Answers
Hi! I'm happy to help! (sorry for the wait, my computer crashed)
A linear function is where one variable is independent (x), and another is dependent. This means that we use x to solve for y, y depends on x to be found.
To solve this, we use an equation call slope intercept form, which states that y=mx+b.
There is only 1 solution line. (to solve for how to find y, you only have to have two verifications)
For our first table, we have x as 1, 2, 3,and 4. y is 3, 6, 12, and 24.
For our first set, with x is one and y is 3, there are infinite solutions, so we have to test and see if it matches the second set of x is 2 and y is 6.
How I like to check for what m will be, I check the first two y values. The first two are 3 and 6. They have an increase of 3, so m will be 3. (this only works when x increases by 1)
With m being 3, we can solve for b, to complete the equation:
3=(3(1))+b
3=3+b
With this, b must equal 0
3=3+0
Now, we just have to check if this equation matches all of the other x values:
6=(3(2))+0
6=6+0
__________________________________
12=(3(3))+0
12=9+0
12≠9
This equation doesn't seem to work, so this is not a linear function.
For our next table, our first two y values are 2 and 5, which have a increase of 3, so our m will be 3 again.
Now, let's solve for b:
2=(3(1))+b
2=3+b
In this case, b will be -1 because 2=3-1
Now, let's check if this matches up with our other values:
5=((3)2)-1
5=6-1
_______________________________
9=((3(3)-1
9=9-1
9≠8
This equation doesn't work, so it is not a linear function.
For our next table, we have our first two y values as -3, and -5. This has a decrease of 2, so our m will be -2.
Now, let's solve for b:
-3=((-2)1)+b
-3=-2+b
In this equation, b will be -1 because -3=-2-1.
Now, let's check our other values:
-5=(-2(2))-1
-5=-4-1
___________________________________________
-7=(-2(3))-1
-7=-6-1
______________________________________________
-9=(-2(4)-1
-9=-8-1
All of these values match, so this is a linear function.
If you wanted to (you don't have to, but if you needed verification) you could check the fourth problem.
Has a decrease of 2, so m would be -2. Plug it in:
-2=(-2(1))+b
-2=-2+b
b would be 0.
Check it on the second problem:
-4=(-2(2))+0
-4=-4+0
Check the third:
-2=(-2(3))+0
-2=-6+0
-2≠-6
The fourth table doesn't match either, so it is not a linear function.
You should choose option 3 because it is a linear function.
I hope this was helpful, keep learning! :D
Related Questions
whats the product for (2z-3)^3
Answers
Answer:
8z^3-36z^2+54z-27
Step-by-step explanation:
(2z-3)^3
(2z)^3*(2z)^2*3+3*2z*3^2-3^3
8z^3-3*4z^2*3+3*2z*9-27
8z^3-36z^2+54z-27
Answer:
\(8z^3-36z^2+54z-27\)
Step-by-step explanation:
\((2z-3)^3\\(2z-3)(4z^2-12z+9)\\2z(4z^2-12z+9)-3(4z^2-12z+9)\\8z^3-24z^2+18z-12z^2+36z-27\\8z^3-36z^2+54z-27\)
N/5 = -1/5 what is n?
Answers
Answer:
n = -1
Step-by-step explanation:
→The fraction \(\frac{n}{5}\) is really just \(\frac{1}{5}n\):
\(\frac{1}{5}n = \frac{-1}{5}\)
→To get n by itself, you must multiply both sides by the reciprocal of \(\frac{1}{5}\), which is 5:
5 · \(\frac{1}{5}n = \frac{-1}{5}\) · 5
n = -1
For a criminal trial, 8 active and 4 alternate jurors are selected. Two of the alternate jurors are male and two are female. During the trial, two of the active jurors are dismissed. The judge decides to randomly select two replacement jurors from the 4 available alternates. What is the probability that both jurors selected are female
Answers
Answer:
The answer would be 1/6
The probability that both jurors selected are female is 1/6.
GivenFor a criminal trial, 8 active and 4 alternate jurors are selected.
Two of the alternate jurors are male and two are female.
During the trial, two of the active jurors are dismissed.
The judge decides to randomly select two replacement jurors from the 4 available alternates.
Total numbers of selected candidates is;
8 + 4 = 12
The judge decides to randomly select two replacement jurors from the 4 available alternates.
Therefore,
The probability that both jurors selected are female is;
\(= \dfrac{2}{12}\\\\= \dfrac{1}{6}\)
Hence, the probability that both jurors selected are female is 1/6.
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Given: ∆MNP, PM = 8 m∠P = 90°, m∠N = 58° Find: Perimeter of ∆MNP
(Not 22.4 or 22.43)
Please answer ASAP, brainly awarded.
Answers
Answer:
Step-by-step explanation:
Triangle MNP is a right triangle with the following values:
m∠P = 90°m∠N = 58°PM = 8Interior angles of a triangle sum to 180°. Therefore:
m∠M + m∠N + m∠P = 180°
m∠M + 58° + 90° = 180°
m∠M + 148° = 180°
m∠M = 32°
To find the measures of sides MN and NP, use the Law of Sines:
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
Substitute the values into the formula:
\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)
\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)
Therefore:
\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)
\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)
To find the perimeter of triangle MNP, sum the lengths of the sides.
\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)
Which expressions are equivalent?
Select Equivalent or Not equivalent for each pair of expressions
3(a−b) and 3a−3b
– 3( a−b ) and 3a−3b
– 3( a−b ) and 3a−3b
2a(2+b) and 4ab
Answers
Answer:
3(a-b) and 3a-3b. Equivalent
2a(2+b) and 4ab. Not equivalent
Step-by-step explanation:
hope this helps:)
the carrying capacity for a population of elk is 52. there are currently 33 elk in the population. the intrinsic growth rate of elk is 0.2 per year. how many elk will be in the herd one year from now? round to a whole number, up or down (we will accept either)
Answers
There will be 38 elk in the herd one year from now, rounded to a whole number.
To solve the given problem, we must use the formula for exponential growth or decay.
We'll use the following formula:
N = N0ert
Where,N is the final population;
N0 is the initial population;
r is the intrinsic growth rate;
e is the base of the natural logarithm; and
t is the time (in years).
According to the problem, the carrying capacity for a population of elk is 52, and there are currently 33 elk in the population.
The intrinsic growth rate of elk is 0.2 per year. We need to find out how many elk will be in the herd one year from now, rounded to a whole number.
Using the formula above, we can write:
N = 33e0.2 × 1= 37.98 ≈ 38
Therefore, there will be 38 elk in the herd one year from now, rounded to a whole number. Answer: 38.
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how is quantitative data from census and survey data provide information about changes in population composition and size in urban areas
Answers
Quantitative data from census and survey data play a crucial role in providing information about changes in population composition and size in urban areas.
These data sources collect numerical information on various demographic characteristics of the population, such as age, gender, ethnicity, education level, income, occupation, and household size. By analyzing this quantitative data, researchers and policymakers can gain insights into the following aspects:
Population Size: Census and survey data provide accurate and comprehensive counts of the population in urban areas. They help determine the total number of individuals residing in specific geographic regions, allowing for the identification of population growth or decline over time.
Population Density: Quantitative data can reveal the concentration of population in urban areas by assessing the number of individuals per unit area. This information is crucial for urban planning, resource allocation, and infrastructure development.
Age Structure: Census and survey data provide information on the age distribution of the urban population. By examining age cohorts and changes over time, it is possible to identify trends such as population aging, shifts in generational composition, and potential implications for healthcare and social services.
Ethnic and Racial Composition: Quantitative data allow for the identification of ethnic and racial groups within urban areas. This information helps monitor changes in diversity and assess the impact of migration patterns, assimilation, and integration processes.
Socioeconomic Characteristics: Census and survey data capture information on income levels, educational attainment, employment status, and occupation. Analyzing these variables provides insights into the socioeconomic composition of urban populations, disparities, and potential social and economic challenges.
Housing and Household Characteristics: Quantitative data provide information on housing types, tenure, overcrowding, and household size in urban areas. This data is valuable for urban planning, housing policies, and understanding the dynamics of residential patterns.
By utilizing quantitative data from censuses and surveys, researchers and policymakers can monitor changes in population composition and size, identify social and economic trends, inform policy decisions, and address the specific needs and challenges of urban areas.
The complete question is:
Explain how quantitative data from census and survey data provide information about changes in Population composition and size in urban areas.
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The top question. X= y= z=
Answers
Answer:x=76, y=76,z= 56
Step-by-step explanation:
x | f(x)
2.0 | 2.8
2.5 | 1.1
3.0 | –0.8
3.5 | –1.2
4.0 | –0.3
4.5 | 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A. between 2.0 and 2.5 and between 4.0 and 4.5
B. between 2.5 and 3.0 and between 4.0 and 4.5
C. between 2.0 and 2.5 and between 3.5 and 4.0
D. between 2.5 and 3.0 and between 3.5 and 4.0
Answers
Answer:
Option B.
Step-by-step explanation:
If the value of function is 0 at x=c, then c is a root or zero of the function. It means the graph of function intersect x-axis at its zeroes.
From the given table it is clear that the value of function are
x | f(x) | Sign
2.0 | 2.8 | Positive
2.5 | 1.1 | Positive
3.0 | –0.8 | Negative
3.5 | –1.2 | Negative
4.0 | –0.3 | Negative
4.5 | 0.7 | Positive
The sign of values of function changes in interval 2.5-3.0 and 4.0-4.5.
It means, the graph of function must intersect x-axis in interval 2.5-3.0 and 4.0-4.5. So, the zeros of the function lie between 2.5 and 3.0 and between 4.0 and 4.5.
Therefore, the correct option is B.
Answer:
between 2.5 and 3.0 and between 4.0 and 4.5
Step-by-step explanation:
B on my computer but always double check!
Write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (−6,5) and is perpendicular to the line whose equation is x=−3.
Answers
The slope-intercept equation of the line is: y = 5
Here, we have,
The equation x = -3 represents a vertical line parallel to the y-axis.
The line perpendicular to this vertical line will be a horizontal line parallel to the x-axis.
Since the line is horizontal, its slope is 0.
Therefore, the slope-intercept equation of the line can be written as:
y = b
where b is the y-intercept.
We know that the line passes through the point (-6, 5).
Plugging in these coordinates into the equation,
we get:
5 = b
Therefore, the slope-intercept equation of the line is:
y = 5
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When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. How tall wa the buh after the two week
Answers
When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is \(\\26 \frac{2}{5}\).
What is improper fractions?
An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.
12 times 120% + 12
12*120%+12
\($$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$\)
Follow the PEMDAS order of operations
Multiply and divide (left to right) \($12 \times \frac{6}{5}: \frac{72}{5}$\)
\(=\frac{72}{5}+12$$\)
Add and subtract (left to right) \($\frac{72}{5}+12: \frac{132}{5}$\)
\(=\frac{132}{5}$$\)
Convert improper fractions to mixed numbers: \($\frac{132}{5}=26 \frac{2}{5}$\)
\(=26 \frac{2}{5}$$\)
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Which of the following are assumptions underlying the simple linear regression model y = Bo B1x e? Check all that apply The variance of the error term e varies for differing values of x. The error term is a random variable with an expected value of zero. The error term is normally distributed. The error term E follows a chi-square distribution.
Answers
The error term is a random variable with an expected value of zero.2. The error term is normally distributed
The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.
The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.
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Using the discriminate. Find the number of real solutions. 2^2+7x-15=0
Answers
Answer:
= 11/7
Step-by-step explanation:
Is dilated by a scale factor of 1. 3 with the origin as the center of dilation to create the image. If the slope and length of are m and l respectively, what is the slope of ? A. 1. 3 m B. 1. 3 l C. 1. 3 (m l) D. M.
Answers
The slope of line XY will be = 1.3l
It is given that XY is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the image X'Y'.
What will be the slope of the line XY?Let the slope and length of XY are m and l respectively.
The dilation shows the enlargement or contraction of the figure. If the scale factor is more than 1 , then it shows enlargement.
If the scale factor is more than 0 but less than 1 , then it shows contraction.
The corresponding sides of image and pre image are parallel to each other. Since the slope of parallel line are equal therefore the slope of XY and X'Y' are equal, i.e., m.
The length of the image is k times of the length of preimage. The length of X'Y' is
X'Y'=XY=1.3l
Hence the slope of line XY will be = 1.3l
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Write the slope intercept equation for given points (3,-1),(5,5)
Answers
Answer:
Hi! The answer to your question is \(y=3x-10\)
Step-by-step explanation:
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Hope this helps!!
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Answer:
y = 3x - 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (3, - 1) and (x₂, y₂ ) = (5, 5)
m = \(\frac{5+1}{5-3}\) = \(\frac{6}{2}\) = 3 , then
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (5, 5 ) , then
5 = 15 + c ⇒ c = 5 - 15 = - 10
y = 3x - 10 ← equation of line
Help me pleas please can i get help
Answers
Answer:
I can't see the question
Step-by-step explanation:
Pls answerrrrr
with simple working
Answers
the answer will be -137
The garden club plants a rectangular garden that.
has been divided into six sections. the members
want to find the area of the sections they planted
with herbs. roberto says they can use the
expression 2(3)+2(3). jay says they can use the
expression (4.9) 3. why are both students
correct? explain your reasoning.
lution
lettuce
3 ft
herbs
2 ft
2 ft
3 ft
3 ft
tomatoes
Answers
Yes, Both the students are correct because both students calculate the area of a rectangular garden.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
Roberto says they can use the expression;
⇒ 2(3)+2(3)
And, Jay says they can use the expression;
⇒ (4.9) 3
Now,
Since, The garden club plants a rectangular garden that.
And, It has been divided into six sections.
Here, The members want to find the area of the sections they planted with herbs.
Roberto says they can use the expression;
⇒ 2(3)+2(3)
Clearly, Robert find the area of garden as;
⇒ 2(3)+2(3) = 12 ft²
And, Jay find the area of garden as;
⇒ (4.9) 3 = 14.7 ft²
Thus, Both the students are correct because both students calculate the area of a rectangular garden.
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Which form of linear equation do you prefer to use: slope-intercept form or point-slope form? List advantages and disadvantages of each.
Answers
Answer:
slope-intercept form
Step-by-step explanation:
point-slope form takes more time to solve, but is also helpful. slope-intercept form is easy but gets harder when you have fractions and decimals.
1. If f(x) = (3x-2)/(2x+3), then f'(x) =
Answers
Answer:
\(f'(x)= \frac{13}{(2x+3)^2}\\\)
Step-by-step explanation:
\(f(x)= \frac{3x-2}{2x+3} \\\)
\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)
\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)
Six equal pieces are cut of a rope of 24/5m. Find length of each piece
Answers
Answer:4 / 5 m
Step-by-step explanation:
In this question, we need to divide the length of the rope by the number of pieces to get the length of each piece.
The length of the rope 24/5 is m
Six equal pieces are cut of a rope, so the length of each piece is:
24/5
6
=4/5m
Answer:
\(\frac{4}{5}\) m
Step-by-step explanation:
\(\frac{24}{5}\) / 6 = \(\frac{24}{5}\) / \(\frac{6}{1}\) = \(\frac{24}{5}\) x \(\frac{1}{6}\) = \(\frac{24}{30}\) = \(\frac{4}{5}\)
what is the diameter of 12mm and 8mm
Answers
Answer:
diameter 12mm
Step-by-step explanation:
select the story problem that this this division problem represents 3/4 divided by 1/3
Answers
Answer:
3/4 divided by 1/3 would equal 2 1/4 or 2.25.
Which are true and which are false?
Answers
The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.
What is the Volume of a Cone and Volume of a Cylinder?The volume of cone (V) = 1/3 * πr²h
Volume of cylinder (V) = πr²h
Where, r is the radius of their bases.
The base area formula for the cone = πr²
Calculate the area of the base of the cone that has a radius (r) of 2.5 in:
Area of the base of the cone = π(2.5)² ≈ 19.6
The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5
≈ 42.5 cubic inches
Volume of cylinder (V) = πr²h = π * 2² * 4
≈ 50.3 cubic inches
The difference in volume = 50.3 - 42.5
= 7.8 ≈ 8 cubic inches
Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.
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Mary has $15.63 left in her wallet after spending $8.01 on snacks. How much did she have in her wallet before she bought the snacks? (Do not put the $ sign in your answer. Just type the amount without the $ sign.
Answers
Solve this system of linear equations. Separate
the x- and y-values with a comma.
15x + 4y = -80
5x + 5y = 10
Answers
Answer:
(-8,10)
Step-by-step explanation:
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The area of the composite shape shown is
ft2
6 ft
T
2 ft
1
5 ft
3 ft-
Answers
Answer:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.
Step-by-step explanation:
there
if p varies inversely as the square root of q, and p=12 when q=36, find p when q=16
Answers
Answer:
Step-by-step explanation:
p = k / sqrt(q)
The first job is to find k.
p = 12
q = 36
Solution for k
12 = k / sqrt(36)
sqrt(36) = +/- 6
Multiply both sides by +/-6
12 * +/- 6 = k
k = +/- 72
Solution for q = 16
p = +/-72/ sqrt(16)
p = +/- 72 / sqrt(16)
p = +/- 72 / +/-4
p = 18
Use the Phytagorean Theorem to answer the problem
The size of a TV screen is given by the length of its diagonal. If the dimension of a TV screen is 16 inches by 30 inches, what is the size of the TV screen?
Answers
The size of the TV screen, represented by the length of its diagonal, is 34 inches.
To find the size of the TV screen, we can use the Pythagorean theorem. The diagonal of a rectangle can be considered as the hypotenuse of a right triangle, with the length and width of the rectangle as the other two sides.
Let's denote the length of the rectangle as L = 30 inches and the width as W = 16 inches. The size of the TV screen is the length of the diagonal, which we'll represent as D.
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse. In this case, we have:
D^2 = L^2 + W^2
Substituting the values, we get:
D^2 = 30^2 + 16^2
D^2 = 900 + 256
D^2 = 1156
Taking the square root of both sides, we find:
D = √1156
D = 34
Therefore, the size of the TV screen, represented by the length of its diagonal, is 34 inches.
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Can someone please help with this kind of problem, I tried multiple times but still didn't get a correct answer. I'd appreciate so much! :(
Answers
The probability that the spinner lands on a gray is 6/8 or 3/4 while the probability that the spinner lands on a blue is 2/8 or 1/4.
Since the probabilities are independent of each other, we simply multiply the probabilities of the two. Thus, we get the following.
\(P(G)\cdot P(B)=\frac{3}{4}\cdot\frac{1}{4}=\frac{3}{16}\)