Answers
Step-by-step explanation:
[tex] \sin(θ) = \frac{2}{5} [/tex]
We know that
[tex] { \sin ^{2} (θ) } + \cos^{2} (θ) = 1[/tex]
Using that we get
[tex] \cos^{2} (θ) = 1 - \sin^{2}( θ) = 1 - { \frac{2}{5} }^{2} [/tex]
[tex] = 1 - \frac{4}{25} [/tex]
[tex] \frac{21}{25} [/tex]
hence
[tex] \cos(θ ) = \frac{ \sqrt{21} }{5} [/tex]
Step-by-step explanation:
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Related Questions
On Tuesday, recess began at 11:43. The students got back to their class at 12:04. How long were they at
recess?
Answers
Answer:
They were out side for 21 minutes
Step-by-step explanation:
you just add 11:43 and add 21 minutes to it and you get 12:04
precio antes de impuestos 1563.60 impuesto 5.4%
Answers
Answer:
precio antes De impuestos 1563.60 impuestos 5.4%
Find the area of a green shaded region in the figur
Answers
Answer:
The answer is 156cm^2
Step-by-step explanation:
Solution:
The shape given is a trapezium.
The area of the green region = Area of the outer trapezium - Area of the inner trapezium.
[tex]Area\: of\:a\:trapezium\:=\frac{1}{2}\:(a+b)h[/tex]
[tex]Where\: a,b\:are\:the\:bases,\:h=height[/tex]
[tex]For,\:outer\:trapezium,[/tex]
[tex]a=10cm,\:b=14cm,h=16cm[/tex]
[tex]Area\:of\:the\:outer\:trapezium=\frac{1}{2}\:(10+14)16[/tex]
[tex]=\frac{1}{2}(24)(16)=192cm^{2}[/tex]
[tex]For\:inner\:trapezium,[/tex]
[tex]a=3cm,b=6cm,h=8cm[/tex]
[tex]Area\:of\:the\:inner\:trapezium=\frac{1}{2}(3+6)8[/tex]
[tex]=\frac{1}{2}(9)(8)=36cm^{2}[/tex]
[tex]193cm^{2}-36cm^{2}[/tex]
[tex]=156cm^{2}[/tex]
The answer is 156cm^2
Can someone please help me with this
Answers
Answer:
1, 4, 6.
Step-by-step explanation:
[tex]\left(2n+8\right)\left(n+4\right)=2n^2+16n+32[/tex]
1. [tex]2(x+4)^2=2n^2+16n+32[/tex]
2. [tex]2\left(n+4\right)\left(n+4\right)=2(n+4)^2[/tex]
3. [tex]16n+32=16n+32[/tex]
4. [tex]2n^2+16n+32=2n^2+16n+32[/tex]
5. [tex]2n^2+8n+32=2n^2+8n+32[/tex]
6. [tex]2(n^2+8n+16)=2n^2+16n+32[/tex]
As you can see from the answers it is 1, 4, and 6.
The sum of two numbers is 21. Their product is 108. What are the two numbers?
Answers
Answer:
9 and 21
Step-by-step explanation:
First we can write the factors of 108:
1,108
2,54
3,36
4,27
6,18
9,12 - these 2 numbers add up to 21 so these 2 numbers is our answer.
Answer:
12 and 9
First, divide 108 by a relatively low number, 12[tex]108 / 12 = 9[/tex]
Now that we have 9, multiply 9 by 12[tex]9 * 12 = 108[/tex]
This is one method that proves the statement true. I call the method mirroring. This method consists of finding the lowest numbers a large number is divisible by, then flipping the problem to a multiplication problem.________________________________________________________
What have we learned?We learned alternative ways to find the sum and product of a number using a similar method.
Questions related to the topic? Ask me in the comments box.
Find the area of the rhombus.
Answers
Step-by-step explanation:
as the graphic shows, we are dealing with a special rhombus : a square.
this is proven by the fact that the angle on one side of the diagonal at the corner is 45°. so, the other side must be 45° too, and so we have 90° angles at the corners.
what is not clear to me is : what is 6 cm long ? a half-diameter, or the whole diameter ?
I assume the half-diameter.
what the graphic is trying to suggest is that we have 4 little right-angled triangles that are also isoceles triangles (their legs are equally long).
every leg is 6 cm long (based on my assumption above).
because they are right-angled, the area of each of these little triangles is leg×leg/2
6×6/2 = 18 cm²
we have 4 triangles, so the total area is
4×18 = 72 cm²
if 6 cm stands for the whole diagonal after all, then the only change is the length of the legs, which would be then 6/2 = 3 cm.
then we would have
3×3/2 = 4.5 cm² for a single triangle
and
4×4.5 = 18 cm² for the whole area.
Find the measure of each angle in the isosceles trapezoid.
Answers
Answer:
J=118
L=62
M=62
Step-by-step explanation:
In an isoseles trapezoid, the top angles are congruent to each other and the bottom angles are congruent to each other. Opposite angles are supplementary, and all angles together add up to 360.
Question: If [tex]$f(x)=\cos \left[2 \tan ^{-1}\left(\sin \left(\cot ^{-1} \sqrt{\frac{1-x}{x}}\right)\right)\right]$[/tex]
Options:
[tex](a) $f^{\prime}(x)(x-1)^{2}-2(f(x))^{2}=0$\\\(b) $f^{\prime}(x)(x-1)^{2}+2(f(x))^{2}=0$\\(c) $f^{\prime}(x)(x+1)^{2}+2(f(x))^{2}=0$\\(d) $f^{\prime}(x)(x+1)^{2}-2(f(x))^{2}=0$[/tex]
Answers
Note that √((1 - x)/x) is defined only as long as 0 < x ≤ 1.
Consider a right triangle with reference angle θ such that
[tex]\cot(\theta) = \sqrt{\dfrac{1-x}x}[/tex]
In other words, on an appropriate domain,
[tex]\theta = \cot^{-1}\left(\sqrt{\dfrac{1-x}x}\right)[/tex]
In such a triangle, you would find that
[tex]\sin(\theta) = \sqrt x[/tex]
so f(x) reduces a bit to
[tex]f(x) = \cos\left(2 \tan^{-1}(\sqrt x)\right)[/tex]
Now consider another triangle with reference angle ɸ such that
[tex]\tan(\phi) = \sqrt x \implies \phi = \tan^{-1}(\sqrt x)[/tex]
In this triangle, you would find
[tex]\cos(\phi) = \dfrac1{\sqrt{1+x}}[/tex]
Recalling the double angle identity for cosine, it follows that
[tex]f(x) = \cos(2\phi) = 2 \cos^2(\phi) - 1 = \dfrac{1-x}{1+x}[/tex]
Differentiating with respect to x yields
[tex]f'(x) = -\dfrac2{(1+x)^2}[/tex]
while
[tex]f(x)^2 = \dfrac{(1-x)^2}{(1+x)^2}[/tex]
It follows that
[tex]f'(x)(x-1)^2 - 2f(x)^2 = 0[/tex]
so B is the correct choice.
This figure represents a garden box that is to be filled with soil.
How much soil will it take to fill the garden box?
Enter your answer in the box.
Answers
Answer:
1728 ft³
Step-by-step explanation:
Lower part:
volume = 19 ft × 12 ft × 6 ft = 1368 ft³
Upper part:
volume = 10 ft × 12 ft × 3 ft = 360 ft³
Total Volume = 1728 ft³
Please help me on Mathematics
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Answers
Answer:
1. 20 km/hr (60km / 3h)
2. 70 m/hr (170m / 2h)
3. 6.5 hr (260cm / 40km)
4. 4.5 s (72cm / 16cm)
5. 184 km (46km * 4h)
Step-by-step explanation:
We'll use d = distance, t = time, s = speed.
Speed over time can be found by dividing distance by time
s = d / t
We can take this formula and manipulate it to find either distance or time if we know two of the values. Keeping in mind division and multiplication cancel each other.
If we wanted to find d for instance we can multiply both sides by t to get
s * t = d
For time we can divide both sides of the above formula by s to get
t = d / s
Answer:
1. 20 km/h
2. 70 m/h
3. 6.5 h
4. 4.5 s
5. 184 km
Step-by-step explanation:
For first two questions, you can use the following formula:
[tex]\displaystyle \large{s = \frac{d}{t}}[/tex]
I denote ‘s’ be speed, ‘d’ be distance and ‘t’ be time. Some books may use ‘v’ for speed instead of ‘s’ but I use ‘s’ variable instead so it makes the equation easier to memorize.
Therefore, speed = distance/time
( 1 ) The first question is given both distance be 60 km and time be 3 hours. Therefore:
[tex]\displaystyle \large{s=\frac{60}{3}}\\\displaystyle \large{s=20 \ \ \sf{km / h}}[/tex]
So for the first question, the speed is 20 km/h
( 2 ) The second is given both distance be 140 m and time be 2 hours. Therefore:
[tex]\displaystyle \large{s=\frac{140}{2}}\\\displaystyle \large{s=70 \ \ \sf{m / h}}[/tex]
Therefore, speed is 70 m/h
For the third and four questions, we will be finding time. From the speed formula:
[tex]\displaystyle \large{s=\frac{d}{t}}[/tex]
Multiply both sides by t.
[tex]\displaystyle \large{st=d}[/tex]
Divide both sides by s.
[tex]\displaystyle \large{t=\frac{d}{s}}[/tex]
Therefore, time = distance/speed
( 3 ) The question is given speed be 40 km/h and distance be 260 km. Therefore:
[tex]\displaystyle \large{t=\frac{260}{40}}\\\displaystyle \large{t=\frac{13}{2} \ \ \sf{h}}\\\displaystyle \large{t = 6\frac{1}{2} \ \ \sf{h}}\\\displaystyle \large{t= 6.5 \ \ \sf{h}}[/tex]
Therefore, time is 6.5 h
( 4 ) The question is given speed be 16 cm/s and distance be 72 cm. Therefore:
[tex]\displaystyle \large{t=\frac{72}{16}}\\\displaystyle \large{t=\frac{9}{2} \ \ \sf{s}}\\\displaystyle \large{t=4\frac{1}{2} \ \ \sf{s}}\\\displaystyle \large{t=4.5 \ \ \sf{s}}[/tex]
Therefore, time is 4.5 s
For the last question, we have to find distance. From the speed formula:
[tex]\displaystyle \large{s=\frac{d}{t}}[/tex]
Multiply both sides by t.
[tex]\displaystyle \large{st=d}\\\displaystyle \large{d=st}[/tex]
Therefore, distance = speed * time
( 5 ) The question is given time be 4 hours and speed be 46 km/h. Therefore:
[tex]\displaystyle \large{d=46 \cdot 4}\\\displaystyle \large{ d=184 \ \ \sf{km}}[/tex]
Therefore, distance is 184 km.
3. Evaluate the following:
a.) What value of Syields the coordinate point (1, 3)?
b.) What value of Syields the coordinate point (3, 1)?
c.) x(710)=
d.) y(V10+ V5)= = B С
e.) x(2)=
f.) y(2.5)=
Answers
Answer: See below
Step-by-step explanation:
Question 3:
[tex]a) \ $S=1$ \ yields \ $(1,3)$ \\ \\b) \ $S=3$ \ yields \ $(3,1)$ \\ \\ c) \ $x(\sqrt{10})=\sqrt{10}$ \\ \\d) $y(\sqrt{10}+\sqrt{5})=1$ \\ \\e) $x(2)=2$ \\ \\f) $y(2,5)=1$ \\[/tex]
Challenge:
[tex]\begin{aligned}&x(s)=s \quad ,s \in[0,4] \\&y(s)=\left\{\begin{array}{cc}3 s & , s \in[0,1] \\5-2 s &, s \in[1,2] \\1 & s \in[2,4]\end{array}\right.\end{aligned}[/tex]
The lengths of two sides of a triangle are 10 and 24, and the third side is x. How many whole number values are possible for x.
Answers
Answer:
[tex]20[/tex].
Step-by-step explanation:
In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex]:
[tex]a + b > c[/tex],
[tex]a + c > b[/tex], and
[tex]b + c > a[/tex].
In this question, the length of the sides are [tex]10[/tex], [tex]24[/tex], and [tex]x[/tex]. The length of these sides should satisfty the following inequalities:
[tex]10 + 24 > x[/tex],
[tex]10 + x > 24[/tex], and
[tex]24 + x > 10[/tex].
Since [tex]x > 0[/tex], the inequality [tex]24 + x > 10[/tex] is guarenteed to be satisfied.
Simplify [tex]10 + 24 > x[/tex] to obtain the inequality [tex]x < 35[/tex].
Similarly, simplify [tex]10 + x > 24[/tex] to obtain the inequality [tex]x > 14[/tex].
Since [tex]x[/tex] needs to be a whole number, the greatest [tex]x[/tex] that satisfies [tex]x < 35[/tex] would be [tex]34[/tex]. Similarly, the least [tex]x\![/tex] that satisfies [tex]x > 14[/tex] would be [tex]15[/tex]. Thus, [tex]x\!\![/tex] could be any whole number between [tex]15\![/tex] and [tex]34\![/tex] (inclusive.)
There are a total of [tex]34 - 15 + 1 = 20[/tex] distinct whole numbers between [tex]15[/tex] and [tex]34[/tex] (inclusive.) Thus, the number of possible whole number values for [tex]x[/tex] would be [tex]20[/tex].
Two years ago my dog, Bau, was five times older than mu cat, Miho. 1 year from now Bau will only be twice as old as Miho. How old is Bau now?
Answers
Using the formula S = P(1 + r)t, where P is the original principal, r is the annual interest rate, and t is the number of years, what is the investment savings, S, if P = $14,500.00, r = 7.5%, and t = 5 years?
Answers
[tex]~~~~~~ \textit{Savings Earned Amount} \\\\ S=P\left(1+r\right)^{t} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$14500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years\dotfill &5 \end{cases} \\\\\\ S=14500\left(1+0.075\right)^{5}\implies S=14500(1.075)^5\implies A\approx 20816.63[/tex]
In a discount basis loan, interest is "pald" at the time the loan is made by deducting the Interest amount from the loan
amount.
“True
False”
Answers
Answer:
true
hope that helps
Step-by-step explanation:
Write an algebraic expression for the following word phrase. The quotient of 69 and x
Answers
Hello!
_____
The quotient of two numbers means we divide one number by another number.
Example :-
The quotient of 6 and a number:-
6÷x
According to the example above, the algebraic expression looks like so:-
69÷x
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
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Ray is x years old. His brother Ron is y years older than Ray.
What will the sum of their ages be in 5 years?
Answers
Answer: X+Y+5
Step-by-step explanation:
There is no single answer you have to write an equation.
Stacy buys a bagel assortment that has 6 oat bagels for every 2 blueberry bagels. Naomi buys a bagel assortment that has 9 oat bagels for every 5 blueberry bagels. Each girl bought 10 blueberry bagels.
Stacy’s Bagels
Oat 6 12 18 24 30 36
Blueberry 2 4 6 8 10 12
Naomi’s Bagels
Oat 9 18 27 36 45 54
Blueberry 5 10 15 20 25 30
Find the number of oat bagels that each girl bought.
Stacy bought
oat bagels, and Naomi bought
oat bagels.
Answers
Answer: Stacy: 30 Naomi: 18
Step-by-step explanation:
Stacy- ratio of oat to blueberry is 6:2 we want to find x:10
10 is 5 times 2, and whatever you do to the bottom you have to do to the top, and 6 times 5 is 30
Naomi- ratio of oat to blueberry is 9:5 we want to find x:10
The 10 is 2 times 5, and whatever you do to the bottom you have to do to the top, and 9 times 2 is 18
If you were to roll two dice, what is the probability that the sum of the numbers showed on the dice is greater than 5?
Answers
The probability that an outcome is greater than 5 is the likelihood of the outcome
The probability that the sum of the numbers showed on the dice is greater than 5 is 13/18
How to determine the probability?The sample size of a roll of two dice is:
n(S) = 36
The number of outcomes that have a sum greater than 5 is:
Greater than 5 = 26
So, the required probability is:
P = 26/36
Simplify
P = 13/18
Hence, the probability that the sum of the numbers showed on the dice is greater than 5 is 13/18
Read more about probability at:
https://brainly.com/question/251701
Alan bought 120 pens at the cost of €2 per pen. He sold 72 of them for €2.50 per pen and the remaining at the price of €2 per pen. Find his percentage profit or loss.
Answers
Answer:
His profit was 15%
Step-by-step explanation:
120*2€ = 240€
72*2.5€ = 180€
120-72 = 48
48*2€ = 96€
And now a simple proportion:
240€ = 100%
276€ = x
x = (276*100)/240 %
x = 115%
115%-100% = 15%
His profit was 15%
Question 13 of 14
Phillipa rode her bicycle every day over the weekend. Phillipa rode [(13.5 + 8.5) ÷ 2]
miles on Friday, [18 − (2 × 4)] miles on Saturday and [20 − (5 − 3)]
miles on Sunday.
On which day did Phillipa ride her bicycle the most?
She rode her bicycle the most on .
Answers
Answer:
Sunday
Step-by-step explanation:
Friday
[(13.5 + 8.5) ÷ 2] = [(22) ÷ 2] = 22 ÷ 2 = 11 miles
Saturday
[18 − (2 × 4)] = 18 - (8) = 18 - 8 = 10 miles
Sunday
[20 − (5 − 3)] = 20 - (2) = 18 miles
18 > 11 > 10
Then She rode her bicycle the most on Sunday
Try:
Rereading your lessons, getting help from your tutor or others.
Answer:
Sundays
Hope this helps and don't forget to hit the thanks button! <3
Written by: RiBu
THE ANSWER IS SUNDAYS.
7, 10, 13, 23, 36, 55, 67
Pt A
Which of these puts the correct classification of the numbers as prime or composite?
A) Prime: 10, 13, 36, 67
Composite:7, 23, 55
B) Prime:7, 15, 55, 67
Composite:10, 36, 23
C)Prime:10, 36, 55
Composite:7, 13, 23, 67
D) Prime:7, 13, 23, 67
Composite:10, 36, 55
Pt B
Which of these are composite numbers?
A)11 and 12
B)28 and 29
C)31 and 32
D)44 and 45
Answers
Answer:
Pt A: D. Pt B: D
Step-by-step explanation:
You can multiply 5x2 which easily equals 10. 6x6 equals 36 and you cannot multiply anything other than one and itself for 7, 13, 23, or 67. for part B, you can multiply 4x 11 to equal 44 and you can multiply 9x5 to equal 45 so it would be composite
44 and 45 are composite numbers.
What are prime and composite numbers?A prime number has only two factors, itself and one.
A composite number has at least three factors, and sometimes a lot more.
1. Prime:7, 13, 23, 67
Composite:10, 36, 55
As, 7, 13, 23 and 67 have only two factors : one and number itself
and 10, 36, 55 have more than 2 factors like 2.
2. 44 and 45 both have more than 2 factors.
Learn more about this concept here:
https://brainly.com/question/303182
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Due in a MINUTE!!! Need help!
Answers
Answer:
GH = 15
Step-by-step explanation:
In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. Therefore:
[tex]9x - 3 = \frac{1}{2} (19 + 5x + 1)[/tex]
[tex]18x - 6 = 5x + 20[/tex]
[tex]13x = 26[/tex]
[tex]x = 2[/tex]
[tex]9(2) - 3 = 18 - 3 = 15[/tex]
Convert the unit of length. Round the answer to one decimal place if necessary. 170 cm ≈ _____ ft ?
Answers
Answer:
5.56 ft
Step-by-step explanation:
30.48 cm per foot
170 cm ÷ 30.48 cm/ft = 5.56 ft
Hope this helps!
Raul is a saver. He sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible, so he puts his money in a savings account which earns 1.5% interest per year.
Answers
The total balance in Raul's account after 40 years when he retires is $65,714.90.
What is the total balance?The formula that can be used to determine the balance of the accout is: monthly amount saved x annuity factor.
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 1.5/12 n = number of periods = 12 x 40 = 480$100 x [(1.00125^480) - 1 ] / 0.00125 = $65,714.90
Here is the complete question:
Raul is a saver. He sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible, so he puts his money in a savings account which earns 1.5% interest per year. What is the balance in the account after 40 years?
To learn more about annuites, please check: https://brainly.com/question/24108530
If the labor force is 740 workers, but 27
are unemployed, what is the
unemployment percentage?
A. .36%
B. 3.6%
C. 36%
D. 360%
Answers
Answer:
3.6% or B quack quack quack quack
The unemployment percentage is 3.6 percent. Therefore, option B is the correct answer.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, the labor force is 740 workers, but 27 are unemployed.
Here, percentage = 27/740 ×100
= 2700/740
= 3.6%
Therefore, option B is the correct answer.
To learn more about the percentage visit:
brainly.com/question/24159063.
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use the equation f(x)=0.003x²-0.083x+2.514. Predict the value for x+20 years.
When x=20 years,f(x)=?
Answers
Answer:
2.054
Step-by-step explanation:
put the value of x in f(x)
Round your answer to the nearest hundredth.
Answers
Answer:
33.69°
Step-by-step explanation:
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
Answer:
33.69°
Step-by-step explanation:
Let's take ∡CBA as y
Tan y = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{6}{9}[/tex]
= 0.6666
y = 33.69°
PLEASE HELP ILL GIVE FIVE STARS AND GIVE BRAINLIEST AND GIVE THANKS PLEASE HELP
Ray is x years old. His brother Ron is y years older than Ray.
What will the difference of their ages be in 5 years?
Answers
ray is x years old
Ron is x+y years old
in 5 years ron will be 5 years older than now, so x+y+5 years old
orAnswer:
x - x + y + 5 - 5 = y or x + y - x = y
Step-by-step explanation:
The difference now,
x + y - x = y
The difference in 5 years,
(x + y + 5) - (x + 5) = x - x + y + 5 - 5
x - x + y + 5 - 5 = y
The difference in their ages never changes
How to solve problems in different ways and how to do them correct and fast so that way I kneo
Answers
Answer:
[tex]Hi!~I~am~beinggreat78~and~I~will~help~you.\\[/tex]
To solve problems, you first must find the source of the conflict, and attempt to let the situation play out, or use a strategy yourself. To solve math problems, go by PEMDAS.
Parentheses 1stExponents 2ndMultiply 3rdDivide 4thAdd 5thSubtract 6thWith this strategy, PEMDAS, you can solve math problems quickly, and like a pro!