NOTE: Angles not necessarily drawn to scale.

Answer:

2

Step-by-step explanation:

By using trigonometric properties, we will see that:

tan(x) = 3/4.

Remember that the sine of the difference is:

sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a).

Here we have:

sin(90° -x ) = 0.8

Expanding the sine:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°)

We know that:

sin(90°) = 1 and cos(90°) = 0, then:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°) = cos(x).

Then we have:

cos(x) = 0.8

And we want to find the tangent of x, which is:

[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]

We already know that cos(x) = 0.8

Now, remember that:

[tex]sin(x)^2 + cos^2(x) = 1\\\\sin(x) = \sqrt{1 - cos^2(x)} \\[/tex]

Because x is an acute angle, sin(x) > 0, that is why we choose the positive root.

Replacing cos(x) we get:

[tex]sin(x) = \sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6[/tex]

Then the tangent of x is:

[tex]tan(x) = \frac{0.6}{0.8} = \frac{6}{10}*\frac{10}{8} = 6/8 = 3/4[/tex]

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Answer: 12 each

Step-by-step explanation: 72 divided by 6 = 12

Answer:

m∠R = 112°

m∠S = 112°

m∠T = 68°

Step-by-step explanation:

Quadrilateral QRST is a cyclic quadrilateral.

A cyclic quadrilateral is a quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.  

The opposite angles in a cyclic quadrilateral sum to 180°.

⇒ m∠Q + m∠S = 180°

⇒ m∠R + m∠T = 180°

Given:

Measure of angle Q

⇒ m∠Q + m∠S = 180°

⇒ 68° + m∠S = 180°

⇒ m∠S = 180° - 68°

⇒ m∠S = 112°

Measure of angles R and T

⇒ m∠R + m∠T = 180°

⇒ (3x + 40)° + (5x - 52)° = 180°

⇒ )8x -12)° = 180°

⇒ 8x° = 192°

⇒ x = 24

Substituting the found value of x into the expressions for angles R and T:

⇒ m∠R = (3(24) + 40)°

⇒ m∠R = 112°

⇒ m∠T = (5x - 52)°

⇒ m∠T = 68°

Answer: 14

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{n}{28}=\frac{7}{n}\\\\n^{2}=196\\\\n=\boxed{14}[/tex]

Answer:

D. y>0.

Step-by-step explanation:

1) the domain of the given function is any real numbers, then

2) if x→+∞, then y→0; if x→-∞, then y→+∞;

3) finally, the required range is y>0; answer D.

Answer:  [tex]\frac{1}{16}[/tex]

Step-by-step explanation:

Whenever an exponent is negative, you flip the solution.

For this, [tex]2^4 = 2*2*2*2 = 4*4 = 16[/tex], however the exponent is negative, so flip 16 to get your final answer of [tex]\frac{1}{16}[/tex]

Answer: Option 4

Step-by-step explanation:

Each value of x maps onto one value of y, meaning the relation is a function.

The sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression can be written as,

[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)[/tex]

The result of the above expression will be,

[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)\\\\=\dfrac{18+72}{9} \times (10)\\\\[/tex]

= (90/9) × 10

= 10 × 10

= 100

Hence, the sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.

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The critical points are within rthe range 3<x<5

These are equations that has a leading degree of 2. Given the expression below.

x²-8x+15<0

Factorize

x²-3x-5x+15<0

Factor out the GCF

x(x-3)-5(x-3) <0

Group

(x-3)(x-5)<0

Find the solution

x < 3 and x <5

Hence the critical points are within rhe range 3<x<5

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A function assigns the values. The statement "The rate of population growth each year is 166%" is true.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function of the population for the town is [tex]P (t) = 45,000(2.66)^t[/tex], where t is the time in years. Comparing the given function to the general function of the population,

P(x) = a(1+b)ˣ

Then, the value of b will be 166%.

Hence, the statement "The rate of population growth each year is 166%" is true.

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The volume of the piece of the metal Gina is found to be 22.82 cubic cm.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of cube or cuboid.

Given the density of the metal = 9.2g/cm3

Given the mass of the piece of the metal = 210 g

Assuming the volume of a piece of metal to be V

The expression for the density is shown below:-

Density = Mass / Volume

9.2 = 210 / V

V = 210 / 9

V =  22.82 cubic cm.

Therefore the volume of the piece of the metal Gina is found to be 22.82 cubic cm.

The complete question is given below:-

Gina was given an irregularly shaped piece of metal and was told that the density of the metal was 10 g/cm3. She measured the mass of the piece to be 210 g. What was the volume of the piece of metal Gina was given?

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Explanation:

This is the given piecewise function

[tex]h(a) = \begin{cases}3a+2 \text{ when } a > 3\\4a+5 \text{ when } a = 3\\3 \text{ when } a < 3\\\end{cases}[/tex]

We can rewrite things like this

[tex]\text{when } a > 3, \ \ h(a) = 3a+2\\\text{when } a = 3, \ \ h(a) = 4a+5\\\text{when }a < 3, \ \ h(a) = 3\\[/tex]

I personally prefer this format better because it mentions the inputs first, and that leads to which function definition we go for.

The input a = 2 fits the description of [tex]a < 3[/tex] since [tex]2 < 3[/tex] is a true statement. Therefore we go for the third line and can see that [tex]h(a) = 3[/tex] becomes [tex]h(2) = 3[/tex]

-----------

As another example, if we had the input a = 7, then we'd go for the first line (since 7 > 3) and get

h(a) = 3a+2

h(7) = 3(7)+2

h(7) = 23

Answer:

15.47 degrees

Step-by-step explanation:

76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or

Answer:

Step-by-step explanation:

The given relations between numbers and prices can be used to write a system of equations for the number of each kind of ticket. One equation will describe ticket numbers; the other will describe ticket revenue.

Let x represent the number of adult tickets, and y the number of student tickets. The given relations can be written as the general-form equations ...

  8x -y -11 = 0 . . . . . . . . . ticket numbers

  5x +3y -895 = 0 . . . . . ticket revenue

The setup using general form equations lends itself to solution using the "cross multiplication method." Using this method, we define three numbers used in the solution:

  Δ = 8(3) -5(-1) = 24 +5 = 29

  Δx = -1(-895) -3(-11) = 895 +33 = 928

  Δy = -11(5) -(-895)(8) = -55 +7160 = 7105

And the solutions are ...

  x = Δx/Δ = 928/29 = 32

  y = Δy/Δ = 7105/29 = 245

32 adult tickets and 245 student tickets were sold.

__

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Answer: -2

Step-by-step explanation:

We can combine the fundamentals of mental math and the brain to calculate the problem when x is -2. You wake up noticing x is -2 and you instantly know the answer and solved in less than a second.

Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).

The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: [tex]M(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].

A diagonal is XZ.

X(2, 5) = (x1, y1)

Z(0, 0) = (x2, y2)

Plug in the values

[tex]M(\frac{0 + 2}{2}, \frac{0 + 5}{2})[/tex]

= (1, 2.5).

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[tex] - 4(n - 6) = 12 \\ (n - 6) = \frac{12}{ - 4} \\ n - 6 = - 3 \\ n = - 3 + 6 \\ n = 3[/tex]

a. The number of shares outstanding after the stock split by Willey’s Grill & Restaurant Corporation is 670,000 (335,000 x 2).

b. If the common stock had a market price of $510 per share before the stock split, the approximate market price per share after the split is $255 ($510/2).

A stock split is a way that a corporation increases the number of its shares by increasing or decreasing the number of shares outstanding.

When a stock split increases the number of outstanding shares, the market price reduces proportionately.

a. What will be the number of shares outstanding after the split? Round your answer to the nearest whole number.

b. If the common stock had a market price of $510 per share before the stock split, what would be an approximate market price per share after the split? Round your answer to the nearest dollar.

Thus, the stock split increased the outstanding shares to 670,000 while reducing the market price to $255.

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Answer:

x = 7.5 km/h

Step-by-step explanation:

• First calculate the distance covered by walking at 3 km/h for 45 minutes ( 0.75 h):

distance = speed × time

              = 3 × 0.75

              = 2.25 km

• Therefore, she covered 2.25 km of the total journey by walking. Since she was 6 km from the starting point at the end of the entire journey, we can calculate the distance remaining, which she had to run:

distance she had to run = 6 - 2.25

                                        = 3.75 km

• Now we can calculate the speed of the 30 minute (0.5 h) run:

speed = distance ÷ time

           = 3.75 ÷ 0.5

           = 7.5 km/h    

This means that she ran at 7.5 km/h for half an hour.

∴ x = 7.5

Answer:

60 Days.

Step-by-step explanation:

Alright. We're told that the elementary menu repeats every 20 days. All right. And the middle school repeats every 15 days. And today they're both serving pizza. It asks how long until they're both saving it serving pizza again. Alright. So we can kind of just write them out and say well, if it's every 20 days, it repeats. Well then in 20 days from now we're going to get pizza again. And then after that another 20 days, so 40 days and then after that another 60 days. Okay. And we're just adding 20 each time. Uh you know, to see when would we get pizza again at the elementary school? Well, we can do the same thing here with middle school. And when are they going to get pizza again? Well, in 15 days from now they would get pizza again and then another 15 days from that. So that's 30 And then 45 and then 60 and then 75 and so on. And the first time that they're going to repeat is well, this is the common factor that are the common multiple that they have, which is 60. This is really just a complicated way of asking what is the least common multiple of 20 and 15. Alright. And your answer is going to be 60. So it'll be 60 days until they serve the same pizza again.

Using the arrangements formula, it is found that there are 1152 ways for the students to be arranged alternatively at the table.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, we have that:

Hence the number of ways is:

2 x 4! x 4! = 1152

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The smallest number of bananas that can grow in a bunch is 126.

To calculate the least amount of bananas that can grow in a bunch, we must identify which are the smallest possibilities, in this case they are 14 fingers per hand and 9 hands per bunch.

According to the above, the least amount of bananas per bunch would be:

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Answer:

25

Step-by-step explanation:

f(5)=x2

=25

Answer:

1) Finance is very important in a business as to meet the expenses from manufacturing a product to solding it capital is required. without finance one cannot run a business . even a small scale business requires some finance.

2) Business has a great impact in our economy. it increases the overall economy and contributes somewhere between 70 to 72% to the GDP.

The area of the figure in the task content is; 14.28in².

The area of the figure in the task content can be evaluated as the area of the semicircle and the rectangle.

Hence, the area of the semicircle is; (3.14/2) × (4/2)² = 6.28in².

The area of the rectangle can be evaluated as; 2 × 4 = 8in².

Hence, the area of the entire figure is; 8+ 6.28 = 14.28in².

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