Answer:
hypotenuse=0.869...
Step-by-step explanation:
soh cah toa
xy is the adjacent side
we are looking for the hypotenuse, which is yz
cos30=6/hypotenuse
0.866=6/hypotenuse
hypotenuse=0.869...
<span>Simplifying
x4 = 16
Solving
x4 = 16
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Simplifying
x4 = 16
Reorder the terms:
-16 + x4 = 16 + -16
Combine like terms: 16 + -16 = 0
-16 + x4 = 0
Factor a difference between two squares.
(4 + x2)(-4 + x2) = 0
Factor a difference between two squares.
(4 + x2)((2 + x)(-2 + x)) = 0
Subproblem 1
Set the factor '(4 + x2)' equal to zero and attempt to solve:
Simplifying
4 + x2 = 0
Solving
4 + x2 = 0
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + x2 = 0 + -4
Combine like terms: 4 + -4 = 0
0 + x2 = 0 + -4
x2 = 0 + -4
Combine like terms: 0 + -4 = -4
x2 = -4
Simplifying
x2 = -4
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:
Simplifying
2 + x = 0
Solving
2 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2
Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2
Combine like terms: 0 + -2 = -2
x = -2
Simplifying
x = -2
Sub-problem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve:
Simplifying
-2 + x = 0
Solving
-2 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2
Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2
Combine like terms: 0 + 2 = 2
x = 2
Simplifying
x = 2Solutionx = {-2, 2}</span>
a. The expression y=5x represent the number of small marbles she has.
b. The expression z=3x+2 represents the number of large marbles she has.
c. Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Medium marbles = x
Let,
Small marbles = y
According to given statement;
She has five times as many small marbles as medium marbles.
y = 5x Eqn 1
The expression y=5x represent the number of small marbles she has.
b. Write an algebraic expression to represent the number of large marbles she has.
Let,
Large marbles = z
The number of large marbles is two more than three times the number of medium marbles.
z = 3x+2 Eqn 2
The expression z=3x+2 represents the number of large marbles she has.
c. If Amy has a total of 560 marbles, how many of each size does she have?
x+y+z= 560 Eqn 3
Putting value of y and z from Eqn 1 and 2 in Eqn 3
Dividing both sides by 9
Putting x=62 in Eqn 1
Putting x=62 in Eqn 2
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Keywords: linear equation, substitution method
Learn more about substitution method at:
#LearnwithBrainly
Answer:
201 miles.
Step-by-step explanation:
If you've traveled 124 miles in 2 hours, than in one hour must've been 62 miles. 62 multiplied by 3 is 186, which is how much miles have been traveled in 3 hours. Plus the 15 minutes would probably be 201 miles. Hope this helps!
Answer:
1598.2
Step-by-step explanation:
I used a calculator on this one.
