The simplified monomial for the first scenario will be 1/8². The simplified monomial for the second situation will be (-3)¹.
What is exponent?Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6*6*6*6. You can write this as 6^4. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6. A number or letter written above and to the right of a mathematical expression known as the base is termed an exponent. It denotes that the base is to be increased in strength. The base is x, while the exponent or power is n.
Here,
The law of exponents say that,
aⁿ/aˣ=aⁿ⁻ˣ
1. 8/8³
=8¹-³
=8⁻²
=1/8²
2. (-3)⁴/(-3)³
=(-3)⁴⁻³
=-3¹
For first case, the monomial resulted after simplifying will be 1/8². For second case, the monomial resulted after simplifying will be (-3)¹.
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CEDAR
1
SOULANICTA
ARANTEN
In the figure below, mZ1 = (x-6)° and m/2=5x°.
Find the angle measures.
2
Answer:
∠ 1 = 25° , ∠ 2 = 155°
Step-by-step explanation:
∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is
x - 6 + 5x = 180
6x - 6 = 180 ( add 6 to both sides )
6x = 186 ( divide both sides by 6 )
x = 31
Then
∠ 1 = x - 6 = 31 - 6 = 25°
∠ 2 = 5x = 5 × 31 = 155°
denise rode 3 kilometers on a bike.clark rode 5000 meters on a bike. how many more meters did clark ride than denise
In linear equation, Clark rode 2 kilometres more than Denise .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations whose variables have a power of one are called linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Denise rode 3 kilometres .
Clark rode 5000 metres which is 5 kilometres .
So , Clark rode 2 kilometres more than Denise .
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mrs jones gave 1/5 of a cake to her neighbour. she then sliced the remainder into 3 pieces for her 3 children, ken, ron and david, in the ratio 1 : 3 : 4. what is the fraction of the cake was ron's pieces
The fraction of the cake that was ron's pieces is 1/5.
What is the fraction of the cake was ron's pieces?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:
= 1 - 1/5
= 4/5
The fraction of the cake that was ron's pieces will be:
= 2/(1+3+4) × 4/5
= 2/8 × 4/5
= 8/40
= 1/5
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(*6./Sean drives from Manchester to Gretna Green.
He drives at an average speed of 50 mph for the first 3 hours of his journey.
He then has 150 miles to drive to get to Gretna Green.
Sean drives these 150 miles at an average speed of 30 mph.
Sean says,
"My average speed from Manchester to Gretna Green was 40 mph."
Is Sean right?
You must show how you get your answer.
Sean's real average speed was less than his predicted 40 mph.
What is average speed?Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time.
Student must calculate average speed, compare it to Sean's response, and determine total distance traveled and time expended. First, the formula must be stated: Average speed = Total distance traveled / Time required.We can rearrange this to determine the distance traveled.Total mileage equals time divided by average speed.We only need to compute the first leg of his travel as we already know the total distance was 150 miles. As a result, we can calculate 150 miles at 50 mph for 3 hours.We now know that the overall distance from Manchester to Greta Green was 300 miles after including the second half of the voyage.Now we have to think about how long it took overall. Rearranging the equation yields the necessary result: Time taken=distance/speed. This brings us back to the comparatively easy formula of 150 miles at 30 miles per hour equals 5 hours. This indicates that the total travel time from Manchester to Gretna Green was 8 hours, not including the initial 3 hours. We now possess all the knowledge required to calculate his average speed over the entire journey. The original equation is still used: Average speed = Total distance traveled / Time taken. After entering all the data, we get the result 300 miles in 8 hours = 37.5 miles per hour.Hence, Sean's real average speed was less than his predicted 40 mph.
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Do you think that practicing
mathematics will bring Peace
and Harmony in your life?.
Explain your thinking.
Practicing mathematics will bring Peace and Harmony in your life It provides us with a method for comprehending patterns, quantifying relationships, and making future predictions.
What do you mean by Peace?In the absence of animosity and violence, peace is the idea of communal friendship and harmony.
Critical thinking about our surroundings is referred to as analytical thinking. Our capacity for reasoning is what allows us to approach problems logically. The ability to think critically and rationally is crucial since it aids in issue solving and solution seeking.
Understanding the world through mathematics also helps us develop mental discipline. Math fosters logical reasoning, critical analysis, inventiveness, abstract or spatial thinking, problem-solving aptitude, and even good communication abilities.
Therefore, It gives us a way of understanding patterns, measuring relationships, and forecasting the future.
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swhat happens to the diagonal of a rectangle when the rectangle is reflected across a line of symmetry? what does this suggest about the diagonals of rectangles?
When reflected across a line of symmetry, a shape having that line of symmetry will fall on itself. These are the actual claims:
(1) The rectangle's diagonals will line up exactly with one another.
(2) A rectangle's diagonals are symmetry lines.
We deduce from the question that the rectangle is mirrored across the symmetry line.
When done, the rectangle's half will fall directly on the other half.
This indicates that the rectangle's diagonal will line up perfectly with the opposite diagonal.
According to the aforementioned claim, a rectangle's diagonal is also its line of symmetry.
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classify the series -1+2+(-4)+8+...as arithmetic or geometric. Then, determine whether the series is convergent or divergent.
Answer:
The series -1+2+(-4)+8+... is an arithmetic series because it has a common difference between consecutive terms. Specifically, the common difference is -4 - 2 = -6.
To determine whether the series is convergent or divergent, we need to find its sum. The sum of an arithmetic series is given by the formula:
sum = (n/2)(a1 + an)
where n is the number of terms in the series, a1 is the first term, and an is the nth term.
Since the series is infinite, we cannot determine its sum using this formula. However, we can determine its sum by taking the limit as n approaches infinity. Using the formula above, we find that the sum is equal to:
sum = (infinity/2)(-1 + infinity)
Since the series contains an infinite number of negative terms, it is divergent.
An investor invested a total of $1,800 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $76, how much was
invested in each mutual fund?
The amount invested in the mutual fund that earned 6% was $
a) Using a system of equations, the amount invested in the mutual fund that earned 6% was $1,600.
b) The amount invested in the mutual fund that earned 4% was $200.
What is a system of equations?A system of equations is two or more equations solved concurrently.
A system of equations is also called simultaneous equations.
Total investment = $1,800
Profit from investment A = 6%
Profit from investment B = 4%
The total investment profit = $76
Let A = Investment A and B = Investment B
A + B = 1,800
A = 1,800 - B
0.06A + 0.04B = 76
0.06(1,800 - B) + 0.04B = 76
108 - 0.06B + 0.04B = 76
108 - 0.02B = 76
-0.02B = -32
B = 1,600
A = 200 (1,800 - 1,600)
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in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks? if necessary, round your answer to the nearest tenth.
The weight of all of the rocks to the nearest tenth is 6.085 pounds .
Given :
in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks if necessary, round your answer to the nearest tenth.
Let x be the total weight or all the weight of rocks .
3 = 49.3 % * x
3 = 49.3 * 1 / 100 * x
3 * 100 = 49.3 * x
300 = 49.3 * x
divide with 49.3 on both sides
300 / 49.3 = 1 * x
x = 300 / 49.3
= 6.085 pounds
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Find h(−5) when h(x) = −3|x − 1| + 4. Show every step.
The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.
How to solve function?
Algebraically evaluate and resolve functions.Analyze functions using data from a table or a graph.The supplied value should be used as the input variable in the formula.Determine the outcome.h(x) = −3|x − 1| + 4
Substitute x = -5
h(-5) = −3|(-5) − 1| + 4
= -3|-6| + 4
= -18 + 4
= -14
h(-5) = -14
Hence, The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.
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Solve the system algebraically.
2x-y=-5
y=1-3x
Answer:
The answer is x= -2/3
Step-by-step explanation:
If m is the centroid of triangle abc, am = 44, ce =54, and dm = 23, find each missing measure. fm=?
If m is the centroid of triangle abc, am = 44, ce =54, and dm = 23, then each missing measure fm=88 and ce=44.
What is the centroid ?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.
How do you find the centroid of a triangle with 3 points?Step 1: Identify each vertex's coordinates.
Step 2: Add together and divide by three all the x values from the coordinates of the three vertices.
Step 3: Add together all the y values from the three vertices and divide the result by three.
Step 4: The centroid coordinate is determined from the values collected in stages 2 and 3.
the ratio of both segments is 2:1.
where;
am = 44 and dm = 23
the longer segment is double of shorter one:
2*23 = 46.
Therefore,
fm = 46-23
= <<23=23>>23
now finding ce:
= 2*44
= 88, so
ce measures
= 88-44
=44.
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Please answer both parts
the area will be fall in between 100≤ 20x ≤1000.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,A quadrilateral should be closed shape with 4 sides
All the internal angles of a quadrilateral sum up to 360°.
The area of a rectangle is A = a*b
Here in the figure the length is given 4x and the breadth is 5.
The area is given in between 100≤A≤1000
So this area will be A = 5x*4 = 20x
Now the area will be lie in between 100≤ 20x ≤1000
hence, the area will be fall in between 100≤ 20x ≤1000.
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Boy : girl
11 : 9
there are 124 more boy than girl
how many pupil are in the chool?
There are 1240 students in the school.
What is Proportionalities (Ratios)?
It is possible to represent absolute connections using ratios or proportions, independent of the variables' actual raw values. For instance, if your business always produces widgets packaged in bundles of 20 widgets each, you will always have a 20 widgets to 1 bundle ratio regardless of how many bundles you produce. Accordingly, if you produce 100 bundles per day, you will have produced 2000 widgets in a single day. The proportion of widgets to bundles is constant and does not change. As long as the other ratio factor quantity is known or can be known, the ratio or proportion can then be used as a conversion factor to calculate the number of an unknown quantity of one ratio factor.
In our problem, we know that there are 11 boys : 9 girls in the school. We also know that there are 124 more boys than girls.
If we let x equal the number of girls in the school, the number of boys will then be x+124. We know the ratio of boys to girls and produce a conversion factor to determine the number of girls present in the school:
( number of boys)[tex]$\left(\frac{\text { girls }}{\text { boys }}\right)=$[/tex] number of girls
[tex](x+124)\left(\frac{9}{11}\right)=x[/tex]
Note that since we are looking to find the number of girls, it appears in the numerator of the conversion factor and boys in the denominator. If we were looking for the number of boys, we would flip the conversion factor to have the number of boys in the numerator and girls in the denominator.
Now let's simplify the equation and solve for x :
[tex]\begin{aligned}(x+124)\left(\frac{9}{11}\right) & =x \\\frac{9 x+1116}{11} & =x \\9 x+1116 & =11 x \\1116 & =11 x-9 x \\1116 & =2 x \\\frac{1116}{2} & =x=558\end{aligned}[/tex]
If we have 558 girls, the number of boys is then:
x+124=558+124=682boys
Adding the number of boys and girls together, we will have the total number of students in the school: 558+682=1240 students
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question 3 in the analyze stage of the data life cycle, what might a data analyst do? select all that apply.
In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle
The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems
The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system
Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
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Solve for X, the figure is a trapezoid. I will give brainiest!!
Answer:
6
Step-by-step explanation:
RS and QT are parallel because it is a trapezoid. This means that the transversal applies. Look at the picture attached to understand what I mean.
So, we know that 18x - 13 = 180(degree of a line)-85. Then, solve the equation.
18x-13=95
18x=108
x=6
please help me with this math problem
Answer:
a - April
b - may
c - they neither made nor lost money that month
hope that helps :)
Step-by-step explanation:
Answer: a) - March
b) - May
c)- it neither made nor lost money that month
Step-by-step explanation:
a) - because -386 is the least out of all of them
b) - because 271 was the most out of all of them
c) - it didn't lose or make it just stayed the same as it was
Russel wants to buy 3 identical gift cards. He wants to make sure the total cost is no more than $2 above or below $60. Which of the following inequalities represents the situation?
Let the cost of each gift card be x.
Three of them will cost 3x.
We need the total cost be no more than $2 above or below $60.
This can be represented as:
3x ≤ 60 + 2 ⇒ 3x ≤ 62,and
3x ≥ 60 - 2⇒ 3x ≥ 58,or as combined inequality:
58 ≤ 3x ≤ 62Solve for n
8n+7=-4n+19
Answer: n= 1
Step-by-step explanation:
8n+7=-4n+19
First, subtract 7 from both sides
8n = 4n +12
Then add 4n from both sides
12n = 12
Then divide by 12 from both sides
n= 1
If you can please give me a Brainliest, thank you!
Answer: n = 1
Step-by-step explanation:
First, you could start off by bringing the -4n to the left side:
8n + 7 = -4n+19 → 12n + 7 = 19
Next, you take the 7 on the left side of the equals sign and subtract it from the 19:
12n + 7 = 19 → 12n = 12
Finally, you divide the 12 on the right by the 12 on the left:
12n = 12 → n = 12/12
A number over itself will always be 1, so n = 1.
please help begging on knees rn.
10. if mB is two more than three times the measure of ZC, and ZB and Care
complementary angles, find each angle measure.
Step-by-step explanation:
First, you should translate everything into math. So,
"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)
"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)
Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:
(3C + 2) + C = 90
4C + 2 = 90
4C = 88
C = 22
Plugging C = 22 back into either equation (1) or (2) gives us
B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)
Thus, ∠B = 68º; ∠C = 22º
hope this helps
Let f(x) be a continuous function such that f(1) = 3 and f '(x) = [tex]\sqrt{x^3+4}[/tex]. What is the value of f(5)?
If f(x) = 3x² - x, find f{-3, 0, 3}
Step-by-step explanation:
so pretty much replace -3, 0 and 3 into the equation
-3 to the power of 2 is 9 and 9(3) is 27. 27-(-3) is 27+3, 30
0 squared is 0 so the 2nd one would be 0
3 squared times 3 is 27 and subtracted by 3 is 24.
Online entertainment streaming services have gained in popularity in recent years as an alternative to traditional television. One such company has seen steady growth in each period of 3 months, called a quarter, over the past 4 years. The scatterplot shows the relationship between the number of quarters passed since January 2014 and the number of members to the streaming service. A least-squares equation that summarizes this relationship is
Based on the residual plot, is a linear model appropriate for summarizing this relationship?
A linear model is appropriate because the value of r is close to 1.
A linear model is appropriate because the residual plot is curved.
A linear model is not appropriate because the residual plot shows a clear pattern.
A linear model is not appropriate because the scatterplot relating time and subscribers shows a clear pattern.
PLS HURRY
Based on the residual plot, is a linear model is not appropriate for summarizing this relationship. Therefore, the correct answer option is: C. A linear model is not appropriate because the residual plot shows a clear pattern.
What is a residual plot?In Mathematics, a residual plot is sometimes referred to as scatter plot and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association or correlation (relationship) between the data set.
Mathematically, a linear model can be represented by this mathematical expression; y = mx + b.
Where:
m represents the slope.x and y are the points.c represents the y-intercept.By critically observing the residual plot (scatter plot) which shows a relationship between the residuals and quarters since January 2011, we can reasonably infer and logically deduce that a linear model is not appropriate because there is a clear pattern between the data points.
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Need this question answer quickly
By applying the exterior angle of a triangle theorem, m<WUV = 19°
What is an exterior angle of a triangle?
The angle created by one side of a triangle and the subsequently extended side is known as the external angle of a triangle. A triangle has three exterior angles, and the sum of those three external angles is always 360 degrees.
Here, we have
The given parameters are;
ΔUVW with side UW extended to X
m∠UVW = (x + 19)°
m∠VWX = (5x +14)°
m∠WUV = (x + 13)°
Applying the exterior angle of a triangle theorem:
m∠WUV + m∠UVW = m∠VWX
(x + 13)° + (x + 19)° = (5x +14)°
2x + 32 = 5x + 14
32 - 14 = 5x - 2x
18 = 3x
x = 6°
Now, we put the value of x in m∠WUV = (x + 13)° and we get
m∠WUV = (6+13)°
m∠WUV = 19°
Hence, by applying the exterior angle of a triangle theorem, m<WUV = 19°
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Chad is decorating a rectangular ballroom ceiling with decorative lights. Beginning in a corner, Chad strings the lights along the length of the ceiling, a distance of 55 feet. Next, Chad strings the lights along the width of the ceiling, a distance of 48 feet. Then Chad strings the lights straight back to the original corner. At this point, how many feet of lights has Chad used? If necessary, round your answer to the nearest tenth. feet
The number of feet of light used by Chad is 176 feet
How to determine the number of feet of light?From the question, we have the following parameters that can be used in our computation:
Length = 55 feet
Width = 48 feet
We start by calculating the distance from the end of the width till the beginning of the length
This is represented by the following Pythagoras theorem
Distance = √(Length² + Width²)
So, we have
Distance = √(55² + 48²)
Evaluate
Distance = 73
The number of feet is then calculated as
Feet = Length + width + distance
So, we have
Feet = 55 + 48 + 73
Evaluate
Feet = 176
Hence, the total distance is 176 feet
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Rewrite the equation in logarithmic form.
9^5 = 59,049
Answer:
[tex]log_{9} 59,049=5[/tex]
Step-by-step explanation:
The equation in logarithmic form is ㏒₉59,049 = 5
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given is an equation, 9⁵ = 59,049, we need to convert it into logarithmic form.
So,
y = aˣ, then x = ㏒ₐY
Applying the same,
9⁵ = 59,049
㏒₉59,049 = 5
Hence, the equation in logarithmic form is ㏒₉59,049 = 5
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how do i solve (4x-5)/(3x+5)>=3?
Answer:
x = -4
Step-by-step explanation:
(4x-5)/(3x+5) = 3
1. Multiply both sides by 3x+5
4x-5 = 3(3x+5)
2. Expand
4x-5 = 9x+15
3. -4x from both sides
-5 = 5x+15
4. -15 from both sides
-20 = 5x
x = -4
It is greater than 3
x = 4
We can solve the equation as
(4x-5) = (3x+5)*3
4x-5=9x+15
x = 4
A stock is priced at $85 per share and pays a quarterly dividend of $2. 10 per share. What is the dividend yield per stock share per year?
The dividend yield per stock share per year is 9.88 %
What Is the Dividend Yield?
The dividend yield, expressed as a percentage, is a financial ratio (dividend/price) that shows how much a company pays out in dividends each year relative to its stock price.
Given,
The stock price per share is = $85
Quarterly dividend is = $2.10
Now, for to find Dividend yield
Dividend Yield = Annual Dividends Per Share / Price per share
Annual Dividends Per Share = 4 * $2. 10
= $8.4
Price per share = $85
Now, plug in the values
Dividend Yield = 8.4 / 85
= 0.0988
Now, in percentage is
Dividend Yield = 0.0988 * 100
= 9.88 %
Hence, the dividend yield per stock share per year is 9.88 %
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can somebody please help
Step-by-step explanation:
The diagram is very helpful, so really go off of that. Coordinates are written in the form (x,y). If you look at the signs (either there's a negative sign, - , or no sign at all, meaning it's +) for each number in a coordinate pair, you can see where each coordinate should go.
If you look at the last example (3, -3), the first digit is positive + and the second digit is negative - . When you look at the diagram, coordinates in the form of (+, -) are put in quadrant 4.
a square has two diagonals, and a convex pentagon has five diagonals. how many diagonals does a convex decagon have?
35 is diagonals does a convex decagon have .
What does a pentagon basic definition entail?
A geometric figure with five sides and five angles is called a pentagon. Here, "Penta" stands for five, while "gon" is an angle.
One of the different kinds of polygons is the pentagon. For a standard pentagon, the total internal angles come to 540 degrees.
There are a total of ¹⁰C₂ ways to connect two different vertices. But connecting neighbouring vertices doesn't count, so we have to exclude the sides from our consideration. There are 10 sides, so we need to take away 10 ways from the 45 ways possible to get the number of diagonals.
Number of diagonals in a decagon = 35
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