Answers
Answer:
[tex]x = \frac{16\sqrt{3}}{3}[/tex]
[tex]y = \frac{32\sqrt 3}{3}[/tex]
Step-by-step explanation:
Calculating (x):
Here, we make use of the tan formula
[tex]tan\theta = \frac{Opp}{Adj}[/tex]
Where
[tex]\theta = 60[/tex]
[tex]Opp = 16[/tex]
[tex]Adj = x[/tex]
This gives:
[tex]tan\ 60= \frac{16}{x}[/tex]
Make x the subject
[tex]x = \frac{16}{tan\ 60}[/tex]
tan(60) in surd form is [tex]\sqrt{3}[/tex]
So:
[tex]x = \frac{16}{\sqrt{3}}[/tex]
Rationalize
[tex]x = \frac{16}{\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]x = \frac{16\sqrt{3}}{3}[/tex]
Calculating (y):
Here, we make use of the tan formula
[tex]sin\theta = \frac{Opp}{Hyp}[/tex]
Where
[tex]\theta = 60[/tex]
[tex]Opp = 16[/tex]
[tex]Hyp= y[/tex]
This gives:
[tex]sin\ 60= \frac{16}{y}[/tex]
Make y the subject
[tex]y= \frac{16}{sin\ 60}[/tex]
tan(60) in surd form is [tex]\frac{\sqrt{3}}{2}[/tex]
[tex]y= \frac{16}{\frac{\sqrt{3}}{2}}[/tex]
[tex]y = 16/\frac{\sqrt 3}{2}[/tex]
[tex]y = 16*\frac{2}{\sqrt 3}[/tex]
[tex]y = \frac{32}{\sqrt 3}[/tex]
Rationalize
[tex]y = \frac{32}{\sqrt 3}*\frac{\sqrt 3}{\sqrt 3}[/tex]
[tex]y = \frac{32\sqrt 3}{3}[/tex]
Related Questions
A parabola can be drawn given a focus of (-4, -5) and a directrix of y=3. Write the equation of the parabola in any form.
Answers
Answer:
The equation of the parabola is (x + 4)² = -16(y + 1)
Step-by-step explanation:
The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where
The vertex of the parabola is (h, k)The focus is (h, k + p)The directrix is at y = k - p∵ The focus at (-4, -5)
∴ h = -4
∴ k + p = -5 ⇒ (1)
∵ The directrix at y = 3
∴ k - p = 3 ⇒ (2)
→ Add equations (1) and (2) to find k
∴ 2k = -2
→ Divide both sides by 2 to find k
∴ k = -1
→ Substitute it in equation (1) to find p
∵ -1 + p = -5
→ Add both sides by 1
∴ -1 + 1 + p = -5 + 1
∴ p = -4
→ Substitute the values of h, k, and p in the formula above
∵ (x - -4)² = 4(-4)(y - -1)
∴ (x + 4)² = -16(y + 1)
∴ The equation of the parabola is (x + 4)² = -16(y + 1)
Luther starts jogging 8minutes on the first day and then increases his time by 4 minutes each day. How many minutes will he jog the fifth day?
Answers
Answer:
80?
Step-by-step explanation:
Answer:
(8+4)x5
Step-by-step explanation:
WA store manager records the number of people who have been in his store compared to the number of hours the store has been open. He graphs the data on the scatterplot below and sketches a trend line.
Store Customers
A graph has hours open on the x-axis, and total customers on the y-axis. A trend line goes through points (1, 25) and (2, 50).
Based on the data collected, if the store has been open 7 hours, which scenario is most likely to be true?
After 1/2 hour, 1 customer had been in the store.
After 6 hours, 129 customers had been in the store.
After 7 hours, 175 customers had been in the store.
After 8.5 hours, 225 customers had been in the store.
Answers
Answer: After 7 hours, 175 customers had been in the store.
Step-by-step explanation:
Did the quiz, Trust me.
Answer:
ccccccccc!
Step-by-step explanation:
Can someone please help me with this question i have 3 minutes left
Answers
Answer:
It will cost 11 cents a day.
Step-by-step explanation:
1.98/18=11
plzz have brainiest
Help me please solve this
Answers
9514 1404 393
Answer:
a) no
b) yes
Step-by-step explanation:
a) You cannot draw the graph around x=0 without lifting your pencil. The function is not continuous at x=0.
__
b) You can draw the graph around x=1 without lifting your pencil. The function is continuous at x=1.
_____
Additional comment
In technical terms, the limit from the left at x=0 is 2; the limit from the right is 3. These are different, so the function is not continuous there.
On the other hand, the left and right limits at x=1 are the same (both 2), and are equal to the value of the function at that point (f(1)=2). Hence, the function is continuous at x=1.
Please help me please
Answers
Answer:
To be honest I don't know I just need some points 1+1=2
Step-by-step explanation:
what is the maximum value of the function? explain what the maximum value of this represents in this situation. make sure to include information about the x-value and y-value in your explanation
Answers
wowwwww he just roasted youuuuuuuuuu!!!!!
What is the K for this story Problem? John bought 27 baseball cards for $9. How many baseball cards can he buy with $84?
Answers
Answer:
210
Step-by-step explanation:
9 divided by 27 = .33333 = .4
you would divide 9 by 27 because if you did 27 divided by 9 he would only have 3 cards
84 divided by .4 = 210
What is the value of the expression below?
2 [32 - (4-1) to the power of 3]
Enter your answer in the box.
Answers
Answer:
the answer is 10
Step-by-step explanation:
What is the y coordinate of the solution
Answers
Answer:
8
Explanation:
3x-7=x^2-7x+18
X= 5
Y=3(5)-7 aka 15-7
=8
pls help me on this iready question I beg u
Answers
Answer:
We conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.
Step-by-step explanation:
Suger needed for a full batch = 3/4Given that Farid is making 1/2 of batchWe need to determine the expression for the amount of sugar Freed needs to make 1/2 batch.
Let 'x' be the batch and 'y' be the amount of sugar
Suger needed for a full batch = 3/4 cup of a sugar
so
x = 3/4yBut, Farid is making 1/2 of the batch.
Thus, multiply both sides by 1/2
[tex]x\times \frac{1}{2}\:=\:\frac{3}{4}y\times \frac{1}{2}[/tex]
[tex]\frac{x}{2}=\frac{3y}{8}[/tex]
Therefore, we conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.
Which expression can be used to find The amount of money for camp leader spends on b books
Answers
Answer:
Part A: A. 7.50 x b
Part B: $90
Step-by-step explanation:
Part A: The cost of a book is $7.50, so the equation that is going to tell you the total cost of however many books purchased is equation A.
Part B: $90. If the cost of a book is $7.50 and the teacher purchases 12 books, you do $7.50 x 12= $90. You can check the equation by adding $7.50 12 times. You will get the same result.
what does nonlinear mean?
Answers
............
Answer:
Not denoting, involving, or arranged in a straight line.
Step-by-step explanation:
I looked it uo on google
im not SmArT
What is the area of a rectangle with a length of 1/3 yards and width of 3/4 yard?
Answers
Answer:
1/4 yards squared
Step-by-step explanation:
Area of a rectangle equals length times width.
1/3 x 3/4 = 3/12, or 1/4
Answer:
It would be 1/4 and if not try 3/12
Step-by-step explanation:
I hope this helped
Abigale drove 20 kilometers in 10 minutes, and Jordan drove 30 kilometers in 15 minutes.
Both Abigale and Jordan drove at a constant speed.
Did Abigale and Jordan drive at the same speed? Explain your reasoning.
Answers
Answer:
15
Step-by-step explanation: 20+10+3+30 =30
HELP ME PLS :(
Janis is 65 inches tall. What is her height in centimeters? (2.54 cm = 1 inch)
Answers
Answer:
I think the answer 165.1 cm tall
Step-by-step explanation:
multiply 2.54 by 65
Answer:
165.10cm
Step-by-step explanation:
i think so
3x + y = 15 What is the solution of this system of equations? (5x+2y=-4
Answers
Answer:
x=34 y=-87 (34,-87)
Step-by-step explanation:
3x+y=15 rewrite to solve for y -----> y=15-3x
5x+2y=-4
Plug y=15-3x into 5x+2y=-4
So, 5x+2 (15-3x)=-4
Distribute: 5x+30-6x=-4
Combine like terms: 30-x=-4
Solve for x -x=-34
Solve for x x=34
Then, to solve for y, plug "x" into 3x+y=15
So, 3(34)+y=15
Distribute: 102+y=15
Solve for y y=-87
Help now please :))))
Answers
Answer: the last one
Step-by-step explanation:
what is the greatest common factor of 3/5
Answers
Answer:
15
Step-by-step explanation:
3 × 5 = 15
Hope this helped <3
HELP PLS! It’s question 15
Answers
Answer:
A: C = 15N
Step-by-step explanation:
30/2 = 15 (the cost of 1 class)
Paula ran 3 1/4 kilometers. Omar ran 4,200 meters. What is the total number of centimeters Omar and Paula ran?
Answers
Answer:
325000 + 420000 = 745000
Step-by-step explanation:
They ran 745000 centimeters all together
What is the answer to -7(-6)
Answers
Answer:
42
Step-by-step explanation:
Hope this helps and have a great day! :)
Answer: -7(-6) is 42
hope this helps :)
Step-by-step explanation:
when You multiply two negative numbers, the answer is positive.
a bow bear could watch 44 in 4 seconds at this rate how far can a brown bear run in 20 seconds
Answers
Answer:
111 is a great place to be your friend
Step-by-step explanation:
I am not it to 3rd or 3rd to be friends
Answer:
220
Step-by-step explanation:
44 divided by 4 = 11
11 times 20 = 220 so that's the answer
BRAINLIEST PLEASE
What is the exact distance from (-5,1) to (3,0).
Answers
Answer:
The distance between the two points is [tex]\sqrt{65} \ \text{units}.[/tex]
Step-by-step explanation:
In order to find the distance between two coordinate pairs, we can use the distance formula:
[tex]\displaystyle \bullet \ \ \ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Our coordinate pairs need to be labeled accordingly, so we can use this naming system:
[tex]\bullet \ \ \ (x_1, y_1), (x_2, y_2)[/tex]
This assigns a name to our points:
[tex]x_1 = -5[/tex][tex]y_1 = 1[/tex][tex]x_2 = 3[/tex][tex]y_2 = 0[/tex]Therefore, we can plug these into the formula and solve:
[tex]d=\sqrt{(3-(-5))^2+(0-1)^2}\\\\d=\sqrt{(8)^2+(-1)^2}\\\\d=\sqrt{8^2+1^2}\\\\d=\sqrt{64+1}\\\\d=\sqrt{65}[/tex]
Therefore, the distance between the two points is [tex]\sqrt{65} \ \text{units}[/tex].
What number is equivalent to 15 and 25
Answers
Answer:
yo are you talking about like absolute value? then it's | -15 | and | -25 |
Step-by-step explanation:
Estimate the quotient for 5,738 divided by 21
Answers
Answer:
its 273 rounded but say 270
Step-by-step explanation:
The estimate is 270.
Check whether (x – 1) (x +2) = x + 3 is a quadratic equation or not.
Answers
Answer:
no, it is not
Step-by-step explanation:
STEP 1: Simplify (x−1)(x+2).
[tex]x^2+x-2=x+3[/tex]
STEP 2: Move all terms containing x to the left side of the equation.
[tex]x^2-2=3[/tex]
STEP 3: Move all terms not containing x to the right side of the equation.
[tex]x^2=5[/tex]
STEP 4: Take the square root of both sides of the equation to eliminate the exponent on the left side.
[tex]x=[/tex]±[tex]\sqrt{5}[/tex]
STEP 5: The complete solution is the result of both the positive and negative portions of the solution.
[tex]x=\sqrt{5} ,-\sqrt{5}[/tex]
What is the 15th term of the sequence an =
-3n+50
D. 95
Answers
Answer:
= 105
Step-by-step explanation:
Answer:
here ya go
Step-by-step explanation:
a
9
=
105 I think
Answer the question for brainliest.
(Simplify Please)
Answers
[tex]1 \frac{2}{5} m - \frac{3}{5} ( \frac{2}{3} m + 1)[/tex]
[tex]\frac{7}{5} m - \frac{6}{15} m - \frac{3}{5} [/tex]
[tex] \frac{21}{15} m - \frac{6}{15} m - \frac{3}{5} [/tex]
[tex]( \frac{(21 - 6)m}{15} ) - \frac{3}{5} [/tex]
[tex] \frac{15}{15} m - \frac{3}{5} [/tex]
[tex]1m - \frac{3}{5} [/tex]
[tex]m - \frac{3}{5} [/tex]
True or False: The commutative property allows you to change the order of an addition problem and division problem.
<333
Answers
Answer:
True!!Step-by-step explanation:
The commutative, associative, and distributive properties help you rewrite a complicated algebraic expression into one that is easier to deal with. When you rewrite an expression by a commutative property, you change the order of the numbers being added or multiplied.
Hope this helps!! Please consider marking brainliest! Have a good one!!