The required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.
Given that,
To arrange the like terms in columns and add them. - a) 2x³ - 7x⁴ + 7x⁵ and 11x³ - 4x⁴ – x b) -2p - 3p² and 1 - 5p + 8p².
The algebraic expression consists of constant and variable. eg x, y, z, etc.
Here,
(a)
= 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
= 7x⁵ - 7x⁴ - 4x⁴+ 2x³ + 11x³– x
= 7x⁵ + 13³ - 11x⁴ - x,
(b)
= -2p - 3p² + 1 - 5p + 8p²
= 1 -2p - 5p -3p² + 8p²
= 1 - 5p + 8p²
Thus, the required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.
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The required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵ – x and - 7p + 5p²+ 1.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.
The polynomials are given in the question :
2x³ - 7x⁴ + 7x⁵, and 11x³ - 4x⁴ – x
-2p - 3p² and,1 - 5p + 8p²
According to the question,
⇒ 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
Rearrange the terms and apply the arithmetic operation,
⇒ 2x³ + 11x³- 7x⁴- 4x⁴ + 7x⁵ – x
⇒ 13x³- 11x⁴+ 7x⁵ – x
⇒ -2p - 3p² + 1 - 5p + 8p²
Rearrange the terms and apply the arithmetic operation,
⇒ -2p - 5p - 3p² + 8p²+ 1
⇒ - 7p + 5p²+ 1
Thus, the required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵ – x and - 7p + 5p²+ 1.
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Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope -1.
The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)
How to represent equation in point slope form?Linear equation can be represented in different form such as point slope form, slope intercept form and standard form.
Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.
Hence,
y - y₁ = m(x - x₁)
where
m = slopey₁ and x₁ are the coordinates of the point.Therefore,
m = slope = -1
using (-12, 15)
Hence,
y - 15 = - 1(x - (-12))
Therefore,
y - 15 = - 1(x + 12)
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Round 3.44570830811 to the nearest hundred-thousandth
Answer:
3.44571
Step by step explanation:
3.44570830811
8 is the number next to the place value of hundred-thousandth, so we round it up to 1 and add it to 0
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Show that the triangles are similar and write a similarity statement.E1427AC 18D21BZACBACEDCSo AABC ~ A
Two triangles are similar if the ratio of their corresponding side equal'
Triangle
Because
Corresponding sides are
Therefore,
Triangle
What is the simplest form of
2√3
√12
Explanation:
though it may not be a simplification,
2√3
can be shown as
√12
.
2=√4
Ariel dropped a golf ball from her second story window. The ball starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the golf ball.
The average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².
Given in the question is:
Since the ball started from rest
Initial velocity; u= 0m/s
Final velocity; v = 14.7 m/s
Time taken for the golf ball to hit the sidewalk; t = 1.5 s
Average Acceleration; g =?
To determine the average acceleration of the golf ball, we use the First Equation of Motion:
v = u + at
The Equation will be :
v = u + gt
Plug the all values in above equation:
14.7m/s = 0 + g x 1.5 s
g = 14.7 / 1.5
g = 9.8m/[tex]s^2[/tex]
Therefore, the average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².
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Find the equation to the line below.y =[?-x ++ [ ]
Note that a line whose equation is in the form :
[tex]y=mx+b[/tex]has a slope of m
and a y-intercept of b
Slope is also equal to rise/run :
[tex]m=\frac{\text{rise}}{\text{run}}[/tex]where rise is the number of vertical units between two points and run is the number of horizontal units between two points.
Note also that upward and right movement is positive, downward and left movement is negative.
From the figure, the vertical units between two given points is 3 units upward, so this is positive.
The horizontal units between them is 2 units to the right which is also positive.
The slope will be :
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{3}{2}[/tex]Next is to solve for b (y intercept).
y-intercept is the point where the line intersects the y-axis.
From the graph, the lines intersects at point (0, 2) on the y-axis
Therefore, the value of b is 2
Rewriting the equation, the answer is :
[tex]\begin{gathered} y=mx+b \\ y=\frac{3}{2}x+2 \end{gathered}[/tex]You are a grant writer for an organization that helps adults complete their high school educations. For the last 5 years, you have applied for and received $45,000.00 in grants. Your boss would like you to try to increase that amount to $60,000.00. How much of an increase does the new amount represent over the previous amount?
Based on the amount you have received in grants, and the amount the boss wants to increase it to, the increase the new amount represents over the previous amount is $15,000 or 33.3%.
How to find the increase?Your boss wants to increase the grants to $60,000 from the current amount of $45,000.
This means that the new amount will represent an increase over the previous amount by:
= 60,000 - 45,000
= $15,000
In percentage terms this is:
= Increase over previous amount / Previous amount x 100%
= 15,000 / 45,000 x 100%
= 33.3%
In conclusion, the difference between the grants applied for in the past 5 years and the amount the boss is asking for, gives the increase of $15,000.
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What is the slope of a line perpendicular to the line whose equation is x+6y=-24
Answer:
[tex]m[/tex]perpendicular = 6
Step-by-step explanation:
Hope this helps! :))
Ms. Wilson invested $30,000 in two accounts, one yielding 8% interest and the
other yielding 9%. If she received a total of $2,590 in interest at the end of the
year, how much did she invest in each account?
The amount invested at 8% was $
The amount invested at 9% was $
Answer:
The amount invested at 8% was $11,000
The amount invested at 9% was $19,000
Step-by-step explanation:
Let the variable x represent the amount in $ invested at 8% and let y be the amount in $ invested at 9%
Total amount invested:
x + y = 30000 [1]
8% = 8/100 = 0.08
9% = 9/100 = 0.09
Interest at 8% on $x = 0.08x
Interest at 9% on $x = 0.09x
Total Interest :
0.08x + 0.09y = 2590 [2]
Using equations [1] and [2] we can solve for x and y
We have
x + y = 30000 [1]
0.08x + 0.09y = 2590 [2]
Multiply equation 1 by 0.08 to get
0.08x + 0.08y = 0.08(30,000)
0.08x + 0.08y = 2,400 [3]
Subtract [3] from [2] :
0.08x + 0.09y = 2590
-
0.08x + 0.08y = 2400
----------------------------------
0x + 0.01y = 190
Divide both sides by 0.01
0.01y/0.01 = 190/0.01
y = = 19,000
Use [1] to get value of x
x + y = 30,000
x + 19,000 = 30,000
x = 30,000 - 19,000
x = 11,000
1. In the graph below, point D is reflected across the y-axis. What are the coordinates of its
image?
2
(3,-1)
(3, 1)
(-3,-1)
(-3, 1)
Answer:
3
Step-by-step explanation:
When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step? Original Equation: 5.x2 + (10x2 + 10) = 3x? First Step: 15x2 + 10 = 3.2 commutative property of multiplication commutative property of addition multiplication property of equality
The original equation is:
5 x^2 + (10 x^2 + 10) = 3 x^2 - 5
The first step the person did was:
15 x^2 + 10 = 3 x^2 - 5
so in this first step the person used the associative property of addition by associating 5 x^2 with 10 x^2 and combining them to give 15 x^2.
Please check if there is an option that states such among your options.
A social scientist researched how the average working hours per worker, over a full year, for two different European countries changed since 1870. she created a scatter plot and found the regression line for each set of data. She then used the regression line to
create a table of values for the residuals. The scatter plots, regression equation, and residuals for the two countries are shown, where z represents the number of years since 1870 and y represents the average working hours per worker over a full year.
We can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.
What is a regression equation?The dependent variable's predicted value in simple linear regression is given by the equation = b₀ + b₁x. In order to minimize the total sum of squared errors, the values of b0 and b1 are calculated from the data using the equation line = b0 + b1X. (the error is the difference between the predicted value and the actual value of y).When two variables, X and Y, are involved, there will be two regression lines: one for X on Y and one for Y on X. Lines of regression X and Y: In this configuration, the variables Y and X are independent, and the best-expected value of X is determined in accordance with the value of Y that is provided.So, according to the given image, we can easily say that Germany has a negative correlation.
Hence, option(C) and (D) are wrong.We can observe that the slope of the regression equation is negative.
Then, the wrong option will be (A) and the correct option will be (B).Therefore, we can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.
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Solve for x in terms of the other pronumerals
ax+ b/4 = x+c/3
Answer:
[tex]x=\cfrac{4c-3b}{3a-4}[/tex]==============================
Given expression[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex]Solve it for x in steps below[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex] Given
[tex]3(ax+b)=4(x+c)[/tex] Cross-multiply
[tex]3ax + 3b=4x+4c[/tex] Distribute
[tex]3ax-4x=4c-3b[/tex] Collect terms with x
[tex]x(3a-4)=4c-3b[/tex] Factor out x
[tex]x=\cfrac{4c-3b}{3a-4}[/tex] Divide both sides by 3a - 4
Yuri bought a new house. The diagram shows the layout of his backyard. Yuri is designing improvements that he wants to make. Yuri plans to fill the patio with concrete, the garden with a special soil mixture, and the remaining areas that surround the hot tub with a wood deck. The table shows the costs associated with each project. How much more will Yuri spend on concrete than on soil and wood? Explain. Click here to view the diagram of Yuri's backyard. Click here to view the table of materials. The area of the patio is yd?, so the cost of concrete is $ The area of the garden is yd?, so the cost of soil is $ The total area of the deck is ft?, so the cost of wood is $1. So, Yuri will spend $ more on concrete than on soil and wood. (Type integers or decimals.) Enter your answer in the edit fields and then click Check Answer. All parts showing
1) Area of patio = 1/2 base x height
Height = 3.1ft
base = 7 + 10 =17 ft
Area = 1/2 x 3.1 x 17
Area of patio = 26.35 square ft
1 yard = 3 ft
1 square yard = 9 square ft
so the area of the patio in yard is
26.35/9 = 2.927777778 square yard
2) Cost of concrete = $10/square yard poured 1/9 yard deep+ $60 delivery fee
for 2.9277777778 square yard it will cost 1/9($10 x 2.9277777778) + $60 =$
3)
Simple Interest QuizIf $3,000 is loaned for 48 months at a 4.5% annual rate, how much is the ending balance?
Given:
Principal (p) =$3,000
Time (T) = 48 months = 4 years
Interest rate = 4.5%
Required :
Ending balance = ?
The simple interest :
[tex]\begin{gathered} SI\text{ = PRT} \\ =\text{ 3000 }\times\text{ 0.045 }\times\text{ 4} \\ =\text{ \$ 540} \end{gathered}[/tex]Ending balance :
[tex]\begin{gathered} \text{Ending balance = Principal + SI} \\ =\text{ \$ 3000 + \$ 540} \\ =\text{ \$ 3540} \end{gathered}[/tex]Ending balance = $ 3540
The telephone company offers two billing plans for local calls. Plan 1 charges $24 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05 per call.
Answer:
plan b
Step-by-step explanation:
unless your making 120 calls or more plan B is better
24-18=6
6/0.05
=120
On the freeway it is unsafe to drive too slowly or two quick the safest driving speeds on the freeway near Allentown worst scientifically determined to be between the minimum and maximum speed in miles per hour according to the equation X -55 in value equals 4.2 which equation can be used to determine the maximum safe driving speed
Equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to x -55 =4.2.
As given in the question,
Given equation :
|x – 55| = 4.2
To determine the maximum and minimum speed in miles per hour from the given equation we have,
x-55 = 4.2 or x-55 =-4.2
Add 55 both the side of the equation,
x-55 +55 =4.2+55 or x-55+55 = -4.2 +55
x =59.2 or x = 50.8
Maximum speed is 59.2 determine by equation x-55 = 4.2
Minimum speed is 50.8 determine by equation x-55 = -4.2
Therefore, equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to
x -55 =4.2.
The complete question is:
On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan’s town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x – 55| = 4.2. Which equation can be used to determine the maximum safe driving speed?
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Round 1.9541 to the nearest tenth
Answer:
2
Step-by-step explanation:
1.9541 lets only worry about 1.95 because it rounds to this rounding up because its five will be 2
In comparative statistics, what type of error occurs when a test indicates a significant difference between two or more populations even though the null hypothesis is true?.
Type 1 error is the error occurs when a test indicates a significate difference between two or more populations.
What does a Type I mistake mean?Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes. The significance level you select (alpha or ) determines the likelihood that you will make this mistake.
Data cleansing—also known as data cleaning, data scrubbing, or data rectification—is the process of correcting inaccurate, insufficient, duplicate, or other wrong data in a data set. It entails locating data mistakes and then correcting them by modifying, updating, or eliminating data.
Using independent samples from two independent groups, the two-sample (independent groups) t-test is used to assess whether the unknown means of two populations are different from one another.
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I need help with this question... the correct answer choice
The transformation on a line such that a line is obtained which is pependicular to previous line is possible only when it is reflected through y = x axis. This can be understood as,
When line is reflected about x-axis, the x coordinate remain same where as y-coordinate changes in opposite sign with same magnitude. So reflection of line x = 3 about x axis remain same.
Simillarly reflection of line x = 3 about x = 1 remain same as x = 3.
The reflection of line x = 3 about y-axis results n a parallel line passing through x = -3.
So answer is reflection across y = x.
Given the information above, what is the size of the wedge to the nearest whole degree foraqua pencils?options:55°12°61°43°
the size of the wedge for aqua pencils is 43°
Explanation:Given:
A table showing the pencil collection
To find:
the portion that represents the aqua pencils in degree
The total number of pencils = 23 + 106 + 62 + 47 + 32
The total number of pencils = 270
In degrees:
Total angle in a circle = 360°
Size of the wedge for aqua = number of aqua pencils/total pencils × 360°
[tex]\begin{gathered} Size\text{ of the wedge = }\frac{32}{270}\text{ }\times360° \\ \\ Size\text{ of the wedge = 42.67\degree} \end{gathered}[/tex]To the nearest degree, the size of the wedge for aqua pencils is 43°
Yesterday, the temperature change for a 5-hour period of time was -degree perhour. Which statement describes this change?AThe temperature rose 5 degrees.BThe temperature rose 45 degrees.СThe temperature fell 4 degrees.DThe temperature fell 5 degrees.AB
The negative sign means that temperature decreases of fell.
Deteremine the change in temperature for 5 hours.
[tex]\begin{gathered} dT=5\cdot(-\frac{4}{5}) \\ =-4 \end{gathered}[/tex]So temperatute fell 4 degrees. Option C is correct.
Determine a series of transformations that would map Figure I onto Figure J
and its not just rotate the figure 90 degrees clockwise, you have the do TWO translations
3 × 90 thus equals 280 degrees.
The figure moves onto the following quadrant of the graph with each 90 degree rotation. In order to shift Figure I to the location of Figure J, you must move the three figure quadrants in a clockwise direction. 3 × 90 thus equals 280 degrees. Only one transformation is needed.
Which transformation corresponds to turning a figure 90 degrees counterclockwise?
The coordinate transformation (x, y) (y, x) is equivalent to a rotation of the origin 90 degrees counterclockwise. The coordinate transformation (x, y) (x, y) is comparable to a 180 degree counterclockwise rotation of the origin.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, making y negative.
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what is the total amount of 67x88=
the answer is 5896. . . . . . ... . . . . . ......................
Hello!
When multiplying 67 x 88, the correct answer would be 5896.
Hope this helped!
Jaida worked 21 1/2 hours last week.She earned $11.60 per hour of work.How much money did jaida earn last week
Answer:
249.40
Step-by-step explanation:
#5 Pam a nurse made $93 in 6 hours determine an equation that represents how much she gets paid per hour #6 using your equation from problem 5 how much would a modern if she work for 15 hours?#7 using your equation from problem 6 how much would Pam earn if she work for 3 1/2 hours?
Pam is a nurse that earns $93 in 6 hrs .The equation that can represents how much she get paid per hour can be computed below
[tex]\begin{gathered} \text{ amount she earned per hr=}\frac{93}{6}=15.5 \\ The\text{ equation that can represent how much she earned per hour is} \\ \text{amount earned per hour = 15.5x} \\ x=\text{ hours worked} \\ \text{amount earned per hour}=15.5(1)=15.5\text{ dollars} \end{gathered}[/tex][tex]\begin{gathered} \text{amount she earned in 15 hrs=}15.5x \\ \text{amount she earned in 15 hrs}=15.5\times15=232.5dollars \end{gathered}[/tex][tex]\begin{gathered} \text{amount earned in 3}\frac{1}{2}\text{hrs}=15.5x \\ \text{amount earned in 3}\frac{1}{2}\text{hrs=15.5}\times\frac{7}{2}=\frac{108.5}{2}=54.25dollars \end{gathered}[/tex]ASAP DUE TODAY!!
Please include answers AND an explanation. Giving branliest <3
(1) The graph is attached with the answer below.
(2)The equation of the line is y = x + 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The points are ( 3, 0 ) and ( 0, 3). The slope of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 3 - 0 ) ( 0 - 3 )
Slope = 1
Calculate the y-intercept,
y = mx + c
3 = 0 + c
c = 3
The equation of the line will be:-
y = x + 3
Therefore, the graph is attached with the answer below the equation of the line is y = x + 3.
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Please answer fast
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
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3. There are 104 males and 121 females
participating in a marathon. To the
nearest percent, what percent of the
participants are female?
There are 54% of the participants are female.
What is percent?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage
Given:
There are 104 males and 121 females
participating in a marathon.
So, the total number of participants are,
104 + 121 = 225.
There are 225 total number of participants.
So, the percent of the female are,
[tex]\frac{121}{225} (100) = 53.78[/tex]
Therefore, the percent of the participants of female are 54%.
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Mark Trumbo of the Arizona Diamondbacks has hit five home runs in the thirty-five times he has been up to bat. At this pace, how many at bats would he need to hit twenty-three home runs?