Answer:
Yes, she can drew a right triangle with these sides
Step-by-step explanation:
To answer this question we first have to prove the Pythagorean theorem
h = hyoptenuse
a = leg 1
b = leg2
h² = a² + b²
We have to replace the values that they gave us in this formula
The hypotenuse always has to be the longest side of a right triangle
(14cm)² = (11.2cm)² + (8.4cm)²
196cm² = 125.44cm² + 70.56cm²
196cm² = 196cm²
As we can see, equality is fulfilled, so she is correct
Answer:
Step-by-step explanation:
You want the slope-intercept equation of the line through (2, 2) and parallel to the line through (-1, 6) and (1, 5).
<h3>Slope</h3>
The parallel line will have the same slope. The slope is given by the equation ...
m = (y2 -y1)/(x2 -x1)
m = (5 -6)/(1 -(-1))
m = -1/2
<h3>Intercept</h3>
We need to find the y-intercept of the desired line. Solving the equation for "b", we get ...
y = mx +b
b = y -mx . . . . . . . subtract mx to find b
b = 2 -(-1/2)(2) . . . . use m=-1/2 and (x, y) = (2, 2)
b = 2 +1
b = 3
The equation we want is ...
y = -1/2x +3
The sample size should be 73.
We use the formula
To find the z-score:
Convert 95% to a decimal: 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975
Using a z-table (http://www.z-table.com) we see that this value goes with a z-score of 1.96. Using this, our value for σ and our margin of error, we have:
Answer:
a. 8
b. 248
Step-by-step explanation:
first, find the derivative:
-2x^2 + 32x + 120
= -4x + 32
then, have that equal 0
-4x + 32 = 0
32 = 4x
8 = x
answer a: 8
plug in answer a into the original equation
-2(8)^2 + 32(8) +120
answer b: 248