According to the characteristics of <em>ticket</em> sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.
<h3>How many children went to the movie theatre?</h3>
In this question we have a <em>word</em> problem, whose information must be translated into <em>algebraic</em> expressions to find a solution. Let be x and y the number of children and adults that went to the movie theatre, respectively.
We need two <em>linear</em> equations, one for the number of people assisting to the theatre and another for the total sales:
x - 4 · y = 0 (1)
6.30 · x + 9.50 · y = 1063.20 (2)
By algebraic procedures the solution to this system is: x = 122.559, y = 30.639. Since the number of tickets sold are integers, then we truncate each result: x = 122, y = 30.
According to the characteristics of <em>ticket</em> sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.
To learn on systems of linear equations: brainly.com/question/27664510
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<span>49 x^6 y^6
Assuming the 2 is an exponent.
I had the same question.
Just square </span>everything.
Ex. 7^2 = 49
Brainiest would be nice.
The value of 'x' is 24.2 and the value of 'y' is 46.5.
To solve this, we do the following steps.
<u>Step 1:</u> Divide 'y' into 2 parts, 'a' and 'b'. 'a' would be the lower leg of the 45°-45°-90° triangle, while 'b' is the lower leg of the 30°-60°-90° triangle.<em>
</em><u>Step 2:</u> Given the hypotenuse (34) of the 30°-60°-90° triangle, solve for 'b' using the cosine of 30°.
cos30° = b/34 [adjacent over hypotenuse]
b = 34cos30° [cross-multiply]
b = 29.4
<u>Step 3:</u> Solve for the 90° leg (the side opposite the 30° angle) using the Pythagorean Theorem. We will name this leg "h" (cuz height).
l² + l² = hyp²
29.4² + h² = 34²
h² = 1156 - 864.36
√h² = √291.64
h = 17.1
<u>Step 4:</u> Solve for 'x' by using the 45°-45°-90° triangle ratio (1:1:√2). √2 would be the hypotenuse of the 45°-45°-90° triangle, while 1 would be both congruent legs.
Side 'h' is one of the legs; side 'a' is the other. Since these legs are congruent, 'a' also measures 17.1. Now all we need to do is solve for 'x', which is our hypotenuse. To do this, we simply multiply the measure of side 'h' or 'a' by √2.
x = 17.1 × √2
x = 24.2
<u>Step 5:</u> Now that we got the value of 'x', solve for 'y' by adding the measures of sides 'a' and 'b' together.<em>
</em><u /> y = a + b
y = 17.1 + 29.4
y = 46.5
And there you have it! <em>Hope this helps.</em>
<em>
</em>
Loretta:
Average driving speed = 55 mph
Time = 4 hours
Distance traveled = 55*4 = 220 miles
Dad:
Average driving speed = 65 mph
Let x = hours driven
Distance traveled = 65x miles
The length of the trip is 610 miles, therefore
65x + 220 = 610
65x = 390
x = 6 hours
Answer: Loretta's dad drove for 6 hours.
