Unit 11: Value & Surface Area Homework 1: Area of planes Figure Pls Help me with #11
1 answer:
Answer:
The area of the triangle is 351cm^2.
Step-by-step explanation:
To find the area of a triangle, the formula is (1/2) x base x height. In this case, the height would be a line that cuts straight through the center of the triangle. However, this height is not given to us. We can still find it through Pythagoras' Theorem though.
Let A be the tip of the triangle, and B and C be the points on either side of the triangle. Assuming an imaginary line that cuts the triangle in a symmetrical half, let T be the point at the end of the line, directly below point A.
Using Pythagoras' Theorem,
AB^2 = AT^2 + TB^2
AT^2 = AB^2 - TB^2
AT^2 = 30^2 - (26/2)^2
AT^2 = 30^2 - 13^2
AT =
AT = 27.0370116692
So the length of AT is our height. We can now find the area of the triangle.
Area of triangle = (1/2) x 26cm x AT
Area of triangle = 351.4811516996
Area of triangle = 351cm^2 (To 3s.f.)
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Answer:
We know that:
She makes $19 per hour of lifeguarding.
She makes $8 per hour walking dogs.
She can work at most 7 hours per week.
She must earn a minimum of $80 per week.
If x represents the number of hours lifeguarding and y represents the number of hours walking dogs, the inequalities will be:
x + y ≥ 7 hours.
(this says that she can work at most 7 hours per week)
x*$19 + y*$8 ≥ $80
(this says that she can earn a minimum of $80)
Then the system of inequalities is:
x + y ≥ 7 hours.
x*$19 + y*$8 ≥ $80
To graph these two we can write them as lines in standard form and simply graph both inequalities, the solution of the system will be the intersection between the solutions of each inequality.
Here we also should add the inequalities:
x ≥ 0
y ≥ 0
So we only look at the first quadrant.
The graph can be seen in the image below: (the dark blue is the solution region for the first inequality, the light blue one is the solution region for the second inequality)
One possible solution can be:
x = 4 and y = 1
or
x = 4 and y = 2
and there are a lot of other possible solutions.
Usando un sistema de ecuaciones, se encuentra que
- Cada manzana cuesta $3.
- Cada pera cuesta $1.
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- Un sistema de ecuaciones soluciona esta pergunta.
- El custo de una manzana es x.
- El custo de una pera es y.
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- <u>Seis manzanas y 8 peras cuestan $26</u>, o sea,
- <u>Cada manzana cuesta el triple de cada pera</u>, o sea,
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Primero, encontramos el cuesto de una pera, substituyendo la segunda en la primera ecuación.
Cada pera cuesta $1.
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<u>Cada manzana cuesta el triple de cada pera</u>, o sea, .
Cada manzana cuesta $3.
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