Using relations in a right triangle, it is found that the values of x and y are given by: x = 24, y = 46.4, given by option a.
<h3>What are the relations in a right triangle?</h3>
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
First, we start with the vertical line h that divides y, that is <u>opposite to an angle of 30º, with hypotenuse 34</u>, hence:
sin(30º) = h/34
0.5 = h/34
h = 17.
Then, h is opposite to an angle of 45º, while the hypotenuse is x, hence:


x = 24.
y is divided into two segments.
- The first is the adjacent to the angle of 30º, while the hypotenuse is 34.
- The second is adjacent to the angle of 45º, while the hypotenuse is 24.
Then:




Then, the value of y is given by:
.
More can be learned about relations in a right triangle at brainly.com/question/26396675
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Answer: The following statements are true:
It is symmetrical.
The first diagonal is all 1’s.
The second diagonal is the counting numbers.
Any number in the triangle is the sum of the two numbers directly above it.
Each row adds to a power of 2.
Problem 3: Let x = price of bag of pretzels Let y = price of box of granola bars
We have Lesley's purchase: 4x+2y=13.50
And Landon's: 1x+5y=17.55
We can use the elimination method. Let's negate Landon's purchase by multiplying by -1. -1x-5y=-17.55
We add this four times to Lesley's purchase to eliminate the x variable.
2y-20y=13.50-70.2
-18y=-56.7
y = $3.15 = Price of box of granola bars
Plug back into Landon's purchase to solve for pretzels.
x+5*3.15=17.55
x+15.75=17.55
x = $1.80 = price of bag of pretzels
Problem 4.
Let w = number of wood bats sold
Let m = number of metal bats sold
From sales information we have: w + m = 23
24w+30m=606
Substitution works well here. Solve for w in the first equation, w = 23 - m, and plug this into the second.
24*(23-m)+30m=606
552-24m+30m=606
6m=54
m=9 = number of metal bats sold
Therefore since w = 23-m, w = 23-9 = 14. 14 wooden bats were sold.
Ages of Dan and Cary are 29 and 33 respectively.
<u>Step-by-step explanation:</u>
Step 1:
Form equations out of the given details. Let the age of Dan be x, then age of Cary is x + 4.
In 7 years, sum of their ages = 76
⇒ (x + 7) + (x + 4 + 7) = 76
⇒ 2x + 18 = 76
⇒ 2x = 58
⇒ x = 29
Step 2:
Calculate age of Cary.
⇒ x + 4 = 33