The equation for the perpendicular bisector of the given line segment is y = 2x + 2.
Here, we are given a line segment with end points (3,−7) and (−9,−1)
Thus, the slope of the line can be calculated as-
(y1 - y2)/ (x2 - x1)
= (-1 + 7)/ (-9 - 3)
= 6/ -12
= -1/2
Now, since we the slope of 2 lines that are perpendicular to each other is negative of the reciprocal, thus-
slope of the perpendicular bisector = 2
Now, the midpoint of the given line segment will be-
{(x1 + x2)/2, (y1 + y2)/2}
= {(3-9)/2, (-7-1)/2}
= {-6/2, -8/2}
= (-3, -4)
Now, we can use the point slope form to find the equation of the perpendicular bisector-
(y- y1) = m(x - x1) where m is the slope and (x1, y1) is a point on the line.
⇒ (y+4) = 2(x+3)
y + 4 = 2x + 6
y = 2x + 2
Thus, the equation for the perpendicular bisector of the given line segment is y = 2x + 2.
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8x + 13
12x + 7
7>>
X
x =
The value of the x for the two given parallel lines is 80.
What is termed as the corresponding angles?Corresponding angles are generated when two parallel lines have been intersected by a transversal. The definition of corresponding angles states that when two parallel lines intersect with a third, the angles that occupy the very same relative position at every intersection are said to be corresponding angles to one another.For the given question;
The value of the angles are given in the form of equation.
∠1 + (12x + 7) = 180 (linear pair)
∠1 = 180 - 12x - 7
∠1 = 173 - 12x
Now,
∠1 = 8x + 13 (corresponding angles)
Put the value of ∠1.
173 - 12x = 8x + 13
On simplification,
173 - 13 = 8x + 12x
160 = 20 x
x = 80
Thus, the value of the x for the two given parallel lines is 80.
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Solve for x
2x^2=5x+3
Answer:
Step-by-step explanation:
ur mom
The sum of the ages of Tameka, Jessica, and Venessa is 57. Tameka is 3 years older than Jessica and 6 years older than Venessa. How old is Tamika?
From the given information Tameka is 22 years old.
Given:
The sum of the ages of Tameka, Jessica, and Venessa is 57
And Tameka is 3 years older than Jessica and 6 years older than Venessa
Let Tameka's age be x
Therefore, Jessica' age will be x-3 and Venessa age will be x -6
Therefore according to the question,
x + (x-3) + ( x-6) = 57
=> 3x = 57 + 3 + 6
=> x = 66/3
x= 22years
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Can you help explain this to me, I’m so lost
Given:
The equation is,
[tex]-x-4y=-10[/tex]Explanation:
Substitute 3 for x and 2 for y in the equation to check for the solution.
[tex]\begin{gathered} -3-4\cdot2=-10 \\ -3-8=-10 \\ -11\ne-10 \end{gathered}[/tex]Point (3,2) not satisfy the equation. So point (3,2) is not a solution of equation
Divide:
a)
b)
(4x4-12x³ + 7x² + 3x - 2) by (2x²-3x-2)
(x² + 4y¹) by (x² + 2y²-2xy)
How are the algebraic expressions divided?
a) (4x4-12x³ + 7x² + 3x - 2) by (2x²-3x-2) = (2x-1) (x-1)
Factorization of the numerator ,
[tex]4x^4-12x^3 + 7x^2 + 3x - 2\\\\= (4x^4+ 7x^2 - 2) -12x^3+3x\\\\= (4x^4- x^2+ 8x^2 - 2) -12x^3+3x\\\\=(4x^4- x^2)+ (8x^2 - 2) -12x^3+3x\\\\= x^2(4x^2- 1)+ 2( 4x^2 - 1) -12x^3+3x\\\\=(4x^2- 1)(x^2+2)-12x^3+3x\\\\=(4x^2- 1)(x^2+2)+(-12x^3+3x)\\\\=(4x^2- 1)(x^2+2)-3x(4x^2-1)\\\\=(4x^2- 1)(x^2+2-3x)\\\\=(4x^2- 1)(x^2-x-2x+2)\\\\=(4x^2- 1)((x^2-x)+(-2x+2))\\\\=(4x^2- 1)(x(x-1)-2(x-1))\\\\=(4x^2- 1)(x-1)(x-2)\\\\=(2x+1)(2x-1)(x-1)(x-2)[/tex]-----(1)
Factorization the denominator ,
[tex](2x^2-3x-2)\\\\= (2x^2+x-4x-2)\\\\= (2x^2+x)+(-4x-2)\\\\=x(2x+1)-2(2x+1)\\\\=(2x+1)(x-2)[/tex] ----(2)
Divide (1) by (2)
= [tex]\frac{(2x+1)(2x-1)(x-1)(x-2)}{(2x+1)(x-2)}[/tex]
= (2x-1) (x-1)
b) (x² + 4y¹) by (x² + 2y²-2xy)
[tex]\frac{x^{2} +4y}{x^{2} +2y^{2} -2xy}[/tex]
This is the simplest form of the algebraic expression.
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What is the slope of the line that passes through the points (−4,4) and (-1, 3)
Write your answer in the
simplest form.
please help I really need and answer!
All three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.So, in the given image filling the blanks as follows:
(A) ∠ACB = ∠CDA = ∠CDB = 90° (Definition of right triangles)
(B) Triangle angle sum theorem:
∠CAD = ∠CBD = 90°∠CAD = ∠CBA = 90°∠CAD = ∠CAB = 90°It is enough to prove that:
△ABC ≅ △ACD ≅ △CBD under AA condition.(C) C.P.C.T (Corresponding parts of congurent triangles)
∠CBD = ∠CAD∠CAD = ∠CBD(D) △ABC ≅ △ACD ≅ △CBD under AA condition.
Therefore, all three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition
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patrons of the grande dunes hotel in the bahamas spend time waiting for an elevator. the wait time follows a uniform distribution between 0 and 3.5 minutes. (round your answers to 2 decimal places.)
It takes 1.75 minutes to an average customer to wait
The waiting times standard deviation is 1.01
The percentage of a customer wait under a minute is 28.57%
42.86% customers wait more than two minutes
What is Uniform distribution?Uniform distribution: n probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds.
Display the 1.00 area under the curve.
The rectangle has a length of 3.5 - 0 = 3.5.
The rectangle's height is 1/3.5.
To determine the area, multiply:
3.5 * 1/3.5 = 1
How long does the average customer have to wait for an elevator?
EV stands for average between high and low.
= (0+3.5)/2
= 1.75
What is the waiting time's standard deviation?
Standard deviation is equal to sqrt(b-a2/12).
= sqrt((3.5-0)^2/12)
= 1.01
What percentage of customers wait under a minute?
It is x/(b-a) = 1/ for less than (3.5-0)
1/3.5
= 28.57%
How many customers wait more than two minutes?
It is 1 - x for greater than (b-a)
(3.5-2)/3.5
= 1.5/3.5
= 42.86%
It takes 1.75 minutes to an average customer to wait
The waiting times standard deviation is 1.01
The percentage of a customer wait under a minute is 28.57%
42.86% customers wait more than two minutes
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train traveling at 35 mph takes 30 hours to travel from chicago to new york. how fast must the train travel to make the trip in 25 hrs
To make the trip in 25 hrs, the train must travel as fast as 42 mph.
Speed is the rate or the change in distance over change in time.
Speed = d / t
where d = distance
t = time
If a train traveling from Chicago to New York has a speed of 35 mph and took 30 hours to cover the distance from the two locations, then the distance is 1050 miles.
Speed = d / t
35 mph = d / 30 h
d = 1050 miles
Covering the same distance, solve for the rate of speed needed by the train to make the trip in 25 hours.
Speed = d / t
Speed = 1050 miles / 25 hours
Speed = 42 mph
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please help!!! you will get brainliest... there are 2 attachments 2nd image first, part one is 2nd image
Answer:
See my photo, bro. i am not really sure if this week should be counted in. And the second question's answer i am not really sure. hope it can help.
Point D is the circumvented. AB= 42 DC= 29DF= 16FC =28AG= 33
Find intersection of
BD , AD DC
Then
BD = BE^2 + ED^2
R = AD = abc/4S = 42• (2•28)•
Determine the quotient of 5/6 and 2/3
Answer:
5/4
Step-by-step explanation:
There is a rule that dividing by a fraction is the same as multiplying by the reciprocal.
So:
[tex]\frac{5/6}{2/3} = \frac56 \cdot \frac32 = \frac{15}{12} = \frac54[/tex]
Compute the diameter of a circle with a circumference of 34 feet
Step-by-step explanation:
we need to remember the formula for the circumference of a circle :
2×pi×r
or
2×r × pi
what is 2×r ? the double radius ? 2 times the radius is the diameter.
so, we know
diameter × pi = 34 ft
diameter = 34/pi = 10.82253613... ft
here is a variable, y, with five observations: 42, 86, 6, 14, 22 the mean of y is 34. here is the formula for calculating the standard deviation: sd y
Two Spiteful Uncles Walking to the Beat
A Short Story
by Grim
Lee Changseon had always loved deprived Falmouth with its magnificent, mutated mountains. It was a place where he felt delighted.
He was a down to earth, splendid, squash drinker with ruddy eyes and handsome ankle. His friends saw him as a bad, breakable barndon harera. Once, he had even helped a silky chicken cross the road. That's the sort of man he was.
Lee walked over to the window and reflected on his creepy surroundings. The snow flurried like thinking puppies.
Then he saw something in the distance, or rather someone. It was the figure of Morwenna Thornton. Morwenna was a sympathetic friend with skinny eyes and tall ankle.
Lee gulped. He was not prepared for Morwenna.
As Lee stepped outside and Morwenna came closer, he could see the squashed smile on her face.
Morwenna gazed with the affection of 747 sinister ordinary owls. She said, in hushed tones, "I love you and I want Internet access."
Lee looked back, even more sneezy and still fingering the cursed gun. "Morwenna, I just don't need you in my life any more," he replied.
They looked at each other with ecstatic feelings, like two hurt, handsome horses drinking at a very brutal snow storm, which had piano music playing in the background and two spiteful uncles walking to the beat.
Lee regarded Morwenna's skinny eyes and tall ankle. "I feel the same way!" revealed Lee with a delighted grin.
Morwenna looked jumpy, her emotions blushing like a narrow, nosy newspaper.
Then Morwenna came inside for a nice beaker of squash.
THE END lol
Which expression values 4? A) (4+5)×3^2-9÷3^2 B) 4+5×(3^2-9)÷3^2 C) 4+5×3^2-(9÷3^2) D) 4+5×3^2-9÷3^2 pls help me
Answer:
B)4+5×(3^2-9)÷3^2 C)
Step-by-step explanation:
What numbers could be added to -4.3? Explain how you know?
Answer:
any number less than 4.3
Step-by-step explanation:
Let x = number that can be added to -4.3
-4.3 + x < 0
Add 4.3 to both sides.
x < 4.3
Answer: any number less than 4.3
CAN SOMEONE HELP MEEEEEEEEEEEEE
It will take Cindy and Latasha and average of 24.44 years to have equal salary
Equivalent EquationsEquivalent equations are algebraic equations having identical solutions or roots. In this question, we would use x to represent the number of years it will take to earn or have equal amount.
x = number of years.The equation can be written as
[tex]40000 + 3300x = 62000 + 2400x \\[/tex]
Each side of the equation represents the increase in salary per year of each person
Lets collect like terms and solve for x
[tex]62000-40000 = 3300x - 2400x\\22000 = 900x\\x = \frac{220}{9}\\x = 24.444[/tex]
It will take 24.44 years for them to have equal amount of salary.
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-9y=3x+81 find slope
Answer:
divide by -9 and you get -3/9x-9 simplify -3/9 to -1/3
Step-by-step explanation:
-1/3x is your slope
Write and solve a word problem that can be solved using decimals addition that requires regrouping the 10th
Lets suppose we used an example of two children, one of them having $7.50 and other one having $8.40, and the total money will be the addition i.e., $15.9 using decimal operations.
As per the question statement, we are supposed to write and solve a word problem for decimal addition. Let the statement be : Two children, one of them have $7.50 and other one having $8.40, the sum total money would be____".
We are supposed to add both decimal numbers:
Total money = $7.50 + $8.40
Total money = $15.9
Hence, the sum total of the money of both the children is $15.9 using the decimal operations.
Decimal: A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole amounts.To learn more about decimals, click on the link given below:
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Answer each part. If necessary, round your answers to the nearest hundredth.(a) Hans bought 11 pounds of rice for $5.How many dollars did he pay per pound of rice?I dollars per pound(b) It takes 16 pounds of seed to completely plant a 3-acre field.How many pounds of seed are needed per acre?pounds per acre
(a) Hans bought 11 pounds of rice for $5.
How many dollars did he pay per pound of rice?
the unit price is given by the total price divided by the total weight, therefore:
[tex]p=\frac{5}{11}=0.45454=0.45[/tex]He payed $0.45 per pound of rice
(b) It takes 16 pounds of seed to completely plant a 3-acre field.
How many pounds of seed are needed per acre?
the pounds of seed per unit area is given by the total pounds used to plant the total acres
[tex]s=\frac{16}{3}=5\frac{1}{3}=5.33[/tex]so, the answer is 5.33 pounds per acre
A 5 kg bag of grass seed covers about 650 m². How many bags should Tshering buy to seed a 60 m-by-80 m football field?
Given: 5 kg bag of grass seed covers 650 m2
To find:
Bags to seed 60m-80m field
Solution:
Area of football field- 60x80=4800m²
Bags required-
Since 650 m² is covered by 5kg
So, 4800m² will be covered by-
=4800/650x5
= 36.9 bags
Therefore, 40 bags are required to seed a 60m-by-80m football field.
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What are the coordinates of the point on the directed line segment from (-1, -2)(−1,−2) to (8, 4)(8,4) that partitions the segment into a ratio of 2 to 1?
The coordinates which divide the segment with endpoint (-1,-2) and (8,4) in the ratio 2 to 1 are (5,2)
What is section formula?
Section formula is used to find the ratio in which a line segment is divided by a point internally or externally. The section formula can be given as
[tex](\frac{mx_{2}+nx_{1} }{m+n} ,[/tex][tex]\frac{my_{2}+ny_{1} }{m+n})[/tex] where [tex](x_{1},y_{1} ),(x_{2},y_{2} )[/tex] are the endpoints of the segment and this points are divided in the ratio [tex]m:n[/tex]
We are given the coordinates as (-1,-2) and (8,4)
This segment is divided in ratio 2:1
We use section formula to find the coordinates
the x- coordinates can be given as
[tex]x=\frac{2(8)+1(-1)}{2+1}[/tex]
[tex]x=\frac{16-1}{3}\\[/tex]
[tex]x=\frac{15}{3}[/tex]
[tex]x=5[/tex]
Similarly the y coordinate can be given as
[tex]y=\frac{2(4)+1(-2)}{2+1}[/tex]
[tex]y=\frac{8-2}{3}[/tex]
[tex]y=\frac{6}{3}[/tex]
[tex]y=2[/tex]
Hence the coordinates which divide the segment with endpoint (-1,-2) and (8,4) in the ratio 2 to 1 are (5,2)
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The nth term of a sequence is given by 2n² + 1.
Write down the first three terms of this sequence.
Answer:
3, 9, 19
Step-by-step explanation:
substitute n = 1, 2, 3 into the nth term formula
n = 1 : 2(1)² + 1 = 2(1) + 1 = 2 + 1 = 3
n = 2 : 2(2)² + 1 = 2(4) + 1 = 8 + 1 = 9
n = 3 : 2(3)² + 1 = 2(9) + 1 = 18 + 1 = 19
the first 3 terms are 3, 9, 19
mr.moore told the class that a right triangle has the following side measurements : 5inces, 12 inches, and 13 inches. which of those measurements would be lenghs of the hypotenuse?
Answer:
13 inches
Step-by-step explanation:
So, the hypotenus is the longest side of a right triangle, so it would be 13. But, if you really want to double check, you can take a2 + b2 = c2 and fill in each letter with a number until it is right. So, we'll do a=5, b=12, and c=13. 5 squared is 25, 12 squared is 144, and 13 squared is 169. 144+25=169.
Macy made an initial deposit of $250 into a bank account. assuming no interest, the function f(x)=80x+250 represents the total amount of money she will have in the account after x months. evaluate and interpret the function for f(9).
Answer:A
Step-by-step explanation:
Repost, can someone help?
Answer:
x=65
y=32
Step-by-step explanation:
2x+x-15=180
combine like terms
3x-15=180
add 15 to both sides
3x=195
divide both sides by 3
x=65
now y's
4y+y+20=180
combine like terms
5y+20=180
subtract 20 from both sides
5y=160
divide both sides by 5
y=32
Answer:
x = 65
y = 32
Step-by-step explanation:
2x + (x - 15) = 180
2x + x - 15
3x - 15 = 180
+15 +15
-------------------
3x = 195
÷3 ÷3
----------------
x = 65
4y + (y + 20) = 180
4y + y + 20 =180
5y + 20 = 180
-20 -20
---------------------
5y = 160
÷5 ÷5
---------------
y = 32
2x + (x - 15) + 4y + (y + 20) = 360
2(65) + (65 - 15) + 4(32) + (32 + 20) = 360
130 + 50 + 128 + 52 = 360
180 + 180 = 360
360 = 360
I hope this helps!
A car takes 49.7 seconds to travel 1 mile. How long does it take the car to travel 3.8 miles? First round to the nearest whole number to find the estimated answer. Then find the exact answer
Answer: 188.6 seconds which is rounded to 189 seconds or 3 minutes and 9 seconds
Step-by-step explanation:
Since we see that a time is given for 1 mile, to find the other distance we multiply the time for 1 mile (49.7 seconds) by the distance required (3.8 miles)
It can be also written like this:
1 mile -------> 49.7 seconds
3.8 miles-------> 49.7 seconds x 3.8 miles = 188.6 seconds rounded to 189 seconds. If asked for minutes, it can be written as 3 minutes and 9 seconds
Hope this helps!
Faith Franklin sells furniture and earns 9% commission on her total sales. Last month she had $33,500 in
sales. How much did she earn?
Answer:
$3015
Step-by-step explanation:
Answer:
$3015
Step-by-step explanation:
Comment
She earned 9% of 33500
To replace th4 % sign, you always divide the number given by 100.
So 9% as a decimal is 9/100 = 0.09. Notice where the 100 goes. It is right underneath the 9. So you are dividing by 100.
So she earned
0.9 * 33500 = $3015
kara is sorting buttons by length for a craft project. the line plot shows the length of each button. if kara lines up all the 3/4-inch button, what would be the total length?
When Kara is sorting buttons by length for a craft project and the line plot shows the length of each button. If Kara lines up all the 3/4 inches buttons, then the total length is [tex]2\frac{1}{4}[/tex] inches
The length of the button = 3/4 inches
Number of 3/4 inch buttons = 3 buttons
Then the total length = Number of 3/4 inch buttons × The length of the button
Substitute the values in the equation
The total length = 3×(3/4)
= 9/4 inches
Convert the simple fraction to the mixed fraction
9/4 inches = [tex]2\frac{1}{4}[/tex] inches
Hence, when Kara is sorting buttons by length for a craft project and the line plot shows the length of each button. If Kara lines up all the 3/4 inches buttons, then the total length is [tex]2\frac{1}{4}[/tex] inches.
The complete question is
Kara is sorting buttons by length for a craft project. the line plot shows the length of each button. if Kara lines up all the 3/4-inch button, what would be the total length?
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pls help need to turn this in
Answer: y - 3 = -2(x + 2)
