The linear equation of the line will be y = -x + 6.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. A2 nd the third parameter is the slope of the line which represents the elevation of the line.
Given that a line passes through the points (−1, 7) and (2, 4). The equation of the line will be calculated by finding the slope of the line.
y = mx + c
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 2 - ( -1 ) / ( 4 - 7)
m = ( 3 / -3 )
m = -1
y = mx + c
( 7 ) = ( -1 )( -1 ) + x
c = 6
The equation will be written as:-
y = mx + c
y = -x + 6
Therefore, the linear equation of the line will be y = -x + 6.
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What is the value of the expression? 3(6/8−1/2)+0.25
Determine the digits of Y from these clues. The digits of Y add to 16. The first digit is 4 times the third digit. The second digit is 3 times the third digit. Y is a three digit number. 268 826 628 862
Answer: 862
Step-by-step explanation:
Let the third digit of Y be x .
Then , the first digit will be 4x and the second digit will be 3x.
Since , the digits of Y add to 16.
Then we have
[tex]3x+4x+x=16\\\\\Rightarrow\ 8x=16\\\\\Rightarrow\ x=\dfrac{16}{8}=2[/tex]
Thus , the third digit of Y = 2
Then the first of Y digit will be [tex]4(2)=8[/tex]
The second digit of Y will be [tex]3(2)=6[/tex]
Hence, the digits of Y must be 862
What did the doctor say to the guy who thought he was a wigwam one day and tepee the next?
a landscape company charges $100 plus $15 per hour. another company charges $75 plus $17 per hour. how long is a job that costs the same no matter which company is used
To find when the job cost is the same for both companies, equate their cost equations. By solving 100 + 15h = 75 + 17h, we find that at 12.5 hours the job would cost the same no matter which company is used.
To determine when a job costs the same for both landscape companies, we need to equate the two cost equations they offer and solve for the number of hours.
Let h be the number of hours the job takes. The first company's cost can be represented as C1 = 100 + 15h, and the second company's cost as C2 = 75 + 17h. To find the number of hours when both companies charge the same amount, we set C1 = C2:
100 + 15h = 75 + 17h.
Rearrange the equation to solve for h:
100 - 75 = 17h - 15h
25 = 2h
h = 12.5 hours.
So, a job that takes 12.5 hours would cost the same amount whether it is done by the first company or the second company.
Pls help!! will give brainiest to best answer!
Kevin tries to climb a wall with a ladder. The length of the ladder is 15 feet and it reaches only 12 feet up the wall. What is the distance between the base of the ladder and the wall?
The solution is Option A.
The distance between the base of the ladder and the wall is 9 feet
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Now , the height of the wall = 12 feet
The measure of AB = 12 feet
The length of the ladder = 15 feet
The measure of AC = 15 feet
Now , the distance between the base of the ladder and the wall = BC
The measure of BC is given by the Pythagoras Theorem , where
Hypotenuse² = base² + height²
AC² = AB² + BC²
Substituting the values in the equation , we get
15² = 12² + BC²
Subtracting 12² on both sides of the equation , we get
BC² = 15² - 12²
BC² = 225 - 144
BC² = 81
Taking square roots on both sides of the equation , we get
BC = 9 feet
Therefore , the value of BC is 9 feet
Hence , the distance is 9 feet
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Write the algebraic expression representing the length and width of Marliens house. Someone please tell me the process of how to do this
Answer:
Length of Marliens house = [tex](\frac{7}{2}x-4)\text{ or }(\frac{9}{2}x-18)[/tex] .
Width of Marliens house = [tex](2x-2)[/tex].
Step-by-step explanation:
We need to find the length and width of Marlien's home in algebraic expressions.
Add length of living room, hallway and kitchen, to find the length of Marlien's home.
Length of Marlien's home = [tex](2x+2)+(\frac{1}{2}x-4)+(x-2)=\frac{7}{2}x-4[/tex]
Or we can add Master bedroom,guest room, hallway and bathroom, to find the length of Marlien's home.
Length of Marlien's home = [tex](2x-10)+(x-2)+(\frac{1}{2}x-4)+(x-2)=\frac{9}{2}x-18[/tex]
Add width of living room and Master bedroom to find the width of Marlien's home.
Width of Marlien's home = [tex]x+(x-2)=2x-2[/tex]
Hence, the length of Marliens house is either [tex](\frac{7}{2}x-4)\text{ or }(\frac{9}{2}x-18)[/tex] and width of Marliens house is [tex](2x-2)[/tex].
What is the product? Enter your answer as a fraction, in simplified form, in the box. 3/8⋅(−3/6)
The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].
Given:
An expression : [tex]\frac{3}{8}.(\frac{-3}{6})[/tex]
To find:
The product of the given expression of fractions in simplified form.
Solution:
[tex]\frac{3}{8}.(\frac{-3}{6})\\\\= \frac{3}{8}\times (\frac{-3}{6})\\\\=\frac{-9}{48}\\\\=\frac{-3}{16}[/tex]
The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].
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Amy class went the fair they saw 22 horses and 18 ponies they also saw 18 rabbits and 37 hares compare the the number of horses and ponies to the number of rabbits and hares that the class saw.
Amy's class saw a total of 40 horses and ponies and 55 rabbits and hares at the fair,
The question involves comparing the numbers of two sets of animals seen at the fair: horses and ponies versus rabbits and hares. To solve this, we will first add the number of horses and ponies together and then do the same for rabbits and hares.
Number of horses and ponies combined:
22 horses + 18 ponies = 40
Number of rabbits and hares combined:
18 rabbits + 37 hares = 55
Comparing the two totals:
40 horses and ponies is less than 55 rabbits and hares. Therefore the class saw more rabbits and hares combined than horses and ponies combined at the fair
Audrey needs to cut 1 meter of yellow ribbon and 28 centimeters of blue ribbon. In total, how many centimeters of ribbon does she need?
centimeters
Answer: She needed 128 cm of ribbon.
Step-by-step explanation:
Since we have given that
Length of yellow ribbon needed to be cut = 1 meter
Length of blue ribbon needed to be cut = 28 cm
We need to find the number of centimeters she needed to be cut.
First of all, we convert meter into centimeter.
As we know that
1 meter = 100 centimeter
So, Total number of centimeters of ribbon she needed is given by
[tex]100+28\\\\=128\ cm[/tex]
Hence, She needed 128 cm of ribbon.
A farmer has 212 acres of land for sale.He divides the land into 18 equal sections.About how many acres are in each section?
The prices of two radios are in the ratio x:y
When the prices are both increased by £20, the ratio becomes 5:2
When the prices are both reduced by £5, the ratio becomes 5:1
Express the ratio x:y in it's lowest terms.
The concept of linear equation and ratios is used to solve for the price of radios. The price of two radios are [tex]x=\pounds 80[/tex] and [tex]y=\pounds 20[/tex].
Given information:
The ratio of prices of two radios is [tex]x:y[/tex].
If the price of both the radios is increased by [tex]\pounds20[/tex], the ratio of price would become 5:2.
The above condition can be written mathematically as,
[tex]\dfrac{x+20}{y+20}=\dfrac{5}{2}\\2x+40=5y+100\\2x-5y=60.........(1)[/tex]
If the prices are both reduced by [tex]\pounds 5[/tex], the ratio will become 5:1.
The above condition can be written mathematically as,
[tex]\dfrac{x-5}{y-5}=\dfrac{5}{1}\\x-5=5y-25\\x-5y=-20\\-x+5y=20.........(2)[/tex]
Add equation (1) and (2), to get the value of [tex]x[/tex] and [tex]y[/tex] as,
[tex]2x-x=60+20\\x=80[/tex]
Solve for [tex]y[/tex] as,
[tex]2x-5y=60\\2\times 80-5y=60\\5y=100\\y=20[/tex]
Therefore, the price of two radios is [tex]x=\pouns 80[/tex] and [tex]y=\pounds 20[/tex].
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How many of the first 10,000 positive integers contain the digit pair “43” in that order?
Final answer:
There are 209 numbers among the first 10,000 positive integers that contain the digit pair '43' in that order, when considering the different placements of the digit pair in a four-digit number.
Explanation:
To find out how many of the first 10,000 positive integers contain the digit pair "43" in that order, let's consider the different places this pair can occur. The '43' pair can be in the units and tens place, the tens and hundreds place, or the hundreds and thousands place.
For the units and tens place, we have '43' fixed and two remaining places that can be any digit from 0 to 9, so there are 10 times 10 = 100 possibilities. However, we need to exclude the combination '043' as it is not a four-digit number but rather '43', giving us 100 - 1 = 99 combinations.
For the tens and hundreds place, we again have 10 possibilities for the other two places (thousands and units). We do not need to exclude any numbers here because even '043x' represents a valid four-digit number. Thus, we have 10 imes 10 = 100 combinations.
For the hundreds and thousands place, there are only 10 possibilities for the units place, as '430x' represents a valid four-digit number, which results in 10 combinations.
Adding them up, we have a total of 99 + 100 + 10 = 209 numbers that contain the '43' pair in the first 10,000 positive integers.
The diameter of a spherical basketball is 10in, what is the volume of the basketball?
Answer:
21
Step-by-step explanation:
hard wok
talent
Please help me Simplify 3x-2x+x-9. I was told my answer was wrong
does 65-(45-20)equal (65-45)-20? how do you know?
Answer:
No, the expression 65-(45-20) is not equal to (65-45)-20.
Step-by-step explanation:
Consider the provided expression.
Consider the expression: 65-(45-20)
Solve the above expression as shown.
65-(45-20)
65-(25)
65-25
40
Now consider the second expression.
(65-45)-20
20-20
0
Now compare both the result.
40≠0
Hence, the expression 65-(45-20) is not equal to (65-45)-20.
Simplify 3(x - 6) - 4(x + 3).
Answer:
B) -x-3
Step-by-step explanation:
If I read and did the math correctly, this should be the answer. :)
Abbey gets paid a flat rate of $10.00 to mow her neighbor's lawn plus an additional $5 per hour to rake the leaves. The money she earns is represented by the equation m = 5h + 10, where m represents the amount of money she earns, in dollars, and h is the number of hours she rakes leaves for. Which of the following equations can be used to find h, the number of hours she rakes leaves for?
The answer choices are:
A. h= m -2
B. h=m -10
C. h= m/5
D. h= m-10/5
Help there are 4 screen shots
How do i do 4/7 divided by 1 3/4
make 1 3/4 an improper fraction:
1 3/4 = 7/4
now you have 4/7 divided by 7/4
now reverse the 7/4 and multiply:
4/7 x 4/7 = 16/49
Which equation is in standard form?
x + 2y = 8
x = -2y + 8
2y = -x + 8
name a segment skew to Wy
A theater seats 1860 people the last 6 shows have been sold out estimate the total number of people attending the last 6 shows
Use a calculator to find the value of Sin 21°
Round to four decimal places.
A. 0.3839
B. 0.3584
C. 0.9336
D. 2.7904
Answer:
Option B is the correct answer.
Step-by-step explanation:
We need to find the value of Sin 21° using calculator and round to four decimal places.
Using calculator
Sin 21° = 0.358367949
Rounding the value of Sin 21° to four decimal places.
Sin 21° = 0.3584
Option B is the correct answer.
Which numbers are a distance of 3 units from 12 on a number line?
Select each correct answer.
3
15
0
9
−9
−15
Answer:
15 and 9 are the correct answers.
Step-by-step explanation:
The numbers that are at a distance of 3 units from 12 on a number line are given as:
We will add 3 to 12 and also subtract 3 from 12 to get both numbers on the left side an right side on the number line.
[tex]12+3 = 15[/tex]
[tex]12-3 = 9[/tex]
So, the correct answers are 15 and 9.
The amounts that two partners invested in a new business are given below. If the partners share the profits in the same ratio as their investment, what is partner B's share in a $3600 profit?
Partner A $4300 Partner B $7700
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function p(t) = -8t + 100. How many minutes would it take the printer to use all 100 sheets of paper?
Using the function p(t) = -8t + 100, where t is time and p(t) is the amount of paper left, we set p(t) to 0 and solve for t. This reveals that it will take 12.5 minutes for the printer to use all 100 sheets of paper.
Explanation:In this problem, we're told that the printer uses paper according to the function p(t) = -8t +100, where t is the time it takes to print and p(t) is the amount of paper left in the printer. We want to find how much time it will take for the printer to use all the 100 sheets of paper, meaning we need to set p(t) to 0 and solve for t.
Therefore, we set up and solve the equation as follows: 0 = -8t + 100. If we solve this equation for t, we get t =100/8, which simplifies to t = 12.5 minutes.
This means it will take the printer 12.5 minutes to use all the 100 sheets of paper. The previous suggestions about other solutions and negative time are not applicable in the context of this problem because time cannot be negative in this instance, and this equation yields only one solution.
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name three quaderlateral that only sometimes have right angle
Donald is giving his old rare coins to his grandchildren. he has 56 coins and 8 grandchildren, and he gives each grandchildren the same number of coins. each coin has a value of $18. which equation can we use to find the value (v) of each grandchildren's coins?
simplify 50 1/2 + 12.3
Someone plz tell me if my answers for the two questions are correct.Also help me with question f without telling the answer.