Answer:
(1) The slope of the line segment AB is 1.[tex]\bar 3[/tex]
(2) The length of the line segment AB is 10
(3) The coordinates of the midpoint of AB is (5, 7)
(4) The slope of a line perpendicular to the line AB is-0.75
Step-by-step explanation:
The coordinates of the line segment AB are;
A(2, 3) and B(8, 11)
(1) The slope of a line segment is given by the following equation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) and (x₂, y₂) are two points on the line segment
Therefore;
The slope, m, of the line segment AB is given as follows;
A(2, 3) = (x₁, y₁) and B(8, 11) = (x₂, y₂)
[tex]Slope, \, m_{AB} =\dfrac{11-3}{8-2} = \dfrac{8}{6} = 1 \frac{1}{3} = 1.\bar3[/tex]
The slope of the line segment AB = 1.[tex]\bar 3[/tex]
(2) The length, l, of the line segment AB is given by the following equation;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Therefore, we have;
[tex]l_{AB} = \sqrt{\left (11-3 \right )^{2}+\left (8-2 \right )^{2}} = \sqrt{64 +36} = 10[/tex]
The length of the line segment AB is 10
(3) The coordinates of the midpoint of AB is given as follows;
[tex]Midpoint, M = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )[/tex]
Therefore;
[tex]Midpoint, M_{AB} = \left (\dfrac{2 + 8}{2} , \ \dfrac{3 + 11}{2} \right ) = (5, \ 7)[/tex]
The coordinates of the midpoint of AB is (5, 7)
(4) The relationship between the slope, m₁, of a line AB perpendicular to another line DE with slope m₂, is given as follows;
[tex]m_1 = -\dfrac{1}{m_2}[/tex]
Therefore, the slope, m₁, of the line perpendicular to the line AB, that has a slope m₂ = 4/3 = 1.[tex]\bar 3[/tex] is given as follows;
[tex]m_1 = -\left (\dfrac{1}{\frac{4}{3} } \right ) = -\dfrac{3}{4} = -0.75[/tex]
The slope, m₁, of the line perpendicular to the line AB is m₁ = -0.75.
Need help asap i’ll give brainlyest
Based on the attendance at past picnics, Luis expects 95% of the students in his class to attend this years picnic. If 120 students are in the class, how many students are likely to attend the picnic?
Answer:
95 / 100 * 120 = 114 students
Thank you and please rate me as brainliest as it will help me to level up
Name one situation in which a humor device would be good to use in your writing?
Cooper is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms, that can room 2 people, and large rooms, that can room 4 people. How many wedding guests could stay in the hotel if Cooper reserved 12 small rooms and 11 large rooms? How many wedding guests could stay in the hotel if Cooper booked ss small rooms and ll large rooms?
Answer:
Step-by-step explanation: s = small room = 2
l = large room = 4
12s + 11l = 28 + 22 = 50
as I said before s = 2 and l = 4
s*s + l*l = 2*2 + 4*4 = 4 + 16 = 20
The long climbing rope is 100 feet long. The long climbing rope is ten times longer than the shorter safety rope. How many feet of rope is the shorter safety rope?
Answer:
10 feet
Step-by-step explanation:
100/10=10
Find the coordinates of the image
Ry=-1(p)
The image is _____?
Answer:
Step-by-step explanation:
y=0,3
x=-4,0
(-4,3)
The required coordinate of the image of p is under y = -1 is given as (-4, 4).
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate the y is called ordinate.
Here,
Coordinates of point P = (-4, 3)
Now,
[tex]R_{y = -1}(p)[/tex]
The question of the image is given that
(x, y) ⇒ (x, -[y + 1])
= (-4, -[3 + 1]) = (-4, -4)
Thus, the required coordinate of the image of p is under y = -1 is given as (-4, 4).
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What is 15x-3y = 0 written in slope-intercept form?
O y = 5x
O y=-5x
O X= 1/5y
O X= 5y
HELP!!!!!!!! I WILL GIVE BRAINLIEST
Adam is three years older than Joe. After three years, Adam's age will be four years less than two times Joe's age. Considering Adam's present age as x years and Joe's present age as y years, write a pair of linear equations to model the above situation.
Answer:
X = 3+y
X = 2y - 4
Step-by-step explanation:
The system of equations for the given situation will be written as X = 3+y and X = 2y - 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Adam is three years older than Joe. After three years, Adam's age will be four years less than two times Joe's age. Considering Adam's present age as x years and Joe's present age as y years.
The equation can be written as,
X = 3+y
X = 2y - 4
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Explain EACH step you would take to solve the following system using substitution.
y = 3x - 5
x = 2
Answer:
y=1
Step-by-step explanation:
y=(3)(2)−5
y=6-5
y=1
Answer:
-3Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is y = m x + b , where m is the slope and b is the y intercept.
y = m x + b
Find the values of m and b using the form y = m x + b .
m =− 5 3 b = 2
The slope of the line is the value of m , and the y-intercept is the value of b .
Slope:
− 5 3
y-intercept: 2
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Choose 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f ( 0 ) = − 5 ( 0 ) 3 + 2
Simplify the result.
Simplify each term.
Cancel the common factor of 0 and 3 .
Factor 3 out of 5 ( 0 ) .
f ( 0 ) = − 3 ( 5 ⋅ ( 0 ) ) 3 + 2
Cancel the common factors.
Factor 3 out of 3 .
f ( 0 ) = − 3 ( 5 ⋅ ( 0 ) ) 3 ( 1 ) + 2
Cancel the common factor.
f ( 0 ) = − 3 ( 5 ⋅ ( 0 ) ) 3 ⋅ 1 + 2
Rewrite the expression.
f ( 0 ) = − 5 ⋅ ( 0 ) 1 + 2
Divide 5 ⋅ ( 0 ) by 1 .
f ( 0 ) = − ( 5 ⋅ ( 0 ) ) + 2
Multiply 5 by 0 .
f ( 0 ) = − 0 + 2
Multiply − 1 by 0 .
f ( 0 ) = 0 + 2
Add 0 and 2 .
f ( 0 ) = 2
The final answer is 2 .
2
The y value at x = 0 is 2 .
y = 2
Choose 3 to substitute in for x to find the ordered pair.
Replace the variable x with 3 in the expression.
f ( 3 ) = − 5 ( 3 ) 3 + 2
Simplify the result.
Simplify each term.
Cancel the common factor of 3 .
Cancel the common factor.
f ( 3 ) = − 5 ⋅ 3 3 + 2
Divide 5 by 1 .
f ( 3 ) = − 1 ⋅ 5 + 2
Multiply − 1 by 5 .
f ( 3 ) = -5 +2
Add − 5 and 2 .
f ( 3 ) = − 3
The final answer is − 3 .
− 3
The y value at x = 3 is − 3 .
y = − 3
Create a table of the x and y values.
x- 0, 3
y- 2, -3
Graph the line using the slope and the y-intercept, or the points.
Slope: − 5 /3
y-intercept: 2
x- 0, 3
y- 2, -3
what is
1.63 x 0.98 =
Answer:
1.5974
Step-by-step explanation:
Answer:
1.5974
Step-by-step explanation:
1.63 x 0.98
We know that there is 4 decimal places for both numbers, meaning we know that there will be 4 numbers following the decimal
1.63 x 0.98 = 1.5974
Enrique is going to a party this weekend. He is bringing 20 liters of soda to the party. A liter of soda costs $1.59.
How much will Enrique spend on soda?
$3.18
$27.40
$29.60
$31.80
You are running a concession stand at a basketball game. You are selling hotdogs and sodas. Each hotdog cost $1.50 and each soda cost $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hotdogs and sodas combined. How many hotdogs did you sell?
Answer:
35 hotdogs
Step-by-step explanation:
You are running a concession stand at a basketball game. You are selling hotdogs and sodas.
Let the number of hot dogs be represented by x
The number of soda be represented by y
You sold a total of 87 hotdogs and sodas combined
x + y = 87
x = 87 - y
Each hotdog cost $1.50 and each soda cost $0.50. At the end of the night you made a total of $78.50.
Hence we have the equation:
$1.50 × x + $0.50 × y = $78.50
1.50x + 0.50y = 78.50
Substitute 87 - y for x
1.50(87 - y) + 0.50y = 78.50
130.5 - 1.50y + 0.50y = 78.50
Collect like terms
- 1.50y + 0.50y = 78.50 - 130.50
-1.00y = -52
y = -52/-1
y = 52 sodas
How many hotdogs did you sell?
Using the equation:
x = 87 - y
x = 87 - 52
x = 35 hotdogs
Hence, you sold 35 hotdogs
Kiran and Clare live 24 miles away they start walking at 8 am Clare is walking 3.4 miles per hour and they get there at 10:30 am how fast was Kiran jogging
Answer:
Kiran is jogging at 9.6 miles per hour.
Step-by-step explanation:
We can find the speed of Kiran as follows:
[tex] v = \frac{x}{t} [/tex]
Where:
v: is the speed =?
x: is the distance = 24 miles
t: is the time
If Clare and Kiran started walking at 8 am and they get to their destination at 10:30 am, then the time is:
[tex] t = 10:30 - 8:00 = (10 h + 30min*\frac{1 h}{60 min}) - 8 h = 2.5 h [/tex]
Then, the speed of Kiran is:
[tex] v = \frac{x}{t} = \frac{24 miles}{2.5 h} = 9.6 miles/h [/tex]
Therefore, Kiran is jogging at 9.6 miles per hour.
I hope it helps you!
i triple my number add four and i get seven whats my number
Answer:
1
Step-by-step explanation:
1 • 3 + 4 = 7
Convert the decimal 19.52 into a mixed fraction
19 and 13/25 is your answer.
Answer:
19 11/20
Step-by-step explanation:
1955/100
391/20
19 11/20
Note: you have to place 19 beside" / "
The first one to answer gets brainliest or whatever
A car is 180 inches long. A truck is 75% longer than the car.
How long is the truck?
135
240
255
315
Answer:
I think it is 315 but I might be wrong
Step-by-step explanation:
Solve this problem
-2/3 x 13/21 + 3/7
Answer:
0.01587301587
Step-by-step explanation:
calculator
if x = 32 what does abc = this is not a real question
Answer:
??????
Step-by-step explanation:
2/4 * 4/8
please give me the correct answer
Answer:
1/4 is the correct answer....
Solve the inequality 5- 1/2 x > 30
Answer:
x < -50
Step-by-step explanation:
[tex]5-\frac{1}{2}x>30[/tex]
[tex]<=>-\frac{1}{2}x >30-5[/tex]
[tex]<=> x<25:-\frac{1}{2}[/tex]
[tex]<=>x<-50[/tex]
Which graph shows the solution set of x-1/x-3 <0
Answer:
answer will be D i believe (As i cant see the graphs, I had too look for the graphs myself, thanks!)\
the graph will show a line chart -5 to 5+ THE HIGHLIGHTS will be between 1 and 3
which property of addition is used in the following (5+12)+6=5+(12+6)
Answer:
Associative property of addition
Step-by-step explanation:
its the same order only the () move
Raja is trying to decide which ice cream shop is the better buy. Cold &Creamy sundaes charges 2.50 per sundae
where is the rest of the question??
A washer and a dryer cost $698 combined. The washer costs $48 more than the dryer. What is the cost of the dryer?
Answer:
277
Step-by-step explanation:
w+d=698
w= d+48
d+48+d=698
2d+48=698
650/2d
325=w
w-48=d
325-48=d
277=d
A basketball player attempted 15 field goals. He scored on 40 percent of his attempts. How many field goals did the player score? Press enter to interact with the item, and press tab button or down arrow until reaching the Submit button once the item is selected A12 field goals B6 field goals C10 field goals D9 field goals
Answer:
B. 6 field goals
Step-by-step explanation:
Given
[tex]Attempts = 15[/tex]
[tex]Scored = 40\%[/tex]
Required
Determine the number of goals scored
To do this, we simply multiply the number of attempts by the percentage scored.
[tex]Number = Attempts * Scored[/tex]
[tex]Number = 15 * 40\%[/tex]
Convert % to decimal
[tex]Number = 15 * 0.40[/tex]
[tex]Number = 6[/tex]
He scored 6 of his 15 attempts
You are shoveling snow from the sidewalks around your neighborhood after a big snowstorm. You work at a steady rate, shoveling 10 feet of sidewalk in 40 minutes. 1) At this rate, how many minutes will it take you to shovel 75 feet of sidewalk?
Answer:
300 minutes
Step-by-step explanation:
Given
10 feet in 40 minutes
Required
Determine the time to shovel 75 feet
Let the required be represented with x
First, we need to represent the given and required as ratios.
[tex]Given = 10 : 40[/tex]
[tex]Required = 75 : x[/tex]
Since you work at steady rate, then both ratios are equivalent.
[tex]10 : 40 = 75 : x[/tex]
Convert to fractions
[tex]\frac{10}{40} = \frac{75}{x}[/tex]
[tex]\frac{1}{4} = \frac{75}{x}[/tex]
Solve forx
[tex]x * 1 = 75 * 4[/tex]
[tex]x = 300[/tex]
Rob Barros $15 from his father and then he borrows three dollars more drag numbers to write an equal using negative integers to represent bobs debit and complete the sentence to show how much money rob his father Numbers may be used once more than once or not at all
Answer:
The amount of money in dollars that Rob owe his father is -$18
Step-by-step explanation:
From the given information:
Rob borrows $15 from his father and then he also borrows $3 more.
Thus, the amount he owes is father is now:
- $15 - $3 = - $18 Since we are using negative integers.
The amount of money in dollars that Rob owe his father is -$18
Freddy bought 5 bags of pebbles to put in his fish tank. Each bag contains 238 pebbles. After he put the right amount of
pebbles in his fish tank, he had 118 pebbles left over. How many pebbles did he put in his fish tank?
Answer:
1,072
Step-by-step explanation:
what is the maximum temperature for hiking cold, potentially hazardous food?
-less than 32 degrees
-less than 45 degrees
-less than 41 degrees
-less than 70 degrees
it must be less than 41 degrees
Which of these is a two-step equation?
A. x + 9 = 21 incorrect answer
B. x = 11 + 2 incorrect answer
C. 2x + 9 = 21 incorrect answer
D. x/3 = 9
Answer: I believe is C
Step-by-step explanation:
2x=21-9
x=12/2
Answer:
d
Step-by-step explanation: