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vesna_86 [32]
3 years ago
15

Line L passes through the points (1, 1) and (7, 8). What is the slope of a line that is perpendicular to line L?

Mathematics
1 answer:
asambeis [7]3 years ago
8 0

When a line passes through the two points (x_{1},y_{1}) and (x_{2},y_{2}) , its slope is given by the formula m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

In this question, a line L passes through the points (1,1) and (7,8)

So, its slope is given by m=\frac{8-1}{7-1}

m=\frac{7}{6}

When two lines are perpendicular, then the product of their slopes is -1.

Since, the slope of the line L is \frac{7}{6} , so the slope of the line which is perpendicular to the given line L is \frac{-6}{7} as the product of \frac{-6}{7} \times \frac{7}{6}=-1.

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The yearly cost y for driving a certain car is $7,800 for 10,000 miles
Licemer1 [7]

Answer:

y = 0.36x + 4200.00

15100.00 miles.

Step-by-step explanation:

If the yearly cost for driving x miles is given by y dollars then the two ordered pairs to find the linear relation between x and y are (10000,7800) and (20000,11400).

So, the equation will be

\frac{y - 11400}{11400 - 7800} = \frac{x - 20000}{20000 - 10000}

⇒ \frac{y - 11400}{3600} = \frac{x - 20000}{10000}

⇒ y - 11400 = \frac{9}{25}(x - 20000)

⇒ y - 11400 = \frac{9}{25}x - 7200

⇒ y = \frac{9}{25}x + 4200

⇒ y = 0.36x + 4200.00 ........... (1) (Answer)

Now, for y = $9636.00, from equation (1),

9636 = 0.36x + 4200

⇒ 0.36x = 5436

⇒ x = 15100.00 miles. (Answer)

6 0
3 years ago
There are 412 students at sunshine middle school. 225 students are in 5th 6th grade and the rest are in 7th or 8th grades. How m
Arada [10]

Answer:

187 students in 7th or 8th grade

17,088 pages

Step-by-step explanation:

412 - 225 is 187.

A dozen is 12

12 x 16 x 89 = 17,088

4 0
3 years ago
What is the smallest value of y in the solution set to the system of equations below?
n200080 [17]

Answer:

The smallest value of y in the given two equations is 78

Step-by-step explanation:

Given as :

The two equation is given as :

y = x² + 6 x +23               ...........1

y = 18 x - 12.                     ..........2

Now, solving both equations

putting the value of y from eq 2 into eq 1

So,  x² + 6 x +23 = 18 x - 12

Or,  x² + 6 x +23 - 18 x + 12 = 0

Or, x² - 12 x + 35 = 0

Or, x² - 5 x - 7 x + 35 = 0

Or, x (x - 5) - 7(x - 5) = 0

Or, (x - 5) (x - 7) = 0

∴ x = 5 , 7

Now, for smallest value of y , take x = 5

∴ put the value of x in eq 2

So, y = 18 x - 12

I.e y = 18 × 5 - 12

Or, y = 90 - 12

∴   y = 78

Hence, The smallest value of y in the given two equations is 78 . answer          

7 0
3 years ago
16 divided by (x + 4) in WORD FORM
motikmotik

Answer:

sixteen divded by the sum of x and 4

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The elves and reindeer are getting ready for a meeting with Santa.
Feliz [49]

Let e and r be the number of elves and reindeers, respectively.

We know that:

r+e=14 (so far 14 of them have arrived)

4r+2e = 38(each reindeer has 4 legs and each elf has two)

If we multiply the first equation by 2 we have 2r+2e=28, and if we subtract this equation from the second we have 2r=10 which implies r=5.

So, there are 5 reindeers and 9 elves (remember that they have to sum up to 14).

3 0
2 years ago
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