Find Sin A, Cos A, Sin B, and Cos B for the following. Enter answers as fractions in simplest form, not decimals.
Answers
Answer:
[tex]\begin{gathered} \sin A=\frac{\sqrt[]{6}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Explanation:
Let x represent unknown side length
We can go ahead and find x using the Pythagorean Theorem as seen below;
[tex]\begin{gathered} (5\sqrt[]{3})^2=5^2+x^2 \\ (25\times3)=25+x^2 \\ 75-25=x^2 \\ 50=x^2 \\ x=\sqrt[]{50}=\sqrt[]{25\times2}=\sqrt[]{25}\times\sqrt[]{2}=5\sqrt[]{2} \\ x=5\sqrt[]{2} \end{gathered}[/tex]Let's find sin A as seen below;
[tex]\begin{gathered} \sin A=\frac{opposite}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \sin A=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \sin A=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Let's find cos A as seen below;
[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \cos A=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find sin B as seen below;
[tex]\begin{gathered} \sin B=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \sin B=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find cos B as seen below;
[tex]\begin{gathered} \cos B=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \cos B=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Related Questions
Question 1 (1 point)Write the equation in slope intercept form13x – 11y = –12Don’t forget to transpose
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Solve for y in the equation in standard form
[tex]\begin{gathered} 13x-11y=-12 \\ -11y=-13x-12 \\ y=\frac{-13x-12}{-11} \\ y=\frac{13}{11}x+\frac{12}{11} \end{gathered}[/tex]Tan theta=10
Find sin(2theta)+cos(2theta)
Answers
Answer: B
Step-by-step explanation:
[tex]\tan \theta=10 \implies \sin \theta=\frac{10}{\sqrt{101}}, \cos \theta=\frac{1}{\sqrt{101}}[/tex]
[tex]\sin 2\theta=2\sin \theta \cos \theta=2 \left(\frac{10}{\sqrt{101}} \right)\left(\frac{1}{\sqrt{101}} \right)=\frac{20}{101}[/tex]
[tex]\cos 2\theta=2\cos^2 \theta-1=2 \left(\frac{1}{\sqrt{101}} \right)^2 -1=-\frac{99}{101}[/tex]
[tex]\therefore \sin 2\theta+\cos 2\theta=\frac{20}[101}-\frac{99}{101}=-\frac{79}{101}[/tex]
Please help!!!!!!!!!
Answers
Answer:
x and y is 59 degrees
Step-by-step explanation:
You can find the angle next to 121 which is 59 degrees considering linear pair. Then, you can figure out y by doing corresponding angles and so this means that y is also 59 degrees. To find x, we know that x is vertical to y and that they are the same value. So, this means that x is 59 degrees as well. Hope this helps!
Farmer jones, and his wife, dr. jones, decide to build a fence in their field, to keep the sheep safe. since dr. jones is a mathematician, she suggests building fences described by y=11x^2and y=x^2+4. farmer jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. what is the area of the enclosed region?
Answers
Given:
The equation is:
[tex]\begin{gathered} y=11x^2 \\ y=x^2+4 \end{gathered}[/tex]Required:
Find the area enclosed by the region.
Explanation:
The given equation is:
[tex]\begin{gathered} y=11x^2 \\ y=x^2+4 \end{gathered}[/tex]Find the intersecting point of the curve.
[tex]\begin{gathered} 11x^2=x^2+4 \\ 10x^2=4 \\ x^2=\frac{4}{5} \\ x=\pm\sqrt{\frac{4}{5}} \\ x=\pm\frac{2}{\sqrt{5}} \end{gathered}[/tex]The enclosed area is:
[tex][/tex]which statement best describes the equation x + 5 imprint c squared + 4 (x + 5) + 12 equals 0
Answers
Given:
[tex](x+5)^2+4(x+5)+12=0[/tex]let u = x+5
so, the equation will become:
[tex]u^2+4u+12=0[/tex]so, the equation is quadratic in form because the substitution u = x+5
The answer is the first statement
Note:
the second statement is wrong, because when the equation expanded, it will be a second degree polynomials not fourth degree
Also, the last 2 statements are wrong, because it is quadratic equation.
please help me i don't even know I'm behind
Answers
Answer: 6.33
Step-by-step explanation:
[tex]x^2 =36 \implies x=\pm 6\\\\x^3 =125 \implies x=5\\\\x^2=81 \implies x=\pm 9\\\\x^3 =512 \implies x=8\\\\x^2 =100 \implies x=\pm 10\\\\x^2 =121 \implies x=\pm 11\\\\x^2 =49 \implies x=\pm 7\\\\x^3 =64 \implies x=4\\\\x^3 =8 \implies x=2\\\\[/tex]
So, the correct answers are 5, 10, and 4, and thus the mean is 19/3, or about 6.33.
Use the figure to answer exercises 6-7. 8 ft 5 ft 6. Frank drew a square pyramid and its net to represent a fort. Complete the net by filling in the missing measure. Choose the correct answer below. OA. ОВ. OC. OD. 1.25ft 42.5ft 18 ft 5 ft 0 LA CA 5ft 1.25ft 8 ft 2.5ft
Answers
Answer:
6. C
7. 105 ft²
Explanation:
The square pyramid has a square base with a side's length equal to 5 ft and a slant height equal to 8 ft.
Now, the only option that shows a square with a side length equal to 5 is C. So, the right net is C.
Then, the amount of fabric depends on the area of the net. The area of the net is equal to the area of the square added to the area of the triangles.
The area of the square is:
Area = side x side = 5 x 5 = 25 ft²
The area of the triangles is:
Area = 1/2 x base x height = 1/2 x 5 x 8 = 20 ft²
Then, the total area of the net is:
Total Area = 25 ft² + 4( 20 ft²)
Total Area = 25 ft² + 80 ft²
Total Area = 105 ft²
So, Frank needs 105 ft² of fabric to make the fort.
Write an equation of a parabola with a vertex at the origin and a diretrix at y=5.
Answers
The equation of the parabola with a vertex at the origin and a directrix at; y = 5 as described in the task content is; x² = -20y.
How to write equation of a parabola with a vertex at the origin?It follows from the task content that the vertex of the parabola is at the origin while it's directrix is the line; y = 5.
Therefore, it follows that the focus of the parabola is; f = -5, since; (f - k) = (k - 5) where, k = 0.
Ultimately, a = 1/4(f-k).
a = 1/4(-5-0) = -1/20.
Recall, the vertex form equation of a parabola takes the form;
y = a(x - h)² + k; where (h, k) is the vertex.
Therefore, since the vertex is at the origin; we have;
y = (-1/20) (x -0)² + 0
y = -x²/20
20y = -x²
Ultimately, the required equation of the parabola is;
x² = -20y.
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Answer:
[tex]y = -\frac{1}{20} x^{2}[/tex]
Step-by-step explanation:
[tex]y = \frac{1}{4(f-k)}(x - h)^{2} + k[/tex] Use the equation of the parabola. The vertex is at the origin, then (h, k) is (0, 0). Substitute 0 for h and k in the equation.
[tex]y = \frac{1}{4(f-0)} (x-0)^{2} + 0[/tex] Simplify.
[tex]y = \frac{1}{4f} x^{2}[/tex]
The directrix is given [tex]y = 5[/tex]. The distance from the focus to the vertex equals the distance from the vertex to the directrix, so
[tex]f - k = k - 5\\f = -5[/tex] Substitute -5 for f in the equation of the parabola above.
[tex]y = \frac{1}{4 * - 5} x^{2}[/tex] Simplify.
[tex]y = - \frac{1}{20} x^{2}[/tex]
I tried doing the method my teacher taught me but i keep getting it wrong
Answers
ANSWER
x = 12
EXPLANATION
By the intersecting chords theorem, the product of each segment of one chord equals to the product of each segment of the other chord:
[tex]15\cdot8=10x[/tex]Solving for x:
[tex]\begin{gathered} 120=10x \\ x=\frac{120}{10} \\ x=12 \end{gathered}[/tex]bebe ené’eben’´´enz’bzva
Answers
Answer:
What?
Step-by-step explanation:
What?
Kimberly wants to invest $3,000 in an account that earns 4% annual interest, and x dollars in an account that earns 7%, so that, on average, she earns 5.5% interest for both accounts. Select the equation to model the situation.A.0.04(3,000) + 0.07x = 0.55xB.0.055(3,000 + x) = 120 + 0.07xC.0.04x + 0.07x = 3,000D.0.055(3,000) = 0.04x + 0.07x
Answers
As given by the question
There are given that the total investment money is $3000 and earns 4% annual interest.
Now,
x dollars in an account that earns 7% and that earns 5.5% interest for both accounts.
Then, for the equation
Assuming that the money is invested at simple interest for one year,
We have:
[tex]\begin{gathered} 0.04(3000)+0.07x=0.055(3000+x) \\ 120+0.07x=0.055(3000+x) \end{gathered}[/tex]Hence, the correct option is B
Answer:
B- .0.055(3,000 + x) = 120 + 0.07x
find the value of x.
Answers
The value of x = - 12°
Isosceles triangleThe triangle which has two equal sides or two equal sides is called an Isosceles triangle. In a Isosceles triangle the angles made by equal sides with 3rd side will be equal
Here from given question we have,
Measure of ∠2 = x + 85
And the measure of another angle = 73
From given picture,
Two sides of triangle are equal then the given triangle will be an Isosceles triangle
As we know in a Isosceles triangle the angles made by the two equal sides with 3rd side will be equal
=> ∠2 = 73
=> x + 85 = 73
=> x = - 85 +73
=> x = -12°
Therefore,
The value of x = -12°
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Put the following rational numbers in ascending order. r 0.4, 7/10, 9/10
Answers
Answer:
Step-by-step explanation:
Ascending is least to greatest.
We can convert the fractions into decimals.
SO,
7/10 can be 0.7 and 9/10 can be 0.9
In least to greatest order, it would be:
0.4, 0.7, 0.9 ANSWER
Question 10 of 10 The graph of the absolute value parent function, f(x) = [xl, is stretched horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
Answers
Answer:
[tex]g(x)=|\frac{x}{3}|[/tex]Explanation:
We are given absolute value function:
[tex]f(x)=|x|[/tex]It has been stretched horizontally by a factor of 3, we need to find a new function that shows the stretched functions:
Stretch-Compress-along x:
[tex]\begin{gathered} g(x)=f(cx) \\ \end{gathered}[/tex]Stretch if:
[tex]0Compress if:[tex]c\text{ }>1[/tex]Since our function is Stretched by a factor of 3, therefore our function g(x) is:
[tex]g(x)=f(\frac{x}{3})=|\frac{x}{3}|[/tex]This is a new function.
Answer:
Step-by-step explanation:
g(x) = |1/3x|
You are hiking a trail over multiple days. At the start of your hike, you decide that you need to hike at least 22 miles in the first 3 days, but can't hike more than 34 miles, as you'll pass into swampy terrain where camping won't be possible. You want to hike the same distance each day. Let x represent the number of miles you hike each day.
Answers
The number of miles you hike each day is 7.4 miles.
What is the unitary method?The unitary approach, to put it simply, is used to determine the value of a single unit from a specified multiple. How to determine the worth of a single pen, for instance, if 40 pens cost Rs. 400. The unitary approach can be utilized. Additionally, after determining the value of a single unit, we can multiply it to determine the value of the other units. Most ratio and proportion concepts are addressed using this methodology. To compute the value of other units using the unitary approach, the value of a unit quantity must first be determined. This can be varied in two different ways.
Direct VariationInverse Variation3 days = 22 miles
1 day = x
x = 7.4 miles
Still 12 miles are left so I will need half a day more approximately.
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Find the minimum, first quartile, median, third quartile, and maximum of the data set below.4.92.76.2.54.75.46.53.812type an integer or decimal
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SOLUTION
The Data set given is
4.9,2.7,6.2,5,4.7,5.4,6.5,3.8,12
The minimum of the data set is the lowest data in the distribution
[tex]\text{minimun}=2.7[/tex]The first quartile is given by
[tex]Q_1=(\frac{N}{4}+1)^{th}[/tex]where N=frequency of the data=9
[tex]Q_1=\frac{9}{4}+1=1.25+1=2.25^{th}[/tex]Then the first quartile becomes
[tex]Q_1=4.7[/tex]The median is the middle number after arrangement
[tex]2.7,3.8,4.7,4.9,5.0,5.4,6.2,6.5,12[/tex][tex]undefined[/tex]
Evaluate the following expression 8!
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The value of the expression 8! is 40320.
What is an expression?It should be noted that an expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, 8! will be:
= 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 40320
This illustrates the concept of multiplication.
Therefore, it is 40320.
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Answer this please question in picture it’s geometry
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The value of P is 1 and value of V is 5 .
In this addition, each letter represents a single digit.
Now, Given that
1 7 2
2 9 4
+ 7 V 6
= P 2 P 2
To find the value of P
To solve this addition:
1 7 2
2 9 4
+ 7 5 6
= 1 2 1 2
Hence, The value of P is 1 and value of V is 5 .
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Find the greatest common factor of the terms of the polynomial.
15z4 -30z³ +6z²
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Find the measure of the side labeled x. Round to two decimal places as needed.
Answers
The Solution:
Given:
We are asked to find the value of x.
By applying the Trigonometrical Ratio, we have:
[tex]\begin{gathered} \sin42.8=\frac{opp}{hypotenuse}=\frac{x}{20.9} \\ \\ \sin42.8=\frac{x}{20.9} \end{gathered}[/tex]Cross multiplying, we get
[tex]x=20.9\sin42.8=14.2003\approx14.20[/tex]Therefore, the correct answer is 14.20
3. Which statement is true? B a.
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The true statement is b.
Period Kuta Software - Infinite Algebra 2 Compound Inequalities Solve each compound inequality and graph its solution. Name Sarandha cedules Date 220 21 1) n+1-3 or 4n
Answers
n+1< -3
n< -3 -1
n<-4
-4n< - 8
n>-8/-4
n > 2
so, the solution is,
n < - 4 or n > 2
how many grams are in a Kilogram?1,0000.0010.01100
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Ok, so
The answer is that there's 1,000 grams in a Kilogram. That's the equivalence.
Name the type of transformation shown. 1. A. 2 IN
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It is a transilation transformation.
The coordinate is moved 6 units to the right and 6 unit to down ward direction.
First find the term that should be added so that the expression is a perfect-square trinomial. w² + 7w + ___Then factor the trinomial.(___)²
Answers
to do a perfect-square trinomial the third term must be the square of the half of the second term
the sencond term is 7,so
[tex](\frac{7}{2})^2=\frac{49}{4}[/tex]so the expresion is
[tex]w^2+7w+\frac{49}{4}[/tex]and the factor
[tex](w+\frac{7}{2})^2[/tex]An example
[tex]w^2+\frac{8}{5}w+\cdots_{}[/tex]the third term is
[tex]\begin{gathered} (\frac{\frac{8}{5}}{2})^2 \\ \\ (\frac{4}{5})^2 \\ \\ =\frac{16}{25} \end{gathered}[/tex]so the percet-square is
[tex]w^2+\frac{8}{5}w+\frac{16}{25}[/tex]defines substitution
Answers
In this case, the answer is very simple.
Defines substitution.
The answer is:
The substitution method for solving systems of linear equations, consists of solving or isolating one of the unknowns (for example, x) and substitute its expression in the other equation.
In this way, we will obtain a first degree equation with the other unknown (y), and once solved ''y'', we calculate the value of ''x'' substituting the value of ''y'', that we already know.
In a forest there are 99,278 trees. Each tree has about 57 branches and each branch has about
1,628 leaves.
Estimate the number of leaves in the forest by giving the answer in billions (for example, 2.12 or
3.56).
Answers
Answer:
9.53
Step-by-step explanation:
Estimate of trees: 99,300
Estimate of branches: 60
Estimate of leaves: 1600
All of the numbers multiplied togethered: 99,300 x 60 x 1600 = 9,532,800,000
9,532,800,000 to the billions is 9.53b
Note: i do not know if this will be accepted since you didn't put any answer choices so yeah
Hi can you help me with this problem i dont understand itIll do anything if your correct
Answers
You can use multiplication to generate an equivalent ratio by multiplying both sides of the ratio by the same factor, this way:
[tex]\begin{gathered} 47\cdot2\colon3\cdot2 \\ 94\colon6 \end{gathered}[/tex]You need a common numerator in order to add or subract two fractions.
O True
O False
Answers
Answer: False
Step-by-step explanation:
You need a common denominator (the bottom number)
Graph the parabola.
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
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The graph of the parabola is added as an attachment
The vertex is (0, 0)The points to the right are (1, 1) and (2, 4)The points to the left are (-1, 1) and (-2, 4)How to graph the parabola?From the complete question (added at the end of the solution), the equation of the parabola is given as
y = x²
When a parabola has the form of y = x², then the vertex of the parabola is
Vertex = (0, 0)
Set x > 0 to determine the points to the right
When x = 1
y = 1² = 1
When x = 2
y = 2² = 4
Set x > 0 to determine the points to the left
When x = -1
y = -1² = 1
When x = -2
y = -2² = 4
So, the points are
(1, 1), (2, 4), (-1, 1) and (-2, 4)
While the vertex is (0, 0)
Next, we plot the graph of the parabola using a graphing calculator
See attachment for the graph
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Complete question
Graph the parabola y = x²
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.