Answer:
[tex]x = 18[/tex]
[tex]y = 6\sqrt{3}[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides as follows:
Cosine Ratio
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Sine Ratio
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
Consider the angle of θ=30°, then we can write:
[tex]\displaystyle \cos 30^\circ=\frac{x}{12\sqrt{3}}[/tex]
Solving for x:
[tex]x=12\sqrt{3}\cos 30^\circ[/tex]
Since:
[tex]\cos 30^\circ=\frac{\sqrt{3}}{2}[/tex]
Then:
[tex]x=12\sqrt{3}\cdot \frac{\sqrt{3}}{2}[/tex]
[tex]x = 18[/tex]
Now apply the sine:
[tex]\displaystyle \sin 30^\circ=\frac{y}{12\sqrt{3}}[/tex]
Solving for y:
[tex]y=12\sqrt{3}\sin 30^\circ[/tex]
Since:
[tex]\sin 30^\circ=\frac{1}{2}[/tex]
Then:
[tex]y=12\sqrt{3}\cdot \frac{1}{2}[/tex]
[tex]y = 6\sqrt{3}[/tex]
Answer:
[tex]x = 18[/tex]
[tex]y = 6\sqrt{3}[/tex]
Since people are sad they missed my 50 points, here is 100 points for the first 2 to answer. First one gets branliest aswell.
Which two numbers have a mean of 10 and a range of 4?
NEED THIS ASAP PLEASE I WILL LEAVE A GOOD RATING
the answer would be 12 and 8
X – y=11
3x + 10y= -6
Answer:
(8, - 3 )
Step-by-step explanation:
Given the 2 equations
x - y = 11 → (1)
3x + 10y = - 6 → (2)
Multiplying (1) by 10 and adding to (2) will eliminate the y- term
10x - 10y = 110 → (3)
Add (2) and (3) term by term to eliminate y
13x + 0 = 104
13x = 104 ( divide both sides by 13 )
x = 8
Substitute x = 8 into either of the 2 equations and solve for y
Substituting into (2)
3(8) + 10y = - 6
24 + 10y = - 6 ( subtract 24 from both sides )
10y = - 30 ( divide both sides by 10 )
y = - 3
solution is (8, - 3 )
Which rational function has vertical asymptotes at x=-3 and 9,a horizontal asymptote at y=1, and an x-intercept of 0?
•h(x)=x^2/x^2-6x-27
Answer:
Yes that function does •h(x)=x^2/x^2-6x-27
Step-by-step explanation:
Yes that function does •h(x)=x^2/x^2-6x-27
what is the rate and unit rate for 115 miles on 9 gallons of gas
Answer:
the actual answer is 12.7777777778 but you can break it down to about 12.8
Step-by-step explanation:
Hope this helps :)
The length of a ship is 247 metres, correct to the nearest metre.
Write down the minimum length of the ship.
Answer:
246.50
Step-by-step explanation:
A car travels 72 miles on 6 gallons of gas. At that rate, how much gas will it need to travel 204 miles?
Answer:
17 gallons
Step-by-step explanation:
First find how many miles it can travel with 1 gallon which would be 72÷6 = 12 So 1 gallon can takes it to 12 miles
Do 204÷ 12 = 17
Answer:
17 galloons
Step-by-step explanation:
72 Miles= 6 galloons
144 miles = 12 galloons
204 miles = 17 galloons
in every 12 miles is equivalent to 1 galloon of gas so basically when you divide 204 into 12 you will get 17. you need 17 galloons of gas
Please please help please please ASAP please
Answer:
14.52
Step-by-step explanation:
With reference angle 32°
perpendicular (p) = 9
base (b) = x
Now
Tan 32° = p / b
0.62 = 9 / x
x = 9 / 0.62
x = 14.52
PLEASE HELP ASAP!! LUL
Answer:
Step-by-step explanation:
it should add up to 360°
360=135 + 120 + 7x-64+5x-4+3x+31+4x+15+6x-8 (seems like too much huh)
360=225+25x ( much better just add the x terms and the constants together)
135 = 25x ( just subtract 225 from each side of the equation)
5.4 = x ( divide 135 by 25 )
Pls helppp and thank you
Answer:
∠ 2 = 60°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles fro 180° for ∠ 2, that is
∠ 2 = 180° - (57 + 63)° = 180° - 120° = 60°
HELP ME PLEASE
Use the table to answer the question.
Avocados Price
$1.15
$2.30
$5.75
$11.50
1
2
5
10
How much will 3 avocados cost?
O $1.15
O $3.45
O $4.45
O $4.60
one Avocado costs 1.15 you need 3
1.15×3=3.45
combine these like terms 4 girls + 2 girls - 3 boys
Answer:
6 girls - 3 boys
Step-by-step explanation:
Answer:
6girls - 3 boys
Step-by-step explanation:
4 girls + 2 girls =6 girls
you cant mix girls and boys so you still have 3 boys
A marketing company is hiring two college students to hand out brochures near an event. Marshall hands out 300
brochures in 2 hours. Silas hands out 240 brochures in 90 minutes. Who handed out more brochures per minute?
Neither. They handed out brochures at the same rate.
Marshall
Silas
Answer:
silas
Step-by-step explanation:
Simplify so it's in slope-intercept form (y=mx+b)
y - 125 = 55(x - 2)
Answer:
y = 55x + 15
Step-by-step explanation:
i think this is it, but it might not be right
Jackson biked k kilometers. Maria biked 8 more kilometers than Jackson. Peter biked 2 fewer kilometers than Jackson.
Drag and drop the expressions into the boxes to write an expression that represents the total number of kilometers Jackson, Maria, and Peter biked in all.
k
8
12
k+2
k+8
k+10
k-2
k-8
Answer:
Step-by-step explanation:
The expression for the total distance covered.
k + (k + 8) + (k - 2)
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Distance biked:
Jackson = k
Maria = k + 8
Peter = k - 2
Now,
The total distance biked.
= k + k + 8 + k - 2
= 3k + 6
= 3 (k + 2)
Thus,
The total distance covered is 3 (k + 2).
Learn more about expressions here:
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Anthony scored 28 points in a recent basketball game. He made a total of 12 baskets. How many 2 and 3 point shots did he make? (Consider only the 2 and 3 point shots: no free throws)
Answer:
8 2-point shots and 4 3-point shots
Step-by-step explanation:
Anthony scored 28 points with 12 baskets. Saying that, (with x-y representing 2 point shots-3 point shots) any combination with a supermajority (at least 75% of) of either shot is out. This leaves just 5 possible combinations. 8-4, 7-5, 6-6, 5-7, and 4-8. Multiply the first number by 2 and the second by 3.
(4 * 2) + (8 * 3) = 8 + 24 = 32 points, so no.
(5 * 2) + (7 * 3) = 10 + 21 = 31 points, so no.
(6 * 2) + (6 * 3) = 12 + 18 = 30 points, so no.
(7 * 2) + (5 * 3) = 14 + 15 = 29 points, so no as well.
(8 * 2) + (4 * 3) = 16 + 12 = 28 points, so this is the combination we're looking for.
Someone please answer this for me ASAP
Please please help! Will mark brainliest!
Answer:
-
Step-by-step explanation:
maya joins two peices of wood together one peice is 36 inches long the total lenght of both peices is 62 how long is the other peice of wood
help ;-;...
Answer: 26
Step-by-step explanation:
62-36=26
Answer: 26
You simply have to subtract 36 from 62
How long it takes for something to travel a certain distance is the definition of:
Answer: boat
Step-by-step explanation: the farthest it can go is weeks
can i have some help please( BRAINLLEST)
Answer:
2
-3
same thing
Step-by-step explanation:
Manny wants to find ways to reduce his current debt. The table below shows Manny’s monthly income, expenses and net income.
Monthly Budget
Amount
Income
Wages
$3,000.00
Expenses
Rent
$1,200.00
Utilities
$269.34
Entertainment
$220.00
Food/Clothes
$368.00
Cell Phone
$89.42
Credit Card #1
$94.62
Credit Card #2
$36.18
Car Insurance
$80.00
Car Payment
$300.00
Gym Membership
$25.00
Net Income
$317.44
After evaluating Manny’s monthly budget, which of the following would be the best option to reduce his debt?
a.
Manny could spend less on entertainment each month and put the money towards a new cell phone.
b.
Manny could pay the minimum monthly payments on his credit cards and put the money towards his car payment.
c.
Manny could spend less on food and clothes and put the money towards his credit card payment.
d.
Manny could cut his utlility costs and put the money towards buying a new house.
Answer:
c. Manny could spend less on food and clothes and put the money towards his credit card payment.
Step-by-step explanation:
Edge 2021
Based on the information given, Manny can reduce his current debt by: C. Manny could spend less on food and clothes and put the money towards his credit card payment.
What is a credit card?A credit card refers to a small rectangular-shaped plastic card that is issued by a financial institution (banks) to its customers, which allows them to purchase goods and services on credit, especially based on the agreement that the amount of money taken would be paid later with an agreed upon interest rate.
How to calculate monthly payment.Mathematically, the monthly payment for a credit card is given by this formula:
[tex]M=P(\frac{r}{1-(1+r)^{-nt}} )[/tex]
Where:
P is the principal.r is the interest rate.M is the monthly payment.t is the time.n is the number of times it's compounded.In this scenario, Manny can reduce his current debt by spending less amount of money on both food and clothes while putting the money towards his credit card payment.
Read more on monthly payment here: https://brainly.com/question/2151013
Solve the fraction problem and reduce the answer to simplest form:
1/5 + 3/4 = ??
7/9 - 3/5= ??
6/8 - 2/7 = ??
5/6 + 5/10 = ??
7/8 - 2/3 = ??
8/10 + 5/6 = ??
9/11 - 2/3 = ??
Answer:
1. 19/20
2. 8/45
3. 13/28
4. 4/3
5. 5/24
6. 49/30
7. 5/33
Fractions are integers that have both a numerator and a denominator. Fraction comes in the form: [tex]\frac{x}{y}[/tex]
where x = numerator and y = denominator.
a) 1/5 + 3/4
We find the Lowest common denominator (5, 4) = 20
Hence: 4 + (5 x 3) / 20
= 4 + 15 / 20
= 19/20
b) 7/9 - 3/5
We find the Lowest common denominator (5, 9) = 45
Hence: (7 x 5) + (9 x 3) / 45
= 35 - 27 / 45
= 8/45
c) 6/8 - 2/7
We find the Lowest common denominator (7, 8) = 56
Hence: (6 x 7) - (2 x 8) / 56
= 42 - 16 /56
= 26/56
= 13/28
d) 5/6 + 5/10
We find the Lowest common denominator (6, 10) = 30
Hence: (5 x 5) + (5 x 3) / 30
= 25 + 15 / 30
= 40/30
= 4/3
= 1 1/3
e) 7/8 - 2/3
We find the Lowest common denominator (3, 8) = 24
Hence: (7 x 3) - (2 x 8) / 24
= 21 - 16 / 24
= 5/24
f) 8/10 + 5/6
We find the Lowest common denominator (6, 10) = 30
Hence: (8 x 3) + (5 x 5)
= 24 + 25 / 30
= 49/30
= 1 19/30
g) 9/11 - 2/3
We find the Lowest common denominator (3, 11) = 33
Hence: (9 x 3) - (11 x 2) / 33
= 27 - 22 / 33
= 5/33
To learn more, visit the link below:
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A cook uses 4 ounces of flour to make
12 cup cakes. How much flour would
he use to make 36 cup cakes?
Answer:
12 ounces flour
Step-by-step explanation:
4 ounces 12 cup cakes
8 ounces 24 cup cakes
12 ounces 36 cup cakes
The cost of a mobile phone processor is directly proportional to its speed.
A 2GHz mobile costs £500.
Let x be the speed of a processor in GHz
Let y be the cost in pounds.
Find a formula linking the variables.
Answer: See explanation
Step-by-step explanation:
We are going to use the formula used in calculating direct proportion which is equal to:
y = kx
where,
x = speed of a processor in GHz
y = the cost in pounds
Therefore, y = kx
500 = 2k
Therefore, y = 2k
hey, can somebody help me please and thank you. :)
Please help I’ll mark you as branlst
Answer:
6
Step-by-step explanation:
Since the degree of the angle is 45, we know that the triangle is isosceles. That means that the sides of the triangle, not including the hypotenuse, has a length of 3√2.
Using the Pythagorean theorem, which is a^2 + b^2 = c^2, we have (3√2)^2 + (3√2)^2 = c^2.
Note: c is the hypotenuse of the triangle.
18 + 18 = c^2
= 36 = c^2
Therefore, c = 6.
If the point (4,-2) Is Included in dun
OA. (4,2)
OB. (-4,-2)
OC. 12,-4)
OD. (-2,4)
On Saturday, Jay went on a trail run. The posted mileage for the trail was 3.8 miles. On Sunday, he ran his usual route
of 4 3/4 miles. How many total miles did Jay run over the weekend?
A 7.5 miles
B 7 3/4 miles
C 8.3 miles
D 8 11/20 miles
A copy machine makes 36 copies per minute. How long does it take to make 126 copies?
Answer:
It will take 3.5 minutes to make 126 copies
Step-by-step explanation:
Answer:
Step-by-step explanation:
We can do 126/36 to get our answer since 126 is the total copies and 36 is the copies we can do in a minute. 126/36 = 3.5 so it will take 3.5 minutes.