All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.
We will also observe that they have a direct connection to the polynomial's factors.
What are polynomial zeros with an example?
Real number k is referred to as the zero of a polynomial P(x) if P(k) = 0. As a result, the polynomial x2 - 3x + 2 has a zero at 1 and a zero at 2.
The equation p(x)=(x-1) (x-3)
Although it is a polynomial of third degree, 2, only has two different zeros. This is due to the zero x=3 having a connection to the factor.
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#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]Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
The property demonstrated by:
a(b+c)=(a.b)+(a.c)
Is the Distributive property
Which property is demonstrated below?Here we have the next expression:
a*(b + c) = (a*b) + (a*c)
So we have the product between a and the sum of b and c, is equal to the sum between the products of a and b, and a and c, so we "distributed" the product.
This property is called the "Distributive property".
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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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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:
Consider the following.
sin(x) + sin(3x) = 4 sin(x) cos2(x)
Prove the identity.
Proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Given,
sin(x) + sin(3x) = 4 sin(x) cos²(x)
We have to prove the above given identity:
So,
sin(x) + sin(3x)
sin(x) + sin(2x + x)
By using the identity sin (A + B) we get,
sin(x) + sin (2x) cos(x) + cos (2x) sin(x)
Now use the identities:
sin 2x and cos 2x
We get,
sin(x) + 2sin(x) cos(x) cos(x) + (2cos²(x) - 1) sin(x)
Then,
sin(x) + 2sin(x) cos²(x) + 2sin(x) cos²(x) - sin(x)
We get,
4 sin(x) cos²(x)
Hence proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
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Find the slope between these two points:
(3, 0), (-11, -15)
Answer:
3/4 or 0.75
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.
Jacob set aside (budgeted) $10 to spend on snacks at the movies. Sodas cost $1.50 each, and a box of popcorn costs $1.75. How many sodas can he buy for him and his friends if he buys 2 boxes of popcorn? Write an Inequality.
Answer:4 sodas
Step-by-step explanation:
1.75 x 2 = 3.5
10- 3.5 = 6.5
6.5 Divided by 1.50 = 4.33333333
(Round that to 4 and he will be left with cents)
Please help gotta get my grade up ASAP this was due the 11th and it’s the 23rd now, super behind!!
Find f(7) if f(x) = 6x + 10. Enter DNE if the value does not exist.
f(7) =
Answer: f(7) = 52
Step-by-step explanation:
x = 7, so you would substitute x for 7
f(7) = 6(7) + 10
f(7) = 42 + 10
f(7) = 52
Hope this helps!
In the diagram below, segment PB is a tangent. IF AC = 18 and PA = 6, find PB.
Explanation
we have a secant and a tangent
To solve the question, we will apply the intersecting secant and tangent theorem
So, for the question
we have
[tex]\begin{gathered} PB^2=PA(PA+AC) \\ \\ PB^2=6(6+18) \\ \\ PB^2=6(24) \\ \\ PB=144 \\ \\ PB=12 \end{gathered}[/tex]Therefore, the value of PB is 12
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.
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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Mrs. Frank asks four of her students to measure four different objects. Here are the results.
Which student had the greatest percent error?
The student that has the greatest percent error is Ebony.
How to calculate the percentage error?The percentage error will be calculated as:
= Change in value / Initial values × 100
From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:
= (Measured length - Actual length) / Actual length × 100
= (2.1 - 1.6)/1.6 × 100
= 0.5 / 1.6 × 100
= 31.25%
Ebony had the higher percentage error.
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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
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
Evelyn is thinking of constructing a swimming pool in the plot next to her house such that it is surrounded by grass as given in the figure below. The dimensions of the plot is 50 ft x 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
The area of a pool from the given situation is 816 ft².
Given that, the dimensions of plot is 50 ft and 40 ft.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Here, area of a plot = Length × Width
= 50 × 40
= 2000 ft²
Area of a pool = Area of a plot - Area of a grass
= 2000 - 1184
= 816 ft²
Therefore, the area of a pool from the given situation is 816 ft².
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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?
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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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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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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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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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
Which of the following equations represents a proportional relationship? Select all that apply. A 5 5 = 11 11 B 3 6 = 6 3 C 2x 12 = 3x 18 D 8 15 = 4 30 E 4 6 = 10 15 F 4x 18 = x 18
The equations that represent proportional relationships are:
A. 2x/12 = 3x/18
C. 4/6 = 10/15
E. 5/5 = 11/11
How to Determine a Proportional Relationship Equation?To determine if an equation represents a proportional relationship, ensure each side of the equation gives the same value when simplified. If they do not have the same value, then the equation does not represent a proportional relationship.
A. 2x/12 = x/6
3x/18 = x/6
Therefore, 2x/12 = 3x/18 represents a proportional relationship.
B. 3/6 = 1/2
6/3 = 2
Therefore, 3/6 = 6/3 does not represent a proportional relationship.
C. 4/6 = 2/3
10/15 = 2/3
Therefore, 4/6 = 10/15 represents a proportional relationship.
D. 4x/18 = 2x/9
x/18 = x/18
Therefore, 4x/18 = x/18 does not represent a proportional relationship.
E. 5/5 = 1
11/11 = 1
Therefore, 5/5 = 11/11 represents a proportional relationship.
F. 8/15 = 8/15
4/30 = 2/15
Therefore, 8/15/2/15 does not represent a proportional relationship.
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Please help! Super confused!
Enter the inverse function of f(x) = -9x - 10.
Answer: [tex]f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
Step-by-step explanation:
[tex]f(x)=-9x-10 \implies x=-9f^{-1}(x)-10\\\\x+10=-9f^{-1}(x)\\\\f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
1x + 2y = 7 and y = -2x + 3
Answer:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
Solve the system of equations:
1x + 2y = 7
y = –2x + 3
Substitute y = –2x + 3 for y in the first equation:
1x + 2y = 7
1x + 2(–2x + 3) = 7
Substract 6 from both sides:
–3x + 6 = 7
–3x + 6 – 6 = 7 – 6
–3x = 1
Divide:
–3x/–3 = 1/–3
x = –1/3
Substitute –1/3 for x in the second equation:
y = –2x + 3
y = –2(–1/3) + 3
y = 11/3
Solution:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
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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:
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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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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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Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of d days that have passed. A. Write an equation for the situation.B. Find the a amount of money he began with.C. How much money does Marty have after 9 days?
Given:
Amount Marty spent per day = $3
Number of days = 14
Remaining amount = $68
Since the amount left depends on the number
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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