Answers
Answer:
AE - 3, EB - 2, EC - 5
Step-by-step explanation:
Use the Pythagorean theorem and you'll find that these are the answers.
I'll answer problem 19
=======================================================
Part (a)
The tickmarks on segments DE and DC indicate they are the same length. We're also told that |DC| = |DE| = 5.
So DE is also 5 cm long. Triangle DAE is a right triangle with the 90 degree angle at angle A. Let x be the length of segment AE.
We'll use the pythagorean theorem to find x
a^2 + b^2 = c^2
(AE)^2 + (AD)^2 = (DE)^2
x^2 + 4^2 = 5^2
x^2 + 16 = 25
x^2 = 25-16
x^2 = 9
x = sqrt(9)
x = 3
Segment AE is 3 cm long
=======================================================
Part (b)
For any rectangle, the opposite sides are parallel and the same length. This means AB = DC = 5 cm.
We found earlier that AE = 3 cm, so,
AE+EB = AB
3+EB = 5
EB = 5-3
EB = 2
Segment EB is 2 cm long
=======================================================
Part (c)
We know that AD = BC = 4 cm, because the opposite sides are the same length.
Earlier in part (b), we found that segment EB was 2 cm long.
Triangle EBC is a right triangle with legs EB = 2 and BC = 4. Let's apply the pythagorean theorem to find EC. Let y = EC.
a^2 + b^2 = c^2
(EB)^2 + (BC)^2 = (EC)^2
2^2 + 4^2 = y^2
4 + 16 = y^2
20 = y^2
y^2 = 20
y = sqrt(20)
y = sqrt(4*5)
y = sqrt(4)*sqrt(5)
y = 2*sqrt(5)
y = 4.4721359
As an exact value, EC is sqrt(20) or 2*sqrt(5) cm long.
As an approximate value, EC is roughly 4.4721359 cm long.
I would ask your teacher if you should use the exact or approximate value.
Related Questions
VW = WX = YW = ZX = VX = view image attached thank youuu!
Answers
Answer:
assuming this is a rectangle:
VW=31
WX=19
YW=36.36
ZX=18.18
VX=36.36
Step-by-step explanation:
VW=VX
VW=31
WX=VX
WX=19
YW^2=19^2+31^2
YW^2=361+961
YW^2=1322
YW=36.36
ZX=1/2VX
ZX=18.18
VX=YW
VX=36.36
The measures of the rectangle are
a) The measure of VW = 31
b) The measure of WX = 19
c) The measure of YW = 36.36
d) The measure of ZX = 18.18
e) The measure of VZ = 18.18
What is the diagonal of a rectangle?The diagonal of a rectangle is calculated by the formula
From the Pythagoras Theorem , The hypotenuse² = base² + height² , and
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
Given data ,
Let the rectangle be represented as VWXY
Now , the diagonals of the rectangle are VX and WY
Substituting the values in the equation , we get
The measure of VY = 19
The measure of XY = 31
Now , for a rectangle the opposite sides are congruent
So , the measure of VY = measure of WX
And , the measure of XY = measure of VW
On simplifying the equation , we get
The measure of WX = 19
The measure of VW = 31
And , the diagonal of the rectangle = √ ( Length )² + ( Width )²
Substituting the values in the equation , we get
The diagonal of the rectangle YW = √ ( 31 )² + ( 19 )²
The diagonal of the rectangle YW = √ ( 961 + 361 )
The diagonal of the rectangle YW = 36.359 ≈ 36.36
And , the measure of VX = measure of YW = 36.36
Now , the measure of ZX = measure of VZ = measure of VX / 2
So , the measure of ZX and VZ = 36.36 / 2 = 18.18
Hence , the diagonal of the rectangles is 36.36
To learn more about diagonals of the rectangle click :
https://brainly.com/question/13583275
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Christina is having a Super Bowl party with 7 of her celebrity friends. Kobe lives 32 miles from Christina. Will Smith has to drive 32 miles to get to Christina’s. Kim Kardashian will drive 15 miles to get there. Wiz Khalifa is going to ride his bike 2 miles to get there. Andre 3000 is going to run 3 miles to get to Christina’s, and Lebron lives 32 miles from Christina’s house as well. Cardi B lives 45 miles from Christina. What is the median, mode, and mean of distance that they can travel? Complete the table below.
Answers
Answer:
Median: 32
Mode: 32
Mean of Distance: 22.60
Step-by-step explanation:
2, 3, 12, 32, 32, 32, 45
kobe 32 miles away
will smith 32 miles away
kim 12 miles away
wiz 2 miles away
andre 3 miles
lebron 32 miles
cardi b 45 miles
A cylindrical can of tennis balls holds a stack of three tennis balls so that they touch the can at the top,bottom,and sides. The radius of each tennis ball is 1.25 inches. Find the volume inside the can that is not taken up by three tennis balls.round to the nearest tenths.
Answers
Answer:
3.7555555536321
Step-by-step explanation:
2. Which equation is equivalent to 2 + 4x = 5 - 3(x + 1)? A. 2 + 4x = 2x - 3 B. 2 + 4% = 5 - 3 -3. C. 6x = 5-(+ 1). D. 2 + 4 = 2/5 1).
Answers
Answer:
B) 2 + 4x = 5 - 3 - 3x
Step-by-step explanation:
By simplifying JUST the right side and re-arranging them
2 + 4x = 5 - 3(x + 1),
2 + 4x = 5 - 3x -3,
2 + 4x = 5 -3 - 3x
Can someone please Classify the angles ? I don’t need a conclusion ....
Answers
Answer:
Right triangle
Step-by-step explanation:
A right triangle is a triangle in which one angle is a right angle.
Which graph shows a proportional relationship?
Answers
There is a linear relationship between the variables x and y. And the line that passes through the origin. Then the correct option is C.
What are ratios and proportions?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
Let the two variables x and y.
Where x is an independent variable and y is the dependent variable that depends on x directly. Then we have
The variable y is directly proportional to the variable x.
y ∝ x
When the proportionality sign is removed a constant k comes into the equation. That is given as
y = kx
There is a linear relationship between the variables x and y.
And the line that passes through the origin.
The graph is shown below.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
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what are the coefficients in the expression 4x+y+6z+12
Answers
Answer:
4, 1, 6
Step-by-step explanation:
The coefficient of x is 4
The coefficient of y is 1
The coefficient of z is 6
The coefficient of a variable is the number that appears before it.
What is the value of the missing angle ?
Answers
Answer:
30
Step-by-step explanation:
? = 180 - 150 = 30
Answer:
30°
Step-by-step explanation:
The line is 180 degrees so all you have to do is subtract 150° from 180°
You should end up with 30°
Whenever you see a straight line (IT HAS TO BE STRAIGHT), it is equal to 180°.
Kira ,Charlie , and Miguel have a total of $105 in their wallets . Kira has $9 less than Miguel. Charlie has 4 times what Miguel has . How much does each have ?
Answers
Let the money with Miguel be x.
Then :
Money with Kira = x - 9
Money with Charlie = 4x
Total money in their wallet = $105
This can be written in an equation as :
[tex] = \tt \: x + x - 9 + 4x = 105[/tex]
[tex] = \tt2x + 4x - 9 = 105[/tex]
[tex] = \tt 6x - 9 = 105[/tex]
[tex] = \tt6x = 105 + 9[/tex]
[tex] = \tt6x = 114[/tex]
[tex] = \tt x = \frac{114}{6} [/tex]
[tex] = \tt x = 19[/tex]
Which means :
Money with Miguel = $19
Money with Kira :
= 19 - 9
Thus, Kira has $10 in her wallet.
Money with Charlie :
= 4 × 19
= 76
Thus, Charlie has $76 in his wallet.
Therefore, Money with Kira = $10Money with Charlie = $76Money with Miguel = $19Answer:
Let the money with Miguel be x.
Then :
Money with Kira = x - 9
Money with Charlie = 4x
Total money in their wallet = $105
This can be written in an equation as :
= \tt \: x + x - 9 + 4x = 105=x+x−9+4x=105
= \tt2x + 4x - 9 = 105=2x+4x−9=105
= \tt 6x - 9 = 105=6x−9=105
= \tt6x = 105 + 9=6x=105+9
= \tt6x = 114=6x=114
= \tt x = \frac{114}{6}=x=
6
114
= \tt x = 19=x=19
Which means :
Money with Miguel = $19
Money with Kira :
= 19 - 9
Thus, Kira has $10 in her wallet.
Money with Charlie :
= 4 × 19
= 76
Thus, Charlie has $76 in his wallet.
Therefore,
Money with Kira = $10
Money with Charlie = $76
Money with Miguel = $19
HELP I WILL GIVE BRAINLIEST
Solve for x.
7x + 14 – 2x = −x + 12 – x − 19
A. x = −3
B. x = −1
C. x = 1
D. x = 3
Answers
Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
X COULD BE 2 OR 7
Step-by-step explanation:
Answer:
A. x= -3
Step-by-step explanation:
firstly collect all the terms . then move the term so it'd look like 5x+14 = -2x - 7 then calculate it then it would look like this : 5x+2x = -7 -14 after you move the terms you again calculate it and then the finish product would look like this : 7x = -21 so after you get that you divide by both sides and the answer is -3 . (im sorry if that don't make sense) but the answer is A.
square abcd has an area of 4m^2. square pqrs has an area of 36m^2. What is the similarity ratio of square abcd to square pqrs
Answers
Answer:
1:9
Step-by-step explanation:
Please tell me the answers i am confused and need help
Answers
Answer:
Simplified= 7x+6 When x=3 the expression=27
Step-by-step explanation:
Indicate below whether the equation in the box is true or false.4/8 = to 6/10
Answers
Answer:
Not equal. So, false.
Step-by-step explanation:
Just cross multiply
40 and 48
so no, they're are not equal.
Answer:
False
Step-by-step explanation:
Add the integers.
-6 + (-4) =( ?
B-2
C 2
D 10
Answers
Answer:
-10
Step-by-step explanation:
Help ASAP please please 14 and 15
Answers
Drag and drop each equation to match the type of solution.
Answers
Answer:
B, A, C
Step-by-step explanation:
Find m<YQR pls need grade gud.
Answers
Answer:
21°
Step-by-step explanation:
We can prove these two triangles congruent by the HL (Hypotenuse-Leg) theorem. Then, we know that m<YQR is congruent to m<PQY. We can then use their given values to form an equation.
5x+6=16x-27
Continue to solve . . .
33 = 11x
x=3
Therefore, we can plug this value of 3 into the expression for the value of m<YQR, and you will get
(16 x 3) - 27, which is equal to 21°.
The senior class at Clearville ISD is having a fundraiser to raise money for their prom. They are seling coupon books in the local community. The number currently sold by each of the students was used to create the box plot shown below. HHH 8 10 12 14 16 18 20 22 24 26 28 30 32 If one of the students calculated the mean of the data to be 14.5, would this be an appropriate mean? OA. Yes, the mean is appropriate. OB. There is not enough information to determine if the mean is appropriate. O C. No, the mean should be lower. OD. No, the mean should be higher. Reset Submit
Answers
Answer:
The answer is D
Step-by-step explanation:
If you add them all, and divide them it wouldn’t get 14.5
Answer:
No, the mean should be higher.
Step-by-step explanation:
Have a good day :)
-2y+6=-12
What does y equal?
Answers
Answer:
y = 9
Step-by-step explanation:
-2y+6=-12
subtract 6 on both sides: -2y=-18
divide both sides by -2: y=9
Answer:
[tex]y = 9[/tex]
Step-by-step explanation:
1) Subtract 6 from both sides.
[tex] - 2y = - 12 - 6[/tex]
2) Simplify -12-6 to -18.
[tex] - 2y = - 18[/tex]
3) Divide both sides by -2.
[tex]y = \frac{ - 18}{ - 2} [/tex]
4) Two negative makes a positive.
[tex]y = \frac{18}{2} [/tex]
5) Simplify 18/2 to 9.
[tex]y = 9[/tex]
So, Yherefor, the answer is, y = 9.
Solve the simulataneous equations. 5x-4y=19 x+2y=8
Answers
Answer:
(5, 1.5 )
Step-by-step explanation:
Given the 2 equations
5x - 4y = 19 → (1)
x + 2y = 8 → (2)
Multiplying (2) by 2 and adding to (1) will eliminate the y- term
2x + 4y = 16 → (3)
Add (1) and (3) term by term to eliminate y
7x + 0 = 35
7x = 35 ( divide both sides by 7 )
x = 5
Substitute x = 5 into either of the 2 equations and solve for y
Substituting into (2)
5 + 2y = 8 ( subtract 5 from both sides )
2y = 3 ( divide both sides by 2 )
y = 1.5
solution is (5, 1.5 )
Which of the following is a solution of x2 + 4x + 6? (1 point)
Answers
Answer:
I LOVE ALGEBRA anyways
othe ans is in the picture and the steps how got the ans
(hope it helps can i plz have brainlist it will make my day :D hehe)
Step-by-step explanation:
You must substitute the (x, y) and check that the POI makes both equations ___.
TRUE because they both check out.
FALSE because they cannot work.
Answers
3x-2y=12 and 3x+5y=33
Answers
Answer:
x=6, y=3. (6, 3).
Step-by-step explanation:
3x-2y=12
3x+5y=33
--------------
-3x+2y=-12
3x+5y=33
-------------------
7y=21
y=21/7=3
3x-2(3)=12
3x-6=12
3x=12+6
3x=18
x=18/3=6
Please Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111
Answers
x+12=38
Lainey bought a set of 20 markers for $6
What is the cost of 111 marker?
Answers
Answer:
370
Step-by-step explanation:
First find the unit rate aka price per pencil: 20 divided by 6 equals 3.333
Then find amount for all pencils
3.333 by 111 is 369.963
Then we round up to have a realistic amount of pencils to 370
the quotient of a number y and 2 When y equals 6
Answers
Answer:3
Step-by-step explanation:
y/2 is what we need. If y is 6. Then 6/2=3.
A local movie theater has an offer that for every seven movies you pay to go see, they will give you free passes for two other movies. If you paid to see 42 movies last year, how many free passes did you receive?
_free passes
A local movie theater has an offer that for every seven movies you pay to go see, they will give you free passes for two other movies. If you paid to see 42 movies last year, how many free passes did you receive?
Answers
Answer: 12
Step-by-step explanation: 42/7 = 6 and you get 2 free passes so 6 x 2 = 12
7 movies = 2 free passes
7x6 = 42
6x2 = 12
please help me on this will give you brainliest!!
Answers
Answer:
9+(c*2)
im pretty sure this is correct, sorry for misreading it at first <3
4 years ago, the age of two sisters combined equal 24 years, and the younger sister was 8 years younger. How old are they today?
Answers
How to find the slope and y intercept from two coordinate pairs
Answers
m = (y2-y1)/(x2-x1)
and then find the y intercept by (0,b)
then plug m and b into
y=mx+b
Answer:
Slope: y2-y1/x2-x1
Step-by-step explanation:
You find slope from two coordinate pairs by using the slope formula(y2-y1/x2-x1) or rise over run from a graph.
To find y-intercept, x needs to be 0 on a graph.
Hope this helps!