Using exponent power property, ³√x²y³ = x^r y^s, where x and y are non-negative real numbers.
r, the exponent of x, is: 2/3
s, the exponent of y, is: 1
What is Exponent power property?According to the Power of a Power Property, you can multiply the exponents if one exponent is increased to a higher exponent. This characteristic may be used to resolve the equation (3 x 2) 3.
³√x²y³ = x^r y^s
Cubing on both sides,
x²y³ = x^3r y^3s
As base is same, equating the powers
⇒ 2 = 3r; r = 2/3
⇒ 3 = 3s; s = 1
The correct question is -The expression
³√x²y³ = x^ry^s
where x and y are non-negative real numbers.
r, the exponent of X, is:
s, the exponent of y, is:
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Jason is driving his car at 55mi/h he needs to keep his car within 5 mi/h of his current speed. write and solve an absolute-value equation to find jason's max and min speeds.
The absolute-value equation to find Jason's max and min speeds is |x| = |55 ± 5| mi/h and the maximum speed is 60 mi/h and the minimum speed is 50 mi/h.
Absolute Value equation:
An absolute value equation in the form | ax + b | has the following properties:
If c < 0 , | a x + b | = c has no solution .
If c = 0 , | a x + b | = c has one solution .
If c > 0 , | a x + b | = c has two solutions .
Given,
Jason is driving his car at 55mi/h he needs to keep his car within 5 mi/h of his current speed.
Here we need to write solve an absolute-value equation to find Jason's max and min speeds.
We know that, the current speed = 55 mi/h
And he want to keep the speeds within 5 mi/h of his current speed.
Let x be the unit that measure the maximum and minimum speed.
So,
The maximum speed.
|x| = 55 + 5 = 60 mi/h
and the minimum speed,
|x| = 55 - 5 = 50 mi/h
So, the absolute value of the equation is,
|x| = |55 ± 5| mi/h
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Please help with photo below
Answer:
No
Step-by-step explanation:
like terms are terms which have the same variable , that is
10x and - 5x are like terms, they both have the same variable x
if a round cake has 30 slices how many slices will represent an angle of 216°?
Answer:18
Step-by-step explanation:360/30=12
216/12=18
The Drama Club sold 900 tickets to the school play. They charged $5.50 for students and $8.00 for non-students.
If they took in $5700, how many non-student tickets were sold?
Answer:
300 non student tickets were sold
Step-by-step explanation:
Let's solve the equation step by step,
In order to solve for how many non student tickets were sold, let's make an equation
5.50x + 8.00y = 5700 --------(equation 1)
x + y = 900 ---------------(equation 2)
Let's solve for x and y
5.5x+8y=5700;x+y=900
Rewrite equations:
x+y=900;5.5x+8y=5700
Step: Solve x+y=900 for x:
x+y=900
x+y+−y=900+−y(Add -y to both sides)
x=−y+900
Step: Substitute−y+900forxin5.5x+8y=5700:
5.5x+8y=5700
5.5(−y+900)+8y=5700
2.5y+4950=5700(Simplify both sides of the equation)
2.5y+4950+−4950=5700+−4950(Add -4950 to both sides)
2.5y=750
2.5y/2.5 = 750/2.5
(Divide both sides by 2.5)
y=300
Step: Substitute300foryinx=−y+900:
x=−y+900
x=−300+900
x=600(Simplify both sides of the equation)
Since y = 300 then 300 non student tickets were sold0.00541 divided by 10^2
Answer:
=0.0000541
Step-by-step explanation:
[tex]\frac{0.00541}{10^2}[/tex]
[tex]\frac{0.00541}{100}[/tex]
[tex]=0.0000541[/tex]
Answer:0.0000541
Step-by-step explanation:
Firstly, you'll simplify 10².
10²÷0.00541 ---> 100 ÷ 0.00541
Then, you'll divide 100 by 0.00541.
100 ÷ 0.00541 ---> 18484.2883549
In a triangle the measure of the first angle is 24 degrees more than the second angle. the measure of the third angle is four times the measure of the second angle. if the total number of degrees in a triangle is 180 what is the measure of the largest angle?
The greatest angle in the given triangle is 104 degrees.
What is a triangle?The polygon with 3 sides, three vertices, and three angles is known as a triangle. A triangle's overall number of degrees is always 180 degrees.Given:
Let, the second angle has a measurement of x degrees.The first angle's measurement is 24 degrees greater than the second angle's measurement. As a result, the first angle is (24+x) degrees.The third angle is four times as large as the second. As a result, the third angle has a measure of 4x.So,
(24 + x) + x + 4x = 1806x = 124 - 486x = 156x = 156/6x = 26As a result, the second angle has a measurement of 26 degrees.
The first angle's measurement is now 24 degrees greater than the second angle's measurement.
Now,
= 24 + 26= 50As a result, the first angle has a measure of 50 degrees.
The third angle is now four times the size of the second angle.
So,
4 × 26 = 104Therefore, the greatest angle in the given triangle is 104 degrees.
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Approximately how much fencing is needed to enclose a circular pond with a diameter of 12. 5 feet?.
Approximately 39.26 feet is needed to enclose a circular pond with a diameter of 12. 5 feet.
What is the circumference of a circle?The circumference (from Latin circumference, meaning "carrying around") is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were finally opened and straightened out to a line segment. In general, the perimeter is the length of the curve around any closed figure. The circumference can also refer to the circle itself, i.e. the locus corresponding to a disk's edge. A sphere's circumference is the circumference, or length, of any of its great circles.To fin the circumference:
Formula: C = 2πrRadius = Diameter/2 = 12.5/2 = 6.25So,
C = 2πr= 2 · π · 6.25≈ 39.26991Therefore, approximately 39.26 feet is needed to enclose a circular pond with a diameter of 12. 5 feet.
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Solve the simultaneous equations
3y + 11 = 4x
10x + 2y + 1 = 0
In linear equation the solution set of the equations x = 1/2, y = -3.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Multiply both sides of the equation by a
coefficient - 2(4x - 3y ) = 11 × 2
3 ( 10x + 2y ) = ( - 1 ) × 3
apply multiplicative distribution law
8x - 6y = 11 × 2
3( 10x + 2y ) = (-1) × 3
calculate the first terms
8x - 6y = 22
3( 10x + 2y ) = ( -1) × 3
remove the parentheses
8x - 6y = 22
30x + 6y = -3
add up the two equation
8x - 6y + ( 30x + 6y ) = 22 + ( -3)
remove parentheses - 8x - 6y + 30x + 6y = 22 -3
cancel the unknown variables - 8x + 30x = 22 -3
combine like terms - 38x = 22 - 3
calculate the sum or difference - 38x = 19
reduce the greatest common factor on both
sides of equation - 2x = 1
divide both sides of the equation by the coefficient of variable - x = 1/2
substitute one unknown quantity into the elimination 8 * 1/2 - 6y = 22
reduce the expression to the lowest term 4-6y = 22
reduce the greatest common factor on both sides of the equation
2 - 3y = 11
Rearrange unknown terms to the left side of the equation - 2 - 3y = 11
calculate the sum or difference -3y = 9
reduce the greatest common factor on both sides of the equation -y = 3
divide both sides of the equation by the coefficient of variable y = -3
the solution set of the equations
x = 1/2
y = -3
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How much money did billy start with if he saves 19 dollars in 5 days?
You plan on going golfing this weekend with a friend. you can either go to your favorite course which is 14 miles north of your house or to your friends favorite course which is 14 miles south of your house. write an absolute value inequality that represents all the distances you may be from your house
An absolute value inequality that represents all the distances you may be from your house is -14 ≤ x ≤ 14.
Inequality:
Basically, inequality is the relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given,
You plan on going golfing this weekend with a friend. you can either go to your favorite course which is 14 miles north of your house or to your friends favorite course which is 14 miles south of your house.
Here we need to write an absolute value inequality that represents all the distances you may be from your house.
Consider your house is in the center.
So, both sides you have the Golf course.
So, it can be written as
-14 for north side one and 14 for the south side one.
And let x be the distance between the house and the golf course.
So, it can be written as the inequality,
=> -14 ≤ x ≤ 14.
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Find x and y. Please
Answer:
x = 4 y = 21
Step-by-step explanation:
16x - 23 = 10x + 1
16x - 10x = 23 + 1
6x = 24
24/6 = x
x = 4
16(4) - 23 = 41
41 + (180 - 62) + y = 180
41 + 118 + y = 180
y = 21
through: (3, 4), perp. to x = 0
Standard form
Answer: y=4
Step-by-step explanation:
If the line is perpendicular to the y - axis and goes through the point (3,4) then it's just y=4
Here is a list of fractions.
15
20
3344
3
One of these fractions is not equivalent to
4
Write down this fraction.
12
16
26
32
21
28
Answer:
So bassiccalyy the answer is 3344/3 because it is not equivalent to 4
1/2|x + 8| = |4x − 1|
Eighth grade > J.10 Solve proportions: word problems 5XV
You have prizes to
Sally's retirement party will cost $34 if she invites 17 guests. If there are 46 guests, how
much will Sally's retirement party cost? Assume the relationship is directly proportional.
Answer:
Practice with this https://www.ixl.com/math/grade-8/solve-proportions-word-problems
Step-by-step explanation:
Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles.
What is the probability of selecting a a green or black marble?
Find the unit vectors that are parallet to the tangent line to the parabola y=x^2 at the point (3,9)
The unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].
What are unit vectors?Unit vectors have a magnitude of exactly one unit. They are extremely useful for a variety of reasons.In particular, the unit vectors [0,1] and [1,0] can be combined to form any other vector.To find the unit vector:
Differentiate y = x² with respect to x.
We get, dy/dx = 2x.
The slope of a tangent:
[tex]\mathrm{P}(2,4)=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{atP}(2,4)}=2 \times 2=4[/tex]
Tangent P equation is:
y - 4 = 4(x - 2)y = 4x - 4y = 4xy = 4x is the equation of a line passing through the origin O and parallel to the tangent at P.
4x = y, z = 0x/1 = y/4, z = 0This line's direction ratios are 1, 4, and 0, and its direction cosines are:
[tex]\pm \frac{1}{\sqrt{1^2+4^2+0^2}}, \pm \frac{4}{\sqrt{1^2+4^2+0^2}}, 0\\\pm \frac{1}{\sqrt{17}}, \pm \frac{4}{\sqrt{17}}, 0[/tex]
The number of unit vectors parallel to the tangent line at P(2,4) is:
[tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\bar{j}\right)[/tex]
Therefore, the unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].
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The correct question is given below:
Find the unit vectors that are parallel to the tangent line to the parabola y=x^2 at the point (2, 4).
y=ax^2+b please solve this
What should the purchase price of a 5-year zero coupon bond be if it is purchased today and has face value of $1,000?
The purchase price of a 5-year zero coupon bond will be $768.87.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
Let x be the price before 5 years.
If it is purchased today and has a face value of $1,000. Then we have
(1 + 0.046)(1 + 0.049)(1 + 0.052)(1 + 0.055)(1 + 0.068) x = 1000
(1.046 × 1.049 × 1.052 × 1.055 × 1.068) x = 1000
1.3 x = 1000
x = $768.87
The purchase price of a 5-year zero coupon bond will be $768.87.
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[tex]\sqrt{180x^{25}y^{23}z^{39}[/tex]
[tex]6[/tex][tex]x^{12}[/tex][tex]y^{11}[/tex][tex]z^{19}[/tex][tex]\sqrt{5xyz}[/tex]
How do you define the square root of a number?
In mathematics, a square root of a number x is a number y such that y^2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 42 = (−4)2 = 16.
[tex]\sqrt{180x^{25 } y^{23} z^{39}[/tex]
[tex]180 = 2*2*3*3*5\\x^{25} = x*x*x........*x 25 times\\y^{23}= y*y*y.........*y 23 times\\ z^{39} = z*z*z........*z 39 times[/tex]
we have
square terms comes out
x is 25 times so we can write x as [tex](x^{12})^{2}[/tex] [tex]*[/tex][tex]x[/tex] therefore [tex]x^{12}[/tex] comes out and only left inside is x
similarly [tex](y^{11})^{2}[/tex] [tex]*y[/tex] therefore [tex]y^{11}[/tex] comes out and only left inside is y
[tex](z^{19})^{2} *z[/tex] therefore [tex]z^{19}[/tex] comes out and left inside is z
then the expression become
[tex]6[/tex][tex]x^{12}[/tex][tex]y^{11}[/tex][tex]z^{19}[/tex][tex]\sqrt{5xyz}[/tex]
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A spherical tank has a capacity of 750 gallons. using the fact that 1 gallon is about 0.1337 ft3, find the radius of the tank (to the nearest hundredth of a foot).
The spherical tank with a capacity of 750 gallons has a radius of 2.88ft.
Volume refers to the total amount of space an object occupies. It also determines the capacity of the object.
Given the fact that 1 gallon is about 0.1337 ft^3, and the spherical tank has a capacity of 750 gallons, then it's volume or capacity can be converted from gallons to ft^3 by multiplying 750 with 0.1337.
1 gallon = 0.1337 ft^3
750 gallons = 750(0.1337 ft^3)
750 gallons = 100.275 ft^3
To solve for the radius of the spherical tank, use the formula for the volume of sphere given by the formula:
V = 4/3πr^3
where V = 100.275 ft^3
100.275 ft^3 = 4/3πr^3
r^3 = 23.93889288 ft^3
r = 2.882048957ft
Rounding off to the nearest hundredth of a foot:
r = 2.88ft
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Thang decided to borrow $7000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 5%. How much interest will Thang pay
Answer:
He will pay $1,050 interest
Step-by-step explanation:
5% interest is paid every year for 3 years
5% * 3(years) = 15%
7000 * 15% = $1,050
$1,050
Your answer should be a polynomial in standard form.
(x - 2)(x - 6)
I can't get this one
Answer:
[tex]8+2z[/tex]
Step-by-step explanation:
[tex]Rule: a\left(b+c\right)=ab+ac\\= 2\left(4+z\right)=2\cdot \:4+2z\\2\cdot \:4+2z\\2\cdot \:4=8\\=8+2z[/tex]
The graph represents this system of equations: A system of equations. 2 x plus y equals 3. 2 x minus 5 y equals 15.
A coordinate grid with 2 lines. One line passes through (0, 3) and (1.5, 0). The other line passes through (0, negative 3) and (2.5, negative 2).
What is the solution to the system of equations represented by the graph?
(0, –3)
(1, 1)
(1.5, 0 )
(2.5, –2)
The solution to the system of equations is (2.5, -2)
How to determine the solution to the system of equations?The system of equations is given as:
2x + y = 3
2x - 5y = 15
Subtract the equations to eliminate the variable x
This is represented as
2x - 2x + y - -5y = 3 - 15
Evaluate the like terms in the above equation
So, we have
y + 5y = 3 - 15
Evaluate the like terms in the above equation
So, we have
6y = -12
Divide both sides of the above equation by 6
So, we have
y = -2
Substitute y = -2 in 2x + y = 3
2x - 2 = 3
This gives
2x = 5
Divide by 2
x = 2.5
Hence, the solution to the system of equations is (2.5, -2)
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what is 6x7(8-0)3+5=
Answer:
1013
Step-by-step explanation:
(6)(7)(8−0)(3)+5
=42(8−0)(3)+5
=(42)(8)(3)+5
=(336)(3)+5
=1008+5
=1013
101+102-103+104-105+106-…-199+200
Please answer asap!!! Will give brainliest!!!!
Answer:
252
Step-by-step explanation:
One way we could think about this problem is by grouping the numbers together into pairs: -103+104 would be a pair, -105+106 would be a pair and et cetera up to the pair -199+200.
As you can see, each of these pairs add to 1 (-103+104=1, -199+200=1 etc.), so to solve this problem we can simply find how many of these pairs there are and multiply the number by 1 since each pair will total to 1.
To find how many pairs there are we need to find the number of numbers between 103 and 200 (incl.) and divide it by 2.
200-103= 97 numbers, adding 1 to count the one we started with gives us 98 numbers between 103 and 200 (incl.).
98/2 = 49 pairs of numbers. Since each pair totals 1, 1x49 is the total sum of all these pairs of numbers.
Now we need to address the other two numbers. The sequence started with 101+102 before we looked at the remaining pairs, so to find the sum, we just need to add together 101+102+49.
101+102+49 = 252
Hope this helped!
1. 60 high school seniors taking AP classes (advanced classes for college credit) were polled (asked a question) to see if they were taking European History or US History. A total Of 29 students said they were taking AP European History and a total of 50 students sald they were taking AP US History. How many students take both AP European History and AP US History? (Hint: Draw a venn diagram.)
The number of students take both AP European History and AP US History is 19 students
A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common.
Let the students take both AP European History and AP US History be x such that;
n(U) = 29 - x + 50 - x
If 60 high school seniors taking AP classes, then n(U) = 60. Substitute to have:
60 = 29 - x + x + 50 - x
60 = 79 - x
-x = 60 - 79
-x =-19
x = 19
Therefore the number of students take both AP European History and AP US History is 19 students
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-4/7+ 2/7x - 14x+4/7
Answer:
-96/7x or 13.714x
Step-by-step explanation:
-4/7+ 2/7x - 14x+4/7
first we do
4/7-4/7 which is zero, so we can cancel those out.
then we do
2/7x-14x ( or you can do -14x+2/7, it’s the same thing
use your calculator to make this easier. if you look you’ll be able to find a fraction button on most
after we do 2/7x-14x , we get -96/7x
if you want it in a fraction just divide and you’ll get -13.714x
Find the distance between (10,6), (1,-4)