3x - y = -7 is the required equation of the line, which will bisect the line segment with endpoints (-7, 6) and (5,2).
the equation for the perpendicular bisector of the line with end points [tex](x_{0},y_{0})\\[/tex] and [tex](x_{1},y_{1})[/tex] are given by:
[tex]2(x_{1} - x_{0})x+2(y_{1}-y_{0})y = x^{2} _{1}-x^{2} _{0}+y^{2}_{1}-y^{2}_{0}[/tex]
in the given case we have,
[tex](x_{0},y_{0})\\[/tex] = (-7,6)
and
[tex](x_{1},y_{1})[/tex] = (5,2)
now substituting the given values in the above equation we get,
2(5-(-7))x + 2(2-6)y = 5²- (-7)² + 2²- 6²
= 24x - 8y = 25 - 49 + 4 - 36
= 24x - 8y = -56
on simplifying by dividing the LHS and the RHS by 6 we get our equation to be,
3x - y = -7
What is a perpendicular bisector?
A line or segment that is perpendicular to another segment and passes through its midpoint is called a perpendicular bisector.
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SOMEONE HELP! I NEED THIS QUICKLY! WILLING TO GIVE 45 POINTS!!! At 1 P.M., the total snowfall is 2 centimeters. At 4 P.M., the total snowfall is 7 centimeters. What is the mean hourly snowfall? Write your answer in simplest form as a fraction or mixed number.
The mean hourly snowfall is (5/3) centimeters per hour, which means that each hour there are 5/3 centimeters more of snow.
What is the mean hourly snowfall?The mean hourly snowfall is given by the quotient between difference between the total snowfall at the two given times and the total time.
Here we have:
Initial snowfall = 2cm
Final snowfall = 7cm
Difference = 7cm - 2cm = 5cm
And that happens between 1 P.M. and 4 P.M., so we have 3 hours.
Then the mean hourly snowfall is:
M = 5cm/3h = (5/3) centimeters per hour.
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what is the answer to Abdul drinks 1 1/2 pints of milk a day. How much is this in cups?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
3 us cups
Step-by-step explanation:
multiply by 2
andrea and lauren are 20 kilometers apart. they bike toward one another with andrea traveling three times as fast as lauren, and the distance between them decreasing at a rate of 1 kilometer per minute. after 5 minutes, andrea stops biking because of a flat tire and waits for lauren. after how many minutes from the time they started to bike does lauren reach andrea?
Lauren will reach Andrea after 65 minutes of biking.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.So, because Lauren is traveling at a speed that is one kilometer per minute slower than Andrea's and vice versa, Andrea's speed is 3/4 km/min and Lauren's is 1/4 km/min.
Thus, Andrea will have biked 3/4 × 5 = 15/4 km in 5 minutes.Lauren will have to bike the following kilometers in total:
20 - 15/4 = 80/4 - 15/4 = 65/4 kmHer speed being 1/4 km/min, the amount of time passed will be:
(65/4)/(1/4) = 65Therefore, Lauren will reach Andrea after 65 minutes of biking.
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In general, the air temperature decreases 12°F for every
4,000 feet increase in altitude. If a hiker climbs 3,000 feet, by how
much can she expect the temperature to decrease?
Answer: 9
Step-by-step explanation:
Factor the expression using the GCF 6y + 3
[tex]3(2y+1)[/tex] I believe is the solution you seek.
You factor 3 out of 6y + 3, leaving you with the solution.
Hope this helps!
LO3
Ollie is paid 65p for each pizza he delivers. He is
paid £49.45 for a weekend shift including £12.40 in
tips.
How many pizzas did he deliver during the shift?
You must show your working.
If the function 5x y = 1 has the domain {-2, 1, 6}, then what is the corresponding range? a. {-9, 6, 31} b. {9, -6, -31} c. {-11, 4, 29} d. {11, -4, -29}
If the function 5x+ y = 1 has the domain {-2, 1, 6}, then {11, -4, -29} is the corresponding range and the answer to your question is: letter D
Function 5x + y = 1
Domain {-2, 1, 6}
Process
Domain is the possible values of the independent variable.
Range is the values of the dependent variable.
Evaluate the function with each of the domain values to get "y"
When x = -2
5(-2) + y = 1
-10 + y = 1
y = 10 + 1
y = 11
When x = 1
5(1) + y = 1
5 + y = 1
y = -5 + 1
y = -4
When x = 6
5(6) + y = 1
30 + y =1
y = 1 - 30
y = -29
Range = { 11, -4 , -29}
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can anybody help me with 15/16 converting it into a decimal
Answer: 15/16 is written as 0.9375 in decimal form.
Step-by-step explanation:
To convert any fraction to decimal form, we just need to divide its numerator by the denominator.
Here, the fraction is 15/16 which means we need to perform 15 ÷ 16.
This gives the result 0.9375
= 15/16
= 15 ÷ 16
= 0.9375
You are given that x = 5^m and y = 5^n
Write 5^m+n/2 in terms of x and y.
Answer:
X + e^(Y-5)/2
Step-by-step explanation:
X = 5^m
Y = 5^n
e^Y = n*e^5
n = e^(Y-5)
Consider the relation R = {(4,7), (5,3), (6,2), (7, 7)}. What is the inverse of R? Enter your answer as a set of ordered pairs.
Check the picture below.
SOMEONE PLEASE HELPPPP!!! LOOK AT THE PICTURE!
Answer:
x+2=3
collect like terms
x=3-2
x=1
x-12=x+30
collect like terms
x-x=30-12
=18
2(x+6)=2x+12
open bracket
2x+12=2x-12
collect like terms
2x-2x=-12+12
=0
3(x-2)=3x-2
open bracket
3x-6=3x-2
collect like terms
3x-3x=-2+6
=4
PLEASEEEEEEEEEE HELP ME I NEED HELP I AM PRACTICING FOR A TEST AND I CANT UNDERSTAND THIS
Answer:
2°C
Step-by-step explanation:
-3 + 5 = 11
Answer:
The temperature is 3°
Step-by-step explanation:
If we start at -3, then we go to -2, then -1, then 0, then 1 and then 2.
Consider the function shown.
Which inequality represents the range of the function?
Answer:
The correct answer is C.
Please SIMPILFY these
Answer:
a) 81
b) 16807
c) 100
d) 78125
PLEASE GIVE ME A BRAIN
Calculate the value of 1 3/5 x 2/5
As a fraction in its simplest form
Answer:
16/25
Step-by-step explanation:
1 3/5 = 8/5
8/5 x 2/5 = 16/25
solve for c -49 = 2c - 29
Answer:
c = -10
Step-by-step explanation:
Hello!
According to the question we need to solve for c in the equation -49 = 2c - 29
-49 = 2c - 29
Flip the equation
2c - 29 = -49
Add 29 to both sides
2c - 29 + 29 = -49 + 29
2c = -20
Divide both sides by 2 to single out the variable
2c/2 = -20/2
c = -10
So, the value of c is -10
9.7g of sugar is needed for every cake made. How much sugar is needed for 4 cakes?
Answer: 38.8g of sugar
Step-by-step explanation:
9.7 x 4= 38.8
6 kg rice is enough for 20 people. How much rice is required for 100 people
Answer:
30.
Step-by-step explanation:
Apologies if I am late, but I believe this is the answer!
Schools A and B are competing in an academic contest. Correct answers earn 12 points. Incorrect answers lose 3 points. In the final round, School A gives the same number of correct and incorrect answers. School B gives no incorrect answers and the same number of correct answers as School A. School A started the final round with 87 points. School B started with 45. The game ends with the two schools tied. Let x represent the number of correct answers given by School A in the final round. Write an equation that models the outcome of the contest. Then find the number of answers that each school got correct in the final round.
School A got 14 questions correct and School B got 14 questions correct.
What are the number of correct answers?The first step is to form a linear equations that represent the scores of the schools in the final round. A linear equation is an equation that has a single variable that is raised to the power of one. When graphed, a linear equation is usually a straight line.
Let x represent the number of correct and incorrect answers scored by School A
Total score at the end of the final round = beginning score + total scores of correct answers - total scores of incorrect answers
Total score at the end of the final round for School A :
87 + (12 ×x ) - (3 × x)
87 + 12x -3x
87 + 9x
Total score at the end of the final round for School B :
45 + (12 ×x )
45 + 12x
If the two schools are tied, it means that both of the above expressions would be equal
45 + 12x = 87 + 9x
12x - 9x = 87 - 45
3x = 42
x = 42 / 3
x = 14
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Answer:
have a great day
Step-by-step explanation:
I have one fair 6-sided die and one unfair 6-sided die. On the unfair die, the probabilities of rolling numbers 2,…,6 are equal and the probability of rolling a 1 has a different value. I roll each die once.
If the probability of rolling one 3 and one 4 is 1/24, what is the probability of rolling two 1’s?
Answer:
[tex]\dfrac{1}{16}[/tex]
Step-by-step explanation:
Probability Distribution Table for X
Where X is the score on a fair, six-sided dice:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(X=x) \phantom{\dfrac11}&\frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \\\cline{1-7}\end{array}[/tex]
Probability Distribution Table for Y
Where Y is the score on an unfair, six-sided dice, and the probabilities of rolling numbers 2, 3, 4, 5 and 6 are equal, and the probability of rolling a 1 has a different value:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&1-5k&k&k&k&k&k\\\cline{1-7}\end{array}[/tex]
Note: The probabilities of all the possible values that a discrete random variable can take add up to 1.
The outcomes of rolling one 3 and one 4 are:
Rolling a 3 with the first die and a 4 with the second die, ORRolling a 4 with the first die and a 3 with the second die.Given the probability of rolling one 3 and one 4 is ¹/₂₄:
[tex]\implies \text{P}(X=3)\; \text{and} \; \text{P}(Y=4) \; \text{or} \; \; \text{P}(X=4) \; \; \text{and} \; \; \text{P}(Y=3)=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{1}{6} \times k +\dfrac{1}{6} \times k=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{k}{6} + \dfrac{k}{6}=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{2k}{6}=\dfrac{1}{24}[/tex]
[tex]\implies 24(2k)=6[/tex]
[tex]\implies 48k=6[/tex]
[tex]\implies k=\dfrac{1}{8}[/tex]
Therefore:
[tex]\implies 1-5k=1-\dfrac{5}{8}=\dfrac{3}{8}[/tex]
Hence, the probability distribution table for the unfair 6-sided dice is:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&\frac{3}{8} & \frac{1}{8} & \frac{1}{8}& \frac{1}{8} & \frac{1}{8}& \frac{1}{8} \\\cline{1-7}\end{array}[/tex]
There is only one possible outcome of rolling two 1's, so the probability of rolling two 1's is:
[tex]\implies \text{P$(X=1)$ and P$(Y=1)$}=\dfrac{1}{6}\times\dfrac{3}{8}=\dfrac{3}{48}=\dfrac{1}{16}[/tex]
Note: Please see attachment for the sample-space diagram showing the possible outcomes of rolling two dice. The possible outcomes of rolling one 3 and one 4 are highlighted in yellow. The possible outcome of rolling two 1's is highlighted in blue.
An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left one hour later. The jet follows the same route as the airplane at a different altitude. How many hours will it take the jet to catch up with the airplane? How many miles will the jet have flown?
Using the distance formula, Jet will take 2.2 hours to catch up with the airplane.
We will find the solution using distance formula.
distance formula is a formula that is used to find the distance between two points. These points can be in any dimension.
d=rt where
d is distance r is rate or speed and t is time
"distance airplane traveled" = "distance jet traveled"
Let x = hours "airplane" was flying
x-1 = hours "jet" was flying
.
180x = 330(x-1)
180x = 330x - 330
180x + 330 = 330x
330 = 150x
330/150 = x
2.2 hours = x
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wrapping paper is on sale at 3 rolls for $4.25. how many rolls can dankia buy with $20
Answer:
12 rolls, because 4.25 go into 20 , four times so u take 4 and multiply it by 3 and get 12.
Help pls math is not my thing
Answer: 2.25 x 10^18
Step-by-step explanation:
When dividing with exponents you subtract
56-38= 18
10 cancels out
(9 x 10^18) / 4
= 2.25 x 10^18
How many non-identical triangles can be made using these side lengths:
5 cm, 7 cm, and 10 cm
By applying the Triangle Inequality Theorem, the number of non-identical triangles that can be made using the given side lengths is one.
What is the Triangle Inequality Theorem?In Mathematics, the Triangle Inequality Theorem can be defined as a type of theorem which states that the sum of any two (2) side lengths of a triangle must be greater than the measure of the third (2) side.
This ultimately implies that, the sum of the lengths of any two (2) sides of a triangle cannot be less than the length of the third (3) side of the triangle in accordance with the Triangle Inequality Theorem, as represented by this mathematical expression:
b - c < a < b + c
Where:
a, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of non-identical triangles is given by:
5 + 7 > 10
12 > 10 (True).
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will give brainliest
write a word problem that could be represented by this number line.
Answer:
John had 8 apples. He gave away 4. How many apples does he have left?
Step-by-step explanation: First, an arrow added 8 on the number line. Then, another arrow took away 4.
Classify the quadrilateral whose vertices are: A(3,2); B(0,5); C(-3,2); D(0,-1)x Select all that apply
Solution
- We can plot the coordinates given using a graphing calculator as shown below:
- From the above, we can see that the sides are equal and the looks like a diamond
- Thus, the quadrilateral is a Rhombus
- Since all the angles are 90 degrees, it is also a square only that it was rotated.
- A square is a special type of rectangle, thus, the shape is also a rectangle
- A parallelogram as its opposite sides parallel and opposite angles equal. This is the same with our figure. Thus, it is also a parallelogram
Find the missing length
√32 or 4√2 is the missing length of the right angle triangle whose other 2 legs measure 4 by 4 units.
What is the missing length of the triangle?Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c = √( a² + b² )
Given the data in the diagram;
Side length a = 4Side length b = 4Hypotenuse c = ?To determine the missing length, plug the given values into the formula above and solve for c.
c = √( a² + b² )
c = √( (4)² + (4)² )
c = √( 16 + 16 )
c = √( 32 )
Hypotenuse c = √32 or 4√2
Therefore, the missing length of the right angle triangle is √32.
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Using the given sample data, calculate the following measures of dispersion, to one decimal place.
Range = 15
Variance = 24.5Explanations
Standard deviation = 5.0
The formula for calculating the range is expressed as:
Range = Highest value - Lowest value
Range = 24 - 9
Range = 15
Calculate the variance
The formula for calculating the variance is expressed as:
[tex]Variance=\frac{\sum(x-\overline{x})^2}{n-1}[/tex]Find the mean
[tex]\begin{gathered} mean=\frac{9+13+15+18+19+20+24}{7} \\ mean\text{ }\overline{x}=\frac{118}{7}=16.9 \end{gathered}[/tex]Determine the variance
[tex]\begin{gathered} S^2=\frac{(9-16.9)^2+(13-16.9)^2+(15-16.9)^2+(18-16.9)^2+(19-16.9)^2+(20-16.9)^2+(24-16.9)^2}{7-1} \\ S^2=\frac{146.9}{6} \\ S^2\approx24.5 \end{gathered}[/tex]Determine the standard deviation
[tex]\begin{gathered} S=\sqrt{variance} \\ S=\sqrt{24.5} \\ S\approx5.0 \end{gathered}[/tex]please help and explain thank you
Answer:
x = 23 degrees
Step-by-step explanation:
Angle on a straight line = 180 degrees
therefore 180 - 75 = 105 degrees
105 + 52 = 157 degrees
Angle in a triangle is 180 degrees
therefore 180 - 157 = 23 degrees
Aaron Rodgers' yearly salary is 2.2 x 10' dollars. The yearly salary of one of his backup
quarterback's is 6.3x105 dollars. How many times greater is Aaron Rodgers' salary than his
backup's salary?
Aaron Rodgers salary is 2.19×[tex]10^1^1[/tex] greater than his backups.
To find how many times a quantity x is greater than y we do subtraction. That is we do [tex]x-y[/tex].
So, here Aaron's salary is given to be $ 2.2× [tex]10^1^0[/tex]
And his quarterback's salary is $ 6.3×[tex]10^5[/tex].
Thus the difference between salaries= 2.2×[tex]10^1^0[/tex] - 6.3 × [tex]10^5[/tex]
= 2.19×[tex]10^1^1[/tex]
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