The functions are illustrations of trigonometry ratios
[tex]\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}[/tex]
The sine of an angle is calculated as follows
[tex]\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}[/tex]
So, we have:
[tex]\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{1 - (15/25)}}[/tex]
Take LCM
[tex]\mathbf{sin\theta = \sqrt{\frac{10}{25}}}[/tex]
[tex]\mathbf{sin\theta = \frac{\sqrt{10}}{5}}[/tex]
[tex]\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}[/tex]
The tangent of an angle is:
[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]
Using Pythagoras theorem, we have:
[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]
So, we have:
[tex]\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}[/tex]
[tex]\mathbf{Hypotenuse^2 = 10 + 4}[/tex]
[tex]\mathbf{Hypotenuse^2 = 14}[/tex]
Take square roots
[tex]\mathbf{Hypotenuse = \sqrt{14}}[/tex]
So, the sine of the angle is:
[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}[/tex]
Rationalize
[tex]\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}[/tex]
[tex]\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}[/tex]
The sine of the angles is:
[tex]\mathbf{sin \theta = \frac{1}{csc\theta}}[/tex]
So, we have:
[tex]\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}[/tex]
[tex]\mathbf{sin \theta = \frac{3}{\sqrt{15}}}[/tex]
Rationalize
[tex]\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}[/tex]
[tex]\mathbf{sin \theta = \frac{\sqrt{15}}{5}}[/tex]
[tex]\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}[/tex]
The sine of an angle is calculated as follows
[tex]\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}[/tex]
So, we have:
[tex]\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{(1 - 9/6)}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{( - 3/6)}}[/tex]
The sine of the angle does not have a real value
[tex]\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}[/tex]
Start by calculating the tangent of the angle
[tex]\mathbf{tan\theta = \frac{1}{cot\theta}}[/tex]
So, we have:
[tex]\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}[/tex]
[tex]\mathbf{tan\theta = \frac{2}{\sqrt 6}}[/tex]
Rationalize
[tex]\mathbf{tan\theta = \frac{2\sqrt 6}{6}}[/tex]
[tex]\mathbf{tan\theta = \frac{\sqrt 6}{3}}[/tex]
The tangent of an angle is:
[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]
Using Pythagoras theorem, we have:
[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]
So, we have:
[tex]\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}[/tex]
[tex]\mathbf{Hypotenuse^2 = 6 + 9}[/tex]
[tex]\mathbf{Hypotenuse^2 = 15}[/tex]
Take square roots
[tex]\mathbf{Hypotenuse = \sqrt{15}}[/tex]
So, the sine of the angle is:
[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}[/tex]
Rationalize
[tex]\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}[/tex]
Rewrite as:
[tex]\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}[/tex]
Read more about trigonometry ratios at:
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x+2y-z=5
-X-y+2z=-13
2x+y-2z=14
Answer:
[tex]x+2y-z=5 ...(1)\\ -x-y+2z=-13...(2) \\ 2x+y-2z=14...(3) \\ \\ add \: (2) + (3) \\\boxed{x= 1} \\ 2 \times (1) + (2) \\ x + 3y = - 3 \\ 1 + 3y = - 3 \\ 3y = - 4 \\ \boxed{y = - \frac{4}{3} }\\ solve \: for \: z \\ x + 2y - z = 5 \\ 1-\frac{4}{3}(2)-z=5\\3-8-3z=15\\3z=-20\\\boxed{z = - \frac{20}{3} }[/tex]
Completely Factor the following equations.
a) 3x^3 + 15x^2 + 18x
hi pls help me!!! thank you
Step-by-step explanation:
Circumference (C):
[tex]C = 2\pi r = 2\pi(5\:\text{ft}) = 31.4\:\text{ft}[/tex]
Area (A):
[tex]A = \pi r^2 = \pi(5\:\text{ft})^2 = 78.5\:\text{ft}^2[/tex]
A sales person at a car dealership earns a monthly salary of $2400 and $250 for each vehicle sold
3. The car dealership sets a goal for each salesperson to sell at least 12 cars per month. The salesperson
achieves this goal every month for the entire year. What is the minimum amount of money the
salesperson earns for the entire year? Show your work.
I
Answer:
8 vehicles
Step-by-step explanation:
Given: Monthly salary of salesperson is $2400
Incentive of salesperson is $250 per vehicle sold.
First, lets compute income to earned apart from salary.
∴ Deduct salary from the target amount
$2000 need to be earned only through incentive, which is $250 per vehicle sold.
Now, solving to get number vehicles to be sold to earn $2000 as incentive.
Number of vehicle=
8 vehicles need to be sold by salesperson to get total earning as $4400.
I know how to do it just then one’s a bit confusing
Answer:
208 ft^3
Step-by-step explanation:
Let the plane through the 4 ft X 4ft square at the top of the figure break the figure into 2 boxes, one has dimensions (8-7) by 3 by 4 = 1ft X 3ft X 4ft, and the other has dimensions 7 by 7 by 4 = 7ft X 7ft X 4ft.
They have volumes of (1)(3)(4) = 12 ft^3, and (7)(7)(4) = 196 ft^3, respectively, so the total volume = 12 + 196 = 208 ft^3, the answer.
Find g(x) for each x value in the table
Answer:
-2 = -2/7
-1= -1/7
0=0
1= 1/7
2= 2/7
Step-by-step explanation:
it gives you a function of 1/7 so you multiply it by x and u get the g(x) also know as Y
Consider the equation below. The value of x in terms of h is . The value of x when h = 4 is .
The value of x when h = 4 is 4.
The given equation is : 4(x − 3) = h. We need to find the value of x in terms of h and the value of x when h = 4.So, we will solve this equation by following the steps given below:
Step 1: Distribute 4 by x and 4 by -3. It gives us:4x - 12 = h
Step 2: Add 12 to both sides of the equation. We get:4x - 12 + 12 = h + 124x = h + 12
Step 3: Divide both sides of the equation by 4. We get:x = (h + 12) / 4
Therefore, the value of x in terms of h is x = (h + 12) / 4.
Now, we need to find the value of x when h = 4. We will put h = 4 in the above equation and get the value of x.x = (4 + 12) / 4 = 16 / 4 = 4.
For more such questions on equation
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Find last year's salary if, after a 4% pay raise, this year's salary is $33,800.
Answer:
1352
Step-by-step explanation:
4% of 33,800 is 1352 last years salary was 32448
How would I be able to simplify 12/3? Please explain step by step
Answer:
4/1
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator. GCD of 12 and 3 is 3.
12 ÷ 33 ÷ 3.
Reduced fraction: 41. Therefore, 12/3 simplified to lowest terms is 4/1.
Answer:
i think you divide 12/3 and you get the answer of 4
Step-by-step explanation:
Graph the line with slope 1 passing through the point (-3, 1).
Answer:
[tex]y = x + 4[/tex]
Step-by-step explanation:
[tex]1 = 1(- 3 )+ b \\ 1 = - 3 + b \\ b = 4 \: \: \: \: y - intercept[/tex]
NEED HELP ASAP RIGHT ANSWER ONLY 69 POINTS
In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision.
(2,−1), (3,0.5), (6,1.5),
Answer:
A Least Square Regression Line is the best thing to use for this because there is inconsistencies and no direct equation to be able to fill all of these points. They may be outliers and therefore we should use a calculator for a Regression Line to be calculated to find the residual.
Step-by-step explanation:
Peter Piper picked 3 pecks of pickled peppers in 2.5
hours. How many pecks of pickled peppers does
Peter pick in 15 hours?
Sowy about all my questions b-b-but please help with another one?
Answer:
A
Step-by-step explanation:
count both sides divide by missing pieices
What is the value of 7x (3 + x/4) when x = −8?
Answer:
Third option
Step-by-step explanation:
[tex]7x (3 + \frac{x}{4}) = -56 * (3 + -\frac{8}{4}) = -56 * (3 - 2) = -56 * 1 = -56[/tex]
Given f(x)=3x(to the scnd power)−5x−2. What is the value of f(−2/3)? 1 8/3 3 10/3
Given:
[tex]f(x)=3x^2-5x-2[/tex]; find f(-2/3)
Answer:
[tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
Step-by-step explanation:
1. Insert [tex]-\frac{2}{3} \\[/tex] as X; [tex]f(-\frac{2}{3}) = 3 (-\frac{2}{3} )^2 - 5 (-\frac{2}{3}) - 2[/tex]
2. Solve equation; [tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
20000 divided by 2 x 56 x 7898 - 100
First to Answer gets brainliest!!!
NO LINKS PLEASE!!!!
Answer:
0.0226122585576093
from a piece 20m long ,100 pieces each 7.5cm are cut off how much remain
Answer:100*7.5=750cm=7.5 m
left rope=20-7.5=12.5m
Step-by-step explanation:
Pa Brainliest Kung Pwede.
Answer:
12.5 metres
Step-by-step explanation:
→ Multiply the pieces by the length
100 × 7.5 = 750 cm
→ Convert to metres
750 cm = 7.5 metres
→ Minus from original length
20 - 7.5 = 12.5 metres
there are 270 sixth grade students and 45 chaperones going on a field trip. how many students will be with each chaperone if the groups are divided equally.
Answer:
6
Step-by-step explanation:
270 divided by 45
=6
NO LINKS OR ASSESSMENT!!!!
Answer:
See below and attachedStep-by-step explanation:
1. There are infinite number of lines going from only one point (2, 5)
No definite solution for line A.2. This is a proportional relationship, since line passes through the origin. The slope is -3.
The line B is:
y = -3x3. Points (-3, -2) and (3, 10)
The slope:
m = (10 + 2)/(3 + 3) = 2The y - intercept:
10 = 2*3 + b ⇒ b = 4The line C is:
y = 2x + 44. The rate of change is m = 2.5
The y- intercept:
1 = 2*2.5 + b ⇒ - 4The line D is:
y = 2.5x - 45. Line E has a slope of 4, no sufficient info to conclude.
y = 4x + b, with any value of b6. Line F has m = -3/4 and passes through (8, -1).
The y -intercept is:
-1 = 8(-3/4) + b ⇒ b = 5The line F is:
y = -3/4x + 57. G is not a linear relationship as the function increases exponentially with common ratio of 3.
What is the answer to this equation
Answer:
-34/45
Step-by-step explanation:
first step you wanna do is Multiply the numbers -1/5- 1 (-2/3)- (5/6)= -1/5 and -5/9 then subtract those two fractions and you get -34/45 since both of the fractions were negative the answer results as a negative aswell
Select all of the terms that are "like." 1/2 xy x 2 2xy -xy xy 2 2x 2y
Answer:
not sure about it this one is tuff
A loan used for buying a home is called a mortgage. The Fortunato family is borrowing $430,000 to buy a home. They are taking out a 30-year mortgage at a rate of 3.55%. a. Compute the monthly payment to the nearest cent. fill in the blank 1 b. Find the total of all of the monthly payments for 30 years. fill in the blank 2 c. What is the total interest? fill in the blank 3 d. Which is greater, the interest or the original cost of the home?
Using compound interest, it is found that:
a) The monthly payments are of $3,401.49.
b) The total of all monthly payments for 30 years is of $1,224,536.
c) The total interest is of $794,536.
d) The total interest is greater.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For the parameters, we have that:
The Fortunato family is borrowing $430,000 to buy a home, hence P = 430000.30-year mortgage, hence t = 30.Rate of 3.55%, hence r = 0.0355.Yearly compounding, hence n = 1.For practicality, first we are going to solve item b.
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(30) = 430000\left(1 + \frac{0.0355}{1}\right)^{30}[/tex]
[tex]A(30) = 1224536[/tex]
The total of all monthly payments for 30 years is of $1,224,536.
Item a:
$1,224,536 is paid in 30 x 12 = 360 months, hence:
1224536/360 = $3,401.49.
The monthly payments are of $3,401.49.
Item c:
The interest is the total subtracted from the principal, hence:
1224536 - 430000 = $794,536.
The total interest is of $794,536.
Item d:
Loan of $430,000, interest of $794,536, hence the total interest is greater.
You can learn more about compound interest at https://brainly.com/question/25781328
is 78.50 is the same as 78.5
Answer:
yes, 78.50 is the same as 78.5Step-by-step explanation:
You can consider 78.50 as 78.5, cause we basically remove the 0 from it. The whole point is, they are both the same.
Hello there!
Yes, 78.50 is the same as 78.5 because you can remove the 0 and the numbers will be identical.
Hope this helps!
~Just a joyful teen
[tex]SilentNature\\(GraceRosalia)[/tex]
Question Choice Worth 2 points)
(02.06Derek has a bird that weighs 4 pounds. Use the double fine diagram below to help you determine approximately how many kilograms this bird weighs
3 5 7
Pounds
1 2 3
Kilograms
15 klograms
O2 xilogram
5 kilograms
7 kilograms
Write an equation that represents the line.
Use exact numbers.
Answer:
y = 1.5x + 3
Step-by-step explanation:
Take the two points marked by the blue dots.
(0,3), (2,6)
Start with (0,3). The zero makes the other number with it = to the y intercept.
So far what you know is
General equation: y = mx + b
b = 3
Partial equation: y = mx + 3
Givens
To get m, you need both points.
y2 = 6
y1 = 3
x2 = 2
x1 = 0
Equation
m = (y2 - y1) / (x2 - x1)
m = (6 - 3) / (2 - 0)
m = 3 / 2
Entire equation
y = 3/2 x + 3
or
y = 1,5x + 3
When converted to a household measurement, 9 kilograms is approximately equal to a
Answer:
D) 19.8 lbs
Explanation:
1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.
1kg is also equal to 2.205 lbs. 9*2.205=19.8416
9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system
a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.
This leaves us with 19.8 lbs
Mr. Candy needs to purchase large bags of Snickers to sell in the school store. A bag of Snickers contains 72 Snicker bars. A bag of Snickers cost $23. How much should Mr. Candy sell the Snicker bars to make a profit of $49?
Answer:
70 cents each snickers bar
Step-by-step explanation:
convert 1040 weeks to months with solution
Answer:
1040 x 0.229984 = 239.18336
months = 239
Data was recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation, , what is the predicted temperature after 3 minutes?
33.45 oC
62.24 oC
65.17 oC
66.69 oC
Answer:
62.24
Step-by-step explanation:
The predicted temperature after 3 minutes will be 62.24 °C. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
A cup of coffee's temperature was measured over a 30-minute period in degrees Celsius.
Let T be the temperature and t be the time. Then the regression equation is given as,
ln T = 4.20 - 0.023 t
Then predicted temperature after 3 minutes is given as,
ln T = 4.20 - 0.023 x 3
ln T = 4.20 - 0.069
ln T = 4.131
T = 62.24 °C
The predicted temperature after 3 minutes will be 62.24 °C. Then the correct option is B.
More about the function link is given below.
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C: infinitely many solutions, help solve fast pls