Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).

Answer:

The correct option is B.

Step-by-step explanation:

The given expression is

[tex]\frac{r^9}{r^3}[/tex]

According to the property of exponent,

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

Using this property of exponent, we get

[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]

[tex]\frac{r^9}{r^3}=r^{6}[/tex]

The expression [tex]r^{6}[/tex] is equivalent to the given expression.

Therefore the correct option is B.

To answer this question you will have to combine like terms.

3z-5+2z=25-5z

Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z

Now you have -5+5z=25-5z

Now you will go ahead and distribute since you can't combine anymore on certain sides.

You can add 5 to 25 on the other side: 25+5=30

Then add 5z to 5z on the other side: 5z+5z=10z

So now your equation should look like this: 10z=30

From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3

So your solution should come to: z=3

we have  

[tex]0.5-\left|x-12\right|=-0.25[/tex]  

we know that        

The absolute value has two solutions

Subtract  [tex]0.5[/tex] both sides

[tex]-\left|x-12\right|=-0.25-0.5[/tex]  

[tex]-\left|x-12\right|=-0.75[/tex]  

Step 1

Find the first solution (Case positive)

[tex]-[+(x-12)]=-0.75[/tex]

[tex]-x+12=-0.75[/tex]

Subtract  [tex]12[/tex] both sides

[tex]-x+12-12=-0.75-12[/tex]

[tex]-x=-12.75[/tex]

Multiply by [tex]-1[/tex] both sides

[tex]x=12.75[/tex]

Step 2

Find the second solution (Case negative)

[tex]-[-(x-12)]=-0.75[/tex]

[tex]x-12=-0.75[/tex]

Adds  [tex]12[/tex] both sides

[tex]x=-0.75+12[/tex]

[tex]x=11.25[/tex]

Statements

case A) The equation will have no solutions

The statement is False

Because the equation has two solutions------> See the procedure

case B) A good first step for solving the equation is to subtract 0.5 from both sides of the equation

The statement is True ----->  See the procedure

case C) A good first step for solving the equation is to split it into a positive case and a negative case

The statement is False ----->  See the procedure

case D) The positive case of this equation is 0.5 – |x – 12| = 0.25

The statement is False

Because the positive case is [tex]0.5-(x-12)=-0.25[/tex] -----> see the procedure

case E) The negative case of this equation is x – 12 = –0.75

The statement is True -----> see the procedure

case F) The equation will have only 1 solution

The statement is False

Because The equation has two solutions------> See the procedure

The equation 0.5 - |x - 12| = -0.25 has no solutions because an absolute value cannot be negative. Attempting to split the equation into positive and negative cases or solving for x is fruitless because the left side of the equation will always be at least 0.5.

When solving the equation 0.5 - |x - 12| = -0.25, we can immediately notice that it will have no solutions because the absolute value is always non-negative, and therefore the left-hand side cannot be less than 0.5. Hence, subtracting 0.5 from both sides is not a good first step. Instead, you would typically isolate the absolute value on one side, but given that the equation equals a negative number, we know it has no solutions without additional steps.

Additionally, splitting the equation into a positive case and a negative case isn't useful here, because no matter what's inside the absolute value, the output cannot lead to a negative result, thus making both cases moot.

The statements that say "The positive case of this equation is 0.5 - |x - 12| = 0.25" and "The negative case of this equation is x - 12 = -0.75" are incorrect as they misinterpret how the absolute value works. Lastly, the equation does not have any solution, so it cannot have only one solution.

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7x4 = 28

5 x z = 28

z = 28/5 = 5.6

Answer: [tex]x-5=\pm 3[/tex] will be the next step of the given expression.

Step-by-step explanation:

Since, Given expression is |x-5|+2=5

On solving the above expression,

Step 1.  [tex]|x-5|+2=5[/tex]

step 2. [tex]|x-5| = 5-2[/tex]

Step 3. [tex]|x-5| = 3[/tex]

Step 4. [tex]x-5=\pm 3[/tex] (because mode takes both positive and negative values)

The initial value of a function is the value of the function when x = 0

 o when x = 0, y = 2 so the initial value is 2

Answer:

2

Step-by-step explanation:

The initial value is what you start off with, so it is 2! :)

A = hours for plan A
B = hours for plan B

Monday: 6A + 5B = 7
Tuesday: 2A + 3B = 3

use elimination by multiplying the 2nd equation by 3.

Doing that we get 3(2A + 3B = 3) = 6A + 9B = 9

So the two equations are now:
6A + 9B = 9

6A + 5B = 7

Subtract and we have 4B = 2

B = 2/4 = 1/2 of an hour

Now put 1/2 back into either equation to solve for A

6A + 5(1/2) = 7
6A + 5/2 = 7
6A = 14/2 -5/2
6A = 9/2
divide by 6 to get A = 9/12 = ¾  hours

Plan A = 3/4 hour

 Plan B = 1/2 hour

Final answer:

By setting up and solving a system of equations, we find that Plan A lasts for 45 minutes per session and Plan B lasts for 30 minutes per session.

Explanation:

Solving for the Duration of Workout Plans

We have information regarding the total duration of workouts and the number of clients for two consecutive days. To find the duration of each workout plan, we use a system of equations. Let A represent the duration of Plan A and B represent the duration of Plan B. The equations based on the given information are:

6A + 5B = 420 minutes (7 hours on Monday)

2A + 3B = 180 minutes (3 hours on Tuesday)

Multiplying the second equation by 3 gives us:

6A + 9B = 540

Subtracting the first equation from this result gives us:

4B = 120 minutes, therefore, B = 30 minutes

Now we substitute B = 30 in the first equation:

6A + 150 = 420, which simplifies to 6A = 270, hence A = 45 minutes

Thus, Plan A lasts for 45 minutes and Plan B lasts for 30 minutes.

Answer:

Transitive

Step-by-step explanation:

Just took the test

Hope it helps :)

Answer:

∠TSR = 93°

Step-by-step explanation:

In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]

∠S = [tex]\frac{131+43}{2}[/tex]

     = [tex]\frac{174}{2}[/tex]

     = 87°

Now we have to find the measure of ∠RST

Since ∠QSR + ∠TSR = 180° [ supplementary angles]

87° + ∠TSR = 180°

∠TSR = 180 - 87 = 93°

Therefore, m∠TSR = 93° is the answer.

If

N = a (mod 10)

N = b (mod 13)

gcd(10,13) = 1

then

N = 10 bx + 13 ay (mod 130)

Where

10x + 13y = 1

-> (10x + 13) (mod 2) = 1 (mod 2)

-> y (mod 2) = 1

y = -3, x = 4

-> N = 40b – 39a (mod 130)

It is given that  ra + sb should be non-negative:

N = 40b – 39a (mod 130)

N = 40b + (130 – 39)a (mod 130)

N = 40b + 91a (mod 130)

Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).

Final answer:

To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.

Explanation:

To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:

n = 10k + a, where k is some integer

n = 13l + b, where l is some integer

Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.

Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).

Final answer:

The range of the given set of heights is 50 cm, which is determined by subtracting the smallest height (132 cm) from the largest height (182 cm) in the set.

Explanation:

The range of a set of numbers is the difference between the largest and the smallest numbers in the set. To find the range of the given heights in centimeters, you first identify the largest and smallest numbers in the set {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}. The smallest height is 132 cm, and the largest is 182 cm.

Now, subtract the smallest value from the largest value to determine the range:

Range = Largest value – Smallest value

Range = 182 cm – 132 cm

Range = 50 cm

Therefore, the range of the given set of heights is 50 cm.

Equations:
8c + 4t = 45
3c + 2t = 20

Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40

Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)

Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20

2t=12.50

T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)

 Table = 6.25 each

Chair = 2.50 each

Check:

3(2.50) + 2(6.25) =

7.50 +12.50 = 20

8(2.50) + 4(6.25) =

20.00 + 25.00 = 45.00

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

Number of cards in a deck = 52

Number of heart = 13

Number of king = 4

But we know that heart contains one king too.

So, to avoid double counting we have to subtract 1 from it.

so, Number of king = 3

So, Probability that Sam picked a heart or a king is given by

[tex]\frac{13}{52}+\frac{3}{52}\\\\=\frac{16}{52}\\\\[/tex]

Hence, Option 'B' is correct.

Answer:

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Step-by-step explanation: I just took the test and got it right.