Answer:
Angle CED must also measure 60°.
Because angle m is shown to be congruent to angles ABC and CDE, this means that angle m has a measure of 60 degrees.
There can only be 180 degrees in a triangle, so the measure of angle ACB must be 180-60-60, which equals 60 degrees.
Using the Vertical Angles Theorem, the measure of angle ACB is the same as the measure of angle CED.
Therefore, angle CED measures 60°.
Step-by-step explanation:
m, because Triangle ABC is similar to triangle EDC
m over 2, because Triangle ABC is congruent to triangle DCE
m + 60 degrees, because Triangle ABC is similar to triangle DCE
120 degrees − m, because Triangle ABC is congruent to triangle DCE
Answer:
Domain = 0≤m≤20 for mEZ+
Range = $100≤A≤$700 for all values of m
Step-by-step explanation:
Initial amount in the account = $100
Amount saved by beth monthly = $30
Amount in the bank after X month = $100+$30X where X is the number of months beth intend to save up to.
The amount in her bank in her first month = $100+$30(1)
= $100+$30
= $130
Amount saved in the second month will be when X = 2
= $100+$30(2)
= $100+$60
= $160
The amount in the bank will keep increasing by $30 monthly until the 20month.
The amount he will have in her bank in the 20th month will be at when X = 20
= $100+30X
= $100+30(20)
= $100+$600
= $700
This means that her money will be $130 in the first month and will keep increasing until it reaches $700 in the 20th month.
The DOMAIN will be the interval of the time she used in saving. Since she saved for 20months, the domain will be expressed as 0≤m≤20 for mEZ+ where m is the number of month she uses to save.
The Range will represent the amount she saved within the specified time and will be expressed as $100≤A≤$700 for all values of m.
Where $100 is the amount in the account initially and $700 is the amount in the account after 20 months.
Given the expression,
We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.
![[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]](https://tex.z-dn.net/?f=%20%5B%288x-56x%5E2%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%5B%28%5Csqrt%7B14x-2%7D%29%28%5Csqrt%7B14x-2%7D%29%5D%20)
If we have 
, we will get 
by multiplying them. And 
.
So here in the problem, we will get,
![[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)](https://tex.z-dn.net/?f=%20%5B%288x-56x%5E2%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%2814x-2%29%20)
Now in the numerator we have 
. We can check 8x is common there. we will take out -8x from it, we will get,
And in the denominator we have 
. We can check 2 is common there. If we take out 2 from it we will get,
So we can write the expression as
![[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]](https://tex.z-dn.net/?f=%20%5B%28-8x%29%287x-1%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%5B2%287x-1%29%5D%20)
is common to the numerator and denominator both, if we cancel it we will get,
We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,
So we have got the required answer here.
The correct option is the last one.
Answer:
Dimensions of rectangle : Width = 
, Length = 
Area of Rectangle = 
Step-by-step explanation:
A rectangle constructed with its base on the x-axis and two of its vertices on the parabola
Supposing coordinates of upper right vertex of rectangle are P = 
Due to parabola symmetry, width of rectangle is twice the horizontal (X) axis distance between Y axis & point P.
Width of rectangle :
Length of rectangle : 
Area of Rectangle = Length x Width
() ()
=
