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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What i want to know is.. why is that possible?
And, why we could add the two inequalities together down side there ??
Answer: Explanation below.
Step-by-step explanation: A good question, since working with inequalities and using the same operations as with "=" equations is a bit uncomfortable. I don't have a mathematical proof for this operation, but approach it with a "Why not?" attitude. If 9>6 and 130 > 30, why wouldn't 139>36? There is nothing in the add operation that should upset the basic inequality. I suggest https://www.storyofmathematics.com/inequalities-math for more information.
Evaluate: - 20 – 6 =
А 26
B. 14
С -14
D - 26
Answer:
- 26
Step-by-step explanation:
- 20 - 6
= - 20 + ( - 6 )
= - 26
solve pls brainliest
Answer:
2 4/9
Step-by-step explanation:
1. To change an improper fraction to a mixed number, divide the numerator by the denominator. Then, write down the quotient as the whole number and the remainder (left over amount) as the numerator. Remember to NOT change the denominator.
2. Given the information above:
22 ÷ 9 = 2 R 4 2 4/9Therefore, 22/9 as a mixed number is 2 4/9.
What is the midpoint of CD?
Answer:
The endpoints of the line segment CD are:
$$C=(x_1,y_1)= (-4, 8) \\ D= (x_2,y_2)= (8, -4) $$
We find the midpoint using th
What is the slope-intercept form of -8x-2y=-24
Answer:
y=−4x+12
Step-by-step explanation:
y=−4x+12
Hope that helps
I'm thinking of 2 numbers. Both numbers have the same absolute value. What number must be true about the 2 numbers?
Answer: they have the same number in them for example -4 and 4
Step-by-step explanation:
F(x)=-(-1)^2+ 2(-1)-1
Answer:
f(x)=-4
I recommend this math site that could help you with these kind of problems
M
A
T
H
W
A
Y
.
C
O
M
Step-by-step explanation:
What is the independent quantity?
A) not enough information
B) types of food I eat
100 Points. Help solve. The sides are X, y, and 8. The reference angle is 60 degrees. Thanks
Step-by-step explanation:
y=8tan60=8√3
x=8/cos60 = 8 × 2 =16
Evaluate the function for each input listed in the table, and graph the resulting ordered pairs on the coordinate plane.
x f(x) = 2x
0
1
2
3
4
Answer:
0
2
4
6
8
Step-by-step explanation:
f(x) = 2x
f(0) = 2 * 0 = 0
f(1) = 2 * 1 = 2
f(2) = 2 * 2 = 4
f(3) = 2 * 3 = 6
f(4) = 2 * 4 = 8
The complete table of the linear function f(x) = 2x for x = 0 to 4 is:
x 0 1 2 3 4
f(x) 0 2 4 6 8
How to evaluate the function values?The function is given as:
f(x) = 2x
When x = 0, we have:
f(0) =2(0) = 1
When x = 1, we have:
f(1) =2(1) = 2
When x = 2, we have:
f(2) =2(2) = 4
When x = 3, we have:
f(3) =2(3) = 6
When x = 4, we have:
f(4) =2(4) = 8
So, the complete table is:
x 0 1 2 3 4
f(x) 0 2 4 6 8
Read more about linear functions at:
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I don't get it please help and show me how to do it
Answer:
Step-by-step explanation:
You plug in the given values and compute s:
s = ut + 1/2 at^2
s = 10*1/2 + 1/2*-2*(1/2)^2
= 5 + -1*1/4
= 4 3/4.
Which fractions are equivalent to 1012?
[tex]50/60[/tex]
That should be your answer
Answer:
Hello, There! I'm here to help!
QuestionWhich fractions are equivalent to 10/12?
AnswerAccording to The Question I'm guessing you mean 10/12
If so The Following Fractions are Equilvalent to 10/12
1. 20/24
2. 30/36
3. 40/48
5. 50/60
Step-by-step explanation:
To get Eqilvalent You Can Multiply Number to the fractions to find out what's Equilvalent
Therefore, I hope this helps you!
The radius of a circle with centre O is 5 cm. The lengths of the chords AB and BC are 6 cm and 8 cm respectively. The midpoints of the chords are X and Y respectively. Find the perimeter of the quadrilateral OXBY.
Answer:
Step-by-step explanation:
AB=6 cm
BX=1/2 AB=1/2 ×6=3 cm
BC=8 cm
BY=1/2×BC=1/2×8=4 cm
perpendicular bisector of a chord always passes through the center.
so quadrilateral OXBY is a rectangle.
Perimeter=2(BX+BY)=2(3+4)=2×7=14 cm.
(BRAINLIEST to best answer) - Write a linear equation that goes through (1, 3) and (2, 6).
Answer:
y = 3xStep-by-step explanation:
Using the given points find the slope and the y- intercept.
y = mx + bThe slope is:
m = (6 - 3)/(2 - 1) = 3/1 = 3The y- intercept is:
3 = 3*1 + b3 = 3 + bb = 0The line is:
y = 3xSlope
m=6-3/2-1m=3Equation in point slope form
y-3=3(x-1)y-3=3x-3y=3xSubtract. (2/9)−(−1/3+5/9)
Answer:
0
Step-by-step explanation:
the answer is in the above
the answer is 0
Reniel is 13 years old. He is two years younger than his brother, Gelo. If Gelo is five times older than their sister, how old is their sister?
please can someone answer all these
Answer:
what is it what math
Step-by-step explanation:
um what kind of math is this high school primary school
The graph of y=3+2x-x^2 is shown.
Please answer will mark BRAINELIST
Answer:
turning point: (1, 4)
Roots: (-1, 0), (3, 0)
Step-by-step explanation:
The turning point is the vertex of the parabola, which occurs at point (1, 4). The roots are the areas where the graph crosses the x-axis, referred to as the x-intercepts. The graph crosses the x-axis at points (-1, 0) and (3, 0).
where is the circumvented of a right isoceles triangle located
Answer:
The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (i.e., the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (i.e. meeting at one point).
Step-by-step explanation:
I hope that helps you and the explanation is in this answer too
solve the equation 3/4x-5=x
give your answers correct to 2 decimal places
Given :
3/4x - 5 = xTo find :-
The value of x .Solution :-
Taking the given equation ,
3/4x - 5 = x x - 3/4x = -5 4x - 3x /4 = -5x/4 = -5x = -5*4x = -20In biology, cell theory is a scientific theory first formulated in the mid-nineteenth century. It has three tenets:
1. Living organisms are made up of cells.
2. Cells are the basic structural/organizational unit of all organisms.
3. All cells come from pre-existing cells.
What technology had the greatest impact on cell theory?
Step-by-step explanation:
The invention of the microscope allowed human to observe plant and animal cells, and as the technology advanced, scientists have been able to gain more knowledge about these different types of cells. This shows that advancements in technology has paralleled the understanding and knowledge we have about these cells.
The invention of the microscope allowed human to observe plant and animal cells, and as the technology advanced, scientists have been able to gain more knowledge about these different types of cells
What is cell theory?In biology, cell theory is a scientific theory first formulated in the mid-nineteenth century, that living organisms are made up of cells, that they are the basic structural/organizational unit of all organisms, and that all cells come from pre-existing cells.
Cells are the basic unit of structure in all organisms and also the basic unit of reproduction.
The invention of the microscope allowed human to observe plant and animal cells, and as the technology advanced, scientists have been able to gain more knowledge about these different types of cells.
This shows that advancements in technology has paralleled the understanding and knowledge we have about these cells.
To know more about cell theory follow
https://brainly.com/question/1594446
4/7 + 2/7 = ? can yall plzz help me simplify the awnser
Answer:
6/7 is the correct answr
Draw a Graph y=3/2x+2
The answer is in the graph.
Answer:in the picture
Step-by-step explanation:
please give me a brainliest answer
The standard deviation of a population is 13.
What is the margin of error?
Given the value of the standard deviation of population, if the critical value is 0.65, the Margin of error will be 0.65.
What is margin of error?Margin of error simply shows how many percentage points a results will differ from the real population value.
It can be expressed as;
Margin of error = Critical value × Standard deviation
Given that;
Standard deviation S = 13Margin of error = ?Margin of error = Critical value × Standard deviation
Lets take critical value to be 0.05
Hence,
Margin of error = 0.05 × 13
Margin of error = 0.65
Therefore, given the value of the standard deviation of population, if the critical value is 0.65, the Margin of error will be 0.65.
Learn more about margin of error here: https://brainly.com/question/10501147
#SPJ2
Simplify.
- 2x - } – 5x + i + x
-
х
-
17/3
-
3
+
10
х
Enter your answer in the box.
Do not use decimals in your answer.
Step-by-step explanation:
Evaluate:
-[-1⅘ ÷ 0.3(1.2)] - 5/6
⇛-[- 20/5 ÷ 0.3(1.2)]-5/6
⇛- [-20/5 ÷ 0.36] - 5/6
⇛-[-20/5 ÷ 36/100] - 5/6
Here I have changed in expression decimal point into fraction by putting 100 in Denominator.
⇛-[-20/5 × 100/36] - 5/6
⇛-[(-20 × 100)/(5×36)] - 5/6
⇛-[-2000/180]-5/6
Remember (-) × (-) = +.
⇛2000/180 - 5/6
Now, LCM of the denominator 6 and 180 is 180.
⇛(2000 - 150)/180
⇛1850/180
Now, reduce the fraction by extracting and cancaling out by 2.
⇛825/80
Again reduce the fraction by extracting and cancaling out by 5.
⇛165/16 Ans.
Hope this helps!!
[tex]\frac{8}{22} + \frac{3}{22} [/tex]
SOLVE It
NO G.OOGLE
Answer:
[tex]\sf\huge\longmapsto \: \frac{11}{22} [/tex]
Step-by-step explanation:
[tex]\sf\huge\longmapsto \frac{8}{22} + \frac{3}{22} [/tex]
[tex]\sf\huge\longmapsto \: \frac{8 + 3}{22} [/tex]
[tex]\sf\huge\longmapsto \: \frac{11}{22} [/tex]
or the 7:30 show time, 140 movie tickets were sold. Receipts from the $13 adult tickets and the $10 senior tickets totaled $1,664. How many adult tickets and how many senior tickets were sold?
Answer:
adult tickets x=88 and senior tickets y=52
Step-by-step explanation:We can take adult ticket as x and senior ticket as y.
Now we will form two equations
x + y = 140
13x + 10y = 1664
This system of equations we will solve using Gaussian algorithm (gradual elimination of the variables)
We will multiply first equation with (-10) and get
-10x-10y=-1400 Than we will add to second equation and get
3x=264 => x=264/3=88 => x=88
Now we will replace x in the first equation before multiplying and get
88+ =140 => y= 140-88= 52 => y=52
adult tickets x=88 and senior tickets y=52
Good luck!!!
Randy needs to buy 5 pens and 3 colored pencils for his art activity. He has P 86.78 to spend. If the pens and pencils have the same price, how much is the pen and colored pencils per piece?
A. 9.50
B. 10.85
C. 8.75
D. 7.55
Betty's height was 119.2 cm, and Beth's height was 105.6 cm. Six months later, Betty gained 0.4 cm per
month, but Beth's height just remains the same. Find their new total height.
A. 227.2cm
B. 223.4cm
C. 231.8cm
D. 229.6cm
The cost of pen and colored pencils per piece is =10.85
The new total length of both Betty and Beth is =227.2cm
Total number of pens Randy needs to buy = 5
Total number of colored pencils Randy needs to buy= 3
The both items are bought at the same prize = a
The cost of five pens is = 5× a = 5a
The cost of colored pencils is = 3 × a= 5a
The money needed to spend on the items= 86.78
To find the cost of each item which is a ,
5a + 3a = 86.78
(5+3) a= 86.78
8a = 86.78
therefore a = 86.78/8
= 10.85
Therefore the prize of each item is = 10.85. That is option B
Betty's height = 119.2 cm
Beth's height = 105.6cm ( which remained the same)
But Betty's height after 6 months = (6× 0.4) + 119.2
= 2.4 + 119.2
= 121.6 cm
Therefore, the total new height= 121.6 + 105.6
= 227.2cm
That is option A.
correct answers Please!!
Answer:
114 miles
Step-by-step explanation:
Which of the following is the balance for a single $2,702 deposit in an account with an APR of 3% that compounds interest monthly and is invested for 37 years?
Answer:
the answer should be 6 if i am not wrong
Step-by-step explanation: