Answer:
20√3 cm
Step-by-step explanation:
Altitude of an equilateral triangle splits it into 2 equal right triangles, it bisects the base and the angle opposite to the base.
<u>Let the altitude be x. Then as per Pythagorean theorem:</u>
- x² = 40² - (40/2)²
- x²= 1600 -400
- x²= 1200
- x= √1200
- x= 20√3 cm
<u>Correct choice is</u> the second one
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:(30/19,2/19)
Equation Form: x=30/19, y=2/19
to see quick score she must use a pie chart
Using translation concepts, it is found that the transformations to create function d are given as follows:
- Horizontal shift right 1 unit.
- Vertical shift up 5 units.
- Frequency multiplied by 2.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent cosine function is given by:
f(x) = cos(x).
The translated function is given by:
d(x) = cos(2x - 1) + 5.
Which means that:
- 1 was subtracted in the domain, hence the was a horizontal shift right 1 unit.
- 5 was added in the range, hence there was a vertical shift up 5 units.
- There was a multiplication by 2 in the domain, hence the frequency is multiplied by 2.
More can be learned about translation concepts at brainly.com/question/4521517
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<span>let x = the original no. of students
then
(x+10) = the actual no. that went on the trip
:
= the original cost per student
and
= the actual cost
:
Original cost - actual cost = $12.50
- = 12.50
multiply equation by x(x+10)
x(x+10)* - x(x+10)* = 12.50x(x+10)
Cancel the denominators
1500(x+10) - 1500x = 12.5x(x+10)
1500x + 15000 - 1500x = 12.5x^2 + 125x
Combine on the right to form a quadratic equation
0 = 12.5x^2 + 125x - 15000
Simplify, divide equation by 12.5
x^2 + 10x - 1200 = 0
You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to
(x + 40(x - 30) = 0
The positive solution is what we want here
x = 30 students in the original group
Check this by finding the cost per student for each scenario
1500/30 = $50.00; original cost
1500/40 = $37.50; actual cost
---------------------
saving: $12.50</span>
