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The trigonometric function gives the ratio of different sides of a right-angle triangle. The area of the triangle is 55.4256 ft².

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

For the given triangle the length of AB and BC can be written as,

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Sin(30^o) = \dfrac{AB}{AC}\\\\\\AB = Sin(30^o) \times 16 \\\\\\AB=8\rm\ ft[/tex]

[tex]Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Cos(30^o) = \dfrac{BC}{AC}\\\\\\BC = Cos(30^o) \times AC\\\\\\BC = 13.8564\rm\ ft[/tex]

Now, the area of the triangle is,

Area of triangle = 0.5× 8 × 13.8564 = 55.4256 ft²

Hence, the area of the triangle is 55.4256 ft².

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Answer:

x = 61°

Step-by-step explanation:

since the triangle has 2 congruent sides then it is isosceles with the 2 base angle being congruent, both x°

the sum of the 3 angles in the triangle = 180° , then

x + x + 58° = 180°

2x + 58° = 180° ( subtract 58° from both sides )

2x = 122° ( divide both sides by 2 )

x = 61°

Answer: The correct answer is D.

Step-by-step explanation: A and B are incorrect because you can plug in 5 for x to get 2, and there are multiple values that can be greater than 5. C is incorrect because you cannot reach lower than 2. Therefore, the correct answer is D.

The y values are all greater than or equal to 2.

The correct option is D.

Given,

Function : f(x) = |x − 5| + 2

Here,

A function is a law that relates a dependent and independent variable.

The function is

f(x) = |x − 5| + 2

The domain of the function is all negative and positive integers.

The range is all the possible function values, the function value will always be greater than or equal to 2.

At x = 5 , f(x) = 2

Therefore, the y values are all greater than or equal to 2. The correct option is D.

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Answer:

-4.625, -4 8/11, -4 4/5, -5.2

Step-by-step explanation:

-4 8/11 = -4.72727272723

-4 4/5 = -4.8

Answer:

5182

Step-by-step explanation:

To figure out the mean of a number, you must add all of the numbers together and divide by the amount of numbers you added up.

To find the total sum, we just need to reverse this process.

We are already given the final number so all we have to do is multiply the mean by 100 and we have our answer of 5182.

Hope this helps :D

The limit of the given function if [tex]\lim_{x \to 0} f(x)=4[/tex] is 64

Given the following limit of a function expressed as;

[tex]\lim_{x \to 0} f(x)=4[/tex]

We are to determine the value of the function

[tex]\frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]

This can also be expressed as

[tex]\frac{1}{4} \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64[/tex]

Hence the limit of the given function if [tex]\lim_{x \to 0} f(x)=4[/tex] is 64

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Answer:

8,000 words

Step-by-step explanation:

If a typewriter types 750 words per hour and she types 8 hours a day she would write 8,000 words a day because 750 x 8 = 8,000.

Therefore, 110 calories are in 1 serving of milk.

Given, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda.

Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk.

Marian consumes 510 calories by drinking 3 servings of milk and 1 soda.

Linear programming, commonly known as LP, is a straightforward technique for representing complex real-world interactions by means of a linear function.

Now,

Let the calories in one serving of milk be x

Let the calories in one serving of juice be y

Let the calories in one serving of soda be z

For Joe, the equation to show the amount of calories is

2x + y + z = 530 -----(1)

For Darius, the equation to show the amount of calories is

x + 2y = 370 ------(2)

For Marian, the equation to show the amount of calories is

3x + z = 510 ------(3)

Now, y=370/2-x/2 and z=510-3x substitute in the equation 2x + y + z = 530.

2x+185-0.5x+510-3x=530

⇒695-1.5x=530

⇒1.5x=165

⇒x=110 calories

Hence, 110 calories are in 1 serving of milk.

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Answer:

its option c (7)

Step-by-step explanation:

trust your bro

Answer:

[tex]C)~ 7[/tex]

Step-by-step explanation:

[tex]\text{Given that,}~~ (x_1,y_1) = (k,3)~ \text{and}~ (x_2 ,y_2) = (2,3)\\\\\text{Distance,}~ \\\\~~~~~~~~d= \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\\\\\implies 5=\sqrt{(2-k)^2 + (3-3)^2}\\\\\implies 5=\sqrt{(2-k)^2 +0}\\\\\implies 5 = \sqrt{(2-k)^2}\\\\\implies 5=|2-k|\\\\\implies \pm 5=2-k \\\\\implies 2-k =5~~~~~~\text{or}~~~~~~~~2-k = -5\\\\\implies k = 2-5~~~~~~\text{or}~~~~~~~~k = 2+5\\\\\implies k = -3~~~~~~~~~\text{or}~~~~~~~~k = 7[/tex]

Answer:

C = A/d - b/d or C = (A - b)/d

Step-by-step explanation:

A = b + cd

A - b = cd

A/d - b/d = c

Based on the calculations, the equation of the triangle's line of symmetry is equal to: B. y = x - 1.

First of all, we would determine the midpoint where the line of symmetry passes through points A and B:

Midpoint at point A = (3 + 7)/2 = 10/2 = 5.

Midpoint at point B = (6 + 2)/2 = 8/2 = 4.

Point D = (5, 4)

Mathematically, the standard equation of a line is given by y = ax + b.

D(5, 4); 4 = 5a + b   ....equation 1.

C(4, 3); 3 = 4a + b    ....equation 2.

Subtracting eqn. 2 from eqn. 1, we have:

1 = a

Next, we would find the value of b:

4 = 5a + b

4 = 5(1) + b

b = 4 - 5

b = -1.

Therefore, the equation of the triangle's line of symmetry is given by:

y = ax + b

y = x(1) + (-1)

y = x - 1.

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Answer:

Approximately 57

Step-by-step explanation:

The Pythagorean theorem says that a^2+b^2=c^2, where a and b are the base and height, while c is the hypotenuse. 53^2+21^2=2809+441=3250. The square root of 3250 is 57.008771255, which rounded to the nearest tenth is 57. Hope this helped!

Answer:

57.008771255 or 57

Step-by-step explanation:

53^2+21^2=57.008771255^2

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 5. The solution to system B will be the same as the solution to system A.

System A equations:

-x - 2y = 7  ------ (1)

5x - 6y = -3  ------(2)

We multiply the first equation by 5, to get :

-5x - 10y = 35 -----(3)

The sum of equation (2) and equation (3) gives:

-16y = 32

y = 32/-16

y = -2

Thus, solution of system B is;

-x - 2(-2) = 7

-x + 4 = 7

x = -3

So, the solution of system B is (-3, -2), that means the solution of both systems are same.

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Answer:

Worldwide, hundreds of marine species have been negatively impacted by marine debris, which can harm or kill an animal when ingested or they become entangled, and can threaten the habitats they depend on.

This lost or abandoned gear is a major problem because it can continue to capture and kill wildlife, damage sensitive habitats, and even compete with and damage active fishing gear.

Step-by-step explanation:

The key idea is that pollution is threatening marine life impact of marine life and the source of marine debris.

Marine debris is risky to a wide variety of marine animals. Animals can ingest debris, which can cause health problems or death, or they may get caught in debris, which can be equally harmful. In addition, marine debris harms the environments in which many species rely on being alive.

The greater part of marine garbage is caused by human activity on land. Marine debris is produced by poor waste management methods, dumping waste, stormwater discharge, and natural disasters such as tsunamis and hurricanes. Furthermore, ocean-based sources, such as wasted fishing gear, contribute to the problem.

The key idea is that pollution is threatening marine life impact of marine life and the source of marine debris.

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Answer:

6.2 , 6.2052 , 6.705 , 6.75

Step-by-step explanation:

Least to Greatest!

[tex]~~~(2x-6)(2x+6)\\\\=(2x)^2 -6^2~~~~~~~~~~~~~~~~~~~~~;[a^2 -b^2 = (a+b)(a-b)]\\\\=4x^2 -36[/tex]

Answer:

see the attachment photo!

to get the equation of any straight line, we simply need two points off of it, let's use the provided points in the picture above.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{1 +3}{1 +0}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{4}(x-\stackrel{x_1}{0}) \\\\\\ y+3=4x\implies y=4x-3[/tex]

The number of ways that Grant can arrange 3 of his 10 plants on a window ledge is 120 ways

The number of ways that Grant can arrange 3 of his 10 plants on a window ledge will be:

= 10!/(10! - 3!)3!

= 10!/7!3!

= (10 × 9 × 8)/(3 × 2)

= 120

When the parade organizer received 8 entries for floats, the number of ways that he can arrange 4 floats out of the 8 entries will be:

= 8!/(8! - 4!)4!.

= 8!/4!4!

= (8 × 7 × 6 × 5)/(4 × 3 × 2)

= 70

4! in expanded form will be:

= 4 × 3 × 2

= 24

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Answer:

Mike started off the day with $27.

Step-by-step explanation:

Using the information given to us, we can set up an equation. Knowing that Mike ended the day with $7, and the amount of money that he spent and received can help us set up an equation. The amount of money that he started the day off with, is unknown, and recognized as x.  [tex]7=x-22-3+5[/tex]

To solve this, we can simply solve the numbers that we know on the right hand side, to get this:

[tex]7=x-20[/tex]

Now, to get our final answer we must isolate x. We can do this by simply adding 20 to both sides. This cancels out the -20 on the right, and makes the 7 on the left become 27.

[tex]27=x[/tex]

Therefore, Mike started the day off with $27.

Answer:

-13.4+2.3c

Step-by-step explanation:

Add the like terms.

-6.5-5.1-1.8=-13.4

-13.4+2.3c

Hope this helps!

If not, I am sorry.

Answer:

18/5

Step-by-step explanation:

you have to times then divide

The exponential function is given by [tex]I(t) = 50000(1.15)^t[/tex]. The initial investment of $50,000 grows at a rate of about 15% annually.

An equation is an expression that shows the relationship between two or more numbers and variables.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the rate of increase per period.

Let I(t) represent Jennifer’s investment account balance after t years, hence:

a = 50000, b = 100% + 15% = 115% = 1.15

[tex]I(t) = 50000(1.15)^t[/tex]

The exponential function is given by [tex]I(t) = 50000(1.15)^t[/tex]. The initial investment of $50,000 grows at a rate of about 15% annually.

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Answer: C, D

Step-by-step explanation:

Acute angles of right triangles are complementary, and the sine of an angle is equal to the cosine of its complement.

Answer: y = 12x - 43

Step-by-step explanation: i hope that helps

if we paint the tank on the outside, we'll be covering SA of surface area, however we're also painting it on the inside, so the area inside assuming the material thickness is negligible, we'll be covering SA as well, so we'll be needing SA + SA = 2SA ft² of paint to do the whole thing.

so, its diameter is 10, that means its radius is 5.

[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=12\\ r=5 \end{cases}\implies \begin{array}{llll} SA=2\pi (5)(12+5)\implies SA=170\pi \\\\\\ \stackrel{\textit{twice as much}}{2SA=340\pi } \end{array}[/tex]

now, hmmm we know that 1 gallon can do 200 ft², how many gallons are there in 340π ft²?

[tex]\begin{array}{ccll} gallons&ft^2\\ \cline{1-2} 1 & 200\\ x& 340\pi \end{array} \implies \cfrac{1}{x}~~=~~\cfrac{200}{340\pi } \\\\\\ 340\pi =200x\implies \cfrac{340\pi }{200}=x\implies \stackrel{gallons}{5.34}\approx x[/tex]

Answer: Cylinder B is 50% bigger than cylinder A

Cylinder A volume:

= πr²h

= π(10)²(5)

= 500π

Cylinder B volume:

= 750π

Cylinder B bigger than Cylinder A by:

= (750π - 500π)/500π × 100 = 50%

[tex]\hrulefill[/tex]

Hence, cylinder B is bigger than cylinder A by 50%

Answer:

Cylinder B is 50% bigger than Cylinder A

Step-by-step explanation:

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Cylinder A

Given:

Substituting the given values into the formula:

[tex]\implies \sf Volume_A=\pi (10)^2(5)=500\pi \:in^3[/tex]

Cylinder B

Given:

[tex]\implies \sf Volume_B=750\pi \:in^3[/tex]

Percentage Change

[tex]\begin{aligned}\sf percentage\:change & =\sf \dfrac{final\:value-initial\:value}{initial\:value} \times 100\\\\& = \sf \dfrac{Volume_B-Volume_A}{Volume_A} \times 100\\\\& = \sf \dfrac{750\pi-500\pi}{500\pi} \times 100\\\\& = \sf \dfrac{1}{2} \times 100\\\\& = \sf 50\%\end{aligned}[/tex]

Therefore, Cylinder B is 50% bigger than Cylinder A

A box plot is used to study the distribution and level of a set of scores. The box plot consists of whiskers which measure the minimum and maximum numbers. The difference between these numbers is the range which measures variability.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.  The difference between the first quartile and the third quartile is the interquartile range.

For the first box plot:

For the second box plot:

For the third box plot:

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Answer:

10

Step-by-step explanation:

4 overtime hours - regular pay + $40

Total $ earned - $160

Total hours - 12 hours (8 reg + 4 overtime)

$160 - $40 = $120

$120/12 = $10

Her regular pay is $10 per hour.