By using the tangent formula, we will see that:
tan(x) = 5/12.
How to get the tangent of x?You just need to remember that we can write the tangent as:
tan(x) = sin(x)/cos(x).
In this case, we know that:
sin(x) = 5/13cos(x) = 12/13We can just replace these two in the tangent equation, we will get:
tan(x) = (5/13)/(12/13) = (5/13)*(13/12) = 5/12
tan(x) = 5/12
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As a pendulum swings , the angle (theta) that it makes with the vertical changes through its swing. The force of gravity pulling on the bob is given by F=mg sin (theta), where g is equal to 9.8m/s^2. If the mass of the pendulum is 0.01 kg, what is the force pulling on the pendulum when it makes a 22.5 degree angle with the vertical?
We have been given that the formula for the force of gravity pulling on the bob is given by [tex] F=m\times g\times sin(\theta) [/tex]), where g is equal to[tex] 9.8m/s^2 [/tex].
Now, we have been given that the mass of the bob of the pendulum is 0.01 kg and that the pendulum makes 22.5 degree angle with the vertical.
Thus, applying the given values in the formula of the given in the question, we get the formula to be:
[tex] F=m\times g\times sin(\theta)=0.01\times9.8\times sin(22.5^{\circ}) [/tex]
[tex] \therefore F\approx0.0375 [/tex] N
In the diagram below of right triangle ACB, altitude CD is drawn by hypotenuse AB. if AB= 36 and AC= 12, what is the length of AD?
The length of AD is 18 units.
To find the length of AD, we can use the fact that the altitude from the right angle of a right triangle divides the triangle into two smaller similar triangles.
Let's denote the length of AD as x.
Since triangle ADC and triangle CDB are similar to triangle ACB, we can set up the following proportions:
For triangle ADC:
AD / AC = CD / AB
For triangle CDB:
BD / AC = CD / AB
We already know that AC = 12, AB = 36, and CD = x. So, let's substitute these values into the proportions:
For triangle ADC:
x / 12 = CD / 36
For triangle CDB:
(36 - x) / 12 = CD / 36
Now, let's solve these equations:
From the first equation:
x / 12 = CD / 36
x = (12 * CD) / 36
x = CD / 3
From the second equation:
(36 - x) / 12 = CD / 36
36 - x = (12 * CD) / 36
36 - x = CD / 3
Now, let's solve for CD using the second equation:
36 - x = CD / 3
36 - (CD / 3) = CD / 3
36 = (2 * CD) / 3
CD = (36 * 3) / 2
CD = 54
Now that we have found CD, we can substitute it into the first equation to find x:
x = CD / 3
x = 54 / 3
x = 18
So, the length of AD is 18 units.
13. What is a simpler form of each product?
(4x - 6y^3)^2
(A). 16x^2 - 24xy^3 + 36y^6
(B). 16x^2 - 48xy^3 + 36y^6
(C). 16x^2 + 36y^6
(D). 16x^2 - 4xy^3 + 36y^6
14. The area of a rectangular garden is given by the trinomial x^2 + 6x - 27. What are the possible dimensions of the rectangle? Use factoring.
(A). x - 9 and x + 3
(B). x + 9 and x - 3
(C). x - 9 and x - 3
(D). x + 9 and x + 3
15. The area of a rectangular garden is given by the trinomial x^2 + x - 30. What are the possible dimensions of the rectangle? Use factoring.
(A). (x - 6) and (x - 5)
(B). (x + 6) and (x - 5)
(C). (x + 6) and (x + 5)
(D). (x - 6) and (x + 5)
What is the factored form of the following expressions?
16. x^2 - 10xy + 24y^2
(A). (x + 6y)(x + 4y)
(B). (x - 2y)(x + 12y)
(C). (x + 2y)(x - 12y)
(D). (x - 6y)(x - 4y)
17. The area of a rectangular barnyard is given by the trinomial 6x^2 + 7x - 20. What are the possible dimensions of the barnyard? Use factoring.
(A). 2x - 5 and 3x + 4
(B). -2x + 5 and -3x + 4
(C). 2x + 5 and 3x - 4
(D). 2x - 5 and 3x - 4
18. The area of a rectangular carpet is given by the trinomial 5x^2 - 3x - 14. What are the possible dimensions of the carpet? Use factoring.
(A). (5x + 7) and (-x - 2)
(B). (5x + 7) and (x - 2)
(C). (5x - 7) and (x - 2)
(D). (5x - 7) and (x + 2)
The answer to question 13 is (B). [tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]
The answer to question 14 is (A). [tex]\(x - 9\) and \(x + 3\)[/tex]
The answer to question 15 is (A). [tex]\((x - 6)\) and \((x - 5)\).[/tex]
The answer to question 16 is (A). [tex]\((x + 6y)(x + 4y)\).[/tex]
The answer to question 17 is (A).[tex]\(2x - 5\) and \(3x + 4\).[/tex]
The answer to question 18 is (B). [tex]\((5x + 7)\) and \((x - 2)\).[/tex]
To find a simpler form of the product [tex]\((4x - 6y^3)^2\)[/tex], we apply the formula for squaring a binomial, which is [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex]. Here, [tex]\(a = 4x\)[/tex] and [tex]\(b = 6y^3\).[/tex]
So, [tex]\((4x - 6y^3)^2 = (4x)^2 - 2(4x)(6y^3) + (6y^3)^2\).[/tex]
Calculating each term, we get:
[tex]\((4x)^2 = 16x^2\),[/tex]
[tex]\(-2(4x)(6y^3) = -48xy^3\),[/tex]
[tex]\((6y^3)^2 = 36y^6\).[/tex]
Putting it all together, we have:
[tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]
To find the possible dimensions of the rectangle, we need to factor the trinomial [tex]\(x^2 + 6x - 27\).[/tex] We look for two numbers that multiply to -27 and add up to 6. These numbers are 9 and -3.
So, [tex]\(x^2 + 6x - 27 = (x + 9)(x - 3)\).[/tex]
We factor the trinomial [tex]\(x^2 + x - 30\)[/tex] by finding two numbers that multiply to -30 and add up to 1. These numbers are 6 and -5.
So, [tex]\(x^2 + x - 30 = (x - 6)(x + 5)\).[/tex]
To factor [tex]\(x^2 - 10xy + 24y^2\)[/tex], we look for two numbers that multiply to \[tex](24y^2\)[/tex] and add up to -10y. These numbers are -6y and -4y.
So, [tex]\(x^2 - 10xy + 24y^2 = (x - 6y)(x - 4y)\)[/tex].
To find the possible dimensions of the barnyard, we factor the trinomial [tex]\(6x^2 + 7x - 20\).[/tex] We need two numbers that multiply to [tex]\(6 \times -20 = -120\)[/tex] and add up to 7. These numbers are 15 and -8. We then split the middle term accordingly and factor by grouping:
[tex]\(6x^2 + 15x - 8x - 20 = 0\),[/tex]
[tex]\(3x(2x + 5) - 4(2x + 5) = 0\),[/tex]
[tex]\((3x - 4)(2x + 5)\).[/tex]
We factor the trinomial [tex]\(5x^2 - 3x - 14\)[/tex] by finding two numbers that multiply to [tex]\(5 \times -14 = -70\)[/tex] and add up to -3. These numbers are -10 and 7. We then split the middle term accordingly and factor by grouping:
[tex]\(5x^2 - 10x + 7x - 14 = 0\),[/tex]
[tex]\(5x(x - 2) + 7(x - 2) = 0\),[/tex]
[tex]\((5x + 7)(x - 2)\).[/tex]
Math help With please
1. if a dozen eggs (12 eggs) are worth 3 cowry shells, how much would 6 dozen be worth?
a. 9 cowry shells
b. 36 cowry shells
c. 18 cowry shells
d. 15 cowry shells
2. I have 7 cowry shells. If a dozen eggs (12 eggs) cost 3 cowry shells, how many dozens can i purchase?
a. 21 dozen
b. 2 dozen
c. 9 cowry dozen
d. 3 dozen,
An organization president conducts a survey to see where the next convention should be held. She uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey. An organization is conducting a survey to see where their next convention should be held. They use a list of their 1008 members listed in alphabetical order and selects every 10th member to participate in the survey Is this sample valid or not valid, and why? A not valid; Since 1008 divided by 10 is not a whole number, there are 8 members who are not accounted for. B not valid; The survey chooses only members of the organization. C valid; There is no bias in the survey. D not valid; The survey chooses only every 10th member.
Answer:
The correct option is:
Option: C
C valid; There is no bias in the survey.
Step-by-step explanation:
It is given that:
An organisation president uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey.
So, the sample used by her is a valid sample.
Since, she sets a random rule to choose the members to participate in the survey.
The sample used by her is unbiased.
( Since, the aim of our survey questions are to capture an unbiased opinion to capture the true sentiments of the survey taker )
Hence, the correct statement regarding her survey is:
C. valid; There is no bias in the survey
What is the similarity ratio of a cube with volume 1,728m3 to a cube with volume 19,683m3?
A. 9:4
B. 4.9
C. 144:729
D. 729:144
A grid shows the positions of a subway stop and your house. The subway stop is located at (6,-2) and your house is located at (3,1) what is the distance to the nearest unit between your house and the subway stop?
A. 10
B. 9
C. 4
D. 3
Find the missing value to the nearest whole number of tan x° =0.9
We have to find the missing value to the nearest whole number of tan x° =0.9.
Since, tan x° =0.9
To evaluate the missing value of 'x', we will take [tex] \arctan (0.9) [/tex]
So, [tex] x^{\circ}=\arctan (0.9) [/tex]
Now, we will find the value of [tex] \arctan (0.9) [/tex]using the calculator, we get,
[tex] x^{\circ}=\arctan (0.9)=41.9^{\circ}=42^{\circ} [/tex]
So, the missing value of 'x' to the nearest whole number is [tex] 42^{\circ} [/tex].
A surveyor measures the lengths of the sides of a triangular plot of land. What is the measure of the angle of the triangular plot at which the surveyor stands? Approximate to the nearest degree.
Answer: B
Step-by-step explanation:
rodney is given two linear equations : x - y = 11 and 2x +y =19. what value if x shkuld he get as a solution for thus system of linwar equations
Answer: 10
Step-by-step explanation:
If somebody uses 1 quart of blue paint each month in one year how many gallons of paint will they use
Celia earned $5.00. She saved $1.00 and spent the rest. What is the ratio of the amount saved to the amount spent?
Solution :
Given that, Celia earned $5.00.
She saved $1.00 and spent the rest.
To find the ratio of the amount saved to the amount spent , we must first calculate the amount spent.
To calculate the amount spent, subtract the amount saved from the total money earned.
Amount spent by Celia = amount earned - amount saved [tex] = 5-1 = 4 [/tex]
[tex] ratio= \frac{amount\:saved}{ amount\:spent} =\frac{1}{4} \\
\\
ratio= 1:4 [/tex]
Hence, 1:4 is the ratio of the amount saved to the amount spent.
Dwayne's garden is triangle-shaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is the longest side?
greatest common factor of −27x2yz5 + 15x3z3
The value of Ari's rolls of coins is $113.00. If pennies and dimes come in rolls of 50 coins each, and nickels and quarters come in rolls of 40 coins each, which of these combinations could Ari have?
A. 5 rolls of pennies, 8 rolls of nickels, 4 rolls of dimes, and 7 rolls of quarters
B. 4 rolls of pennies, 8 rolls of nickels, 7 rolls of dimes, and 5 rolls of quarters
C. 4 rolls of pennies, 8 rolls of nickels, 5 rolls of dimes, and 7 rolls of quarters
D. 5 rolls of pennies, 8 rolls of nickels, 7 rolls of dimes, and 4 rolls of quarters
Answer:
Option C is correct.
Step-by-step explanation:
Given is :
The value of Ari's rolls of coins is = $113
The coins are pennies, dimes, nickels and quarters.
Total money is represented by = penny + nickle + dime + quarter All values in dollars are represented by:
113 = .01* pennies + .05* nickles + 0.1* dimes + 0.25* quarters
Further calculating we get,
113 = .01* 50*penny rolls + .05 * 40*nickle rolls + .1 * 50*dime rolls + .25 * 40*quarter rolls
[tex]113=.5p+2n+5d+10q[/tex]
where p is the number of penny rolls, n is the number of nickle rolls, d is the number of dime rolls, and q is the number of quarter rolls
Now checking all the options by putting values.
A. [tex]113=.5(5)+2(8)+5(4)+10(7)[/tex]
[tex]113\neq 108.5[/tex]
B. [tex]113=.5(4)+2(8)+5(7)+10(5)[/tex]
[tex]113\neq 103[/tex]
C. [tex]113=.5(4)+2(8)+5(5)+10(7)[/tex]
[tex]113=113[/tex]
D. [tex]113=.5(5)+2(8)+5(7)+10(4)[/tex]
[tex]113\neq 93.5[/tex]
Therefore, option C is the right option.
Evaluate |c2 + b2|, given a = 5, b = -3, and c = -2.
A.) 2
B.) 6
C.) 10
D.) 13
The answer to this should be 13
Substitute the value of the variable into the expression and simplify
Substitute: |-2^2 + -3^2|
Simplify: |-2^2|= 4, |-3^2|= 9
Solve: 4 + 9 = 13
Given a = 5, b = -3, and c = -2, the absolute value of |c2 + b2| is calculated by squaring the values of c and b, adding them, then taking the absolute value, resulting in 13.
Explanation:The question asks us to evaluate the expression |c2 + b2|, given that a = 5, b = -3, and c = -2. The vertical bars indicate that we are dealing with the absolute value, which means we want the positive result of the expression inside the bars.
First, substitute the given values into the expression, we get |-22 + (-3)2| which is |4+9|.
Second, add the squares of c and b together to get 13.
Finally, since the absolute value of 13 is still 13, this is our answer, corresponding to option D.
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the value 3 is an upper bound for the zeros of the function shown below. f(x)=-3x^3+20x^2-36x+16 True or Flase
The statement "The value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16" is FALSE.
To determine whether the value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16, we need to check if the function has any real roots greater than 3.
One way to approach this is by analyzing the behavior of the function as x approaches infinity. We can check the sign of the leading coefficient (-3) and the constant term (16) to determine the overall behavior of the function.
Leading coefficient:
The leading coefficient of -3 indicates that the highest power of x in the function is negative. This means that as x approaches infinity, the function will decrease without bound.
Constant term:
The constant term of 16 indicates that the function intersects the y-axis at y = 16.
Considering these observations, we can infer that the function starts at a positive value (y = 16) and approaches negative infinity as x increases. This implies that the function f(x) = -3x^3 + 20x^2 - 36x + 16 will have at least one real root greater than 3.
Therefore, the statement "The value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16" is FALSE.
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Larry has 62 nickels, 24 dimes, 17 quarters, and 11 fifty-cent pieces. How much money does he have?
A. $17.15
B. $16.30
C. $15.25
D. $16.75
Answer:
Larry has 1525 cents or 15.25 dollars.
Step-by-step explanation:
The following are the values for each of the coins:
1 Nickel=5 cents
1 Dime = 10 cents
1 Quarter = 25 cents
1 Fifity-cent = 50 cents
So the total value of the Larry's have is
Total money = 62*5 cents + 24*10 cents + 17*25 cents + 11*50 cents
Total money = 310 cents + 240 cents + 425 cents + 550 cents
Total money = 1525 cents
This is equal to 15.25 dollars.
A swing set is going to be placed over a region of mulch that is shaped like a trapezoid. The bases of the trapezoid have a length of 12 and 15 feet, and the perpendicular distance between the bases is 8.5 feet. What is the area of the region under the swing set? If necessary, round your answer to the nearest tenth.
Answer:
[tex]114.8\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
In this problem we have
[tex]b1=12\ ft[/tex]
[tex]b2=15\ ft[/tex]
[tex]h=8.5\ ft[/tex] ----> the height of the trapezoid is the perpendicular distance between the bases
substitute the values
[tex]A=\frac{1}{2}(12+15)(8.5)[/tex]
[tex]A=\frac{1}{2}(27)(8.5)=114.75\ ft^{2}[/tex]
Round to the nearest tenth
[tex]114.75=114.8\ ft^{2}[/tex]
Answer:
114.8 is the answer
Step-by-step explanation:
got it on edgen
Please help! Thanks!
miles is buying a chair that regularly costs $250. today the chair is on sale for 30% off. if the tax rate is 6%, what is the sale price of the chair including tax?
The sale price of the chair including tax is $185.5.
What is tax?In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.
Given that, Miles is buying a chair that regularly costs $250.
Today the chair is on sale for 30% off
So, the new cost is 250-30% of 250
= 250 - 30/100 ×250
= 250-75
= $175
The tax rate is 6%
Sale price = 175+6% of 175
= 175+6/100 ×175
= 175+0.06×175
= $185.5
Therefore, the sale price of the chair including tax is $185.5.
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The value of y directly varies with x, and y=5.4 when x =9. Find y when x= negative 10
Final answer:
The value of y, which directly varies with x, is found by first determining the constant of variation when x = 9 and y = 5.4. Using this constant, we calculate the value of y for x = -10, resulting in y = -6.
Explanation:
The value of y directly varies with x, which means the relationship between x and y can be described by the equation y = kx, where k is the constant of variation. Since y = 5.4 when x = 9, we first find the constant of variation as follows: k = y/x = 5.4/9 = 0.6. Now, to find y when x is -10, we use the constant of variation k in the equation: y = kx = 0.6(-10) = -6.
The relationship between y and x is one of direct variation, represented by the equation y = kx, where k is the constant of variation. Given that y = 5.4 when x = 9, the constant k is calculated as 0.6. Applying this constant, when x = -10, the value of y is found to be -6. This process showcases the direct variation principle in determining y based on the given x values and the constant of variation.
Line AB and BC for a right angle at point B. If A(-3,4) and B(4,4) what is the equation of line BC?
Answer: The required equation of line BC is [tex] x=4.[/tex]
Step-by-step explanation: As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).
We are to find the equation of line BC.
We know that the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the line AB will be
[tex]m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.[/tex]
Therefore, the equation of the line AB is
[tex]y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.[/tex]
Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.
So, its equation will be of the form
x = constant.
Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have
[tex]x=4.[/tex]
Thus, the required equation of line BC is [tex] x=4.[/tex]
Match each economic term with its description. Tiles There are no barriers to entry in the market. There is a single seller in the market. Three companies secretly enter into a price agreement. Every company in this market structure is aware of the actions of the other companies. Pairs monopoly arrowBoth oligopoly arrowBoth perfect competition arrowBoth collusion arrowBoth \
Each economic term is matched with its appropriate description as follows:
OLIGOPOLY || There are no barriers to entry in the market.
MONOPOLY || There is a single seller in the market.
COLLUSION || Three companies secretly enter into a price agreement.
PERFECT COMPETITION || Every company in this market structure is aware of the actions of the other companies.
There are no barriers to entry in the market is the match of - Oligopoly (The market is shared by many sellers )
There is a single seller in the market is the match of - Monopoly
Three companies secretly enter into a price agreement is the match for - Collusion
Every company in this market structure is aware of the actions of the other companies is the match for Perfect Competition.
Write this number in standard form.
1 x 1 + 8 x 1/100 + 9 x 1/1000,
Find all the zeros of the equation. Need help finding the zeros.
-3 x^{4} } +27 x^{2} +1200=0
Final answer:
The zeros of the equation -3x^4 + 27x^2 + 1200 = 0 can be found by substituting y = x^2 to create a quadratic equation, solving for y using the quadratic formula, and then solving for x for each y value found.
Explanation:
To find all the zeros of the equation -3x^4 + 27x^2 + 1200 = 0, we can treat the equation as a quadratic in form by substituting y = x^2, which reduces the equation to -3y^2 + 27y + 1200 = 0. This is now a standard quadratic equation that can be solved using the quadratic formula, y = (-b ± sqrt(b^2 - 4ac))/(2a), where a = -3, b = 27, and c = 1200. Once we find the values for y, we substitute back x^2 = y to get the values of x which are the zeros we are looking for.
The quadratic equation would provide us with two values for y, say y1 and y2. For each y value found, we solve for x by taking the square root, resulting in two x values for each y, giving us a total of four zeros for the original quartic equation.
we can re-write our expression as:
-3a^2+27a+1200=0
-3(a^2-9a-400)=0
a^2-9a-400=0
factorizing the above we have:
a^2+16a-25a-400=0
a(a+16)-25(a+16)=0
(a+16)(a-25)
thus replacing back x^2 we have:
(x^2+16)(x^2-25)
=(x^2+16)(x-5)(x+5)
factorizing (x^2+16) we get
x^2=+/-√-16
x=+/-4i
thus the zeros of the expression are:
x=-5, x=5 , x=-4i, x=4i
Roberto's toy car travels at 40 centimeters per second (cm/sec) at high speed and 25 cm/sec at low speed. If the car travels for 30 seconds at high speed and then 51 seconds at low speed, what distance would the car have traveled?
Answer:
2475 cm
Step-by-step explanation:
We are given that Roberto's toy car travels 40 cm/sec at high speed and 25 cm/sec at low speed.
We have to find that the distance would have the car traveled
Speed of car at high speed=40 cm/sec
Speed of car at low speed=25 cm/sec
If car takes time to travel at high speed=30 seconds
If car takes time to travel at low speed=51 seconds
[tex]Distance=speed\times time[/tex]
Using this formula
Distance traveled by the car at high speed=[tex]40\times 30=1200 cm[/tex]
Distance traveled by the car at low speed=[tex]51\times 25=1275 cm[/tex]
Total distance traveled by the car =1200+1275=2475 cm
Hence, the distance would have traveled by the car=2475 cm
What is the x intercept for y=3x+4
3. Some investments in the stock market have earned 12% annually. At this rate, earnings can be found using the formula A = P(1.12)n, where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested. If $5000 is invested in the stock market at this annual rate of return, what is the expected total value after 20 years?
( Please show your work so I can understand how you got that answer! Thanks in advance! )