Answer: [tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
Step-by-step explanation: Given that
[tex]\sin\theta=-\dfrac{1}{2}[/tex] and [tex]\theta[/tex] lies in Quadrant III.
We are to find the value of [tex]\tan \theta.[/tex]
We will be using the following trigonometric identities:
[tex](i)~sin^2\theta+\cos^2\theta=1,\\\\(ii)~\dfrac{\sin\theta}{\cos{\theta}}=\tan \theta.[/tex]
We have
[tex]\tan\theta\\\\\\=\dfrac{\sin\theta}{\cos\theta}\\\\\\=\dfrac{\sin\theta}{\pm\sqrt{1-\sin^2\theta}}\\\\\\=\pm\dfrac{-\frac{1}{2}}{\sqrt{1-\left(\frac{1}{2}\right)^2}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\\=\pm\dfrac{1}{\sqrt3}.[/tex]
Since [tex]\theta[/tex] lies in Quadrant III, so tangent will be positive.
Thus,
[tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
In a theater, there are 4 long rows of chairs, each with an equal number of chairs. There are 5 short rows of chairs, each with an equal number of chairs. On a crowded day, the ushers added 2 chairs to each long row and 3 chairs to each short row. If x represents the number of chairs in each long row and y represents the number of chairs in each short row, the total number of chairs in the theater is given by the expression 4(x + 2) + 5(y + 3). An equivalent expression is
Answer:
HERE IS THE ABSWER SRRY FOR CAPS 4(x+2) + 5(y+3)
4x+8 + 5y + 15
4x + 5y + 23
Step-by-step explanation:
Nayelly is weighing how much of a solid resulted from a chemical reaction on a scale that reads to the nearest 18 ounce. The measurement of the solid is 678 ounces. If the answer calls for the measurement to be rounded to the nearest tenth of an ounce, Nayelly should report that the solid weighed __________ ounces. Enter your answer as the decimal number that correctly fills in the blank in the previous sentence, like this: 42.6
I need help with this question.
Which inequality is graphed below?
3x + 2y < –6
3x + 2y > –6
3x – 2y > 6
3x – 2y < 6
Answer:
3x - 2y > 6
C is correct
Step-by-step explanation:
We are given a graph of inequality function and we need to find out the equation of graph.
First we find the equation of equality and then find inequality.
x-intercept: (2,0)
y-intercept: (0,-3)
Now we find equation of line intercept form:
[tex]\dfrac{x}{2}-\dfrac{y}{3}=1[/tex]
[tex]3x-2y=6[/tex]
Now we find inequality sign
If we take (0,0) as test point. It would be false because (0,0) is not in shaded area.
Put (0,0) into 3x-2y=6
3(0) - 2(0) ____ 6
0 ___ 6
We make it false
0 > 6
So, correct equation is 3x - 2y > 6
Hence, The equation of the given graph is 3x - 2y > 6
Keenan is checking his bicycle’s wheel. The wheel has a radius of 21 cm, and its center is 56 cm above the ground. Keenan is rotating the wheel at a constant speed of 165°/s. The height of a point on the tire as a function of time is given by h = 56 + 21 sin(165t), where h is the height in centimeters and t is the time in seconds. Find h when t = 17 s. Round your answer to the nearest tenth of a centimeter.
Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth Decay
y=100(1−12)^t
y=0.1(1.25)^t
y=((1−0.03)12)^2t
y=426(0.98)^t
y=2050(12)^t
A function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
We have the following equation:
[tex]y=100(1-12)^t[/tex]
That can be written as:
[tex]y=100(-11)^t[/tex]
Recall that the definition of exponential functions establishes that:
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
That is:
[tex]a \ \mathbf{must} \ be \ greater \ than \ 1[/tex]
In this problem, [tex]a=-11[/tex], therefore this is not an exponential function.
The function:
[tex]y=0.1(1.25)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=0.1 \ and \ a=1.25[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. This means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 1. This represents a growth.
The function:
[tex]y=((1-0.03)12)^{2t}[/tex] can be written as:
[tex]y=11.64^{2t}[/tex]
and is an exponential function because is a function of the form [tex]f(t)=a^{bt} \\ \\ where \ a>0 \ and \ b \ constant[/tex]
So [tex]a=11.64 \ and \ b=2[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]2t[/tex], the function increases. As in the previous exercise, this means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 2. This represents a growth.
The function:
[tex]y=426(0.98)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=426 \ and \ a=0.98[/tex]. Since [tex]a \ is \ less \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function decreases. Here this means that [tex]y[/tex] decreases as [tex]t[/tex] increases as illustrated in Figure 3. This represents a decay.
The function:
[tex]y=2050(12)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=2050 \ and \ a=12[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. So in this function [tex]y[/tex] also increases as [tex]t[/tex] increases as illustrated in Figure 4. This represents a growth.
Answer:
1. isn't an exponential function
2. growths
3. growths
4. decay
5. growths
Step-by-step explanation:
The exponential functions has the form: y = k1*k2^(k3*t), where k1, k2 and k3 are a constants, and k2>0. Graph of exponential functions always decrease or always increase. To know if a function growths or decay just evaluate the function in 2 points, for example t = 0 and t = 1, and compare their results.
1.
y = 100*(1−12)^x = 100*(−11)^x
Since (-11) is negative, then y is not an exponential function
2.
y(0) = 0.1*(1.25)^(0) = 0.1
y(1) = 0.1*(1.25)^(1) = 0.125
y(1) > y(0) -> growths
3.
y(0) =((1−0.03)12)^2(0) = 1
y(0) =((1−0.03)12)^2(1) = 135.4896
y(1) > y(0) -> growths
4.
y(0) = 426(0.98)^(0) = 426
y(1) = 426(0.98)^(1) = 417.48
y(1) < y(0) -> decay
5.
y(0) = 2050(12)^(0) = 2050
y(1) = 2050(12)^(1) = 24600
y(1) > y(0) -> growths
Twice the difference between 6 times h and 3 gives 30
Find the geometric mean of 6/5 and 120. Show in simplest radical form.
Over the last 4 years, Michael has earned $240 interest on an initial investment of $2,000. What simple annual interest rate is the bank paying on this account?
If Michael has earned $240 interest on an initial investment of $2,000. , then simple interest is 3% for paying in bank.
What is simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan.
Given that,
I = interest = $240
P = principal (investment)=2000
R = simple interest rate=?
T = years= 4 years
Formula: I = PRT
Plug into formula:
240 = 2000(R)4
Multiply right side 2000×4
240 = 8000R
Divide both sides by 8000.
R = 240/8000
R = 0.03
Now multiply with 100
The simple annual interest rate was .03 or 3%.
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Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents. (b3)2
Answer:
[tex]b^6[/tex]
Step-by-step explanation:
Given expression is,
[tex](b^3)^2[/tex],
By the power rule of exponent,
[tex](a^m)^n=a^{mn}[/tex]
Thus, we can write,
[tex](b^3)^2=b^{3\times 2}=b^6[/tex]
Since, further simplification is not possible,
Hence, the simplified form of the given expression,
[tex]b^6[/tex]
A child rides around on a ferris wheel twice. Click on the graph until the graph that best represents the given statement appears.
Answer:
The second graph.
Step-by-step explanation:
When the time is 0, the ride has not yet begun. Therefore the height above ground is nearly nothing.
As time increases, the ride goes up until it hits the top. The ride then goes back down nearly to the ground. This is one time around.
The ride then goes back up to the top and back down to the starting point.
This is the motion of the second graph, so the second graph is correct.
The second graph is used to represent A child rides around on a ferris wheel twice.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points
In the given graphs, the relationship between the height above ground and times are represented.
The second graph given is best suited to represent "A child rides around on a ferris wheel twice"
When the time is 0, the ride has not yet begun. Therefore the height above ground is nearly nothing.
As time increases, the ride goes up until it hits the top. The ride then goes back down nearly to the ground. This is one time around.
The ride then goes back up to the top and back down to the starting point.
This is the motion of the second graph, so the second graph is correct.
Hence second graph is used to represent the given situation.
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What x-value makes the set of ratios equivalent? Tiles 2 : 3 = 6 : x ,4 : 7 = x : 42 , 2x : 48 = 3 : 12, 12 : 15 = x : 20
Pairs691624
The missing x-values are 9, 24, 12, and 16, ensuring proportions remain equal in each ratio set.
To find the missing values that make the sets of ratios equivalent, we can use proportions.
1. Tiles 2 : 3 = 6 : x
Cross multiplying, we get: 2x = 18
So, x = 9
2. 4 : 7 = x : 42
Cross multiplying, we get: 7x = 168
So, x = 24
3. 2x : 48 = 3 : 12
Cross multiplying, we get: 12x = 144
So, x = 12
4. 12 : 15 = x : 20
Cross multiplying, we get: 15x = 240
So, x = 16
Therefore, the x-values that make the sets of ratios equivalent are:
1. x = 9
2. x = 24
3. x = 12
4. x = 16
What is the remainder of 860 divided by 14?
The distance between the baseball stadium and the airport is 1.6×106 centimeters. Which unit of measurement is most appropriate to measure this distance? inches kilometers feet milimeters
Final answer:
The most appropriate unit of measurement to measure the distance between the baseball stadium and the airport, which is 1.6 × 10⁶ centimeters, would be kilometers.
Explanation:
The most appropriate unit of measurement to measure the distance between the baseball stadium and the airport, which is 1.6×10⁶ centimeters, would be kilometers.
When measuring long distances, kilometers are commonly used. Kilometers are larger units of measurement compared to centimeters and millimeters, making them appropriate for measuring large distances like the one mentioned in the question.
uncle sammy invests money on stocks and makes 7 to 13 percent the range of money Uncle sammy will make if he invests his next paycheck of $2,300. express the solution set in set notation and interval notation.
So we are given an increase of 7% to 13%, so we multiply the capital with 1.07 and 1.13. So the range is:
minimum = $2,300 * 1.07 = $2,461
maximum = $2,300 * 1.13 = $2,599
The set notation is:
interest, X = {7%, 13%}
money, Y = {$2461, $2599}
The interval notation is:
[$2461, $2599]
What is the simplified form of the following expression?
(n5)(n2)
Mr. Chen goes to the post office to buy small and large boxes. He needs at least 4 small boxes. Altogether, he will buy no more than 15 boxes. The post office has 10 small boxes and 9 large boxes in stock. The graph shows the feasible region, where x represents the number of small boxes and y represents the number of large boxes. Which ordered pairs meet all the constraints and make sense in context of the situation? Select each correct answer. (6, 9) (7,10) (8,6) (9,8) Graph of lines and a shaded region on a coordinate plane whose axes are labeled x and y. A solid vertical line passes through 4 comma 0. Another solid vertical line passes through 10 comma 0. A solid horizontal line passes through 9 comma 0. A solid diagonal line passes through 0 comma 15, 4 comma 11, 6 comma 9, and 10 comma 5. The polygon whose vertices are at 4 comma 9, 6 comma 9, 10 comma 5, 10 comma 0, and 4 comma 0 is shaded.
Find (f - g)(x).
f(x) = -3x + 2
g(x) = x3
Answer:
[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]
Step-by-step explanation:
The new function is:
[tex](f-g) (x) = -3\cdot x + 2 -x^{3}[/tex]
[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]
Fresh side grocery sells 7 bagels for $4.41. value mart sells 5 bagels for $3.60. how do the unit rates compare?
The unit rate for a bagel at Fresh side is $0.09 cheaper than the unit rate at
Value mart for bagels.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Fresh side grocery sells 7 bagels for $4.41.
∴ The cost of one bagel at Fresh side is $(4.41/7) = $0.63.
Value mart sells 5 bagels for $3.60.
∴ The cost of one bagel at Value mart is
= $(3.60/5).
= $0.72
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The chart shows data for four moving objects , which object has the greatest acceleration?
Answer:
Y
Step-by-step explanation:
Write an equation that describes the function.
What is 0 to the 0 power?
The value of 0 to the power of 0 (0^0) is undefined, it may be treated as 1.
Explanation:The value of 0 raised to the power of 0 (0^0) is undefined.
Mathematically, any nonzero number raised to the power of 0 is equal to 1. However, 0^0 is an indeterminate form, meaning that it does not have a well-defined value.
When evaluating expressions involving 0^0, different contexts may assign different values to it. In some cases, it may be treated as 1, while in others, it may be considered as undefined.
The apartments in Brian's apartment house are numbered consecutively on each floor. The sum of his number and his next-door neighbor's number is 1419. What are the two numbers?
Which type of correlation would you expect between a company's advertising budget and its volume of sales? Why?
A) 0; relatively no correlation
B) The correlation cannot be predicted.
C) positive; advertising increases, sales increase.
D) negative; fewer sales, less money for advertising.
Answer:is c
Step-by-step explanation:
I did on usatestprep
The slope of a line is –2 and its y-intercept is (0, 3). What is the equation of the line that is parallel to the first line and passes through (2, 2)? A. 2x + y = 6 B. y = –2x + 3 C. 2003-10-03-00-00_files/i0060000.jpg D. y = –2x – 6
Answer:
The answer is A) 2x + y = 6
Step-by-step explanation:
Since the first line has a slope of -2, we know that the second does as well. We know this because parallel lines have the same slope. Now we can use that slope along with the point in point-slope form to get the equation.
y - y1 = m(x - x1)
y - 2 = -2(x - 2)
y - 2 = -2x + 4
y = -2x + 6
In this case, to find an equation that is similar, we could put it into standard for.
y = -2x + 6
2x + y = 6
This is answer A
Javier wants to inscribe a circle inside of the triangle ABC shown in the following figure. He begins by constructing the angle bisectors of angles A and B and finding their intersection at point D.
If Javier is trying to inscribe a circle inside of triangle ABC in as few steps as possible, which of the following steps would be the best step for him to take next?
1) Construct the perpendicular line from point D to the line BC.
2) Find the altitude from point C.
3) Use the distance from D to any of the triangle's vertices to set the width of the compass.
4) Construct the angle bisector of angle C.
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Timothy bought concrete mix for several projects. He used
3.5 bags of concrete mix for a new set of stairs and 2.25 bags
of concrete mix for a garden wall. Timothy mixed
345 pounds of concrete in all.
a. Model with Math Write an equation that can be
represented by the bar diagram.
b. Solve for y. How many pounds of concrete does each bag make?
Answer:
The required model is [tex]3.5y+2.25y=345[/tex]
60 pounds of concrete each bag make.
Step-by-step explanation:
Consider the provided information.
Let the number of concrete bags are used is represented by y.
Part (A)
3.5 bags of concrete mix for a new set of stairs and 2.25 bags of concrete mix for a garden wall.
This can be written as:
[tex]3.5y+2.25y[/tex]
Timothy mixed 345 pounds of concrete in all.
Therefore, [tex]3.5y+2.25y=345[/tex]
Hence, the required model is [tex]3.5y+2.25y=345[/tex]
Part (B) Solve for y. How many pounds of concrete does each bag make?
Consider the above equation.
[tex]3.5y+2.25y=345[/tex]
Solve the equation for y as shown.
Add the like terms.
[tex]5.75y=345[/tex]
Divide both the sides by 5.75
[tex]y=60[/tex]
Hence, 60 pounds of concrete each bag make.
John has six more nickels than dimes in his pocket for a total of 2.25 write an equation to determine the number of dimes, x in his pocket
PLEASE HELP ME. NO ONE IS HELPING ME. I AM SO CONFUSED. MY TEACHERS AND MY PARENTS WONT HELP ME EITHER.
Factor over the expression over the complex numbers.
x^2+20
Factor over the expression over the complex numbers.
x^2+36
Factor over the expression over the complex numbers.
x^4-81
Factor over the expression over the complex numbers.
y^4+14y^2+49
Factor over the expression over the complex numbers.
y^2+2y^2+16y+32
Jim’s fundraiser BBQ needs to make at least $1000 in sales on Saturday. He sells hot dogs for $2 each and hamburgers for $3 each, and he wants to sell at least twice as many hamburgers as hot dogs. He brought 300 hot dogs and 800 hamburgers to sell. The graph shows the feasible region, where x represents the number of hot dogs sold and y represents the number of hamburgers sold. Which ordered pairs meet all the constraints for a successful fundraiser and make sense in context of the situation?
Select each correct answer.
(275, 0)
(100.5, 800.5)
(0, 350)
(250, 700)
(200, 350)
How many times will he get heads and tails when flipped 8 times?