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2 years ago

Express the area of the entire triangle? What is the area?

Mathematics

2 answers:

Korvikt [17]2 years ago

6 0

Answer:

2x+21

Step-by-step explanation:

Area=Base*height

(x+7)*(x+3)

x*x=2x

7*3=21

2x+21

Vinil7 [7]2 years ago

6 0

Answer:

Area=Base*height

(x+7)*(x+3)

x*x=2x

7*3=21

2x+21

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Two streams flow into a reservoir. Let X and Y be two continuous random variables representing the flow of each stream with join

zlopas [31]

Answer:

c = 0.165

Step-by-step explanation:

Given:

f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,

f(x, y) = 0 otherwise.

Required:

The value of c

To find the value of c, we make use of the property of a joint probability distribution function which states that

$\int\limits^a_b \int\limits^a_b {f(x,y)} \, dy \, dx = 1$

where a and b represent -infinity to +infinity (in other words, the bound of the distribution)

By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have

$\int\limits^3_0 \int\limits^3_0 {cxy(1+y)} \, dy \, dx = 1$

Since c is a constant, we can bring it out of the integral sign; to give us

$c\int\limits^3_0 \int\limits^3_0 {xy(1+y)} \, dy \, dx = 1$

Open the bracket

$c\int\limits^3_0 \int\limits^3_0 {xy+xy^{2} } \, dy \, dx = 1$

Integrate with respect to y

$c\int\limits^3_0 {\frac{xy^{2}}{2} +\frac{xy^{3}}{3} } \, dx (0,3}) = 1$

Substitute 0 and 3 for y

$c\int\limits^3_0 {(\frac{x* 3^{2}}{2} +\frac{x * 3^{3}}{3} ) - (\frac{x* 0^{2}}{2} +\frac{x * 0^{3}}{3})} \, dx = 1$

$c\int\limits^3_0 {(\frac{x* 9}{2} +\frac{x * 27}{3} ) - (0 +0) \, dx = 1$

$c\int\limits^3_0 {(\frac{9x}{2} +\frac{27x}{3} ) \, dx = 1$

Add fraction

$c\int\limits^3_0 {(\frac{27x + 54x}{6}) \, dx = 1$

$c\int\limits^3_0 {\frac{81x}{6} \, dx = 1$

Rewrite;

$c\int\limits^3_0 (81x * \frac{1}{6}) \, dx = 1$

The $\frac{1}{6}$ is a constant, so it can be removed from the integral sign to give

$c * \frac{1}{6}\int\limits^3_0 (81x ) \, dx = 1$

$\frac{c}{6}\int\limits^3_0 (81x ) \, dx = 1$

Integrate with respect to x

$\frac{c}{6} * \frac{81x^{2}}{2} (0,3) = 1$

Substitute 0 and 3 for x

$\frac{c}{6} * \frac{81 * 3^{2} - 81 * 0^{2}}{2} = 1$

$\frac{c}{6} * \frac{81 * 9 - 0}{2} = 1$

$\frac{c}{6} * \frac{729}{2} = 1$

$\frac{729c}{12} = 1$

Multiply both sides by $\frac{12}{729}$

$c = \frac{12}{729}$

$c = 0.0165 (Approximately)$

8 0

3 years ago

What is the predecessor and successor of 9,852

sweet [91]

Answer:

Predecessor: 9851

Successor: 9853

Step-by-step explanation:

The predecessor of a number is 1 less than it.

The successor of a number is 1 more than it.

PLS GIVE BRAINLIEST

5 0

2 years ago

Read 2 more answers

Given the function g(x) = x2 - 4x + 0, determine the average rate of change of

kozerog [31]

Answer:

Step-by-step explanation:

ARC = $\frac{g(b) -g(a)}{b-a}$ , b = 7, a = 1

24/6 = 4

3 0

2 years ago

Relationship A has a lesser rate than Relationship B. This table represents Relationship B.

Alja [10]

Answer:

y = 18.1x ; and y = 18x

Explanation:

The rate of change in Relationship B can be found by using the formula for slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

Using the first two points, we have

$m=\frac{73-36.50}{4-2}=\frac{36.50}{2}=18.25$

We know that Relationship A has a lesser rate than this. The choices given for Relationship A are written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept (in this case b = 0).

The slope of the first equation is 18.1; this is less than 18.25.

The slope of the second equation is 18.6; this is greater than 18.25.

The slope of the third equation is 18.3; this is greater than 18.25.

The slope of the fourth equation is 18; this is less than 18.25.

6 0

2 years ago

Read 2 more answers

Expand and simply following expression.<br> 5(n – m) +3(n – m)

Brilliant_brown [7]

Answer:

$n = x \\ m = y \\ 5x - 5y + 3x - 3y = 8x - 8y = 8(x - y)$

4 0

2 years ago