The result of simplifying the expression y⁵/₇ / y³/₁₄ using the exponent rules is [tex]\sqrt{}[/tex](y)
To solve this exercise we have to resolve algebraic operations following the exponent rules.
[(y)⁵/₇] / [(y)³/₁₄]
Using the quotient that indicates that: the exponent result will be the subtraction of these exponents, we have:
(y)⁵/₇ ⁻ ³/₁₄
(y) ⁽¹⁰⁻³⁾/¹⁴
(y) ⁽⁷/¹⁴)
(y) ¹/²
As we have a fractional exponent, you must convert the exponent to root:
[tex]\sqrt{}[/tex](y)
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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The sum of two numbers is 56 and the difference is 24. What are the numbers?
Answer:
16 and 40Step-by-step explanation:
The sum of two numbers is 56 and the difference is 24. What are the numbers?
remove the difference from the sum and divide by two, you have the first number, add the difference to the first number and you will have the second number
(56 - 24) : 2 =
32 : 2 =
16 (1st number)
16 + 24 =
40 (2nd number)
The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 38 feet. Find the length and width of the rectangle.
Width =
Length
The length of the rectangle is 9 feet and the width of the rectangle is 10 feet.
What is the Perimeter of a Rectangle?The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.
A rectangle has four 90° angles.The lengths of a rectangle's diagonals are equal.Let the length of the rectangle be x feet
Then, the width of the rectangle will be x+1feet
We know that the perimeter of a rectangle is given by
P= 2(l+w)
Here
P= perimeter of a rectangle
l=length of the rectangle
w= width of the rectangle
Put l=x, w= x+1 and P= 38 in the perimeter formula
38 = 2(x+x+1)
Divide both sides by 2
19= x+x+1
19= 2x+1
Subtract 1 from both sides
18=2x
Divide both sides by 2
x=9 feet
This is the length of the rectangle.
Now, the width x+1 of the rectangle will be
9+1 = 10 feet
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Evalute1111011 ×1101 in base tow
Step-by-step explanation:
11dvccvgtgcgt5cjuuhh
A grocery store sells 6 oranges for $2. The cost of the oranges varies directly with the number of oranges.
The answer will be y =2
x and y graph also known as the x and y-axis are two important lines that make a graph. A graph consists of a horizontal axis and a vertical axis where data can be represented. A point can be described in a horizontal way or a vertical way, which can be easily understood using a graph. These horizontal and vertical lines or axis in a graph are the x-axis and y-axis respectively.
A x and y graph can be defined by the two axes i.e. x-axis and the y-axis that form a coordinate plane for a graph. The horizontal axis is represented by the x-axis and the vertical axis is represented by the y-axis. The point where the x and y-axis intersect is known as the origin and is used as the reference point for the plane.
y = 1/3x
when x =0
y = 0
when x =3
y = 1/3×3 = 1
when x=6
y=1/3×6= 2.
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Louie drove 50 1/8 miles and used 2.5 gallons
of gas. find the number of miles driven per
gallon of gas.
The number of miles driven per gallon is 401/20
How to calculate the number of miles ?Louie drove 5- 1/8 miles
He used 2.5 gallons for this journey
Therefore the number miles per gallon can be calculated as follows
401/8 = 2.5
x= 1
Cross multiply both sides
2.5x= 401/8
x= 401/8 ÷ 2.5
x= 401/8 × 1/2.5
= 401/20
Hence the number of miles per gallon is 401/20
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What is $210 to $35?
Answer:
210:35 = 6:1
Step-by-step explanation:
210:35
if divided by 35, then 6:1
What will be the median of the following set of numbers? 126,132,128,124,134,142,134,146,134,132
Answer:
133
Step-by-step explanation:
for that we need to sort the numbers :
124,126,128,132,132,134,134,134,142,146
the median is the number, for which half of the other numbers are smaller, and the other half of the other numbers is larger.
as we have 10 numbers, there is no such single middle number.
instead, we take the 2 middle numbers and calculate their mean value. that is then the median.
the 2 middle numbers are based on our sorted list above
132, 134
the mean value is
(132 + 134)/2 = 133
and that is then the median.
Sylvia has 6 1/2 boxes of chocolate to share at a family picnic. If she gives each person 1/3 of a box, how many people can receive chocolate?
The number of persons that would be able to receive the chocolates based on the question is 19
How to solve for the numberThe total number of chocolate = 6 1/2
This can be written to be 13 / 2 or 6.5
The number or amount that she has to give from what is contained in the box to each person is 1/3 = 0.33
Hence to get the number of people that would receive the chocolate we would have
6.5 / 0.33
= 19.5
This can be approximated to 19
Hence the total number that would receive the chocolate is 19
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Tavon have a gift card for $130 that loses three dollars for each 30 day It is not used he another gift card for $110 that loses 2.5 for each 30 day. It’s not used write and solve an equation for the number of 30 days periods Until the value of kid cards will be equal what will the value of each card Be when they have equal value
The equation for the number of 30 days periods until the value of both cards will be equal is 130 - 3x = 110 - 2.5x
Equationlet
Number of 30 days period = x
Gift card 1:
130 - 3x
Gift card 2:
110 - 2.5x
Equate both gift cards130 - 3x = 110 - 2.5x
130 - 110 = -2.5x + 3x
20 = 0.5x
divide both sides by 0.5x = 20/0.5
x = 40
So,
Gift card 1:
130 - 3x
= 130 - 3(40)
= 130 - 120
= $10
Gift card 2:
110 - 2.5x
= 110 - 2.5(40)
= 110 - 100
= $10
Therefore, the value of each card when they have equal value is $10
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A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $79. A season ski pass costs $350. The skier would have to rent skis with either pass for $30per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Answer:
Let s =cost of skiing per day. Here's what we know:
450 + 20s = 64s + 20s (the season pass plus ski rentals equates to daily skiing plus ski rentals)
We have 20s on both sides, so those cancel out easily:
450 = 64s
Divide both sides by 64:
7.03 ≈ s
You can't pay for a partial day, so the skier will have to ski for at least 8 days to make the season pass cheaper than getting daily passes.
Step-by-step explanation:
Hope this helps :D
2. Twelve cans of sparkling water weigh 9 pounds.
a. How much would 4 cans of sparkling water weigh?
Answer:
Step-by-step explanation:
3 pounds
12 divided by 4= 3 pounds
Factor each expression. x²-6 x+8
We will use factorization for the given equation. The factors of the expression x²-6 x+8 are x = 2, x = 4
What is factorization?Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics. For instance, the polynomial x2 - 4 and the number 15 may both be factored using the formula 3 × 5.
Given,
x²-6 x+8
Using factorization,
x² -4x - 2x + 8
⇒ x(x - 4) - 2(x - 4)
⇒ (x-2) (x-4)
⇒ x = 2, x = 4
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25x+5y=15
what would be the answer
Answer:
3-y/3
The slope is -2/5
Step-by-step explanation:
Could someone help me on this please
Answer:
4, 0, 3
Step-by-step explanation:
You want to know which numbers are possible values of m, given a graph of the values of m.
Interpreting a number line graphThe graph shows an empty circle at m=6, and an arrow extending to the left from that point. The empty circle means that m=6 is not a possible value of m.
The arrow extends through possible values of m, and extends to negative infinity. That means m may have any value less than 6. Such values on the offered list are ...
4, 0, 3
__
Additional comment
The values 6, 7, 9 are not covered by the dot or the arrow, so are not possible values of m.
Answer:
0, 3, 4
Step-by-step explanation:
When the circle is open and pointing to the left, it means that the variable is less than the number the circle is at. In this case, it means that the variable is less than 6, so you would select all values that are less than 6!
I hope I helped!
What is the slope of the line on the graph?
Enter your answer in the box
Answer:
Step-by-step explanation: the answer is D. because all of the oher choices don't make sense obviously.
What is solution of the equation -16=x²+8 x ?
After solving, the factor of equation -16 = x²+8x is:
(x+4)What is an equation, exactly?A mathematical statement composed of two representations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We obtain the value for the variable x as x = 7 after solving this equation.So,
Given equation: -16 = x²+8x
Then,
-16 = x²+8xx²+8x+16x²+x( + ) +16x²+x(4+4)+16x²+4x+4x+16x(x+4)+4(x+4)Factors are: (x+4) and (x+4)
Therefore, after solving, the factor of equation -16 = x²+8x is:
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At the end of the summer, I decide to drain the swimming pool. I noticed that it drains
faster when there is more water in the pool. That was interesting to me, so I decided to measure the rate at which it drains. I found that it was draining at a rate of 3% every 5
minutes. How many gallons are left in the pool after 50 minutes? About how many minutes will it take to have less than 1000 gallons in the pool? Justify your answer with a
mathematical model of the problem situation.
An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = eˣ
Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 - r)^t
Where:
P(t ) represents the volume of water in gallons.t represents the time or number of years.I represents the initial volume of water.r represents the decay rate.Substituting the given parameters into the formula, we have;
P(t) = I(1 - r)^t
P(50) = 1500 × (1 - 0.3)^0.2{50}
P(50) = 1500 × (0.97)^10
P(50) = 1,106 gallons.
Therefore, there would be 1,106 gallons of water left in the pool after 50 minutes.
Next, we would determine the amount of time it would take to have less than 1000 gallons in the pool:
P(t) = I(1 - r)^t
1000 = 1500 × (1 - 0.3)^0.2t
1000 = 1500 × (0.97)^0.2t
1000/1500 = (0.97)^0.2t
2/3 = (0.97)^0.2t
Taking the log of both sides, we have:
log0.97(0.2t) = log(2/3)
t = log(2/3)/(0.27log0.97)
Time, t = 66.6 minutes.
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Complete Question:
A pool drains at a rate of 3% every 5 minutes. If it starts with 1500 gallons, how many gallons are left in the pool after 50 minutes? About how many minutes will it take to have less than 1000 gallons in the pool? Justify your answer with a mathematical model of the problem situation.
what does a graph look like if a line passes through the point (3,-4) and has a slope of 1/3?
Answer: The diagonal line would have a negative slope
Step-by-step explanation:
Divide.
−5 5/8÷5
Responses
−118
, , negative 1 and 1 over 8
−58
, , negative 5 over 8
58
5 over 8
118
The simplified value of the expression −5 5/8 ÷ 5 is −1 1/8
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
−5 5/8 ÷ 5
Convert the mixed fractions to improper fractions
So, we have
−5 5/8 ÷ 5 = −45/8 ÷ 5
Express the quotient as a product
So, we have
−5 5/8 ÷ 5 = −45/8 x 1/5
Evaluate the product of the numerators in the above expression
So, we have
−5 5/8 ÷ 5 = −45/8 x 1/5
Evaluate the product of the denominators in the above expression
So, we have
−5 5/8 ÷ 5 = −45/40
Simplify the result
So, we have
−5 5/8 ÷ 5 = −9/8
Express as a mixed number
So, we have
−5 5/8 ÷ 5 = −1 1/8
Hence, the simplified value of the expression −5 5/8 ÷ 5 is −1 1/8
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Put the numbers in order from greatest to least. (photo down below)
Answer: 1 1/2> 5/4> 100%> 7/10> 0.25
Step-by-step explanation:
1 1/2= 1.50
5/4= 1.25
0.25
7/10= 0.70
100%= 1
1.50>1.25>1>0.70>0.25
Fill in the blanks
A=P e rt is known as the ______ formula.
A=P e rt is known as the continual" growth formula.
What is a PE RT formula?
A = PRT, where "A" is the ending amount, "P" is the beginning amount (principal, in the case of money), "r" is the growth or decay rate (represented as a decimal), and "t" is the time (in whatever unit was used on the growth/decay rate), is the equation for "continual" growth (or decay).
What is the purpose of a PE RT?
Often referred to as a PERT diagram, a PERT chart is a project management tool used to plan, schedule, and coordinate tasks within a project. Project managers can deconstruct each individual activity in the project for analysis since it provides a graphical depiction of the project's timeline.Learn more about continual" growth
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What is 23 divided by 2746
The stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008.
What is the best prediction of the population in the year 2013? Round to the nearest whole number.
try do to division, 14÷3800
I'm not sure about the round though
A cooler contains eleven bottles of sports drinks: three lemon-lime flavored, five orange-flavored, and three fruit-punch flavored. You randomly grab a bottle. It is a lemon-lime or a fruit punch..
The probability of grabbing a lemon-limbed or a fruit punch bottle from the cooler is 6/11.
What is 'AND' and 'OR' statements in probability?'AND' represents multiplication and 'OR' represents addition.
The total number of bottles of sports drinks which is also our sample space
N(S) = 11.
The number of lemon-lime flavored bottles [tex]N(L_l)[/tex] = 3.
The Number of fruit punch flavored bottles [tex]N(F_p)[/tex] = 3.
So, the probability of grabbing a lemon-lime bottle [tex]P(L_l)[/tex] = [tex]\frac{N(L_l)}{N(S)}[/tex] = 3/11.
And, the probability of grabbing a fruit punch bottle [tex]P(F_p)[/tex] = [tex]\frac{N(F_p)}{N(S)}[/tex] = 3/11.
∴ The probability of grabbing a lemon-lime or a fruit punch bottle is the sum of the probability [tex]P(L_l) + P(F_p)[/tex].
= 3/11 + 3/11.
= 6/11.
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please help me with this
Answer:
x=30
Step-by-step explanation:
on the left you have a ninety-degree angle.
5(x-12) = 90
5x-60=90
+60 +60
5x=150
/ /
5 5
x=30
The equation y = 2.391x +57.420 models the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving.
What does the y-intercept of the equation represent in context of the situation?
A cereal with 0 grams of sugar has a rating of about 57.
A cereal with 0 grams of sugar has a rating of about 2.391.
The average number of grams of sugar is 57.
The average number of grams of sugar is 2.
D
The y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
where -
m → slope of line
c → y-intercept of line
Given a equation → y = 2.391x + 57.420 that models the taste rating of a cereal 'y' and 'x' represents the number of grams of sugar per serving.
The y-intercept of the equation represents the point at which the graph of the equation cuts the y - axis. Now, the coordinates of the y-intercept is of the form (0, y). Therefore, the x-coordinate will be 0. Now, the equation given is -
y = 2.391x + 57.420
Comparing it with the general equation of line -
y = 2.391x + 57.420
y = mx + c
The y - intercept is c = 57.420
At x = 0, the equation becomes -
y = 2.391 x 0 + 57.420
y = 57.420
Now -
Number of grams of sugar per serving = 0
Taste rating of a cereal = y = 57.420
Therefore, the y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.
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-32x-2 pls help i know i should know this
Answer:
Step-by-step explanation:
64
Answer: -2 (16x + 1)
Step-by-step explanation:
Solve for x .
23≥3x−4 or 32<3x−4
Responses
9 12 or x≤9
Answer:
1. x≤9
2. x>12
Step-by-step explanation:
1. Rewrite so x is on the left side of the inequality.
3x−4≤23
Move all terms not containing x to the right side of the inequality.
3x≤27
Divide each term in 3x≤27 by 3 and simplify.
x≤9
2. Rewrite so x is on the left side of the inequality.
3x-4>32
Move all terms not containing x to the right side of the inequality.
3x>36
Divide each term in 3x>36 by 3 and simplify.
x>12
Given the function, find f(-1) and f(3).
The value of function f(x) at x = - 1 and x = 3, will be -
f(-1) = 3
f(3) = 3
We have a function f(x).
We have to evaluate it at x = -1 and x = 3.
What is a function ?A function in mathematics is a relation between a dependent and independent variables [y and x respectively]. In a function, the dependent variable (y) always depends on independent variable (x) for its value. It is denoted by - y = f(x).
According to the question, we have -
f(x) = [- x + 2 , x ≤ 1] and f(x) = [x² - 4x + 6, x > 1]
Now, for x = -1, f(x) will be -
f(- 1) = - (-1) + 2 = 3
and
for x = 3, f(x) will be -
f(3) = 3² - 4 x 3 + 6 = 3
Hence, the value of function f(x) at x = - 1 and x = 3, will be -
f(-1) = 3
f(3) = 3
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Pls answer next 5 Minutes
The answer to the value gotten without the significant figure doesn't make sense as there's a huge difference.
How to calculate the number?It should be noted that 13822 to 1 significant figures will be 13000.
Also, it should be noted that 623 to 1 significant figure will be 600.
14 to 1 significant figure will be 10.
Therefore, the multiplication will be:
= (13000 × 600) / 10
= 780000
Therefore, the answer to the value gotten without the significant figure doesn't make sense as there's a huge difference since the earlier value was 615079.
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