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2 years ago

13

Greg is traveling north on a road while Peter is traveling south on the same road. They pass by each other at noon, Greg driving

at 40 mph and peter driving 30 mph. At what time will they be at 315 mph?

1 answer:

max2010maxim [7]2 years ago

5 0

40x+30x=315

70x=315

315/70= 4.5 hours

12:00 noon + 4.5 hours = 4:30 pm

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Carlos has 4/5 of a tank of fuel In his car. he uses 1/10 of a tank per day. How many days will his fuel last?

damaskus [11]

Answer:

8 days

Step-by-step explanation:

4/5= 8/10

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3 years ago

2x-5y+5z=-10<br> 5x-4y+3z=-19<br> X-y+5z=17

yarga [219]

Answer:

x = -125/71 , y = 448/71 , z = 356/71

Step-by-step explanation:

Solve the following system:

{2 x - 5 y + 5 z = -10 | (equation 1)

5 x - 4 y + 3 z = -19 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Swap equation 1 with equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

2 x - 5 y + 5 z = -10 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 2/5 × (equation 1) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - (17 y)/5 + (19 z)/5 = (-12)/5 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Multiply equation 2 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 1/5 × (equation 1) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y/5 + (22 z)/5 = 104/5 | (equation 3)

Multiply equation 3 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y + 22 z = 104 | (equation 3)

Subtract 1/17 × (equation 2) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+(355 z)/17 = 1780/17 | (equation 3)

Multiply equation 3 by 17/5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+71 z = 356 | (equation 3)

Divide equation 3 by 71:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 19 × (equation 3) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y+0 z = (-7616)/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 2 by -17:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Add 4 × (equation 2) to equation 1:

{5 x + 0 y+3 z = 443/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 3 × (equation 3) from equation 1:

{5 x+0 y+0 z = (-625)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 1 by 5:

{x+0 y+0 z = (-125)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Collect results:

Answer: {x = -125/71 , y = 448/71 , z = 356/71

5 0

3 years ago

2. Find the slope, or rate of change, represented in the table below. x -1 0 1 2 3 У -8 3 14 25 36

kirza4 [7]

Answer:

11

Step-by-step explanation:

slope is change in y over change in x. so, if x is increasing by one every time and y is increasing by 11, then the slope is 11/1, which we write as 11.

3 0

3 years ago

A carnival game has 3 identical boxes. The boxes have the following amounts of money: one has $30.00, one has $6.00, and one has

garri49 [273]

$200 divided by 100 customers = 2$.

So, if he wants to make a profit of $200, he would have to make each customer pay $2. :)

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3 years ago

A student's course grade is based on one midterm that counts as 15% of his final grade, one class project that counts as 15% of

kow [346]

Answer:

Overall final score = 77.75% ; Grade = C.

Step-by-step explanation:

The approach to solve this question is to realize that the marks have to be converted into the respective percentages of the whole course. This means that the marks of all the components have to be normalized according to the grading breakdown.

Project Marks = 97/100. Weightage = 15%. So 97*15/100 = 14.55/15.

This means that the student received 14.55 marks in the project out of 15.

Similarly for other components:

Mid-Term Marks = 83/100. Weightage = 15%. So 83*15/100 = 12.45/15.

Homework Marks = 82/100. Weightage = 35%. So 82*35/100 = 28.7/35.

Finals Marks = 63/100. Weightage = 35%. So 63*35/100 = 22.05/35.

After the conversion process, add up the normalized marks, which are now acting as the percentages earned in all the components.

Aggregate Percentage = 14.55 + 12.45 + 28.7 + 22.05 = 77.75%.

According to the grade scale, the student receives a C because 70 is less than 77.75 and 77.75 is less than 80.

Summarizing, the student receives a C at 77.75%!!!

7 0

3 years ago