Answer:
So, the point-slope form of the equation that represents the line passing through the points [tex]\((-6,4)\) and \((2,0)\)[/tex] is:
[tex]\[ y - 4 = -\frac{{1}}{{2}}(x + 6) \][/tex]
Explanation:
To find the equation of the line passing through the points [tex]\((-6,4)\) and \((2,0)\)[/tex] , we can use the point-slope form of the equation of a line:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.
First, let's find the slope [tex]\(m\):[/tex]
[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]
Using the coordinates of the given points:
[tex]\[ m = \frac{{0 - 4}}{{2 - (-6)}} \][/tex]
[tex]\[ m = \frac{{-4}}{{2 + 6}} \][/tex]
[tex]\[ m = \frac{{-4}}{{8}} \][/tex]
[tex]\[ m = -\frac{{1}}{{2}} \][/tex]
Now that we have the slope, let's choose one of the given points to plug into the point-slope form. We'll use [tex]\((-6,4)\):[/tex]
[tex]\[ y - 4 = -\frac{{1}}{{2}}(x - (-6)) \][/tex]
[tex]\[ y - 4 = -\frac{{1}}{{2}}(x + 6) \][/tex]
[tex]\[ y - 4 = -\frac{{1}}{{2}}x - 3 \][/tex]
Now, let's simplify and put the equation in slope-intercept form:
[tex]\[ y = -\frac{{1}}{{2}}x - 3 + 4 \][/tex]
[tex]\[ y = -\frac{{1}}{{2}}x + 1 \][/tex]
brainiest to best answer!
The deepest part of the Mariana trench (the deepest trench in the world’s oceans) is at an elevation of -11.033 kilometers. The elevation of the deepest part of the Atacama trench is -8.065 kilometers. What is the net change in elevation from the Atacama trench to the Mariana trench?
19.098 kilometers
2.968 kilometers
-2.968 kilometers
-19.098 kilometers
The net change in elevation from the Atacama trench to the Mariana trench is 2.968km.
What is the net change in elevation from the Atacama trench to the Mariana trench?
We know that the deepest part of Mariana trench is at -11.033 km, while the deepest part of the Atacama trench is -8.065km.
To find the net change, we need to find the difference between the largest value and the smallest value.
So we get:
D = -8.065km - (-11.033 km) = 2.968km
Then the correct option is the second one.
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Tom usually earns $40.85 per hour. he has a 6% pay raise. which keys must he press on his calculator?
"+" & "=" button key Tom will press in the calculator.
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
To calculate Tom's pay raise, he can perform the following calculation on his calculator:
= 40.85 x 0.06
= 2.4510
So Tom's pay raise is $2.45 per hour.
To calculate Tom's new hourly rate, he can perform the following calculation:
= 40.85 + 2.45
= 43.30
So Tom's new hourly rate is $43.30.
Here is how the calculation can be done on most calculators:
Enter 40.85 and then press the "+" button.
Enter 2.45 and then press the "=" button.
The result should be 43.30, which is Tom's new hourly rate with a 6% pay raise.
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Work out the value of 3x + 2y when x=4 and y=-5
3x + 2y =
3*4 + 2*-5=
12 + -10 = 2
PLEASE HELP!!!
WILL GIVE BRAINIEST TO FIRST ANSWER
Which of the following inequalities is graphed on the coordinate plane?
A. y > 1/2x - 1/2
B. y is less than or equal to 1/2x - 1/2
C. y is greater than or equal to 1/2x - 1/2
D. y < 1/2x - 1/2
Answer:
Option C
Step-by-step explanation:
Equation of any line is of the form y=mx+b where m is the slope and b the y intercept.
The given line has y intercept [tex]\frac{-1}{2}[/tex] and slope as [tex]\frac{1}{2}[/tex]
Hence equation of given line is :
[tex]y= \frac{1}{2}x-\frac{1}{2}[/tex]
Taking point (0,0) to check the inequality we have:
0≥[tex]\frac{-1}{2}[/tex]
The statement is true so option C [tex]y\geq \frac{1}{2} x-\frac{1}{2}[/tex] is right .
48 out of 120 equals what percent
what is the square root of 49
Critical thinking write a recursive rule for a sequence where every term is the same.
Graph the equation 5x+2y=10
Please help! Create a set of five positive numbers (repeats allowed) that have a median of 10 and a mean of 14. What thought process did you use to create your numbers?
Find the slope of a line parallel to the line through the given points. P(-2, 4), Q(6, -2) 4/3 3/4 -3/4
Answer:
Option 3 - [tex]m=-\frac{3}{4}[/tex]
Step-by-step explanation:
Given : P(-2, 4), Q(6, -2)
To find : The slope of a line parallel to the line through the given points?
Solution :
First we find the slope of the line passes through given points P(-2, 4), Q(6, -2)
The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-2-4}{6-(-2)}[/tex]
[tex]m=\frac{-6}{8}[/tex]
[tex]m=-\frac{3}{4}[/tex]
When two lines are parallel then there slope are equal.
Therefore, The slope of a line parallel to the line through the given points is
[tex]m=-\frac{3}{4}[/tex]
So, Option 3 is correct.
whats 10 minutes plus 7minutes plus 48minutes plus 1 hour and 29 minutes equal?
Answer: 2 hours and 34 minutes
Step-by-step explanation:
10 minutes plus 7 minutes plus 48 minutes plus 60 minutes plus 29 minutes equals 154 minutes. 154 minutes equals 2 hours and 34 minutes.
If 5x + 5 =25 + 3x then x = ? (im in pre algebra)
To solve the equation 5x + 5 = 25 + 3x, subtract 3x from both sides, subtract 5 from both sides, and divide by 2 to find x = 10.
Explanation:To solve the equation 5x + 5 = 25 + 3x, you need to isolate the variable x. First, subtract 3x from both sides of the equation to combine like terms: 5x - 3x + 5 = 25. Simplify: 2x + 5 = 25. Next, subtract 5 from both sides of the equation to isolate the variable: 2x = 20. Finally, divide both sides of the equation by 2 to solve for x: x = 10.
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Jonah and his friends went to the movie theater. He bought a movie ticket, and he split the cost of a giant popcorn with his friends. Jonah's costs are represented by the expression 11+15/x . What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description. Cost of movie ticket Total cost of popcorn Jonah's portion of popcorn cost
Answer:
Cost of movie ticket = 11
Total cost of popcorn = 15
Jonah's portion of popcorn cost = 15/x
Step-by-step explanation:
1. I
2. Took
3. The
4. Test
An athlete eats
60
grams of protein per day while training. How much is this in milligrams?
Be sure to include the correct unit in your answer.
How do you solve cot^2x + cscx= 1
(0,2pi)
A rectangle has a length of 8 cm and breadth 6cm . What is the perimeter in cm of the rectangle
Joseph’s garden is 9 feet wide and 12 feet long. Alana’s garden is 7 feet wide and 25 feet long.
How much greater is the area of Alana’s garden than Joseph’s garden?
Please help!! Will give 15 points!
area of Josephs garden = 9*12 = 108 square feet
area for Alana's garden = 7 *25 = 175 square feet
175/108 = 1.62
Alan's garden is 1.62 times larger
Tali started a pool cleaning business. She purchased cleaning supplies and charged the same amount for each pool cleaned. The expression −243+24x represents the profit Tali has earned from cleaning pools.
Which expression represents the total amount Tali earns from pool cleaning?
24x
24
−243
x
Answer:
24x
Step-by-step explanation:
The variable x is used to represent the independent variable in a situation. In this situation, the independent variable would be the number of pools cleaned; this means that x represents the number of pools cleaned.
24x would then indicate that Tali charges $24 per pool cleaned; this makes 24x her total earnings from cleaning pools.
Answer:
A. [tex]24x[/tex]
Step-by-step explanation:
We have been given an expression [tex]-243+24x[/tex], which represents he profit Tali has earned from cleaning pools. We are also told that Tali purchased cleaning supplies and charged the same amount for each pool cleaned.
Upon looking at our expression we can see that [tex]-243[/tex] is constant term and it is negative, so it will represent the amount spent by Tali on supplies.
The term [tex]24x[/tex] contains independent variable [tex]x[/tex], which represents the number of pools cleaned and 24 represents Tali's earning from each pool.
Since Tali cleaned [tex]x[/tex] pools, so total amount of Tali's earning from cleaning [tex]x[/tex] pools will be [tex]24x[/tex] and option A is the correct choice.
Simplify 5(a - b) + 6(a + b) - 7(a - 2b)
The length of the base of a triangle is twice its height. if the area of the triangle is 100 square kilometers, find the height.
Based on research by barsh and colleagues (2000), _____ genes appear to be related to body weight regulation.
You went shopping and found a pair of shoes that were $45.00 on sale for $27.50. what was the percent of decrease of the shoes? your answer should go 1 decimal place)
What classification best represents a triangle?
Need help ASAP real quick ????????????
If a set of data is in the direction of a downward line, which of the following would be the best model for this data?
Quadratic regression model
Exponential regression model
Linear regression model
None of the above
60 POINTS!!
What are the missing parts that correctly complete the proof?
the guy below/above is correct
Help me solve this please...in detail.
I really need help on this problem can i get help on how to solve the problem please
If f(x) = + 8, what is f(x) when x = 10?
Answer:
13
Step-by-step explanation:
it correct
1. what are some different types of numbers that you have herd of before?
2. why do you think it is important to classify (sort) different types of numbers