In the given figure ABCD is a tripepizeum with AB||CD. If AO = x-1, CO = BO = x+1 and CD = x+4. Find the value of x.
Answers
[tex]\longmapsto[/tex]The value of "x" is 5.
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
A trapezium ABCD in which AB || CD such that
AO = x - 1CO = BO = x + 1OD = x + 4Now,
[tex]\rm In \: \triangle \: AOB \: and \: \triangle \: COD[/tex]
[tex]\rm \: \angle \: AOB \: and \: \angle \: COD \: \: \{vertically \: opposite \: angles \}[/tex]
[tex]\rm \: \angle \:ABO \: and \: \angle \: CDO \: \: \{alternate \: interior \: angles \}[/tex]
[tex]\bf \: \triangle \: AOB \: \sim \: \triangle \: COD \: \: \: \{AA \: similarity \}[/tex]
[tex]\bf\longmapsto\:\dfrac{AO}{CO} = \dfrac{BO}{DO} [/tex]
[tex]\rm \longmapsto\:\dfrac{x - 1}{x + 1} = \dfrac{x + 1}{x + 4} [/tex]
[tex]\rm \longmapsto\:(x - 1)(x + 4) = {(x + 1)}^{2} [/tex]
[tex]\rm \longmapsto\: {x}^{2} - x + 4x - 4 = {x}^{2} + 1 + 2x[/tex]
[tex]\rm \longmapsto\: 3x - 4 = 1 + 2x[/tex]
[tex]\rm \longmapsto\: 3x - 2x= 1 +4[/tex]
[tex]\bf\longmapsto \:x = 5[/tex]
Related Questions
helppppppppppppppppppppppppppppppppppp
Answers
Answer:
24 kilograms of catfish
Step-by-step explanation:
Take the percentage of catfish as a decimal or fraction and multiply it by the total amount of fish caught. The percent of catfish is 40% which is the same thing as 0.4. Multiply that by the total 60 kg of fish to get 24 kg of catfish.
The force (F) needed to cause the acceleration (a) of an object of mass, m, is given by the equation, F=ma where m is the object’s mass. If a 12-Newton force causes the object to accelerate to 3 m/s2, what is that object’s mass? The unit for this mass is kg.
Answers
Answer:
F=36
Step-by-step explanation:
F= 12 times 9 divided 3 = 36
The question requires calculating the objects mass in kilogram (kg)
The mass in kg of the objects is 4 kg
Given:
F = ma
Where,
F = Force (N)
M = mass (kg)
a = acceleration (m/s²)
If
F = 12-Newton
m = 3 m/s²
a = ?
F = ma
12 = m × 3
12 = 3m
divide both sides by 3
m = 12/3
m = 4 kg
Therefore, the mass in kg of the objects is 4 kg
Read more:
https://brainly.com/question/25250873
Alexis is selling team cards for her volleyball fundraiser. She expects to sell 4 cards for every 5 houses that she visits. If she wants to sell 20 cards total, how many houses should she expect to visit?
Answers
Answer:
5 houses
Step-by-step explanation:
She needs to visit 5 houses as 20 divided by 4 is 5
What is the slope of the line on the graph?
Enter your answer in the box.
No links Nothing unrelated
Answers
Answer:
6
Step-by-step explanation:
(y1-y2)/(x1-x2) = (-1-5)/(0-1) = -6/-1 = 6
WHAT IS THE MEASURE OF ANGLE A
WHAT IS THE MEASURE OF ANGLE B
WHAT IS THE MEASURE OF ANGLE C
Answers
Answer:
∠A = 100
∠B = 50
∠C = 30
Step-by-step explanation:
Sum of all angles of triangle = 180
∠A + ∠B + ∠C = 180
2x +x + x - 20 = 180 {Combine like terms}
4x - 20 = 180
Add 20 to both sides
4x = 180 + 20
4x = 200
Divide both sides by 4
x = 200/4
x = 50
∠A = 2x = 2*50 = 100
∠B = x = 50
∠C = x - 20 = 50 - 20 = 30
what is 20.1000÷300000
Answers
Answer:
0.000067
or
6.7*10^-5
Step-by-step explanation:
brainliest plz
What are unit rates, and how are they used?
Answers
hope it helps
Answer:
A unit rate means a rate for one of something
they are and can be used as speed limits or signs for someone to do something. like go and stop
Step-by-step explanation:
The mean of 3 numbers is 10. 2 of the numbers are 7 and 4. Find the 3 number
Answers
Answer:
The Third number is 19
Step-by-step explanation:
7 + 2 = 11 then add 19=
11 + 19 = 30 After divide by three because there are 3 numbers
30.6 ÷ 3 = 10
Remember: To find the mean you add all the numbers together and divide by how many numbers are there.
For example: you have 2, 5, 8 you add them together which is 15. There are 3 numbers so you divide 15 by 3 which is 5.
what is the value of x for 10x+1=3(4x+2)-3?
Answers
Answer:
x= 7
Step-by-step explanation:
Answer:-1
Step-by-step explanation:
10x+1=3(4x+2)-3
10x+1=12x+6-3
10x+1=12x+3
1=2x+3
-2=2x
1=x
I need help with my Algebra 1 ugh plz help! Sorry there’s a typo
Answers
Answer:
x + 8 > 11
dot at 11 going to the right.
Can someone please help me with this question.
Thank you.
Answers
Answer:
okay so..
Given
<2 = 110°
• <2 = <4 so <4 = 110°
Step-by-step explanation:
Solution
• <4 is equal with it's front facing angle(the angle next to <1) let's call that angle <x
<4 = <x = 110°
<x + <1 = 180°
110° + <1 = 180°
<1 = 180° - 110°
<1 = 70°
• <4 + <3 = 180°
110° + <3 = 180°
<3 = 180° - 110°
<3 = 70°
#6.
In the diagram below ABC~DEF, DE=4, AB=x AC=x+2 and DF= x+6
Determine the length if AB
Please help me with this one!
Answers
Answer:
x = 2
Step-by-step explanation:
Since the triangles are similar then corresponding sides are in proportion, that is
[tex]\frac{AB}{DE}[/tex] = [tex]\frac{BC}{EF}[/tex] , substitute values
[tex]\frac{7x}{7}[/tex] = [tex]\frac{4}{x}[/tex] ( cross- multiply )
7x² = 28 ( divide both sides by 7 )
x² = 4 ( take square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
Use either direct or synthetic substitution to evaluate the following:
f(x)=2x2-3x2+2x-5 for f(3).
Answers
why is -2/4 bigger than -7/12
Answers
Answer:
-2/4 can be written as -6/12
in negetive integers:: if the numerical vallues goes on increasing then the numbers are in decreasing order
so, -6/12 > -7/12
but 6/12 < 7/12
hope you understood
brainliest plz
Answer:
Step-by-step explanation:
To compare both fractions should have same denominator.
LCM of 4 and 12 is 12
[tex]\dfrac{-2}{4}=\dfrac{-2*3}{4*12}=\dfrac{-6}{12}[/tex]
[tex]\dfrac{-6}{12} \ is \ bigger \ than \ \dfrac{-7}{12}\\\\\dfrac{-2}{4} \ is \ bigger \ than \ \dfrac{-7}{12}\\\\[/tex]
How do you do this question?
Answers
Answer:
The answer I think, might be or possibly is A 20 aq ft. Bcuz, if you use the 1:4 scale, you'll get like for an example, 20:80..So, 5:? must be 5:20..get what I mean??? it's kinda tuff for me to explain since English is not my first language but thereee you go XD
I need help on the one about slope
Answers
If you divide -1/2 and then 4/1 you will get -5/1 or also known as -5
James drove to his brother’s house, which was 225 miles away. It took him 3 hours to get there. What was his average speed per hour
75
55
85
62.5
Answers
Answer:
75
225÷3=75
Step-by-step explanation:
hshshshshs
Answer:
75
Step-by-step explanation:
Transpose for = + working out too
Answers
Answer:Music in a major key can be transposed to any other major key; music in a minor key can be transposed to any other minor key. (Changing a piece from minor to major or vice-versa requires many more changes than simple transposition.) A piece will also sound higher or lower once it is transposed.
Step-by-step explanation:
Consider the system of equations.
y=3x−2−7x−2y=−9
Solve the system of equations algebraically.
Answers
Answer:
(x, y) = (-5/13, -41/13)
Step-by-step explanation: (Assuming the following corrections:)
y = 3x-2
-7x-2y = 9
-7x-2(3x-2) = 9
-7x-6x+4 = 9
-13x = 5
x = -5/13
y = -5/13(3) - 2
y = -15/13 - 2 = -41/13
Earlier, you were told about a toy rocket fired into the air from the top of a barn. Its height (h) above the
ground in yards after a seconds is given by the function:
h(x) = -52% + 100 + 20
What was the maximum height of the rocket?
Solution
The maximum height was reached by the rocket at one second as you found in part b from the previous
example. It takes second to reach the maximum height. We will substitute that value in for x in our
function and simplify.
The maximum height reached by the rocket was 25 yards. What is the time it takes for the rocket to hit
the ground? (Use a graph or any other method to solve.)
It takes approximately 3.2 seconds for the rocket to hit the ground. (Round to the nearest tenth.)
Answers
Using quadratic function concepts, it is found that:
It takes 1 second to reach maximum height.The maximum height is of 25 yards.It takes approximately 3.2 seconds for the rocket to hit the ground.The height of the rocket after x seconds is given by:
[tex]h(x) = -5x^2 + 10x + 20[/tex]
Which is a quadratic function with coefficients [tex]a = -5, b = 10, c = 20[/tex].
The maximum height will be a reached at a time of [tex]x_v[/tex], and will be of [tex]y_v[/tex], considering the vertex given by:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{\Delta}{4a}[/tex]
[tex]\Delta = b^2 - 4ac[/tex]
Then:
[tex]x_v = -\frac{10}{2(-5)} = 1[/tex]
[tex]\Delta = 10^2 - 4(-5)(20) = 500[/tex]
[tex]y_v = -\frac{500}{4(-5)} = 25[/tex]
Thus:
It takes 1 second to reach maximum height.The maximum height is of 25 yards.It hits the ground when [tex]h(x) = 0[/tex], thus:
[tex]-5x^2 + 10x + 20 = 0[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-10 + \sqrt{500}}{2(-5)} = -1.2[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-10 - \sqrt{500}}{2(-5)} = -3.2[/tex]
We want the positive root, so, it takes approximately 3.2 seconds for the rocket to hit the ground.
A similar problem is given at https://brainly.com/question/24705734
can you PLEASE tell me the answer
Answers
Answer:
A
Step-by-step explanation:
Hope it helps!
Answer:
B
Step-by-step explanation:
corresponding sides of similar triangles are same ratio
[tex]\dfrac{JK}{UT}=\dfrac{KL}{TS}\\\\\dfrac{x}{20}=\dfrac{8}{16}\\\\x=\dfrac{8}{16}*20\\\\x=10[/tex]
Given the following functions, find the indicated values,
f(x)= 1 - 5x
(a) f(-4) (b) f(0) (C) f(5)
(a) f( – 4)=0
Answers
Answer:
Riley restoration rotators
What is the product (−4)(7)(−2)
Answers
Answer:
98
Step-by-step explanation:
1. (-4)(-2) equals 14 beacuse when you muiltpy two negatives yiui get a postive.
2. 14(7) equals 98
True or False
An example of an annual expense would be electricity because you receive a bill each month.
Answers
Answer:
True
Step-by-step explanation:
Employees hourly rate work is $2.90.each employee works for 8 hours a day. What would be the daily income of the employee
Answers
Answer:
$23.20
Step-by-step explanation:
1 hour of work = $2.90
8 x 2.90 = 23.20
8 hours of work will get an employee $23.20
If they worked 8 hours daily in a week:
7 x 23.20 = 162.40
Working 8 hours every day in a week will get them $162.4
help please, im confused
Answers
Since x = 1/2y + 5
You can plug that in second equation
2(1/2y + 5) + 3y = -14
y + 10 + 3y = -14
4y = -24, y = -6
Plug into first equation
x = 1/2(-6) + 5 = 2
Solution: (2, -6)
Step-by-step explanation:
x=½y+5. ......i
2x+3y=-14. .....ii
putting the value of x in equation ii.
2(½y+5)+3y=-14
y+10+3y=-14
4y=-24
y=-6
Now, putting the value of y in first equation.
x=½y+5
x=(½×-6)+5
x=-3+5
x=2.
therefore, the value of x=2 and y=-6.
So, option D is correct answer.
hope this helps you.
2x+10=12
so x=??
[tex]\huge \dag \sf{Help \: me}[/tex]
Answers
Answer:
[tex]\sf\longmapsto\sf\boxed {x = 1}[/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: 2x + 10 = 12[/tex]
[tex]\sf\longmapsto \: \: 2x + 10 - 10 = 12 - 10[/tex]
[tex]\sf\longmapsto \: 2x = 2[/tex]
[tex]\sf\longmapsto \: \frac{2x}{2} = \frac{2}{2} [/tex]
[tex]\sf\longmapsto \: x = 1[/tex]
Answer:
[tex]\boxed {\sf x=1}[/tex]
Step-by-step explanation:
[tex]\sf 2x+10=12[/tex]
[tex]\boxed{\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}}[/tex]
[tex]\sf 2x+10-10=12-10[/tex][tex]\sf 2x=2[/tex][tex]\boxed{\mathrm{Divide\:both\:sides\:by\:}2}[/tex]
[tex]\sf \cfrac{2x}{2}=\cfrac{2}{2}[/tex][tex]\sf x=1[/tex][tex]\boxed{\sf Hope\: it\:helps!}[/tex]
Linear vs non linear functions
I’m completely confused on how to do linear vs non linear functions. Does anyone have step by step on how to do them?
Answers
Answer:
A linear function has a constant rate of change. A nonlinear function does not
Also, Lnear functions show a straight line when they are graphed and nonlinear functions don't.
My advice is to graph it and look at the points.
Good luck! Pls give brainliest!
Answer:
See Picture & I hope this helps!:)
Step-by-step explanation:
[tex]\sf 2x+7+8x=35[/tex]
Answers
Answer:
x=14/5
Step-by-step explanation:
Group like terms
2x+8x+7=35
Add similar elements: 2x+8x=10x
10x+7=35
Subtract 7 from both sides:
10x+7−7=35−7
Simplify
10x=28
Divide both sides by 10
10x/10 =28/10
Simplify:
x=14/5
Answer:
[tex]2x+7+8x=35[/tex]
[tex]2x+8x+7=35[/tex]
[tex]10x+7-7=35-7[/tex]
[tex]10x=28[/tex]
[tex]\cfrac{10x}{10}=\cfrac{28}{10}[/tex]
[tex]x=\cfrac{14}{5}[/tex]
or
[tex]x=2.8[/tex]
4×____×1=12 ?=____. please help me solve this question
Answers
Answer:
4 x 3 x 1 = 12
12 = 12
Step-by-step explanation:
I used a calculator, pls let me know if im incorrect