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]
Of 350 students polled, some have a cat, some have a dog, and some have both. One hundred seventy-five students have a cat and 140 have both types of pets. How many students have a dog only? Explain.
I believe the answer was:
175; Since 175 have a cat or a cat and dog, then the number that have a dog only is 350 − 175 = 175.
But I just needed to check
Developing it says constructing equations from a table
12a + 12b + 12c + 12d
Michael writes the expression shown here as 12(a + b + c + d). He is correctly using the ___________ property.
A) associative
B) commutative
C) distributive
D) symmetric
The expression shown here is using the distributive property.
What is distributive property?The distributive property simply states that multiplication distributed over addition. Multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
For the given situation,
The expression is 12a + 12b + 12c + 12d.
The formula for the distributive property is expressed as,
a × (b + c) = (a × b) + (a × c).
Michael writes the expression shown as
⇒ [tex]12a + 12b + 12c + 12d = 12(a + b + c + d)[/tex]
The above expression is of the form of the formula for the distributive property.
Hence we can conclude that the expression shown here is using the distributive property.
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Eight less than 1/3 a number n is -13
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.
Evaluate the expression 40÷1+3-(3×7)+7-5
63 is 90% of what number using number lines
what is the angle of n
What integer can be represented by 15 positive tiles and 16 negative tiles?
Balance the equation
What is the standard form for Three thousand four hundred and eighty two
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?
1/8 divided by 3/4 please help
180 is the LCM of 12 and what?
Which expression is equivalent to 4(3x+5y+2z)+3(x-z)
A. 12x+20y+8z
B. 5(3x+4y-z)
C. 15x+20y+5z
Final answer:
The expression 4(3x+5y+2z)+3(x-z) is equivalent to 15x+20y+5z.
Explanation:
To simplify the expression 4(3x+5y+2z)+3(x-z), you need to distribute the 4 and 3 to each term inside the parentheses.
When you distribute the 4 and 3, you get 12x+20y+8z+3x-3z. Combine like terms to simplify further, which gives us 15x+20y+5z.
Therefore, the expression 4(3x+5y+2z)+3(x-z) is equivalent to C. 15x+20y+5z.
The negative sign can be read as "the opposite of."
2/2 + 1.75 - 176%
Enter your answer as an exact decimal or simplified fraction.
You have a box that has a volume of 412 cm3 and weighs 42 g what is its density
Which decimal number is equal to 7/9 0.7 0.7¯ 0.78 0.78¯
Answer:
0.7
Step-by-step explanation:
Write the first six terms in the number pattern. Start with 83 and subtract 9 repeatedly.
11. The preferred overall competition area in judo, including the mats, is a square with an area of 256 m2.
a) How do you know that the length and width of the competition area are between 10 m and 20 m?
b) What are the possible last digits of the dimensions if the side lengths are whole numbers? c)
Use your answers to parts (a) and (b) to predict the dimensions.
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
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 ;-;
What is 0.02 written as a decimal
The fractions 1/50 or 2/100 are written as a decimal 0.02.
We have,
Expression:
0.02
This can be written in fraction form as,
= 002/100
= 2/100
Simplify the fraction.
2/100
= 2/(2 x 50)
= 1/50
Thus,
The fractions 1/50 or 2/100 are written as a decimal 0.02.
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Wallace received a 28 percent discount on an item priced at $275. What is the total price that he paid for it?
28% = 0.28
multiply:
275 * 0.28 = 77 ( discount
now subtract:
275 - 77 = 198 ( price after discount )
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:
Mr. Gomez paid a total of $267 for the repairs on his car. The cost of the labor was two thirds of the total charge. Find the charge for labor
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
Philip had $674.31 in his student lunch account at the beginning of the school year.by the end of the school year, he had spent $782.75 on lunches. What was the balance in Philips lunch account at the end of the school year?
Answer:
-108.44
Step-by-step explanation: this is the answer