Answer:
AC ≅ AE
Step-by-step explanation:
According to the SAS congruence theorem, if two triangles have 2 corresponding sides that are equal, and also have one included corresponding angle that are equal to each other in both triangles, both triangles are regarded as congruent.
Given ∆ABC and ∆ADC in the question above, we are told that segment AB ≅ AD, and also <BAC ≅ <DAC, the additional information that is necessary to prove that ∆ABC and ∆ADC are congruent, according to the SAS theorem, is segment AC ≅ segment AE.
This will satisfy the requirements of the SAS theorem for considering 2 triangles to be equal or congruent.
X=3.1:
Step-by-step explanation:
You would make two mountains because you need to compare the two factor mountains
5.500
p-1/4-(21/4)=0
Step by step solution :
STEP
1
:
21
Simplify ——
4
Equation at the end of step
1
:
1 21
(p - —) - —— = 0
4 4
STEP
2
:
1
Simplify —
4
Equation at the end of step
2
:
1 21
(p - —) - —— = 0
4 4
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 4 as the denominator :
p p • 4
p = — = —————
1 4
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
p • 4 - (1) 4p - 1
——————————— = ——————
4 4
Equation at the end of step
3
:
(4p - 1) 21
———————— - —— = 0
4 4
STEP
4
:
Adding fractions which have a common denominator :
4.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(4p-1) - (21) 4p - 22
————————————— = ———————
4 4
STEP
5
:
Pulling out like terms :
5.1 Pull out like factors :
4p - 22 = 2 • (2p - 11)
Equation at the end of step
5
:
2 • (2p - 11)
————————————— = 0
4
STEP
6
:
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
2•(2p-11)
————————— • 4 = 0 • 4
4
Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2 • (2p-11) = 0
Equations which are never true:
6.2 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
6.3 Solve : 2p-11 = 0
Add 11 to both sides of the equation :
2p = 11
Divide both sides of the equation by 2:
p = 11/2 = 5.500
Approximated:
cm
Exact:
or
Explanation:
It's always best for these types of questions to visualise it. A right triangle has base angle of 90°. Mark in what you know, and leave out the rest. Notice how the question doesn't ask for a hypotenuse. This means that you might be using the tangent function as the tangent function also doesn't require a hypotenuse.
So now, you have a side of 12cm, with the corresponding 39° angle marked.
To find the missing length, you can use the tangent function to approximate the length:
(opposite/adjacent)
Now, isolate the variable, x:
(exact form)
cm (approximated to 1 decimal place)
