Answers
Answer:
x^8
Step-by-step explanation:
You want to simplify x^10/x^2.
Rule of exponentsThe applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
ApplicationUsing this rule on the given expression, we find ...
(x^10)/(x^2) = x^(10-2) = x^8
__
Additional comment
An exponent can be considered to be an indicator of repeated multiplication. That is, it tells how many times the base is a factor in the product. Knowing this, you can use the usual rules of division to cancel common factors:
[tex]\dfrac{x^{10}}{x^2}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x}=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x=x^8[/tex]
Related Questions
A construction crew needs to pave a road that is 202 miles long. The crew paves 9 miles of the road each day. The length, L. (in miles), that is left to be paved
after d days is given by the following function.
L(d)=202-9d
Answer the following questions.
(a) How many miles of the road does the crew have left to pave after 12 days?
94 miles
(b) If 139 miles of the road is left to be paved, how many days has the crew been.
paving the road?
days
Answers
Answer:
7 days.
Step-by-step explanation:
139 = 202 - 9d subtract 2002 from both sides of the equation
-63 = -9d Divide both sides of the equation by -9
7 = d
Turtoneom Has a half-life of four years. Suppose a company has 400 mg of tortoni him. How much will be left after 20 years?
Answers
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &400\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &4 \end{cases} \\\\\\ A=400\left( \frac{1}{2} \right)^{\frac{20}{4}}\implies A=400\left( \frac{1}{2} \right)^5\implies A=12.5[/tex]
Before art class starts, Gordon makes sure that each table has a full bowl of paint. He has 1/2 of gallon of paint and it able to fill the bowls for all 7 tables. How many gallons of paint does each table have?
Answers
Based on the fact that Gordon has 1/2 gallons of paint and is able to fill up bowls in 7 tables, the number of gallons of paint each table has is 1/14 gallons of paint
How to find the number of gallons?Gordon has 1/2 gallons of paint and knows that this amount of paint can given each bowl in all 7 tables, a full bowl of paint.
The amount of paint that each bowl gets can therefore be calculated by the formula:
= Gallons of paint Gordon has / Number of tables
Solving for the paint each bowl has gives:
= 1/2 ÷ 7
= 1/2 x 1/7
= 1/14 gallons of paint
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Using the side lengths
Answers
Given
The three sides are given 24, 30 and 18.
Explanation
To find the triangle is acute, obtuse or right triangle.
To determine whether the triangle is acute, right, or obtuse.add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute.
A
If the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.
Now c.
[tex]\begin{gathered} 30^2=24^2+18^2 \\ 900=576+324 \\ 900=900 \end{gathered}[/tex]Answer
Hence the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.
The correct option is A.
Determine whether the function is bounded above, bounded below, or bounded on its domain.
y = 2
Answers
D. The function is neither above nor below its bounds.
What do "bounded" and "unbounded" functions mean?An unbounded function is one that is not bounded. The function is referred to as being bounded (from) above by A if it has real values and f(x) A for all x in X. The function is referred to as being bounded by B (from below) if f(x) B for all x in X
How do you know whether a sequence is bounded or not?A sequence is considered to be constrained if it has bounds above and below. Unbounded sequences exist when a sequence is not bounded. Because 1/n1 for all positive integers n, for instance, the sequence 1/n is confined above. Further, it
If there is an integer 2 such that for all x from the domain D(f), one has f (x) 2, we say that a real function f is bounded from below. If there is a number K such that for every x from the domain D(f), one has f (x) 2, then we say that a real function f is bounded from above.
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Darla wants to buy 3 identical gift cards. She wants to make sure her total
cost is no more than $3 above or below $75. Which of the following
inequalities represents this situation?
A. 13c-75 ≤3
B. 175+3c| ≤ 3
C. 13c-21 ≤60
D. 13c+21 ≤60
Answers
The inequality that represents this situation is Option(A.) 3c - 75 ≤ 3.
What are Inequalities?Inequality is created when two or more algebraic expressions are compared using the symbols >, <, ≥, or ≤. They represent mathematical expressions when neither side is equal. The majority of the time, size comparisons between two numbers on the number line are made using inequalities.Given:
Darla wants to buy 3 identical gift cards.
The total cost is no more than $3 above or below $75.
Let's assume that the cost of one gift card is $c.
Total Cost of 3 gift cards = $3c
Also, the total cost is no more than $3 above or below $75.
Hence, it would be -75 and less than 3.
Therefore, the inequality is 3c - 75 ≤ 3.
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what does 2056x18394= / anyone up to ta lk
Answers
The product of the multiplication of (2056 * 18394) is 37818064.
As per the question statement, we are provided with the multiplicative statement of two numbers, 2056 and 18394.
We are required to perform the above mentioned multiplication and determine the product in the simplified form a number.
To solve this question, we simply need to multiply 2056 and 18394, and mention the upcoming product as our required answer, i.e.,
(2056 * 18394) = 37818064.
Hence, The product of the multiplication of (2056 * 18394) is 37818064.
Multiplication: In Mathematics, Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division which means the repeated addition of groups of equal sizes. Product: In mathematics, a product is the result of a multiplication, or an expression that identifies two or more factors or numbers of decimals to be multiplied.To learn more about Multiplication & Products, click on the link below.
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Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the time it takes to run a mile. Is the random variable x discrete or continuous?
Answers
The variable represents time. The time in which a person runs a mile will depend on the speed of that person, and that can take almost any value, thus, here the variable is continuous.
Is the variable discrete or continuous?First, when a variable is discrete and when it is continuous?
A variable is discrete if it only can take some selected values on a given interval, while a variable is continuous if it can take any value (or at least a dense set) of values in that interval.
For example, the numbers that one can roll on a dice form a discrete set, because the values can only be {1, 2, 3, 4, 5, 6}, just to given an example.
Now, in this case, the variable represents time. Time almost always is a continuous variable, in this case, the time is the time in which a person runs a mile. So that variable can take almost any value (depends on the speed of the person).
So we conclude that this is a continuous variable.
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A player tosses a fair coin n times. Each time, if the coin lands on Head, the player
win a dollar, otherwise, the player loses a dollar. What is the expected earning of the
player? What is the variance of the earning of the player? Now the player apply a
new strategy: the player will play the game until he gets a head. What is the expected
earning of the new strategy? Does the result depend on n?
Answers
what transformations take f(x) = 3x+1 to g(x) = −3x−5 ?
Answers
The transformation that took f(x) = 3x+1 to g(x) = −3x−5 is reflection and translation 4 units downwards
How to find the transformationsgiven data
f(x) = 3x+1
g(x) = −3x−5
Reflection
Reflections changes the sign of the both coordinates
from to
f(x) = 3x + 1 f'(x) = -3x - 1
Translation
Translation downwards leads to subtraction with the required units in the y coordinates. In this case 4 units
from to
f'(x) = -3x - 1 f''(x) = -3x - 5
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Answer:
Either of ...
reflection across the y-axis, and translation down 6reflection across the x-axis and translation down 4Step-by-step explanation:
You want the transformations that take f(x) = 3x+1 to g(x) = -3x-5.
TransformationThe x-term of the transformed function has a sign opposite that of the original function. That can be accomplished by either of (a) reflection across the y-axis (replaces x by -x), or by (b) reflection across the x-axis (replaces f(x) by -f(x)).
Either way, an additional translation is required. That translation can be either vertical or horizontal, and may be done either before or after the reflection.
Horizontal reflectionReflecting f(x) across the y-axis means it becomes ...
f(-x) = 3(-x) +1 = -3x +1
In order to make that into -3x-5, we must add -6 to the function value:
g(x) = f(-x) -6 = (3(-x)+1) -6 = -3x -5
F(x) will be taken to g(x) = -3x-5 by reflection across the y-axis and translation down 6 units.
Vertical reflectionReflecting f(x) across the x-axis means it becomes ...
-f(x) = -(3x +1) = -3x -1
In order to make that into -3x-5, we must add -4 to the function value:
g(x) = -f(x) -4 = -(3x +1) -4 = -3x -5
F(x) will be taken to g(x) = -3x-5 by reflection across the x-axis and translation down 4 units.
__
Additional comment
As noted above, the translation can be either horizontal or vertical. For example, translating the function 2 units to the right makes it f(x-2). Then reflection across the y-axis replaces x by -x, so we have ...
g(x) = f(-x-2) = 3(-x-2)+1 = -3x -6 +1 = -3x -5
To get g(x), we could translate right 2 units, then reflect across the y-axis.
We also note that point (-1, -2) is shared by f(x) and g(x), so reflection horizontally across the line x=-1, or vertically across the line y=-2 would also give the required transformation.
Which of the following is true?
C
70°
1/2
B
D
130°
A. m<BCD - m<DBC = 10°
B. m<BCD - m<DBC = 20°
C. m<BCD - m<DBC = 60°. D. m<BCD m<DBC = 80°
Answers
The correct answer is [a] m<BCD - m<DBC =10°
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
What is an angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves.
Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius. The arc is centered at the vertex and defined by the sides in the case of a geometric angle. When there is a rotation, the arc is defined by any other point and the rotation's image, and it is centered at the rotation's center.
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what is the equation for finding the volume of a rectangular solid ?
Answers
Answer: Width x length x height = volume
i think
Step-by-step explanation:
the ______ is a point at which three or more lines intersect OPTIONS;A.median B.angleC.point of concurrencyD.perpendicular bisector
Answers
ANSWER:
C. point of concurrency
STEP-BY-STEP EXPLANATION:
The only point where these lines cross each other is called the point of concurrency.
Therefore:
The point of concurrency is a point at which three or more lines intersect.
The correct answer then is C. point of concurrency
Stacia needs 39 bulbs for every 3 chandeliers she makes.
Complete the table using equivalent ratios.
Answers
13 diamonds, y = 3 chandeliers, x = 52 diamonds, x = 130 diamonds, y = 40 chandeliers. this is the complete table using equivalent ratios.
What is equivalent ratio?When we compare any two kinds of ratios, they are said to be equivalent. To determine whether these two or more ratios are equivalent, they can also be compared to one another. For instance, the ratios 1:2 and 2:4 can be called as equivalent.
Describe ratioSimply put, a ratio is a comparison of two numbers. When a ratio is equal, the proportionate relationship remains constant. By multiplying the first value by the same ratio, or unit of proportion, you can determine your own equivalent ratios.
Which ratio is equivalent?It is possible to treat an equivalent ratio and a proportion interchangeably. An equivalent ratio is the result of simplifying the two ratios to the same fraction.
Let us take the value of x -----> the number of diamonds
Let us take the value of y ----> the number of chandeliers
we know that
The ratio present between the number of diamonds to that of the number of chandeliers is equal to
[tex]\frac{x}{y} = \frac{39}{3}[/tex]
1) for y = 1,
x = 13 diamonds
2) for x = 39
y = 3 chandeliers
3) for y = 4
x = 52 diamonds
4) y = 10
x = 130 diamonds
5) x = 520
y = 40 chandeliers
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Answer: 52 and 130
Step-by-step explanation:
what's the result of adding these two polynomials: (2x+y+1) + (2x⁶-y+1)? I'm doing a test and the correct answer says is 4x⁶-2y+1 but I'm not very sure it is the correct one. Can someone help me? :3
Answers
Answer
[tex]\begin{equation*} 2x^6+2x+2 \end{equation*}[/tex]Step-by-step explanation
Given the polynomials:
[tex]\begin{gathered} 2x+y+1 \\ \text{ and} \\ 2x^6-y+1 \end{gathered}[/tex]To add them we need to add the similar terms (terms with the same variable and degree), as follows:
[tex]\begin{gathered} (2x+y+1)+(2x^6-y+1)= \\ =2x^6+2x+(y-y)+(1+1)= \\ =2x^6+2x+2 \end{gathered}[/tex]How do I determaine the best answer for this?
Answers
The function 1 is,
[tex]y=\frac{1}{3}x[/tex]So rate of function is 1/3.
From the table function 2 it can be observed that the value of y is one third of x. The mathematical expression of function 2 is,
[tex]y=\frac{1}{3}x[/tex]So rate of function 2 is also 1/3.
Thus function 1 and function 2 have the same rate, 1/3.
I need help with this problem
Answers
We have,
[tex]\begin{gathered} e^{\ln x}=x \\ \log _ex=\ln x \end{gathered}[/tex]The given expression is,
[tex]\ln 5x=4[/tex]This can be written as,
[tex]\begin{gathered} \ln 5x=4 \\ \log _e5x=4 \\ e^4=5x \end{gathered}[/tex]pls help me with math i’ll give you brainlist
Answers
Answer:
8
Step-by-step explanation:
8+8=16 see i helped u GIVE ME BRAINLIST NOW PLSS I BEG :.)
Please pls pls j beg
Answers
Answer:
Y/n had nothing in his hand. His friend gave him 8 oranges for him to eat. But on his way home he saw a hungry child and decided to give away 4 oranges to the child. How many oranges does he have now?
2.сBOP-6-5-4-3-2-10В'Por boloAlA. (x.A. (x,y)+(-x,y+6)B. (x,y) → (x + 6,-y)(x,y) - (x - 12. y+6)D. (x,y)-(-x+6,-y)B.
Answers
SOLUTION
For the image point A has the coordinates (-3, 6) and A' is (3, -6) so with a translation of
[tex](x,\text{ y )}\rightarrow\text{ (}x+6,\text{ -y )}[/tex]We see A(-3, 6) as
[tex]A(-3,6)\rightarrow(-3+6,-6)\rightarrow A^{\prime}(3,-6)[/tex]And B(-2, 2) as
[tex]B(-2,2)\rightarrow(-2+6,-2)\rightarrow B^{\prime}(4,-2)[/tex]Therefore the correct translation is
[tex](x,\text{ y )}\rightarrow\text{ (}x+6,\text{ -y )}[/tex]Option B is the correct answer.
Written as a simplified polynomial in standard form, what is the result when (x+7)^2 is subtracted from7
Answers
7-(x^2+14x+49)
7-x^2-14x-49
-x^2-14x-42
What is f(g(13))?
A mapping diagram is shown.
Answers
Answer:
(c) 32
Step-by-step explanation:
Given a map between x, g(x), and f(g(x)), you want to find f(g(13)).
Using a mapYou want the function value that results when 13 is the argument of g(x), and g(x) is the argument of f(x).
Locate the input (13) in the left column of the diagram. Follow the arrow to find g(13) = 16. Follow the arrow again to find f(16) = 32.
f(g(13)) = 32
Solve the equation. e – 36 = 133 A. e=97 B. e=107 C. e= 169 D. e=179
Answers
Answer:
d
Step-by-step explanation:
2. The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much
does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.
6RI2
Answers
Answer:
$3.33 (rounded) per hour
Step-by-step explanation:
The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.
hours run per month = daily hours × days in month
hours run per month = 5 × 30
hours run per month = 150
if the total bill was $500 for 150 hours then:
$500 ÷ 150 = $3.33 (rounded) per hour.
A square has an area of 25cm squared. What is the length of each side?
(b) A square has a perimeter of 28cm. What is the length of each side?
Answers
Step-by-step explanation:
the length of each side will be 5 because the area of a square is L×Lwhich can also be said as 5×5=25
2. perimeter is addition of all sides which is solved as L+L+L+L= 28cm
also: 7+7+7+7= 28cm
The function f(x) = 1(3)x models the number of virus cells present in a sample after x minutes. About how many cells will be present after 1 1/2 minutes? (round to the nearest whole number)
Answers
Answer:
The number of cells that will be present is;
[tex]5\text{ cells}[/tex]Explanation:
Given that the function f(x) models the number of virus cells present in a sample after x minutes.
[tex]f(x)=1(3)^x[/tex]Aftere 1 1/2 minutes, the number of cells present can be calculated by substituting;
[tex]x=1\frac{1}{2}[/tex]In the model.
Substituting, we have;
[tex]\begin{gathered} f(x)=1(3)^x \\ f(1\frac{1}{2})=1(3)^{1\frac{1}{2}} \\ f(1\frac{1}{2})=1(3)^{1.5} \\ f(1\frac{1}{2})=5.196 \\ f(1\frac{1}{2})\approx5 \end{gathered}[/tex]Therefore, the number of cells that will be present is;
[tex]5\text{ cells}[/tex]In the figure below, line LN is tangent to circle O.
Which of the following can be concluded from the information?
A) ON is a radius of the circle.
B) angle MNO is a right triangle.
C) angle ONM is an obtuse angle.
D) angle OMN is a central angle of circle O.
Answers
The right information of the circle is as follows:
Triangle MNO is a right triangle.How to find the correct information of the circle?The line LN is the tangent to the circle O.
Tangent to a circle is a line that touches the circle at one point.
The point where tangent meets the circle is called point of tangency.
The tangent is perpendicular to the radius of the circle, with which it intersects.
Tangent to a circle is always perpendicular to the radius.
Therefore, the correct information from the circle can be found as follows:
Line ON is not the radius of the circle. The radius of a circle is a straight line from the centre of a circle to the circumference of a circle.The triangle MNO is a right triangle is the right information of the circle.Angle ONM is not an obtuse angle because it's less than 90 degrees. The angle OMN is 90 degrees. Therefore, the sum of the angles ONM and MON is equals to 90 degrees.OMN is not the central angle of the circle. The central angle of the circle is angle MON.learn more on tangent to circle here:https://brainly.com/question/4331689
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Answer: A) ON is a radius of the circle
Step-by-step explanation:
The line ON starts from the midpoint of the circle showing that it is half of the distance(radius)
Noah invested $2500 in an account paying 3% simple interest. What was the total
amount in his account after 5 years?
Answers
Answer:
$2,875
Step-by-step explanation:
Interest = Principal x rate x time
Interest = $2500 x 0.03 x 5
Interest = $375
Original value + interest = Total amount
$2,500 + $375 = $2,875
Write the scale factor
Answers
Let:
[tex]\begin{gathered} FO\cdot k=QK \\ \end{gathered}[/tex]Where:
k = scale factor
so:
[tex]\begin{gathered} 18k=24 \\ k=\frac{24}{18} \\ k=\frac{4}{3} \end{gathered}[/tex]now, we can find y and x:
[tex]\begin{gathered} \frac{4}{3}\cdot x=28 \\ x=\frac{28\cdot3}{4} \\ x=21 \end{gathered}[/tex][tex]\begin{gathered} 15\cdot\frac{4}{3}=y \\ 20=y \end{gathered}[/tex]Micaela is working two summer jobs, making $13 per hour tutoring and making $10
per hour landscaping. In a given week, she can work at most 13 total hours and must
earn a minimum of $140. If a represents the number of hours tutoring and y
represents the number of hours landscaping, write and solve a system of inequalities
graphically and determine one possible solution.
Answers
The equations will be a+ y ≤ 13, since Micaela can't work more than 13 hours and also she needs to earn at least $140 each week, so other equation will be 13a + 10y ≥ 140.
What is inequalities?Inequality, a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
a = number of hours spent tutoring
y = number of hours spent landscaping
Micaela can't work more than 13 hours, so a + y ≤ 13.
Also, she needs to earn at least $140 each week, so 13a + 10y ≥ 140.
Using intercepts, you may graph things in this format on paper. They must be transformed into slope-intercept form in order to be graphed on a standard graphing calculator.
For instance, if a = 12 and y = 2, then a + y = 13 hours, and 12(13) + 2(10) = $176. Micaela puts in her maximum number of hours and earns more than she should.
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