The line MN is shown on the grid.
Find the equation of the perpendicular bisector of line MN.
Answers
Find midpoint coordinates:
[tex]\rightarrow \sf (\dfrac{-1+3}{2} ), \ (\dfrac{7+(-1)}{2} )[/tex]
[tex]\hookrightarrow \sf (1, \ 3)[/tex]
Find the gradient of MN:
[tex]\dashrightarrow \sf \dfrac{-1-7}{3-(-1)}[/tex]
[tex]\dashrightarrow \sf -2[/tex]
slope of perpendicular bisector:
[tex]\rightarrow \sf \dfrac{1}{2}[/tex]
Equation:
[tex]\sf \rightarrow y = \dfrac{1}{2}x+\dfrac{5}{2}[/tex]
Answer:
[tex]y=\dfrac12x+\dfrac52[/tex]
Step-by-step explanation:
M = (-1, 7)
N = (3, -1)
[tex]\sf slope\:of\:MN=\dfrac{y_n-y_m}{x_n-x_m}= \dfrac{-1-7}{3-(-1)}=-2[/tex]
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line perpendicular to MN is:
[tex]\sf \implies -2 \times m=-1[/tex]
[tex]\sf \implies m=\dfrac12[/tex]
If the line bisects the line MN, it will intersect it at the midpoint of MN:
[tex]\begin{aligned}\textsf{Midpoint of MN} & =\left(\dfrac{x_m+x_n}{2},\dfrac{y_m+y_n}{2}\right)\\ & =\left(\dfrac{-1+3}{2},\dfrac{7+(-1)}{2}\right)\\ & =(1,3)\end{aligned}[/tex]
Finally, use the point-slope form of the linear equation with the found slope and the midpoint of MN:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=\dfrac12(x-1)[/tex]
[tex]\implies y=\dfrac12x+\dfrac52[/tex]
Related Questions
2. When plotting a point on a coordinate grid using an ordered pair, the
first number tells you to go up.
O True
False
Answers
Explanation:
Any point is of the form (x,y)
The first coordinate is x which tells us to go either left or right depending on whether x is negative or positive.
Example: (-2,3) means we go left 2 units
Another example: (5,7) means we go to the right 5 units.
The starting point is the origin where the x and y axis meet up.
Answer:
False
Step-by-step explanation:
The hexagon shown is divided into 4 triangles and a rectangle.
What is the area of the hexagon in square centimeters?
Answers
Answer: My good friend this answer is 222.4 because if you take the 16 cm and the 13.9 cm and mulitply the you will get 222.4 and thank you for chosing me.
Step-by-step explanation:
What is the mode of the data set? 78, 82, 91, 78, 92, 77, 80, 74, 81
A. 92
B. 78
C. 85.5
D. 77
Answer: B
Answers
Answer:
B. 78
Step-by-step explanation:
78 It is the most frequent data (2)
Hope this helps
GIVING BRAINLIEST FOR THIS ONE QUESTION, THANKS
Answers
Answer:
[tex](6\times 4)^3 = 6^3 \times 4^3[/tex]
Step-by-step explanation:
For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why. (Select all that apply.)
(a) H0: ? = 15, Ha: ? = 15
This pair complies.This pair does not comply because ? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(b) H0: p = 0.5, Ha: p > 0.6
This pair complies.This pair does not comply because p is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(c) H0: ? = 121, Ha: ? < 121
This pair complies.This pair does not comply because ? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(d) H0: ? = 123, Ha: ? = 125
This pair complies.This pair does not comply because ? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(e) H0: p? = 0.2, Ha: p? ? 0.2
This pair complies.This pair does not comply because p? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
Answers
It can be inferred that H0: ? = 15, Ha: ? = 15 doesn't comply because both hypothesis use an equal sign.
How to illustrate the hypothesis?From the information, H0: p = 0.5, Ha: p > 0.6 doesn't comply because the two hypothesis use different numbers.
Furthermore, H0: ? = 121, Ha: ? < 121 shows that the pair complies. Also, H0: ? = 123, Ha: ? = 125 doesn't comply as they use the equal sign and different numbers.
Lastly, H0: p? = 0.2, Ha: p? ? 0.2 doesn't comply because p is not a population characteristic.
Learn more about hypothesis on:
https://brainly.com/question/11555274
A: x+90=180
B: 2x+90=180
C: x-90=180
D: Not enough info
Answers
Answer:
(B) 2x + 90 = 180 is an equation that could be used to find x.
Step-by-step explanation:
Observing at the triangle, we can see that..
- We are aware of two angel measurements, both of which are 45 degrees.
One triangle is exactly 180 degrees and if you add both 2 angel measurements from the triangles...
45 + 45 = 90 degrees
180 - 90 = 90 degrees
As a result, we know that x = 90. Now we find the equation. Lets look at equation B. ( 2x + 90 = 180 )
Step 1 : 90 should be subtracted from both sides.
2x + 90 − 90 = 180 − 90
2x = 90
Step 2 : Divide both sides by 2.
(When I use the symbol /, it signifies I'm dividing.)
2x/2 = 90/2
x = 45
Step 3: Examine your solution to see whether it is right.
2x + 90 = 180
2(45) + 90 = 180
90 + 90 = 180 ✓
This shows that 2x + 90 = 180 is an equation that could be used to find x.
Hope this helps! :D
help, I’m terrible with percentages
Bob has a 1% chance of getting a prize from a cereal box, while the other prizes have a 99% chance for him to get. How many cereal boxes does Bob have to buy in order to get the prize? Show your work.
I’m pretty sure you’re supposed to find out something like “one in a million chance!”
Answers
Answer:
99 boxes im sure
d. A bag of fertiliser is made up of nutrients: nitrogen, phosphorus and potassium in the ratio 3:1:2. If the bag of fertiliser contains 14 kg of phosphorus, calculate how much nitrogen it contains. [3]
Answers
42
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Step-by-step explanation:[tex]14\times 3\div 1[/tex]
______________________________________________
Calculate
[tex]14\times 3[/tex]
______________________________________________
Calculate the product or quotient
[tex]42[/tex]
I hope this helps you
:)
NEED HELP ASAP I WILL MARK BRAINLIEST IF ANSWERED CORRECTLY
NO LINKS IF YOU DO NOT KNOW THE ANSWER PLEASE SKIP OVER THIS THREAD
Answers
Answer:
I think this Cyclic quadrilateral 180degree
An observation tower is 65m high. A support wire is attached to the tower 30m from the top. If the support wire and the ground form an angle of 56 degrees, what is the length of the support wire, to the nearest tenth?
Answers
The support wire is the hypotenuse of the right triangle formed. Therefore, the length of the support wire is 42.2 meters.
The situation forms a right angle triangle.
Right angle triangleA right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, the height of the tower where the wire was attached is the opposite side of the triangle formed.
The wire was attached 30 m from the top. Hence, 65m - 30m = 35 m.
Therefore,
sin 56° = opposite / hypotenuse
sin 56° = 35 / x
The hypotenuse is the length of the support wire.
Therefore,
x = 35 / 0.82903757255
x = 42.2195416164
x = 42.2 m
learn more on right angle here: https://brainly.com/question/9495022
I WILL GIVE BRAINLYEST
Rectangle PQRS is plotted on a coordinate plane. The coordinates of P are (– 1, 4) and the
coordinates of Q are (– 1, – 4). Each unit on the coordinate plane represents 1 centimeter, and
the area of Rectangle PQRS is 64 square centimeters. Find the coordinates of Points R and S
given these conditions:.aPoints R and S are to the left of Points P and Q.bPoints R and S are to the right of Points P and Q
Answers
Answer:
See belowStep-by-step explanation:
Given points P and Q have same x-coordinate but different y- coordinates.
The distance between P and Q is the difference of y- coordinates:
PQ = 4 - (-4) = 8 units = 8 cmThe area is 64 cm², it means the adjacent sides are
PS = QR = 64/8 = 8 cma)
If the points R and S are to the left, their coordinates are
S = (-1 - 8, 4- 0) = (- 9, 4)R = (-1 - 8, - 4 - 0) = (- 9, -4)b)
If the points R and S are to the right, their coordinates are
S = (-1 + 8, 4 + 0) = (7, 4)R = (-1 + 8, - 4 + 0) = (7, -4)Answer:
Points R and S are to the left of Points P and Q
R = (-9, 4)
S = (-9, -4)
Points R and S are to the right of Points P and Q
R = (7, 4)
S = (7, -4)
Step-by-step explanation:
Given coordinates:
P = (-1, 4)Q = (-1, -4)Points P and Q have the same x-value.
The vertical distance between these two points is:
[tex]\begin{aligned}\implies \sf y_P-y_Q & =\sf 4-(-4)\\ & =\sf 4+4\\ & =\sf 8\:units \\ & =\sf 8\:cm\end{aligned}[/tex]
Area of a rectangle = width × length
If the area of the rectangle PQRS is 64 cm² then:
[tex]\begin{aligned} \implies \sf 64 & = \sf width \times 8\\\implies \sf width & = \sf \dfrac{64}{8}\\\implies \sf width& = \sf 8 \: cm \end{aligned}[/tex]
This means that the y-values of points R and S will be the same as points P and Q, but the x-values will either be 8 less or 8 more.
Points R and S are to the left of Points P and Q
R = (-1 - 8, 4) = (-9, 4)
S = (-1 - 8, -4) = (-9, -4)
Points R and S are to the right of Points P and Q
R = (-1 + 8, 4) = (7, 4)
S = (-1 + 8, -4) = (7, -4)
In parallelogram ABCD, mLA
4x + 20 and m2C = x + 26
Find the value of x.
Then find the measure of LA.
Answers
Answer:
Step-by-step explanation:
In a parallelogram, opposite angles are congruent.
∠A = ∠C
4x + 20 = x + 26
Step 1: To find the valu of 'x', first subtract 20 from both sides
4x = x + 26- 20
4x = x + 6
Step2: Now, subtract 'x' from both sides
4x -x = 6
3x = 6
Step:3: divide both sides by 3
x = 6/3
x = 2
∠A = 4*2 + 20
= 8 + 20
∠A = 28°
If you can buy 15 bags of potatoes for $20, then how many can you buy with $4?
Answers
Answer:
Step-by-step explanation:
15 bags for $20 can be represented with 15/20
so x bags for $4 can be represented with x/4
now if you proportion it out (ricochet), 4x15 is 60, 60 divided by 20 is 3, so you can buy 3 bags of potatoes with $4.
OR
you could do 15/20 is 0.75
0.75 times 4 is 3, so $4 can buy you 3 bags.
Answer:
Step-by-step explanation:
Remark
This is a proportion problem. It assumes that if you know 3 of the four parts of a 2 ratio proportion, you can solve for the 4th one.
Givens
number of bags = 15
Cost = 20
Different cost = 4
number of bags = ?
Formula
Number of bags / Cost = different number of bags/ New Cost
Solution
15/20 = x / 4 Multiply both sides by 4
15*4/20 = x / 4 * 4
60/20 = x
Answer x = 3
That is 4 dollars gets you 3 bags of potatoes
Find the missing side of the right triangle. Leave answer in
simplest radical form.
If the legs of a right triangle are 6 and 8, then the hypotenuse
is
a 40
b 30
C 20
d 10
Answers
Altitude (AB) = 6cm
Base (BC) = 8cm
To FindHypotenuse (AC) = ?
[tex] \fbox \text{According To Pythagoras Theorem = }[/tex]
[tex] \text{(Hypotenuse)² = (Altitude)² + (Base)²}[/tex]
Inserting The Values
[tex] \text{(Hypotenuse)²} =( {6})^{2} + (8) {}^{2} [/tex]
[tex] (\text{AC}) {}^{2} = (6) {}^{2} + (8) {}^{2} \\ \implies \text{(AC)} {}^{2} = 36 + 64 \\ \implies\text{AC} = \sqrt{100} \\ \implies\text{AC} = 10 \\ \\ \therefore \text{Hypotenuse (AC)} = 10 \text{cm}[/tex]
Correct Option D= 10cm
Hope this helpsA law firm charges $450 per hour for its services. To raise revenues, the firm increases its fees by
10%. What is the new rate that the firm charges per hour?
Answers
Answer:
The correct answer would be $495 per hour
Step-by-step explanation:
The equation would be
450 divided by 10= 45
=450+45=495
= $495
Please help! First answer correct BRAINLIEST
Answers
Answer:
8.......................
Step-by-step explanation:
It's clear that the figure is rhombus (because diagonals make right angle).
Rhombus area formula: (AC×BD)÷2
So if we have area and one diagonal then it's easy to find another diagonal.
S=AC×BD÷2
14.5×BD÷2=58
14.5BD=58×2
14.5BD=116
BD=116÷14.5
BD=8
If you are traveling in your car at an average rate of r miles per hour for T hours, then the distance d in miles that you travel is described by the formula d=rt that is distance equals rate times time. A distance of 60 miles at an average rate of 40 miles per hour is covered in ___ hours?
Answers
Answer:
1.5 hr
Step-by-step explanation:
d = rt
re-arrange to
d/r = t
60 miles / 40 miles/hr = 1.5 hr
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
y = 3/4x - 1
Step-by-step explanation:
m = (1-4)/(4-8) = -3/-4 = 3/4
b = (0, -1)
y = mx + b
y = 3/4x - 1
BRAINLIEST please if this helps!-1 is the lines y-intercept
And from (4,1) to (8,4) it goes up 3 and to the right 4
ind the area of the figure.
A) 14 cm2
B) 50 cm2
C) 60 cm2
D) 64 cm2
Answers
Answer:
D) 64
Step-by-step explanation:
(10 x 12) - (8 x7) = 120-56 = 64
answer: 64 square cm
Please help :) (its for my friend, cause she wont belive me!)
If your friend has 7 apples, you take 3. How much do you have?
Answers
Answer:
the answer its 3 :)
Step-by-step explanation:
matematicas amigo
if p and q are two propositions,use truth table technique to show that a) (p=q) ^ (q=p)= p=q and b) [(p=q) ^ p]=q is a Tautology
Answers
Answer:
see attached
Step-by-step explanation:
The truth table technique shows the first proposition is True. However, the second proposition cannot be shown to be a tautology, because it isn't true.
__
a.The "equals" relation is commutative: (a=b) ≡ (b=a), hence the expression ...
(p=q)∧(q=p)
is equivalent to
(p=q)∧(p=q)
We know that the And of p with itself is just p, so that fact ensures the truth of ...
(p=q)∧(p=q) = (p=q)
Hence
(p=q)∧(q=p) = (p=q)
The top truth table in the attached shows the final comparison of the two expressions is true for all values of p and q.
__
b.The attached truth table shows that the given relation is not a tautology.
Which answer is the explicit rule for the sequence 11, 8.5, 6, 3.5, 1
Answers
I think it's an= 13.5 - 2.5n
[tex]a_n=13.5-2.5n[/tex]
Step-by-step explanation:[tex]11,\ 8.5,\ 6,\ 3.5,\ 1...[/tex]
[tex]So\ d=8.5-11=b-8.5=3.5-6=1-3.5[/tex]
[tex]=-2.5[/tex]
[tex]And\ a_1=\parallel \left\{Anithmetic\ \left.\ sequence\right\}\right.[/tex]
[tex]so\ a_n=a_1+d(n-1)[/tex]
[tex]=11-2.5(n-1)[/tex]
[tex]=13.5-2.5n[/tex]
[tex]The\ answer:a_n=13.5-2.5n[/tex]
I hope this helps you
:)
Help picture below problem 6
Answers
Answer:
i think that B..is a right answer
Answer:
An octagon is a polygon with eight sides.
Step-by-step explanation:
Octa or Octo means eight. Like an octopus. They call it an octopus because it has eight limbs.
A stop-sign is an examle of an octagon.
Hope that helps!
Helppp PLEASE ASPPP HELP HELP HELP PLEASE HELP
Answers
Answer:
c. 17/12
Step-by-step explanation:
Sal is making bracelets for a fundraiser. He uses 6 inches of yarn per bracelet. how many bracelets can Sal make?
Answers
Answer:
He should consider using an exuberant amount of yarn to raise money for charity. How much yarn is available?
Select the correct answer.
A parabola passes through the points (0,5), (1,4), and (2,5). What function does the graph represent?
f(x) = -x2 + 2x + 5
f(x) = -x2 + x +5
O
f(x)=x²+x-2
Of(x) = x2 – 2x+5
Submit
Answers
Answer:
X^2-2x+5 is the answer
Step-by-step explanation:
The line L passes through the points (5, -5) and (1, 2).
Find the gradient of line L.
Answers
gradient of L = -7/4
Explanation:
[tex]\sf gradient = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Insert the following values.
[tex]\rightarrow \sf \dfrac{2-(-5)}{1-5}[/tex]
[tex]\rightarrow \sf \dfrac{7}{-4}[/tex]
[tex]\rightarrow \sf -\dfrac{7}{4}[/tex]
Use the slope formula:-
(the slope is the same as the gradient)
[tex]\sf{\displaystyle\frac{y2-y1}{x2-x1} }[/tex]
[tex]\sf{\displaystyle\frac{2-(-5)}{1-5}}[/tex]
[tex]\sf{\displaystyle\frac{2+5}{-4} }=\frac{7}{-4} ={\boxed{-\frac{7}{4} }}\leftarrow\sf{slope~of~line~L}}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Solve, using the correct order of
operations, when x = 8 and y = 6.
2x - (4 + y)
Answers
Step-by-step explanation:
When x = 8 and y = 6
= 2x - ( 4 + y )
Put the value of x and y ...
= 2 × 8 - 4 × 6
Multiply 2 and 8 and 4 and 6 ...
= 16 - 24
Subtract it
= - 8
Hence...the answer is -8 ....
José is painting a backdrop for the school
play. The rectangular backdrop is
60 inches by 45 inches. If his container of
paint can cover 25 square feet, does
he have enough to paint the backdrop?
Answers
Answer:
Definitely not
Step-by-step explanation:
60*45 = 2700 and 2700 square inches converted into feet is 225 square feet
Question 7 (Essay Worth 5 points)
(7.03)
An equation is shown below:
6(2x - 11) + 15 = 21
Write the steps you will use to solve the equation and explain each step.
Answers
Answer:
x=6
Step-by-step explanation:
The first thing you should start with is distributing the 6 inside the parentheses, which would give us (12x - 66) + 15 = 21. Now we can add like terms on this side of the equation to get: 12x -51 = 21. Add the 51 to the right side to get 12x = 72, then divide both sides by 12 to get x = 72/12 or 6.
x=6
Hope this helps!
Marking this brainliest also helps me out too :)
