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2 years ago

Graph the inequality on the axes below. 3x +y > -7

Mathematics

1 answer:

irina1246 [14]2 years ago

4 0

Step-by-step explanation:

use desmos it's a graphing calculator just put in the equation

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A kite was broken into two triangles of the same size and shape .

babunello [35]

ANSWER

Each triangle:40 cm²

Kite : 80cm²

EXPLANATION

The area of a triangle is

$\frac{1}{2}bh$

The height of the triangle is

$h = \frac{1}{2} (10)=5cm$

and the base is 16 cm.

The area of each triangle is

$= \frac{1}{2}(16)(5) = 40 {cm}^{2}$

2. The total area of the kite is 2 times the area of one triangle.

$= 2 \times 40 = 80 {cm}^{2}$

7 0

3 years ago

Read 2 more answers

Suppose that Y has density function

zvonat [6]

I'm assuming

$f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}$

(a) f(x) is a valid probability density function if its integral over the support is 1:

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1$

Compute the integral:

$\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16$

So we have

k / 6 = 1 → k = 6

(b) By definition of conditional probability,

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).

We have

$\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y$

Then

P(Y ≤ 0.4) = F (0.4) = 0.352

P(Y ≤ 0.8) = F (0.8) = 0.896

and so

P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value φ such that

P(Y ≤ φ) = 0.95

In terms of the integral definition of the CDF, we have solve for φ such that

$\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95$

We have

$\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95$

which reduces to the cubic

3φ² - 2φ³ = 0.95

Use a calculator to solve this and find that φ ≈ 0.865.

8 0

3 years ago

Please help thank you.

andre [41]

You have a rectangle and 2 triangles:
rectangle = 12 *6 = 72

larger triangle on left, find the base:
base = 6 / tan(45) = 6

area = 1/2 x b x h = 1/2 x 6 x 6 = 18

smaller triangle:
area = 1/2 x b x h
1/2 x 2 x 6 = 6

total area:
72 +6 +18 = 96 cm^2

5 0

2 years ago

If the endpoints of the diameter of a circle are (−14, 4) and (−2, 0), what is the standard form equation of the circle? a) (x −

Stels [109]

The answer to this question is 10

8 0

3 years ago

Read 2 more answers

Identify the solution to the system of linear equations Y=-x-2 Y=x-6

NikAS [45]

Answer:

(-4, 2)

Step-by-step explanation:

By looking at the graph, the solution to the system of linear equations will always be where they intercept. If they both are the same line it means that there are infinite solutions, and if they don't intercept at all, that means there are no solutions.

6 0

2 years ago