The table represents some points on the graph of a linear function. Which equation represents the same relationship?A: y-3=-2(x+6)B: y-6 = - 1/2 (x+3)C: y+3=-1/2(x-6)D:y-6=-2(x+3)
Answers
To determine which of the options best defines the table, we will have to determine the equation of the line that defines the table.
To find the equation of a line
let us select the first two points of the table
\(\begin{gathered} \text{when } \\ x=-4,\text{ y=2} \\ \text{when} \\ x=-2,\text{ y=1} \end{gathered}\)We can now use the equation of the line formula
\(\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \frac{y-2}{x-(-4)}=\frac{1-2}{-2-(-4)} \\ \\ \frac{y-2}{x+4}=\frac{1-2}{-2+4} \\ \\ \frac{y-2}{x+4}=\frac{-1}{2} \end{gathered}\)The next step will be
to cross multiply
\(y-2=-\frac{1}{2}(x+4)\)To find the option that conforms to the expression
\(\begin{gathered} \text{let us add 5 to both sides} \\ y-2+5=-\frac{1}{2}(x+4)+5 \\ \\ y+3=-\frac{1}{2}x-2+5 \\ y+3=-\frac{1}{2}x+3 \\ \text{This is equivalent to} \\ y+3=-\frac{1}{2}(x-6) \end{gathered}\)ThusThe correct answer is option C
Related Questions
for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.
Answers
An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:
Example 1:
Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
For such more question on equations
https://brainly.com/question/22688504
#SPJ11
Centerville Middle School spends $13 for every workbook it buys. At most how many
workbooks can Centerville Middle School buy if it has $26 to spend?
Answers
Answer:
they can buy 2
Step-by-step explanation:
13 x 2 = 26
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the numbers which satisfy this condition.
Answers
Answer: 4 and 2
Step-by-step explanation:
a + b = 6
a - b = 2
Sum these equations, we get 2a = 8, then a = 4
Substitute to one of these equations, we get 4 - b = 2, so b = 2
Prove: The sum of 24 and 42 is 66, and 4 and 2 differ by 2 are both correct!
Write the set using interval notation. How to simplify if you need to and what if your answer involves a union with a singleton set.
Answers
For the set notation { x | x ≤ -9 or x ≥ 9}, we get the interval notation as ( - ∞ , -9 ] U [ 9, ∞ )
We are given a set that:
{ x | x ≤ -9 or x ≥ 9}
We need to write it an interval notation.
For x ≤ -9:
Since x is smaller than or equal to -9, we will get the interval as:
( - ∞ , -9 ]
For x ≥ 9:
Since x is greater than or equal to 9, we will get the interval as:
[ 9, ∞ )
or means union.
So, the final interval becomes:
( - ∞ , -9 ] U [ 9, ∞ )
Therefore, for the set notation { x | x ≤ -9 or x ≥ 9}, we get the interval notation as ( - ∞ , -9 ] U [ 9, ∞ )
Learn more about sets here:
https://brainly.com/question/2166579
#SPJ9
You are cutting pieces of fabric for a craft project. You need three pieces that measure 6 2/3 inches, 4 1/2inches, and 3 5/8inches.
What is the total length of fabric that you need ?
Answers
Answer:
Step-by-step explanation:
14/19/24
If x = 10 find the value of 2x2 + 21
Answers
Answer:
221
Step-by-step explanation:
If x = 10,
2x² + 21 = 2(10)² + 21
= 200 + 21
= 221
Hope it helps :)
Please mark my answer as the brainliest
State YOUR thoughts/reactions
WRITE AT LEAST 4 COMPLETE SENTENCES IN PARAGRAPH FORMAT.
When Saul died, David was crowned king. David united the tribes and continued the fight against the Philistines and other enemies. He captured Jerusalem and made it his capital, starting its transformation into one of history’s most important cities.
David’s son Solomon inherited a peaceful kingdom. He built a great stone temple in Jerusalem. Solomon’sTemple became the focus of religious life. Solomon used trade and taxes to fund other huge building projects. However, most of the tax burden fell on the northern tribes, who came to resent Solomon’s
Answers
Answer:
All you have to do is write how you feel about this it's simple :|
Step-by-step explanation:
Which decimal is the best best estimate of the fraction 29/40?
Answers
Answer: 0.725
Step-by-step explanation: this is the answer. in order to get to this answer you would put The line in a fraction that separates the numerator and denominator can be rewritten using the division symbol. So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.
i sure hope this was helpful.
Enrique borrowed 23500 to buy a car
Answers
6=-3(x+2)
I need help please help! I’ll give you extra points
Answers
Answer:
x = -4
Step-by-step explanation:
6 = -3(x + 2)
distribute the -3
6 = -3x - 6
add 6 to both sides
12 = -3x
divide by -3
-4 = x
Answer:
x=-4
Step-by-step explanation:
6=-3(x+2)
6=-3x-6
6+6=-3x
12=-3x
x=12/-3
x=-4
I really need help with this
Answers
Because -6x+18<30
(-18)
-6x<12
(divide by -6)
x< -2
simplify 36ab divided by 40ab
Answers
Featured snippet from the web
What is 36/40 Simplified? - 9/10 is the simplified fraction for 36/40.
Identify the y-coordinate
(9,[?])
![Identify the y-coordinate(9,[?])](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/8eoWzsxykrluRoXw0S3JGiWQyOVyEmD1.png)
Answers
Answer:
(9,16)
Step-by-step explanation:
We Know
The equation y = 3x - 2
Find the y coordinate (9, ?)
We just simply put 9 in for x and solve for y
y = 3(9) - 2
y = 18 - 2
y = 16
So, the coordinate are (9,16)
The seller was told by the bank that she has a prepayment penalty due at the time of closing the penalty is 6 months’ interest on the current loan balance. Based on 6% interest, her month payment is 569.57 principal and interest, and her loan balance was $95,000.00 the moth before closing. Once she makes her next monthly payment, how much will she owe in Prepayment penalty at the time of closing
Answers
The seller will owe $2,847.16 in prepayment penalty at the closing of the loan balance.
Some lenders include prepayment penalties in their loan agreements. This penalty represents a fee that they charge the borrowers for paying off all or a portion of their loans before their expiration or maturity date. The purpose is to discourage borrowers from repaying loans before the due date.
Data and Calculations:
Prepayment penalty = 6 months' interest on current loan balance
Current loan balance = $95,000
Current monthly payment = $569.57
Month's interest on loan = $475 ($95,000 x 6% x 1/12)
Principal repayment = $94.57 ($569.57 - $475)
Closing loan balance = $94,905.43 ($95,000 - $94.57)
Prepayment penalty = $2,847.16 ($94,905.43 x 6% x 6/12)
Thus, the prepayment penalty that she will owe at the closing of the loan is $2,847.16, which is six months' interest on the loan balance.
Learn more about prepayment penalty here: https://brainly.com/question/501927 and https://brainly.com/question/2025156
Students at Sunnyvale Middle School volunteered to work a 2-hour shift at a
car wash fundraiser. The table shows the number of people who worked each
shift and how many cars they washed.
Is the relationship between the number of
cars washed and the number of workers
proportional? Complete the statement.
The number of cars washed per person
?
of workers, so the relationship is
the same for each number
?
People Working
4
6
8
10
Cars Washed
8
12
20
25
Answers
The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The ratios between the output and the inputs are given as follows:
8/4 = 2.12/6 = 2.20/8 = 2.5.25/10 = 2.5.Different ratios, hence the relationship is not proportional.
A similar problem, also featuring proportional relationships, is presented at https://brainly.com/question/7723640
#SPJ1
Solve the following quadratic inequality x^2+x-6>0
Answers
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
I need help with all 4 questions plz
Answers
QUICK HELP ME DUE IN 3 MINUTES 123456789x123456789
Answers
Answer:
1.5241579e+16 is the answer
i d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d ki d kv
In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt. Which interval is the 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt
Answers
Answer:
The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).
In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt.
This means that \(n = 352, \pi = \frac{92}{352} = 0.2614\)
99% confidence level
So \(\alpha = 0.01\), z is the value of Z that has a p-value of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).
The lower limit of this interval is:
\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 - 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.2011\)
The upper limit of this interval is:
\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 + 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.3217\)
As percent:
0.2011*100% = 20.11%
0.3217*100% = 32.17%.
The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).
4x-y+ 2z=-1
Given the system -x+2y + 5z = 2, which is true?
|-x+y-3z= 1
Answers
Answer:
Y = 0
X= 1/2
Z = -1/2
Step-by-step explanation:
4x-y+ 2z=-1
-x+y-3z= 1
-x+2y + 5z = 2
Solving simultenously
Y= 4x + 2z -1
Y =1+ 3z+ x
Y =x/2 -( 5z/2) - 1
Equating y will give two equations
3x-z = 2
3x + 11z = -4
Subtracting the equations
-12z =6
Z= -1/2
Substituting z
3x +1/2 = 2
3x = 3/2
X= 1/2
Substituting x and z to find y in
-x+y-3z= 1
-1/2 + y +3/2 = 1
Y = 1-1
Y = 0
Answer: b) is answer
Step-by-step explanation:
PLEASE HELP
A busy candy stores going to replace their current gumball machine with a giant gumball machine. The globe on the current gumball machine is 22 inches in diameter and the volume is 5575 in.³ compared to what has been ordered the current gumball machines volume is 532 in.³ less than 1/4 of the volume of the globe of the giant gumball machine.
3. Carry out your plan from question to what is the volume of the globe on the new gumball machine you can round your final answer to the nearest whole number. Be sure to check your work.
4. Is your answer to question through the real solution or an extraneous solution explain how you?
Answers
3. The volume of the new gumball machine is of 861.75 in³.
4. This is a real solution, as it is a positive number.
How to obtain the volume of the new machine?The volume of the old machine was of:
5575 in.³
(as stated in the problem)
The volume of the new machine is obtained as follows:
532 in.³ less than 1/4 of the volume of the globe of the giant gumball machine.
One fourth of the volume of the old machine is obtained as follows:
1/4 x 5575 in³ = 1393.75 in³.
532 in.³ less than that is obtained as follows:
1393.75 - 532 = 861.75 in³.
An extraneous volume is a negative value to the volume, as the volume cannot be negative. Since the number is positive, it represents a real solution.
More can be learned about volumes at https://brainly.com/question/463363
#SPJ1
What’s the difference between solving a whole number and a fraction?
There’s these two methods I saw but not sure when I should use them when I do stumble on a problem.
1 method: start by multiply the numerator towards the whole number and once u do then divide the numerator and denominator separately.
2 method: start by giving the whole number a 1 of the denominator and find the lCD of the fraction and start finishing the problem from either adding or subtracting.
Answers
Both the methods can be used to solve a mixed fraction including a whole number and a fraction or solving the difference of a whole number and a fraction.
What is Mixed Fraction?Mixed fractions are type of fractions which involve a whole number and a fraction. This is of the form a \(\frac{b}{c}\). This is actually a + \(\frac{b}{c}\).
You can use either methods when solving a whole number and a fraction.
Let us take a whole number 3 and a fraction \(\frac{2}{10}\) for instance.
First Method :
Solve it by cross multiplication.
Let the denominator of the whole number 3 be 1.
\(\frac{3}{1}\) ± \(\frac{2}{10}\) = [(3 × 10) ± (2 × 1)] / (1 × 10) = [30 ± 2] / 10
If the question is for adding, we get, \(\frac{3}{1}\) + \(\frac{2}{10}\) = (30 + 2) / 10 = 32/10
If the question is finding difference, we get, \(\frac{3}{1}\) - \(\frac{2}{10}\) = (30 - 2) / 10 = 28/10
Second Method :
Again let the denominator of the whole number be 1.
Find the LCD (Least Common Denominator) of 1 and 10.
This is 10.
So we have to make the denominator of \(\frac{3}{1}\) to 10.
Multiply both numerator and denominator with 10, we get 30/10.
A normal multiplication of fractions, if the denominator is same add or subtract the numerators let the denominator be as such.
Now add or subtract \(\frac{30}{10}\) ± \(\frac{2}{10}\) = (30 ± 2) / 10.
Hence both the methods can be used.
To learn more about Mixed Fractions, click :
https://brainly.com/question/29264210
#SPJ1
cylinder has a volume of 2,034.72 cubic millimeters and a radius of 6 mm, whats the height?
Answers
Answer:
2,260.80 cubic millimeters
Step-by-step explanation:
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters
Help me please
I will give brainliest
Answers
Answer:
23
Step-by-step explanation:
if you want the steps lmk in the comments (not everyone wants them). hope this helps Happy Holidays
Will mark brainlest help
Answers
Answer:
I fr think its C
Step-by-step explanation:
Rose wants to buy a toy that costs $14. If she gives the cashier $20, which equation will tell you how much change Rose gets back?
Answers
Answer:
$20-$14=$6
Step-by-step explanation:
this is correct because if you give the $20 to them and the toy costs $14 then you subtract that from the amount you gave them then whatever is left is how much you get back.
brainliest?
A city in China is one of the world's coldest cities and is known for its ice and snow festivals. In February, the average nightly low temperature is −40°C and the average daily high temperature is −9°C. What is the temperature drop (in °C) from day to night?
Answers
The temperature drops by \(31\°C\) from day to night in this city.
To calculate the temperature drop from day to night in \(\°C\), we subtract the average nightly low temperature from the average daily high temperature.
Given:
Average nightly low temperature: \(-40\°C\)
Average daily high temperature: \(-9\°C\)
The temperature drop can be calculated as:
Temperature drop = Average daily high temperature - Average nightly low temperature
Substituting the given values:
Temperature drop = \(-9\°C - (-40\°C)\)
Simplifying the equation:
Temperature drop = \(-9\°C + 40\°C\)
Temperature drop = \(31\°C\)
The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.
Therefore, the temperature drops by \(31\°C\) from day to night in this city.
For more questions on temperature drops:
https://brainly.com/question/24746268
#SPJ8
Supreme Auto Parts produces components for motorcycle engines. It has plants in Amarillo, Texas, and Charlotte, North Carolina, and supply factories in Detroit and Atlanta. Production and cost data for a major component are as follows. Freight Costs Plant Detroit Atlanta Capacity Unit CostAmarillo $15 $9 $1,500 $110Charlotte $7 $5 $3,300 $120Demand 2,100 1,000 Formulate a transportation model to determine the best distribution plan. If the constant is equal to one, enter "1".Let: X11 = number of components produced in Amarillo and supplied to DetroitX12 = number of components produced in Amarillo and supplied to AtlantaX21 = number of components produced in Charlotte and supplied to DetroitX22 = number of components produced in Charlotte and supplied to Atlanta Min X11 + X12 + X21 + X22 Subject to the constraints X11 + X12 -Select-≤≥=Item 7 X21 + X22 -Select-≤≥=Item 11 + X21 -Select-≤≥=Item 15 X12 + X22 -Select-≤≥=Item 19 X11, X12, X21, X22 ≥ 0
Answers
According to the given information the Minimize equation is
Z = 110X11 + 120X12 + 120X21 + 130X22.
What is Statistics ?
Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It provides methods and techniques to make sense of complex data sets, to draw conclusions and make decisions based on the data. Statistics can be applied to a wide range of fields, including business, economics, social sciences, medicine, and many others. Some key topics in statistics include probability theory, hypothesis testing, regression analysis, and data visualization.
Minimize:
Z = 110X11 + 120X12 + 120X21 + 130X22
Subject to:
X11 + X12 ≤ 1500 (capacity constraint for Amarillo)
X21 + X22 ≤ 3300 (capacity constraint for Charlotte)
X11 + X21 ≥ 2100 (demand constraint for Detroit)
X12 + X22 ≥ 1000 (demand constraint for Atlanta)
where:
X11 = number of components produced in Amarillo and supplied to Detroit
X12 = number of components produced in Amarillo and supplied to Atlanta
X21 = number of components produced in Charlotte and supplied to Detroit
X22 = number of components produced in Charlotte and supplied to Atlanta
Therefore, according to the given information the Minimize equation is
Z = 110X11 + 120X12 + 120X21 + 130X22
To know more about statistics visit :
https://brainly.com/question/15525560
#SPJ1
Without graphing, determine how many x-intercepts the function has.
y=3x^2 + 3x +4
Answers
y = 2x^2 + 3x + 3 has 0 x intercepts
y = 3x^2 + 3x + 4 has 0 x intercepts
A jar contains 1200 ml of milk.
How many litres and ml of milk is in
the jar?
Answers
Answer:
1.2 liters
Step-by-step explanation: