Use the law of sines to find the value of a.



Law of sines:

What is the best approximation of the value of a?

2.4 cm
2.7 cm
3.0 cm
3.3 cm

[tex]n^2=\dfrac{1}{16}\\\\n=-\dfrac{1}{4} \vee n=\dfrac{1}{4}[/tex]

Answer:

Distance = 3r

Step-by-step explanation:

We are to write an algebraic expression and then simplify it for the given situation:

The distance traveled by a train in three hours with a constant speed of r miles per hour.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

Answer:

choice number 2) 10 in, 18.5 in 31.5 in

Step-by-step explanation:

we collect and evaluate the like terms.like terms means the ones that can be evaluated. like 2y and 7y are like terms. they either can be added or subtracted to get an answer . 7y-2y =5y. but you cant subtrac or add 7y  with 5 because they are not like terms.

2y +1 + 7y + 3y + 5 = 60

(2y+7y+3y)+(1+5) = 60

12y + 6 = 60

The 6 crosses the equal sign to the other side because of like terms.And becomes a minus

12y = 60 - 6

12y = 54

y = 4.5

so,

2y +1= 2 x 4.5 + 1 =10

7y = 7 x 4.5 = 31.5

3y + 5= 3 x 4.5 + 5 =18.5

Answer is 10 in, 18.5 in, 31.5 in

If you need any clarification or more explanation pls do mention at the comment section so that i can help more thx

Hope this helps and if it does pls mark as branliest answer thx

[tex]\dfrac{3}{5x}+\dfrac{9}{5x}=\dfrac{12}{5x}[/tex]

The sum of the given expression will be equal to 12 / 5x.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression is:-

[tex]=\dfrac{3}{5x}+\dfrac{9}{5x}[/tex]

[tex]= \dfrac{3+9}{5x}[/tex]

[tex]=\dfrac{12}{5x}[/tex]

Therefore the sum of the given expression will be equal to 12 / 5x.

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Five solutions of  y = 20x  with integer values for  x  ranging from -2 to 2 are (-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).

To find five solutions of the equation  y = 20x , we can choose integer values for  x  starting with -2 and ending with 2, and then calculate the corresponding values of  y  using the given equation.

Starting with  x = -2 :

y = 20(-2) = -40

So, the first solution is (-2, -40).

Moving to  x = -1:

y = 20(-1) = -20

So, the second solution is (-1, -20).

At  x = 0 :

y = 20(0) = 0

So, the third solution is (0, 0).

Proceeding to  x = 1 :

y = 20(1) = 20

So, the fourth solution is (1, 20).

Finally, for  x = 2 :

y = 20(2) = 40

So, the fifth solution is (2, 40).

Therefore, the five solutions of the equation  y = 20x  with integer values for  x  ranging from -2 to 2 are:

(-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).

Answer:

(-2)3 = -8

-2 × -2 = 4

4 × -2 = -8

Step-by-step explanation:

-2 multiply 3 times

negative times a negative equals a positive

negative times positive equals a negative

see results below

-2 × -2 = 4

4 × -2 = -8

For this case we have a function of the form [tex]y = f (x)[/tex]

They ask us to find the value of the function when[tex]x = 2[/tex], that is, [tex]f (2).[/tex]

If we look at the figure, and we mark x = 2 in the graph, we obtain a value of[tex]y = 4[/tex]

So, we have that the function has a value of 4 when[tex]x = 2[/tex]

Answer:

Option C

Answer:

C) Domain: -3, -1, 0, 3

Range: -1, 0, 1, 2, 3

Step-by-step explanation:

Domain is using x values

Range is using y values

Answer:

x = 1 + √6

x = 1 - √6

The two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]

From the question,

We are to determine the values of x that are roots to the quadratic equation x² +2x -5=0

Using the quadratic formula

[tex]x= \frac{-b \pm \sqrt{b^{2} -4ac} }{2a}[/tex]

From the given equation x² +2x -5=0

[tex]a = 1, \ b = 2, \ and \ c=-5[/tex]

Putting the values into the equation, we get

[tex]x= \frac{-(2) \pm \sqrt{(2)^{2} -4(1)(-5)} }{2(1)}[/tex]

This becomes

[tex]x= \frac{-2 \pm \sqrt{4 --20} }{2}[/tex]

[tex]x= \frac{-2 \pm \sqrt{4+20} }{2}[/tex]

[tex]x= \frac{-2 \pm \sqrt{24} }{2}[/tex]

Then,

[tex]x= \frac{-2 \pm 2\sqrt{6} }{2}[/tex]

∴ [tex]x= -1 \pm \sqrt{6}[/tex]

[tex]x= -1 + \sqrt{6} \ OR \ x= -1 - \sqrt{6}[/tex]

Hence, the two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]

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Answer:

Option D. Alia gets 3³ - 4² = 11 jelly beans.

Step-by-step explanation:

Kathy gives Kelly 3³ jelly beans.

Kathy gives Alia 4² fewer jelly beans than Kelly. This means that Alia gets the number of jelly beans obtained by Kelly decreased by 4².

To summarize:

#Kelly = 3³ = 27

#Alia = #Kelly - 4² = 3³ - 4² = 27 - 16 = 11

Then, option D is correct.

Answer:

Isolating the x.

Step-by-step explanation:

The first step to solving this problem is to isolate the variable, x.

To do so, subtract 8x and 5 from both sides.

Step #1)

5 - 2x < 8x - 3

5 (-5) - 2x (-8x) < 8x (-8x) - 3 (-5)

-2x - 8x < -3 - 5

-10x < -8

~

Answer:

x>4/5

Step-by-step explanation:

Subtract by 5 from both sides of equation.

5-2x-5<8x-3-5

Simplify.

-2x<8x-8

Subtract by 8x from both sides of equation.

-2x-8x<8x-8-8x

Simplify.

-10x<-8

Multiply by -1 from both sides of equation.

(-10x)(-1)>(-8)(-1)

Simplify.

10x>8

Divide by 10 from both sides of equation.

10x/10>8/10

Simplify, to find the answer.

8/10=4/5

x>4/5 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

16

Step-by-step explanation:

cos60°=8/x

x=8/cos60°

The explicit formula that can be used to find the account's balance at the beginning of year 6 is B = P(1 + r/n)^(nt), which  gives the value as [tex]300(1.04)^6[/tex]

The explicit formula that can be used to find the account's balance at the beginning of year 6 is:

[tex]B = P(1 + r/n)^(nt)[/tex]

Where:

In this case, Jonah's initial investment is $300, the annual interest rate is 4%, interest is compounded annually (n = 1), and the number of years is 6 (t = 6). Plugging these values into the formula:

[tex]B = 300(1 + 0.04/1)^(1*6)[/tex]

[tex]B = 300(1 + 0.04)^6[/tex]

[tex]B = 300(1.04)^6[/tex]

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Answer:

slope = [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 4) ← 2 points on the line

m = [tex]\frac{4+1}{2-0}[/tex] = [tex]\frac{5}{2}[/tex]

The marginal relative frequency of the number of people who prefer to read books is 0.42

Answer:

.42

Step-by-step explanation:

Answer:

First, third, fourth and fifth statements describe a parabola

Step-by-step explanation:

The correct statements are:

A parabola is the set of all points equidistant from the directrix and focus.

The focus is a fixed point inside the parabola.

The line of symmetry intersects the focus and directrix.

The line of symmetry and the directrix are perpendicular.

Answer:

1, 3, 4, and 5 are the correct answers.

2 and 6 are not.

Answer:

B. 19,531

Step-by-step explanation:

Answer:

The correct answer is option (2) 19,531

Step-by-step explanation:

Given Data;

a = 1 (first term)

r = 5 (five offspring)

n = 7 ( number of hours)

Using the formula of a geometric progression, we have

S₇ = [tex]\frac{a(r^{n} - 1) }{r -1}[/tex]

Substituting, we have

S₇ = [tex]\frac{1(5^{7} -1) }{5-1}[/tex]

S₇ = 78124/4

    = 19531

Therefore, there are 19531 number of organisms at hour seven.

hope this helps. goodluck

Answer:

It's the red figure.  This is because it is rotated 180 degrees.

Step-by-step explanation:

Please mark for Brainliest!! :D Thanks!!

For more questions or more information, please comment below!

Answer:

4

Step-by-step explanation:

I'm not sure what question you are asking about but the one you had answer is incorrect.

You are given the long side which is 2sqrt(3).

Compare this to xsqrt(3) and hopefully you see x is 2 and is the short side.

The hypotenuse is twice the short side measurement so 2(2)=4.

Answer: 4

Answer:

Step-by-step explanation:

48

This is a 30-60-90 triangle, and we are given the [tex]x[/tex] value for the triangle, which makes it easier.

The hypotenuse for a 30-60-90 triangle will always be [tex]2x[/tex], while the adjacent side for a 30-60-90 triangle will always be [tex]x*\sqrt{3}[/tex].

So the hypotenuse is 14, and the adjacent side is [tex]7*\sqrt{3}[/tex]/

49

This is also a 30-60-90 triangle, and we can use the rules explained above.

The x value is [tex]5*\sqrt{3}[/tex] so the hypotenuse is [tex]10*\sqrt{3}[/tex] and the adjacent side is 15.

51

This is also a 30-60-90 triangle, and the root three value is [tex]2*\sqrt{3}[/tex], making the x value 2 and the hypotenuse 4.

52

This is a 45-45-90 triangle, and the same side value is [tex]4*\sqrt{2}[/tex].

This means that the adjacent side is also [tex]4*\sqrt{2}[/tex] and the hypotenuse is 8.

The probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that three of the 15 people in the Latin club are chosen at random to wear togas to school to promote the club. Therefore, the number of ways 3 people can be chosen out of 15 is,

Number of ways to choose 3 people = ¹⁵C₃ = 455

Now, the number of ways Joseph, Heidi, and Katy can be chosen in only one way. Therefore, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is,

Probability = 1 /455 = 0.002197

Hence, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.

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Answer:

Option C.

Step-by-step explanation:

we have that

The correct question is

Louis calculated the height of a cylinder that has a volume of 486pie cubic centimeters and a radius of 9 centimeters her work is shows below

V=BH

STEP 1: 486pie=pie9^2h

STEP 2: 486pie=81pieh

STEP 3: 486pie/81pie=81pie/81pie h

STEP 4: h=6pie cm

what error did Louise make when calculating the height of the cylinder

A. in step 1 she substituted into the volume formula incorrectly

B. in step 2 she calculated 9^2 incorrectly

C. in step 4 the pie should have canceled making the correct answer 6 cm

D. Louise correctly calculated the height of the cylinder

we know that

The volume of the cylinder is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the cylinder

we have

[tex]V=486\pi\ cm^{3}[/tex]

[tex]r=9\ cm[/tex]

Find the area of the base B

[tex]B=\pi r^{2}[/tex]

substitute

[tex]B=\pi (9)^{2}[/tex]

step 1

substitute the values in the formula of volume

[tex]486\pi=\pi (9)^{2}h[/tex]

step 2

[tex]486\pi=81\pi h[/tex]

step 3

Divide both sides by 81π

[tex]486\pi/81\pi=81\pi h/81\pi[/tex]

step 4

Simplify

[tex]6=h[/tex]

rewrite

[tex]h=6\ cm[/tex]

therefore

In step 4 the pie should have canceled making the correct answer 6 cm

Answer:

In step 4, the x should have canceled, making the correct answer 6 cm.

Answer: The missing term for W is 10.5.

Step-by-step explanation:

W + 9/6 = 12

W +9/6 - 9/6 = 12- 9/6

W = 12 - 1.5

W = 10.5

Answer:

Answer is 6/10 and 12/20

Step-by-step explanation:

Let the numerator be x.

3/5=x/10

x=30/5

x=6

The required fraction is 6/10

Now same method applies for taking 20 as denominator

3/5=x/20

x=60/5

x=12

The required fraction is 12/20

Answer:

2 is not in the domain of f of g

Step-by-step explanation:

* Lets revise at first the meaning of f of g (composite function)

- A composite function is a function that depends on another function

- A composite function is created when one function is substituted into

 another function

- Example:

# f(g(x)) is the composite function that is formed when g(x) is

  substituted for x in f(x).

- In the composition (f ο g)(x), the domain of f becomes g(x)

* Now lets solve the problem

∵ f(x) = 4x + 3

∵ g(x) = √(x - 9)

- Lets find f(g(x)), by replacing x in f by g(x)

∴ f(g(x)) = f(√(x - 9)) = 4[√(x - 9)] + 3

∴ f(g(x)) = 4√(x - 9) + 3

∵ The domain of f is g(x)

- The domain of the function is the values of x which make the

  function defined

∵ There is no square root for negative values

∴ x - 9 must be greater than or equal zero

∵ x - 9 ≥ 0 ⇒ add 9 for both sides

∴ x ≥ 9

∴ The domain of f of g is all the real numbers greater than or equal 9

∴ The domain = {x I x ≥ 9}

∵ 2 is smaller than 9

∴ 2 is not in the domain of f of g

Answer:

a = b

b = c

So they're all equal, therefore a would be the same as c

Step-by-step explanation:

Answer: True

Step-by-step explanation: Since a||b and b||c, a||c is correct a is b and b is c.

Answer:

It's B

Step-by-step explanation:

B,     16x2-9y2

Answer:  The correct option is (B) [tex]16x^2-9y^2.[/tex]

Step-by-step explanation:  We are given to find the following product :

[tex]P=(4x+3y)(4x-3y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the given product, we will be using the following formula :

[tex](a+b)(a-b)=a^2-b^2.[/tex]

The product (i) can be calculated as follows :

[tex]P\\\\=(4x+3y)(4x-3y)\\\\=(4x)^2-(3y)^2\\\\=16x^2-9y^2.[/tex]

Thus, the required product is [tex]16x^2-9y^2.[/tex]

Option (B) is CORRECT.

Answer:

12.5698 (approximately 12.5, rounding to the nearest half)

Step-by-step explanation:

The area of a square is represented by the following equation:

[tex]A=a^2[/tex]

Whereas "a" represents the length of any one of the sides.

Since all sides of a square are equal in length, we can reverse engineer this formula to find the length of one side.

[tex]158=a^2[/tex]

Simply take the square root of both sides and you will have your answer.

[tex]12.5698=a[/tex]

To determine the length of one side of a square sign with an area of 158 feet, calculate the square root of the area which is approximately 12.57 feet.

A square sign has an area of approximately 158 feet. To find the length of one side of the sign, you need to calculate the square root of the area:

Side length = √(Area)

Side length = √(158) = 12.57 feet

Answer:

Step-by-step explanation:

what is the finance charge?

Answer:

n = 8.

Step-by-step explanation:

I am assuming that the sum is 255.

The last term is 128 and the common ratio is 2 so we can work backwards until we reach a sum of 255.

Term n = 128 so the previous term must be 128/2 = 64.

So following this pattern we have:

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.

So we see that n = 8.

Answer:

3

Step-by-step explanation:

3 pounds were picked per hour

Answer: Hello there!

We know that the number of blueberries picked varies directly as the number of hours worked.

Direct variation means that: b = kh

where b is the number of blueberries, k is a constant of proportionality and h is the number of hours worked.

we know that in 10 hours there are 30 pounds of blueberries collected, then we can replace these numbers in the equation and solve it for k. And you want that I don't include units in the answer, so I will not include them.

30 = k*10

k = 30/10 = 3

Then the constant of proportionality is 3, whit is the amount of punds of blueberrys collected in one hour.