Let's identify what we are looking for in terms of variables. Sandwiches are s and coffee is c. Casey buys 3 sandwiches, which is represented then by 3s, and 5 cups of coffee, which is represented by 5c. Those all put together on one bill comes to 26. So Casey's equation for his purchases is 3s + 5c = 26. Eric buys 4 sandwiches, 4s, and 2 cups of coffee, 2c, and his total purchase was 23. Eric's equation for his purchases then is 4s + 2c = 23. In order to solve for c, the cost of a cup of coffee, we need to multiply both of those bolded equations by some factor to eliminate the s's. The coefficients on the s terms are 4 and 3. 4 and 3 both go into 12 evenly, so we will multiply the first bolded equation by 4 and the second one by -3 so the s terms cancel out. 4[3s + 5c = 26] means that 12s + 20c = 104. Multiplying the second bolded equation by -3: -3[4s + 2c = 23] means that -12s - 6c = -69. The s terms cancel because 12s - 12s = 0s. We are left with a system of equations that just contain one unknown now, which is c, what we are looking to solve for. 20c = 104 and -6c = -69. Adding those together by the method of elimination (which is what we've been doing all this time), 14c = 35. That means that c = 2.5 and a cup of coffee is $2.50. There you go!
Answer:
<u>x = 18</u>
Step-by-step explanation:
1. Let's solve for x, using the supplementary angles theorem, this way:
∠ C = 180 - 7x + 2 because they are supplementary angles. And these angles add up to 180 degrees.
∠ D = 180 - 9x + 31 because they are supplementary angles. And these angles add up to 180 degrees.
∠ E = 180 - 4x - 33 because they are supplementary angles. And these angles add up to 180 degrees.
Now, let's recall that the interior angles of a triangle add up to 180 degrees. Thus:
∠ C + ∠ D + ∠ E = 180 °
Replacing with the real values for solving for x:
180 - 9x + 31 + 180 - 4x - 33 + 180 - 7x + 2 = 180
- 20 x + 540 = 180
- 20 x = 180 - 540 (Subtracting 540 to both sides)
- 20 x = - 360
<u>x = 18 (Dividing by - 20)</u>
<u>Proving that x = 18 is correct</u>
180 - 9x + 31 + 180 - 4x - 33 + 180 - 7x + 2 = 180
180 - 9 (18) + 31 + 180 - 4 (18) - 33 + 180 - 7 (18) + 2 = 180
180 - 162 + 31 + 180 - 72 - 33 + 180 - 126 + 2 = 180
573 - 393 = 180
180 = 180
<u>We proved that x = 18 is correct</u>
Pierre ran 19 and 13/20 miles.
Given:
marathon length : 26 2/10 miles
pierre's length ran : 3/4 of the way.
Multiply the fractions.
Convert the marathon length from a mixed fraction into a fraction.
26 2/10 = ((26*10)+2)/10 = (260+2)/10 = 262/10
262/10 * 3/4 = (262*3) / (10*4) = 786/40 = 19 26/40
19 26/40 simplified to 19 13/20 miles
26 ÷ 2 = 13
40 ÷ 2 = 20
Answer:
B 29 words/min
Step-by-step explanation:
I just put it into desmos and went to the third number line
Answer:
why does my computer make me submit and anser when I have no idea what this is.
Step-by-step explanation:
