if sin(theta) = -2/5, and theta is in quadrant 111, then find

Answer:

h

Step-by-step explanation:

Answer:

Step-by-step explanation:

The values of the trigonometry ratios are sin(21) = √(1 -  k²), cos(201) = -k,  cos(42) = 2k² + 1 and cos(51) = k√3/2 - 1/2√(1 -  k²)

Given that cos 21° =k

Next, we calculate the trigonometry ratios as follows

(1) sin 21°

Here, we use

sin²(x) + cos²(x) = 1

So, we have

sin²(21) + cos²(21) = 1

This gives

sin²(21) + k² = 1

By subtraction, we have

sin²(21) = 1 -  k²

Take the square roots

sin(21) = √(1 -  k²)

(2) cos 201⁰

This is calculated using

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

So, we have

cos(180 + 21) = cos(180)cos(21) - sin(180)sin(21)

Evaluate the ratios

cos(201) = -1 * k - 0 * √(1 -  k²)

So, we have

cos(201) = -k

(3) cos 42°

Here, we have

cos(a + a) = cos²(a) - sin²(a)

So, we have

cos(21 + 21) = cos²(21) - sin²(21)

Evaluate the ratios

cos(42) = k² + 1 +  k²

So, we have

cos(42) = 2k² + 1

(4) cos 51°

This is calculated using

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

So, we have

cos(30 + 21) = cos(30)cos(21) - sin(30)sin(21)

Evaluate the ratios

cos(51) = √3/2 * k - 1/2 * √(1 -  k²)

So, we have

cos(51) = k√3/2 - 1/2√(1 -  k²)

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The total area of all four white boards is 84 square feet, obtained by multiplying the dimensions of one board (7ft × 3ft) by the number of boards (4)

Area is the measure of the size of a two-dimensional surface, usually expressed in square units such as square inches, square feet, or square meters.

Square feet is a unit of area commonly used to measure the size of a surface in the US customary and Imperial measurement systems. One square foot is equal to the area of a square with sides of one foot in length.

According to the given information:

Barb covered 4 walls with white boards, and each board measured 7ft × 3ft. To find the total area of all 4 boards, we need to multiply the area of one board by the number of boards:

Total area = area of one board × number of boards

Total area = (7 ft × 3 ft) × 4

Total area = 21 ft² × 4

Total area = 84 ft²

Therefore, the total area of all four white boards is 84 square feet.

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Based on the expression, the answer to the question is, and the condensed expression is 1/(25k²).

A value is represented by an expression, which is made up of symbols, variables, constants, and operators. Expressions are used in computer programming to alter data and carry out calculations. Expressions may be straightforward or intricate, and they may contain arithmetic, logical, or conditional assertions. Expressions in mathematics can stand in for equations, functions, and other abstract ideas. Expressions can be used to describe actual phenomena, such as how things move or how systems behave.

To simplify the expression (1/5k)², we square the numerator and denominator separately, as follows:

(1/5k)² = (1²) / (5k)²

= 1 / (25k²)

Therefore, the simplified expression is 1/(25k²).

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Particles P and Q travel in consonance whenever: 0 < t < 10/g or t > 10/g

Assuming particle P is launched downwards, its velocity shifts according to the equation:

vP = gt,

where g is the acceleration due to gravity (roughly 9.81 ms^-2).

Conversely, particle Q emerges vertically with a speed of 10 ms^-1, thus making its velocity at a later point t :

vQ = 10 - gt.

It should be noted that to spot the points in time where both particles transit in the same direction, we arm ourselves by finding out when vP and vQ yield the equivalent sign. This happens when either:

The two velocities are positive (i.e., upwards motion for both) or;

Velocities of each particle yields negative signal (transiting downwards for both).

Case 1: Both velocities are positive

In this case, we have:

gt < 10

t < 10/g

Considering that t stands for time beginning from the projection of particle P, we must follow the condition t > 0. Thinking thus, the set of values which ensure simultaneous upward motion for both particles is:

0 < t < 10/g

Case 2: Both velocities are negative

As per our hypothesis:

gt > 10

t > 10/g

At the same time, noticing that particle Q starts 5 m approx. above the land surface, it will experience its maximum height when:

10 - gt = 0    

t = 10/g

Which means, the set of values useful to determine downwards movement of both particles ought to be:

t > 10/g

In conclusion, to sum up, Particles P and Q travel in consonance whenever: 0 < t < 10/g or t > 10/g

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Answer:

I'd assume D

Step-by-step explanation:

Hanna has 5 letters and 4 are 2 letters that are the same therefore 4 letter out of 5 chance

Answer:

[tex]y=\frac{-4}{3}x+9[/tex]

Step-by-step explanation:

[tex]y=slope*x+y intercept[/tex]

Given a slope of -4/3 and y-intercept of 9, the equation will be:

[tex]y=\frac{-4}{3}x+9[/tex].

Answer:

271.17 is the answer

Step-by-step explanation:

we know that the housing and fixed expenses of $813.52/month.

6 months emergency funds 

= 813.52 × 6 = 4881.82

We know that you want to have it funded in 18 months

put it fraction will solve the problem:

[tex]\frac{4881.12}{18}[/tex] = 271.17

271.71 being the answer

Translate triangle JKL left 1 unit and downward 10 units; the triangles are congruent

From the question, we have the following parameters that can be used in our computation:

Triangle JKL to triangle MNO

From the figure, we can see that translating the triangle JKL left 1 unit and downward 10 units would give triangle MNO

The above also implies that the triangles are congruent

This is because translation is a rigid transformation

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The probability that a student randomly chooses to play drums is  34.29%

The total number of students in seventh grade = 35

The number of students who choose drums in seventh grade is 14

The total number of students in eighth grade = 35

The number of students who choose drums in eighth grade is 10

Total number of students who play drums = 14 + 10 = 24

Total number of students = 35 + 35 = 70

The probability that a student randomly chooses to play drums is:

Probability = Total number of students who play drums / Total number of students

Probability = 24 / 70

Probability = 0.342857 (rounded to 6 decimal places)

probability = 34.29%

Hence,  the probability that a student randomly chooses to play drums is  34.29%

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The domain and the range of the function are given as follows:

The function approaches y = 0 as x approaches positive infinity.

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The complete statement is -

There have been two especially important shifts in how markets are defined in recent decades: one involves technology  and the other involves globalization.

Given is that there have been two especially important shifts in how markets are defined in recent decades. It is asked to fill in the blanks with correct values.

We can fill the statement as -

There have been two especially important shifts in how markets are defined in recent decades: one involves technology  and the other involves globalization.

Therefore, the complete statement is -

There have been two especially important shifts in how markets are defined in recent decades: one involves technology  and the other involves globalization.

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The slope of the line is given as follows:

m = -1/8.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

From the table, we have that when x increases by 8, from x = -16 to x = -8, y decays by one, from y = 8 to y = 7, hence the slope m is given as follows:

m = -1/8.

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Answer:

1247

Step-by-step explanation:

the answer is 1247

I hope this helps

Lily will need to invest $16,483.29 in the account now to have $40,000 in 18 years.

The two types of interest computations utilised in finance are simple interest and compound interest.

Simple interest is just computed on the principal, or the initial amount borrowed or invested. For a specific amount of time, the interest rate is applied to the principal sum, and each period's interest earned or charged is the same.

On the other hand, compound interest is calculated using both the original principal and any prior interest payments. The principal is increased by the interest generated in each month, and the new sum serves as the foundation for computing interest in the following period.

The compound interest is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Isolating the value of P we have:

[tex]P = A/(1 + r/n)^{(nt)}[/tex]

Now, substituting the values A = $40,000, r = 0.06 (6% as a decimal), n = 2 (compounded semi-annually), and t = 18 years:

[tex]P = $40,000/(1 + 0.06/2)^{(2*18)}\\P = $40,000/(1.03)^{36}[/tex]

P = $40,000/2.4271

P = $16,483.29

Hence, Lily will need to invest $16,483.29 in the account now to have $40,000 in 18 years.

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The only ordered pair that is a solution to the given system of inequalities is (0, -1).

Inequalities are mathematical statements that describe a relationship between two values or expressions that are not necessarily equal. In an inequality, the symbols "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to) are used to indicate the relationship between the expressions.

In the given questions,

To determine if an ordered pair is a solution to a system of inequalities, we must check if the pair satisfies all the inequalities in the system.

For the given system of inequalities:

y < -x² + x

y > x² - 4

Checking each of the given ordered pairs:

(0, -1):

-1 < -0² + 0 is true

-1 > 0² - 4 is true

So, (0, -1) is a solution to the system of inequalities.

(1, 1):

1 < -1² + 1 is false

1 > 1² - 4 is true

So, (1, 1) is not a solution to the system of inequalities.

(2, -3):

-3 < -2² + 2 is true

-3 > 2² - 4 is false

So, (2, -3) is not a solution to the system of inequalities.

(3, -6):

-6 < -3² + 3 is false

-6 > 3² - 4 is false

So, (3, -6) is not a solution to the system of inequalities.

Therefore, the only ordered pair that is a solution to the given system of inequalities is (0, -1).

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The length of the missing leg is √29 units

Given that c=5 km and b=2 km

We have to find the value of a

The length of the missing leg is a which is hypotenuse which we have to find.

c²+b²=a²

5² + 2² =a²

25+4=a²

29=a²

Square root on both sides

a=√29 units

Hence, the length of the missing leg is √29 units

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For the given figure the measurement or lengths are:

AB = 4.5 cm.

ED = 9 cm.

DF = cannot be determined since it is a chord and it needs more information.

CA = 4.5 cm.

We have the radius of the given circle is 4.5 cm.

Now we have to find the lengths of the mentioned line segment from the circle figure.

A is the center of the circle and B is a point on circumference of circle.

So, AB is a radius of the circle. So, AB = 4.5 cm.

Now, E and D are two points on circumference of circle and segment ED passes through the center A.

So, ED is a diameter for the circle.

We know that Diameter = 2*Radius

So, ED = 2*4.5 = 9 cm.

F and D are two points on circumference of circle but segment DF does not pass through the center A. So it is not diameter it is a general chord.

So we cannot determine this due to inadequate information.

A is the center of the circle and C is a point on circumference of circle.

So, CA is a radius of the circle. So, CA = 4.5 cm.

Hence, AB = 4.5 cm.; ED = 9 cm.; DF = cannot be determined; CA = 4.5 cm.

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The question is incomplete. The complete question will be -

"The circle below has a center at point A and a radius of 4.5 cm.

Find the measurement of the line segments that you can determine. For anyone you cannot determine, explain your reasoning why.

Segment AB

Segment ED

Segment DF

Segment CA"

a) The range of values that the game operator can use to represent a winner getting a stuffed animal is given as follows:

1 to 45.

b) The percentage of the 10 simulated winners who got a stuffed animal is of: 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There is a 45% theoretical probability of getting a stuffed animal, hence the range of values can be given as follows:

1 to 45.

From the table, out of 10 winners, 4 have numbers ranging from 1 to 45, hence the percentage is given as follows:

p = 4/10 x 100%

p = 40%.

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Consider the function f(x) = (x² - 4)/(x - 2).

For x gives us x = -2 and x = 2 which are the x-intercepts of f(x) and we have f(0) = -4/2 = -2 which is the y-intercept of f(x)

What is meant by function?

A function is a mathematical rule that assigns a unique output value for each input value in a specified domain. It is a relationship between two or more variables that describes how one variable depends on the others.

What is meant by the x-intercept?

The x-intercept of a function is the point where the graph of the function intersects the x-axis. It is the value of the input variable (usually denoted as x) that makes the output of the function equal to zero.

According to the given information

Consider the function f(x) = (x² - 4)/(x - 2). To find the x-intercept, we set f(x) = 0 and solve for x. We get (x² - 4)/(x - 2) = 0 which means that x² - 4 = 0 since division by zero is undefined. Solving for x gives us x = -2 and x = 2 which are the x-intercepts of f(x). To find the y-intercept, we set x = 0 and solve for y. We get f(0) = -4/2 = -2 which is the y-intercept of f(x)

The complete question is:

For this rational function, Use algebra to find the x-intercepts and

y-intercepts. The given function is f(x) = (x² - 4)/(x - 2)

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The inequality that represents the number line given in the image above is: D. x > -1.

A number line is a straight line that represents the set of real numbers, with each point on the line corresponding to a unique real number, as shown in the given diagram above.

There's an unshaded or open circle on the number -1, and an arrow extending from zero to your right. This means that -1 is not included in the possible values of x. It also means the x is greater than -1.

Therefore, the inequality is: D. x > -1.

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The statement that is true is a) The horsepower associated with an engine speed of 2.5 rpm would be 85 hp.

To use the equation ŷ = 10 + 30x, we need to plug in the value of x (engine speed in rpm) to find the predicted value of y (horsepower).

a) For x = 2.5, ŷ = 10 + 30(2.5) = 85. Therefore, the horsepower associated with an engine speed of 2.5 rpm would be 85 hp.

b) For x = 3.5, ŷ = 10 + 30(3.5) = 115. Therefore, the statement is false.

c) For x = 0.5, ŷ = 10 + 30(0.5) = 25. Therefore, the statement is false.

d) For x = 1.5, ŷ = 10 + 30(1.5) = 55. Therefore, the statement is false.

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Answer:

+ 27

Step-by-step explanation:

-27     +27    = 0

Answer: +27

Step-by-step explanation:

If you think of a number line -27 is 27 units left of 0

so you would need to move 27 units in the positive direction to get to 0

+27

The volume Colton store inside the new shed is 640 cubic feet.

We are given that;

length=10, width=8, height=6

Now, we can calculate the volumes of each part:

Volume of base prism = lwh Volume of base prism = (10)(8)(6) Volume of base prism = 480 cubic feet

Volume of roof prism = Bh Volume of roof prism = (0.5)(8)(4)(10) Volume of roof prism = 160 cubic feet

Volume of shed = Volume of base prism + Volume of roof prism Volume of shed = 480 + 160 Volume of shed = 640 cubic feet

Therefore, by the given prism the answer will be 640 cubic feet.

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Answer:

circumference of a circle = 30.473 cm

Step-by-step explanation:

solution: given diameter- 9.7cm

so radius (pie) = d/2 = 9.7/2 = 4.85

circumference of a circle is 2(pie)r

circumference = 2 × 22/7 × 4.85

circumference = 30.47345 = 30.473 to 3 sf.

circumference of a circle = 30.473 cm

The value mean of variable 1 is approximately 170.42 and the median is 153.75.

We are given that;

Variable 1 = 190,187,186,183,182,182,181,181,180,164,161,160,140,158,156,155,152.5,151

Now,

To Find the mean by adding up all the values and dividing by the number of values

Mean = (190 + 187 + 186 + 183 + 182 + 182 + 181 + 181 + 180 + 164 + 161 + 160 + 140 + 158 + 156 + 155 + 152.5 + 151) / 18 Mean = (3067.5) / 18 Mean ≈ 170.42

Find the median by arranging the values in ascending order and locating the middle value

Median = (140 ,151 ,152.5 ,155 ,156 ,158 ,160 ,161 ,164 ,180 ,181 ,181 ,182 ,182 ,183 ,186 ,187 ,190) Median = (152.5 + 155) / 2 Median = (307.5) / 2 Median = 153.75

Therefore, by mean and median answer will be 170.42 and 153.75.

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Answer:

For this question you can use simultaneous equation, both elimination method or substitution method. In math when you are trying to solve for something but you don't have the answer to it, you can always use x.

soooo
5x + 3y = 27 (equation 1)

7x + 9y = 51 (equation 2)

soo im using substitution method

From equation 1, we can solve for y in terms of x:

y = (27 - 5x) / 3

Substitute this expression for y into equation 2 and solve for x:

7x + 9[(27 - 5x) / 3] = 51

Multiplying both sides by 3 to eliminate the fraction:

21x + 27 - 15x = 153

Simplifying and solving for x:

6x = 126

x = 21

Now, we can substitute this value for x into either equation 1 or equation 2 to solve for y:

5(21) + 3y = 27

105 + 3y = 27

3y = -78

y = -26

Since a negative cost doesn't make sense, we need to double-check our work. We made an error by switching the signs of the cost variables in our equations. So, the correct answers are:

The cost per pound of almonds is $21.

The cost per pound of jelly beans is $26.