Determine the attributes of the hyperbola represented by this equation:
(y-21)^2/20^2-(x+20)^2/21^2=1

The vertices are A: (-41,21) and (1,21), B: (-20,0) and (-20,42), C: (-20,1) and (-20,41), D: (20,1) and (20,41).
The foci are A; (-50,21) and (10,21), B: (-20,-8) and (-20, 50), C: (-20,-10) and (-20,52), D; (20,-8) and (20,42)

Answer:

x = -8

Step-by-step explanation:

4( 3x +5 ) - 3 = 9x -7

Distribute

12x +20 -3 = 9x -7

Combine like terms

12x+17 = 9x-7

Subtract 9x from each side

12x-9x +17 = 9x-9x-7

3x +17 = -7

Subtract 17 from each side

3x+17-17 = -7-17

3x = -24

Divide each side by 3

3x/3 = -24/3

x = -8

Answer: x= -8

Step-by-step explanation:

4 ( 3x + 5 ) - 3 = 9x - 7

12x + 20 - 3 = 9x - 7

12x + 17 = 9x - 7

subtract 9x from both sides

12x + 17 - 9x = -7

3x + 17 = -7

subtract 17 from both sides

3x= -7-17

3x= -24

divide both sides by 3

x= -24/3

simplify

x= -8

Answer:

B. 2

Step-by-step explanation:

f(2) means the value of y when x = 2.

Look in the graph. Start at (0, 0), which is the point where the x-axis and the y-axis intersect. Now go 2 units to the right. That is where x = 2. Go up from there until you get to the red curve and stop. Now look to the left to see at what y-value you are. It is 2 on the y-axis. Since at x = 2, y = 2, then

f(2) = 2

Answer:

In set theory, the power set (or powerset) of a a Set A is defined as the set of all subsets of the Set A including the Set itself and the null or empty set. It is denoted by P(A). Basically, this is the combination of all subsets including null set, of a given set

Answer:

When x = 1 or -1.

Step-by-step explanation:

When the denominator x^2-1 is zero the expression is undefined.

So the values of x cannot be  1  or -1.

Answer:

[tex] \boxed{z = 3} [/tex]

Step-by-step explanation:

[tex] = > - 8z + 17 = - 13 + 2z \\ \\ = > - 8z - 2z + 17 = - 13 \\ \\ = > - 10z + 17 = - 13 \\ \\ = > - 10z = - 13 - 17 \\ \\ = > \cancel{-} 10z = \cancel{-} 30 \\ \\ = > 10z = 30 \\ \\ = > z = \frac{30}{10} \\ \\ = > z = 3[/tex]

Answer:

z = 3

Step-by-step explanation:

→Add 8z to both sides:

-8z + 17 = -13 + 2z

17 = -13 + 10z

→Add 13 to both sides:

30 = 10z

→Divide both sides by 10:

3 = z

Answer:

The height equation is:

h(t)=-16t^2 +100t+10

A) To find the maximum height, we must find the time where the velocity is 0, so we must derive it with respect to the time.

v(t) = -2*16*t + 100 = 0

       t = 100/(2*16) = 3.125s

Now we put this time in our height equation:

h(3.125s) = -16*3.125^2 + 100*3.125 + 10 = 166.25 ft.

B) The lowest heigth of the potato will be h = 0ft, when the potato hits the ground.

C) the lowest time that works for that function is t = 0s, when the potato is fired by the gun.

D) the maximum time can be finded when the potato hits the ground, afther that point the equation does not work anymore, let's find it,

h(t) = 0 = -16t^2 +100t+10

we can solve it using Bhaskara's equation:

[tex]t = \frac{-100 +- \sqrt{100^2 +4*16*10} }{-2*16} = \frac{-100 +- 103.2}{-32}[/tex]

So the two solutions are:

t = 6.3s

t = -0.1s

We need to chose the positive time, as we already discused that the minimum time that works for the equation is t = 0s.

so here the answer is t = 6.3s

E) the domain is  0s ≤ t ≤ 6.3s

The range is 0ft ≤ h ≤ 166.25 ft.

Answer:

£42.04 is the correct answer.

Step-by-step explanation:

Cost of pack of 15 bread rolls = £1.91

Cost of pack of 20 cheese slices = £2.23

She has to buy exactly twice as many cheese slices as bread rolls.

She has to make more than 100 cheese sandwiches.

Number of bread rolls required for 100 bread rolls.

Minimum 15[tex]\times[/tex]7 = 105 bread rolls are to be bought.

105 bread rolls mean 210 cheese slices but it is a pack of 20 cheese slices.

So, at least 220 cheese slices can be bought.

But, 220/2 = 110 bread rolls are not possible to be bought.

So, at least 120 (15 [tex]\times[/tex] 8 i.e. 8 packs) bread rolls have to be bought and 120 [tex]\times[/tex] 2 = 240 (20 [tex]\times[/tex] 12 i.e. 12 packs) of sandwiches have to be bought.

So, minimum amount to be spent for at least 100 cheese sandwiches

= 1.91 [tex]\times[/tex] 8 + 2.23 [tex]\times[/tex] 12 = £42.04

Answer:

£42.04

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

[tex] - 8 {x}^{2} + 24 \\ = 8( - {x}^{2} + 3) \\ [/tex]

Answer:

8

Step-by-step explanation:

-8(x^2-3)

Answer:

The answer would be D

Step-by-step explanation:

Answer:

cosΘ = [tex]\frac{9}{15}[/tex]

Step-by-step explanation:

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{15}[/tex]

The exact of the trigonometric function associated with the right triangle is cos θ = 3 / 5.

In this question we have a right triangle, whose all side lengths are known and the exact value of a trigonometric function (cosine function) associated with an angle must be found:

cos θ = x / r

Where:

If we know that x = 9 and r = 15, then the exact value of the trigonometric function is:

cos θ = 9 / 15

cos θ = 3 / 5

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Answer:

3

Step-by-step explanation:

in slope-intercept form, the slope is the x's coefficient, which in this case is 3,

so, m=3

Answer:

A closed cone has 0 verticals.. but 1 vertice

Step-by-step explanation:

Answer:

You need 14 cups of water for 6 scoops of drink mix  since it is simply double the amount of scoops

Step-by-step explanation:

(1) 7 cups water/ 3 scoops mix=7/3

(2) x cups water/6 scoops mix=x/6

(3) 7/3=x/6

(4) 42/3=x

Answer:

Opaca= 290kg   Llama=160kg

Step-by-step explanation:

x+y=450

3x=190+y

Answer:

yes it can

Step-by-step explanation:

yes

Answer:

No

Step-by-step explanation:

You need to use the Pythagorean Theorem.  This will show you if the ratio between the sides is accurate.

a² + b² = c²

8² + 11² = 13²

64 + 121 = 169

185 ≠ 169

The measurements will not fit in a right triangle.

Answer:

Step-by-step explanation:

Answer:

The correct option is;

The data for suitcase 1 have an outlier but the data for suitcase 2 does not

Step-by-step explanation:

Range of a box plot

Interquartile range (IQR) for bot suitcases we have

Here we have for suitcase 1

IQR = Q₃ - Q₁ = 12 - 8 = 4

For suitcase 2

IQR = Q₃ - Q₁ = 18 - 5 = 13

Lower outlier = Q₁ - 1.5×IQR

Higher outlier = Q₃ + 1.5×IQR

For suitcase 1 we have;

Lower outlier = 8 - 1.5×4 = 2 (No lower outlier)

Higher outlier = 12 + 1.5×4 = 18

Hence, whereby the whiskers range from 4 to 30, suitcase 1 has a higher outlier

For suitcase 2 we have;

Lower outlier = 5 - 1.5×13 = -14.5  (No lower outlier)

Higher outlier = 18 + 1.5×13 = 37.5

Hence, whereby the whiskers range from 2 to 20, suitcase 2 has no outlier.

Therefore, the correct option is the data for suitcase 1 have an outlier but the data for suitcase 2 does not.

Answer:A

Step-by-step explanation:

took the test

Answer: w=2r

Step-by-step explanation:

so let say the amount of water is y instead of w and the cup of rice is x instead of r.

so if we were to create a table we use the numbers given

x     y

1      2      so as the cup of rice increase by 1 cup the amount of water increase

2     4       by two.

3       6       so we know the slope is 2/1 so  the equation is w=2r  

Answer:

a

Step-by-step explanation:

it can be solved

Answer:

C.

Step-by-step explanation:

Answer:

Each ring costs $.18

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = mx + c

y = 5x - 7

Slope m = 5

y-intercept c = -7

Answer:

m = 5

c = -7

Step-by-step explanation:

the formula for a line is mx+c where m is the gradient and c is the intercept.

In this case:

m = 5

c = -7

Hope this helps

Good Luck

Answer: $36.8

Step-by-step explanation:

From the question, we are told that Brady and 3 friends went to lunch at Mazzio’s Pizza and that their meal cost $32, and they left a 15% tip. Their total bill will be $32 plus 15% of $32. This can be written mathematically as:

= $32 + (15% of $32)

= $32 + (15/100 × $32)

= $32 + (0.15 × $32)

= $32 + $4.8

= $36.8

Their total bill is $36.8

Answer:

The answer is 10

Step-by-step explanation:

The answer is 10 because you asked how long it would take for them to work altogether,3hrs + 7hrs is 10hrs

Answer:   last choice

In general if we have first term a[1] and common difference d, such that

a[n] = a[n-1] + d

then the explicit formula is

a[n] = a[1] + d(n-1)

First choice has d=-4 so needs a minus sign in the explicit formula.

Second choice has a=-100 so needs a negative sign for the 100.

Third choice swaps a[1] and d, oops.

IT IS D!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

-24+4v

Step-by-step explanation:

8v-24-12v

-24+4v

Answer:

c

Step-by-step explanation:

I think this is right

Answer: 12

Step-by-step explanation:

If you subtract 6 dollars from 50, you’ll get 44. 44 minus 12 three times is equal to 8

Answer:

$12

Step-by-step explanation:50-6

50-6-3(x)=8

44-3x=8

-3x=8-44

3x=36

36/3=12

Answer:

True

Step-by-step explanation:

I'm not 100% but 90%

It is true that the triangles shown in the diagram are congruent triangles.

Two triangles are considered to be congruent triangles if two triangles have similar sizes and shapes. This implies that two triangles are defined to be congruent if the lengths of their individual sides and angles are the same.

The angle-angle-side (AAS) theorem states that when two angles and any side of a triangle are identical to two angles and any side of some other triangle, then the triangles are considered to be congruent triangles.

Therefore, since these assertions are true of the triangles given, we can conclude that the two triangles are congruent triangles.

Learn more about congruent triangles here:

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Answer:

It represents the price that ray is actually paying. Instead of paying for 100% of the price, he is now only paying for 90%

Step-by-step explanation: