Given:
Two points are A(-7,2) and B(3,4).
To find:
The perpendicular bisector of AB.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Slope of AB is
[tex]m_1=\dfrac{4-2}{3-(-7)}[/tex]
[tex]m_1=\dfrac{2}{3+7}[/tex]
[tex]m_1=\dfrac{2}{10}[/tex]
[tex]m_1=\dfrac{1}{5}[/tex]
Procut of slopes of perpendicular line is -1.
So, slope of perpendicular bisect is opposite of reciprocal of [tex]\dfrac{1}{5}[/tex].
[tex]m_2=-5[/tex]
Midpoint of AB is
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-7+3}{2},\dfrac{2+4}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-4}{2},\dfrac{6}{2}\right)[/tex]
[tex]Midpoint=\left(-2,3\right)[/tex]
Slope of perpendicular bisector is -5 and it passes through (-2,3), so the equation of perpendicular bisector is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope.
[tex]y-3=-5(x-(-2))[/tex]
[tex]y-3=-5(x+2)[/tex]
[tex]y-3=-5x-10[/tex]
Add 3 on both sides.
[tex]y=-5x-10+3[/tex]
[tex]y=-5x-7[/tex]
Therefore, the equation of perpendicular bisector is [tex]y=-5x-7[/tex].
Select True or False.
The expression 3x – 4(2x – 5) is equivalent, to the expression 20 – 5x.
True
O false
Answer:
true
Step-by-step explanation:
[tex]3x - 4(2x - 5) = \\ 3x - 8x + 20 = \\ - 5x + 20 = \\ 20 - 5x = > \: true[/tex]
Answer:
true
Step-by-step explanation:
3x -4(2x-5)
3x-8x+20
5x+20
Identify the value for the variable
Answer:
-12, 4
Step-by-step explanation:
7^-9 x 7^-3 = 7^-12
When you multiply exponents with the same base, you add them.
11^-4/11^-8 = 11^4
When you subtract exponents with the same base, you subtract the exponent in the numerator by the exponent in the denominator.
Given 45-45-90 triangle with hypotenuse of 3cm solve for the other sides.
Answer:
[tex]\sqrt{\frac{9}{2} }[/tex]
Step-by-step explanation:
Given dimensions:
The right angle system is a 45 - 45 - 90
Hypotenuse = 3cm
Unknown:
Adjacent and opposite sides = ?
Solution:
In this triangle, the adjacent and opposite sides are equal to one another. So,
Let adjacent = y
opposite = y
For right angle triangles as this, using the Pythagoras theorem,
hypotenuse² = adjacent² + opposite²
Insert the parameters and solve;
3² = y² + y²
2y² = 9
y² = [tex]\frac{9}{2}[/tex]
y = [tex]\sqrt{\frac{9}{2} }[/tex]
what’s the simplified value of 12.4x(-6.3)
Answer:
-78.12
Step-by-step explanation:
Answer: u just divide the small number to the big number and add and get ur answer that is -78.12
Step-by-step explanation:
Use the complement rule for probabilities
Question
arces
Over the course of a week, an airline has 42 flights between New York and Los Angeles. Of these flights, 28 are considered
to be "on-time."
If you chose a particular flight at random, what is the probability that it would not be on-time? Express your answer as a
fraction.
Provide your answer below:
Answer:
The probability that a particularly randomly chosen flight will not be on time is 1/3
Step-by-step explanation:
The number of flights available between New York and Los Angelis = 42 flights
The number of flights that are considered to be on time = 28 flights
The probability that a particularly randomly chosen flight will not be on time = 1 - The probability that the flight will be on time
The probability that the flight will be on time = (The number of flights considered to be on time)/(The total number of flights available)
The probability that the flight will be on time = 28/42 = 2/3
∴ The probability that a particularly randomly chosen flight will not be on time = 1 - 2/3 = 1/3
The probability that a particularly randomly chosen flight will not be on time = 1/3.
Your answer
2. Find the slope of the line that passes through each of the points. Make
sure you simplify! *
1 point
(4,-2)and (10,-2)
1/2
-1/2
O 0
1/6
A school purchases calculators from a store for $6 each.
Create an equation that represents the total cost, d, in dollars, for the number of calculators purchased, c. Use both
variables in your equation.
Answer:
Cost =6(Cal)
Step-by-step explanation:
Calculators: 6$
Calculators: Cal
Cost=C
Cost =6(Cal)
Answer:
1=6
Step-by-step explanation:
Suzanne Attired makes fashionable garments. During a particular week employees worked 360 hours to produce a batch of 132 garments, of which 52 were seconds (meaning they were flawed). Seconds are sold for $90 each at Attired's Factory Outlet Store. The remaining 80 garments are sold for $200 each. What is the labor productivity ratio of this manufacturing process
Answer:
$57.44 per hour
Step-by-step explanation:
Given that :
Hours worked = 360 hours
Production = 132 batches of garment
Of the 152:
52 were flawed (sold at $90 each)
80 were sold at $200 each
Labor productivity ratio: (output value / input value (hours worked))
Output value = [(52*$90) + (80*$200)]
Output value = $20,680
Labor productivity ratio = $20,680 / 360 hours
Labor productivity ratio = $57.44 per hour
Ter.
Identify the property used in this equation:
(-2) + 6 + 1 = 1 + 6 + (-2)
Use the interactive tool tahyaluate the expression.
Answer:
commutative property
Step-by-step explanation:
Answer:
its commutative property and 5
A manufacturer allows a discount of 30% on the list of prices of goods bougth by wholesalers. Calculate the discount allowed on the following prices. 800,000
Answer:
$ 560,000 hope this helps
Step-by-step explanation:
240,000 what taken off of 800,000 the final price is 560,000
Using the existing midpoints of each side of the triangle, create the three medians. What do you observe about the way the medians Intersect?
Answer:
The three medians intersect at a single point.
Step-by-step explanation:
PLATO MAKE BRAINLIEST PLZZ
Centroid is that point where median draw from the center of each side in a triangle meet.
What is centroid?The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians.
Let,
There is a triangle ΔABC
Mark midpoints on sides AB, BC and CA which lets P, Q and R respectively.
Join PC, RB and QA
The point where PC, RB and QA meets called centroid.
Hence, the point of intersection of three medians is Centroid.
Learn more about Triangles:
https://brainly.com/question/2773823
#SPJ2
hey what 4a + 5 - 7a = 35
find the measure of each angles
Answer:
7; = 135
1;= 135
2; = 45
3; = 135
Is this right pls tell me ASAP
Sam and Jude went to the cinema. Here is the list of prices: 4.75 $ for a ticket, 1.75 $ for a drink, 0.85 $ for a sweet. They paid with a bill of 20 $. How much change did they receive?
Jonathan has a board that is 12 1/2 feet long that he needs cut into 5 equal pieces how long should each piece be
Answer:
2 1/2 per piece
Step-by-step explanation:
Shaun thinks that pi * 0 results in an irrational number. He thinks so because irrational and is rationalthe product of a rational number and an irrational number is irrational. Is Shaun correct? Explain why or why not.
Answer: No, Shaun is incorrect because pi never ends and is infinite and doesnt repeat not because its irrational and is rational the product of a rational number and an irrational number is irrational.
Step-by-step explanation:
Theres not really and explanation of how to get this answer you just need to think about it and see what would make sense.
determine the range of the following graph
Answer:
Range: [-6, 8]
Step-by-step explanation:
Range is the set of y-values that are outputted by function f(x).
From the graph we see that our y-values span from -6 to 8. Since both are closed dot, they are included in the range:
[-6, 8] or -6 ≤ y ≤ 8
A penguin walks South. It completes the first 1/3 mile in 1/5 of an hour and continues at the same rate. What is the penguin's rate in Miles per hour?
Answer:
Its walking at 3/5 miles per hour
The complementary angle of 56° is
Answer:
90 degrees
Step-by-step explanation:
trust
I NEED HELP!!!
Convert to find the equivalent rate,
inches
yards
60
min ute
second
Answer:
36 seconds
Step-by-step explanation:
Answer:
Dnbsflvi jvidkdkeicucyccgdmjcjvh
Step-by-step explanation:
crying for help here..
Answer:
ST=32
Step-by-step explanation:
We know the two sides are equal, so first solve for p.
9p-4=4p+16
9p-4p=16+4
5p=20
p=4
Now subsitute p back in for ST
9(4)-4=32
A tennis racket normally cots $70. The tennis racket is on sale for 40% off. What is the sale price of the tennis racket?
Answer:
$42
Step-by-step explanation:
Answer:
$42
Step-by-step explanation:
To find the sale price of the tennis racket, multiply the original price by 0.6:
70(0.6)
= 42
So, the sale price of the tennis racket is $42
Bicycle rentals cost $5.00 per hour for an adult and $2.50 per hour for a child.
A family with one adult and 2 kids decide to rent bicycles.
Which equation represents the relationship between the cost in dollars
for the family, c, and the time they rent the bicycles in hours, t?
A) c = 5.00t + 2.50
B) c = 7.50t
C) c = 5.00 + 2.50t
Dc = 10.00t
Answer:
B
Step-by-step explanation:
Have a good day!
Nathan will be working between 30 to 39 hours inclusive this week, which is 3 more than triple
what he worked last week. How many hours could have Nathan work last week?
(4, 5) and (-4, 3)
What’s the answer I need help
Answer:4(3)/(5)
Step-by-step explanation:
which equation represents this sentence? one half the sum of a number and four is less than the quotient of five and the number
Answer:
The fourth one
Step-by-step explanation:
Three less then the quotient means you are subtracting 3 from a division problem. 1/2 the sum of a number and four means that there is going to be a variable and 4 in parenthesis that you will add before you multiply by 1/2.
Point Q is the image of Q (-5,1) under a translation by 6 units to the right and 2 units down.
What are the coordinates of Q?
Answer:
(1,-1)
Step-by-step explanation:
The graph is being shifted 6 units to the right which affects the x-value and it is also being affected 2 units down which affects the y-value.
I need to turn that into an equation but I cant figure it out.
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
The equation will be...
[tex]\frac{3x-6}{2} +12[/tex]
I don't know if you need to solve it but here you go anyways...
[tex]\frac{3}{2}x+9[/tex]
The price of one share of a company’s stock declined $13.89 every day for 2.5 days. What was the stock’s total decline in price?
Which estimate uses compatible numbers to estimate the problem?
What is the exact answer?
Answer:
-$14(2.5) & -$34.73
Step-by-step explanation:
Which estimate uses compatible numbers to estimate the problem?
✔ -$14(2.5)
What is the exact answer?
✔ -$34.73
Answer:
answer is above
Step-by-step explanation:
