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4 years ago

11

What are the domain restrictions of a + 1 / a^2-5a-36?

1 answer:

velikii [3]4 years ago

3 0

All real numbers except -4 and 9.

The domain of an expression is the range of all values for which the expression is defined. Looking at the expression, it will legal everywhere except when a^2 - 5a - 36 is equal to 0. Since that's a quadratic equation, we can use the quadratic formula to find where its value is 0, giving -4 and 9.

Therefore the domain of the expression is, All real numbers except -4 and 9.

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A movie Theater charges $6.50 for morning tickets and $8.75 for night tickets the theater sold 378 tickets for a total amount of

Xelga [282]

Answer:

The number of sold morning tickets are 168.

Step-by-step explanation:

Given,

Total number of tickets = 378

Total earned amount = $2929.50

Charge of each morning ticket = $6.50

Charge of each night ticket = $8.75

Solution,

Let the number of morning tickets be 'x'.

And also let the number of night tickets be 'y'.

So, the total number of tickets is the sum of number of morning tickets and number of evening tickets.

So, framing in equation form, we get;

$x+y=378\ \ \ \ equation\ 1$

Again, Total earned amount is the sum of number of morning tickets multiplied with charge of each ticket and number of evening tickets multiplied with charge of each ticket.

So, framing in equation form, we get;

$6.50x+8.75y=2929.50\ \ \ equation\ 2$

On multiplying equation 2 by 100 on both side, we get;

$100(6.50x+8.75y)=2929.50\times100\\\\650x+875y=292950\ \ \ \ equation\ 3$

Now multiplying equation 1 by '650', we get;

$650(x+y)=378\times650\\\\650x+650y=245700\ \ \ \ equation\ 4$

Now subtracting equation 4 from equation 3, we get;

$(650x+875y)-(650x+650y)=292950-245700\\\\650x+875y-650x-650y=47250\\\\225y=47250\\\\y=\frac{47250}{225}=210$

Now substituting the value of'y' in equation 1, we get;

$x+y=378\\\\x+210=378\\\\x=378-210=168$

Hence The number of sold morning tickets are 168.

Whereas The number of sold night tickets are 210.

5 0

3 years ago

(100 pts.) Pre-Al Ratios and Proportionality, check img attactched

uysha [10]

Answer:

16

Step-by-step explanation:

Make a proportion:

66/12 = (104-r)/r

Simplify:

r = 16

8 0

3 years ago

Read 2 more answers

Jen spent $35 at the mall and now has $76 left. How much money did Jen have before she went shopping? Construct an equation to r

Levart [38]

Answer:

111

Step-by-step explanation:

x-35=76

x=111

4 0

3 years ago

Read 2 more answers

The area of triangle ABC is 3√2 square inches. Find the measure of the acute angle, A, if b = 9 meters and c = 2 meters.

taurus [48]

Answer:

$A\approx 28^{\circ}$

Step-by-step explanation:

Please find the attachment.

We have been given that area of triangle ABC is 3√2 square inches.

$\text{Area}=\frac{1}{2}\text{Base}\times \text{height}$

We know that area of triangle an be found using trigonometry as:

$\text{Area}=\frac{1}{2}\times c\times h$

$\text{sin}(A)=\frac{h}{9}\\h=9\cdot \text{sin}(A)$

$3\sqrt{2}=\frac{1}{2}\times 2\times 9\cdot \text{sin}(A)$

$3\sqrt{2}=9\cdot \text{sin}(A)$

$9\cdot \text{sin}(A)=3\sqrt{2}$

$\text{sin}(A)=\frac{3\sqrt{2}}{9}$

$\text{sin}(A)=\frac{\sqrt{2}}{3}$

Now, we will use inverse sine to find the value of angle A as:

$A=\text{sin}^{-1}(\frac{\sqrt{2}}{3})$

$A=28.1255057^{\circ}$

$A\approx 28^{\circ}$

Therefore, the measure of angle A is approximately 28 degrees.

3 0

3 years ago

((write an equation using y=mx+b format))

butalik [34]

Answer: y = 2x + 5

Step-by-step explanation:

8 0

4 years ago