In a circle of radius 30 inches, a central angle of 35° will intersect the circle
forming an arc of length

Answer:

Part 1) [tex]sin(\theta)=-\frac{5\sqrt{61}}{61}[/tex]  or [tex]sin(\theta)=-\frac{5}{\sqrt{61}}[/tex]

Part 2) [tex]csc(\theta)=-\frac{\sqrt{61}}{5}[/tex]

Part 3) [tex]cot(\theta)=\frac{6}{5}[/tex]

Step-by-step explanation:

we know that

The point (-6,-5) lies on the III Quadrant

so

sin(theta) is negative

csc(theta) is negative

cot(theta) is positive

Part 1) Find the sine of angle theta

we know that

The function sine is equal to divide the opposite side to the angle theta by the hypotenuse

[tex]sin(\theta)=\frac{y}{r}[/tex]

we have

[tex]x=6\ units,y=5\ units[/tex]

Applying the Pythagoras Theorem

[tex]r^{2}=x^{2}+y^{2}[/tex]

substitute

[tex]r^{2}=6^{2}+5^{2}[/tex]

[tex]r^{2}=61[/tex]

[tex]r=\sqrt{61}\ units[/tex] -----> the hypotenuse

substitute

[tex]sin(\theta)=\frac{5}{\sqrt{61}}[/tex]

Simplify

[tex]sin(\theta)=\frac{5\sqrt{61}}{61}[/tex]

Remember that the sin(theta) is negative

so

[tex]sin(\theta)=-\frac{5\sqrt{61}}{61}[/tex]

Part 2) Find the cosecant of angle theta

we know that

The function cosecant is equal to divide the hypotenuse by the opposite  side to the angle theta

[tex]csc(\theta)=1/sin(\theta)=\frac{r}{y}[/tex]

we have

[tex]sin(\theta)=-\frac{5}{\sqrt{61}}[/tex]

so

[tex]csc(\theta)=-\frac{\sqrt{61}}{5}[/tex]

Part 3) Find the cotangent of angle theta

we know that

The function cotangent is equal to divide the adjacent side to the angle theta by the opposite side to the angle theta

[tex]cot(\theta)=\frac{x}{y}[/tex]

we have

[tex]x=6\ units,y=5\ units[/tex]

substitute

[tex]cot(\theta)=\frac{6}{5}[/tex]

The exact values of sin theta, csc theta, and cot theta for a point (-6, -5) on the terminal side are -5/sqrt(61), sqrt(61)/-5, and 6/5 respectively.

In this problem we have a point (-6, -5) on the terminal side of theta. The x-coordinate corresponds to the cosine of theta and the y-coordinate corresponds to the sin theta.

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Answer:

-100

Step-by-step explanation:

[tex] \frac{x}{5} + 6 = - 14[/tex]

Subtract 6 from both sides

[tex] \frac{x}{5} = - 20[/tex]

Multiply both sides by 5

[tex]x = - 100[/tex]

The value of the x is -100.

Equation, statement of equality between two expressions consisting of variables and/or numbers.

We have an equation with one variable. We will try to have the unknown on the left side and all the numerical values on the right side.

x/5 +6  = -14for making all numerical terms on the right side, we will have to do the following steps:

Step 1:Subtracting -6 on both sides x/5 +6 - 6 = -14-6x/5 = -20

Step 2 :Multiplying 5 on both sides x/5 *5 = -20x5x = -100

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The answer is D: 351 ft2. Hope it helps

Answer= D) 351 ft2

Step-by-step explanation: Alright check it. First lets break it down. 2 rectangles which we need the area for. 24*9 for the bottom one and since 18-9=9 then the top rectangle is 15*9 so basically (15*9) + (24*9) = 135+216=351

Answer:

[tex]\large\boxed{-\dfrac{1}{3}-\dfrac{\sqrt{14}}{3}i,\ -\dfrac{1}{3}+\dfrac{\sqrt{14}}{3}i}[/tex]

Step-by-step explanation:

Use

[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]3x^2+2x+5=0\\\\a=3,\ b=2,\ c=5\\\\b^2-4ac=2^2-4(3)(5)=4-60=-56\\\\\sqrt{b^2-4ac}=\sqrt{-56}=\sqrt{(4)(-14)}=\sqrt4\cdot\sqrt{-14}=2\sqrt{-14}[/tex]

Use

[tex]i=\sqrt{-1}[/tex]

[tex]\sqrt{-14}=\sqrt{(-1)(14)}=\sqrt{-1}\cdot\sqrt{14}=i\sqrt{14}[/tex]

Therefore:

[tex]x=\dfrac{-2\pm 2i\sqrt{14}}{2(3)}=-\dfrac{2}{6}\pm\dfrac{2i\sqrt{14}}{6}=-\dfrac{1}{3}\pm \dfrac{\sqrt{14}}{3}i[/tex]

The complex solution of the given quadratic equation 3x^2+2x+5=0 is x = (1/6)[ -2 ± i√56].

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.

As per the given quadratic equation, 3x^2+2x+5=0

x = [-2 ±√(4 - 4 x 3 x 5)]/(2 x 3)

x = (1/6)[ -2 ± i√56]

Hence "The complex solutions of the given quadratic equation 3x^2+2x+5=0 is x = (1/6)[ -2 ± i√56]".

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Answer:

y=$2.95x+$479.4

Step-by-step explanation:

Let

x----> the number of movie rentals

y ----> the cost for movie rentals

we know that

The expression that represent the monthly cost is equal to

y=$2.95x+$39.95

1 year has 12 months

so

The expression that represent the yearly cost is equal to

y=$2.95x+$39.95*(12)

y=$2.95x+$479.4

Answer:

A

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

(b+3c)+(b+3c)

=2(b+3c)

Note:x+x=2x

[tex]2(b+3c)=2b+2(3c)=b+3c+b+3c[/tex]

The answers are B and C.

Hope this helps.

r3t40

Answer:

well this old so like yeah u prob know by now...

Step-by-step explanation:

Answer:

[tex]a_t=ar^{t-1}[/tex]

t=6 months

Step-by-step explanation:

We are given that the number of people playing a new phone app game triples every month

When the app first launch , the number of people started playing the  game  right away=800

According to question

The number of peoples are currently playing the game=194,400

We solve by using the formula of  geometric series because we get a geometric series pattern

The number of people playing the game when app game launch=800

The number of people playing game after one month=2400

800,2400,7200,........,194,400

[tex]a_1=800,a_2=2400,a_3=7200,a_t=194,400[/tex]

We are finding common ratio

[tex]\frac{a_2}{a_1}=\frac{2400}{800}=3[/tex]

[tex]\frac{a_3}{a_2}=\frac{7200}{2400}=3[/tex]

Hence, the common ratio is 3 therefor nth term of  G.P

[tex]a_t=ar^{t-1}[/tex]

a=800,r=3,[tex]a_t=194,400[/tex]

Substitute the values then we get

[tex]194,400=800(3)^{t-1}[/tex]

[tex]\frac[194400}{800}=(3)^{t-1}[/tex]

[tex]243=3^{t-1}[/tex]

[tex]3^5=3^{t-1}[/tex]

When base are same on both side then the power are equals

Therefore, t-1=5

t=5+1=6

Hence, when there are 194,400 people currently playing the game then

the number of months ,t=6 that have passed since the app launched.

Answer:

800(3)^t = 194,400; t = 5 months

Step-by-step explanation:

Answer:

6y - 3y - 7 = -2 +3

Simplify both sides:

3y -7 = 1

Add 7 to both sides:

3y = 8

Divide both sides by 3:

y = 8/3 = 2 2/3

There is only one solution.

Answer:

AB

Reflexive Property

BE

SSS

Definition of perpendicular

Step-by-step explanation:

Answer:

This question is based on concept of geometry. Therefore, the answers are as follows:

1) AB         2) Reflexive property           3) BE          4) SSS

5) definition of perpendicularity.

Given that:

ABCD is a square.

In this question, we have to fill the blanks and complete the sentence where it is looking like incomplete.

According to question,

Therefore, at first It is given that, if we consider triangle AEB and Triangle AED, we observe that side AB side is congruent to side AD.

(2) We know that, side AE is congruent to side AE by using the Reflexive property because sides of a square are congruent.

(3) Finally, we know that side DE is congruent to side BE because the diagonals of a square bisect each other.

(4)Therefor triangle AEB is congruent to triangle AED by SSS congruency.

(5) We see that angle AED and angle AEB are a linear pair, and congruent  by CPCT , the angle AED and AEB are a linear pair and the measure of these angle will be 90 because ABCD is a square and thus diagonal AC is perpendicular to diagonal BD by the definition of perpendicularity.

Therefore, the answers are as follows:

1)AB

2)Reflexive property  

3)BE  

4)SSS

5) definition of perpendicularity.

Step-by-step explanation:

The sister is 4n yrs old.

That is because 4 times n is 4n.

Answer: a^2+b^2=c^2

Step-by-step explanation: (18^2=14^2+c^2)=324=196+c^2

324-196=128 and the square root of 128 is 8 radical 2 or in decimal form 11.31

Answer:

11.3137085 ft

Step-by-step explanation:

The length (l) of the ladder is 18ft

The height (h) of the ladder from the ground is 14 ft

The distance (x) of the foot of the ladder to the bottom of the house is:

Applying the Pythagorean theorem:

x² = l² - h²

x = [tex]\sqrt{l^2 - h^2}[/tex]

x = [tex]\sqrt{18^2 - 14^2}[/tex] = 11.3137085 ft

The answer is:

The third option,

c) [tex]h(x)=2.25x-22[/tex]

We are given the functions E(x) and K(x), since they both are function of the same variable, we need to calculate the difference between them.

From the statement we know the functions:

[tex]f(x)=9.75x+62[/tex]

and

[tex]g(x)=7.5x+84[/tex]

So, calculating the difference the functions we have:

[tex]h(x)=f(x)-g(x)[/tex]

[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]

[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]

[tex]h(x)=9.75x-7.5x+62-84[/tex]

[tex]h(x)=2.25x-22[/tex]

Hence, the answer is the third option,

c) [tex]h(x)=2.25x-22[/tex]

Have a nice day!

Answer: Option C

[tex]h(x)=2.25x-22[/tex]

Step-by-step explanation:

To find the function h(x) that models the difference between Hector's and Cari's gains, subtract the functions f(x) with g(x)

That is to say:

[tex]h (x) = f (x) -g (x)[/tex]

We know that

[tex]f (x) = 9.75x + 62\\\\g (x) = 7.5x + 84[/tex]

Then we can find the function h(x)

[tex]h(x) = 9.75x + 62 - (7.5x + 84)\\\\h(x) = 9.75x + 62 -7.5x -84[/tex]

[tex]h(x)=2.25x-22[/tex]

Answer:

- 10

Step-by-step explanation:

Given

3(x - 4) ≥ 5x + 2 ← distribute left side

3x - 12 ≥ 5x + 2 ( subtract 3x from both sides )

- 12 ≥ 2x + 2 ( subtract 2 from both sides )

- 14 ≥ 2x ( divide both sides by 2 )

- 7 ≥ x ⇒ x ≤ - 7

The only value from the list that is in the solution set is

x = - 10

The value of x is -10

The correct option is (A)

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables.

Given expression:

3(x - 4) ≥ 5x + 2

Using distributive law,

3x - 12 ≥ 5x + 2

- 12 ≥ 2x + 2 ( subtract 2 from both sides )

- 14 ≥ 2x ( divide both sides by 2 )

- 7 ≥ x

x ≤ - 7

Hence, x is less than and equal -7 so the only solution is -10

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Answer: -2, 0, 4

Set the equation equal to zero.

x³ - 2x² - 8x = 0

Factor out x in the equation, since all the terms (x³, -2x², and -8x) are divisible by x. You can check your accuracy using the Distributive Property.

x(x² - 2x - 8) = 0

Factor out the polynomial. To do this, find two numbers that multiply to get the last term, -8, and add together to get the middle term, -2. In this case, those two numbers are -4 and 2 (-4 × 2 = -8 and -4 + 2 = -2). Don't forget about the x that was factored out before!

x(x - 4)(x + 2) = 0

Set each factor equal to zero and solve for x. The factors in the equation are x, (x - 4), and (x + 2).

        x = 4

        x = -2

The zeros of the polynomial function are -2, 0, and 4.

Find the volume of what the full rectangle would be then find the area of the missing piece and subtract:

10 x 12 x = 960 cm^3

4 x 5 x 8 = 160 cm^3

960 - 160 = 800 cm^3

Answer: r and s because these are the lines that 1 and 9 are on

The answer is r and s.

Hope this helps!

40% of the figure is shaded.

The image depicts many grids. These small squares has 10 rows and 10 columns. So, the total number of squares are:

10 x 10=100 squares.

Out of 100 squares, 4 rows and their 10 columns are shaded. So,

4*10=40 squares

So, 40 squares are shaded. To find the percentage we can use the formula:

Shaded/ Total Squares x 100

= 40/100 x 100

= 40%

Therefore, 40 percent of the figure is shaded.

To find what percent of a figure is shaded, calculate the shaded area divided by the total area and multiply by 100. In probability distributions, shading indicates the probability that a variable falls within a specific range, such as the 80th or 90th percentile of a distribution.

To determine what percent of the figure is shaded, one must first understand the concept of percentage calculations. The percentage is computed by dividing the part (shaded area) by the total area, then multiplying by 100. In the case of probability distributions, the shaded area represents a probability, such as the probability of a variable falling between two values, or the specific percentile of a distribution.

For example, if we have a graph with a horizontal axis for X, and we need to shade the region corresponding to a certain probability or percentile, we need to identify the region under the curve that equates to that percentage. This could involve calculating the area between two x-values or finding a value that corresponds to a given area under the curve, such as the 80th percentile or 90th percentile. To express the result as a percentage, multiply the probability by 100.

Sometimes, the question may provide specific conditions, such as indicating that the shaded area under one curve is equal to the area of another shape, like a rectangle or another curve. In this case, we can assume the two percentages are equal and express the probability of one as the same percentage as the other.

Quotient means divide so 7 divided by 1/5 is 35

answer:35

reason: because all you are doing is dividing 7 and 1/5

Answer:

See the procedure

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

a,b,c the lengths side of triangle

c is the greater side

The perimeter is equal to

P=a+b+c

P=36 cm

If c=18 cm

then

a+b=18

Applying the Triangle Inequality Theorem

a+b > c

18 > 18  ----> is not true

therefore

Principal Aranda is incorrect

The larger side cannot measure 18 cm

The largest side must be less than 18 cm

Answer:

see below

Step-by-step explanation:

We can round the original price of the jacket to 100 dollars

30% off means we pay 70%

70 % of 100

.70*100 = 70

The jacket will cost just less than 70 dollars

Our estimate is high since we rounded up

Answer:

[tex]P (even,\ then\ not\ 2) = \frac{5}{12}[/tex]

Step-by-step explanation:

When launching a numerical cube there are 6 possible results

S = {1, 2, 3, 4, 5, 6}

Among these possible outcomes only 3 are even numbers

S = {2, 4, 6}

So the probability of obtaining an even number is

[tex]P = \frac{3}{6}\\\\P = \frac{1}{2}[/tex]

Then, the probability of obtaining a number other than 2 is:

[tex]P = \frac{5}{6}[/tex].

If 2 launches are made then the events are independent,

Thus:

P(even, then not 2) is

[tex]P (even,\ then\ not\ 2) = \frac{1}{2} * \frac{5}{6}\\\\P (even,\ then\ not\ 2) = \frac{5}{12}[/tex]

Answer:

[tex]x=1[/tex] and [tex]x=4[/tex]

Step-by-step explanation:

We have the following system of equations:

[tex]y=\sqrt{x}[/tex] and [tex]y=x-2[/tex]

To solve the problem, we need to equal the two equations:

[tex]x-2=\sqrt{x}[/tex] ⇒ [tex](x-2)^{2} =x[/tex] ⇒ [tex]x^{2} -4x + 4 = x[/tex]  

⇒ [tex]x^{2} -5x + 4 = 0[/tex]  

So you need to find two numbers that added equal to 5 and multiplied equal to 4. These two numbers are [tex]x=-1[/tex] and [tex]x=-4[/tex].

Then, the factorized form of the polynomial is: [tex](x-1)(x-4)[/tex].

The, the solution to the system of equations is: [tex]x=1[/tex] and [tex]x=4[/tex].

Answer:

x=1.5 & x=1.2

Step-by-step explanation:

I took the mastery test for Edmentum and I got it right :)

Answer:

A.) The are of the circle depends on the square of the radius

Step-by-step explanation:

To find the area, use the formula A= pi r^2

A= pi(18^2)= 1017.88

so A and B are not correct

Pi is a constant and is never changing.

Central Angle doesn't apply to this problem

so the correct answer is the first choice

The following statements are correct with reference to the circle given -

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is a circle with the radius 18 cm.

The area of the circle is given by -

A = πr²

A = 18 x 18 x π

A = 324π

Therefore, we can conclude that the following statements are correct with reference to the circle given -

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Answer:

31.5 litres

Step-by-step explanation:

If Mel uses all 30 litres of yellow paint, then:

5 / 2 = 30 / x

5x = 60

x = 12

Mel would need 12 litres of blue paint, but she only has 9 litres.  So the amount of yellow paint she needs is:

5 / 2 = x / 9

2x = 45

x = 22.5

Mel will use 22.5 litres of yellow paint with 9 litres of blue paint to make a total of 31.5 litres of green paint.

She can make a maximum of 28 litres of green paint.

To find the maximum amount of green paint Mel can make with her yellow and blue paint, we must use the ratio of 5:2 (yellow to blue) given for mixing the green paint.

Firstly, calculate the number of batches of green paint that can be made with the available yellow paint:

Mel has 30 litres of yellow paint and needs 5 litres per batch of green paint, so she can make 30 ÷ 5 = 6 batches from the yellow paint.

Next, calculate the number of batches that can be made with the blue paint:

Mel has 9 litres of blue paint and needs 2 litres per batch of green paint, so she can make 9 ÷ 2 = 4.5 batches from the blue paint.

However, since we cannot have half a batch, the maximum number of full batches Mel can produce from the blue paint is 4.

The limiting reactant here is the blue paint since it allows fewer batches to be made. Therefore, Mel can only make 4 full batches of green paint.

To find the total amount of the green paint from the batches:

Combine the ratios, which add up to 7 parts (5 parts yellow and 2 parts blue).

Multiply the number of batches by the sum of the parts: 4 batches × 7 parts per batch = 28 litres of green paint.

Thus, the maximum amount of green paint Mel can make is 28 litres.

I ussually think of them as arrows telling me where to go.

if it is >   you go ----->

if it is < you go <------

ANSWER

[tex]a_n=4( { (- 2)}^{n - 1} )[/tex]

for n≥1

EXPLANATION

The explicit equation for a geometric sequence is found using the formula:

[tex]a_n=a_1( {r}^{n - 1} )[/tex]

where

[tex]a_1 = 4[/tex]

is the first term and

[tex]r =\frac{- 8}{4}=-2[/tex]

is the common ratio.

We substitute the values into the formula to obtain,

[tex]a_n=4( { (- 2)}^{n - 1} )[/tex]

This is the explicit formula for the geometric sequence.

The domain is n≥1

Answer:

to everyone that needs it the awnser is 29.0% its not 0.31

i got it correct

Step-by-step explanation:

Therefore, Option ( C ),P(Microbial Contamination from Salmonella | Capsule A)=0.31%

The probability of capsule B having microbial contamination is greater than the probability of capsule D having it.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

It is given that the table shows the probabilities of contamination in medicine capsules from the presence of heavy metals and different types of microbes.

Now, By given table, we have;

The probability of capsule B having microbial contamination is, 0.33%

And, the probability of capsule D having it is, 0.22%

Hence, The probability of capsule B having microbial contamination is greater than the probability of capsule D having it.

Above is the table of conditional probabilities of contamination from various sources given type of capsules.

P(Microbial Contamination from Salmonella | Capsule A)=0.31%

Thus, the chance the is from contamination salmonella option (C) is correct.

Correct Answer:

The probabilities of contamination in medicine capsules due to the presence of heavy metals and different types of microbes are given in the table.

The probability of capsule B having microbial contamination is [blank] the probability of capsule D having it.

Answer choices in drop down menu are:

A. the same as

B. greater than

C. less than​

Answer:

-8.5

Step-by-step explanation:

-4x+8=42

42-8=34

34/-4=8.5

Answer:

x = -8.5

Step-by-step explanation:

minus 8 on both sides and the eight should cancle on the left side

42 minus 8 is 34

then you divide negative 4 on both sides

Answer:

The answer is 11 100%FOR SURE BELIEVE ME!!!

Step-by-step explanation:

A,B= (2*11)=22-3= 19

B,C= (11+1)=12

A,C= 19+12= 31

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