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3 years ago

Are the lines y=7x+15 and y=7x+4 perpendicular, parallel, and explain.

Mathematics

1 answer:

dsp733 years ago

8 0

Answer:

The lines would be parallel because their slopes are the same and their y-intercepts are different.

Step-by-step explanation:

First, start with the two equations:

y = 7x + 15

y = 7x + 4

So for lines to be parallel, they must have the same slope. For lines to be perpendicular, one of the lines must be the negative reciprocal of the other. In other words, it should be the opposite sign (+ or -) and the reciprocal (flip the numerator and denominator.

In this case, the lines are in slope-intercept form:

y = mx + b

so the slope is already given.

Slope of line 1 = 7x

Slope of line 2 = 7x

Because these lines have the same slope but different y-intercepts, they would be parallel to each other. You can check this by graphing it.

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3 years ago

22. Many rectangles have a perimeter of 81 feet. Find the dimensions for the one with the maximum enclosed area.

melisa1 [442]

Let
x----------> the length of the rectangle
y---------> the width of the rectangle

we know that
perimeter of rectangle=2*[x+y]
area of rectangle=x*y
P=81 ft
so
81=2*[x+y]-----------> 40.5=[x+y]

case A) 20.25 feet × 20.25 feet
P=2*[20.25+20.25]-----> 81 ft----------> the perimeter is ok
A=20.25*20.25-----> 410.06 ft²

case B) 11 feet × 29.5 feet
P=2*[11+29.5]-----> 81 ft----------> the perimeter is ok
A=11*29.5-----> 324.5 ft²

case C) 9 feet × 9 feet
P=2*[9+9]-----> 36 ft----------> the perimeter is not 81
A=9*9-----> 81 ft²

case D) 17.5 feet × 23 feet
P=2*[17.5+23]-----> 81 ft----------> the perimeter is ok
A=17.5*23-----> 402.5 ft²

the answer is
case A) 20.25 feet × 20.25 feet

5 0

3 years ago

Help me answer the last question

givi [52]

We have the equation 1/2x + 200 =1200 so we know that we have 200 already as one of the numbers so 1/2 is half of x + 200 equals 1200 since we have 200 we know that 1/2 of x is going to be 1000 because 1000+200=1200 meaning x is 2000. So your answer would be x=2000 or 1/2 2000 + 200=1200

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3 years ago

a group of 169 students needs to be seated in the square formation for a yearbook photo how many students should be in each row

andriy [413]

13 students per row
13 rows total
(169\13=13)

5 0

4 years ago

Use the definition of the derivative as a limit to find the derivative f′ where f(x)= √ x+2.

MA_775_DIABLO [31]

Step-by-step explanation:

If the equation is

$\sqrt{x + 2}$

Then, here is the answer.

The definition of a derivative is

$\frac{f(x + h) - f(x)}{h}$

Also note that we want h to be a small, negligible value so we let h be a value that is infinitesimal small.

So we get

$\frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h}$

Multiply both equations by the conjugate.

$\frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \times \frac{ \sqrt{x + h + 2} + \sqrt{x + 2} }{ \sqrt{x + h + 2} + \sqrt{x + 2} } = \frac{x + h + 2 - (x + 2)}{h \sqrt{x + h + 2} + \sqrt{x + 2} }$