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3 years ago

What’s the value of x?

Mathematics

1 answer:

viva [34]3 years ago

6 0

Answer:

x=6

Step-by-step explanation:

We know that <AWV is 90, so we can set up an equation. This equation is 54+3x+18=90, we know this is true because the two smaller angles are complementary. Then to find x simply solve the equation.

First, add like terms

3x+72=90

Then, subtract 72 from both sides

3x=18

Finally, divide both sides by 3

x=6

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Mr. Richard owns an orchard that has a rectagular fence . The orchard is 36 yards long and 18 yards wide . if he walks across th

Sergio [31]

Answer:

40.2 Yards

Step-by-step explanation:

To find the diagonal length of the orchard, we need to use the Pythagorean Theorem. The formula of the Pythagorean Theorem is:

c²= a² + b²

a = 36 Yards

b = 18 Yards

Now let's plug in our values to the formula.

c² = a² + b²

c² = 36² + 18²

c² = 1296 + 324

c² = 1620

Now to find the value of c we need to get the square root of both sides.

$\sqrt{c^{2}}=\sqrt{1620}$

c = 40.2

So the diagonal length of Mr. Richard's orchard is 40.2 Yards.

7 0

4 years ago

Factor 2x2 + 7x + 3. <br> (2x + 2)(x + 1) <br> (2x + 3)(x + 1) (2x + 1)(x + 3)

maks197457 [2]

<h3>Answer:</h3>

(2x + 1)(x + 3)

<h3>Step-by-step explanation:</h3>

It is probably easier to try the answer choices than to try to factor the expression yourself.

(2x + 2)(x + 1) = 2x² +4x +2

(2x + 3)(x + 1) = 2x² +5x +3

(2x + 1)(x + 3) = 2x² +7x +3 . . . . . correct choice

_____

<em>Constructed solution</em>

If you want to factor this yourself, you can look for factors of "ac" that add to give "b". That is, you want factors of 2·3 = 6 that add up to give 7. You don't have to look very far.

... 6 = 1·6 = 2·3 . . . . . . the first factor pair adds to give 7

Now, rewrite the x term using the sum of these numbers.

... 2x² +(1 +6)x +3

... 2x +x +6x +3 . . . . eliminate parentheses

... (2x +x) +(6x +3) . . . . group pairs of terms

... x(2x +1) +3(2x +1) . . . . factor each pair

... (x +3)(2x +1) . . . . . . matches the last selection

6 0

3 years ago

First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

7 0

4 years ago

30<br> 20<br> Y<br> Find x<br><br> Can someone please help me

irakobra [83]

Answer:

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos30° = $\frac{\sqrt{3} }{2}$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{x}{20}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2x = 20 $\sqrt{3}$ ( divide both sides by 2 )

x = 10 $\sqrt{3}$ → B

7 0

3 years ago

Can anyone help me please

ki77a [65]

Answer:

Here, you have been given x=5 and an equation 3x.

Step-by-step explanation:

Using the method of plugin, you need to plug in x=5 in 3x which will give you 3(5) = 15

3 0

3 years ago