Consider the 30°-60° right triangle shown whose hypotenuse is equal to one. Clearly this triangle is half of an equilateral triangle. Please help me. Thank you! （╹◡╹）
Answers
Answer:
Step-by-step explanation:
Given triangle ABC is a right triangle.
m∠ACB = 60°
m∠CAB = 30°
m(AC) = 1 unit
A). Shorter side of the given triangle = Side BC
By applying cosine rule,
cos(∠C) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(60°) = [tex]\frac{BC}{AC}[/tex]
BC = [tex]\frac{1}{2}(AC)[/tex]
BC = [tex]\frac{1}{2}[/tex]
Length of the shorter side = 0.5 units
B). Longer side of the given triangle = side AB
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
1² = AB² + [tex](\frac{1}{2})^2[/tex]
1 = AB² + [tex]\frac{1}{4}[/tex]
AB = [tex]\sqrt{1-\frac{1}{4}}[/tex]
AB = [tex]\sqrt{\frac{3}{4}}[/tex]
AB = [tex]\frac{\sqrt{3} }{2}[/tex]
Length of the longer side = [tex]\frac{\sqrt{3}}{2}[/tex]
Related Questions
A cylinder has a volume of 659.4 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder?
(Assume = 3.14)
A.
42 cm
B.
2.1 cm
C.
8.4 cm
D.
21 cm
Answers
The height is 8.4.
Calculated with H = V / πr^2, with H for height, V for volume, and r for radius (the diameter divided by 2).
□×19=(16×10)+(16×□)
answer?
Answers
Answer:
16 and 9
Step-by-step explanation:
16 × 19 using the distributive property
16 × 10 + 16 × 9
You leave the Calmecac at 7 (-4,-5) and head toward the Eagle Gate at (0, -8). How many units did you travel?
Answers
Answer:
Solution given:
(x1,y1)=(-4,-5)
(x2,y2)=(0,-8)
distance=?
we have
distance=[tex] \sqrt{(x2-x1) ²+(y2-y1) ²}[/tex]
d=[tex] \sqrt{(0+4)²+(-8+5) ²}[/tex]
d=[tex] \sqrt{25}[/tex]
d=[tex] 5[/tex]units
[tex] 5[/tex]units I travelled.
find the area of the shape shown below units 2
Answers
Answer:
81
Step-by-step explanation:
go hgv thx bgg TV vvt g h.c g ccx d
100 points. You earned $1600 in interest in your savings account over 10 years at a rate of 8%. How much money did you originally deposit into your savings account?
Answers
A = p(1+r)^t
1600 = p(1+0.08)¹⁰
P = 1600/2.1589
P= 741.12
741.12 dollar money did you originally deposit into your savings account!
Answer:
Simple interest: Principal = $2000
Annual compound interest: Principal = $1380.59
Step-by-step explanation:
As the question does not stipulate which type of interest was applied, please find below calculations for both simple interest and annual compound interest.
Simple Interest Formula
I = Prt
where:
I = interest accruedP = principalr = interest rate (in decimal form)t = time (in years)Given:
I = $1600r = 8% = 0.08t = 10 yearsSubstitute the given values into the formula and solve for P:
[tex]\implies \sf 1600=P(0.08)(10)[/tex]
[tex]\implies \sf 1600=0.8P[/tex]
[tex]\implies \sf P=\dfrac{1600}{0.8}[/tex]
[tex]\implies \sf P=2000[/tex]
Therefore, the initial deposit (principal) was $2000.
.....................................................................................................
Annual Compound Interest Formula
[tex]\large \text{$ \sf I=P\left[\left(1+r\right)^{t} -1\right]$}[/tex]
where:
I = interest accruedP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
I = $1600r = 8% = 0.08t = 10 yearsSubstitute the given values into the formula and solve for P:
[tex]\implies \sf 1600=P\left[\left(1+0.08)^{10}-1\right][/tex]
[tex]\implies \sf 1600=P\left[\left(1.08)^{10}-1\right][/tex]
[tex]\implies \sf 1600=P\left[2.15892...-1\right][/tex]
[tex]\implies \sf 1600=P\left[1.15892...\right][/tex]
[tex]\implies \sf P=\dfrac{1600}{1.15892...}[/tex]
[tex]\implies \sf P=1380.5897...[/tex]
Therefore, the initial deposit (principal) was $1380.59 (nearest cent).
Learn more about simple interest here:
https://brainly.com/question/27743947
Learn more about compound interest here:
https://brainly.com/question/27747709
Find the values of x, y, and z
Answers
5
Select the correct answer.
A circle has a radius of 6 inches and a central angle of 60°. What is the measure of the arc length associated with this angle?
ОА.
67 inches
B. 7 inches
OC, 24 inches
D.
37 inches
Reset
Next
Answers
Answer:
The length of the arc is 6.28 inches
Step-by-step explanation:
Given
[tex]\theta = 60[/tex]
Required
Length of the arc
This is calculated as:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{60}{360} * 2 * \frac{22}{7} * 6[/tex]
[tex]L = \frac{15840}{2520}[/tex]
[tex]L = 6.28in[/tex]
pls help this stuff is so hard to understand
Answers
Answer:
y = 0.5 (2)^x
Step-by-step explanation:
3rd option
you can plug in a coordinate point like (2, 2) to check this.
Solve for x, rounding to the nearest hundredth.
6 - 10x= 1
Answers
peeeeeeeeeeeeeeeeeeeeeeeeeenas
PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!!
The legs of a right triangle are
___ longer than the hypotenuse.
a.) sometimes
b.) always
c.) never
Answers
Answer:
C. Never
Step-by-step explanation:
The legs of a right triangle are never longer than the hypotenuse. Otherwise, the legs would never connect to the hypotenuse.
3
Select the correct answer from the drop-down menu.
Find the missing term.
) + (7 - 31) + (5 +91) + 131 = 10 - 51.
Reset
Next
Answers
Random text Random text
Please answer this question I have 5 more minutes to complete it THIS IS TIMED
Answers
Answer:
648 sq meters is correct.
Step-by-step explanation:
Multiply the two diagonals (18 + 18 = 36)(15 +21 = 36), then divide by 2
(36)(36)/2 = 1296/2 = 648
What is the solution to this equation?
8(25 +1 = 4
СА.
In(0.5)
T =
- 1
OB.
Ос.
In(0.5) + 1
2
In(0.5)
+1
2
In(0.5) - 1
OD
Answers
Answer:
Option (D)
Step-by-step explanation:
Given equation is,
[tex]8e^{2x+1}=4[/tex]
Taking natural log on both the sides of the equation,
[tex]\text{ln}(8e^{2x+1})=\text{ln}(4)[/tex]
[tex]\text{ln}(2^3)+\text{ln}(e^{2x+1})=\text{ln}(2^2)[/tex]
3ln(2) + (2x + 1)[ln(e)] = 2ln(2)
2n(2) - 3ln(2) = (2x + 1)
2x = -ln(2) - 1
[tex]2x=\text{ln}(\frac{1}{2})-1[/tex] [Since, -ln(2) = ln(1) - ln(2) = [tex]\text{ln}(\frac{1}{2})[/tex]]
[tex]2x=\text{ln(0.5)}-1[/tex]
[tex]x=\frac{\text{ln(0.5)-1}}{2}[/tex]
Therefore, Option (D) will be the correct option.
the variables height and weight could reasonably be expected to have a positive linear correlation coefficient, since taller people tend to be heavier, on average than shorter people. Give an example of a pair of variables which you would consider to have a negative linear correlation and explain why. Then give an example of a pair of variables whose linear correlation coefficient is likely to be close to zero
Answers
Answer:
i) Speed and travel time
ii) Coffee and car
Step-by-step explanation:
i) Example of a pair of variable that have a negative Linear correlation
A negative correlated pair of variables simply means that the variables are inversely proportional to each other .and an example of such pair of variables is
Speed and Travel Time
Increase in speed causes a decrease in travel time. ( because the faster a car travels the shorter the travel time spent by the car while the slower a car travels the longer the travel time spent by the car )
ii) Example of a pair of variable with no linear correlation ( almost zero )
A close to zero linear correlation shows that there i no actual relationship between the variables.
Coffee and car
Increase or decrease in the cost of coffee will have no significant effect ( either negative or positive ) on the price of cars in the open market.
Find m RS
Please please this is on my final !
Answers
Answer:
[tex] \large{ \tt{☄ \: STEP- BY - STEP \: EXPLANATION}} : [/tex]
Observing the figure , We can see chord RS & TU equal. We're provided the value of RS i.e ( 6x - 28 ) ° & TU i.e ( 4x + 20 )°. Now , Just set up an equation & solve for x ![tex] \large{ \bf{❃ \: (6x - 28) \degree = (4x + 20) \degree}}[/tex]
[tex] \large{ \bf{↬6x - 28 \degree = 4x + 20 \degree}}[/tex]
[tex] \large{ \bf{↬ \: 6x - 4x = 20 \degree + 28 \degree}}[/tex]
[tex] \large{ \bf{↬2x = 48 \degree}}[/tex]
[tex] \large{ \bf{↬x = \frac{48 \degree}{2}}} [/tex]
[tex] \large{ \bf{↬ \boxed{ \bf{x = 24 \degree}}}}[/tex]
Now , Replacing the value of x :[tex] \large{ \bf{⇢m \: RS = (6x - 28) \degree = (6 \times 24 - 28) \degree = \boxed{ \bf{116 \degree}}}}[/tex]
[tex] \large{\boxed{ \boxed{ \tt{⟿ \: OUR \: FINAL \: ANSWER : \boxed{ \underline{ \bf{116 \degree}}}}}}}[/tex]
[tex] \large{ \tt{✺ \: STUDY \: TIP}} : [/tex]
Work consistently. Do your homework , read over your notes and revise for each test / quiz - no matter how insignificant !ツ Hope I helped! ۵
☼ Have a wonderful day / evening ! ☃
# StayInAndExplore ! ☂
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How do you find X and Y?
4y + 5z = 60
5x + 3y = 60
4x + 3z = 60
Answers
Answer:
1. y=5 x=8
2. x=9 y=5
3. x=12 z=4
Step-by-step explanation:
1. 4(5)+5(8)=60
2. 5(9)+3(5)=60
3. 4(12)+3(4)=60
Please guys help please
Answers
GUYS HELP ME There are 6 classes on a field trip . Each class has 28 students and 7 adults going on the field trip they are all traveling by van. Each van holds 9 passengers. What is the fewest number of vans they will need ?
Answers
Answer:
24
Step-by-step explanation:
Total number of students and adult per class = 28 + 7 = 35
Van capacity = 9
Number of classes = 6
Total number of students including adults = (35 * 6) = 210
Number of vans needed = total / van capacity
= 210 / 9
= 23.333
Atleast 24 vans
How do we solve for x
Answers
Answer:
Use Cross product Or Multiply both sides by 6 to get x alone
x/6 = 4/5
Multiplying 6 on both sides
we have
x=4/5 x 6
x=24/5 = 4.8
Tell whether the two figures are similar. Explain your reasoning.
Answers
Answer:
i think its A
Step-by-step explanation:
if its not I'm sorry- um i think this cuz in the first figure where it says 8 its the same height side to side same thing with the 12. the second shape is also doing the same thing. really only thing that differes is the size. the second image is like a smaller version of the first one.
A cone has a slant height of 6 inches and a lateral surface area of
47.1 square inches. What is the base radius of the cone?
Answers
Answer:
Radius, r = 2.50 inches
Step-by-step explanation:
Given the following data;
Slant height of cone = 6 inches
Lateral surface area (LSA) of cone = 47.1 sq inches
To find the radius of the cone;
Mathematically, the lateral surface area of a cone is given by the formula;
LSA = πrl
47.1 = 3.142 * r * 6
47.1 = 18.852r
Radius, r = 47.1/18.852
Radius, r = 2.50 inches
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round your answer to four decimal places. Enter your answers as a comma-separated list.) (See attachment)
c = ?
Answers
Answer:
Step-by-step explanation:
f'(x)=-sin x
[tex]f'(x)=\frac{cos \frac{\pi }{3} -cos (\frac{-\pi }{3}) }{\frac{\pi }{3} -(\frac{-\pi }{3}) } \\-sin x=\frac{\frac{1}{2} -\frac{1}{2} }{\frac{\pi }{3} +\frac{\pi }{3} } \\sin x=0\\at x=c ,sin c=0,c=0[/tex]
c=0∈(-π/3,π/3)
Jonathan's preschool class has 9 girls and 6 boys. Which proportion can be used to determine the percent, P, of boys in class?
A) 6/15 = P/9
B) P/6 = 100/15
C) P/100 = 6/9
D) P/100 = 9/15
Answers
Answer:
B
Step-by-step explanation:
you are comparing percent to percent and total boys to total class.
Answer:
P/100=6/9
Step-by-step explanation:
P represent percentage and percentage is 100. so
CRISSY IS BUILDING A RECTANGULAR PRISM WITH
A VOLUME OF 360 CUBIC UNITS. THE HEIGHT OF
THE PRISM IS IO UNITS. CHRISSY CLAIMS THAT THE
BASE OF THE PRISM MUST BE A SQUARE. WHAT
ARE THE DIMENSIONS FOR A RECTANGULAR PRISM
THAT SHOWS CRISSY IS NOT CORRECT?
Answers
Answer: Crissy is correct
Step-by-step explanation:
Given
The volume of the rectangular prism is [tex]360\ units^3[/tex]
The height of the prism is [tex]h=10\ units[/tex]
Suppose A is the area of the base
So, the volume is given by
[tex]\Rightarrow V=A\times h[/tex]
Insert the values
[tex]\Rightarrow 360=A\times 10\\\Rightarrow A=36\ \text{or}\ 6\times 6\ units^2[/tex]
As 36 is the perfect square of 6, therefore, the base is a square with the dimension of [tex]6\times 6\ units^2[/tex]
Crissy's claim is correct.
Hanna's favorite character is sold wearing one of many outfits
Answers
(Help please !)
Of the total babies born in America, 51.2% are boys. If 3000 babies are born in a certain hospital this year, what is the expected number of boys?
Answers
Answer:
1536 boys.
Step-by-step explanation:
Quite simple! 51.2% is 0.512, which we can use to calculate the number.
[tex]3000 * 0.512 = 1536[/tex] boys.
Alternative notation: 3000 * 51.2% = 1536
The ratio of the length to the width of a table is . How many times the width of the table is the length of the table? Mark all that apply.
Answers
Answer: need the answer
Step-by-step explanation: to answer
Someone plz help meeeee!!!!
Answers
AND
The median age is 11
Please please Pleas answer this question please please
Answers
Answer:
3 can
Step-by-step explanation:
there
only real answers very serious