find CE 14 6 x - 5 2x + 3
Answers
The value of x from the similar triangles is x = 9 and the length of CE of the triangle ACE is CE = 35
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔACE
Let the second triangle be represented as ΔBDC
The measure of side AB = 6
The measure of side BC = x - 5
The measure of side AC = x + 1
The measure of side CD = 14
The measure of side DE = 2x + 3
The measure of side CE = 2x + 17
Now , ΔACE and ΔBDC are similar
So , the corresponding sides of similar triangles are in the same ratio
Substituting the values in the equation , we get
AC / CE = BD / CD
( x + 1 ) / ( 2x + 17 ) = ( x - 5 ) / 14
On simplifying the equation , we get
14x + 14 = 2x² - 10x + 17x - 85
Subtracting 14x + 14 on both sides of the equation , we get
2x² - 7x - 99 = 0
On factorizing the equation , we get
x = 9 or x = -11/2
Substituting the value of x in the equation , we get
The length of line segment CE = 2x + 17
The length of line segment CE = 2 ( 9 ) + 17
The length of line segment CE = 35
Hence , the length of CE is 35
To learn more about similar triangles click :
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Related Questions
Which is the answer. A B C D?
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Answer:
A) T'(-2,3), U'(0,5), V'(-1,0)
It takes Diego 1/24of an hour to complete a lap on a circular bike track. The track is 1/3 of a mile long. What is Diego's bike speed in miles per hour?
Answers
Answer:
Step-by-step explanatio
1mile = 5280 feet
607,200 / 5280 = 115
607,200 feet per hour = 115 miles per hourn
find the area of the semi-circle with a diameter of 55cm
Answers
Answer:86.35
Step-by-step explanation: 3.14*55/2=86.35
hoped this helped.
What y’all think helps guysss!!!:((((
Answers
Answer:
pretty sure it's a yes
Step-by-step explanation:
Did it on khan a few months ago
sorry if I made it wrong, my memory isn't too well right now
Answer:
Yes.
Step-by-step explanation: Figure B is just a larger scale of figure A.
0.4x+y=45x+.55y=18.75
Answers
Answer:
4x+y=45x+0.55y=18.75
Step-by-step explanation:
The two triangles are similar. Find the unknown variables.
Answers
Answer:
Y= 57°
Q at both of them 33° each.
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180-147=33
Sandra has a 1/3 chance of making the team. What is the probability that Sandra will not make the team?
please help!
Answers
Answer:
2/3 is the probability that Sandra will not make the team.
Hope it helps!!!
Answer:
2/3
Step-by-step explanation:
If something will happen with 100% certainty, then the probability is 1 or 100%.
If she has a 1/3 chance of making the team, the the chance of not making the team is 1 - 1/3 which equals 2/3.
Answer: 2/3
Write an equation of the line below.
Answers
Answer:
y = 4x-2
Step-by-step explanation:
y = mx+b
y = 4x+b
y = 4x-2
Edwin buys a painting of the beach online for $23. If shipping and handling are an additional 30% of the price, how much shipping and handling will Edwin pay?
Answers
Answer:
$6.90
Step-by-step explanation:
23/100 X 30 = $6.90
Simplify the following expression:
x(x+2) - x(x+3)
Answers
Answer:
-x
Step-by-step explanation:
The equation of the line A is 3x+2y=10.line B is parallel to line A and passes through the points (4,6).find the equation of the line B.
Answers
Answer: [tex]y=-\frac{3}{2}x+12[/tex]
Step-by-step explanation:
To find the equation of line B, we need to find the slope first, then the y-intercept. We first want to convert line A into slope-intercept form, so we can find the slope.
[tex]3x+2y=10[/tex] [subtract both sides by 3x]
[tex]2y=10-3x[/tex] [divide both sides by 2]
[tex]y=5-\frac{3}{2}x[/tex]
With the slope-intercept form of line A, we can see that the slope is [tex]-\frac{3}{2}[/tex]. We take the slope and the given point (4,6) to find the y-intercept of line B.
[tex]y=-\frac{3}{2}x+b[/tex] [plug in (4,6)]
[tex]6=-\frac{3}{2}(4)+b[/tex] [multiply]
[tex]6=-6+b[/tex] [add both sides by 6]
[tex]b=12[/tex]
With the y-intercept, we know the equation for line B is [tex]y=-\frac{3}{2}x+12[/tex].
How far is the Earth away from the Sun? Question 4 options: 1 AU (astronomical unit) 1 light year 10 AU 10 light years
Answers
Answer: The answer to your question is 1.
Answer:
1 AU
Step-by-step explanation:
I searched on the web.
It takes 8 light-years, so options 2 & 4 are out.
The internet says 1 AU so that is the answer.
Good Luck!
What is the intersection (x, y) of the two lines generated by the 2 equations:
y= x+3
y=-x +7
Answers
Answer:
x=2
y=5
Step-by-step explanation:
y= x+3...(1)
y= -x+7...(2)
(1) + (2):
y+y= (x+3) + (-x+7)
2y= (x-x) + (3+7)
2y= 10
y= 5
By substituting y=5 into (1),
we have
5= x+3
x+3=5
x= 5-3
x= 2
Find the volume of a pyramid with a square base, where the side length of the base is 4.7\text{ in}4.7 in and the height of the pyramid is 4.5\text{ in}4.5 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
33.1in³
Step-by-step explanation:
Volume of the square based pyramid = BH/3
B is the base area
H is the height
Base area = L²
Base area = 4.7²
Base area = 22.09 square inches
Height = 4.5in
Get the volume
Volume of the pyramid = 22.09*4.5/3
Volume of the pyramid = 22.09 * 1.5
Volume of the pyramid = 33.135in³
Hence the volume of the square based pyramid to the nearest tenth of a cubic inch is 33.1in³
(5 x 10^2)^−2
i dont get it
Answers
Answer:-250,000
Step-by-step explanation:
PLEASE HELP!!! I REALLY NEED IT!!!
So, this is kind of random, but can someone give, like, a step-by-step explanation of how to do this equation?
(22+(-6/20)) * (214-10(-6/20)) - (284.75)=4424.15
Thank you so much, I just... I cannot will myself to figure out this problem today. Love youuu!
Answers
Step-by-step explanation:
(22 + (-6/20) × (214 - 10 ( -6/20)) - (284.75)
(22 - 6/20) × (214 + 60/20) - (284.75)
(22 - 0.3) × (214 + 3) - (284.75)
(21.7 × 217) - 284.75
4708.9 - 284.75
= 4424.15
A bank teller had 125 Bills in $10 and $20 bills to start the day. If the total in her register was $1650, how many of each bill did the teller start off with ?
Answers
Answer:
40 twenties and 85 tens
Step-by-step explanation:
10x+20y=1650
10x+10y=1250
10y=400
y=40
which are the complementary angles?
Answers
Answer:
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
Step-by-step explanation:
please amrk this answer as brainliest
PLEASE HELP ME !!! IT’S DUE AT 11:30pm
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Answer:
ok soo ik links are dangerous here but here is a app that can help you with you dont trust its ok I would`t
Step-by-step explanation:
Find the value of y if x = 174
Answers
Answer: 348
Step-by-step explanation: y is going to be 2x
PLEASE HELP!!!!
Quadrilateral ABCD is similar to quadrilateral EFGH. What is the value for x, the length
of side CD?
A-10
B-16
C-14
D-18
Answers
-》D
Answer:
D 18
Step-by-step explanation:
8. Which choice is a graph of the solution set for -12 + 5x < 8?
A
B
+
-2
0
2
2
D
С
+
6
4
-2
0
0
2
4
6
8
Answers
Answer:
B
Step-by-step explanation:
A bank put $25 into a savings account when you opened the account. Nine weeks later, you have a total of $97. Assume you saved the same amount every week
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Answer:
no jaja putoyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy y
Find the distance between the points (1,3) and (3,4)
Answers
Answer:
[tex]\sqrt{} 5[/tex]
Step-by-step explanation:
Answer:
Square root of five
Step-by-step explanation:
Write the absolute value equations in the form |x−b|=c (where b is a number and c can be either number or (an expression) that have the following solution sets:
Two Solutions: x=2, x=14
Answers
Answer:
|x − 8| = 6Step-by-step explanation:
|x − b| = c1. x - b = c ⇒ x = b + c2. x - b = -c ⇒ x = b - cWe have solution:
b + c = 14b - c = 2Add up these two equations:
2b = 16b = 8Find c:
c = 8 - 2 = 6The original equation is:
|x − 8| = 6QUESTION IN JPG CAN YOU ANSWER A B AND C
Answers
Answer: 8:10, 7:54, 26 minutes
Step-by-step explanation:
a) Go to the row labeled Church Street, start in the column with time 7:59, read down until you get to the row labeled Bus Station.
b) Go to the High Street row. The latest arrival time that is still before 8:30 is 8:10. Starting in the column with 8:10, read UP to the Hope Street row. The bus leaves there at 7:54
c) Pick any column in the row for School Road. In that column, read down to the Bus Station row. The difference between the two times is 26 minutes no matter which column is selected.
Find m angle ADB !!!!!
Answers
Answer:
[tex]<ADB=9[/tex]×[tex]5+4[/tex][tex]=49[/tex]
Step-by-step explanation:
[tex]<(13x-16)=<(9n+4)\\\\13x-9x=4+16\\\\4x=20\\\\x=\frac{20}{4} \\\\x=5\\\\<ADB=9*5+4=49[/tex]
hope it helps....
PLEASE HELP ME !!
If you put $375 into a savings account that pays 6% interest compounded monthly, how much money would you have in your account after 3 years?
How much did you earn in interest?
Answers
Answer:
$448.76
$73.76
Step-by-step explanation:
We are to calculate the future value with monthly compounding
The formula for calculating future value:
FV = P (1 + r/m)^mn
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
$375 x ( 1 + 0.06/12)^12 x 3
$375 x (1.005)^36 = $448.76
Interest earned = future value - amount saved
$448.76 - $375 = $73.76
Sarah needs a PVC pipe with a diameter of 10 inches and a heigh of 2 inches, how much
material is needed to make 5 pipes?
Answers
Answer:
314.2in^2
Step-by-step explanation:
GIven data
diameter= 10in
radius= 5in
Height= 2in
The expression for the curved surface area (CSA) of a cylinder is given as
CSA=2πrh
CSA=2*3.142*5*2
CSA=62.84 in^2
The material needed to make one pipe is 62.84in^2
Hence the material need for 5 pipes is
=62.84*5
=314.2in^2
Manuel borrowed $1,500 from his bank and signed a
contract to make monthly payments for two years at 4%
interest compounded annually. How much total interest
will Manuel pay on this loan?
Answers
Answer:
The total interest to pay back on the loan is $122.40
Step-by-step explanation:
Here. we want to get the amount of interest on the loan
We are going to use the compound interest formula here
A = P(1 + r/n)^nt
where A is the amount to be paid back
P is the amount borrowed called the principal which is $1,500
r is the interest rate which is 4% annually
This is same as 4/100 = 0.04
n is the number of times the interest will be compounded per year ; annually means yearly and so for this case, n = 1
t is the number of years = 2
So we have;
A = 1500(1 + 0.04/1)^(2)(1)
A = 1500(1.04)^(2)
A =$ 1,622.40
So the amount of interest is the difference between the amount borrowed and the value to pay back
That will be;
$1,622.40 - $1,500
= $122.40