Justin was asked to write six different equations based on the triangle below.
600
10
Four of the six equations that Justin wrote are correct. Select FOUR equations that are correct.
tan (60) = 73
tan ( 30 ) =
A
B.
c.
cos ( 30") =
D.
sin ( 60 ) = ?
E. F
cos (60) =
sin ( 30 ) = 3
Answers
Answer:
ADEF
Step-by-step explanation:
Four of the six equations that Justin wrote are correct which are Trigonometric functions as sin 60° =√3/2, cos 60° = 1/2, tan 60° = √3, and cot 60° = 1 /√3.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
Given that ΔABC
∠A = 60° and ∠B = 90° which is given in the figure
⇒ sin 60° = perpendiculer /hypotenuse
⇒ √3/2 = BC/10
⇒ BC = √3/2 × 10
⇒ BC = 5√3
⇒ tan 60° = perpendiculer /base
⇒ √3 = 5√3/AB
⇒ AB = 5√3/√3
⇒ AB = 5
⇒ sin 60° = 5√3/10 = √3/2
⇒ cos 60° = base / hypotenuse
⇒ cos 60° = 5/10 = 1/2
⇒ tan 60° = perpendiculer /base
⇒ tan 60° = 5√3/5 = √3
⇒ cot 60° = 1 /√3
Hence, four of the six equations that Justin wrote are correct which are Trigonometric functions as sin 60° =√3/2, cos 60° = 1/2, tan 60° = √3, and cot 60° = 1 /√3.
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Related Questions
Solve the following equation:
a/3.5 - 4.8 = 6.3
a= ______
Answers
Answer:
a= 38.85
Step-by-step explanation:
Answer:
[tex]\boxed {a = 38.85}[/tex]
Step-by-step explanation:
Solve for the value of [tex]a[/tex]:
[tex]\frac{a}{3.5} - 4.8 = 6.3[/tex]
-Add both sides by [tex]4.8[/tex]:
[tex]\frac{a}{3.5} - 4.8 + 4.8 = 6.3 + 4.8[/tex]
[tex]\frac{a}{3.5} = 11.1[/tex]
-Multiply both sides by [tex]3.5[/tex]:
[tex]a = 11.1 \times 3.5[/tex]
[tex]\boxed {a = 38.85}[/tex]
Therefore, the value of [tex]a[/tex] is [tex]38.85[/tex].
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene's car had 6.4 gallons in the 14-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost $3.90 per gallon. How much did Irene spend on gas?
Answers
Answer:
$24.96
Step-by-step explanation:
Total number of gallons irede had in his tank = 6.4gallons
Price per gallon is $3.90
To get the cost of 6.4gallons;
If 1 gallon = $3.90
6.4gallons = $x
Cross multiply
1 * x = 3.90 * 6.4
x = 24.96
Hence Irene spent $24.96 on gas
Felix can grow 6 plants with every seed packet. Write an equation that shows the relationship between the number of seed packets x and the total number of plants y. Write your answer as an equation with y first, followed by an equals sign.
Answers
Answer:
I believe it’s:
Y= 6x
Step-by-step explanation:
maria wanted to invest $10,000 at the bank. she invested part of her money in a cd account paying 2.1% simple interest and invest the rest of her money in a checking account paying 1.5% simple interest. After 1 year, her interest income was $195. How much did Maria invest in each account
Answers
Answer:I = ?, P = $500, r = 6%, t = 3 years
Step-by-step explanation:
Haley bought 1.6 pounds of almonds for $13.20. How much did she pay per pound for the almonds? Record your answer and fill in the bubbles on your answer document. Be sure to use correct place value. +/- .
Answers
Answer:
She paid $8,25 per pound
Step-by-step explanation:
Given
[tex]Weight = 1.6\ lb[/tex]
[tex]Total= \$13.20[/tex]
Required
Determine the amount paid per pound
To do this, we simply divide the amount by the weight of Almonds.
[tex]Amount = \frac{Total}{Weight}[/tex]
[tex]Amount = \frac{\$13.20}{1.6\ lb}[/tex]
[tex]Amount = {\$8.25/\ lb[/tex]
Hence, she paid $8,25 per pound
The ratio of blueberries to strawberries in a fruit salad is 4:3. If there are 45 strawberries in a salad, how many blueberries are there.. Blueberries 4 Strawberries 3
Answers
Answer:
60 blueberriesStep-by-step explanation:
Given the ratio of blueberries to strawberries in a fruit salad to be 4:3. The total ratio = 4+3 = 7
If there are 45 strawberries in the salad then we can first calculate the total mixture of both as shown;
amount of strawberries = 3/7 * x = 45
x is the total amount of mixture
from the expression;
3x/7 = 45
cross multiply
3x = 7*45
3x = 315
x = 315/3
x = 105
The amount of blueberries present = 105 - 45 = 60
Hence the amount of blueberries present is 60 blueberries
due soon will give brainalist no fake answers!!
Answers
Answer:
90gr strawberry jelly
6 sponge fingers
315ml custard
135gr tinned fruit
Step-by-step explanation:
120/4 = 30 * 3 = 90
8/4 = 2 * 3 = 6
420/4 = 105 * 3 = 315
180/4 = 45 * 3 = 135
which of the following is an arithmetic sequence with common difference 2
A. 1, -3, 5, -7, 9
B. 2, 4, 8, 16, 32
C. 10, 8, 6, 4, 2
D. 13, 15, 17, 19, 21
Answers
Answer:
C is the answer.
C has a common difference of "2"
Step-by-step explanation:
You could say that the word "difference" also means Subtraction, so in a simpler way of saying "The common difference of 2" you could say, "Which one of the following is subtracting by 2?"
PLEASE MARK BRAINLIEST
Simply.
[tex] \frac{ab - a}{a} = [/tex]
[tex] \frac{2x + y}{y} = [/tex]
I mainly forgot how to do it. Do I divide -ab to get it alone? How do I do it?
Answers
Answer:
Required Answer:-First go to first equation[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac{ab-a}{a}}[/tex]
Take common[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {{\bcancel {a }}(b-1)}{{\bcancel {a}}}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]{\underline{\boxed{\bf b-1)}}}[/tex]
A circular garden has a diameter of 8 feet, and a rectangular garden has side lengths of 5 feet by 9 feet.
find the difference in square feet between the two gardens
Answers
Answer:
rectangular
Step-by-step explanation:
Answer:
The square of a number decreased by 8 times the number equals 9. Determine the two possible values of the number. X2-8x=9. +1-9 ... 9. Basic Area of Rectangles. 16 The length of a rectangular room is 5 less than ... 17 The total area of Jon's backyard is 144 square feet. ... the length of a side of the original square garden.
Step-by-step explanation:
i hope this helps!
there are 1,920fence posts used in a 12-killometer strech fence how many fence posts are used in one kilometer
Answers
Answer:
160
Step-by-step explanation:
Just divide 1920 into 12
how do I do this?
I don't understand geometry and it's really confusing can one of you help me?
Answers
Answer:
lol im stuck too
Step-by-step explanation:
please someone help me please??!!!
Answers
Answer:
how should I know?
Step-by-step explanation:
Answer:
a.)
x= -2 , -1, 0, 1, 2, 3
y=8 , 7, 6, 5, 4, 3
and for b just plot the point and then connect them. im not sure how i can show you
Step-by-step explanation:
Please Hurry! Due by tonight!
Answers
Step-by-step explanation:
the y-intercept is 1 because it's on the y(axis). the line from 1 goes down 1 over three so the slope is 1/3.
your equation would be y=1/3x+1
The number of avocados ( a ) (a) a particular tree produces each year can be modeled by the function a ( y ) a(y). What does a ( 12 ) = 364 a(12)=364 mean?
Answers
Answer:
[tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.
Step-by-step explanation:
Let [tex]a[/tex] the number of avocados that a particular tree produces at a year. [tex]a(y)[/tex] is the number of avocados that a particular tree produces at y-th year. Hence, [tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.
in the equation (m^5/6) (m^1/6)^7 = m^x , what is the value of x that makes the equation true?
Answers
The value of x in the equation (m^5/6) (m^1/6)^7 = m^x is 2
What is the law of exponent?The exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent: a^m×a^n = a^(m+n); a^m÷a^n = a^(m−n);
(am)ⁿ = a^mn.
Given an equation, (m^5/6) (m^1/6)^7 = m^x
Using the law of exponent, we get,
(m^5/6) (m^1/6)^7 = m^5/6*m^7/6
= m^(5/6+7/6)
= m^12/6
= m^2
Hence, the value of x in the equation (m^5/6) (m^1/6)^7 = m^x is 2
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Peter is painting his bedroom. His bedroom has four walls. Yesterday, he painted 1 2/5 walls. What fraction of the walls is left to paint?
Answers
Answer: 2 3/5ths are left or 13/5
Step-by-step explanation: 1 2/5 + 2 3/5 = 4 total walls
if if x equals 3 and Y equals negative 2 - x 3 - Y2
Answers
Answer:
13
Step-by-step explanation:
x=3, y=-2 so 3(3)-(2)2=13
okay so i got (1,1) but it's not on here ;-;
Answers
You can use 0 to substitute for x. That makes (0,4.5) a possible ordered pair. Another possible answer is using 1 or 2, but that is not one of the answers provided. Hope this helped!
Solve each equation. For each step. Identify the property used.
14 + 3n = 8n - 3(n-3)
22x + 11 = 4x - 7
(P.S. The properties that the problem is asking for are the properties of equality. Division property of equality, etc, etc.)
Answers
Answer:
Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2
Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1
Step-by-step explanation:
We will solve the equations one by one
So,
[tex]14 + 3n = 8n - 3(n-3)[/tex]
Applying Distributive property
[tex]14 + 3n = 8n - 3n+9\\14+3n = 5n+9[/tex]
Subtraction property of equality (Subtracting 14 from both sides)
[tex]14+3n-14 = 5n+9-14\\3n = 5n-5[/tex]
Subtraction property of equality (Subtracting 5n from both sides)
[tex]3n-5n = 5n-5-5n\\-2n = -5[/tex]
Division property of equality (Dividing both sides by -2)
[tex]\frac{-2n}{-2} = \frac{-5}{-2}\\n = \frac{5}{2}[/tex]
Second Equation:
[tex]22x + 11 = 4x - 7[/tex]
Subtraction property of equality (Subtracting 11 from both sides)
[tex]22x + 11-11 = 4x - 7-11\\22x = 4x-18[/tex]
Subtraction property of equality (Subtracting 4x from both sides)
[tex]22x-4x = 4x-18-4x\\18x = -18[/tex]
Division property of equality (Dividing both sides by 18)
[tex]\frac{18x}{18} = \frac{-18}{18}\\x = -1[/tex]
Hence
Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2
Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1
For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy???
Answers
Answer: 4 and a half
Step-by-step explanation:
What is the total number of servings the modified recipe will make?
Answers
9514 1404 393
Answer:
B. 4
Step-by-step explanation:
Equating exponents, we have ...
2x +7 = 15
2x = 8 . . . . . subtract 7
x = 4 . . . . . . divide by 2
The equation is true when the value of x is 4.
hope this helps enjoy.
Please quickly! Out of 5,500 people who attended the football game, fifty-six percent were rooting for the home team. How many people rooted for the home team?
Answers
Jamie tossed a coin 50 times. The coin landed on heads 27 times and landed on tails
23 times. What is the relative frequency of landing on heads?
Answers
Answer: 54%
Step-by-step explanation:
The relative frequency of landing on heads is 0.54 or 54%.
Given that Jamie tossed a coin 50 times.
Head showed for 27 times.
Tails showed for 23 times.
We need to find the relative frequency of landing on heads,
The relative frequency of an event is calculated by dividing the number of times the event occurred by the total number of trials or occurrences.
In this case, Jamie tossed a coin 50 times, and it landed on heads 27 times.
To find the relative frequency of landing on heads, we divide the number of times the coin landed on heads (27) by the total number of tosses (50):
Relative Frequency of landing on heads = Number of heads / Total number of tosses
Relative Frequency of landing on heads = 27 / 50
Simplifying this fraction, we get:
Relative Frequency of landing on heads = 0.54
This means that, based on the given data, the coin landed on heads approximately 54% of the time in the 50 tosses performed by Jamie.
Therefore, the relative frequency of landing on heads is 0.54 or 54%.
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A 14 foot long ramp is being built to access a front door in a house. The door is 5 feet above the ground. How far away from the base of the house must the ramp be placed? What angle will the ramp make with the ground?
Answers
Answer:
The ramp must be placed 13.08 feet from the base of the house.
The angle the ramp will make with the ground is 20.92°.
Step-by-step explanation:
An illustrative diagram for the scenario is shown below.
In the diagram, d represents the distance of the door from the ground, r represents the length of the ramp and x represent the distance of the ramp from the base of the house.
To determine how far away from the base of the house the ramp must be placed, that is to determine x in the diagram.
The diagram is a right angle triangle and x can be determine using the Pythagorean theorem which states " the square of the hypotenuse equals sum of the squares of the other two sides"
In the diagram, the hypotenuse is r
∴ r² = d² + x²
r = 14 ft
d = 5 ft
∴ 14² = 5² + x²
196 = 25 + x²
Then, x² = 196 - 25
x² = 171
x = √171
x = 13.08
Hence, the ramp must be placed 13.08 feet from the base of the house.
Now, to determine what angle the ramp will make with the ground, that is θ in the diagram.
From the formula
Sinθ = Opposite / Hypotenuse
In the diagram, opposite = d = 5ft
and Hypotenuse = r = 14ft
∴ Sinθ = 5ft / 14ft
Sinθ = 0.3571
∴ θ = Sin⁻¹(0.3571)
θ = 20.92°
Hence, the angle the ramp will make with the ground is 20.92°.
The matrices show the number of indoor and outdoor volunteers in different age groups
create a matrix that shows the total number of indoor and outdoor volunteers in different age groups. name the matrix T.
what is the value of the element t11 and what does the value indicate?
create a matrix by subtracting the women's matrix from the mens matrix. name the matrix D.
what is the value of the element at d12 and what does that value indicate?
Answers
Answer:
(a) M + W = Indoor= [26 55] Outdoor = [32 49]
(b) The value indicates the sum of the indoor volunteers ages 18-39 so the Value would be, 34.
(c) M – W = Indoor = [8 15] Outdoor = [-16 3]
(d) This value indicates the difference of the volunteers indoors 40. So the value would be 15.
Step-by-step explanation:
If this is wrong my apologies i tried LOL
but i will let you know when i get the results back asap!
The value of the element t11 is 34 and the value of the element at d12 is 15.
When are two matrices called being equal?Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.
M + W = Indoor= [26 55] Outdoor = [32 49]
The value indicates the sum of the indoor volunteers ages 18-39,
Therefore, the Value would be, 34.
To create a matrix by subtracting the women's matrix from the mens matrix.
Now the difference;
M – W = Indoor = [8 15] Outdoor = [-16 3]
This value indicates the difference of the volunteers indoors 40 so
Therefore the value would be 15.
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Need help in math ASAP
Answers
Answer:
B
Supplementary means they add to make 180 deg, so solve (4x-8)+(2x+2)=180
Answer:
angle a + angle b=180
4x-8+(2x+2)=180
6x-6=180
6x=180+6
x=186/6
{x=31°}
Given: m || n and p is a traversal.
Prove: m<2=m<7
What is the missing reason in the proof?
Answers
Answer:
Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are congruent.
Use the quadratic formula to solve the equation.
5x2-3x + 1 = 0
X=
Answers
Answer:
x= 11/3
Step-by-step explanation:
Name a ray with an endpoint of A.