Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y plus five squared divided by nine = 1

ANSWER

[tex]x = 4.1[/tex]

EXPLANATION

The line segment connecting the center and the chord bisects the chord.

Half of the length of this chord forms one of the shorter legs of the right triangle.

[tex] = \frac{15.6}{2} = 7.8[/tex]

We use the Pythagoras Theorem to obtain;

[tex] {x}^{2} + {7.8}^{2} = {8.8}^{2} [/tex]

[tex] {x}^{2} = {8.8}^{2} - {7.8}^{2} [/tex]

[tex] {x}^{2} = 16.6[/tex]

[tex]x = \sqrt{16.6} [/tex]

[tex]x = 4.1[/tex]

Answer:

  yellow area ≈ 48.3 cm²

Step-by-step explanation:

The area of the yellow region is the difference between the area of a square with side length 15 cm and the area of a quarter circle with radius 15 cm. It is helpful to know the formulas for area for a square and a circle.

  Area of the square = s² = (15 cm)² = 225 cm²

The area of the full circle is ...

  Area of circle = πr² = π(15 cm)² = 225π cm²

Then the area of 1/4 of that circle will be ...

  Area of quarter circle = (225π cm²)/4 = 56.25π cm²

--

The difference of these areas is the yellow area:

  yellow area = 225 cm² - 56.25π cm² ≈ 48.2854 cm²

  yellow area ≈ 48.3 cm²

Answer: $10

Step-by-step explanation:

Let's analize the information given: We know that  she had $94 to spend on 8 books and after buying these books she had $14. So, we need to calculate the amount of money she spent. Subtract $94 and $14:

[tex]Total\ spent=\$94-\$14\\Total\ spent=\$80[/tex]

Then, to calculate the cost of each book, we need to divide the "Total spent" by 8:

[tex]cost\ of\ each\ book=\frac{Total\ spent}{8}\\\\cost\ of\ each\ book=\frac{\$80}{8}\\\\cost\ of\ each\ book=\$10[/tex]

Answer:

D. Cylinder

Step-by-step explanation:

Consider the rectangle that has to be rotated about the axis as shown in the picture. In attached diagrams this rectangle is black rectangle ABCD.

While rotating each point of the rectangle will describe the circle. The circles with the greatest radii will be circles made by the points from the side that is opposite to the side on the axis of rotation.

Formed figure appear to be cylinder.

Answer:

Option 3.

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable.

The argument of a square root can take negative values, then:

So x+3 must be greater than 0. So x+3> 0 -> x> -3.

Then, the domain of the function is: [-3, +inf)  

The range of a function is the complete set of all possible resulting values of the dependent variable after we have substituted the domain.

So in this case, we know that the square root always is going to throw a positive value, but given that the square rooth is multiplied by a minus, the result is always going to be negative.

The least value the square root can take is 0, so in that case, the maximum value the function can take is y = -2.

So the range is (-inf, -2]

So, the correct option is option 3

Answer:

Explanation:

1) Principal quantum number, n = 2

2) Second quantum number, ℓ

The possible values of ℓ are from 0 to n - 1.

Hence, since n = 2, there are two possible values for ℓ: 0, and 1.

This gives you two shapes for the orbitals: 0 corresponds to "s" orbitals, and 1 corresponds to "p" orbitals.

3) Third quantum number, mℓ

The possible values for mℓ are from - ℓ to + ℓ.

Hence, the poosible values for mℓ when n = 2 are:

4) Fourth quantum number, ms.

Therfore the full set of possible states (different quantum number for a given atom) for n = 2 is:

That is a total of 8 different possible states, which is the answer for the question.

-4 x -4d=16d

-4 x-5=20

16d+20

Answer: -36d

Step-by-step explanation:

-4(-4d-5)

You have to multiply -4x-4d= -16d

Then do -4x5=-20

After you have to solve -16-20d

Which equals to -36d

Answer:

  a. 3 (see below for explanation)

  b. Ln = 4 + 3(n -1)

  c. 48

  d. dn = 6n +2

Step-by-step explanation:

a. The common difference is found by subtracting any given term from the next one: 7 -4 = 3, or 10 -7 = 3. The common difference is 3.

__

b. The general expression for an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 + d(n -1)

Here, the first term is 4 and the common difference is d. We choose to name the n-th term of Levy's sequence "Ln", so we can fill in the numbers to get ...

  Ln = 4 + 3(n -1)

__

c. We can call the terms of Zack's sequence Zn, so we have ...

  Zn = 3·Ln = 3·(4 + 3(n -1)) = 12 +9(n -1)

Putting 5 where n is in this equation, we find ...

  Z5 = 12 +9(5 -1) = 48

The 5th term of Zack's sequence is 48.

__

d. The difference of n-th terms of the two sequences is ...

  dn = Zn -Ln = (3·Ln) - Ln = 2Ln = 2(4 +3(n -1)) = 8 +6(n -1)

  dn = 6n +2

The distance between him and school is 1.59 miles. Of course this distance is linear to make this problem simple. He walks with a speed of 3 miles per hour or 0.00083 mile per second.

To calculate time from distance and speed we use this formula: [tex]t=\frac{d}{s}=\frac{3mil}{0.00083mil/s}\approx3614.46sec[/tex] seconds. To convert minutes we divide number of second by 60. [tex]t\div60=3614.46sec\div60\approx\boxed{60.24min}\approx\boxed{1h}[/tex].

It will take him approximately 60 minutes to get to school.

Answer:

20 minutes

Step-by-step explanation:

The wording of this question is a bit strange.  Are you saying that Zeke can walk to school 3 times per hour?  

If so, then the total distance he'd walk in 1 hour would be 3(1.59 miles), or

4.77 miles.  So he walks 4.77 mph.

How long to talk to school?  Divide 1.59 miles by 4.77 mph.  The result is:

1/3 hour or 20 minutes.

Answer:

A

Step-by-step explanation:

sin is opposite/hypotenuse, which is 24/26, simplifying to 12/13

For this case, we have that by definition:

[tex]Sin (C) = \frac {24} {26}[/tex]

That is, the sine of angle C will be given by the leg opposite the angle C divided by the hypotenuse of the traingule.

[tex]Sin (C) = \frac {24} {26}[/tex]

Simplifying:

[tex]Sin (C) = \frac {12} {13}[/tex]

Answer:

Option A

For this case we have the following function:

[tex]f (x) = 7x ^ 2 + 4[/tex]

By definition, we have that a linear equation is of the form [tex]y = mx + b[/tex]

On the other hand, a quadratic equation is of the form[tex]y = ax ^ 2 + bx + c[/tex]

Then, the given equation is not a linear equation, it is not of the form [tex]y = mx + b[/tex]

Answer:

No, the equation is not linear. It is not of the form [tex]f (x) = mx + b.[/tex]

Hey there!

Here goes your answer ↓

Question:- State whether the given equation or function is linear. Write yes or no. Explain your reasoning. f(x) = 7x² + 4

(a) Yes, the equation is linear. It is of the form f(x) = m + b

(b) Yes, the equation is linear form. It is of the form f(x) = mx + b.

(c) No, the equation is not linear. It is in the form x + y = c.

(d) No, the equation is not linear. It is not of the form f(x) = mx + b.

Answer :- Option (D)

Explanation :-

Given equation :- f(x) = 7x² + 4

•The form of any equation should be → y - mx + b

The given equation does not satisfy the above rule, and hence it is not a linear equation.

Hope it helps.

Have a great day ahead!

Answer:

  see below

Step-by-step explanation:

Each point moves to a location 3 times its current distance from the center of dilation. The dilated figure connects those moved vertices.

___

In the attached figure, the orange lines show how the points move to their new location (3 times the original distance). The blue lines connect the dots to make the dilated figure.

Answer:

  ∠H = 120°

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary:

  ∠H +∠T = 180

  (2x +60) + (x +30) = 180

  3x = 90 . . . . . . . subtract 90, collect terms

  x = 30 . . . . . . . . divide by the coefficient of x

Then the measure of angle H is ...

  ∠H = 2·30 +60 = 120 . . . . . degrees

ANSWER

D. 22-8√5

EXPLANATION

We want to expand

[tex](2 \sqrt{5} - 4)(3 \sqrt{5} + 2)[/tex]

We use the distributive property to obtain,

[tex]2 \sqrt{5} (3 \sqrt{5} + 2) - 4(3 \sqrt{5} + 2)[/tex]

We expand to get,

[tex]6(5) + 4 \sqrt{5} - 12 \sqrt{5} - 8[/tex]

Simplify to get,

[tex]22 - 8 \sqrt{5} [/tex]

The correct answer is D.

Depends really:

If you think about it everywhere has a different temperature my lowest on Friday was 45 degrees and that was the lowest that week.

SO PLEASE CLARIFY

Answer:

3 * -1 x 3   +  5 * 3 - 6 = 0

Step-by-step explanation:

Replace (a)s and (b)s with the given numbers

so (a)s becoming -1 and (b)s becoming 3.

this leads up to the given expression:

3 * -1 x 3   +  5 * 3 - 6

3 times -1 = -3 multiplied by that 3 is -9

since a negative multiplied by a positive is a negative.

With that you have -9 +  5  x 3 - 6

take 5 and 3, multiply them to get 15 and subtract 6.

this ends up with '9'

Lastly ending up with -9+9 = 0

The value of 3ab + 5b - 6 = 0.

Let a = -1 and b = 3.

If 3ab + 5b - 6 then

substituting the values of a and b in the given equation, we get

[tex]3 *( -1) * (3) + 5 * (3) - 6[/tex]

3a = [tex]3 * -1 = -3[/tex]

3ab = [tex]-3*3=-9[/tex]

Then, [tex]3*(-1)*3 =-9[/tex] and

5b = [tex]5*3=15[/tex]

Therefore, we get 3ab + 5b - 6 = 0.

since a negative multiplied by a positive is a negative.

With that you have [tex]-9 + 5 * 3 - 6[/tex]

take 5 and 3, multiply them to get 15, and subtract 6.

this ends up with '9'

Lastly ending up with -9 + 9 = 0

Therefore, the value of 3ab + 5b - 6 = 0.

To learn more about finding the values

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Final answer:

The statement is true, as adding the probabilities of walking with the beagle (20%) and with the golden retriever (70%) correctly calculates the probability of walking with any dog as 90%.

Explanation:

The question involves calculating the probability of an event occurring, specifically the event of a neighbor walking with any dog. To determine whether the statement "We could find the probability of walking with a dog by adding P(beagle) and P(golden retriever)" is true or false, let's examine the given percentages. According to the information, the neighbor walks 20% of the time with her beagle, 70% of the time with her golden retriever, and 30% of the time she walks alone.

Adding the probabilities of walking with the beagle (20%) and with the golden retriever (70%) gives us a total of 90%. This calculation suggests that the neighbor walks with a dog 90% of the time, which is a valid way to find the probability of walking with any dog. Hence, the statement is true. However, it is important to ensure that the events (walking with the beagle and walking with the golden retriever) are exclusive and do not overlap, which is implied in this scenario.

Answer:

The volume of the stack is [tex]425.250\pi\ mm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder (DVD stack) is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the stack

Find the area of the base B

The area of the base B is equal to the area of the larger circle minus the area of the hollow center

[tex]B=\pi (r2^{2} -r1^{2})[/tex]

we have

[tex]r2=120/2=60\ mm[/tex] -----> the radius is half the diameter

[tex]r1=15/2=7.5\ mm[/tex] -----> the radius is half the diameter

substitute

[tex]B=\pi (60^{2} -7.5^{2})[/tex]

[tex]B=3,543.75\pi\ mm^{2})[/tex]

Find the height of the stack

[tex]h=100*(1.2)=120\ mm[/tex]

Find the volume

[tex]V=(3,543.75\pi)(120)=425.250\pi\ mm^{3}[/tex]

Answer:

b) .474

Step-by-step explanation:

If 62% go to a four-year college, that means that those who don't represent 38% of the high-school graduates.

You pick up someone who is NOT going to a four-year college (so, he's among the 38%)... what's the chance he's in the 18% of the whole high-school graduates population that found a job?

To calculate that probability, we have to divide 18% by 38%.

P = 18% / 38% = 0.4736, so 0.474

Since we are sure he doesn't go to a four-year college, there's 47.4% of chances he finds a job.

Answer:

15.50+n=325.00

Step-by-step explanation:

15.50+what she had in the bank already = what she has now

Answer:

The answer is $15.50 + n = $325.00.

Step-by-step explanation:

Fifteen dollars plus "n" (her account balance before the deposit) equals $325.00. Hope this helps! :D

Answer:

[tex]f(x)=3^x[/tex]

Step-by-step explanation:

From the table;

When x=2, [tex]y=9=3^2[/tex]

When x=3, [tex]y=27=3^3[/tex]

When x=4, [tex]y=81=3^4[/tex]

We can infer from the pattern that;

[tex]f(x)=3^x[/tex]

Answer:

The number of faces is 29

Step-by-step explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

[tex]V- E + F = 2[/tex]

In this problem we have

[tex]V=16[/tex]

[tex]E=43[/tex]

Substitute in the formula and solve for F

[tex]16- 43 + F = 2[/tex]

[tex]-27 + F = 2[/tex]

[tex] F = 2+27[/tex]

[tex] F = 29[/tex]

Answer: Option C

[tex]g(x) = 4 ^ x-1[/tex]

Step-by-step explanation:

If we have a function f(x) and we want to move its graph vertically then we apply the transformation:

[tex]g (x) = f (x) + k.[/tex]

So:

If [tex]k> 0[/tex] the function g(x) will be the function f(x) displaced k units up

If [tex]k <0[/tex] the function g(x) will be the function f(x) displaced k units down.

In this case we know that the graph of f(x) moves 5 units up.

then [tex]k> 0[/tex] and [tex]k = 5[/tex]

Therefore [tex]g (x) = f(x) +5[/tex]

[tex]g(x) = 4 ^ x - 6 +5\\\\g(x) = 4 ^ x-1[/tex]

[tex]\displaystyle\\\text{If we have the radius of the circle, we use the formula: }\\V=\pi R^2\cdot h\\\\\text{If we have the diameter of the circle, we use the formula: }\\\\V=\frac{\pi D^2}{4}\cdot h\\\\\text{It is given:}\\{\bf D=3~in}\\{\bf h=3~in}\\\\\text{Is required:}\\{\bf V=?}\\\\\text{Solution:}\\\\V=\frac{\pi D^2}{4}\cdot h=\frac{\pi 3^2}{4}\cdot 3=\frac{27\pi}{4}=\boxed{\bf6.75\pi~in^2}[/tex]

Answer:

  (0, -3), (-1, 1)

Step-by-step explanation:

The equation can be simplified to a form more helpful for graphing.

Subtract 7:

  24x +18 = -6y

We note that all of the coefficients are multiples of 6, so we can divide by -6:

  y = -4x -3

This is slope-intercept form, so it tells you that the y-intercept is -3, which means one point on the graph is (0, -3).

The slope is -4, so an x-value in the negative direction will give a more positive y-value. We can choose x=-1 and find y:

  y = -4(-1) -3 = 4 -3 = 1

Then another point on the graph is (-1, 1).

Two points on the graph are (0, -3) and (-1, 1).

Answer:

y=-2/3x -6

Step-by-step explanation:

y=-6 so b=-6

rise/run=-2/3

Put that into an equation of y=mx+b and you get y=-2/3x -6

Answer:

2x

Step-by-step explanation:

x        ?

---- = ------

8          16

To get from 8 to 16, we multiply by 2

Multiply x/8 by 2 on the top and bottom

x/8 * 2/2 = 2x/16

? = 2x

What number do

You need help with

Answer:

A

Step-by-step explanation:

sin(60) can be simplified into sqrt(3)/2.

The sine of 60° is √3/2.

The ratio between the hypotenuse and the leg opposite the angle, when viewed as a component of a right triangle, is the trigonometric function for an acute angle.

Given

height = √3

hypotenuse = 2

sin θ = height/ hypotenuse

sin θ = √3/2

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C is the median.

to find the median we need to put all the numbers given in order from smaller to largest

12, 18, 34, 55, 59, 67, 80, 80

then find the middle number of these

well we have to middle numbers 59 and 55

so we need to find the mid number between these two which 57.

The answer to this question is 57

hope this helped

Answer:

The answer is 18