The addition or subtraction of a constant to a function will change its position in the cartesian plane. Depending on the sign of the constant, it can shift upwards or downwards.
Let a quadratic function be f(x) = 2x^2.
Let c be the positive constant.
It is now necessary to determine what will happen if we add or subtract a constant to the function.
The function f(x) = 2x^2 is a parabola opening upwards.
Now, if we add the positive constant c, then the graph of the function will shift upwards by c units and nothing will change. If we subtract the positive constant c, then the graph of the function will shift downwards by c units.
Thus, the addition or subtraction of a constant to a function will change its position in the cartesian plane. Depending on the sign of the constant, it can shift upwards or downwards.
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the numerical coefficient of x2 in 3x2-3x
Answer:
Step-by-step explanation:
the numerical coefficient of x2 here is 3.
In the table the (p) profit is a function of the number of shirts sold (n) at a store
Which equation describes the relationship between n and p
p=4n+2 equation describes the relationship between n and p
How to find a function?
To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.
Here the coordinates are (1,6),(2,10),(3,14),(4,18)
take two coordinates arbitrarily
ie. (1,6) and (3,14)
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
[tex]m=\frac{14-6}{3-1}\\ = \frac{8}{2}[/tex]
=4
we know the equation
[tex]y-y_{0} = m(x-x_{0} )[/tex]
where [tex](x_{0},y_{0})= (1,6)[/tex]
y-6 = 4(x-1)
y-6 = 4x-4
y = 4x-4+6
y = 4x+2
here y is the profit and x is the number of shirts
∴p=4n+2
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There are 32 triangle on each of 21 quilt. How many triangle are on all of the quilt ?
Total triangles on all the quilt are 672.
What is quilt?
Quilts are often made of two or more layers of cloth or fibre and are multi-layered textiles. Three layers and a filler substance are frequently employed. These layers are often made up of a woven top, a batting or wadding layer, and a woven back that are all connected using quilting techniques.
Main Body:
Number of triangles on 1 quilt = 32
Total number of quilt = 21
So total triangles can be calculated by simply multiplying the two values,
Total triangles = 32*21
= 672 quilts
Hence total number of triangles = 672
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which of the points A(5,6) or B(5,3) is closer to point C(-3,2)
The solution is
The distance between the point A and C is greater than the distance between the points B and C
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be = A
The value of A = A ( 5 , 6 )
Let the second point be = B
The value of B = B ( 5 , 3 )
Let the reference point be C = C ( -3 , 2 )
Now , the distance between the points A and C = P
The distance between the points B and C = Q
Now , the value of P is calculated from the distance formula
Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Substituting the values in the equation , we get
P = √ ( 5 - ( - 3 ) )² - ( 6 - 2 )²
P = √ ( 8 )² + ( 4 )²
P = √ ( 64 + 16 )
P = √80 units
Now , the value of Q is calculated from the distance formula
Substituting the values in the equation , we get
Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Q = √ ( 8 )² + ( 1 )²
Q = √ ( 64 + 1 )
Q = √65 units
So , the value of Q is less than value of P
Therefore , the distance of point B to C is lesser than point A to C
Hence , The point B ( 5 ,3 ) is closer to the point C ( -3 , 2 )
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A student was asked to name all values of n that make the relation a function. Correct the error. Justify your answer.
{(2,8), (6,0), (4,2), (2n,n)}
n can be any value except 2,6, or 4
For n as 5,7,8 and 9 the relation will become function
What is a function?A relation is a function if it has only One y-value for each x-value.
The given relation is two comma eight comma six comma zero comma four comma two comma two times of n comma n.
{(2,8), (6,0), (4,2), (2n,n)}
We need to make it function for which n should not be 2,6, or 4.
When n is 1, it is not function
n is 3, it is not function
n is 5, it is function
n is 7, it is function
n is 8, it is function
n is 9, it is function
Hence for n as 5,7,8 and 9 the relation will become function
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A girl weighs 400 N. She runs up a flight of stairs of height 5 m in 4 seconds. Her
power is:
Answer: 500 W (watt)
Step-by-step explanation:
Power = P = Work / time = W/t
W = Fd = Force x distance = 400N x 5m = 2000J
P = 2000J/4s = 500 W
The ratio of donuts to muffins at the restaurant is 10:6. If the total number of breakfast treats 48, how many muffins are there?
Answer:
Step-by-step explanation:
there would be 18 muffins.
if you multiply each number by 3 then add them it will end up at 48.
6x3=18
10x3=30
30+18=48
30:18
The volume of a right cone is 448 pi units to the 3rd . If its height is 21 units, find its radius.
The radius of the cone if the volume of a right cone is 448 π cube units and if its height is 21 units is 8 units.
First, let us understand the cone:
It is a solid or hollow item with a round or approximately circular base that tapers to a point.
The volume of the cone is given by;
Volume = 1/3 π r^2 h
where r = radius of the base of the cone
and h = height of the cone
We are given;
The volume of a right cone is 448 π cube units.
Height is 21 units.
Put the values in the volume formula;
448 π = 1/3 π r^2 * 21
448 π = 7 π r^2
r^2 = 448 π / 7 π
r^2 = 64
r = 8 units
So, the radius of the base is 8 units.
Thus, the radius of the cone if the volume of a right cone is 448 π cube units and if its height is 21 units is 8 units.
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Answer:
8
Step-by-step explanation:
don't know how to explain it but I had he same problem and I got 8 and it was right.
a doctor is measuring the average height of male students at a large college. the doctor measures the heights, in inches, of a sample of 40 male students from the baseball team. using this data, the doctor calculates the 95% confidence interval (63.5, 74.4). which one of the following conclusions is valid?
The correct conclusion is:
"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."
Given,
At a huge institution, a doctor is determining the typical height of the male students.
Inches are used to measure the heights of a sample of 40 male baseball team players.
The doctor computes the 95% confidence interval using this information (63.5, 74.4).
The following conclusions is valid:
"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."
We can guarantee that the target variable will be within the confidence interval for a given confidence level since we know the confidence interval reflects an interval.
The true mean of heights for male students at the college where the doctor measured heights is represented by the provided case's confidence level of 95% and confidence interval of (63.5, 74.4).
The doctor is therefore 95% certain that the range of the mean height of male students at the college is valid (63.5, 74.4).
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Alejo records the time it takes
to download a variety of file types. How is the
download time related to the file size? Explain.
The ratios for each pair of data are
so the download time and the file size are
The ratios for each pair of the data are the same, so the download time and the file size are proportional.
What is a proportional relationship?A proportional relationship is a linear function that has the following features.
Slope as the constant of proportionality.Intercept of zero.Hence the output variable y is given by the multiplication of the input variable x and the constant of proportionality k, hence the equation is:
y = kx.
A set of data is only proportional if the division of the output by the input is the same for all pairs of values.
For this set of data, this division is given as follows:
1.25/25 = 0.05 MB/s.3.6/72 = 0.05 MB/s.6.25/125 = 0.05 MB/s.Same ratios, hence the measures are proportional.
Missing InformationThe data is given by the image at the end of the answer.
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represents 29 students in a class
B represents students who have a brother
S represents students who have a sister
ԱՄՐ
B
a) One student from the class is chosen at random.
What is the probability that the student has a sister?
Optional working
7
Answer
b) One of the students who has a brother is chosen at random.
What is the probability that this student has a sister?
4
2x
S
x + 3
The student's having a sister is 0.4827 likely. And a random student is chosen who has a brother. Therefore, the probability that this student has a sister is 0.3636.
The fundamental assumption that something will almost certainly occur is known as probability. the percentage of positive occurrences to all occurrences.
Next, the probability is given as
P = (a favorable event) / (Total event)
The letters £ stand for the 29 students in the class, B for those who have brothers, and S for those who have sisters.
Next, the equation will be presented.
7 + 4 + 2x + x + 3 = 29
3x = 29 - 14
3x = 15
x = 5
2x will then have the value
2x = 2(5)
2x = 10
After that, x + 3 will have the value.
x + 3 = 5 + 3 = 8
The probability of the student having a sister is
P = (10 + 4) / 29
P = 14 / 29
P = 0.4827
If a student with a brother is randomly selected, the probability that this student also has a sister will be
P = 4/11
P = 0.3636
As a result, the probability that the student has a sister is 0.4827. And at random, one of the students with a brother is chosen. The likelihood that this student has a sister is then 0.3636.
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Calculate the area of the triangle PQX.
The area of the triangle PQX is 9.8 cm².
Given,
on this circle
∠PQX = ∠SXR
since vertical angles are equal.
∠PQX = ∠XRS and ∠QPX = ∠XSR
since the angle is the same as the angle opposite the arc.
so triangle PQX is similar to triangle SRX
three angles are equal.
since two triangles are similar:
so, RX/QX = SX/PX = SR/PQ = 10/7
and since S Δ PQX = 1/2 . QX . PX . sin∠PXQ
SΔSRX = 1/2 . RX . SX . sin∠SXR
= 10/7 × 10/7
= 100/49
S Δ PQX = 49.SΔSRX/100
= 9.8 cm²
Hence we get the area as 9.8 cm²
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please help with this aswell these are just confusing
The solutions of the quadratic equation are:
x = (-1 +√8*i)/4x = (-1 -√8*i)/4How to solve the quadratic equation?A general quadratic equation:
a*x^2 + b*x + c = 0
Has solutions of the form:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4a} }{2a}[/tex]
In this case, the quadratic is:
2*x^2 + x + 2 = 0
a = 2
b = 1
c = 2
Then using above formula we get the two solutions:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*2} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-8} }{4}[/tex]
So the solutions are:
x = (-1 +√8*i)/4
x = (-1 -√8*i)/4
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What greater number of bicycles had the company previously produced to make the same profit? Round your answer to the nearest tenth.
million bicycles
Answer:
Step-by-step explanation:
black wombat in the dessert jungle
i know its wrong but its right
trust it
the process
Which is an equivalent form of the expression 1800(1.2) '?
300 (2)
1800
O 1800
O
()*
6
6
1800 (8)
5
O1800
1800 (7)
Answer:a
Step-by-step explanation
let me know if this helps
243 x 35
Please explain how to do it step by step. For my little sister, this is math I haven’t done in 4 years lol
Answer:
8505
Step-by-step explanation:
Step 1
Firstly, work out 5 × 243. The smaller figures in green are the tens figures carried over. Working from right to left:
5 × 3 = 15
Put the 5 in the appropriate column and carry the 1.
5 × 4 + 1(carried) = 21
Put the 1 in the appropriate column and carry the 2.
5 × 2 + 2(carried) = 12
Put the 2 in the appropriate column and carry the 1.
Step 2
Lastly, work out 30 × 243.
This can be written as 3 × 243 × 10.
Because we are multiplying by 10, we place 1 zero to the right and then work out 3 × 243.
3 × 3 = 9
3 × 4 = 12
Put the 2 in the appropriate column and carry the 1.
3 × 2 + 1(carried) = 7
Step 3
Finally, the 2 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.
0 + 5 = 5
9 + 1 = 10
Put the 0 in the appropriate column and carry the 1.
2 + 2 + 1(carried) = 5
7 + 1 = 8
So: 243 × 35 = 8505
An exercise mat is 3.3 times as long as it is wide. Write expressions in simplest form that represent the
perimeter and the area of the exercise mat.
The expression that represents the perimeter is 8.6b and the expression that represents the area of the exercise mat is 3.3b² .
In the question ,
it is given that ,
the exercise mat is is 3.3 times as long as it is wide .
let the width of the exercise mat be = "b" .
So , the length of the exercise mat will be = 3.3b
The Perimeter of the exercise mat = 2( length + width)
= 2(3.3b + b)
= 2(4.3b)
= 8.6b
the perimeter is = 8.6b
The Area of the exercise mat = length × width
= 3.3b × b
= 3.3b²
the area is = 3.3b²
Therefore , The expression that represents the perimeter is 8.6b and the expression that represents the area of the exercise mat is 3.3b² .
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Molly had 55 stuffed animals. She decided to donate 30 of them. What percentage of stuffed animals did Molly donate?
Answer: she donated 25%
Step-by-step explanation:
Answer:
54.54
Step-by-step explanation:
30x100 then divided by 55
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Find the value of y. Pls help
simplify the expression
(0.2a^2b^3)(-5a^3b)^2
The simplified expression for (0.2a²b³)(-5a³b)² is given as follows:
5a^8b^5.
What is the simplified expression?The expression for this problem is given as follows:
(0.2a²b³)(-5a³b)²
First we apply the power of power simplification, in which the square of each term inside the parenthesis is calculated as follows:
Square of -5: 25.Square of a³: a^6 -> keeps the base a and multiplies the exponents 3 and 2.Square of b: b² -> keeps the base b and multiplies the exponents 1 and 2.Now the expression is:
(0.2a²b³)(25a^6b²).
Then:
0.2 x 25 = 5 -> multiplies the numeric constants.a² x a^6 = a^8 -> product with terms of same base and different exponents, keep the base and add the exponents.b³ x b² = b^5 -> same as above, keeps the base b and adds the exponents 3 and 2.Hence the simplified expression is:
5a^8b^5.
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Last week, Jennifer volunteered at the hospital for 12 hours. This week, she volunteered for 15 hours. What is the percent increase in the number of hours she worked?
Jennifer had 25 percent increase in number of hours worked
Percentage IncreasePercentage increase describes the eventual increase in the quantity in percent form. The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.
Data;
Last week = 12 hoursThis week = 15 hoursPercentage Increase = [(15 - 12) / 12] * 100
Percentage Increase = 3/12 * 100
Percentage Increase = 0.25 * 100
Percentage Increase = 25%
The increase is 25%
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Help please tho please help me
Answer:
b is the answer
Step-by-step explanation:
hi hope it helps
Jude is training for a marathon his goal is to run a total of 7 3/15 miles so he can beat last years record. Jude plans to run 2 3/15 miles on monday, 1 1/5 miles on tusday, and 2 1/3 miles on wensday. How many more miles will he need to run on thursday? Please hurry
The miles that Jude needs to run on Thursday is 1 3/5 miles.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Total fraction = 7 3/15
Monday race = 2 3/15
Tuesday race = 1 1/15
Wednesday race = 2 1/3
The miles remaining will be:
= 7 3/15 - (2 3/15 + 1 1/15 + 2 1/3)
= 7 3/15 - 5 9/15
= 1 9/15
= 1 3/5 miles
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Find the 16th term in the arithmetic sequence 9, 3, –3, –9, –15,...
22. Four friends went to the movies. Tickets cost $9 each. They bought two popcom buckets to
share which cost $6.50 each. Each of the friends got a soft drink for $3.75. How much did they
spend?
Answer:
$64.00
Step-by-step explanation:
4(9) + 2(6.5) + 4(3.75)
36 + 13 + 15
64
Can anyone help me with this proof
Find the value of the discriminant. Describe the number and type of root for the equation.(explain by step by step please!)(I need rlly need help on this one!)
2x^2+10x+9=9x
The value of the discriminant is -71. The roots of the equation are imaginary and two in number.
We are given a quadratic equation. The equation is given below.
2x² + 10x + 9 = 9x
We will simplify this equation.
2x² + x + 9 = 0
We need to find the discriminant of the equation. If the general quadratic equation is represented by ax² + bx + c = 0, then the discriminant is given below.
D = b² - 4*a*c
D = 1² - 4(2)(9)
D = 1 - 72
D = -71
The discriminant is negative, so no real roots exist for the given quadratic equation. Thus, there exist two imaginary roots for the given quadratic equation.
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PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
I belive c
Step-by-step explanation:
PLEASE HURRYYY!!!! U.S. Bureau of Labor Statistics, 2006.
Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn't want to go to college.
Which of the following occupations fits her plan?
a. Makeup artist
b. Mathematician
C. Private detective
d. Massage therapist
The occupations that fits her plan is Private detective
How would you define statistics?
Statistics is the study of data gathering, analysis, presentation, and interpretation. Early government demands for census data and knowledge of various economic operations were a major source of inspiration for the study of statistics.
What three sorts of statistics are there?
They are (i) the mean, (ii) the median, and (iii) the mode. The study of statistics involves gathering, analyzing, interpreting, presenting, and organizing data in a particular way.
According to the table, the private detective and mathematical activities are the professions that have an average pay over $ 33,500, desired by Jasmine. She must attend college, which she does not want to do, in order to become a math teacher. She can therefore choose to work as a private investigator.
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x/4 -10 =11
Find the value of x
Answer:
x = 84
Hope this helped! If you need to know the steps, just let me know and I'll add it :)
Answer:
Step 1: Simplify both sides of the equation.
x/4−10=11
1/4x+−10=11
1/4x−10=11
Step 2: Add 10 to both sides.
1/4x−10+10=11+10
1/4x=21
Step 3: Multiply both sides by 4.
4*(1/4x)=(4)*(21)
x=84
Answer:
x=84