All categories

2 years ago

Which equation is the inverse of y = 2x2 – 8?

Mathematics

2 answers:

irakobra [83]2 years ago

7 0

Answer:

$y = \sqrt{\frac{x+8}{2}}$

Step-by-step explanation:

Here, the given equation,

$y=2x^2-8$

For finding the inverse, interchange x and y,

$x=2y^2-8$

Add 8 on both sides,

$x+8=2y^2$

Divide both sides by 2,

$\frac{x+8}{2}=y^2$

Taking square root on both sides,

$\sqrt{\frac{x+8}{2}}=y$

$\implies y = \sqrt{\frac{x+8}{2}}$

Which is the required inverse of the given equation.

goblinko [34]2 years ago

4 0

I posted an image instead.

You might be interested in

The slope of a line is 2. The y-intercept of the line is -6. Which statements accurately describe how to graph the function

Law Incorporation [45]

It’s a. Start at the y intercept and rise over run to the next point.

8 0

2 years ago

Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian

777dan777 [17]

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\B=30^o$

Applying the law of sines

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(A)}=\frac{2}{sin(30^o)}$

$sin(A)=1$

$A=90^o$

Find the measure of angle C

In a right triangle

we know that

$B+C=90^o$ ----> by complementary angles

$B=30^o$

therefore

$C=60^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}$

$c=2\sqrt{3}\ units$

therefore

The dimensions of the triangle are

$A=90^o$

$B=30^o$

$C=60^o$

$a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units$

<em>Second case</em>

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\A=30^o$

Applying the law of sines

Find the measure of angle B

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(30^o)}=\frac{2}{sin(B)}$

$sin(B)=0.25$

using a calculator

$B=14.48^o$

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

$A+B+C=180^o$

$A=30^o\\B=14.48^o$

therefore

$30^o+14.48^o+C=180^o$

$C=135.52^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{a}{sin(A)}$

substitute the given values

$\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}$

$c=5.61\ units$

therefore

The dimensions of the triangle are

$A=30^o$

$B=14.48^o$

$C=135.52^o$

$a=4\ units\\b=2\ units\\c=5.61\ units$

see the attached figure to better understand the problem

4 0

2 years ago

A random sample of 1,175 people in a certain country were asked whether they thought climate change was a problem. The sample pr

il63 [147K]

Answer: c. We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.

Step-by-step explanation:

Interpretation for 95% confidence interval :

A person can be 95% confident that the true population parameter lies in it.

By considering the given information , we have

population parameter→ p (Proportion of people who think climate change )

95 percent confidence interval = (0.146, 0.214)

Interpretation : We can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214.

So , the correct answer is

c. We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.

8 0

2 years ago

Rework problem 9 from section 3.2 of your text, involving independent and disjoint events. For this problem, assume that Pr[A∪B]

tatuchka [14]

Two events are said to be Disjoint or Mutually Exclusive if the two events can not happen at the same time.For example when we throw a die getting an even number is disjoint to getting an odd number.

I.e Probability(A∩B)=0

Let me explain this concept through venn diagram.

Pr[A∪B]=0.7, Pr[A]=0.25

Since events are Disjoint

Pr[A∩B]=0

Pr[A∪B]=Pr[A] + Pr[B]

0.7=0.25 +Pr[B]

0.7-0.25=Pr[B]

⇒Pr[B]=0.45=45/100=9/20

Now events are said to be independent if Pr[A and B]=Pr[A] ×Pr[B]

Events are said to be independent if occurrence of one is not affected by occurrence of other.For example getting multiple of 2 as one event and getting multiple of 3 as second event when we throw a die.

Pr[A∪B]=0.7, Pr[A]=0.25

Pr[A∪B]= Pr[A]+ Pr[B]-Pr[A∩B]

But Pr[A∩B]= Pr[A] ×Pr[B]

⇒Pr[A∪B]= Pr[A]+ Pr[B]- Pr[A] ×Pr[B]

⇒0.7=0.25+p-0.25×p

⇒0.7-0.25=p- 0.25 p

⇒0.45=0.75 p

⇒p= 0.45/0.75

⇒p =3/5

5 0

2 years ago

What is the product of 5.86 × 10–7 and 3.1 × 104 1. Write the expression: (5.86 × 10–7)(3.1 × 104) 2. Rearrange the expression:

Reil [10]

Answer:

The value of the exponent of the base 10 for this product is -2.

Step-by-step explanation:

$5.86\,\,10^{-7}\,\,*\,\,3.1\,\,10^4=18.166\,\,10^{-7+4}=18.166\,\,10^{-3}$

Now, in order to represent this number in scientific notation, we need to reduce the coefficient 18.166 to a coefficient larger or equal to 1 and smaller strictly than 10, by using division or multiplications by powers of 10. In order to reduce it to 1.8166, we need to divide the original 18.166 by ten so we do the following in order not to change the given number (multiply and divide by ten at the same time):

$\frac{18.166\,\,10}{10} \,10^{-3}=1.8166\,*\,10\,*\,10^{-3}=1.8166\,\,10^{-2}$

3 0

2 years ago

Read 2 more answers