A 30-60-90 triangle has a short leg of 6.
What is the length of the long leg?

Answer:

6. 21.0°

7. 39.6°

8. 58.0°

9. 72.9°

Step-by-step explanation:

6. Reference angle (θ) = x°

Hypotenuse = 15

Adjacent = 14

Apply CAH:

[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]

Plug in the values

[tex] Cos(x) = \frac{14}{15} [/tex]

[tex] x = Cos^{-1}(\frac{14}{15}) [/tex]

x ≈ 21.0° (nearest tenth)

7. Reference angle (θ) = x°

Opposite = 19

Adjacent = 23

Apply TOA:

[tex] Tan(\theta) = \frac{Opposite}{Adjacent} [/tex]

Plug in the values

[tex] Tan(x) = \frac{19}{23} [/tex]

[tex] x = Tan^{-1}(\frac{19}{23}) [/tex]

x ≈ 39.6° (nearest tenth)

8. Reference angle (θ) = x°

Hypotenuse = 17

Adjacent = 9

Apply CAH:

[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]

Plug in the values

[tex] Cos(x) = \frac{9}{17} [/tex]

[tex] x = Cos^{-1}(\frac{9}{17}) [/tex]

x ≈ 58.0° (nearest tenth)

9. Reference angle (θ) = x°

Opposite = 43

Hypotenuse = 45

Apply SOH:

[tex] Sin(\theta) = \frac{Opposite}{Hypotenuse} [/tex]

Plug in the values

[tex] Sin(x) = \frac{43}{45} [/tex]

[tex] x = Sin^{-1}(\frac{43}{45}) [/tex]

x ≈ 72.9° (nearest tenth)

Answer:

the correct answer is 7√3

It becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.

Logarithms arise in problems of exponential growth

and decay because they are inverses of exponential functions. Because of the Laws of Logarithms, they also turn out to be useful in the measurement of the loudness of sounds, the intensity of earthquakes, and other processes that occur in nature

We can write an exponential function to represent the situation.

We know that the current population is 100,000.

The population doubles each day.

The standard exponential function is given by P(t) = A (2)^t

Since our current population is 100,000, a = 100000.

Since our rate is doubling, r = 2.

So

P(t) = 100000 (2)^t

We want to find the population five days ago.

So, we can say that t = -5. The negative represent the number of days that has passed.

Therefore

P(-5) = 100000 (2)^-5 =100000*(1/32) =3125

However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.

We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:

P(t) = A (2)^t

After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:

100000 =A[tex]2^5[/tex]

And solving for A, we acquire     :[tex]\frac{100000}{2^5}[/tex]

                                                      =3125

So, our function in terms of the original day is:

P(t) = 3125 (2)^t

So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.

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Since the tallest man is a lone individual, he can only take a seat in the center. The four other men can sit in 4! = 24 different positions.

We'll take pictures of five people standing in a row, all of varying heights. The tallest individual must be in the middle, so. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The likelihood that an event will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely alternatives that result in a given occurrence. Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. If we throw a coin into the air,

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Answer:

the one that is not equivalent to the others would be 116-34

Step-by-step explanation:

because its 116 and the others dont have anything to do with 116 :)

Answer: The statement that is not equivalent should be D. |16-34

the probability that the card is either a queen or a diamond is: 4/13

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.

Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.

Number of cards, n(S) = 52

Let E = Event of getting a diamond

F = Event of getting a queen

(E ∩ F) = Event of getting a diamond of queen.

Then, n(E) = 13

n(F) = 4 ,

n (E ∩ F)=1

P(E) = 13/52 = 1/4

P (F) = 4/52 = 1/13

P (E ∩ F) = 1/52

(E or F) = P(E ∪ F) = P(E) + P(F) × P(E ∩ F)

P (E or F) = 1/4 + 1/13 - 1/52

P (E or F) = (13 + 4 - 1)/52

P (E or F) = 16/52

P (E or F) = 4/13

The required probability of getting either diamond or a queen is 4/13

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Answer:

Rhombus

Let's solve your equation step-by-step.

4x+5=7x−16

Step 1: Subtract 7x from both sides.

4x+5−7x=7x−16−7x

−3x+5=−16

Step 2: Subtract 5 from both sides.

−3x+5−5=−16−5

−3x=−21

Step 3: Divide both sides by -3.

−3x/ −3 = −21/ −3

x=7

Answer:

5.) B 6.) A

Step-by-step explanation:

A(Rhombus) = 1/2(9)(12) = 54 cm²

Answer:

A

Step-by-step explanation:

A triangular prism has two rectangles on each side, then two triangles on the other sides. I hope this helps! :)

The solution to the system of equations is x = 4 and y = 2.

We would use the elimination method to solve the system of equations:

Let's eliminate the variable y by adding equations 1 and 2:

4x + 8y = 24

2x + y = 19

.

.

.,

6x + 9y = 43

Now we can eliminate the variable x by subtracting equation 3 from the above equation:

6x + 9y = 43

3x + y = 15

.

.

.

3x + 8y = 28

We now have an equation with one variable: 3x + 8y = 28. We can solve for x by dividing both sides by 3:

x = (28 - 8y) / 3

Now we can substitute this expression for x into one of the original equations and solve for y. Let's use equation 4:

4x + 2y = 12

Substituting x = (28 - 8y) / 3:

4((28 - 8y) / 3) + 2y = 12

If we simplify:

Finally, we can use this value of y to find x by plugging it into the expression we found earlier:

x = (28 - 8(2)) / 3

x = (28 - 16) / 3

x = 12 / 3

x = 4.

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After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be  E = 20H.

After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be

E = 20H.

We would enter H = 17

into the formula to get Mai's pay after 17 hours of tutoring.

E = 20 × 17 E = $340 is the result.

The complete question is:

Mai tutors history. For each hour that she tutors, she earns 20 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Mai's earnings after tutoring for 17 hours.

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Answer:

a: School W is has the most consistent attendance

b:  School W has the highest average attendance

Step-by-step explanation:

For a:

The most consistent school will be the school whose data has the smallest variance.  *Consistent doesn't mean the best, it's just the least differing among it's own data.  The variance tells us how spread out the data is, so the school with the smallest variance is the most consistent.  

See photo 1 for the calculations of the variances of each school...

For b:

Take the mean for each school.  Whichever has a higher value is the school with the highest average.  

See photo 1 for the calculations if the means for each school.  (the mean is used to calculate variance, so we will do this part first)

There are three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

Therefore, the three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

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Yes, the sides with 5,12,13 make a triangle.

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude is called Pythagorean Triples.

Pythagorean triples describe the three integer side lengths of a right triangle.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

which contain three positive integers a, b, and c.

the original Pythagorean triplets, two of the numbers are prime, but one is even. If all three numbers are multiplied by a factor, the triplet is called a relatively prime.

The most well-known examples are (3,4,5) and (5,12,13)

consider c=13 a=12, b=5 substitute in above formula:

13²=12²+5²

⇒169=144+25

⇒169=169

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Answer:

20a^7

Step-by-step explanation:

a^b(a^c)=a^(b+c)

Step-by-step explanation:

Answer:

r = 9.77205024 yds

Step-by-step explanation:

The width of the frame is 8 inches.

Now, According to the question:

The length of a rectangular frame is 15 inches

The diagonal length of the frame is 17 inches.

To find the width of the frame in inches.

Let's take the width of the frame is = w

Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.

This will be:

17² = 15² + w²

289 = 225 + w²

289 - 225 =  w²

64 =  w²

w = [tex]\sqrt{64}[/tex]

w = 8

Hence, The width of the frame is 8 inches.

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To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).

The equation of a vector is typically written like this:

v = (x, y, z)

To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation. For example, let's say you are given the point (1,2,3) and the direction of the vector is (2,3,4). The components of the vector, v, would be x = 2, y = 3, and z = 4, so the equation for that vector would be:

v = (2, 3, 4)

To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).

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Answer:

5

Step-by-step explanation:

4x-3=17

+3 on both sides = 4x=20

divide 20 by 4 and your answer is 5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{4x - 3 = 17}[/tex]

[tex]\text{ADD 3 to BOTH SIDES}[/tex]

[tex]\mathsf{4x - 3 + 3 = 17 + 3}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{4x = 17 + 3}[/tex]

[tex]\mathsf{4x = 20}[/tex]

[tex]\text{DIVIDE 4 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{20}{4}}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{x = \dfrac{20}{4}}[/tex]

[tex]\mathsf{x = 5}[/tex]

[tex]{\huge\text{Therefore, your answer should be:}[/tex][tex]\huge\boxed{\mathsf{x = 5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

10 mm

Step-by-step explanation:

Draw an equilateral triangle. Label each side 12 mm.

Draw one altitude from one vertex perpendicular to the opposite side. Label the length of the altitude h.

The altitude divided the opposite side into two congruent segments, each one measuring 6 mm.

Now use the Pythagorean Theorem.

a² + b² = c²

(6 mm)² + h² = (12 mm)²

36 mm² + h² = 144 mm²

h² = 144 mm² - 36 mm²

h² = 108 mm²

h = 6√3 mm

h ≈ 10 mm

Answer: 3.5 cm or 35 mm

Step-by-step explanation:

12/3 =4 for each side of triangle

cutting the triangle in half, bottom side(a) 4 becomes 2

2^2 + b^2 = 4^2

4 + b^2 = 16

subtract 4 from both sides

b^2 = 12

b = 3.464 cm or 3.5 cm

convert 3.5 cm to 35 mm

The rectangular prism in figure 2 has the same volume of 108 m².

Given that the square prism's measurements are as follows:

area = 36 m²

h = 3 m

As a result, the volume of this prism is equal to side² h = area h = 36 3 = 108 m2.

Now, we'll figure out how much each prism in the image is worth.

1) Because it is a right-angled tent or prism, the volume calculation will be

V = 1/2 (base length base width) Height

= 1/2×(3×2×6) = 36/2 = 18 m²

2. Volume of a rectangular prism is equal to length, width, and height, which is 2 18 3 = 108 m2.

3. A tent's or prism's volume is equal to half of its base's length, width, and height

= 1/2×4×9×3 = 1/2×108 = 54 m²

Consequently, the rectangular prism in figure 2 has the same volume of 108 m2.

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Answer:

137 ft^2

Step-by-step explanation:

The triangle has base 3 ft and height 6 ft; its area is A = (1/2)(base)(height), which here is A = (1/2)(3 ft)(6 ft) = 9 ft^2.

The lower, rectangular area has length 16 ft and width 8 ft, and thus it has the area (16)(8) ft^2, or 128 ft^2.

The total area of this irregular shape is A = 9 ft^2 + 128 ft^2  =  137 ft^2

Answer: √96

Step-by-step explanation:

The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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Answer:

The answer is 3036.7

Have a great day

Answer:

25x^6y^2

Step-by-step explanation:

Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.

Answer:

-x + 5

Step-by-step explanation:

x - (-3) + 8 - 2x - 6 = x - 2x + 3 + 8 - 6 = -x + 5

Answer:

[tex] \sf \: -x + 5 [/tex]

Step-by-step explanation:

Given expression,

→ x - (-3) + 8 - 2x - 6

Let's simplify the expression,

→ x - (-3) + 8 - 2x - 6

→ x + 3 + 8 - 2x - 6

→ (x - 2x) + (3 + 8 - 6)

→ (-x) + (5)

→ -x + 5

Hence, the answer is -x + 5.

Answer: 1/2

Step-by-step explanation:

The question is asking you to find how many centimeters in the scale drawing equal 1 foot on the actual building. The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter, or A.

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