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math




math geniuses pls help!!!




pls check other questions as well thanks,!

The equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

The foci are given as:

(1, 7) and (1, -13)

The foci of a hyperbola are represented using: (m, n+p) and (m, n-p)

Where the center of the hyperbola is (n,p)

By comparison, we have:

m = 1

n + p = 7

n - p =13

Where n = ae

The solution to the above system of equations is

m = 1, n = 10 and p = -3

The directrix is given as:

y = 64/10

The directrix is represented as:

y = a/e

So, we have:

a/e = 64/10

Substitute n = ae in n = 10

ae = 10

Solving ae = 10 and a/e = 64/10, we have:

a = 8 and e = 10/8

To calculate b, we make use of:

[tex]b = a\sqrt{(e^2 - 1)[/tex]

So, we have:

[tex]b = 8\sqrt{(\frac{10}{8}^2 - 1)[/tex]

Evaluate

b = 8 * 0.75

b = 6

The equation of the hyperbola is then calculated using:

[tex]\frac{(y - p)^2}{a^2} -\frac{(x - m)^2}{b^2} = 1[/tex]

This gives

[tex]\frac{(y + 3)^2}{8^2} -\frac{(x - 1)^2}{6^2} = 1[/tex]

Evaluate

[tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

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Answer:

( x-7)^2+(y-6)^2 = 25

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2

where ( h,k) is the center and r is the radius

( x-7)^2+(y-6)^2 = 5^2

( x-7)^2+(y-6)^2 = 25

Answer:

(x-7)^2+(y-6)^2=25

Explanation:

If I were you, I would mark 7 as x and 6 as y. Whatever is in your parenthesis for center of the circle, do the opposite in your equation. Since you have positive 7 & positive 6, turn those into negative numbers for your equation. And for the radius, just times it two times. So 5•5=25

the following statement is true

The values of x given the following expression are ∛243/7 and 7^1/4

Given the following expression

7x³ =243
x³ = 243/7

x = ∛243/7

For the expression

5x⁴ + 7 = 42
5x⁴  = 42 - 7

5x⁴ = 35

x⁴ = 7

x = 7^1/4

Hence the values of x given the following expression are ∛243/7 and 7^1/4

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The equation of the circle of radius 4 and center at (-1, 1) is given as follows:

[tex](x + 1)^2 + (y - 1)^2 = 16[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem:

Hence, the equation is given as follows:

[tex](x - (-1))^2 + (y - 1)^2 = 4^2[/tex]

[tex](x + 1)^2 + (y - 1)^2 = 16[/tex]

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The simplified value of the exponential expression is 2.

Here we need to simplify the expression:

[tex]16^{1/4}[/tex]

First, you need to remember that:

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

Then we can just write:

[tex]16^{1/4} = \sqrt[4]{16}[/tex]

And now, you can remember that:

2*2 = 4

Then:

2*2*2*2 = 4*4 = 16

From this, we can conclude that:

[tex]2^4 = 16\\\\\sqrt[4]{16} = 2[/tex]

So we conclude that the simplified value is 2.

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Answer:

The simplified value of the exponential expression is 2.

How to get the simplified expression?

Here we need to simplify the expression:

First, you need to remember that:

Then we can just write:

And now, you can remember that:

2*2 = 4

Then:

2*2*2*2 = 4*4 = 16

From this, we can conclude that:

So we conclude that the simplified value is 2.

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Step-by-step explanation:

the last option is your answer

Answer:

6 years ago

Step-by-step explanation:

[tex]6(14-x)=54-x\\84-6x=54-x\\30-6x=-x\\30=5x\\6=x[/tex]

So, Pete's grandfather was 6 times as old as Pete 6 years ago. This means that when Pete was 8 years old, his grandfather was 48 years old.

Answer:

14

Step-by-step explanation:

40 plus 2 is 42

42 divided by 3 is 14

Answer:

B) D) E)

Step-by-step explanation:

Basically, the more days missed, the lower their grades are, so it is a negative linear relationship that has no clusters or outliers.

Answer:

hope this will help you

[tex] \frac{180}{t} = \frac{?}{4} \\ t = 180 \times 4 \\ t = 720[/tex]

Answer:

3rd one

Step-by-step explanation:

Answer:

$10.50

Step-by-step explanation:

2/3 of $21 = $14

1/4 of $14 = $3.50

$14 - $3.5 = $10.50

Answer:

D. 57

PLEASE GIVE BRAINLIEST THANK YOU!!!

The option that best describes independent events is the results of all previous events do not affect the probability of future events.

Independents events are events whose occurrence do not depend on each other. They are random events.

For example, there is no relationship between the the colour of shoes you wear and the chances that it would rain. Thus, they are independent events.

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Answer:

D ✔️

Step-by-step explanation:

"The results of all previous events do not affect the probability of future events."

Answer:

discrete?

according to probability of basic things we know that there are more people different than same so there is more than enough probability of those sizes being discrete.

Answer:

1/2¹⁵ or 2⁻¹⁵

Step-by-step explanation:

2³ / (2⁶)³
2³ / 2¹⁸ (The exponents multiply in such cases)
1 / 2⁽¹⁸⁻³⁾
1/2¹⁵ or 2⁻¹⁵

Answer:

area=112

perimeter=56

Answer:

60 ft³

Step-by-step explanation:

Concepts

The volume of any prism is represented as Bh, where B = Area of the Base and h = height of the prism.

Application

In this case, we're given the area of the base as five feet² and the height as 12 feet. Now, we just multiply these two numbers to get the volume.

Solution

Answer:

We are given a length of 9 cm and a width of 4 cm and we are also told that it our shape is a rectangle.  This means that we are able to use the rectangle formula which is [tex]A=l*w[/tex].

Therefore, we can just multiply 9 cm by 4 cm and we get [tex]A = 36\ cm^2[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

Getting sum 6 when rolling two dice

The number of stray cats in the town in t=0 years will be 243.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The given function is:-

[tex]f(t) = 243(\dfrac{1}{3})^t[/tex]

f(t) is representing the number of the stray cats in t years so in t=0 years the number of the cats will be:-

[tex]f(t) = 243(\dfrac{1}{3})^0= 243[/tex]

f(t) = 243 cats

It states that initially at t=0 years there were 243 cats in the town.

Therefore the number of stray cats in the town in t=0 years will be 243.

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Work Shown:

[tex]-4(d-2) < -12\\\\-4d+8 < -12\\\\-4d < -12-8\\\\-4d < -20\\\\d > -20/(-4)\\\\d > 5[/tex]

In the second to last step, the inequality sign flips because we divided both sides by a negative number.

Multiplication is the process of multiplying. The amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given a medicine provides 3.6 milligrams of medicine. Therefore, the amount of medicine the dog will have in a week is,

The amount of medicine = 3.6milligrams × 7 = 25.2 milligrams

Hence, the amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.

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Answer:

[tex]x = 0[/tex]

[tex]y = 7[/tex]

The distance between the points (9, –6) and (–4, 7) will be 13√2. Then the correct option is C.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D² = (x - p)² + (y - q)²

The points are (9, –6) and (–4, 7). Then the distance will be

D² = (-4 - 9)² + (7 + 6)²

D² = 13² + 13²

D² = 169 + 169

D² = 338

D = √338

D = 13√2

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Considering the given table, it is found that he recorded 35 observations, hence option B is correct.

We have to look at the number of rows and columns the table. The table has 7 rows, each with 5 columns, hence the number of observations is given by:

N = 7 x 5 = 35.

Hence option B is correct.

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