Find the missing information. PLEASE HELP ITS A QUIZ DUE SOON

Mathematics

1 answer:

xxTIMURxx [149]2 years ago

7 0

Answer:

x = 13

∠F = 28°

∠S = 28°

y = 9

DE = 38 ft

Step-by-step explanation:

We are told that △DEF = △QRS

Looking at both triangles and by comparison, it is clear that;

∠R = ∠E = 123°

∠Q = ∠D = 29°

∠S = ∠F = 180 - (123 + 29) = 28°

Also,QR = DE

Thus; 5y - 7 = 38

5y = 38 + 7

5y = 45

y = 45/5

y = 9

Thus,y = 9 and DE = 38 ft

We see in the image that ∠S = (2x + 2)°

From earlier we deduced that ∠S = 28°

Thus; 2x + 2 = 28

2x = 28 - 2

2x = 26

x = 26/2

x = 13

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<u>Solution:</u>

Given, Getting home from trick or treat celia and emma counted their candies. Half of celias candies is equal to 2/3 of emmas candies.

They had a total of 105 candies altogether.

We have to find how many candies did each of them have.

Let the number of candies with celias be n, then number of candies with emma will be 105 – n.

Now according to given condition.

$\begin{array}{l}{\frac{1}{2} \times \text { celias candies count }=\frac{2}{3} \times \text { emmas candies count }} \\\\ {\rightarrow \frac{1}{2} \times n=\frac{2}{3} \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 n=4(105-n)} \\\\ {\quad \rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n+4 n=420} \\\\ {\rightarrow 7 n=7 \times 60} \\\\ {\rightarrow n=60}\end{array}$