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butalik [34]
3 years ago
11

A line has a slope of 1 over 4 and passes through the point 0.2 4 over 5 find the value of b , the y intercept

Mathematics
1 answer:
Finger [1]3 years ago
7 0

Answer:

it equals 7

Step-by-step explanation:

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Can someone answer and explaine this to me
vampirchik [111]
4x - 26 = 3x + 4
-3x          -3x
x - 26 = 4
    +26   +26
x = 30
Since the 2 angles are opposite of each other you would set them equal to each other.
6 0
2 years ago
If all of the pieces of candy were lined up end to end, what would be the total length of candies? 1/8in, 2/8in, 3/8in, 4/8in ,
VashaNatasha [74]

Answer:

4 1/2 inches

Step-by-step explanation:

8 0
3 years ago
Betty sold 21 out of the 70 quilts she made. What percent of her quilts did Betty sell?
Nina [5.8K]

Answer:

The answer is <em>C</em> or 30%

I divided 21 by 70 (21/70) to get 0.3 or 30% of 100...

Hope this helps

3 0
3 years ago
Urgent, It is a Calculus question and I’ll appreciate your help. Thanks
BaLLatris [955]

Answer:

  4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

  (12p)(12r) = -1

  r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

  slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

  tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

__

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

  slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

  6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

  d^2 = (6r^2 -6p^2)^2 +(r -p)^2

  d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

  Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

<em>Comment on the solution</em>

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.

6 0
3 years ago
What is the total amount in an account after 3 years if the interest is compounded annually on an amount of $3200 at 4%?
lorasvet [3.4K]

Answer:

$3599.57

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r)^t

where Accrued amount is to be determined

P = principal; $3200

r = 4% = 0.04

t = number of years = 3

Therefore

Accrued amount = 3200 (1 + 0.04)^3

= 3200 x 1.04^3

= 3200 x 1.1249

= 3599.57

The total amount after 3 years is $3599.57

8 0
3 years ago
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