Answer: The length of AC should be between 5 inches and 25 inches
Step-by-step explanation:
Jose in this problem draws a triangle, AABC.
We know the length of two sides of the triangle:
AB = 10 inches
BC = 15 inches
The length of the third side in a generic triangle can be calculated using the cosine theorem: where
a, b, c are the three sides
is the angle opposite to side
Looking at the formula, we observe that:
- The maximum value for is obtained for , so that . In this case, the length of the missing side (AC, in this case) is
So, the length of AC must be between 5 and 25 inches.
Answer:
b
Step-by-step explanation:
Answer:
x = $3.50; y = $2.25
Step-by-step explanation:
First, come up with your two equations where x= price of walnuts and y= price of chocolate chips: 8x + 4y = 37 and 3x + 2y = 15. Solve the first equation.
3x + 2y = 15
3x = 15 - 2y
x = (15 - 2y)/3
Plug in the answer to your second equation.
8(15 - 2y)/3 + 4y = 37
(120 - 16y)/3 + 4y = 37
120 - 16y + 12y = 111
120 - 4y = 111
-4y = -9
y = 2.25
Plug in your answer to find <em>x.</em>
3x + 2(2.25) = 15
3x + 4.5 = 15
3x = 10.5
x = 3.5
Check your equation.
1) 3(3.5) + 2(2.25) = 15
10.5 + 4.5 = 15
15 = 15
2) 8(3.5) + 4(2.25) = 37
28 + 9 = 37
37 = 37
Answer:
In order to have ran 33 miles, Bobby would have to attend <em>32 track practices.</em>
Step-by-step explanation:
Solving this problem entails of uncovering the amount of track practices Bobby must attend in order to have ran 33 miles. Start by reading the problem carefully to break down the information provided.
You can see that Bobby has already ran one mile on his own. This is important to remember for later. The problem also states that he expects to run one mile at every track practice.
Setting up an equation will help us solve. Here is how we could set up the equation:
(<em>amount of miles already ran</em> = 1) + (<em>number of track practices</em> = x) = (<em>total miles to run</em> = 33)
1 + x = 33
The equation is now in place. You can solve this, or isolate <em>'x',</em> by using the subtraction property of equality. This means we will subtract one from both sides of the equation, thus isolating the variable.
1 + x = 33
1 - 1 + x = 33 - 1
x = 32
The variable is the only term left on the left side of the equation. This means Bobby must attend track practice <em>32 times</em> in order to have ran 33 miles.
We can write this in algebraic terms as:
16+8x = 24+6x
so
2x = 8
x = 4
The number is 4.