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2 years ago

Help!! The angle measurements in the diagram are represented by the following expressions.

Mathematics

1 answer:

borishaifa [10]2 years ago

5 0

Answer:

$\boxed{\bf \angle A=84^o}$

Step-by-step explanation:

From the given diagram, we can see that ∠B & ∠C are corresponding angles, which means that they are equal. The two angles that form a straight line are supplementary angles (the sum of two supplementary angles is 180°).

$\bf 5x+34^o+\angle C=180^o$

$\bf 5x+34^o+\angle B=180^o$

$\bf 5x+34^o+2x+76^o=180^o$

Now, let's solve for x :-

$\bf (5x+34^o)+(2x+76^o)=180^o$

$\bf (5x+2x)+(34+76)=180^o$

$\bf 7x+110=180^o$

$\bf (7x+110)-110^o=180-110^o$

$\bf 7x=70^o$

$\bf \cfrac{7x}{7} =\cfrac{70}{7}$

$\boxed{\bf x=10^o}$

Now, in order to find ∠A will substitute the value of x into the expression:- $\bf \angle A=5x+34^o$

$\bf \angle A=5(10)+34^o$

$\bf \angle A=84^o$

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Rewrite the function by completing the square. 4x^2-4x+1=0

andrey2020 [161]

Do in completing the square method.

${4x}^{2} - 4x + 1 = 0 \\ 4x^{2}-4x=-1 \\ \frac{4x^{2}-4x}{4}=\frac{-1}{4} \\ x^{2}+\frac{-4}{4}x=\frac{-1}{4} \\ x^{2}-x=\frac{-1}{4} \\ x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-\frac{1}{4}+\left(-\frac{1}{2}\right)^{2} \\ x^{2}-x+\frac{1}{4}=\frac{-1+1}{4} \\ x^{2}-x+\frac{1}{4}=0 \\ \left(x-\frac{1}{2}\right)^{2}=0 \\ \sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{0}$

Now simplify.

$x-\frac{1}{2}=0 \\ x-\frac{1}{2}=0 \\ \\ \rightarrow \: x=\frac{1}{2} \\ \rightarrow \: x=\frac{1}{2}$

So, answer is..

$\boxed{x=\frac{1}{2} }$

Now rewrite the equation.

$4 x ^ { 2 } - 4 x + 1 = 0 \\ \boxed{4\times \left(\frac{1}{4}\right)-4\times \left(\frac{1}{2}\right)+1=0 }$

Verification :-

$4 x ^ { 2 } - 4 x + 1 = 0 \\ 4\times \left(\frac{1}{4}\right)-4\times \left(\frac{1}{2}\right)+1=0 \\ 1-4\times \left(\frac{1}{2}\right)+1=0 \\ 1-\frac{4}{2}+1=0 \\ 1-2+1=0 \\ -1+1=0 \\ \underline{ 0 = 0} \: \\ \dashrightarrow \text{true}$