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Nookie1986 [14]
3 years ago
8

The slope of the line below is -3. Use the coordinates of the labeled point to find a point-slope equation of the line.

Mathematics
1 answer:
Reptile [31]3 years ago
8 0
Answer:
y-y₁ = -3(x-x₁)

First of all, when you start an equation with a slope, since the question gave the slope -3, I'm not sure what your looking for, but I'll give you an example

Example:
y-y₁ = m(x-x₁)
m = -3
y₁ = ? - I'll just put a random # = -1
x₁ = ? - I'll just put a random # = 5
<span>y-(-1) = (-3)(x-(5))
</span>y+1 = -3x+15 - I'm guessing

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I don’t know how to use the triangle area to calculate the area of the inscribed polygons
Trava [24]

First of all, let's recall the area of a triangle, knowing its base (b) and height (h):

A = \cfrac{bh}{2}

The exercise is showing you that, if you inscribe a polynomial with more and more side, the area of the polynomial will approximate the area of the circle better and better (you can see youself that the polygon is "filling" the circle more and more as the number of sides increase).

Now, the second column tells you the area of each of the triangles the polygon is split into. So, we can see that the first polygon is split into 3 triangles, each of them having base 1.73 and height 0.5.

So, the area of each triangle is

A = \cfrac{1.73 \cdot 0.5}{2} = 0.4325

There are three of these triangles, so the area of the whole polygon is

A = 0.4325 \cdot 3 = 1.2975

In the second case, you have six triangles, each with base 1 and height 0.87. So, the whole area is

A = 6 \cdot \cfrac{1\cdot 0.87}{2} = 0.87 \cdot 3 = 2.61

Finally, in the last case you have 8 triangles, each with base 0.77 and height 0.92. So, the whole area is

A = 8 \cdot \cfrac{0.77\cdot 0.92}{2} = 0.77\cdot 0.92 \cdot 4 = 2.8336

3 0
3 years ago
A vegetable garden is in the shape of a parallelogram with the dimensions shown.Parallelogram A B C D is shown. The length of A
olga55 [171]

Answer:

t needs 68 feet to enclose the garden.

Step-by-step explanation:

In this problem, we are to solve the sides of a parallelogram ABCD to know the measurement to enclose a garden.

Take note that a parallelogram has two equal lengths and two equal widths. Let us assume that the parallelogram AB = CD is the length and AD = BC is the width.

Solving the problem

First, let us solve for r using the condition AD = BC

AD = BC

3r + 8 = 2r + 12

Simplify the equation

3r - 2r = 12 - 8

r = 4

Next, let us substitute the value of r to AB, BC, CD, and AD.

For AB:

AB = 4r - 2

AB = 4(4) - 2

AB = 16 - 2 = 14

For BC:

BC = 2r + 12

BC = 2(4) + 12

BC = 8 + 12 = 20

For AD:

AD = 3r + 8

AD = 3(4) + 8

AD = 12 + 8 = 20

For CD:

But AB = CD Therefore, CD = 14

Finally, let us solve the perimeter of the parallelogram

Perimeter = AB + BC + CD + AD

Perimeter = 14 + 20 + 20 + 14

Perimeter = 68 feet

Therefore, the fencing needed to enclose the garden is 68 feet.

To learn more, just click the following links:

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Find the value of a if given points are collinear (5,1) (3,2) and (1,a)​
Ksenya-84 [330]

9514 1404 393

Answer:

  a = 3

Step-by-step explanation:

The x-values 5, 3, 1 form an arithmetic sequence. The y-values will do the same: 1, 2, a = 1, 2, 3 -- a common difference of +1.

  a = 3

8 0
3 years ago
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
erma4kov [3.2K]

Answer:

\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}

Step-by-step explanation:

Given

5 tuples implies that:

n = 5

(h,i,j,k,m) implies that:

r = 5

Required

How many 5-tuples of integers (h, i, j, k,m) are there such thatn\ge h\ge i\ge j\ge k\ge m\ge 1

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed:  This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

^{n}C_r => ^{n + 4}C_5

^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}

^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}

Expand the numerator

^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}

<u><em>Solved</em></u>

6 0
3 years ago
Write log7t using the natural logarithm.
VARVARA [1.3K]

Answer:

log₇t = ln t / ln 7

Step-by-step explanation:

Given:

log₇t

Computation:

We know that

logₐb = log b / log a

So,

log₇t = log t / log 7

= log₇t = ln t / ln 7

4 0
3 years ago
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