A line passes through the points (6,5) and (2,2) . Select all that describe this line.
1. y − 5 = 3/4 (x − 6)
2. y − 5 = −4/3 (x − 2)
3. y − 2 = −3/4 (x − 6)
4. y − 2 = 3/4 (x − 2)
The equations that describe the line passing through the points (6,5) and (2,2) are: [tex]1. y-5=\frac{3}{4}(x-6)$\\2. $y-2=\frac{3}{4}(x-2)$[/tex]
To determine which of these equations describe the line passing through the points (6,5) and (2,2), we can use the point-slope form of a linear equation:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line, and [tex]\left(x_1, y_1\right)[/tex] is one of the given points.
Let's find the slope using the two points:
[tex]\begin{aligned}& m=\frac{y_2-y_1}{x_2-x_1} \\& m=\frac{2-5}{2-6}=\frac{-3}{-4}=\frac{3}{4}\end{aligned}[/tex]
So, the slope of the line passing through these points is m=3/4
Now, let's plug in one of the given points into the point-slope form to check which equations match:
[tex]y-5=\frac{3}{4}(x-6)\\\text{If we plug in the point (6,5)} :\\& 5-5=\frac{3}{4}(6-6) \\& 0=0\end{aligned}$$[/tex]
This equation holds true for the point (6,5).
[tex]y-5=-\frac{4}{3}(x-2)\\\\text{If we plug in the point (2,2)} :\\2-5=-\frac{4}{3}(2-2) \\& -3=0\end{aligned}$$[/tex]
This equation does not hold true for the point (2,2).
[tex]y-2=-\frac{3}{4}(x-6)\\\text{If we plug in the point (6,5)} :\\& 5-2=-\frac{3}{4}(6-6) \\& 3=0\end{aligned}$$[/tex]
This equation does not hold true for the point (6,5).
[tex]y-2=\frac{3}{4}(x-2)\\\text{If we plug in the point (2,2)} :\\& 2-2=\frac{3}{4}(2-2) \\& 0=0\end{aligned}$$[/tex]
This equation holds true for the point (2,2).
So, the equations that describe the line passing through the points (6,5) and (2,2) are:
[tex]1. y-5=\frac{3}{4}(x-6)$\\2. $y-2=\frac{3}{4}(x-2)$[/tex]
Evaluate. 53−(648)+102 Enter your answer in the box.
The final result is 803.
To evaluate the given expression 53 − (−648) + 102, we need to follow the rules of arithmetic operations, particularly the order of operations known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, we look inside the parentheses. Since we have a negative sign before the parentheses, we understand that we are subtracting a negative value which is the same as adding its positive equivalent. So our expression will become 53 + 648 + 102.
Next, we perform the addition operation: 53 + 648 = 701 Adding 102 to 701: 701 + 102 = 803
The final result of evaluating the expression is 803.
{35 POINTS)What are the solutions of 2a^3-3a^2=8a-12 ?
Simplify 26/5(5/13b+10/26) .
3. The equation y = 12x describes the amount of money Louis earns, where x is the number of hours he works and y is the amount of money he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
Carl’s Earnings
Time (h) 3 5 8 10
Money earned ($) 45 75 120 150
(a) How much money does Carl earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Carl’s earnings over time in hours. Remember to label the axes.
Carl earns $45 per hour. We cannot determine who earns more per hour without the earnings of Louis given. To represent Carl's earnings over time in hours, a graph can be drawn using the data points provided in the table.
Explanation:To find the amount of money Carl earns per hour, we need to divide the money earned by the number of hours worked. So, for each data point in the table:
For 3 hours worked, Carl earns $45 per hour.For 5 hours worked, Carl earns $75 per hour.For 8 hours worked, Carl earns $120 per hour.For 10 hours worked, Carl earns $150 per hour.From these calculations, we can see that Carl earns $45 per hour.
To determine who earns more per hour, we need to compare the amount of money Carl and Louis earn. Since we do not have Louis' earnings given, we cannot determine who earns more per hour.
Finally, to draw a graph that represents Carl's earnings over time in hours, we can plot the data points from the table on a graph with the x-axis representing time in hours and the y-axis representing money earned. Each data point will be represented by a coordinate (x, y), where x is the time in hours and y is the money earned. Connecting the data points will give us a graph that represents Carl's earnings over time.
Developing it says constructing equations from a table
2/2 + 1.75 - 176%
Enter your answer as an exact decimal or simplified fraction.
Which decimal number is equal to 7/9 0.7 0.7¯ 0.78 0.78¯
Answer:
0.7
Step-by-step explanation:
Norma spent $13.25 on school supplies. She bought 3 binders that cost $3.75 each and some paper. Which equation could be used to figure out the cost of the paper? A. 13.25 = 3.75 + n B. 13.25 = 3.75 – n C. 13.25 = 3 × 3.75 + n D. 13.25 = 3 × (3.75 + n) i suck at math ;-;
Relationship A has a greater rate than Relationship B. This table represents Relationship B.
Hours worked (2 ) (4 ) (5 ) (8 )
Amount paid (30.40) (60.80) (76) (121.60)
Which equation could represent Relationship A? Hours worked is represented by x and Amount paid is represented by y.
Select each correct answer.
A. y = 16.4x
B. y = 14.9x
C. y = 15.4x
D. y = 15.2x
The correct equation that could represent Relationship A, which has a greater rate than Relationship B, is A. y = 16.4x as it is the only rate per hour greater than that of Relationship B's $15.20 per hour.
The student's question concerns comparing rates of pay in two different linear relationships. Given the table for Relationship B, we can calculate the rate per hour for Relationship B and then compare this to the rates provided in the equations for Relationship A. By looking at the data provided for Relationship B, we can see that the rate is constant. For example, for 2 hours worked, the amount paid is $30.40, which results in a rate of $30.40 / 2 hours = $15.20 per hour.
Because Relationship A has a greater rate than Relationship B, we are looking for an equation where the rate (slope) is greater than $15.20 per hour. Therefore, we eliminate any option where the rate is less than or equal to $15.20. Looking at the provided options:
A. y = 16.4x
B. y = 14.9x
C. y = 15.4x
D. y = 15.2x
Since options B ($14.9 per hour), C ($15.4 per hour), and D ($15.2 per hour) have rates that are either less than or equal to the rate of Relationship B, they cannot represent Relationship A which has a greater rate. Therefore, the only possible option is A. y = 16.4x, which represents a rate that is greater than the rate we determined for Relationship B.
how many kilometers could 217 km red car travel in 12 hours write an equation to show your work
Answer:
The required equation is: [tex]217\times 12=2,604[/tex]
The red car can travel 2,604 Km in 12 hours.
Step-by-step explanation:
Consider the provided information.
It is given that the speed of red car is 217 km\hr
We need to write an equation and find how many kilometers could red car travel in 12 hours.
The required equation is: [tex]217\times 12=2,604[/tex]
Hence, the red car can travel 2,604 Km in 12 hours.
How do you use the distributive property to solve 24 + 36 using a(b+c) form
You have a box that has a volume of 412 cm3 and weighs 42 g what is its density
what are algebraic expressions?
Solve the equation 3/7k=12/35
explain how fractions strips can be used to find five fractions bequal to 3/6 list three equivalent fractions
What integer can be represented by 15 positive tiles and 16 negative tiles?
A section of a boardwalk is made using 15 boards. Each board is 9 1/4 inches wide. The total width of the section is 144 inches. The spacing between each board is equal. What is the width of the spacing between each board? Write your answer in simplest form.
A 25-foot long ladder is propped against a wall at an angle of 18° with the wall. How high up the wall does the ladder reach? Round the answer to the nearest tenth of a foot. 13.8 ft 23.8 ft 26.3 ft 80.9 ft
Answer:
B) 23,.8 feet
Step-by-step explanation:
It forms a right triangle.
We use the trigonometric ratio of cos to find the answer.
cos = adjacent /Hypotenuse
Here hypotenuse is the length of the ladder and adjacent side represent the ladder toughs the wall from the ground.
cos 18 = adjacent / 25
adjacent = 25*cos18
adjacent = 23.8 feet
Answer: B) 23,.8 feet
Hope this will helpful.
Thank you.
Answer:
B) 23.8 ft
Step-by-step explanation:
Is the graph of a function that relates a squares side length to its perimeter continuous or discrete
90/ [10(3squared - 4)
Vivian draws three right triangles in each figure she measures a pair of angles shown which conjecture is reasonable for Vivian to make
complementary angles
my book is 52 pages. I have already read 18 pages. I plan to read 10 pages each day until I finish the book.
Estimate about how many days it will take to finish reading the book.
A. 3
B. 7
C. 12
D. 30
Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.
Solve 24 - 3 x = -27.
Answer:
17
Step-by-step explanation:
Given,
24 - 3 x = -27.
24+27 = 3[tex]x[/tex]
3[tex]x[/tex] = 51
[tex]x[/tex] = [tex]\frac{51}{3}[/tex]
[tex]x[/tex] = 17
Ron what to make a rectangle basketball court if the length is 4 whole number 3/4 yd and the width is 3 whole number is 2/5 yd. what is the area
Quick help: 7th grade hw question
"You are buying flowers to hand out at a school dance. Roses cost 30$ for a dozen but cost more if bought individually. With the money you have, you can buy 7 dozen and four single roses (64). How much is one rose? How much money do you have?
Eight less than 1/3 a number n is -13
Find the mean, median, mode, and range of this data: 49, 49, 54, 55, 52, 49, 55. If necessary, round to the nearest tenth. A. 51.9, 52, 49, 6 B. 52.9, 52, 49, 104 C. 51.9, 53, 49, 6 D. 52, 52.9, 49, 104
Find unit rate. The tub fills with 12 gallons of water in 5 minutes?
A robot can complete 3 tasks in 4/5 hour. Each task takes the same amount of time.
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?