Determine if each function is linear or nonlinear. Drag each function into a box to correctly classify it.
Answers
y= x/2 -3 , y+3x = 12 and y = x are determined as linear equations , while y=6/x -2 and y= 3x^3 +5 are non-linear equations.
What do you mean by linear equations?A linear equation is a mathematical equation that forms a constant straight line on a graph.
What exactly is a nonlinear equation?Non-linear equations are functional equations that form different types of curves or other non-linear shapes on a graph.
According to the slope-intercept formula of the straight line : y=mx+b
1. y=6/x - 2 ,is not satisfying the above formula of straight line , having x in the denominator, hence it is a non-linear equation.
2. y=x/2-3 , here slope(m)=1/2 and intercept(b)=-3 which are real numbers and satisfy the straight line formula , hence it is a linear equation.
3. y=-3x+12, here slope(m)=-3 and intercept(b)=12 as real numbers and satisfy the straight line graph formula , hence it is a linear equation.
4. y = 3x^3+5, here slope(m)=3x^2 which is not a real number, hence not satisfying the given formula it is a non-linear equation.
5. y = x , here slope(m)=1 and intercept(b) =0 which are real numbers and satisfy the straight line graph formula ,hence it is a linear equation.
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Related Questions
9. The product of 1000 whole numbers is 1000. What is the
largest possible value the sum of these numbers can have?
A) 1000
B) 1992
C) 1993
D) 1999
Answers
Answer:
1000
Step-by-step explanation:
The vertex form of the quadratic function f(x)=-6x^2-60x-151 is f(x)=a(x-h)^2+k
Answers
The values of a, h and k for the given quadratic function are:
a = -6, h = -5 and k = -1
What is vertex form?
This is one way of writing a quadratic function:
f(x) = a(x-h)² +k
(h, k) = vertex
a = vertical stretch
According to the given question:
We're given:
f(x)= -6x² - 60x - 151
To write a quadratic function in vertex form, we must complete the square.
⇒ Put parentheses around the first two terms containing x and x²:
f(x)= (-6x² - 60x) - 151
⇒ Factor out -6 (keeping the x's in the parentheses):
f(x)= -6(x² + 10x) - 151
⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.
⇒ In this case, the coefficient of x is 10.
⇒ Half of this value is 5.
⇒ The square of 5 is 25.
⇒ Add this inside the parentheses:
f(x) = -6(x² + 10x + 25) - 151
⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:
f(x) = -6(x² + 10x + 25) - 151 - (-6 x 25)
f(x) = -6(x² + 10x + 25) - 151 - (-150)
f(x) = -6(x² + 10x + 25) - 151 + 150
f(x) = -6(x² + 10x + 25) - 1
⇒ Finally, complete the square.
Remember: (a + b)² = a² + 2ab + b²
In this case, a is x, and b is 5:
f(x) = -6(x + 5)² - 1
On comparing with f(x) = a(x-h)² +k we get the values of a, h and k as:
a = -6
h = -5
k = -1
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IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
Out of a randomly selected 3700 people from the population, how many of them
would have an IQ less than 66, to the nearest whole number?
Answers
Since we want to find the number of people with an IQ less than 66, which is less than one standard deviation from the mean, we can use the first part of the rule. We know that 68% of the values fall within one standard deviation of the mean, so we can say that 100% * (1 - 0.68) = 32% of the values fall outside of one standard deviation from the mean.
Since the standard deviation of the IQ scores is 15, we can say that 32% of the values fall below the mean - 15 and above the mean + 15. We can also say that 32% of the values fall below 100 - 15 = 85 and above 100 + 15 = 115.
Therefore, out of the 3700 people selected from the population, we can expect that 32% * 3700 = <<32*.01*3700=1184>>1184 of them will have an IQ less than 85 or greater than 115.
Since we are interested in the number of people with an IQ less than 66, we need to subtract the number of people with an IQ greater than 115 from the total. This means that 1184 - (3700 - 1184) = 1184 - 2516 = <<1184-(3700-1184)=1184-2516=-1332>>-1332 of the people selected will have an IQ less than 66.
Since it is not possible for a person to have a negative IQ score, the number of people with an IQ less than 66 is 0.
Write a linear function $f$f with f of 0 is equal to 7$f\left(0\right)=7$f(0)=7 and f of 3 is equal to 1$f\left(3\right)=1$f(3)=1 . $f\left(x\right)=$f(x)=
Answers
The required linear function is
f(x) = -2x+ 7
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Let the linear function f(x) = ax + b
f(0) = 7
a [tex]\times[/tex] 0 + b = 7
b =7
f(x) = ax + 7
f(3) = 1
3a + 7 = 1
3a = 1 - 7
3a = -6
a = [tex]-\frac{6}{3}[/tex]
a = -2
The given linear function is
f(x) = -2x+ 7
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Find the greatest common factor
12=
16=
Answers
Answer:
4
Step-by-step explanation:
it's the best because of my friend its the greatest factor
Please help For each of the following problems, answer the 3 questions (show all
a) What angle upstream must the boat be directed?
b) With what speed will the boat cross the river?
c) How long will it take the boat to reach the opposite shore?
1. The boat can travel 3.5 m/s and the river has a flow of 1.9 m/s. The river is 150m wide.
2. The boat can travel 5 m/s and the river has a flow of 3 m/s. The river is 75m wide.
3. The boat can travel 4.2 m/s and the river has a flow of 1 m/s. The river is 125m wide.
4. The boat can travel 8 m/s and the river has a flow of 5.6 m/s. The river is 110m wide.
Answers
Answer:
Step-by-step explanation:
the answer is a
A 750ml of red wine bottle and has 12% alcohol, 330ml of beer bottle with 5% alcohol. How many bottles of beer do we have to consume in order to be equal in red wine alcohol
Answers
Answer: five beers' worth of alcohol in a bottle of wine.
Step-by-step explanation:
In order to have an equivalent amount of alcohol as red wine, we would need to consume approximately 6 bottles of beer.
To determine how many bottles of beer need to be consumed in order to have an equivalent amount of alcohol as red wine, we can compare the alcohol content in both beverages.
The red wine has a volume of 750 ml and an alcohol content of 12%. This means that the red wine contains 750 ml x (12/100) = 90 ml of alcohol.
The beer has a volume of 330 ml and an alcohol content of 5%. This means that each bottle of beer contains 330 ml x (5/100) = 16.5 ml of alcohol.
To find the number of beer bottles needed to match the alcohol content of the red wine, we divide the total amount of alcohol in the red wine by the amount of alcohol in one beer bottle:
The number of beer bottles:
90 ml / 16.5 ml = 5.45
Since we can't have a fraction of a beer bottle, we round up to the nearest whole number.
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12=7+15x solve for x
Answers
Answer:
x = 1/3
Step-by-step explanation:
12=7+15x
12-7=15x
5=15x
5/15=x
Simplify
x = 1/3
Answer:x=1/3 or x=0.3 I hope this helpful mark me brainlist if correct
Step-by-step explanation:
12=7+15x
Move the variable to the left-hand side and change its sign
12-15x=7
Then move the constant to the right-hand side and change its sign
-15x=7-12
Calculate the difference
-15x=-5
Divide both sides of the equation by -15
x=1/3 or x=0.3
Here are summary statistics for randomly selected weights of newborn girls: n = 36, x-bar = 3222.2 g, s = 686.7 g. Use a confidence level of 95%.
A. Identify the critical value t_a/2 used for finding the margin of error.
Answers
The margin of error, a statistic, is a measure of how much random sampling error there is in survey data.
The margin of error exists 0.07728.
What is meant by margin of error?A statistic known as the margin of error describes how much random sampling error there is in survey data. Less faith should be placed in a poll's results representing the outcome of a population census as the margin of error increases.
A survey's margin of error, also known as the confidence interval, is a measurement of error in the data, particularly when the sampling method of a survey is used. This indicator lets researchers know to what extent survey findings should be taken as representative of the entire community under study.
Given : n = 36
x-bar = 3222.2 g
s = 686.7
Confidence level 95%
The 2 - critical Valve = 2.03
A) Let the equation be
[tex]$S F=\sqrt{\frac{\bar{x}(1-\bar{n})}{n}}$$[/tex]
substitute the values in the above equation, we get
[tex]$& \Rightarrow \sqrt{\frac{(3222.2)(1-3222.2)}{100}} \\[/tex]
SE = 0.03807
B) Margin of error = (0.03807)(2 ×[tex]I_2[/tex] )
Margin of error = 0.07728
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-1+3 (10-12) to the third power divided by -16
Answers
Answer:
0.5
Step-by-step explanation:
-1+3(10-12)^3/-16
-1+3(-2)^3/-16
-1+(-24)/-16
.5
What is the 9th term of the geometric sequence 5, -25, 125,
Answers
Answer: 1953125
Step by Step:
5^9 and because it is an odd exponent it is a positive answer for this problem
Which of the following points is in the solution set of y < 2x²-3x - 12?
(0,-12) | (4,-4) (0,-15) (3,-3) | (-2,1) (-2,2)
Answers
The point [tex]B(1,8)[/tex]is not a solution of the given inequality. Whereas the points [tex]C(-5,10) \text { and } D(3,6) \\[/tex]are the solutions of the given inequality.
What is inequality?
The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
It can be found out simply by substituting [tex](x, y)[/tex] values in the given equation
[tex]y < 2 x^2+3 x-5[/tex]
let us start with the point [tex]3(1,8)[/tex]
here [tex]x=1 \text { and } y=8[/tex] therefore [tex]y < 2 x^2+3 x-5[/tex]
[tex]8 < 2\left(1^2\right)+3(1)-5=2+3-5=0[/tex]
that means, [tex]8 < 0[/tex] which is an incorrect inequality, therefore the point
[tex]B(1,8)[/tex] is not a solution of the given inequality.
similarly, for [tex]C(-5,10)[/tex]
[tex]10 < 2(-5)^2+3(-5)-5=50+15-5=60[/tex]
that is [tex]10 < 60[/tex], which is correct.
therefore[tex]C(-5,10)[/tex] is a solution of the given inequality.
next[tex]D(3,6)[/tex]
[tex]6 < 2(3)^2+3(3)-5=18+9-5=22[/tex]
that is[tex]6 < 22[/tex], which is correct . Therefore the point D is a solution of the given inequality.
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Reflect the point0, -9 across they -axis:
Answers
The point when reflected across the y-axis is (0, -9)
How to reflect the pointFrom the question, we have the following parameters that can be used in our computation:
Point = (0, -9)
Transformation = Reflect the point across the y-axis:
The rule of reflection across the y-axis is represented as
(x, y) = (-x, y)
Substitute the known values in the above equation, so, we have the following representation
Image = (0, -9)
Hence, the image is (0, -9)
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Carlos buys 4 cans of dog food and 6 cans of cat food for $12.00. Then the next week, he purchased 2 cans of dog food and 3 cans of cat food for $6.00. Based on this information, will you be able to figure out the price of one can of each type of canned food in the same manner of operating on two equations? Explain your reasoning.
Answers
We will not be able to figure out the price of one can of each type of canned food in the same manner of operating on two equations.
This is because the equation are identical.
How to calculate the price?Let the dog food be represented by d.
Let the cat food be represented by c.
Since Carlos buys 4 cans of dog food and 6 cans of cat food for $12.00. This will be:
4d + 6c = 12
This cane b reduced to lowest term as 2d + 3c = 6
Then the next week, he purchased 2 cans of dog food and 3 cans of cat food for $6.00. This will be:
2d + 3c = 6
Since the equations are the same, we can't calculate the price.
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Satellites KA-12 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-12 so they can later determine its size. The distance between these satellites is 900 km. From KA-12's perspective, the angle between the UFO and SAL-11 is 60∘. From SAL-11's perspective, the angle between the UFO and KA-12 is 75∘. How far is the UFO from KA-12?
Answers
The distance between UFO and KA-12 is 1229.7 Km
Given,
Satellites KA-12 and SAL-11 have spotted a UFO.
Distance between Satellites KA-12 and SAL-11 = 900 km
Angle between UFO and SAL-11 = 60°
Angle between UFO and KA-12 = 75°
We have to find the distance between UFO and KA-12;
Here,
Consider as a triangle;
Sum of interior angles of a triangle = 180 degree
So,
The third angle here will be = 180 - 60 + 75 = 180 - 135 = 45°
Now, use sin rule;
x / sin 75 = 900 / sin 45
x = sin 75 × 900 / sin 45
x = 900 × 0.966 / 0.707
x = 869.4 / 0.707
x = 1229.7
That is,
UFO is 1229.7 Km far from KA-12
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can you plant a tree in early spring when you planted a tree it was_feet tall tree grows at a constant rate every year it grows_feet.
Answers
You plant a tree in early spring. When you planted a tree it was 2 feet tall. The tree grows at a constant rate. Every year it grows ⅔ feet.
What is season of spring?The spring season is the season of the year that occurs between winter and summer which is characterized by a gradual increase in temperature.
From the graph given in the diagram above, the X axis represents the number of years while the y axis represents the height of the trees in feet.
From the table, when X is 0; Y is 2. This means that when the tree was planted, it was 2 feet tall.
Also from the table, if after every 3 years the tree = 4 feet which is 2 feet difference from start. It then means that each year would be ;
3 years = 2 feet
1 year = 2/3 feet
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20x-45y=650 solve for x
Answers
Answer:
x = 45y + 650/2
Step-by-step explanation:
20x - 45y = 650
20x - 45y + 45y = 650 + 45y
20x = 650 + 45y
20x/20 = (650 + 45y)/2
x = 45y + 650/2
Thus, The value of x is 45y + 650/2
Help me out please. Easy points
Answers
Answer: 12/15
Step-by-step explanation:
John earns $500 in a work week. A regular work week for John consists of 5 work days with 8 hours a day. How much does John earn each hour?
Answers
Answer:
$12.5
Step-by-step explanation:
500/40 = 12.5
The coefficient of in the expansion of ( + 3)( - 1) is?
Answers
Answer:
-3
Step-by-step explanation:
3 times negative 1 is -3 since a positive times a negative is a negative
hopes this helps
Which equation correctly compares the hundreds place and tens place in 5,555? A. 50 ÷ 5 = 10 B. 500 ÷ 50 = 10 C. 500 ÷ 5 = 100 D. 5,000 ÷ 50 = 100
Answers
Answer:
B
Step-by-step explanation:
Answer:
Step-by-step explanation:
The answer is B. 500 / 50 = 10
because the first place is the thousands place and the next is hundreds place and then the next is tens place and lastly the next is the ones places
its pretty much in order.
Write a recursive formula that defines the following sequence f(1)=1, f(2)=9, f(3)=17, f(4)=25, f(5)=33.
Answers
The recursive formula for the sequence f(1)=1, f(2)=9, f(3)=17, f(4)=25, f(5)=33 is aₙ₋ =aₙ₋₁ +d
How to determine the recursive formula?We should know that a recursive sequence is a sequence in which the terms are gotten using one or more previous terms along with an initial condition.
The given sequence is f(1)=1, f(2)=9, f(3)=17, f(4)=25, f(5)=33
This forms an Arithmetic Progression (AP)
The terms are 1, 9, 17, 25, 33, ...
The common different is 9-1 = 8
The terms are
a₁, a₂+d, a₃+d, a₄+d, + .....+ aₙ+(n-1)d
Therefore the The recursive formula for the sequence f(1)=1, f(2)=9, f(3)=17, f(4)=25, f(5)=33 is aₙ₋ =aₙ₋₁ +d
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4/10 in simplified form
Answers
Answer:
2/5
Step-by-step explanation:
SOLVE EACH PROPORTION
Answers
The linear equation can be solved by using arithmetic operation the answer for 13 is 27/4 etc.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
13)
9/16 = x/12
x = 27/4
14)
(x - 13)/18 = 12/9
x = 37
15)
7/11 = 18/(x+1)
x = 191/7
16)
(3x-4)/14 = 9/10
x = 83/15
17)
17/15 = 10/(2x -2)
x = 92/17
18)
(x - 16)/(x + 6) = 3/5
x = 49
Thus, the linear equation can be solved by using arithmetic operation the answer for 13 is 27/4 etc.
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Question 2 of 3
What is the rule for this pattern?
17, 20, 19, 22, 21 …
A. Start with 17, then add 3 and subtract 2 repeatedly.
B. Start with 17, then add 4 and subtract 1 repeatedly.
C. Start with 17, then add 2 and subtract 3 repeatedly.
D. Start with 17, then add 3 and subtract 1 repeatedly.
Answers
Answer: B
Step-by-step explanation:
the equation of a line is y = 4x + 8
what is the y-intercept of the line?
Answers
Answer:
The y-intercept is 8.
A line passes through the points (16, 20) and (10, 14). What is its equation in slope-intercept form?
Answers
Answer:
y= x +4
Step-by-step explanation:
2 point form : y -20 = x- 16
slope intercept form: y = x + 4
Please help asap, I will mark the brainliest
Answers
Hi!
The parrot starts off knowing 60 phrases at time 0.
This is the y intercept, it occurs at x = 0
A point is (x, y)
at 0, the line is equal to 60
the y intercept is (0, 60)
Each night, the parrot learns one bad phrase.
Equation of a line given y intercept and slope is
y = mx + b
y (answer of equation) = m (slope) x(input of equation) + b (y intercept)
Slope is 1 because every time a day passes, it learns a new phrase.
y = 1x + 60
y = x + 60
Hope this helps,
Jeron
An example of civic virtue is
A) doing chores around the house
B) supporting local sports teams
C) attending and graduating from college
D) volunteering for a community program
Answers
Therefore, the correct answer is D) volunteering for a community program.
multiplications of matrices
Answers
The value of matrix multiplication is
a) [tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]
b) [tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the first be A
[tex]A = \left[\begin{array}{ccc}1 &2 \\ 3 & 4 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}4 &6 \\ 5 & 7 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}1\cdot \:4+2\cdot \:5&1\cdot \:6+2\cdot \:7\\ 3\cdot \:4+4\cdot \:5&3\cdot \:6+4\cdot \:7\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]
b)
Let the first matrix be A
[tex]A = \left[\begin{array}{ccc}3 &5 \\ 4 & 6 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}-1 &0 \\ 2 & 7 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}3\left(-1\right)+5\cdot \:2&3\cdot \:0+5\cdot \:7\\ 4\left(-1\right)+6\cdot \:2&4\cdot \:0+6\cdot \:7\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]
c)
Let the first matrix be A
[tex]A = \left[\begin{array}{ccc}4 &6 \\ 5 & 7 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}1 &2 \\ 3 & 4 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}4\cdot \:1+6\cdot \:3&4\cdot \:2+6\cdot \:4\\ 5\cdot \:1+7\cdot \:3&5\cdot \:2+7\cdot \:4\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]
d)
Let the first matrix be A
[tex]A = \left[\begin{array}{ccc}-1 &0 \\ 2 & 7 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}3 &5 \\ 4 & 6 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}\left(-1\right)\cdot \:3+0\cdot \:4&\left(-1\right)\cdot \:5+0\cdot \:6\\ 2\cdot \:3+7\cdot \:4&2\cdot \:5+7\cdot \:6\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]
Hence , the matrix multiplication is solved and the results are given
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