Angle x is an acute angle in a triangle. If cos x=4/5, then the sin x=
Answers
Answer:
[tex]\bf \sin x =\frac{3}{5}[/tex]
Step-by-step explanation:
Angle x is an acute angle in a triangle.
The measure of cosine angle is given to be :
[tex]\cos x = \frac{4}{5}[/tex]
Now, we need to find the measure of the sine angle for the same triangle.
[tex]\cos x = \frac{Base}{Hypotenuse}[/tex]
⇒ Base = 4 units and Hypotenuse = 5 units
So, Length of perpendicular = 3 units ( By using Pythagoras theorem)
[tex]\sin x=\frac{Perpendicular}{Hypotenuse}\\\\\implies\bf \sin x =\frac{3}{5}[/tex]
Related Questions
what is the slope of the line that passes through (1,4) and (1,-3)?
A. 7
B. -7
C. undefined
D. 0
Answers
M = y2 - y1 / x2 - x1
= -3 - 4 / 1 - 1
= -7 / 0
= undefined.
Therefore the answer is C.
x1 = 1
y1 = 4
The second point is (1,-3) meaning that (x2,y2) = (1,-3). So,
x2 = 1
y2 = -3
Now use the slope formula. Plug in those four values mentioned above
m = (y2 - y1)/(x2 - x1)
m = (-3 - 4)/(1 - 1)
m = -7/0
This is where we run into issues. The denominator is 0. We CANNOT divide by zero. So the result is undefined.
Your calculator may say "UND" for "Undefined", it might say "NaN" for "Not a Number", or it might produce some other type of error.
Answer: Choice C) undefined
Note: if you draw a line through the two given points, the line is completely vertical
The Empire State Building is just over 1,450 feet tall. In anticipation of visiting this landmark on your vacation, you create a model of it using blocks.
a. Suppose you are making a model where one block represents 2 feet. About how many blocks tall is your model of the Empire State Building? What is the scale factor?
Answers
Number of blocks=1,450 feet * (1 block/2 feet)
Number of blocks = 725 blocks
Therefore, you would use a model requiring 725 blocks. The scale factor for the model is 1 block per two feet.
Answer:
725, 1 per every 2 ft.
Step-by-step explanation:
It gives the actual height for the building, 1,450, and it says one block is two feet. Divide 1,450 by 2 and you'd get 725. And we already know dat one block is two feet so it's 1:2
(why did I start singing ``You Reposted in the Wrong Hero Academia?`` UwUz)
The graph of F(x) can be compressrd vertically and shifted to the right to produce the graph of G(x). If F(x) = x^3, which of the following could be the equation of g(x)?
A.) G(x) = 1/2(x-6)^3
B.) G(x) = 2(x-6)^3
C.) G(x) = 2(x+6)^3
D.) G(x) = 1/2(x+6)^3
Answers
It is option A. A vertical compression means that
the function is only a "fraction" of its original height, hence the
fractional coefficient.
REMEMBER, movement along the x-axis is always the OPPOSITE of
what you think. So left = + and right = -
So (x-6) actually means a shift 6 units to the right. (NOT
left like you would naturally think)
Tables of values for f(x) and g(x) are given below. Write g(x) as a transformation of f(x).
Answers
[tex]x_{g} = x_{f} + 8[/tex]
then the values of f and g match.
Therefore
f(x+8) = g(x)
or
g(x) = f(x+8)
The required transformation is a left shift in x by -8 units for f(x).
A composite graph of f(x+8) and g(x) confirms that the transformation is correct.
What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squared over 6 times x to the fourth power ?
Answers
(30x⁶/14y⁵)(7y²/6x⁴)
It can be observed that the numerator of the first and the denominator of the second have a common factor of 6x⁴. Also, the denominator of the first and the numerator of the second expression have a common factor of 7y².
((6x⁴)(5x²)/(7y²)(2y³))(7y²/6x⁴)
Cancellation of the common terms will give us an answer of,
5x²/2y³
Therefore, the simplified version of the involved operation is 5x²/2y³.
Order of operation:3[10-(27 divided by 9)] sorry I don't have the division sign
Answers
first you do parthesis (27/9) = 3
then you subtract from 10 [10-3] = 7
then multiply 3 (this is last because it is outside the parenthesis and [ ].
7 x 3 = 21
21 is your answer
hope this helps
Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) and Z(10,1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer?
Answers
d = √(x₂ - x₁)² + (y₂ - y₁)²
Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165
Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012
Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters
Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.
How do I find the coordinates of angels lab.
Answers
thus
[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 4}}\quad ,&{{ 6}})\quad % (c,d) &({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)[/tex]
[tex]\bf \left(\cfrac{{{ x}} + {{ 4}}}{2}\quad ,\quad \cfrac{{{ y}} + {{ 6}}}{2} \right)=(\underline{7,2})\implies \begin{cases} \cfrac{x+4}{2}=\underline{7}\\\\ x+4=14\\ x=14-4\\ \boxed{x=10}\\ ----------\\ \cfrac{y+6}{2}=\underline{2}\\\\ y+6=4\\ y=4-6\\ \boxed{y=-2} \end{cases}[/tex]
The graph of f(x)=x^2 has been shifted into the form f(x)=(x-h)^2+k
What is the value of h?:
A. 1
B. -1
C. -3
D. 3
Answers
Answer:
D. 3
Step-by-step explanation:
Here h represents the horizontal shift. In the given graph, the graph shifted 3 units to the right from the origin.
Therefore, h = 3.
Answer: D. 3
Hope this will helpful.
Thank you.
Find the volume of each figure to the nearest tenth. Show your work. please
Answers
[tex] \frac{4}{3} \pi 6^3 [/tex]
[tex] \frac{4}{3}*216 \pi [/tex]
[tex]288 \pi [/tex]
V = 288π = 288*3,14 = 904,3 m³
Cone volume: [tex] \frac{ \pi r^2h}{3} [/tex]
We don't have the height, so we should find it firstly.
Watch the triangle "inside" the cone. It is a right triangle. The apothem is the hypothenuse and the radius is the shortest leg.
Apply Pitagora.
h (longest leg) = √13²-5² = √169-25 = √144 = 12 m
V = [tex] \frac{ 5^2*12 \pi}{3} [/tex]
[tex] \frac{25*12* \pi }{3} [/tex]
[tex] \frac{300 \pi }{3} [/tex]
(300*3,14)/3 = 942/3 = 314 m³
Parallelepiped volume: a*b*h
a = 11, b = 5, h = 6
V = 11*5*6 = 330 cm³
what is 345,000 in expanded form
Answers
To put something in expanded form, start with the first digit, and turn the rest of the numbers to 0s, add it to the second digit, also turning the numbers to the right to 0s, and si on and so on.
300,000 + 40,000 + 5,000 (the rest are just zeroes so..)
The answer is 300,000 + 40,000 + 5,000
Hopefully this makes sense, and good luck! :)
A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?
Answers
To calculate the probability of correctly predicting 14 or more coin tosses out of 20, we can use the binomial probability formula.
Explanation:To calculate the probability of correctly predicting 14 or more coin tosses out of 20, we can use the binomial probability formula. The probability of getting exactly k successes in n independent trials with a probability p of success in each trial is given by:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where C(n, k) is the binomial coefficient, n! / (k! * (n - k)!), p is the probability of success (0.5 for a fair coin), and n is the number of trials (20 tosses).
To find the probability of getting 14 or more successes, we need to sum the probabilities of getting 14, 15, 16, ..., 20 successes.
P(X >= 14) = P(X = 14) + P(X = 15) + P(X = 16) + ... + P(X = 20)
We can calculate these probabilities and then add them together to get the overall probability.
Learn more about Probability here:https://brainly.com/question/32117953
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Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the approximate volume of the toy ice cream cone? Use 3.14 for ππ .
Answers
the approximate volume of the toy ice cream cone is around [tex]\( \frac{32}{3}π \)[/tex]cubic inches, considering the half-sphere as[tex]\( \frac{16}{3}π \)[/tex] and the cone as [tex]\( \frac{16}{3}π \).[/tex]
let's calculate the approximate volume of the toy ice cream cone step by step.
First, we need to determine the volume of the half-sphere, which is the ice cream part.
The formula for the volume of a sphere is:
[tex]\[ V_{\text{sphere}} = \frac{4}{3}πr^3 \][/tex]
But since we only have a half-sphere, we'll divide the result by 2.
Now, we need to find the radius ((r)) of the half-sphere. We can do this by measuring the radius of the ice cream cone's base.
Let's say the radius of the ice cream cone's base is (r = 2) inches.
Substituting the value of (r) into the formula:
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(2)^3 \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(8) \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{32}{3}π \][/tex]
[tex]\[ V_{\text{half-sphere}} = \frac{16}{3}π \][/tex]
Now, let's find the volume of the cone part.
The formula for the volume of a cone is:
[tex]\[ V_{\text{cone}} = \frac{1}{3}πr^2h \][/tex]
Where (h) is the height of the cone.
Let's say the height of the cone is (h = 4) inches.
Substituting the values into the formula:
[tex]\[ V_{\text{cone}} = \frac{1}{3}π(2)^2(4) \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3}π(16) \][/tex]
[tex]\[ V_{\text{cone}} = \frac{16}{3}π \][/tex]
Now, to find the total volume of the ice cream cone, we'll add the volumes of the half-sphere and the cone together:
[tex]\[ V_{\text{total}} = V_{\text{half-sphere}} + V_{\text{cone}} \][/tex]
[tex]\[ V_{\text{total}} = \frac{16}{3}π + \frac{16}{3}π \][/tex]
[tex]\[ V_{\text{total}} = \frac{32}{3}π \][/tex]
So, the approximate volume of the toy ice cream cone is [tex]\( \frac{32}{3}π \)[/tex]cubic inches.
A-town and b-ville are connected by a straight, 420-mile road. at noon, atu left a-town for b-ville, and brek left b-ville for a-town. if atu travels at 56 miles per hour and brek travels at 49 miles per hour, how many miles apart will atu and brek be 1 hour before they meet?
Answers
56x + 49x = 420
105x = 420
The value of x from the derived equation is equal to 4 hours.
One hour less than the number of hours calculated above is 3 hours. The distances covered are calculated below.
Atu = (56 mph)(3 hours) = 168 miles
Brek = (49 mph)(3 hours) = 147 miles
The total distance covered is equal to 315 miles.
Subtracting this distance from the given total distance.
difference = 420 miles - 315 miles = 105 miles
ANSWER: 105 miles
A computer company makes a rectangular screen with a diagonal of 20 inches. The width of the screen is 4 inches less than its length. The dimensions of the computer screen are modeled by the equation x2 + (x – 4)2 = 202. What is the value of x, the length of the screen?
A.) x = –16
B.) x = –12
C.) x = 12
D.) x = 16
*The answer is D, x=16. If anyone wants to answer with an explanation of how this is the answer, I will reward them with brainliest.*
Answers
x^2 +(x-4)^2 =20^2
x^2 +(x-4)^2 =400
x^2 +(x-4)^2 -400=0
factor:
2x^2-8x-384=0
Factor the 2 out of 2X^2
2(x-16) (x+12) =0
Divide both sides by 2
(x-16) (x+12) =0
X=16 , x=-12
Number cannot be negative so x=16
Answer: D.) x = 16
Step-by-step explanation:
Given: The dimensions of the computer screen are modeled by the equation :
[tex]x^2+(x-4)^2=20^2[/tex]
To find the value of x , we need to solve the equation.
Now, the above equation can be written as :
[tex]x^2+x^2+16-8x=400\\\\\Rightarrow\ 2x^2-8x+16=400\\\\\Rightarrow2x^2-8x+384=0\\\\\Rightarrow\ 2(x^2-4x+192)=0\\\\\Rightarrow\ x^2-4x+192=0\\\\\Rightarrow(x-16)(x+12)=0\\\\\Rightarrow\ x=16\ or\ x=-12[/tex]
Since side cannot be negative therefore, x= 16
Which number line represents the solutions to |x – 2| = 6?
Answers
x-2=6 add two to both sides
x=8
and
x-2=-6 add two to both sides
x=-4
So x=-4 and 8
So the solution on the number line is solid dots as x=-4 and x=8
Answer: D IS THE ANSWER
If the circumference of a circle is 24, and the angle measure of an arc is 120o, which is the length of the arc?
Answers
The arc length is 8.
2x+7=12x-6 looking for x
Answers
Let's start by writing the problem:
[tex]2x+7=12x-6[/tex]
Subtract 7 from both sides.
[tex]2x+7-7=12x-6-7[/tex]
[tex]2x=12x-13[/tex]
Subtact 12x from both sides.
[tex]2x-12x=12x-13-12x[/tex]
[tex]-10x=-13[/tex]
Divide both sides by -10.
[tex]\frac{-10x}{-10}=\frac{-13}{-10}[/tex]
[tex]x=\frac{13}{10}[/tex]
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish
-10x+7=-6 subtract 7 from both sides
-10x=-13 divide both sides by -10
x=13/10
x=1.3
#23 please!!! Thanks
Answers
45|3
15|3
5|5
1
[tex]xy^2=3^2\cdot5[/tex]
Since x and y are both positive integers, then there's only one possible solution to the above - [tex]x=5,y=3[/tex]
So E.
how do i solve this??
Answers
area for the hexagon = 1/2*p*a
p = perimeter = 18*6=108
a = apothem = 15.59
108*15.59 = 1683.72/2 = 841.86 sq units
Area of rectangle = 18 x 21 = 378
841.86-378 = 463.86 rounded to 464 square units
(01.01) Evaluate −6 − (−3). Answers:18 −9 3 −3
Answers
-6 - (-3) = -6 + 3
-6 + 3
So, -3 is the answer.
so here since we have -6 - -3 we switch 3 signs 3 becomes positive -6 + 3=-3
and there's your answer
Use Gauss-Jordan elimination to solve the following linear system. –4x + 4y + 5z = 9 –2x + 2y + z = 3 –4x + 5y = 4
Answers
- 4 x + 4 y + 5 z = 9
- 2 x + 2 y + z = 3
- 4 x + 5 y = 4
-------------------------
Let`s take the 1st and the 2nd equation:
- 4 x + 4 y + 5 z = 8
- 2 x + 2 y + z = 3 / * ( - 2 ) / multiply both sides of equation by - 2 . /
------------------------------------
- 4 x + 4 y + 5 z = 9
+
4 x - 4 y - 2 z = - 6
------------------------------
3 z = 3 = > z = 1
Then the 2nd and the 3rd equation:
- 2 x + 2 y = 3 - 1 / * ( - 2 )
- 4 x + 5 y = 4
--------------------------------------
4 x - 4 y = - 4
+
- 4 x + 5 y = 4
----------------------------
y = 0
- 4 x + 5 * 0 = 4
- 4 x = 4
x = - 1
Answer: x = - 1, y = 0, z = 1.
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $2510 to rent trucks plus an additional fee of $125.25 for each ton of sugar. The second company does not charge to rent trucks but charges $250.75 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same?
Answers
2510 = 250.75s - 125.25s
2510 = 125.50s
2510 / 125.50 = 20 = s.......they charge the same at 20 tons of sugar
they will both cost : 250.75(20) = $ 5015
The two companies charge the same when transporting 20 tons of sugar, for $5015 for transporting that amount.
To determine what amount of sugar the two companies charge the same, we should set up an equation where both companies' cost functions are equal. For the first company, the cost function is C1 = 2510 + 125.25x, where x is the number of tons of sugar. For the second company, the cost function is C2 = 250.75x. To find the point at which C1 equals C2, we solve for x:
2510 + 125.25x = 250.75x
Subtract 125.25x from both sides:
2510 = (250.75 - 125.25)x
2510 = 125.5x
Divide both sides by 125.5:
x = 2510 / 125.5
x = 20 tons
Therefore, the two companies charge the same for transporting 20 tons of sugar. To find the cost when they charge the same, substitute x into one of the cost functions:
C1 = 2510 + 125.25(20) = 2510 + 2505 = $5015
Thus, the cost when the two companies charge the same is $5015 for 20 tons of sugar.
Why are techniques like cluster sampling and multistage sampling just as externally valid as simple random sampling?
Answers
Due to the fact that they all contain elements of random selection, techniques like cluster sampling and multistage sampling are just as externally valid as simple random sampling due to the fact that they all contain elements of random selection.
Cluster sampling are more or less alike, each heterogeneous and resembling the overall population. The population is split into representative clusters, then a selection is done one or few from the clusters, then lastly, a census is performed with those selected clusters.
In multistage sampling, several methods are combined in sampling schemes and occasionally utilized the same method or different methods or more than once. Though they have different steps in being done, they both have random selection elements.
#12 with work please
Answers
[tex]\bf \pm\sqrt{3^2-2^2}=b\implies \pm\sqrt{9-4}=b\implies\boxed{ \pm\sqrt{5}=b}\\\\ -------------------------------\\\\ cos^{-1}\left( \frac{2}{3} \right)=\theta \implies sin\left[ cos^{-1}\left( \frac{2}{3} \right) \right]\implies sin(\theta ) \\\\\\ sin(\theta )=\cfrac{\pm\sqrt{5}}{3}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}[/tex]
it doesn't say the angle is in a certain quadrant, thus the +/- versions of it are both valid.
Which of the following are geometric sequences? Check all that apply. A. 10, 5, 2.5, 1.25, 0.625, 0.3125 B. 5, 10, 20, 40, 80, 160 C. 3, 6, 9, 12 ,15, 18 D. 1, 3, 9, 27, 81
Answers
The options that are geometric progressions are:
D. 1, 3, 9, 27, 81A. 10, 5, 2.5, 1.25, 0.625, 0.3125B. 5, 10, 20, 40, 80, 160 What is a geometric progression?This is a progression of numbers which usually have a defined ratio that is between them.
The ratio in the options above are:
[tex]\frac{1}{2} , \frac{3}{1} , \frac{2}{1}[/tex]
Read more on geometric progressions here:
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Answer:it’s a,c,d
Step-by-step explanation:
solve the inequality 9x-11 > 4x +12
Answers
Find the arc length of a central angle of pi/4 in a circle whose radius is 8 inches
A) pi/32 in
B) 2pi in
C) 360 in
D) 60 in
Answers
Arc Length = 2πR.(C°/360°), where R is the radius, C°(in degrees) is the central angle of the arc:
We are given:
R = 8 in
Central angle = π/4 ≈ (180°/4) = 45°
Length of the arc= 2π x 8 x (45°/360°) →16π(1/8) :
Length of the arc = 2π in (answer B)
The arc length of a central angle of π/4 in a circle whose radius is 8 inches is 2π inches. Therefore, option B is the correct answer.
What is arc length of a circle?The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining the center to the end-points of the arc.
The formula to find the arc length of a circle is θ/360° ×2πr.
Given that, θ=π/4 =180/4 = 45° and radius = 8 inches.
Now, arc length = 45°/360° ×2×3.14×8
= 1/8×2×3.14×8
= 6.28 inches or 2π inches
Therefore, option B is the correct answer.
Learn more about the arc length of a circle here:
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The length of a rectangle is 9 feet longer than the width. if the perimeter is 78 feet, find the length and width of the rectangle.
Answers
Width - w
Given,
Perimeter = 78 ft
2(l + w) = 78
l + w = 39
l = 39 - w
Given,
l = 9 + w
39 - w = 9 + w
2w = 30
--- w = 15
--- l = 39 -w = 39 - 15 = 24
Therefore, the length of the rectangle is 24 ft and width is 15 ft.
A family has 8 girls and 4 boys. A total of 2 children must be chosen to speak on the behalf of the family at a local benefit. What is the probability that 2 girls and no boys are chosen?
A. 7/55
B. 14/33
C. 12/33
D. 1/6
Answers
P(GG)=56/132
P(GG)=14/33
Answer: The correct option is (B) [tex]\dfrac{14}{33}.[/tex]
Step-by-step explanation: Given that a family has 8 girls and 4 boys. A total of 2 children must be chosen to speak on the behalf of the family at a local benefit.
We are to find the probability that 2 girls and no boys are chosen.
Total number of children in the family = 8 + 4 =12.
Let S denote the sample space of choosing 2 children from the family of 12 children and A denote the event of choosing 2 girls and no boys.
Then, according to the given information, we have
[tex]n(S)=^{12}C_2=\dfrac{12!}{2!(12-2)!}=\dfrac{12\times11\times10!}{2\times1\times10!}=66,\\\\\\n(A)=^8C_2\times^4C_0=\dfrac{8!}{2!(8-2)!}\times1=\dfrac{8\times7\times6!}{2\times1\times6!}=28.[/tex]
Therefore, the probability of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{28}{66}=\dfrac{14}{33}.[/tex]
Thus, the required probability is [tex]\dfrac{14}{33}.[/tex]
Option (B) is CORRECT.