Which is an equivalent expression for 14+10x+6−8x?14+10x+6−8x?

(x+3y=6 16x + 18y = 36

jonny [76]

Answer:

X = 0 , y=2

Step-by-step explanation:

Check attachment

7 0

3 years ago

Find the equation of the line tangent to the graph of

garik1379 [7]

Answer:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

$\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}$

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

$\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}$

Simplify:

$\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}$

We can factor out the denominator within the square root:

$\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}$

Simplify:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}$

So, we can find the slope of the tangent line at x = 5/2. By substitution:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}$

Evaluate:

$\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}$

We will also need the point at x = 5/2. Using our original equation, we acquire that:

$\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})$

Distribute:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}$

Isolate. Hence, our equation is:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

7 0

2 years ago

Jamie has $114.56 in her savings and count and her bank just raised the interest paid on her savings account by 1/2%. if her old

zaharov [31]

Answer:

0.5025%

Step-by-step explanation:

The question is on increase and decrease

The old interest rate= .5%⇒0.5%

percentage increase= 1/2%= 0.5%

New rate= it requires you to increase 0.5 by 0.5%

New rate is ⇒100%+ 0.5%=100.5%

New rate⇒(100.5/100)×0.5 =0.5025

New rate as a decimal is 0.5025%

5 0

2 years ago

What is the slope...?

Margarita [4]

Answer:

slope = -2

Step-by-step explanation:

To find the slope, you can use the slope formula, $\frac{y_2-y_1}{x_2-x_1}$ . $x_1$ and $y_1$ represent the x and y values of one point the line passes through, and $x_2$ and $y_2$ represent the x and y values of another point the line also passes through.

So, in order to answer the question, we need two points from the line. To find these points, look at the x and y values of the table - they form points. Thus, (-2, 0) and (-1,-2) would be two points the line passes through. Use those x and y values and substitute them into the formula. Then, solve:

$slope = \frac{y_2-y_1}{x_2-x_1}\\= \frac{(-2)-(0)}{(-1)-(-2)}\\= \frac{-2-0}{-1+2} \\= \frac{-2}{1} \\= -2$

Thus, the slope is -2.

8 0

2 years ago

Read 2 more answers

The length of a rectangle is twice its width. if the perimeter of the rectangle is 60 ft , find its length and width.

german

L = 2W
P = 2L + 2W
60 = 2(2W) +2W
60 = 4w +2w
60 = 6w
60/6 = 6w/6
w = 10
L= 2(10)
L = 20

Check

P = 2L + 2W
60 = 2(20) +2(10)
60 = 40 +20
60 = 60

4 0

3 years ago