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3 years ago

Straight line A has the equation y = 3x + 2. Find the equation of the line parallel to A and goes

Mathematics

1 answer:

arlik [135]3 years ago

6 0

Answer:

y = 3x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

To find c substitute (3, 8 ) into the partial equation

8 = 9 + c ⇒ c = 8 - 9 = - 1

y = 3x - 1 ← equation of parallel line

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A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

3 years ago

Which of the following are the factors of 4b^2-16?

vladimir2022 [97]

The answer is B hope this helps

6 0

3 years ago

Read 2 more answers

Find the dicontinuities of the function.

elena-s [515]

Answer:

Step-by-step explanation:

I'm assuming you meant to type in

$f(x)=\frac{x^2+12x+27}{x^2+4x+3}$ because you can only have removable discontinuities where there is a rational (fraction) function. Begin by factoring both the numerator and denominator to

$f(x)=\frac{(x+3)(x+9)}{(x+1)(x+3)}$ and cancelling out like terms would have us eliminating the (x + 3). That is where there is a removable discontinuity. It leaves a hole. The other discontinuity, (x + 1) doesn't cancel out so it is a non-removable discontuinity, which is a vertical asymptote.

The removable discontinuity is at -3. There is no y value at x = -3 (remember there's only a hole here), because -3 causes the denominator to go to 0 and we all know that having a 0 in the denominator of a fraction is a big no-no!!!

5 0

3 years ago

What is the value of e in e^x

Nookie1986 [14]

Answer

approximately 2.718

Step-by-step explanation

The exponential constant is an important mathematical constant and is given the symbol e. Its value is approximately 2.718. It has been found that this value occurs so frequently when mathematics is used to model physical and economic phenomena that it is convenient to write simply e.

7 0

3 years ago

First correct response gets brainliest

Simora [160]

Answer:

x = 13

Step-by-step explanation:

This question is based on Secant Secant theorem.

Secant Secant theorem gives us the following formula:

(AB + BD)AB = (AC + CE).AC

From the above question we have the following parameters

AB = 5

BD = x

AC = 7.5

CE = 4.5

Hence,

(AB + BD)AB = (AC + CE).AC

(5 + x)5 = (7.5 + 4.5)7.5

25 + 5x = 90

Collect like terms

5x = 90 - 25

5x = 65

x = 65/5

x = 13

5 0

2 years ago