All categories

3 years ago

-1/4b + 1/2 = 5/6Find b

Mathematics

1 answer:

QveST [7]3 years ago

7 0

Answer:

b = -4/3

Step-by-step explanation:

First, subtract the 1/2 over

-1/4b+1/2=5/6

5/6-1/2

To get a common denominator of 6, multipy 1/2 by 3

5/6-1/2(3)

5/6-3/6=2/6

-1/4b=2/6

Next, multiply by the reciprocal of -1/4, or -4

(-4)-1/4b=2/6(-4)

b=-4/3

You might be interested in

How do you rationalize the numerator in this problem?

maw [93]

To solve this problem, you have to know these two special factorizations:

$x^3-y^3=(x-y)(x^2+xy+y^2)\\ x^3+y^3=(x+y)(x^2-xy+y^2)$

Knowing these tells us that if we want to rationalize the numerator. we want to use the top equation to our advantage. Let:

$\sqrt[3]{x+h}=x\\ \sqrt[3]{x}=y$

That tells us that we have:

$\frac{x-y}{h}$

So, since we have one part of the special factorization, we need to multiply the top and the bottom by the other part, so:

$\frac{x-y}{h}*\frac{x^2+xy+y^2}{x^2+xy+y^2}=\frac{x^3-y^3}{h*(x^2+xy+y^2)}$

So, we have:

$\frac{x+h-h}{h(\sqrt[3]{(x+h)^2}+\sqrt[3]{(x+h)(x)}+\sqrt[3]{x^2})}=\\ \frac{x}{\sqrt[3]{(x+h)^2}+\sqrt[3]{(x+h)(x)}+\sqrt[3]{x^2}}$

That is our rational expression with a rationalized numerator.

Also, you could just mutiply by:

$\frac{1}{\sqrt[3]{x_h}-\sqrt[3]{x}} \text{ to get}\\ \frac{1}{h\sqrt[3]{x+h}-h\sqrt[3]{h}}$

Either way, our expression is rationalized.

7 0

3 years ago

For each equation, find y when x=-3. Then find x when y = 2 1. y = 6x + 8

crimeas [40]

⬇ Hey, the answer is down below! :) ⬇

For y: x = -3

For y it stays the same.

For x: y = 2

For x it stays the same too.

For 1.): $x = \frac{1}{6}y + \frac{-4}{3}$

Step-by-step explanation:

For y there is no step-by-step explanation unfortunately.

For x there isn't a step-by-step explanation too unfortunately.

⬇ For 1.) there is a step-by-step explanation! ⬇

For step 1 we should flip the equations.

6x + 8 = y

For step 2 we should add -8 to both sides.

6x + 8 + − 8 = y + −8

= 6x = y − 8

For step 3 we should divide both sides by 6.

$\frac{6x}{6} = \frac{y - 8}{6}$

= x = $x = \frac{1}{6}y + \frac{-4}{3}$

In result we should have $x = \frac{1}{6}y + \frac{-4}{3}$ as the answer!

7 0

3 years ago

Convert the rectangular coordinates to polar coordinates with

NikAS [45]

Given:

Rectangular coordinate = (8, 6)

To convert:

Rectangular coordinate to polar coordinate with r > 0 and 0 ≤ θ < 2π.

Solution:

Let us find r:

$r=\sqrt{x^{2}+y^{2}}$

$r=\sqrt{8^{2}+6^{2}}$

$r=\sqrt{100}$

r = 10

Now, find θ:

$$\tan \theta=\frac{y}{x}$

$$\tan \theta=\frac{6}{8}$

Cancel the common factor 2.

$$\tan \theta=\frac{3}{4}$

$$\theta=\tan^{-1} \left(\frac{3}{4}\right)$

θ = 36.87°

The polar coordinates are (r, θ) = (10, 36.87°).

6 0

3 years ago

Name angle 2 in as many different ways as possible

Artist 52 [7]

Acute is one way struggling to find any more

7 0

3 years ago

Is the answers i picked right?

Ksivusya [100]

Half right. The discriminate is whats under the square root in the quadratic equation, so when it's negative you get 2 complex conjugate roots. It's the +/- before it that gives one root for + and one root for -
2 roots, non-real

8 0

3 years ago

-1/4b + 1/2 = 5/6Find b​

-1/4b + 1/2 = 5/6Find b