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The equation of the line that passes through the points ( -3,18 ) and ( 2,-7 ) is f(x) = -5x + 3.
What is the equation of line passing through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point 1( -3,18 )
x₁ = -3y₁ = 18Point 2( 2, -7 )
x₂ = 2y₂ = -7First, we find the slope of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -7 - 18 ) / ( 2 - (-3) )
m = ( -25 ) / ( 2 + 3 )
m = ( -25 ) / ( 5 )
m = -5
Next, next we find the y-intercept
y = mx + b
18 = (-5)(-3) + b
18 = 15 + b
b = 18 - 15
b = 3
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-5)x + 3
y = -5x + 3
Therefore, the equation of the line is y = -5x + 3
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Related Questions
line m and n are parallel when x=
Answers
we have those angles must measure the same so
[tex]\begin{gathered} 4x-6=150 \\ 4x=156 \\ x=\frac{156}{4}=39 \end{gathered}[/tex]so x=39
the mass of a car is 1990kg rounded to the nearest kilogram. the mass of a person is 58.7kg rounded to one decimal place. write the error interval for the combined mass, m, of the car and the person in the form _______
Answers
The error interval for the combined mass (m) of the car and the person is 2047.7 ≤ m < 2049.7
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).The error interval for the mass of car is given by:
Mass of car = 1990 ± 0.5;
Mass of car = 1990 + 0.5 = 1990.5
Mass of car = 1990 - 0.5 = 1989.5
The error interval for the mass of a person is given by:
b = 1990 ± 0.5;
b = 58.7 + 0.5 = 59.2
b = 58.7 - 0.5 = 58.2
For the value of a and b, we have:
a = 1989.5 + 58.2 = 2047.7
b = 1990.5 + 59.2 = 2049.7
Next, we would calculate the combined mass (m):
m = 1990 + 58.7
m = 2048.7
Now, we can write the error interval for the combined mass (m) of the car and the person as follows:
a ≤ m < b
2047.7 ≤ m < 2049.7
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Eric and Nancy both had a successful year selling fish tanks for theirrespective employers, and so they were both given raises.Eric: Eric's base salary is still $1400, but now he makes a commission of$100 for each fish tank that he sells.Nancy: Nancy now gets a base salary of $500 per month, but her commissionhas stayed the same at $250 per fish tank.Eric and Nancy still want to make sure that they contribute the same amountto their total monthly income, and Nancy proposes using algebra to figureout how many fish tanks that they would each need to sell. She tells Ericthat he can calculate his monthly income by using the formula f(x) = 100x +1400. She says that she can calculate her own salary by using the functiong(x)=250x + 500.1 What does the variable x represent in Nancy's formulas?How do you know?
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Answer:
The variable x represents the number of fish tanks he/she sells.
Explanation:
Given that Eric's base salary is still $1400, but now he makes a commission of
$100 for each fish tank that he sells and Nancy now gets a base salary of $500 per month, but her commission has stayed the same at $250 per fish tank.
Eric's total income would be;
$1400 plus $100 times the number of fish tanks he sells.
[tex]f(x)=1400+100x[/tex]and Nancy's total income would be;
$500 plus $250 times the number of fish tanks she sells.
[tex]f(x)=500+250x[/tex]Therefore, the variable x represents the number of fish tanks he/she sells.
The number of fish tanks each of them sells will determine the total commission and also determines their total income.
what is the quotient of (6.47 x 10^-15) / (3.36 x 10^-29)
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2. Perform the indicated operation. Express your answer in simplest form. Show any necessary work. Then answer the question. (a) -2.48/12.4 (b) -12.5/-0.025 (c) Imagine your friend uses long division to determine the quotients, and is confused by how quickly you were able to determine the correct answer without performing long division. Explain how you were able to determine the quotients without performing long division.
Answers
Part a
we have the expression
[tex]\frac{-2.48}{12.4}[/tex]Multiply the fraction by 100/100 to remove decimal numbers
[tex]\frac{-2.48}{12.4}\cdot\frac{100}{100}=-\frac{248}{1,240}[/tex]Simplify the fraction
[tex]-\frac{248}{1,240}=-\frac{1}{5}[/tex]Part b
we have the expression
[tex]\frac{-12.5}{-0.025}[/tex]Multiply the expression by 1,000/1,000 to remove decimal numbers
so
[tex]\frac{-12.5}{-0.025}\cdot\frac{1000}{1000}=\frac{12,500}{25}[/tex]Simplify
[tex]\frac{12,500}{25}=\frac{500}{1}=500[/tex]Part c
to determine the quotients without performing long division
step 1
Convert the decimal numbers of the quotient to integer numbers, multiplying the numerator and denominator by a fraction of the form 10/10, 100/100,1000/1000, etc
step 2
Simplify the fraction in the simplest form
Penny is selling candles for $3 each at a fundraiser.
If she starts selling with $4 to help her make change, how many candles, x, will she
have to sell to end up with $19?
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3x + 4 = 19
Subtract 4 from both sides
3x=15
Divided by 3 on both sides
X= 5
She needs to sell 5 candles to end up with $19
Answer: x=5
Step-by-step explanation: Based on the given conditions formulate:: 4+3[tex]x[/tex]x=19
Rearrange variables to the left side of the equation: 3x=19-4
Calculate the sum or difference: 3x=15
Divide both sides of the equation by the coefficient of the variable: x=[tex]15/3[/tex]
Cross out the common factor: x=5
Select the two values of x that are roots of this equation.
x2 + 3x – 5 = 0
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The two values for the quadratic equation [tex]x^{2} +3x-5=0[/tex] is [tex]\frac{-3+\sqrt{29} }{2}[/tex] and [tex]\frac{-3-\sqrt{29} }{2}[/tex]
What is quadratic equation?
Quadratic equation is a second-order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
The solution of the x = [-b±√(b2-4ac)]/2a
where b= 3 a= 1 and c = -5.
x = -3±[tex]\sqrt{3^{2}-4(1)(-5) } /2[/tex]
x=[tex]\frac{-3-\sqrt{29} }{2}[/tex]
and x = [tex]\frac{-3+\sqrt{29} }{2}[/tex]
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The population of a small town in central Florida has shown a linear decline in the years 1995-2005. In 1995 the population was 24100 people. In 2005 it was 14800 people.
Answers
Part A:
Since the population is showing a linear decline, we can express the function P(t) as
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given two points
(1995,24100), and (2005,14800)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{IF }\mleft(x_1,y_1\mright)=\mleft(1995,24100\mright),\text{ and }(x_2,y_2)=\mleft(2005,14800\mright),\text{ THEN} \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{14800-24100}{2005-1995} \\ m=\frac{-9300}{10} \\ m=-930 \end{gathered}[/tex]Now that we have solved for the slope, we can now solve for the y-intercept. We will use the point (2005,14800), but using (1995,24100) will work just as well.
[tex]\begin{gathered} \text{IF }m=-930,\text{ and }(x,y)=\mleft(2005,14800\mright),\text{ THEN} \\ \\ y=mx+b \\ 14800=(-930)(2005)+b \\ 14800=-1864650+b \\ 14800+1864650=+b \\ 1879450=b \\ b=1879450 \end{gathered}[/tex]Convert the function x into a function of time t, then the the function is
[tex]P(t)=-930t+1879450[/tex]Part 2:
What will be the population in 2007.
Substitute t = 2007.
[tex]\begin{gathered} P(t)=-930t+1879450 \\ P(2007)=-930(2007)+1879450 \\ P(2007)=-1866510+1879450 \\ P(2007)=12940 \end{gathered}[/tex]Therefore, in the year 2007, the population will be 12940.
Jonas wants to make a poster of a drawing he made. The original drawing is 8 inches wide, and he wants the poster to be 30 inches wide. What zoom button setting will he have to use on the library copier to create a poster of this size?
Answers
Answer:
He should use a 375% zoom to create a 30-inch wide poster.
Step-by-step explanation:
30/8 = 3.75, and 8*3.75=30. So 375%.
Mark as brainliest please.
Here is the imagine of the triangle ABC and it’s dilations using center D and scale factor 2
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(3) The question state that we should explain the relationship between angle ACB and A'C'B' in the given diagram.
From the the diagram in the question, we can see that wa have two different triangle which are ABC and A'B'C'.
The relationship between angle ACB and angle A'C'B' is that they are corresponding angles. because they are on the same side of the line.
Corresponding angles are any pair of angles each of which is on the same side of one of two lines cut by a trasnsversal and on the same side of the transversal.
Therefore, the relationship between angle ACB and angle A'C'B' is that they are corresponding angles.
Can someone please answer this question for me:
Answers
Answer:
16c²+ 32 cd +16d²
Step-by-step explanation:
area of rectangle is side²
(4c+4d)²
16c²+ 16cd+16cd+16d²
16c²+32cr+16d²
That is just the chart. Disregard question 6. 7. A survey of 381 adult females produced a mean height of 65.2 inches with a standard deviation of 2.8 inches. Construct a confidence interval based on a 95% confidence level.O (64.92, 65.48)© (64.83, 65.57)O (65.19, 65.21)© (64.96, 65.44)
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Step 1
Given;
[tex]\begin{gathered} n=381\text{ adults} \\ Mean\text{ \lparen}\mu)=65.2 \\ \sigma=2.8 \end{gathered}[/tex]Step 2
The confidence interval is given as follows;
[tex]CI=\mu\pm t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n}})[/tex]The test statistic for a 95% confidence interval with α = 0.05, the degrees of freedom, df= n-1 = 381-1=380
[tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}[/tex][tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}=1.97[/tex][tex]\begin{gathered} C.I=65.2\pm1.97(\frac{2.8}{\sqrt{381}})=65.2\pm0.2825932406 \\ C.I=(64.92,65.48) \end{gathered}[/tex]Answer;
[tex]C.I=(64.92,65.48)[/tex]solve for x.
0.4x-2.8/4=1.5
x=
Answers
Answer:
5.5
Step-by-step explanation:
0.4x = 2.2
x = 5.5
Mrs. M purchased milk for $3.50 per gallon. Which represents the number of gallons of milk, g, Mrs M can purchase if she plans to spend $10.50 on milk.all of the > and < have a line beneath them a. g>0 and g<3b. g>0 and g<14c. g> 0 and g< 7d. g>0 and 8<2
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Let x be the number of gallons Mrs M can purchase;
Given information:
Price per gallon: $3.50
Mrs M. Total budget: $10.50
[tex]\begin{gathered} 3.50x\text{ }≤\text{ }10.50 \\ \end{gathered}[/tex]Solving for the number of gallons Mrs M can purchase:
[tex]\begin{gathered} x\leq\frac{10.50}{3.50} \\ \\ x\text{ }\operatorname{\leq}\text{ }3 \end{gathered}[/tex]ANSWER
a. g>0 and g<3
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
80.58
Step-by-step explanation:
do you need an explanation or will this be fine?
The measures of the angles of a triangle are shown in the figure below. Solve for x.
34°
46°
x°
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The measures of the angle x in the triangle is 100 degrees
How to determine the measures of the angle?From the question, we have the following parameters that can be used in our computation:
Angles = 34, 46 and x
The sum of angles in a triangle add up to 180 degrees
This is represented as
Sum of angles = 180
Substitute the known values in the above equation
So, we have
34 + 46 + x = 180
Evaluate the like terms in the above equation
So, we have
80 + x = 180
Evaluate the like terms in the above equation
So, we have
x = 100
Hence, the value of x is 100
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Please help withstandard deviation with measurements
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Answer: Standard Deviation, σ: 0.23979157616564
Count, N: 8
Sum, Σx: 33.6
Mean, μ: 4.2
Variance, σ2: 0.0575
Steps
σ2 =
Σ(xi - μ)2
N
=
(4.5 - 4.2)2 + ... + (4.1 - 4.2)2
8
=
0.46
8
= 0.0575
σ = √0.0575
= 0.23979157616564
Step-by-step explanation: but here
it isnt letting me do the fraction or the other things so yeah it will look wrong but its write for the entire graph
Determine weather the sequence 6,12,24,48 could be an an arithmetic sequence.
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Answer:
The sequence cannot be arithmetic.
Explanation:
Given the sequence: 6,12,24,48
We want to determine if the sequence is arithmetic.
An arithmetic sequence is a sequence made in which the next term is obtained by the addition of a constant term called the common difference.
In the given sequence:
[tex]\begin{gathered} 12-6=6 \\ 24-12=12 \\ 48-24=24 \end{gathered}[/tex]The difference between the terms is not constant.
Therefore, the sequence cannot be arithmetic.
Determine the average rate of change of f(x) = 4x²+x+3 over the interval [-2, 2].
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Answer: The average rate of change is 1.
Step-by-step explanation:
The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)
a=−2 , b=2, f(x)=4X^2+x+3.
(f(b)-f(a))/(b-a)= (3+(2)+4(2)^2-(3+(-2)+4(-2)^2)) / (2-(-2)) = 1
A tailor has 20 yards of shirt fabric. How many shirts can she
complete if each shirt requires 2% yards of fabric?
Answers
Answer:
2%/100% ×20=
Step-by-step explanation:
from this one of the zeros from the hundred would cancel the zero from 20 which will give you 2/10×2 and mind you percentage cancel percentage. from this 2 will cancel 10 leaving the answer 2 over 5
Jay's family is moving to a new home they packed 22 boxes in 1 5/6 hours what is the average number of boxes they packed per hour Pls asap
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=> 22/(11/6) => 12 boxes per hr
2y + 6 = y — 7. What is the value of y?
Answers
y=-13
Step-by-step explanation:
2y+6=y-7
2y+6-6=y-7-6
2y=y-13
2y-y=y-13-y
y=-13
The value after solving the given expression will be equal to -13.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given expression in the question is,
2y + 6 = y - 7
Rearrange the equation,
2y - y = -7 - 6
y = -13
Therefore, the obtained value for y will be -13.
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what is the scale factor that creates the copy triangle DEF
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The required scale factor is;
[tex]\frac{DE}{AB}=\frac{1.34}{2}=0.67=\frac{67}{100}[/tex]So, the required scale factor is 0.67 or 67/100
Which is the area of the circle shown? Use 3.14 for π.
1. 18.84 m^2
2. 37.68 m^2
3. 113.04 m^2
4. 354.95 m^2
Answers
Answer:
3: 113.04 m^2
Step-by-step explanation:
pi r^2
3.14 x 36
= 113.04 m^2
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Finding the absolute maximum and minimum of a function given the graph
Answers
Explanation
An absolute maximum point is a point where the function obtains its greatest possible value.
Similarly, an absolute minimum point is a point where the function obtains its least possible value.
Step 1
check the graph of g:
The y- coordinates (output) at the highest and lowest points are called the absolute maximum and absolute minimum
To locate absolute maxima and minima from a graph, we need to observe the graph to determine where the graph attains it highest and lowest points on the domain of the function
so, for G
[tex]\begin{gathered} \text{maximum}=\text{ None ( the graph continues raising up)} \\ \text{minimum}=-3 \end{gathered}[/tex]Step 2
Now, for h
[tex]\begin{gathered} \text{ Minimum; -5} \\ \text{ ma}\xi mum\colon5 \end{gathered}[/tex]I hope this helps you
please I just need help with these two questions
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Question 1:
Each of these options can be read as "8 to 15", except for 15:8. This is read as "fifteen to eight". Lets say in 8:15 you have 8 of a and 15 of b. In 15:8, however, you have 15 of a and 8 of b. These are not the same ratio.
Question 2:
The amount of people that can go down the slide in 1 minute is 6, because 18/3 = 6. So:
12/6 = 2
6ppl/1min (multiply both terms by 2)
12ppl/2min
It would take 12 people 2 minutes to go down the slide.
Write the rule for the table, use z for the input.Input-1Output7012co woo WN3.4F(0)
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Lets assume that the input values are x values and the output values are y values.
Then you will have pairs of coordinate values as shown;
(-1,7) , (0,2) , (1,-3) , (2,-8), (3,-13), (4,-18)
Using the coordinates find the slope a;
(-1,7) and (0,2) ---------slope is change in y-values/ change in x-values , (2-7) /(0--1)
= -5/ 1 = -5
Do the same for the next pair of coordinates ,(0,2) and (1,-3) , (-3-2) / (1-0) = -5/1 = -5
If you continue the procedure to the next pair which is (1,-3) and (2,-8) to get the slope as : (-8- -3) / (2-1) = -5/1 = -5
This means that the slope is -5
The relation will be represented by the equation y= mx + c where m is the slope and c is the y-intercept
First plot the points to visualize the graph
From the plot, you notice that when the points are joined, a straight graph is formed sloping to the negative side and intersecting the y-axis at point (0,2).
So to determine the rule, we apply the equation y= mx + c with m= -5 and c =2
This gives y= -5 x + 2
The rule is f(x) = -5x +2 -----------answer
A bicycle company is manufacturing a new bicycle and trying to decide on a price that will maximizing their profit. the graph below represents profit (P), in thousands of dollars,generated by the price of each bike (x), in hundreds of dollarsIf the company wants to make a maximum profit,what should the price of the bicycle be?
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The graph shows the profit (measured in thousands of dollars) on the y-axis and the price per bike (measured in hundreds of dollars) on the x-axis, the parabola describes the relationship between both variables.
As you can see the parabola opens downwards, which means that the maximum value of the relationship is determined by the vertex of the curve.
The coordinates of the vertex indicate the value of the bikes (x-coordinate) that allows the company to make the maximum profit (y-coordinate)
Looking at the graph the coordinates for the vertex are, approximately, (6, 160)
x-coordinate: 6 hundreds of dollars
y-coordinate 160 thousands of dollars
The maximum profit will be $160,000, and they will reach it when the bicycles cost $600
in ABC, The sum of measures of A and B is 90°. A is 30° less than twice B use this information to find the measure of each angle
Answers
Given:
The sum of measures of A and B is 90°
so, we have the following equation:
[tex]A+B=90\rightarrow(1)[/tex]And, A is 30° less than twice B
so, we have the following equation:
[tex]A=2B-30\rightarrow(2)[/tex]Solving the equations (1) and (2)
Substitute with A from equation (2) into equation (1)
[tex]\begin{gathered} 2B-30+B=90 \\ 3B=120 \\ B=\frac{120}{3}=40 \end{gathered}[/tex]Substitute with B into equation (2) to find A:
[tex]A=2\cdot40-30=50[/tex]So, the answer will be:
The measure of angle A = 50
The measure of angle B = 40
9 is subtracted from the square of a number