Answer:
See below
Step-by-step explanation:
[tex] In\: \triangle AKL, \:\\ AK = 9,\: \\m\angle K = 90\degree, \: \\m\angle A= 60\degree \\
\therefore m\angle L = 30\degree\\
By \:30°-60°-90° \:\triangle \:theorem:\\
AK = \frac{1}{2} \times AL\\(SIDE\: OPPOSITE \:TO \:30\degree) \\\\
9 = \frac{1}{2} \times AL\\\\
AL = 9\times 2\\\\
\huge\red{AL = 18}\\\\
KL = \frac{\sqrt 3}{2} \times AL\\(SIDE\: OPPOSITE \:TO \:60\degree) \\\\
KL = \frac{\sqrt 3}{2}\times 18\\\\
KL = 9\times \sqrt 3\\\\
\huge\purple{KL = 9\sqrt 3}\\\\
P(\triangle AKL) = AK + KL + AL\\
P(\triangle AKL)= 9 + 9\sqrt 3+18\\
\huge\orange{P(\triangle AKL)=(27 + 9\sqrt 3) \: units} \\\\
A(\triangle AKL) = \frac{1}{2} \times KL\times AK\\
A(\triangle AKL) = \frac{1}{2} \times 9\sqrt 3\times 9\\
A(\triangle AKL) = \frac{81\sqrt 3}{2} \\
\huge\pink{A(\triangle AKL) = 40.5\sqrt 3\: units^2} [/tex]
What are the roots of the equation x2 + 15x = -57 in simplest a + bi form?
Answer:
Step-by-step explanation:
Rewrite x2 + 15x = -57 as x^2 + 15x + 57 = 0, in which the coefficients of this quadratic are {1, 15, 57}.
Then the discriminant is b^2 - 4ac = 225 - 4(1)(57) = -3
Because the discriminant is negative, we know that the two roots will be complex. They are:
-15 ±i√3
x = ---------------
2
9514 1404 393
Answer:
x = -7.5 ± i(√3)/2
Step-by-step explanation:
We can add (15/2)² to complete the square:
x² +15x +(15/2)² = -57 +(15/2)²
(x +7.5)² = -0.75
x +7.5 = ±i(√3)/2 . . . . take the square root
The roots are ...
[tex]x=\displaystyle\left \{ {{-\dfrac{15}{2}+i\dfrac{\sqrt{3}}{2}} \atop {-\dfrac{15}{2}-i\dfrac{\sqrt{3}}{2}}} \right.[/tex]
(x - 2)^5 binomial expansion
12 m
9 m
What is the length of the hypotenuse?
C =
meters
Step-by-step explanation:
AC^2=AB^2+BC^2
c^2=9^2+12^2
c^2=81+144
c^2=225
c=15
The angle of elevation to an airplane viewed from
the control tower at an airport is 7º. The tower is
200 feet high and the pilot reports that the altitude is
5200 feet. How far away from the control tower is
the airplane? Round your answer to the nearest foot.
Evaluate if x=-4 and y=13 3(2x- y)
Answer:
-63
Step-by-step explanation:
6x - 3y
= 6 × -4 - 3 × 13
= -24 - 39
= -63
Please help me pass this class
Answer:
b
Step-by-step explanation:
What is the perimeter, in units, of polygon UVWXYZ? Enter your answer in the box.
Given:
Consider the below figure attached with this question.
To find:
The perimeter of the polygon UVWXYZ.
Solution:
All sides and vertical and horizontal. So, we can easily find the side lengths of the given polygon by counting the boxes between two points.
From the figure it is clear that,
UV = 9 units
VW = 2 units
WX = 3 units
XY = 3 units
YZ = 6 units
ZU = 5 units
Now, perimeter is the sum of all the sides.
[tex]Perimeter=UV+VW+WX+XY+YZ+ZU[/tex]
[tex]Perimeter=9+2+3+3+6+5[/tex]
[tex]Perimeter=28[/tex]
Therefore, the perimeter of UVWXYZ is 28 units.
Find the particular solution to y ' = 2sin(x) given the general solution is y = C - 2cos(x) and the initial condition y of pi over 3 equals 1 . (5 points)
-2cos(x)
closeIncorrect
3 - 2cos(x)
checkCorrect
2 - 2cos(x)
-1 - 2cos(x)
Answer:
[tex]y=2-2\cos(x)[/tex]
Step-by-step explanation:
We have the differential:
[tex]y^\prime=2\sin(x)[/tex]
With the general solution:
[tex]y=C-2\cos(x)[/tex]
And we want to find the particular solution such that it satisfies the initial condition:
[tex]\displaystyle y\Big(\frac{\pi}{3}\Big)=1[/tex]
So, we have:
[tex]y=C-2\cos(x)[/tex]
Substituting π/3 for x and 1 for y yields:
[tex]\displaystyle 1=C-2\cos\Big( \frac{\pi}{3} \Big)[/tex]
Solve for C. Evaluate:
[tex]\displaystyle 1=C-2(\frac{1}{2})[/tex]
Simplify:
[tex]1=C-1[/tex]
Hence:
[tex]C=2[/tex]
Therefore, our particular solution will be:
[tex]y=2-2\cos(x)[/tex]
Hence, our answer is C
I NEED HELP WITH THIS ASAP THERE IS ALSO ONE MORE QUESTION TO THIS PROBLEM PLEASE HELP
Answer:
whoa hold up there friend
Step-by-step explanation:
it will be 4,6,8,10 and the 2nd one is $10,$15,$20,$25
28/n=7/9 help me with this
Answer:
n = 36
Step-by-step explanation:
[tex]\frac{28}{n}[/tex]=[tex]\frac{7}{9}[/tex]
=> 28 x 9 = n x 7
=> 252 = 7n
=> n = 252 ÷ 7 = 36
Answer:
n= 36
Step-by-step explanation:
solve for n by cross multiplying
Hope this helped you :)
Two sisters, Beyunka and Tamu, made resolutions to save their money regularly in 2016. They are both going to save a certain amount of money every month. After how many months will Beyunka and Tamu have saved the same amount of money?
Answer:12months
Step-by-step explanation:
There are 12 months in a year
1 yard of fabric costs $3.25. If you need 4.2 yards, how much will it
cost to purchase the fabrics needed?
Answer:
12.50$
Step-by-step explanation:
3 dollars for 1 yard
3x4=12
.25x2=50
12.50$
Which fraction represents the solution to -6/5/(-3/25) in simplest form?
A. -10
B. -18/125
C. 10
D. 18/125
The fraction represents the solution to (-6/5)/(-3/25) in the simplest form will be 10. Then the correct option is C.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The fraction numbers are given below.
-6/5 and -3/25
Then the division of the numbers -6/5 and -3/25 will be given by putting a division sign between them. Then we have
⇒ (-6/5) ÷ (-3/25)
⇒ (-6/5) / (-3/25)
⇒ (6/5) x (25 / 3)
⇒ 150 / 15
⇒ 10
The part that addresses the answer for (- 6/5)/(- 3/25) in the most straightforward structure will be 10. Then the right choice is C.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
helpppppppppppppppppp
The 1st option is correct.
Answer:
m/15=-3
Step-by-step explanation:
When you see quotient it means to divide
is means equal
I hope this helps
If p(x) = 5(x² + 1) + 16, what is value of p(11)?
Answer: The answer is 626
Step-by-step explanation:
Substitute 11 for x, you get 626.
Ellis is making some beef burgers for his friends. His recipe 500g of beef mince and 120g of cheese to make four burgers. He buys 1.5 of mince and 400g of cheese, and makes as many burgers as possible. How much cheese will he have left over
Given :
Ellis is making some beef burgers for his friends.
His recipe 500g of beef mince and 120g of cheese to make four burgers.
He buys 1.5 of mince and 400g of cheese, and makes as many burgers as possible.
To Find :
How much cheese will he have left over.
Solution :
500 g and 120 g of beef mince and cheese respectively make 4 burgers.
125 g and 30 g of beef mince and cheese respectively make 1 burgers.
Now, we will keep increasing the ingredients until there is any shortage of any ingredients.
1000 g and 240 g will make 8 burgers.
1500 g and 360 g will make 12 burgers.
1625 g and 390 g will make 13 burgers.
Cheese left is ( 400 - 390 ) g = 10 g.
Therefore, 10 grams of cheese will be left.
PLZ HELP IN MATH PLZ
Answer:
3L
Step-by-step explanation:
Chloe was out at a restaurant for dinner when the bill came. Her dinner came to $28. She wanted to leave a 25% tip. How much was her meal plus the tip, before tax, in dollars and cents?
Answer:
25 upon 100 into 28
And add to 28 for total
Step-by-step explanation:
What I did was I found what 25% of $28 is, which is $7. The equation came to this:
[tex]28+7=35[/tex]
The total price with the 25% tip is $35
Thank you! Btw can I please get brainly :3
How much is left on the card after Carl has seen the maximum number of movies
Answer:
how much was on it and how many is the maximum movies
Step-by-step explanation:
Sam opened a savings account with a deposit of $50. Every month after that, he
deposited $20 more. Is this a proportional relationship? Why or Why not?
Step-by-step explanation:
It is given that,
Sam opened a savings account with a deposit of $50. Every month after that, he deposited $20 more.
It is not a proportional relationship. As initial amount was $50 and every month he deposited $20 more. The ratio is not constant for the deposited amounts.
To make the relationship proportional, he must start with zero balance and then should have deposited $20 every month.
A speed limit is 35 mph. A car is travelling 10 mph over the speed limit. I’d that a sum of 0
Answer:
The car is going 45 mph
Step-by-step explanation:
Since the speed limit is 35 mph and the car is 10 mph over the speed, we can add them to find out how fast the car is going. We can solve 35+10 which will give us 45. So it is not a sum of 0 but instead a sum of 45.
(hope this helped)
Answer:
35+10 =45
Step-by-step explanation:
add 10 to 35 then divide by 2
You and your friend are standing back-to-back. Your friend runs 8 feet forward, and then 6 feet right. At the same time, you run 4 feet forward, and then run 3 feet to the right. You stop and throw a football to your friend, who catches it. How far did you throw the football?
Answer:
15 feet
Step-by-step explanation:
you and your friend basically formed two different triangles, and in order to determine the distance that the ball traveled we must calculate both hypotenuses:
triangle 1:
hypotenuse = √(8² + 6²) = √100 = 10 feet
triangle 2:
hypotenuse = √(4² + 3²) = √25 = 5 feet
total distance traveled by the ball = 10 + 5 = 15 feet
$9.05 - 75cents =
hi guys answer this calculation with the working pls
Answer: 9.05-0.75=$8.3
Step-by-step explanation:
solve by completing the square or square root method x^2-4x+9=0?
Please use numbers
Find the slope and the y-intercept of the graph of y=−7x+12.
Hi!
[tex]\spadesuit[/tex] We're given an equation in slope-intercept form.
The formula for slope-intercept is:[tex]\clubsuit~~~\large\boldsymbol{y=mx+b} ~~~\clubsuit[/tex]
where:
[tex]\clubsuit ~\boldsymbol{m - > slope}[/tex]
[tex]\clubsuit~~\boldsymbol{b- > y-intercept}[/tex]
Therefore,
[tex]\stackrel{\heartsuit}{\boxed{\boxed{\textsc{Answers:}\begin{cases}\bold{Slope:-7}\\\bold{y-intercept:12}\end{cases}}}}[/tex]
Cheers!!I hope that helped, have a wonderful day. :)
If angle 2=3x+17 and angle 3 = 5x- 21 what is angle 1
Answer:
(3x - 17)
Step-by-step explanation:
hope this helps
I need answer ASAP OLZ
Answer:
the second one
Step-by-step explanation:
Evaluate 2x+5(x-8) when x = 2
HELLPPP PLEASE!!!!
What is the meaning of the the point (4, 22)?
and am I wrong for the first one?
Answer:
The meaning of (4,22) is Magi had run 4 mike's in 22.5 mins
Have a nice Day , Hope this helped you I would appreciate it if you could mark my answer brainliest
Answer:
No, you are correct for the first one. The meaning of the point (4, 22) is that Magi took 22 minutes to run 4 miles.
Step-by-step explanation:
(4, 22) is written as (x, y) where x is the number of miles Magi ran and y is the number of minutes Magi took.
Thus, when Magi ran 4 miles, she took 22 minutes.
Write an equation in slop intercept for of the line with the following:
Slope: -3/4
y-intercept: -5
Answer:
y = -3/4x -5
Step-by-step explanation:
The slope always goes first, then variable x and the y intercept comes last