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choli [55]
3 years ago
10

Natalie ran to the library from home. Then she ran 0.25 mile to the track. She ran 1.5 miles around the track and then took the

same route home. Let m represent the distance in miles from Natalie’s home to the library. Which expression represents the total distance in miles that Natalie ran?
A. m+0.25+1.5

B. m+2(0.25 +1.5)

C. 2m+0.25+1.5

D. 2(m+0.25) +1.5
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
3 0

Answer:I got B :)))

Step-by-step explanation:

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X=7

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3 years ago
Consider the line y=−4/3x+3. Find the equation of the line that is parallel to this line and passes through the point , −4 6. Fi
andriy [413]

Answer:

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .

Step-by-step explanation:

Parallel means equal slopes. Hence, the slope of the line parallel to y=4/3x+3 is 4/3 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=4/3(x−4)  

y−6=4/3x−16/3  

y=4/3x−7/3  

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

Question #2:

Perpendicular means negative reciprocal slopes. Hence, the slope perpendicular to y=4/3x+3 is y=−3/4 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=−3/4(x-4)  

y−6=−3/4x+6  

y=−3/4x+10

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .

7 0
2 years ago
At the north campus of a performing arts​ school, ​20% of the students are music majors. At the south​ campus, 70​% of the stude
antoniya [11.8K]

Answer:

The north campus had 800 while the south campus had 200.

Step-by-step explanation:

The question stated that there are 1000 students in the merged campus. That's the sum of the number of students in the north and the south campus before the merger.

Let x denote the number of students in the north campus before the merger. The other (1000 -x) students would all belong to the south campus before the merger.

Before the merger, 20\% of the students of the north campus are of music majors. In terms of x, that's (20\%)\cdot x = 0.20\,x students.

On the other hand, 70\% of the students of the south campus are of music majors. That corresponds to (70\%)\cdot (1000 - x) = 0.70\cdot (1000 - x) = 700 - 0.70\, x students.

With a similar logic, the number of music students in the merged east campus will be 30\% \times 1000 = 300.

The question implies that the sum of students in the two campuses should be equal to the number of music students in the east campus. That is:

0.20\, x+ (700 - 0.70\, x) = 300.

Solve for x:

x = 800.

In other words, there are 800 students in the north campus and (1000 - 800) = 200 students in the south campus before the merger.

6 0
3 years ago
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