Answers
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2
Slope of line segment
= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)
= \frac{4 + 8}{5 + 7}=5+74+8
= \frac{12}{12}=1212
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)
Midpoint of line segment
= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)
= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
Related Questions
746 divided by 40 with remainder
Answers
Answer:
Quotient: 18; Remainder: 26
Step-by-step explanation:
Please open the PDF file for work.
Hoped this helped.
[tex]GeniusUser[/tex]
−4 1/2÷(−2 2/3) i need help
Answers
Answer:
[tex]1\frac{11}{16}[/tex]
Step-by-step explanation:
Convert mixed numbers into improper fractions.
= [tex]\frac{-\frac{9}{2}}{\left(-2\frac{2}{3}\right)}[/tex]
= [tex]\frac{-\frac{9}{2}}{\left(-\frac{8}{3}\right)}[/tex]
= [tex]\frac{\frac{9}{2}}{\frac{8}{3}}[/tex]
= [tex]\frac{9\cdot \:3}{2\cdot \:8}[/tex]
= [tex]\frac{27}{2\cdot \:8}[/tex]
= [tex]\frac{27}{16}[/tex]
Convert improper fraction into mixed number.
= [tex]1\frac{11}{16}[/tex]
-
16
Write an equation for the situation: Kristian has $200 which is two times Alejo's money plus $20.
Answers
Answer:
x= 2y + 20
Step-by-step explanation:
we could say kristian and alejo, Bob and Bill, shelled and Jackie or just about any other two words so let's call them x any y. kristian is x and also is y.
so kristian (x) has twice as much money plus another 20.
this means x has 2 times plus 20 more than y.
so x= 2y + 20
what is the rate of change for these data?
Answers
Answer:
-2 gallons per minute
Step-by-step explanation:
As we can clearly see, the water is continuously decreasing every 15 minutes by 30 gallons.
So, the rate of change is -30 gallons per 15 minutes
However, we can simplify this ratio by dividing both sides by 15, so we get
-2 gallons per minute
The level of significance that determines the area of the critical region for a hypothesis
test, should be chosen before the statistical test findings are evaluated, as to not allow
biasing of the test results by the individuals conducting the hypothesis test.
O True
O False
Answers
The Level of significance that determines the area of the critical region for a hypothesis test, should be chosen before the statistical test findings are evaluated, as to not allow biasing of the test results by the individuals conducting the hypothesis test. - False
What is level of significance?Level of significance is the" measurement of the statistical significance. It defines whether the null hypothesis to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected. The level of significance, also denote as alpha".
The Level of significance that determines the area of the critical region for a hypothesis test, should be chosen before the statistical test findings are evaluated, as to allow biasing of the test results by the individuals conducting the hypothesis test.
Hence, the given question is False.
To learn more about Level of significance here
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f(x)=x^2-12x+20
a. f(0) = ?
b. f(2) = ?
c. f(x) = 0,x = ?
d. f(x)= 9,x = ?
Answers
Answer:
c . f(x)=0,x=????????????
Find the equation of the line that passes thru (-1,-5) and is parallel to 3x+y=-5. Show work.
Answers
Answer:
[tex]y=-3x-8[/tex]
Step-by-step explanation:
slope-intercept form:
[tex]y=mx+b[/tex]
Start with the given equation, and to find the slope, convert it to slope-intercept form by solving for y.
[tex]3x+y=-5[/tex]
In this case, all you need to do is subtract 3x from both sides.
[tex]y=-3x-5[/tex]
Here, the slope is -3. The slope of a parallel line will also be -3.
Now, we have 3 known variables. We have the slope and the x and y of a known point. Use those 3 knowns to solve for the 1 unknown, the y-intercept.
[tex]y=mx+b\\-5=(-3)(-1)+b\\-5=3+b\\-8=b\\b=-8[/tex]
Finally, with the slope and the y-intercept, you can write the equation of the line:
[tex]y=-3x-8[/tex]
Function 1 is defined by the equation y=-1/4r-5
Answers
Step-by-step explanation:
and what is function 2 ?
but I think I can risk a guess based on the little piece of the graph I can see.
the y-intercept is simply the point on the y-axis (that means x=0), where the line crosses.
in other words, it is the y-value when x = 0.
the y-intercept of function 1 is therefore -5.
and the picture suggests that the visible line would cross the y-axis at about y=-6.
as -5 is greater than -6, function 1 has the greater y-intercept.
how do you convert a whole number to a fraction?
Answers
Answer:
Step-by-step explanation:
Example 1: Changing the whole number 5 into a fraction.
Take the whole number (5), add a line below it (/), then add a 1 to the denominator.
5 = 5/1
Example 2: Changing the whole number 5 into a fraction.
Take the whole number (5), multiply it by 2 add a line below it (/), then add a 2 to the denominator.
5 = (5*2)/2 = 10/2
***This can be reduced to 5/1***
Example 3: Changing the whole number 5 into a fraction.
Take the whole number (5), multiply it by 3 add a line below it (/), then add a 3 to the denominator.
5 = (5*3)/3 = 15/3
***This can also be reduced to 5/1***
If you follow the pattern, you will realize all whole numbers are fractions already.
They are fractions with a denominator of 1. This fraction can be manipulated with all of the same standard rules you would traditionally use with fractions, even when the denominator isn’t shown.
A fraction is simply a way to describe portions of a whole. The denominator simply tells you how many pieces to break the whole into. When the denominator is 1, you are breaking the whole into one piece (or not breaking it apart at all.
I hope this helps.
my bro has homework and he needs help but I don't have the time to help him
Answers
Answer: 25
Step-by-step explanation:
Subtract 46.50 - 46.25 and you’ll get 25
3. The lacrosse team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for $24.00 each and slices of cheesecake for $3.50 each. If they want to raise at least $700, how many of each could they sell?
Part A: List three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal of raising at least $700.
Part B: Write an inequality to represent the situation.
Part C: Graph the inequality and shade where the solutions are. y X
Part D: What is the difference in the amount of money raised for ordered pairs falling on the line and the ones that fall in the shaded area?
Part E: What do the x- and y-intercepts represent?
Answers
To reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.
To determine, if they want to raise at least $ 700, how many of each could they sell, listing three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal, the following calculation must be performed:
C + S = 700 24 x 20 = 480 700 - 480 = 220 / 3.5 = 62.85 24 x 10 = 240 700 - 240 = 460 / 3.5 = 131.42 24 x 15 = 360 700 - 360 = 340 / 3.5 = 97.14Therefore, to reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.
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Write each verbal expression as an algebraic expression.
The product of a number, b, and nine =
A number, x, raised to the fifth power =
Twelve divided by the product of number, y, and three =
Seven added to the difference of one and a number, k =
Answers
2.x^5
3.(3y)/12
4.(1-k)+7
Ms. Jackson wants to rent a van for a week. It will cost the weekly fee plus $0.80 per mile driven. Let m = the number of miles Ms. Jackson drives during the week. Use this information and the table to answer 13-15.
Answers
jamie uses 54 buttons to make shirts. jamie uses 6 buttons to make each shirt. how many shirts did she make?
Answers
Answer: 9 shirts I think
Step-by-step explanation: 54/6=9
You have a Right Triangle with side lengths of 9ft and 12ft; solve for its perimeter and area.
Answers
Step-by-step explanation:
of course, we have to use Pythagoras.
c² = a² + b²
c is the Hypotenuse = the side opposite of the 90° angle.
and here is the problem : are 9 and 12 the legs. or is one of them the Hypotenuse ?
I don't know from the description.
let's see what we get one way or the other :
assumption : the known sides are the "legs".
c² = 9² + 12² = 81 + 144 = 225
c = 15 ft
that is a nice number. so, it looks like that was the intention.
just to be sure, here also the other options :
9² = 12² + side²
81 = 144 + side² that makes side² negative, so, not valid.
12² = 9² + side²
144 = 81 + side²
63 = side²
side = sqrt(63) this is not a nice round number, so, we go with the first option.
therefore, the 3 sides are
9 ft, 12 ft, 15 ft
perimeter = 9+12+15 = 36 ft
area = baseline×height/2
since this is a right-angled triangle, the "legs" with the enclosed 90° angle serve as baseline and height.
area = 9×12/2 = 9×6 = 54 ft²
Choose the equation of the horizontal line that passes through the point (2,4).
Oy = 2
O x= 2
O y = 4
O x=4
Answers
Answer:
y = 4
Step-by-step explanation:
Refer to the two images below
For the graph:
y = 2 - red
x = 2 - blue
y = 4 - green
x = 4 - purple
Horizontal lines are parallel to the x axis. The only two equations parallel to the x axis are y = 2 and y = 4 so x = 2 and x = 4 cannot be the answer.
The point (2,4) is graphed as well as the equations and the only equation that's horizontal and passes through the point (2,4) is y = 4
9. A box of cereal weighs 600 grams. How much is this weight in pounds?
Explain or show your reasoning. (Note: 1 kilogram = 2.2 pounds)
Answers
Answer:
1.323 pounds I think I'm not too sure thi sorry
Answer:
1.32 pounds
Step-by-step explanation:
convert 1kg to 1000g
[tex]1000g = 2.2pounds[/tex]
Find out how many pounds per 100g
[tex]100g = 0.22 \: pounds[/tex]
multiply by 6 to get 600g and multiply right hand side of the equation as well
[tex]600g = 0.22 \times 6[/tex]
[tex]600g = 1.32 \: pounds[/tex]
If Janet earned e extra credit points. Mona earned 32 fewer extra credit points than Janet.
What is the expression that shows how many extra credit points Mona earned?
How many terms are in the expression?
Answers
Find the slope of the line that passes through (19, 72) and (20, -1).
Answers
Step-by-step explanation:
please mark me as brainlest
If [tex]a\ \textless \ b[/tex], there are three ordered pairs of positive integers [tex](a,b)[/tex] that satisfy [tex]a^{2}+b^{2}=10(123)^{2}[/tex] If two of these ordered pairs are [tex](39,387)[/tex] and [tex](201,333)[/tex]. What is the third such ordered pair?
Answers
The third ordered pair that satisfies the equation of the circle is (123, 369).
The given parameters;
[tex]a^2 + b^2 = 10(123)^2[/tex]First pair of the equation, = (39, 387)Second pair of the equation = (201, 333)The third ordered pair of the equation can be determined by using general equation of a circle;
[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]
The radius of the circle is calculated as;
[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]
The value of a can be obtained by randomly choosing numbers less than the radius as values of b.
[tex]b < r\\\\b < 388.96[/tex]
[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]
Thus, the third ordered pair that satisfies the equation of the circle is (123, 369).
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After the elves had hung 25% of the ornaments on the North Pole tree, there
were 480 more ornaments to hang. How many ornaments were in the box to
begin with?
Answers
Answer:
640
Step-by-step explanation:
x = total amount of ornaments
480 = 0.75x
(480 is 7 percent of the ornaments after you hang 2 percent of them)
x = 640
.872 to scientific notation
Answers
Answer:
8.72×10²
Step-by-step explanation:
8.72×10²=872The movement of the progress bar may be uneven because questions can be worth more or less (ir
Add: (– 15xz + 4xy) + (20xy - 9yz + 16xz)
O 24x2 y2 – 9yz + x² zº
0 16xyz
0 5xy – 5 yz + 16xz
024xy - 9yz + xz
Answers
Your Answer Is : - 31xz + 16xy - 9yz
write an equation of the line passing through point p that is parallel to the given line.
3. P(6,10),y=-3x+13
Answers
Answer:
Step-by-step explanation:
y=-3x+13
y = mx + b, where m is the slope and b is the y-intercept.
A line parallel to this line will have the same slope, -3. We can start by writing:
y = -3x + b
No matter what is chosen for the value of b, this line will be parallel. We do want the line to go through point (6,10), however. The way that can be done is to find a value of b that would shift the line to go through (6,10).
Find b by entering the point (6,10) into the equation, and then solve for b:
y = -3x + b
10 = -3(6) + b
10 = -18 + b
b = 28
The line becomes y = 3x + 28
See the attachment.
write the L.C.M of 5,8
Answers
From the given question we are asked to find the least common multiple of two given numbers. Here for this question, we will use the prime factorisation method and find the factors for the two given numbers and then we find the least common multiple for the numbers given. So, we proceed with our solution as follows.
Required Answer :-2 | 5, 8
_______
2 | 5, 4
_______
2 | 5, 2
_______
5 | 5, 1
_________
1, 1
2×2×2×5 = 40
Additional information :-We should remember the concept of least common multiple, which means the smallest number that two numbers both can get to or which is the common multiple between two numbers. We should know that we have different method to find the least common multiple like listing the multiples, prime factorization and division
I do not know how to do this
Answers
What is the value of y in the solutions of the system of equations: 3x + 4y = 3 and 2x – 4y = 12?
Answers
Answer:
y = -3
Step-by-step explanation:
3x + 4y = 3
2x - 4y = 12
5x = 15 Add the two equation together because the y terms are
opposite each other and goes out when you add the equations
x = 5
Substitute into the first equation and solve for y when x = 5
3x + 4y = 3
3(5) + 4y = 3
15 + 4y = 3
4y = 3 - 15
4y = -12
y = -3
Step 1) Solve the second equation for
y
2
x
+
y
=
−
8
−
2
x
+
2
x
+
y
=
−
2
x
−
8
0
+
y
=
−
2
x
−
8
y
=
−
2
x
−
8
Step 2) Substitute
(
−
2
x
−
8
)
for
y
in the first equation and solve for
x
:
−
3
x
+
4
y
=
12
becomes:
−
3
x
+
4
(
−
2
x
−
8
)
=
12
−
3
x
+
(
4
×
−
2
x
)
+
(
4
×
−
8
)
=
12
−
3
x
+
(
−
8
x
)
+
(
−
32
)
=
12
−
3
x
−
8
x
−
32
=
12
(
−
3
−
8
)
x
−
32
=
12
−
11
x
−
32
=
12
−
11
x
−
32
+
32
=
12
+
32
−
11
x
−
0
=
44
−
11
x
=
44
−
11
x
−
11
=
44
−
11
−
11
x
−
11
=
−
4
x
=
−
4
Step 3) Substitute
−
4
for
x
in the solution to the second equation at the end of Step 1 and calculate
y
:
y
=
−
2
x
−
8
becomes:
y
=
(
−
2
×
−
4
)
−
8
y
=
8
−
8
y
=
0
The Solution Is:
x
=
−
4
and
y
=
0
Or
(
−
4
,
0
)
Which of the following completes the formula of cos (a + B) =
A. sin a cos B - cos a sin B
B. sin a cos B + cos a sin B
O C. cos a cos B- sin a sin B
OD. cos a cos B+ sin a sin B
Answers
Answer:
cos a cos B-sin a sin B is the right answer
Apply distributive 15+22
Answers
Answer:37
Step-by-step explanation:
There is a cookie jar in Julio's kitchen filled with 7 cookies. His mother bakes some more cookies. Now there are 14 cookies. How many cookies did Julio's mother bake.
Answers
Answer:
His mother baked 7 more cookies
