math help
simplify. your awnser should contain only positive exponents with no fractional exponents in the denominator
Answers
The solution using laws of exponents is: [tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
How to use laws of exponents?
Some of the laws of exponents are:
- When multiplying by like bases, keep the same bases and add exponents.
- When raising a base to a power of another, keep the same base and multiply by the exponent.
- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.
The expression we want to solve is given as:
[tex]\frac{(x^{-\frac{3}{2} } y^{\frac{5}{3} } z^{-1})^{-1} }{zx^{\frac{3}{2} } y^{-\frac{1}{4} } * y^{-2} z^{\frac{1}{2} } }[/tex]
Using laws of exponents, we have:
[tex]x^{0} * y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
=[tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
Related Questions
Find the measure of angle EPH Enter your answer in the box.
Answers
Answer:
50
Step-by-step explanation:
Jake paid $13.50 for admission to the country fair and bought 9 tickets to play games. If he spent a total of $36, what is the cost, c, of one ticket? Write and solve an equation.
Answers
Answer:
$2.50
Step-by-step explanation:
Jake's total expenditure is ...
total = admission + c × (number of tickets)
36 = 13.50 + 9c . . . an equation to solve
4 = 1.50 +c . . . . . . . divide by 9
2.50 = c . . . . the cost of one ticket
Each ticket cost Jake $2.50.
Graph f(x)=1/2x+2. Use the line tool and select two points to graph the line.
Answers
Step-by-step explanation:
Since f is a linear function then its graph must be a line
to draw a line ,all you need is plotting two points.
f(0)=1/2(0)+2=0+2=2 then the line passes through the point (0,2)
f(2)=1/2(2)+2=1+2=3 then the line passes through the point (2,3)
look ok at the photo below for the graph.
what is the measurement of
Answers
Answer: Angle A = 120° and angle C = 45°
Step-by-step explanation: The first thing to note at the back of our minds is that the sum of the interior angles of a triangle equals 180°. Given that the three angle are available, we can start by adding them all together. Hence,
{12x + 12} + 15 + {3x + 18} = 180
12x + 12 + 15 + 3x + 18 = 180
By collecting like terms, we arrive at,
12x + 3x + 12 + 15 + 18 = 180
15x + 45 = 180
Subtract 45 from both sides of the equation
15x = 135
Divide both sides of the equation by 15
x = 9
At this point, we can now substitute for the value of x = 9 in the expressions representing angles A and C.
Angle A = 12x + 12
= 12(9) + 12
= 108 + 12
= 120
Angle A = 120°
Angle C = 3x + 18
= 3(9) + 18
= 27 + 18
= 45
Angle C = 45°
list the sample space for odd numbers between 20 and 30
Answers
The sample space for odd numbers between 20 and 30 is {21, 23, 25, 27, 29}. These are integers that are not wholly divisible by 2.
Explanation:The sample space is a term used in mathematics, specifically in statistics and probability, to describe all possible outcomes of an experiment. In this case, the experiment is to find all odd numbers between 20 and 30. An odd number is an integer that is not exactly divisible by 2. The odd numbers between 20 and 30 are: 21, 23, 25, 27, and 29. Therefore, the sample space you are looking for is {21, 23, 25, 27, 29}.
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The distance a car can travel in miles is modeled by the equation y=23x-6, where x represents the number of gallons of gas the car uses. If the car traveled 86 miles, how many gallons of gas did it use
Answers
Answer:
4 gallons
Step-by-step explanation:
86 = 23x -6
92 = 23x
x = 4
Answer:
4
Step-by-step explanation:
y=23x-6
86=23x-6
92=23x
x=92/23
x=4
Dave works for 5 hours double time and he earns $98 find his normal hourly year rate
Answers
Answer: $9.8 per hour
Step-by-step explanation:
If Dave works for 5 hours at double time, then he gets paid for 10 hours of work. If he earned $98 for 10 hours of work, all you need to do is divide the amount of money earned by the hours of work. [tex]\frac{98}{10}[/tex]=9.8 dollars per hour.
Typically, what percentage of the home cost should you have available for a down payment? 5%, 50%, 25%, 30%
Answers
Answer:
25%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
I had this question on a test and i made an 100%
which point is an x intercept of the quadratic function f(x) =(x-8)(x+9)
Answers
Answer:
(- 9, 0) and (8, 0)
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
(x - 8)(x + 9) = 0
Equate each factor to zero and solve for x
x + 9 = 0 ⇒ x = - 9
x - 8 = 0 ⇒ x = 8
The x- intercepts are x = - 9 and x = 8
What is slope = 3/4 goes through the point (0,6)
Answers
Answer:
y=3/4x+6
Step-by-step explanation:
y-y1=m(x-x1)
y-6=3/4(x-0)
y-6=3/4(x)
y-6=3/4x
y=3/4x+6
A 500-kilogram horse runs at 5 meters/second. The horse’s kinetic energy is (blank)joulese g = 9.8 N/kg.)
Answers
Answer:
KE = 6250 Joule.
Step-by-step explanation:
Every moving body has kinetic energy and it is given by the expression
[tex]KE = \frac{1}{2}mv^{2}[/tex]
where the moving body has m as the mass and v as the velocity.
If m is in Kg and v is in meter/sec, then KE will be expressed in Joule.
Now, in this case, m = 500 and v = 5 meter/sec.
So, [tex]KE = \frac{1}{2} \times 500 \times (5)^{2} = 6250[/tex] Joule. (Answer)
Rewrite the following in the form log(c).
log(6) – log(2)
Answers
Answer:
Step-by-step explanation:
㏒(6)-㏒(2)=㏒(6/2)=㏒ 3
The expression log(6) – log(2) in form of log(c) is log(12).
What is Logarithm?Logarithms are another way of writing exponents in mathematics. A number's logarithm with a base equals another number. Exponentiation is the inverse function of logarithm.
A logarithm is defined as the number of powers to which a number must be increased in order to obtain some other numbers. It is the simplest way to express enormous numbers.
We have to write the expression log(6) – log(2) in form of log(c).
Using product property for logarithms
log a + log b= log (ab)
Here, a= 6 and b= 2 then
ab = 6 . 2= 12
Thus, the required form of log(6) – log(2) is log(12).
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Daniel is constructing a deck like the one shown. What is the area of the deck? Explain how you found the answer.
Answers
Answer:
Well if the deck was sown i would know butt... ill just give an example so if the height is 5 and the length 10 then you do 5 times 10 and get 50 A=50
Step-by-step explanation:
Answer:
119.5
Step-by-step explanation:
um....well i looked it up so yeah
Two people working together can complete a job in 5 hours. If one of them works
twice as fast as the other, how long would it take the faster one working alone?
Answers
Answer:
5 hours
Step-by-step explanation:
because he is working twice as fast which means he will get the job done faster
So your awnser would therefore be 5
Write a ratio as a ratio of whole numbers in lowest terms
$1.00 to $1.50
Answers
Answer:
Step-by-step explanation:
50
The ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e. [tex]\mathbf{\dfrac{2}{3}}[/tex]
A ratio of two integers a and b can be represented into a fraction as numerators and denominators.
[tex]\mathbf{\dfrac{a \to numerator}{b \to denominator}}[/tex]
To recognize and determine the ratio of the whole numbers in their lowest terms, we will multiply both the numerator and the denominator by 10.
i.e.
[tex]\mathbf{=\dfrac{1.00}{1.50}}[/tex]
[tex]\mathbf{=\dfrac{1.00\times 10}{1.50 \times 10}}[/tex]
[tex]\mathbf{=\dfrac{10}{15}}[/tex]
DIvide both the numerator and denominator by 5;
[tex]\mathbf{=\dfrac{2}{3}}[/tex]
Therefore, we can conclude that the ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e. [tex]\mathbf{\dfrac{2}{3}}[/tex]
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F is directly proportional to a.
If F = 24 when a = 8 find,
a when F = 18
Answers
Answer:
K = 3
a = 6
Step-by-step explanation:
F is directly proportional to a
That’s F = Ka
K is the constant
Divide both sides by a to get the constant k
K = F/a
When F = 24 and a =8
K = 24/8
= 3
When F = 18
a = ?
F = Ka
18 = 3 x a
18 = 3 x a
Divide both sides by 3
18/3 = 3 x a /3
6 = a
a = 6
I need to know the answers to these please
Answers
The answer is 40.
7/8=x/40. We had to multiply 8 by 5 to get 40.
Whatever you do to denominator you must do to numerator. Multiply 7 and 5 to get 35.
Now we have 7/8 is equal to 35/40.
Next, for the 9/10 part. We multiplied 10 and 4 to get 40 so multiply the numerator by 4 as well and you get 36.
Now we have 9/10 is equal to 36/40
The problem is now 35/40 and 36/40
35/40 < 36/40
Which is the same as
7/8 < 9/10
Write the equation.
During the year,
Myong travels 5,678
miles by airplane.
He travels twice as
many miles by train.
How many miles
does Myong travel
by train?
Answers
Answer:
11,356
Step-by-step explanation:
We multiply 5,678 by 2 because the word 'twice' is the same as multiplying by 2
given S (-1,8), and T (7,-9) what is the length of ST?
Answers
Answer:
ST = √353 or 18.79
I can add a step-by-step explanation if you want me to.
The length of ST is approximately 18.79 units.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
We are given that;
Points= S (-1,8), and T (7,-9)
Now,
x1=−1
y1=8
x2=7
y2=−9
Substituting these values into the formula, we get:
d=(7−(−1))2+(−9−8)2
d=(8)2+(−17)2
d=64+289
d=353
d= 18.79
Therefore, by the distance the answer will be 18.79 units.
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Rita has n dollars yo being with. She just spent 23 dollars. Using n , write an expression for the number of dollars she has left.
Answers
n - 23 = x
I’m not entirely sure but this is my understanding.
Answer:
i think n-23=x
the question is worded weirdly
How to solve systems using elimination
Answers
See explanations below on solving simultaneous equations by elimination.
Step-by-step explanation:
In solving simultaneous equations by elimination, you make one side of the variables equal and eliminate that side by either addition or subtraction, then solve the remaining variable whose value is then used in one of the equations to find the other variable. For example;
(i) 4x - 2y= 10
(ii) x+ y =4
Making the x variable part equal to eliminate x
1(4x-2y=10)--------multiply by 1
4(x+y=4) ---------multiply by 4
4x -2y =10
4x+4y=16
Apply subtraction to eliminate the x variables
0 +6y =6
6y=6
y=6/6 = 1
Use the value of y =1 in the equation x+y= 4
x+y=4
x+1=4
x=4-1 = 3
x= 3, and y=1
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What is the value of t in the following equation? t + 14 = 2 712
Answers
Answer: t = 2698
Step-by-step explanation: Subtract 14 from 2712 to get the value of t
There are two functions that can be used to describe the percent of people 25 years and older who have completed at least high school. For both functions f(x)=0.44x + 87.5 and g(x)=0.008x^2 + 0.42x + 87.5 is the number of years since 2008, and any y (or f(x) or g(x)) is the percent of people 25 and older completing at least high school. Assume that the trend of g(x) continues. Find g(15) and describe in words what this means.
g(15)=
Answers
Answer:
[tex]g(15)=93.8\%[/tex]
see the explanation
Step-by-step explanation:
Let
x ----> the number of years since 2008,
g(x) ----> the percent of people 25 years and older who have completed at least high school
we know that
[tex]g(x)=0.008x^2+0.42x+87.5[/tex]
so
For x=15 years since 2008
substitute
[tex]g(15)=0.008(15)^2+0.42(15)+87.5=93.8\%[/tex]
That means
In the year 2023 (2008+15) the percent of people 25 and older completing at least high school will be 93.8%
Final answer:
To find g(15), we substitute x with 15 in the function g(x) = [tex]0.008x^2 + 0.42x + 87.5[/tex], yielding g(15) = 95.6%. This means that in 2023, it's projected that 95.6% of people 25 and older will have completed high school according to the given quadratic trend.
Explanation:
The student is asking for the evaluation of the function g(x) = [tex]0.008x^2[/tex] + 0.42x + 87.5 at x = 15, which represents the number of years since 2008. To find g(15), we need to substitute x with 15 in the given function:
g(15) = 0.008(15)2 + 0.42(15) + 87.5
Calculating the value step by step:
152 = 225
0.008 × 225 = 1.8
0.42 × 15 = 6.3
1.8 + 6.3 + 87.5 = 95.6
Therefore, g(15) = 95.6.
In words, this means that if the trend described by function g(x) continues, then in the year 2023 (15 years after 2008), 95.6% of people aged 25 and older will have completed at least a high school education. This is a projection of graduation rates over time.
Combine like terms to create an equivalent expression 2/5m - 4/5 - 3/5m
Answers
Answer:
-1/5m-4/5
Step-by-step explanation:
2/5m-4/5-3/5m
2/5m-3/5m-4/5
-1/5m-4/5
The Outstanding O's cereal box has been redesigned with a new size and shape.
20 cm
30 cm
8 cm
How much material will it take to make the new box with no overlaps?
Answers
Answer:
Step-by-step explanation:
2(20x30)+ 2(8x30) + 2(20x8) - I > 1200 + 480 + 320= 2000 hope this helps :D
The material required for making a new cereal box with new dimensions is 2000 sq. cm. This is obtained by calculating the total surface area of the box with new dimensions.
The surface area of the cuboid:Cuboid has 6 faces (each face looks like a rectangle)To get the surface area of the cuboid, add the areas of all the 6 faces of the cuboid.For the length (L), width (W), and height (H), the surface area is given as S.A=2(LW + WH + LH). Since the area of the rectangle is L×W, adding areas of each face.Calculating the required material:It is given that,
The Outstanding O's cereal box has been redesigned with the new size and shape
The new dimensions are,
L=20 cm
W=8 cm
H=30 cm
To get the required material, the surface area of the box with new dimensions is to be calculated.
So,
S.A=2(LW + WH + LH)
=2(20×8+8×30+30×20)
=2(160+240+600)
=2(1000)
=2000 sq. cm
Therefore, the material required for the new box is 2000 sq. cm
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How can this 12×2+2³ make 120
Answers
Step-by-step explanation:
[tex]12\times(2+2^3)\qquad\text{use PEMDAS}\\\\\text{first power}\\\\=12\times(2+8)\\\\\text{next addition in parentheses}\\\\=12\times10=120[/tex]
In 2000 the median home price in a certain city was about $290,000, and from 2000 to 2006, home prices in the city rose in an average of about 11.3% per year. If prices continue to rise at that rate what would be the median home price would have been in 2018? Compare to the actual median price of about $400,000 in 2018. (median home price would be approximately ____ minion in 2018.
Answers
Answer:
5000
Step-by-step explanation:
Skyler is 104 miles away from Marcus. They are traveling towards each other. If Marcus travels 8 mph faster than skyler and they meet after 4 hours, how fast was each traveling?
Answers
Speed of skyler is 204 mph and speed of marcus is 212 mph
Solution:
Skyler is 104 miles away from Marcus
Therefore,
Distance = 104 miles
They meet after 4 hours
Time taken = 4 hours
Let "x" be the speed of sklyer
Marcus travels 8 mph faster than skyler
Therefore,
Speed of marcus = 8 + x
They are traveling towards each other
Since they are traveling towards each other, we can add up their speeds
Speed = x + 8 + x = 2x + 8
The distance is given by formula:
[tex]distance = \frac{speed}{time\ taken}\\\\104 = \frac{8+2x}{4}\\\\104 \times 4 = 8 + 2x\\\\8 + 2x = 416\\\\2x = 416-8\\\\2x = 408\\\\x = 204[/tex]
Thus speed of skyler = x = 204 mph
Speed of marcus = 8 + x = 8 + 204 = 212 mph
Thus speed of skyler is 204 mph and speed of marcus is 212 mph
Mrs. Rivera ate 3/8 of a
pizza and Ms. Carter ate 4/8
of a pizza. How much pizza
did they eat altogether?
Answers
Answer:
They ate 7/8 of a pizza altogether.
Step-by-step explanation:
So, you know Mrs. Rivera ate 3/8 of a pizza and Ms. Carter ate 4/8 of a pizza.
You add 3/8 + 4/8 and you get 7/8.
The ate 7/8 of a pizza altogether.
The quantity of pizza that Mrs. Rivera and Ms. Carter ate altogether is equal to [tex]\frac{7}{8}[/tex]
Given the following data:
Fraction Rivera ate = [tex]\frac{3}{8}[/tex]Fraction Carter ate = [tex]\frac{4}{8}[/tex]To calculate how much (quantity) pizza they ate altogether:
A fraction can be defined as a numerical quantity that isn't a whole number.
Hence, a fraction is simply a part of a whole number.
In this exercise, we would add up the two fractions, so as to calculate how much (quantity) pizza they ate altogether.
[tex]Total \;quantity = \frac{3}{8} + \frac{4}{8}[/tex]
Lowest common multiple (LCM) = 8
[tex]Total\;quantity = \frac{4\;+\;3}{8} \\\\Total\;quantity = \frac{7}{8}[/tex]
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An object is launched from a platform.
Its height (in meters), x seconds after the launch, is modeled by:
h(x)=-5x2verb +20x+60
What is the height of the object at the time of launch?
Answers
Answer:
60 feet
Step-by-step explanation:
The height, h (in meters), of the object launched from a platform is represented by the equation
[tex]h=h(x)=-5x^2+20x+60[/tex]
where x is the time (in seconds) passed after the launch.
The time of launch is [tex]x=0[/tex] (0 seconds passed after the launch)
Substitute [tex]x=0[/tex] to find the height:
[tex]h=h(0)=-5\cdot 0^2+20\cdot 0+60=60\ feet[/tex]