch board into two pieces, you can call one of the pieces x units long.
And, since the other piece is 12 inches longer than your first piece, its length is x + 12.
And, when you place these two pieces back together, their lengths should add up to be 72 inches.
You can write this last statement about adding the two pieces together to get a 72 inch piece
In equation form as:
x + (x+12) = 72
2x + 12 = 72
To solve this begin by subtracting 12 from both sides;
2x = 60
Now just divide both sides by 2 to find that:
x = 30
So, one of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
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2 mandy is playing a game. early in the game she had - 250 points. now
mandy has 350 points. what was the change in mandy's score?
The change of Mandy's score is 600 points.
Here,
Mandy is playing a game.
Early in the game she had - 250 points.
Now, Mandy has 350 points.
We have to find the change of Mandy's score.
What is difference of two number?
To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.
Now,
Early in the game she had - 250 points.
And, now Mandy has 350 points.
So, The change of Mandy's score = 350 - (-250) = 350 + 250 = 600
Hence, The change of Mandy's score is 600 points.
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If a person drives 360 miles at an average of 35 miles per hour, then their distance d from the destination (in miles) is a function of the number of hours h driven.
The required function is d = 360 - 35h, 0 ≤ h ≤ 10.29.
We know that distance travelled is equalled to speed multiplied by time.
Let d be the distance from the destination.
Let d₁ be the distance travelled in h hour.
And h be the number of hours driven.
Given that the average speed is 35 miles per hour.
Therefore, we have d₁ = 35h
And the initial distance from the destination is 360 miles.
Note at time h= 0 the distance from the destination is the maximum which is 360 miles.
Therefore, we have d₁ = 35h
Distance from the destination is 360 - d₁.
⇒ d = 360 - d₁
⇒ d = 360 - 35h
Time taken to reach destination = d/v = 360/35 = 10.29 hours
Therefore the required function is d = 360 - 35h, 0 ≤ h ≤ 10.29
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Find the area of the shaded figure.
OF
80 mm 120 mm
PLS HELP
Answer: 2000π mm^2
Step-by-step explanation:
A=area of entire circle. B=Area of Inside circle. C=Area of shaded region
A-B=C
π(120/2)^2 -π(80/2)^2=
π(60)^2 -π(40)^2=
3600π-1600π=2000π mm^2
Paul's Bikes rents bikes for $11 plus $4 per hour. Amanda paid $31 to rent a bike. For how many hours did she rent the bike?.
As given Paul's Bikes rents bikes for $11 plus $4 per hour and Amanda paid $31 to rent a bike shows she rent the bike for 5hours.
As given in the question,
Let 'h' represents the number of hours
Paul's Bikes rents bikes for $11 plus $4 per hour
Amanda paid $31 to rent a bike
Required equation is:
31 = 11 + 4h
⇒4h = 20
⇒h = 5hours
Therefore, as given Paul's Bikes rents bikes for $11 plus $4 per hour and Amanda paid $31 to rent a bike shows she rent the bike for 5hours.
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Solve.
5r+5= 3(5r - 4) – 10r
Answer: No solution
Step-by-step explanation:
5r + 5 = 3(5r - 4) - 10r Do multiplication
5r + 5 = 15r - 12 - 10r combine like terms
5r + 5 = 5r - 12 This is impossible. 5r cannot equal 5 and 12 meaning there is no value of r that makes this equation true so there's No Solution.
You could continue
5r + 17 = 5r
-5r =-5r
17=0 which is also not true
1. Which of the following points are on the circle centered at the origin with 2 = 89 ?
A) (25,64)
B) (5, -8)
C) (-3,-9)
D) (√89, √89)
The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).
Which of the following points are on the circle centered at the origin with r² = 89?It follows from the task content that the circle in discuss has a center at the origin, (0,0).
Hence, the since the square of the radius is; = 89.
It follows that the point which fits into the equation of the circle; x² + y² = r² is;
Choice C; (5)² + (-8)² = 25 + 64 = 89.
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The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).
Which of the following points are on the circle centered at the origin with r² = 89?It follows from the task content that the circle in discuss has a center at the origin, (0,0).
Hence, the since the square of the radius is; = 89.
It follows that the point which fits into the equation of the circle; x² + y² = r² is;
Choice C; (5)² + (-8)² = 25 + 64 = 89.
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Solve the given initial-value problem. the de is a bernoulli equation. y1/2 dy dx y3/2 = 1, y(0) = 9
A differential equation with some initial conditions is used to solve an initial value problem.
The required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
What is meant by an initial-value problem?An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.
Let the given equation be [tex]$y^{1/2} dy\ dx y^{3/2} = 1[/tex], y(0) = 9
[tex]$(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1[/tex] …..(1)
Divide the given equation (1) by [tex]$\sqrt{ y} $[/tex] giving
[tex]$y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$[/tex], which is in Bernoulli's form.
Put [tex]$u=y^{(1+1 / 2)}=y^{(3 / 2)}$[/tex]
Then [tex]$(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$[/tex].
Multiply (2) by [tex]$\sqrt{ } y$[/tex] and we get
[tex]y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1[/tex]
(2/3) [tex]u^{\prime}+u=1$[/tex] or [tex]$u^{\prime}+(3 / 2) y=3 / 2$[/tex],
which is a first order linear equation with an integrating factor
exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is
[tex]u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$[/tex] or
[tex]\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}[/tex]
To obtain the particular solution satisfying y(0) = 4,
put x = 0, y = 4, then
8 = (9/4) + c
c = (23/4)
Hence, the required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
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Use the given information to find the unknown value. y varies inversely with the cube of x. when x=9, then y=1. find y when x=1. enter the exact answer.
When the value of x = 1, the value of y = 729.
What is inverse relation?An inverse relationship is one where the value of one parameter decreases as the value of the second parameter increases. It is frequently described as a bad relationship.
In other phrases, an inverse relationship, also recognized as a negative relationship, is a negative relationship between two variables that moves in the opposite direction. Like, we have two variables X and Y. As X increases, so does Y, and as Y increases, so does X.Now, as per the question.
y varies inversely with the cube of x.
y ∝ 1/x³
Removing inverse, a constant of proportionality will come (say k)
y = k/x³
k = x³y.
When x = 9 then y = 1. Substitute the values and find k.
k = 9³(1)
k = 729
Now, estimate the value of y when x = 1.
y = k/x³ ( put the value of k and x )
y = 729/1³
y = 729
Thus, the value of y when the value of x = 1 is 729.
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please help with this question. n refers to the number of sides.
Answer:
n = 18
Step-by-step explanation:
The sides in a regular polygon are equal in length.
⇒ BC = CD
If BC = CD then ΔDCB is an isosceles triangle.
As the base angles of an isosceles triangles are equal:
⇒ ∠DBC = ∠BDC = 10°
Interior angles in a triangle sum to 180°.
⇒ ∠DBC +∠BDC + ∠DCB = 180°
⇒ 10° + 10° + ∠DCB = 180°
⇒ 20° + ∠DCB = 180°
⇒ ∠DCB = 180° - 20°
⇒ ∠DCB = 160°
Therefore, the interior angle of the regular polygon is 160°.
The interior angles of a regular polygon are equal in size.
[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Interior angle of a polygon}\\\\$\dfrac{(n-2) \times 180^{\circ}}{n}$\\\\where $n$ is the number of sides.\\ \end{minipage}}[/tex]
To find the number of sides, equate the formula to the found value of the interior angle and solve for n:
[tex]\begin{aligned}\implies\dfrac{(n-2) \times 180^{\circ}}{n} & =160^{\circ}\\(n-2) \times 180^{\circ} & =n \times 160^{\circ}\\ 180(n-2) & = 160n\\180n-360 & = 160n\\180n & = 160n+360\\180n-160n & = 360\\20n & = 360\\n &= \dfrac{360}{20}\\n & =18\\\end{aligned}[/tex]
Therefore, the regular polygon has 18 sides.
In the figure below, m1= (x+24)° and m2=5x°,
Find the angle measures.
12
Measure of angle 1 is 50° and that of angle 2 is 130°
The sum of all the angles on a straight line is equal to 180°.
Here, we are given two angles ∠1 and ∠2
Also, we are given that
m∠1 = (x+24)°
and m∠2 = 5x°
As we can see from the given figure, ∠1 and ∠2 lie on a straight line
⇒ m∠1 + m∠2 = 180
⇒ (x+24) + 5x = 180
x + 24 + 5x = 180
x + 5x + 24 = 180
6x + 24 = 180
6x = 180 - 24
6x = 156
x = 156/ 6
x = 26
Therefore,
m∠1 = 26 + 24
= 50
and m∠2 = 5(26)
= 130
Thus, the measure of the two angles is 50° and 130°
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Your question was incomplete. Check for the missing figure below.
900 students attend Ridgewood Junior High School. 4% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
12^-2 in simplest form
Answer:
Step-by-step explanation:
1/144
hope this helps :)
help please !!! example is not needed :)
Answer:
b
Step-by-step explanation:
Find the equation of the line that passes through points A and B.
A(1,7)
B(-3,-1)
The equation for the line that connects the locations is y = 2x + 5.
What is the Slope of a Line?The slope of a line, commonly known as the gradient, is defined as the value of the steepness or direction of a line in a coordinate plane. Slope can be determined using many ways given the equation of either a line or the coordinates of points on the straight line. . The slope is defined mathematically as "climb overrun" (change in y divided by change in x).
According to the given data:x₁ = 1
y₁ = 7
x₂ = -3
y₂ = -1
To obtain the equation of a line, we must first determine its slope. This is computed as:
m = [y₂ - y₁ ]/[x₂ - x₁]
Substituting the value we get:
m = [(-1) - 7 )/((-3) - 1)]
= -8/-4
= 2
The slope of the line = 2.
The line's intercept is:
The slope is the next step toward solving for a such equation of the line.
A typical linear equation is presented as:
y = mx + c
Let us substitute the slope and intercept values.
y = 2x + 5
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PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Answer:
12/15
Step-by-step explanation:
A coordinate plane with a horizontal line passing through (negative 3, negative 3), (negative 3, 0) and (negative 3, 3).
Which is true of the standard form of the equation of the line graphed?
Answer:
x = - 3Step-by-step explanation:
GivenThe line passes through the points:
(-3, -3,), (-3, 0) and (-3, 3)Since all x- coordinates are same, the line is vertical and its equation is:
x = - 3Here is a liner equation in two variables 2x + 4y - 31 = 123 determine whether each statement is true or false. the equation solved for x is x = 154 - 4y true or false ?
the equation solved for y is y = 77-x- 2 true or false ?
Answer:
Both sentences are false.
Step-by-step explanation:
Let's solve for x:
2x + 4y - 31 = 123
2x = 123 - 4y + 31
2x = 154 - 4y
x = 77 - 2y
Let's solve for y:
x = 77 - 2y
2y = 77 - x
y = 38.5 - 0.5x
a guest total is $5.45 and they give you $10 how much change do you owe them
Answer: $4.55
Step-by-step explanation:
Just subtract $10.00 from $5.45 and you will get $4.55
Answer:
$4.55
Step-by-step explanation:
To find the change, we have to subtract the money they give you ($10) with the guest total ($5.45).
10 - 5.45
= $4.55
$4.55 is your answer.
Take care and have a lovely rest of your day! :)
