Prove the diagonals of the square with vertices P (0,4), Q (4,4), R (0,0) and S (4,0) are perpendicular bisectors of each other.
Step 1: calculate the slope of the diagonals.
The slope of diagonal PS is ____
The slope of diagonal QR is ____
Step 2: calculate the midpoint of the diagonals
The midpoint of PS is ___
Midpoint of QR is ___
Answers
The diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.
Given information:
The square with vertices P (0,4), Q (4,4), R (0,0) and S (4,0).
It is required to prove that the diagonals of the given square are perpendicular bisectors.
First, calculate the slope of the diagonals.
The slope of diagonal PS will be,
[tex]m = \dfrac{0-4}{4-0}\\m = -1[/tex]
So, the slope of diagonal PS is -1.
The slope of diagonal QR will be,
[tex]m' = \dfrac{0-4}{0-4}\\m' = 1[/tex]
So, the slope of diagonal QR is 1.
From the slope of the diagonals, the diagonals are perpendicular because the product of slope is -1.
Now, it is required to find the mid-point of the diagonals.
The midpoint of PS will be,
[tex](x,y)=(\dfrac{0+4}{2},\dfrac{4+0}{2})=(2,2)[/tex]
Midpoint of QR will be,
[tex](x,y)=(\dfrac{4+0}{2},\dfrac{4+0}{2})=(2,2)[/tex]
So, the midpoint of both the diagonals is also same.
Therefore, it can be said that the diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.
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Answer:
-1, 1, (2,2), (2,2), and perpendicular and share the same midpoint
Step-by-step explanation:
Related Questions
Suppose that (y) varies with (x). Write an equation for the inverse variation.
y=4 when x=7
A: y= x/28
B: y=3x
C: x= y/3
D: y= 28/x
Answers
y = k/x, where k is the constant
if x = 7 and y = 4
4=k/7
k = 4*7 = 28
y = 28/x
answer is D
40% of a 12,000 acre forest is being logged how many acres will be logged
Answers
12000 - 4800 = 7200
7200 acres are being logged
hope this helps
0.40 (12,000) = 4,800
answer
4,800 acre is 40% of a 12,000 acre
Determine the solution of the system. Show your work.
Y = 5x – 9
Y = 2x + 6
Answers
5x-9=2x+6
3x-9=6
3x=15
x=5
Then plug in x into any of the equations
y=2(5)+6
y=10+6
y=16
Final answer: (5,16)
The solution is (x, y) = (5, 16). My "work" is to make use of a graphing calculator.
_____
You can subtract the second equation from the first. This gives
... 0 = 3x -15
Then, divide by 3 and add 5.
... 0 = x - 5
... 5 = x
Substitute this value into either equation to find y.
... y = 2x +6
... y = 2·5 +6
... y = 16
The strategy to subtract the second equation from the first is based on the observation that both equations give expressions for y, and the x-coefficient in the first equation is the larger of the two x-coefficients. Thus, the subtraction we chose will eliminate y and give an x-term with a positive coefficient.
Staci has seven more cats then Taylor. Write an expression that illustrates how many cats Staci has. Use x to represent the number of cats Taylor has./4899345/032a37eb?utm_source=registration
Answers
Staci has seven more than this so:
x + 7 = number of cats Staci has
Parallelogram JKLM is shown on the coordinate plane below:
If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side JM in the image parallelogram?
Answers
Answer-
The coordinates of the endpoints of the side congruent to side JM will be,
(-2, -6) and (1, -5).
Solution-
When rotating a point 270° clockwise or 90° counter-clockwise around the origin, we apply the rule (x, y) → (-y, x).
The co-ordinates of the original parallelogram are,
J = (-6, 2)
M = (-5, -1)
L = (-3, 3)
K = (-4, 6)
After the rotation, the new co-ordinates will be,
J = (-2, -6)
M = (1, -5)
L = (-3, -3)
K = (-6, 4)
∴ The coordinates of the endpoints of the side congruent to side JM will be,
(-2, -6) and (1, -5).
Can u solve 6x-21=5x+17+x
Answers
6x - 21 = 6x + 17
6x - 6x = 21 + 17
0 = 38, untrue
cannot be solved
hope this helps
In November 2010, ING Direct was offering 2.4% interest on its Orange Savings Account, with interest reinvested quarterly.† Find the associated exponential model for the value of a $3,000 deposit after t years
Answers
i = (1 + r/m)^m - 1
where m is the number of quarters in a year (m = 4)
i = (1 + 0.024/4)⁴ -1
i = 0.024217
The model would then be:
Future Worth = $3,000(1 + 0.024217)^t, where t is the number of years
If a measurement follows a normal (bell-shaped) frequency curve, then percent of the population will have a z-score below .36.
Answers
From the normal distribution tables, when z < 0.36, obtain
P(z < 0.36) = 0.6406 ≈ 64 percent
Answer: 64% (nearest integer)
Jeff wants to make an a in his math course this semester. To do so, he must have an average of 90 or above. If his test scores this semester or 88, 92 and 96 what is the score that he would need to make on his final test to attain an average on exactly 90
Answers
(276 + x) / 4 = 90
276 + x = 90 * 4
276 + x = 360
x = 360 - 276
x = 84 <=== he would need an 84
Complete the steps to the factor the tens. 30x40=( n x 10) x ( n x 10)=( n x n) x (10 x10)= n x 100 = n
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Algebra problem below!
The sum of two consecutive even integers is -50
What are the numbers?
Answers
The formula is:
x + (x + 2) = -50
Solving:
2x + 2 = -50
2x = -52
x = -26
Finding the second number:
-26 + 2 = -24
-24,-26
Hope this helps!
Which trigonometric ratios are correct for triangle ABC? Check all that apply
Answers
Let
OPP denote the length of the side opposite to M,
ADJ denote the length of the side adjacent to M, and
HYP denote the hypotenuse.
then:
Sin(M) = OPP/HYP
Cos(M)= ADJ/HYPP
Tan(M)=OPP/ADJ
Back to our problem,
using the Pythagorean we can find the length of AB:
[tex]|AB|^2+|AC|^2=|BC|^2\\\\|AB|^2+9^2=18^2\\\\|AB|^2=18^2-9^2\\\\|AB|^2=(18-9)(18+9)=9 \cdot 27=9 \cdot 9 \cdot3\\\\|AB|=9 \sqrt{3} [/tex]
[tex]Sin(C)= \frac{OPP}{HYP}=\frac{9 \sqrt{3} }{18}= \frac{ \sqrt{3} }{2}[/tex]
[tex]Cos(B)= \frac{ADJ}{HYP}= \frac{9 \sqrt{3}}{18}= \frac{ \sqrt{3}}{2} [/tex]
[tex]Tan(C)= \frac{OPP}{ADJ}= \frac{9 \sqrt{3} }{9}= \sqrt{3} [/tex]
[tex]Sin(B)= \frac{OPP}{HYP}= \frac{9}{18}= \frac{1}{2} [/tex]
[tex]Tan(B)= \frac{OPP}{ADJ}= \frac{9}{9 \sqrt{3}}= \frac{1}{ \sqrt{3} }= \frac{ \sqrt{3}}{3} [/tex]
Answer: 1, 3, 4
Points a, b, c, and d are collinear. in how many ways can the line be named using only these points
Answers
The distributive property is used to help simplify math experssions. True False
Answers
hope it helped
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TRUE
This is because when you distribute 1 thing between 2 (or more) things, it (in a way) simplifies the problem...
For Example:
solve for x
f(x) = 5*(x - 4)
The only way to solve a question like this would be to distribute the 5 to the x and to the 4...
So...
The answer is: TRUE
Evaluate these questions
3a+2a=
c+d there is a line under this one
ad
Answers
1)
For this question we can combine the terms together as they are like:
[tex]3a+2a[/tex]
Combine like terms.
[tex]=5a[/tex]
Hope this helps.
-Benjamin
What is the answer for this problem
Answers
9 + 3 x 13 =
9 + 39 = 48
3x13=39
39+9=48
Mikel creates the table below to help her determine 40% of 70
Answers
To Find: 40 % of 70
Solution:
x % of y means = [tex]\frac{x \times y}{100}[/tex]
40 % of 70= [tex]\frac{40 \times 70}{100}=\frac{2800}{100}=28[/tex]
This is the way Mikel can determine 40 % of 70.
what do you add 15/4 to make 4
Answers
Point M is the midpoint of segment JK. Find JK when JM=6x-7 and MK=2x+3.
Answers
so
6x-7=2x+3
minus 2x both sides
4x-7=3
add 7 both sides
4x=10
divide both sides by 4
[tex]x=\frac{10}{4}[/tex]
[tex]x=\frac{5}{2}[/tex]
sub back
JM=6x-7
[tex]JM=6(\frac{5}{2})-7[/tex]
[tex]JM=\frac{30}{2}-7[/tex]
[tex]JM=15-7[/tex]
JM=8
JM=MK=8
JM+MK=8+8=16=JK
[tex]x=\frac{5}{2}[/tex] and JM=8=MK and JK=16
The value of JK will be 16.
It is given that M is the midpoint of segment JK.
We have to find out the value of JK.
What will be the value of x , if 4x + 12 = 8x + 4 ?
The value of x will be 2.
As M is the midpoint of JK.
JK = MK + JM
So,
MK = JM
2x + 3 = 6x - 7
4x = 10
x =2.5
So ,
MK = 2x + 3 = 8
JM = 6x - 7 = 8
Hence ,
JK = MK + JM = 8 + 8
JK = 16
Thus , value of JK will be 16.
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Find a point on the y-axis that is equidistant from the points (4, −4) and (1, 1).
Answers
a point on the y-axis is : P( 0, y)
PA = PB or PA² = PB².... A(4 , -4) B(1,1)
(4-0)²+(-4-y)² = (1-0)² + (1-y)²
16 +y² +8y +16 = 1 + 1 -2y +y²
10y = -30
y = -3
Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.
How many points was each multiple choice question worth?
Enter your answer in the box.
Answers
NOT Guaranteed this is the Answer. Best of luck to you.
Find the angle measure of the hands of a clock at the given time. 5:00
Answers
[tex] \frac{5}{12}*360=5*30=150^o [/tex]
Answer is 150°
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
We know that the hour hand will be on 5 and the minute hand will be on 12 at 5:00 o'clock.
Then the angle measured by the hands of a clock at the given time at 5:00 will be
⇒ (360° / 12) x 5
⇒ 30° x 5
⇒ 150°
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
More about the angled link is given below.
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Write a story that matches the expression
42x - 5
Answers
Answer: Hello there!
The equation is: 42x - 5
That can be phrased as "the difference between 42 times a number x and 5"
And we want to write a story that matches this.
an example can be:
Suppose that Jon craft musical instruments and he sells them in the beach, then you could write:
"The revenue in a day for Jon is equal to $42 for each instrument that he sells, less a 5 dollar fee that he needs to pay every day"
where the number of instruments would be x.
What is the area of a circle with radius 14 units, to the nearest hundredth?
Answers
14×2=28
28×pi=88
One month, Ruby worked 8 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 112 hours. Find the number of hours each person worked.
Answers
S=4R
R+I+S=112
R+R-8+4R=112
6R=120
R=20
So therefore, Ruby worked 20 hours, Svetlana worked 80 hours, and Isaac worked 12 hours.
Solve x(−2) 2 =4(−2)
Answers
x(−2) 2 =4(−2) = -2
Explanation:To solve this equation, we first need to understand the order of operations in mathematical equations. The acronym PEMDAS is often used to remember the order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
In this equation, we have parentheses and exponents. According to PEMDAS, we need to solve the parentheses first before moving on to the exponent. So, let's start by simplifying the parentheses on the left side of the equation.
x(-2)^2 = 4(-2)
= x(4) = -8
= 4x = -8
= x = -2
In the first step, we distributed the exponent of 2 to the -2 within the parentheses, resulting in (-2)^2 = (-2)(-2) = 4. This simplifies the left side of the equation to x(4) = 4x.
In the second step, we substituted the value of -2 on the left side of the equation, resulting in 4(-2) = 4x. This simplifies to -8 = 4x.
To isolate x, we divide both sides by 4, resulting in x = -2. This gives us our final answer.
In conclusion, when solving equations with multiple operations, it is important to remember the order of operations and follow it step by step. In this equation, we simplified the parentheses first, then solved for x by isolating it on one side of the equation. By following these steps, we were able to find the value of x, which is -2.
If cot= 2/3 what is the value of Csc
Answers
Tan= opposite over adjacent. So 3/2
This means the hypotenuse is square root of 13
Csc is inverse sin
Sin = opposite \ Hypotenuse
Sin = 3/Square root of 13
Csc = square root of 13/ 3
what numbers are divisible by 7?
a.75 b.35 c.20 d.30
Answers
Thanks (;
How can I evaluate this question?
Answers
[tex]\bf \\\\\\ \begin{cases} x^2\cdot x^{\frac{1}{3}}+3x^3-4x^2\\\\ -2x^{-\frac{1}{2}}\cdot x^{\frac{1}{3}}-2x^{-\frac{1}{2}}\cdot 3x+2x^{-\frac{1}{2}}\cdot 4\\\\ +x^{\frac{1}{3}}+3x-4 \end{cases} \\\\\\ \begin{cases} x^{2+\frac{1}{3}}+3x^3-4x^2\\\\ -2x^{-\frac{1}{2}+\frac{1}{3}}-6x^{-\frac{1}{2}+1}+8x^{-\frac{1}{2}}\\\\ +x^{\frac{1}{3}}+3x-4 \end{cases}[/tex]
[tex]\bf x^{\frac{7}{3}}+3x^3-4x^2-2x^{-\frac{1}{6}}-6x^{\frac{1}{2}}+8x^{-\frac{1}{2}}+x^{\frac{1}{3}}+3x-4 \\\\\\ \sqrt[3]{x^7}+3x^3-4x^2-\cfrac{2}{x^{\frac{1}{6}}}-6\sqrt{x}+\cfrac{8}{x^{\frac{1}{2}}}+\sqrt[3]{x}+3x-4 \\\\\\ x^2\sqrt[3]{x}+3x^3-4x^2-\cfrac{2}{\sqrt[6]{x}}-6\sqrt{x}+\cfrac{8}{\sqrt{x}}+\sqrt[3]{x}+3x-4[/tex]
1. Find the perimeter and area of a rectangle with a length of 3.2 m and a width of 1.5 m.
A) p=4.7 m; A=2.25 m^2
B) p=4.7 m; A=4.8^2
C) p=9.4 m; A=2.4 m^2
D) p=9.4 m; A= 4.8^2
2. Find the area of a triangle with a base of 27 feet and a height of 14 feet.
A) 41 ft^2
B) 82 ft^2
C) 189 ft^2
D) 378 ft^2