Answer:
2 I.e 3 and 7
Step-by-step explanation:
(L U K)={0,3,4,7} [ elements are not repeated in set ]
odd numbers = 3 & 7
The graph of a function f is illustrated below. What is the graph of the inverse function of f?
The graph of the inverse function of f(x) is given by the image shown at the end of the answer.
How to obtain the inverse function?The function in this problem is defined as follows:
f(x) = 1/x + 4.
The definition of the function is given because of the asymptotes as follows:
Vertical asymptote at x = 0 -> function is not defined at x = 0.Horizontal asymptote at y = 4 -> when x goes to infinity, y goes to 4.To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:
x = 1/y + 4.
Then the variable y has to be isolated, as follows:
1/y = (x - 4).
y(x - 4) = 1
y = 1/(x - 4)
Meaning that the inverse function is defined as follows:
[tex]f^{-1}(x) = \frac{1}{x - 4}[/tex]
Which has the graph given by the image shown at the end of the answer.
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Answer: B
Step-by-step explanation: literally just did it
Dr. Sparrow is a social psychologist who studies romantic relationships. Several researchers have found that there is a link between income and marital satisfaction (e.g., Dakin & Wampler, 2008). Dr. Sparrow is curious as to whether there is a causal link between the two variables, such that having a higher income causes higher levels of marital satisfaction. He is confident that he cannot reasonably or ethically manipulate people's income level, so he decides to use a multivariate design. He is also curious as to whether there is a causal link between these two variables or if two other variables (number of arguments and life satisfaction) can explain the relationship. He measures his three variables in a sample of 124 married couples recruited from a local community center. Below are his results.
DV: Marital Satisfaction
Variable Beta (b) Significance ( p)
Income
.69
.03
Number of arguments
-.73
.01
Life satisfaction
.13
.81
Refer to Research Study 9.2 to answer the following four questions.
Given Dr. Sparrow's design, which of the following problems is his study best able to overcome?
Given Dr. Sparrow's design, his study is best able to overcome the issue of causality, as well as the issue of some potential third variables.
By using a multivariate design, Dr. Sparrow is able to examine the relationships between multiple variables simultaneously, which can help to identify the potential influence of each variable on the outcome of interest (marital satisfaction in this case). This can help to establish a causal link between the variables if one is present, as it allows for the examination of multiple variables at the same time, rather than just two variables as in a simple bivariate design.
Additionally, by controlling for other potential confounding variables, Dr. Sparrow is able to account for the potential influence of these variables on the relationship between income and marital satisfaction, which helps to establish a more robust understanding of the potential causal link between these two variables.
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PLEASE HELP
An equation of a line is shown. A second line is perpendicular to the given line and passes through the point (0,1).
Which is the equation of the perpendicular line?
The equation of the perpendicular line is (c) y = 2/9x - 1
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y + 17 = -9/2(x - 3)
Also, from the question;
We have the following points
Point = (0, -1) i.e. (x, y) = (0, -1)
The equation of a line can be represented as
y - y₁ = m(x - x₁)
Where
Slope = m
By comparing the equations, we have the following
m = -9/2
This means that the slope is -9/2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is 2/9
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = 2/9
(x₁, y₁) = (0, -1)
So, we have
y + 1 = 2/9(x - 0)
Evaluate
y = 2/9x - 1
Hence, the line has an equation of y = 2/9x - 1
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Match the following graph with the name of the graph
Absolute value: C
Quadratic: D
Constant: A
Square root: E
Linear: B
There are the equations for the graphs on the bottom:
y=2 is constant because the y value never changes
y=x is linear because the y value changes at a constant rate
y= |x| is absolute value because |x| is the absolute value of x
y=x^2 is quadratic because quadratic functions have a degree of 2
y=sqrt(x) is a square root because y= square root of x
Use the information below to complete the problem: p(x) = 1/(x+1) and q(x)= 1/(x-1) Perform the operation and show that it results in another rational expression. p(x) / q(x)
Answer:
p(x)/q(x) = (x+1)/(x-1)
Step-by-step explanation:
see image.
p(x)/q(x) is just dividing the two functions. So we'll put p(x) on top and q(x) on the bottom.
Now it looks like a fraction over a fraction. Use Keep-Change-Flip to simplify. Keep the top. Change the divide to times. Flip the bottom. See image.
(You can always use Keep-Change-Flip for numbers only, radicals, and algebraic expression in fraction over a fraction situations)
To multiply fractions, multiply top×top and bottom×bottom straight across.
see image.
In art class students are mixing blue and red paint to make purple paint. Hassan
mixes 1 cup of blue paint and 3 cups of red paint. Skylar mixes 5 cups of blue paint
and 3 cups of red paint. Whose purple paint will be bluer?
The person whose purple paint will be bluer is Skylar.
Whose purple paint will be bluer?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Hassan mixes 1 cup of blue paint and 3 cups of red paint. The percentage for blue paint will be:
= 1 / (1 + 3) × 100
= 1/4 × 100
= 25%
Skylar mixes 5 cups of blue paint and 3 cups of red paint. The percentage for blue will be:
= 5 / (5 + 3) × 100
= 5/8 × 100
= 62.5%
Skylar has bluer paint.
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Try it
Using a Grid to Estimate Perimeter
Estimate the perimeter of the figure if each block on the
grid is 1 square unit.
The perimeter of the figure is about
units.
The Perimeter of of the Figure is shown below.
What is Scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object. If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined.
Gives:
We have area of each small square is 1 sq cm.
So, We have three grids a
For figure (i) there are 11 small square
So, Perimeter of the given figure =( 18 ×1)cm
=18 cm
For figure (ii) there are 13
Perimeter of the given figure =(28×1)cm
=28 cm
For figure (iii) there are 13
Perimeter of the given figure =(28×1)cm=28 cm.
=28 cm
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Emily go out to dinner eight times a month the average cost is $35 per meal how much does she spend each month? How much cause she save if she cut back to five times a month?
Answer:
She spend $280 a month when she goes out to eat 8 times a month.
She will save $105 a month if she cuts back to 5 times a month.
Step-by-step explanation:
35 x 8= 280
35 x 5 = 175
280 - 175 = 105
Answer:
8 * $35 per meal = $280
She spends $280 per month for 8 dinners$280 - (5 * $35)
= $280 - ($175)
= $105
Therefore, Emily will save $105 if she eats 5 times a month only.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Write 28 as a product of prime factors.
Answer: 2×2×7
The prime factorization of 28 = 2×2×7.
Step-by-step explanation: Do the prime factorization
28
7 4
2 2
i am very confused on this question
It will take kangaroo 7.5 minutes to travel 5 kilometers.
The kangaroo will travel 1.33 kilometers in 2 minutes.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Kangaroo hopes 2 kilometers in 3 minutes.
To find the time taken by kangaroo to travel 5 kilometers,
Use ratio property,
2 kilometers = 3 minutes,
1 kilometer = 3/2 minutes
5 kilometer 15/2 minutes.
In 15/2 or 4.5 minutes, kangaroo will travel 5 kilometers.
The distance travelled by kangaroo in 2 minutes,
In 3 minutes = 2 kilometers covered
in 1 minute = 2/3 kilometers covered
in 2 minutes = 4/3 kilometers will be covered.
So in 2 minutes the kangaroo will cover 4/3 or 1.33 kilometers.
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the difference between the measure of two supplementary angles is 92. find the measure of both angles.
The measure of both angles on calculation is found to be 44° and 136° respectively.
What are supplementary angles ?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.
Given : difference between the measure of two supplementary angles is 92 .
Let the two angles be x and y then , x - y = 92
Since , supplementary angles add up to 180 degrees
x + y = 180 (say 1)
x - y = 92(say 2)
---------------add(1 & 2)
2x = 272
x = 272/2
x = 136 <=== this is one angle
x + y = 180
136 + y = 180
y = 180 - 136
y = 44 <=== this is the other angle
Hence , the measure of both angles on calculation is found to be 44° and 136° respectively.
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In ΔVWX, x = 77 cm, ∠X=74° and ∠V=16°. Find the length of w, to the nearest 10th of a centimeter.
Answer:
The length of w is 50.0 cm.
Step-by-step explanation:
To find the length of w, we can use the Law of Sines:
w / sin V = x / sin X
Plugging in the values given in the question, we get:
w / sin 16° = 77 cm / sin 74°
Solving for w, we get:
w = 50.0 cm
Rounding to the nearest 10th of a centimeter, we get:
w = 50.0 cm
Therefore, the length of w is 50.0 cm.
Answer:
w=80.1 cm
Step-by-step explanation:
According to the Law of Sines:
[tex]\frac{\sin(\alpha)}{a}=\frac{\sin(\beta)}{b}=\frac{\sin(C)}{c}[/tex]
For this problem, let
[tex]\alpha[/tex]=∠X=74°
[tex]\beta[/tex]=∠V=16°
Since the sum of the angle measures in all triangles must equal 180°, ∠w must equal 90°. So, for this problem, let
C=∠W=90°.
And let
a=x=77 cm
c=w
So,
[tex]\frac{\sin(74)}{77\ cm}=\frac{\sin(90)}{w}\\0.01248\ cm=\frac{1}{w}\\w=80.1\ cm[/tex]
This can be checked using the Law of Sines with all values entered.
To find b, use the Pythagorean Theorem:
[tex](80.1\ cm)^2=(77\ cm)^2+b^2\\6416.01\ cm^2=5929\ cm^2+b^2\\487.01\ cm^2=b^2\\b=22.07\ cm[/tex]
So,
[tex]\frac{\sin(74)}{77\ cm}=\frac{\sin(16)}{22.07\ cm}=\frac{\sin(90)}{80.1\ cm}\\0.0125\ cm=0.0125\ cm=0.0125\ cm[/tex]
8x10^-5
help pleaseeeeeeeeeeeeeeeeeeeeeeeee
Answer:
.00008
Step-by-step explanation:
8x10^-5 = .00008
Your moving the dot over 5 times to the left since its negative. If it was postive you wold move the dot 5 times to the right
Answer: 0.00008
Step-by-step explanation: Yes, I know there are A LOT of zeros. So, to find this answer, you would rewrite the answer like this:
- 8*10^(-5)
So, here's a little trick, you multiply 8 by 10, to get 80. Then, since it is -5, you move 5 decimal places to the LEFT. This is why there are so many zeros. I hope this explanation helped!
Neils refrigerator has stopped working and he needs to get a new one. He purchases a new ref for P36,700. He paid a 10% deposit and obtain a loan for the balance. The interest charged on the loan was 7.5% APR compounded annually. He repaid the loan and interest in equal monthly installment for over a period of two years. Calculate the loan he made and the total amount to be repaid.
a) The loan that Neil made for the purchase of a new refrigerator is P33,030.
b) The total amount to be repaid over a period of two years is P35,672.16.
What is the loan amount?The loan amount is the difference between the purchase price of a new refrigerator and the deposit (down payment).
The total amount to be repaid over the loan period includes the loan amount and the interest.
These amounts can be computed using an online finance calculator, including the monthly payments.
The cost of a new refrigerator = P36,700
Deposit (down payment) = 10%
The amount of the loan = P33,030 (P36,700 - P3,670)
N (# of periods) = 24 months (2 years x 12)
I/Y (Interest per year) = 7.5%
PV (Present Value) = P33,030
FV (Future Value) = P0
Results:
PMT = P1,486.34
Sum of all periodic payments = P35,672.16 ($1,486.34 x 24)
Total Interest = P2,642.16
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Which of the following is false about the central limit theorem (CLT)? O If we take more samples from the original population, the sampling distribution is more likely to be nearly normal. O If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. O As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution. O The CLT states that the sampling distribution will be centered at the true population parameter.
Only the first statement is false. The rest are true statements about the Central Limit Theorem.
The Central Limit Theorem (CLT) is a fundamental theorem in probability and statistics which states that, given a sufficiently large sample size from a population with a given mean and standard deviation, the sampling distribution of the mean will be nearly normal, regardless of the shape of the original population distribution.
It is important to note that the first statement presented is false. Taking more samples from the population will not necessarily result in a more normal sampling distribution. The CLT does not guarantee that the sampling distribution will be normally distributed, only that it is more likely to be so as the sample size increases.
The second statement is true. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. The third statement is also true. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.
Finally, the fourth statement is also true. The CLT states that the sampling distribution will be centered at the true population parameter. This means that the mean of the sampling distribution will be equal to the mean of the population.
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Consider 4x + 12 ≤ 28. Which value of x makes the given inequality TRUE?
Responses
A 1010
B 77
C 33
D 6
We know that,
Inequality-
In mathematics, the relationship between two expressions or values that are not equal is called an inequality.
Group terms with the same variable and move the constant to the other side of the inequality
What causes inequality?
Inequality image result
The main factors behind the widening domestic income inequality mentioned in the literature include technological progress, globalization, commodity price cycles, and domestic economic policies such as redistributive fiscal policies, labor and product market policies. It is included.
According to the question,
Given data in the question,
4x + 12 ≤ 28
Substrating (28-12)=16
We can say that,
4x ≤ 16
16 divided by 4.
Therefore,
(16/4)=
x<4
the value of x is less than 4,
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3 is the value of x which makes the given inequality true.
What is Inequality?A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers. To represent various types of inequalities, a variety of notations are used:
A < B, such as a, denotes that an is greater than b.
A > B indicates that an is greater than b.
A and b are not equivalent in either scenario. As a result, an is strictly less than or strictly greater than b, and these relationships are referred to as strict inequalities. Equivalence is disregarded.
According to the question,
Given data in the question,
4x + 12 ≤ 28
Substrating (28-12)=16
We can say that,
4x ≤ 16
16 divided by 4.
Therefore,
(16/4)=
x<4
the value of x is less than 4,
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write an equation in slope intercept form that is perpendicular to y = 8 and passes through the point (-1,-8)
Answer:
Step-by-step explanation it will be 23 cups
How many meters per second are in 37 miles per hour? Round to one
decimal.
Answer:
16.5 m/s
Step-by-step explanation:
Hose A can fill 3/4s of a pool in 1 hour. Hose B can full 2/4s of the same pool in 1 hour. How long will it take to fill the pool if you use both hoses?
The time required to fill the pool by using both the hoses is 4/5 hours.
What is algebra?Algebra is the study of mathematical expressions, in which letters and other generic symbols are used to represent numbers and quantities in formulas and equations.
Given that,
Time taken by hose A to fill 3/4 of the pool = 1 hour.
And time taken by hose B to fill the 2/4 of the same pool = 1 hour.
From the given information,
Time taken by hose A to fill the whole pool = 1 x (4/3) = 4/3 hours
And time take by hose B to fill the whole pool = 1 x (4/2) = 1 x 2 = 2 hours.
The LCM of 4/3 and 2 is 4, which can be considered as total capacity of pool.
The efficiency of hose A = 4/(4/3) = 3
The efficiency of hose B = 4/2 = 2
Total time taken to fill the whole pool by using both hoses
= 4 / (3+2) = 4 / 5 hours
If both hoses are uses, then it will take 4/5 hours to fill the pool.
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You’re involved in the design of a new facility. It is important for people to move between work stations quickly. Based on the figure below, how many feet would a person need to walk to get from Work Station 1 to Work Station 3?
The distance from work station 1 to work station 3 is 13 feet.
How to find the side of a right triangle?The figure shows the distance between workstation. The figure represents a right angle triangle.
The distance from work station 1 to work station 3 can be calculated as follows:
using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore, the distance from work station 1 to work station 3 is the hypotenuse side of the right triangle.
Hence,
5² + 12² = c²
25 + 144 = c²
c² = 169
c = √169
c = 13 ft
The distance between the work stations is 13 ft.
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question 11 options: in a random sample of 64 orders from on online retailer the proportion of orders made by women is 86%. construct a 95% confidence interval for the true population proportion of online orders made by women. round answers to 3 decimal places, i.e., .xxx. do not put as a percent. do not include leading or ending zeros. lower limit
The Lower limit is 0.745 and the Upper limit is 0.976.
In data, an easy random sample is a subset of people (a pattern) chosen from a larger set (a population) wherein a subset of individuals are selected randomly, all with identical possibilities. it is a system of choosing a pattern in a random manner. In SRS, each subset of okay individuals has the identical chance of being chosen for the sample as every other subset of okay individuals. An easy random pattern is an independent sampling approach. simple random sampling is a fundamental sort of sampling and may be an element of other extra complicated sampling strategies.
In statistics, an easy random pattern is a subset of individuals (a pattern) selected from a bigger set (a population) in which a subset of individuals are chosen randomly, all with identical chances. it's far a manner of choosing a pattern in a random way. In a random sample, every subset of okay people has the identical possibility of being chosen for the pattern as any other subset of okay individuals. An easy random pattern is an impartial sampling approach. simple random sampling is a fundamental type of sampling and can be an issue of other extra complex sampling strategies.
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Jonas spent $134 last month eating at restaurants. He decides he needs to spend 36% less
on eating at restaurants this month. How much can he spend at restaurants this month?
Answer:
I think its $12..? if you subtract the two numbers than you should get my answer
how can you divide polynomials
Polynomials can be divided using long division method and
synthetic division method.
What is a polynomial?
Algebraic expressions which are made up of coefficients and variables are called polynomials.
For example x + 3, 3y² -10, r³, t³ + 4t³ - 80, etc.
Polynomials can be classified as monomials, binomials and trinomials based upon the number of terms present.
According to the given question:
There are two methods that can be employed while dividing two given polynomials:
1. Long Division Method
The long division method is the most frequent and general method for dividing polynomials by binomials or any other form of polynomials.
Steps:
Step 1: Divide the dividend’s first term by the divisor’s first term, and use it as the quotient’s first term.
Step 2: Multiply the divisor, then place the product beneath the dividend
Step 3: To make a new polynomial, subtract.
Step 4: Use the new polynomial obtained after subtraction to repeat the operation.
2. Synthetic Division Method
It is a technique for dividing a polynomial by a linear binomial using only the coefficient values. We write the polynomials in standard form from the greatest degree term to the lowest degree term in this manner.
Steps:
Step 1: Ensure that the divisor is in the form of x − k.
Step 2: Write the dividend coefficients on the right and k on the left to set up the division.
Step 3: Now, reduce the coefficient of the dividend’s highest degree term to zero.
Step 4: Multiply k by that leading coefficient and write the product below the second coefficient on the dividend’s left side.
Step 5: Multiply the numbers in the second column.
Step 6: Multiply k by the number obtained in step 5 and write the result in the next column to the right.
Step 7: Finally, we’ll write the final solution, which will be one degree below the dividend.
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f ( x ) = ( x − 2 ) ( x + 4 ) ( x + 5 ) ( x − 1 ) ( x − 9 ) has zeros at x = -5, x = -4, x = 1, x = 2, x = 9
What is the sign of F on the interval -4 < x < 1?
The sign of F on the interval -4<x<1 is 0
How to do substitution in a function?We know that in mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.
The given function is
f(x)=(x-2)(x+4)(x+5)(x-1)(x-9)
The Interval is given as -4<x<1
Substituting the values of x in the function we have
f(x)=(-5-2)(-4+4)(1+5)(2-1)(9-9)
This implies that
f(x)=(0)(0)(6)(1)(0)
Multiplying the brackets to have
f(x)=0
In conclusion, the sign of F on the interval -4<x<1 is 0
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Which graph shows an image and preimage after reflecting across y = -x ? *
Option 1
Option 2
Option 3
Option 4
The image of the correct option is attached below(image two)
What is the graph?The coordinates of the image's bottom-most vertex are (- 2, 2).
The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed).
As a result, following reflection, the chosen vertex's coordinates are (2, -2).
As a result, option 3's graph displays the image and preimage after reflection while taking the selected vertex into account.
Therefore Option three satisfies the solution
image of option 3 is attached below
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The complete Question was found and attached below
When a firm applies statistical techniques to develop and maintain its ability to produce high-quality goods and services, it is implementing statistical _____.
When a company applies statistical techniques to develop and support its ability to produce high-quality goods and services, it is implementing statistical quality control.
What is quality control?Quality control (QC) is a procedure or set of actions intended to make sure that a manufactured product or performed service complies to a described set of quality standard or meets the conditions of the client or customer. QC is similar to quality assurance (QA), but not exactly same.
The quality control applied in a business is greatly dependent on the product or the industry. For example, in food and drink manufacturing, quality control also includes certifying the product will not make a consumer unwell, so the company does chemical and microbiological examination of samples from the production line.
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Write an equation in y = mx + b form to represent this table.
Answer:
y = 3x + 2
Step-by-step explanation:
In the equation [tex]y = mx + b[/tex], m represents the slope, and b represents the y-intercept. To write the equation in this form, we must substitute m and b into this equation.
. . . . . . . . . . . Finding "b"
The y-intercept is another name for the y-value when the x- value = 0. So, we need to look at the table and find the y-value for when x = 0.
⭐ y = 2 when x = 0. Thus, b = 2.
. . . . . . . . . . . Substitute "b" into the equation
y = mx + 2
. . . . . . . . . . . One way to find "m"
m, your slope, can be found using the slope formula: [tex]m = \frac{y__2 - y__1}{x__2 - x__1}[/tex], where [tex](x__1, y__1)[/tex] and [tex](y__2, y__1)[/tex] are coordinates that you are given.
I am going to choose the coordinates (0,2) and (1,5), but you can choose any other 2 coordinates from the table.
m = (5 - 2)/(1-0)
m = 3/1
⭐ m = 3
. . . . . . . . . . . Another way to find "m"
m, your slope, can be found by substituting a coordinate that you are given into your equation with b already found.
y = mx + 2
I am going to use the coordinate (1,5), but you can choose another coordinate from the table if you'd like.
-2 + 5 = 1(m) + 2 -2
⭐ 3 = m
. . . . . . . . . . . Substitute "m" into the equation
y = 3x + 2
Answer:
(0,2)
2 = b
(1,5)
5 = m + b
(2,8)
8 = m(2) + b
(3,11)
11 = m(3) + b
(4,14)
14 = m(4) + b
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-A circle with center H is shown in the figure below
What is the relation between the variables in the equation
a.
varies inversely as y
b. varies directly as y
Please select the best answer from the choices provided
A
OB
OC
OD
-
y
-1?
=
c. y varies directly as **
d.
y varies inversely as **
Answer:
y varies as ob and c because oof the linear expression Ox (x)
Nicholas has 5 1/2 cups of flour. One recipe for a cake he is making calls for 3 3/4 cups of flour. He also needs 8 cups of flour for a cookie recipe. How much more flour will nicholas need to make the cake and cookies?
Nicholas has a total of 5 1/2 cups + 3 3/4 cups = <<5.5+3.75=9.25>>9.25 cups of flour.
To make the cake and cookies, he needs a total of 3 3/4 cups + 8 cups = <<3.75+8=11.75>>11.75 cups of flour.
Therefore, Nicholas will need an additional 11.75 cups - 9.25 cups = <<11.75-9.25=2.5>>2.5 cups of flour to make the cake and cookies.