Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.
Given:
A figure.
To find:
The values of x and y.
Solution:
We know that, in a right angled triangle,
[tex]\sin \theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin 60^\circ =\dfrac{x}{16}[/tex]
[tex]\dfrac{\sqrt{3}}{2} =\dfrac{x}{16}[/tex]
Multiply both sides by 16.
[tex]\dfrac{\sqrt{3}}{2}\times 16=\dfrac{x}{16}\times 16[/tex]
[tex]8\sqrt{3}=x[/tex]
And,
[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]
[tex]\cos 60^\circ =\dfrac{y}{16}[/tex]
[tex]\dfrac{1}{2}=\dfrac{y}{16}[/tex]
Multiply both sides by 16.
[tex]\dfrac{16}{2}=y[/tex]
[tex]8=y[/tex]
Therefore, the missing side lengths are [tex]x=8\sqrt{3}[/tex] and [tex]y=8[/tex].
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
What is 1/4 divided by 9/10 rewritten with an important fraction?
Step-by-step explanation:
[tex]{:}\hookrightarrow\sf \dfrac {1}{4}\div \dfrac {9}{10}[/tex]
[tex]{:}\hookrightarrow\sf \dfrac {1}{4}\times \dfrac {10}{9}[/tex]
[tex]{:}\hookrightarrow\sf \dfrac {10}{36}[/tex]
[tex]{:}\hookrightarrow\sf \dfrac {5}{18}[/tex]
help me. please math
Answer:
$16
Step-by-step explanation:
60 + 4 = 64
64 ÷ 4 = 16
CHECK:
16 x 4 = 64
64 - 4 = 60
Which rational number is also an integer
A. - 86 / 6
B. - 65/13
C. 43/5
D. 70/25
This is because 65/13 = 5 when using a calculator or long division. There are no fractional or decimal parts to the result 5, so 5 is an integer.
Something like 86/6 = 14.333 approximately showing the result is not an integer. The same applies to choice C and choice D as well.
Please help 15 points!!!
Answer:
she earns $10 per hour, and can earn $1 in 6 minutes (60 min divided by $10)
Step-by-step explanation:
Solve the system of equations y = -2x - 9 and -x + 3y = 8 using the substitution method.
Answer: (-5,1)
Step-by-step explanation: Explanation in picture.
A gym membership costs $25 to join, plus a $12 monthly fee. If Adam has spent $133 on his gym membership this year, for how many months has he been a member?
Answer:
HELP ME I GOT THE SAME QUESTION AND I'M DUMB :(
Step-by-step explanation:
can someone explain how to solve this?
{(-15, 3), (-5, 1), (0, 0), (10, -2)}
Constant:
Equation:
Direct & inverse variation (identify the constant of variation,then write the direct variation equation to represent the relationship) please helppp!!
Answer:
[tex]k = -\frac{1}{5}[/tex] -- Constant
[tex]y = -\frac{x}{5}[/tex] -- Equation
Step-by-step explanation:
Given
[tex]\{(-15, 3), (-5, 1), (0, 0), (10, -2)\}[/tex]
Solving (a): The constant of variation
The given parameter is of the form (x,y) and the variation constant is calculated using:
[tex]k = \frac{y}{x}[/tex]
For:(-15,3), k is calculated as
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{3}{-15}[/tex]
[tex]k = -\frac{1}{5}[/tex]
For (-5,1)
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{1}{-5}[/tex]
[tex]k = -\frac{1}{5}[/tex]
The equation is calculated using the following rule:
[tex]y = kx[/tex]
Substitute [tex]-\frac{1}{5}[/tex] for k
[tex]y = -\frac{1}{5} * x[/tex]
[tex]y = -\frac{x}{5}[/tex]
Then she needs to find her "heart rate reserve" h by subtracting her average resting heart rate r from her maximum heart rate m. Write an equation she can use
Answer:
r-m=h
Step-by-step explanation:
help me thank you ! appreciate it
Answer:
what does it mean by equation
PLS HELP I'LL TRY TO GIVE BRAINLIEST
Solve each equation and prove that your answer solves the original equation.
25 - 3x = 40 1/3x - 12 = -3
Answer:
25 - 3x = 40 x=-5
1/3x - 12 = -3 x=27
Step-by-step explanation:
25-3x=40 -> subtract 25 each side .... -3x=15 -> divide -3 each side...... x= -5
Sydney purchased a used car for $3,500. Her state charges a 5% tax for the car, $85 for registration, $60 for a new title certificate, and $35 for a state safety and emissions inspection. How much does Sydney need to pay for these extra charges, not including the price of the car?
Answer:
$355
Step-by-step explanation:
85+60+35=180
5% of 3,500 is 175
175+180=355
so if i did the math right that means the answer is $355
Hopefully the right answer
determine the domain on the following graph
Answer:
(-3,7)
Step-by-step explanation:
what is the slope of (-4,-6) (2,-4)
Answer:
The slope is 1/3
Step-by-step explanation:
Answer:
y2-y1/x2-x1
-4-(-6)/2-(-4)
a negative and a negative turns to a positive.
2/6 or 1/3
Step-by-step explanation:
Maggie has three pages of homework to do.If she can do 1/4 of a page in one hour, how many will her homework take
Answer:
The answer is 12 hours.
Step-by-step explanation:
If she completes 1/4 of a page in an hour completing one page will take her 4 hours after that you multiply it by 3 and get the total of 12 hours that is takes for her to do her homework
Answer:
the answer is 12 :)))))
A rectangle is located on a coordinate plane. If the ordered pair (t, u) represents a vertex of this rectangle, which algebraic representation describes the effect of translating the rectangle 8 units up and 3 units left?
Answer: (t,u) -> (t-3, u+8)
Step-by-step explanation: Up is the y value and left is the x value.
In the point ( t,u) t is the x value and u is the y value.
Moving to the left, you subtract the value and moving up you add the value.
The answer would be (t, u) → (-t – 3, u + 8)
What is the quotient 5/8 + 1/5?
Answer:
33/40
Step-by-step explanation:
cross multiply
5 x 5 = 25
8 x 1 = 8
25 + 8 = 33 (our numerator)
8 x 5 = 40 (our least common denominator)
A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family? (This is a hard one)
Answer:
there are 3 girls and 4 boys in the family. The girl has 3 sisters and 3 brothers.
Step-by-step explanation:
If there are 4 girls and 3 boys than the girl has 3 sisters and 3 brothers.
the boy has 4 sisters and 2 brothers. 2 is half of 4.
3x+2y=8
5x+2y=12
what is the solution of the system of equations shown above?
The value of x=2 and y=1.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
3x+2y=8
5x+2y=12
Now, solving both using method of Elimination Method
3x - 5x = 8-12
-2x= -4
x = -4/ -2
x= 2
and, 3x+ 2y = 8
3(2) + 2y = 8
6 + 2y = 8
2y = 8-6
2y = 2
y = 2/2
y= 1
Hence, the value of x=2 and y=1.
Learn more about equation here:
https://brainly.com/question/10413253
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One fifth of a number is equal to triple that number less 28.
Let the unknown number be x. Write this word problem as an equation using the variable x.
Answer:
x=10
Step-by-step explanation:
x=(3x-28)5
-14x=-140
x=10
1) Suzanne will pay $14 to get her hair cut. She wants to leave the hairdresser a 15% tip. What is the total cost of the haircut, including tip?
Answer:
$16.10
Step-by-step explanation
14.00x .15=2.10
14.00+2.10=16.10
Which triangle is congruent to triangle ABC?
I need help ASAP!!
Thanks
Answer:
-|x+2|+2
Step-by-step explanation:
2. Find the equation of the line with a slope of -2 and through the points (1,-17)
Answer:
y=−2x−15
Step-by-step explanation:
Anton's mechanic charged $75 for a radiator and $50 per hour for labor. The total cost to install the radiator was $325. Approximately how long did it take the mechanic to install the radiator?
Answer: 5 hours
Step-by-step explanation: because 50 multiply by 5 is 250 and more 75 for radiator
Clark bought a 3.2 Ib bag of potatoes , which had 10 potatoes. How many potatoes would there be in a 10 Ib bag?
9514 1404 393
Answer:
31
Step-by-step explanation:
If we assume the number of potatoes is proportional to the weight, then we can write the equation ...
n/10 = 10/3.2
n = 100/3.2 = 31.25 . . . . . . . multiply by 10
There may be 31 potatoes in a 10-lb bag.
Which statement is true about minus 14 and minus 8?
Answer:
minus 14 less than minus 8 because minus 14 is located to the left of minus 8 on the number line.
Step-by-step explanation: Hope this is right! and I hope it helps you UwU
Nina’s dog weighed 23.54 pounds last year. This year, her dog weighs 25.38 pounds. How many pounds did her dog gain this past year? PLS HELP ME!!!!!!!!!
Answer:
1.84
Step-by-step explanation:
25.38-23.54