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3 years ago

The vertical asymptote is x = ?y=a/x-h +k

Mathematics

1 answer:

gtnhenbr [62]3 years ago

4 0

Answer:

x=a/(y-k)+h

Step-by-step explanation:

y-k=a/(x-h)

(y-k)(x-h)=a

xy-hy-kx+kh=a

xy-kx=a+hy-hk

x(y-k)=a+h(y-k)

x=a/(y-k)+h

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Mark got 20% raise for his salary. If this salary was $1800 what is the new salary

elena-14-01-66 [18.8K]

Salutations!

Mark got 20% raise for his salary. If this salary was $1800 what is the new salary?

So lets solve this!

Mark got 20% "raise" for his salary. It clearly indicates that it is percentage of increase, so therefore, after solving out all the sum, we would be adding up 1800 to get the total of the new salary.

Lets form this into statements ----

Percentage increase = 20%

Mark's old salary = $1800

Mark's new salary = 20 × 1800/100

Cancel out the zeros to make it more logical ----

20 × 18/1

= 360.

Now, we need to add 1800 and 360 to get Mark's new salary

1800 + 360 = $2160.

Mark's new salary is $2160.

Hope I helped :D

7 0

3 years ago

If alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha

castortr0y [4]

$6x^2+x-2=6x^2+4x-3x-2=2x(3x+2)-1(3x+2)\\\\=(3x+2)(2x-1)\\\\3x+2=0\to x=-\frac{2}{3}\\\\2x-1=0\to x=\frac{1}{2}\\\\\alpha=-\frac{2}{3};\ \beta=\frac{1}{2}\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{-\frac{2}{3}}{\frac{1}{2}}+\frac{\frac{1}{2}}{-\frac{2}{3}}=-\frac{2}{3}\cdot\frac{2}{1}-\frac{1}{2}\cdot\frac{3}{2}=-\frac{4}{3}-\frac{3}{4}\\\\=-\frac{16}{12}-\frac{9}{12}=-\frac{25}{12}=-2\frac{1}{12}$

$use\ Vieta's\ formula:\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2}{\alpha\beta}-2\\\\\alpha+\beta=\frac{-b}{a};\ \alpha\beta=\frac{c}{a}\\\\\frac{(\alpha+\beta)^2}{\alpha\beta}-2=\frac{\left(\frac{-b}{a}\right)^2}{\frac{c}{a}}-2=\frac{b^2}{a^2}\cdot\frac{a}{c}-2=\frac{b^2}{ac}-2$

$6x^2+x-2\\\\a=6;\ b=1;\ c=-2\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{1^2}{6\cdot(-2)}-2=\frac{1}{-12}-2=-2\frac{1}{12}$

7 0

3 years ago

After completing the fraction 8 devided 1/6 Pastel found a quotient of

Rama09 [41]

The answer is 2 be 8/16 is 2

3 0

3 years ago

Can someone solve this! Need it done soon

Airida [17]

Answer:

117.5 ft²

Step-by-step explanation:

To find the area of the shaded area, we can find the area of the square, then subtract the areas of the two semicircles.

First, we will find the area of the given square, by using the formula $lw$ , multiplying the length and width. The dimensions of this square are 14×14.

14 · 14 = 196

The area of the square is 196 ft².

We can now find the area of the two congruent half-circles. Since they are identical, we can simply find the area of one circle if it was whole. To find the area of a circle, we'll use the formula $A=\pi r^2$ . With some simple deduction, we can see that the diameter of the circle is 10 ft, so the radius would be 5 ft long. Plug our values into the formula.

A = $\pi$ 5²

We will use 3.14 for $\pi$ .

A = 78.5

The area of both the semicircles is 78.5 ft².

Now, we can subtract.

196 - 78.5 = 117.5

The area of the figure is 117.5 ft².

Good luck ^^

7 0

3 years ago

A paper manufacturer is evaluating their packing procedures. Currently, they package twelve reams of paper in a box—in three sta

olga2289 [7]

Each ream weighs 5 lb . so, reducing 10 lb means removing 2 reams from the 12. so, how do we arrange the 10 reams so that its easy to carry?
i thinks that 3 stacks will not work as it wont be a symmetric arrangement as 1 will be left out. So, 2 stacks of 5 each would be easy to carry. but the stacks should be placed in such a way that the lengths are parallel to each other and not in-line which would increase the length making it comparatively longer. its easier to hold a (2*8.5,11,2*5=17,11,17)compact box.

4 0

3 years ago

The vertical asymptote is x = ?y=a/x-h +k​

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