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Given to find the side of right angle triangle.
use the formula,
\(\sin \theta=\frac{opposite\text{ }}{\text{hypotenouse}}\)\(\begin{gathered} \sin 30^{\circ}=\frac{\sqrt[]{2}}{y} \\ \frac{1}{2}=\frac{\sqrt[]{2}}{y} \\ y=2\sqrt[]{2} \end{gathered}\)\(\begin{gathered} \sin 60^{\circ}=\frac{x}{2\sqrt[]{2}} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{2\sqrt[]{2}} \\ 2x=2\sqrt[]{2}\cdot\sqrt[]{3} \\ x=\sqrt[]{6} \end{gathered}\)\(\begin{gathered} \tan 60=\frac{x}{\sqrt[]{2}} \\ \sqrt[]{3}=\frac{x}{\sqrt[]{2}} \\ x=\sqrt[]{6} \end{gathered}\)so the answer is,
\(x=\sqrt[]{6}\)Related Questions
Mary’s bedroom rug is shown below. Find the perimeter and area of the rug.
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classify the following set of measurements as accurate, precise, both, or neither. checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g
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The dimensions listed above are thus neither exact nor precise.
In the given question the chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively and we have to classify the following set of measurements as accurate, precise, both, or neither.
It is the "value" that a buyer is prepared to pay for an object, particularly a used or second-hand car; typically, the "real worth" of any used car is a predetermined price tag after determining its value based on its condition and usage.
The chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively. This demonstrates that the weight of chocolate chips is not comparable to their actual worth.
The dimensions listed above are thus neither exact nor precise.
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The perimeter of the triangle shown is 225 feet, find the length of each side
X feet = How many Feet?
5x feet = how many feet?
(6x - 3) feet = for many feet?
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Answer:
I have solved it and attached in the explanation.
Step-by-step explanation:
Judy bought 12 roses for
$36. Jackie bought 20 roses
for $80. Which is the better
buy?
Answers
Answer:
judy had the better buy
Step-by-step explanation:
Answer:
I would buy the ones Judy has
Step-by-step explanation:
Solve. 10x^2 - 6 = 9
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Answer:
x = ±sqrt(3/2)
Step-by-step explanation:
10x^2 - 6 = 9
Add 6 to each side
10x^2 - 6+6 = 9+6
10x^2 =15
Divide each side by 10
10x^2/10 = 15/10
x^2 = 3/2
Take the square root of each side
sqrt(x^2) = ±sqrt(3/2)
x = ±sqrt(3/2)
i got 90.50. does that seem right?
Answers
Step-by-step explanation:
90.50. as money if it is it would be $90.50
if as a number 9,050
Determine if y varies with x. and if so find the constant variation of k and write the equation
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Suppose y varies directly as x then we have
\(y\propto x\)This implies
\(y=kx\)Where k is a constant of variation
From the table
When x = 7, y = 11
This implies
\(\begin{gathered} 11=7k \\ k=\frac{11}{7} \end{gathered}\)We need to check if the value of k satisfy other pairs of x and y
From the table
when x = 8, y = 13
Using the value of k
we have
\(13=\frac{11}{7}\times8\)But this equation is not true because the LHS is not equal to RHS
That is
\(13\ne\frac{11}{7}\times8\)Hence the value of k is not unique for the given values of x and y
Therefore, y does not vary directly with x
Lorri had a gross income of $3256.15 during each pay period in 2010. If she got paid monthly, how much of her pay was deducted for FICA in 2010?
Answers
FICA is 7.65%
39,073.8*0.0765= 2,989.15
FICA deducted 2,989.15
the following questions use 3, 6, 5, 4, 7, 5, 6, 4 Round any decimal numbers to the
hundredths place.
4. Find the mean.
5. Find the median.
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Answer:
Mean: 5
Median: 5
Step-by-step explanation:
To find the mean you have to add up all the numbers then divided by the total number of numbers you have.
- 3+6+5+4+7+5+6+4=40
- There are 8 numbers so we would do 40 divided by 8 to get our answer,5
To find the median you have to put the numbers from least to greatest then you have to find the middle number.- 3,3,4,4,5,5,6,6,7
You start by taking one number from the smallest number then from the largest number.
-3,3,4,4,5,5,6,6,7 goes to 3,4,4,5,5,6,6,7 then to 3,4,4,5,5,6,6 to 4,4,5,5,6,6 to 4,4,5,5,6 to 4,5,5,6 to 4,5,5 to 5,5 to 5
You repeat that until you are left with the middle number, sometimes you might be left with 2 numbers, you have to add those 2 numbers together then divide the sum by 2. With this situation there aren't 2 medians so you're just left with your answer, 5.
Vertex R is ______ units from vertex T.
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Answer:
The answer is 7 units from vertex T
The length of the diagonal of a squere is 36 feet. Find the length of the side of the square.
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Answer:
Length of the side of a square is 18 sqrt(2)
Step-by-step explanation:
a and b are the sides of square and c is the diagonal.
a^2+b^2=c^2
a^2+b^2= 36^2
As all sides are equal we can take b=a
2a^2=36^2
a^2= (36×36)/2
a^2 = 18×36 = 2×9×9×4
Taking squareroot on both sides we get
a= sqrt(2×9×9×2×2)
a=18 sqrt(2)
a flying squirrel jumped from a tree 11 feet in the air at an initial velocity
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Answer:
A flying squirrel jumped from a tree 11 feet in the air at an initial velocity of 9 feet per second. The equation h=-2t^2+9t-11 models his jump where h is height in feet and t is time in seconds
Step-by-step explanation:
A hall is thrown straight up, from 3 m above the ground, with a velocity of 14m/s. When does it hit the ground? Use the vertical motion formula.
Answers
In this question, to find the total height first, we must also take into consideration the acceleration due to gravity as well. To find the distance by which acceleration due to gravity pulls the ball down must know the Initial velocity.
In the answer key, it says that gravity changes the ball's height by a distance of -5t^2
Is initial velocity in this question 0 or 14m/s? Because if it is 14, then gravity should change the balls position by -(14+5t^2), not -5t^2, because if I remember correctly, the formula for finding distance is vt(initial velocity)+(1/2)at^2 ,and not just (1/2)at^2
solving matrices, solve for x
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The value of X, given the matrices, can be found to be X = [ [ 4 ], [-1.5 ] ].
How to solve the matrix ?We are told that the value of X can be found to be :
2X + A = B
Solving this would give:
X = (B - A) / 2
We can then apply this to the matrices to give:
B - A = [ [ 11 - 3 ], [1 - 4 ] ]
B - A = [[ 8 ], [ -3 ] ]
X = [ [ 8 / 2 ], [ -3/2 ] ]
X = [ [ 4 ], [-1.5 ] ]
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PLEASE HELP Find the value of x.
X
15
12
Answers
Answer: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
What’s 393 + ___ = 708 + 176
Answers
Answer: 393 + 491 = 708 + 176
Step-by-step explanation:
Simplify the right side and use a variable for the blank
393+x=708+176
393+x=884
Now subtract 393 on both sides
393-393+x=884-393
x=491
the product of six and a number is equal to sixty
Answers
Answer: 10
Step-by-step explanation:
Let the number be A
6 x A = 60
Hence, A = 60/6 = 10
HELP WITH ALL OF IT PLEASE I WILL GIVE BRAINLEIST
Answers
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36
can someone please help
Answers
Answer:
The measure of CD is 46
Step-by-step explanation:
From the midpoint theorem, we have,
FG = (1/2)CD
so,
\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)
Now,
\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the banks if you had this question before!!
Answers
An equation for the total cars and trucks for dealership A is: x + y = 164.
An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.
The number of cars that dealership A sold is: 98 cars.
The number of trucks that dealership B sold is: 66 trucks.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of cars sold.Let the variable y represent the number of trucks sold.Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;
x + y = 164.
Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;
2x + 0.5y = 229.
By solving the systems of linear equations simultaneously, we have:
2x + 0.5(164 - x) = 229
1.5x + 82 = 229
x = 98 cars.
For the y-value, we have;
2(98) + 0.5y = 229
0.5y = 229 - 196
y = 33/0.5
y = 66 trucks.
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One day a store sold 36 sweatshirts. White ones cost $10.95 and yellow ones cost $11.50. In all, $404.65 worth of sweatshirts were sold. How many of each color were sold?
The store sold ____ white sweatshirts
Answers
Answer:
17 white sweatshirts were sold and 19 yellow sweatshirts were sold.
Step-by-step explanation:
Let w represent the number of white sweatshirts sold and y represent the number of yellow sweatshirts sold.
We can write a system of equations to represent the situation.
Since the store sold a total of 36 sweatshirts, the sum of the white and yellow sweatshirts must total 36. So:
\(y+w=36\)
And since each white sweatshirt cost $10.95 and each yellow sweatshirt cost $11.50 and the total profit was $404.65:
\(10.95w+11.5y=404.65\)
Solve the system. I'll use substitution this time (though elimination will work just as perfect). From the first equation, subtract w from both sides:
\(y=36-w\)
Substitute this into the second:
\(10.95w+11.5(36-w)=404.65\)
Distribute:
\(10.95w+414-11.5w=404.65\)
Simplify:
\(-0.55w=-9.35\)
Divide both sides by -0.55:
\(w=17\)
So, 17 white sweatshirts were sold.
Using the modified equation, substitute:
\(y=36-(17)=19\)
Therefore, 17 white sweatshirts were sold and 19 yellow sweatshirts were sold.
Can someone please help me I will mark u brilliant
Last answer for number 6 is the number that occurs the most.
Answers
Answer: the answer to question 6 is order least to greatest
Step-by-step explanation:
I'm helping someone with her daughter's homework. What is the term for this definition: take a part a number to write it in a new way. In mcgraw hill my math grade 1
Answers
Answer:
hello mate.. i am glad ur helping someone for her hw.. nice nice
well as per my understanding
'' take apart a number to write it in a new way ''
this answer must be '' subtraction''
as in subtraction we take apart number and resulting number is new way of writing the difference of first 2 ....
go on.. help more ppl ... we are here to support
On a distance-time graph,a horizontal straight line corresponds to motion at __+
Answers
On a distance time graph, a horizontal straight line corresponds to motion at zero speed constant speed increasing speed decreasing speed.
Luisa and Rachelle are competing for employee of the month. It is the last week, and the employee who processes the most client accounts will win. Luisa processed 15 accounts Monday, 22 accounts Tuesday, and 17 accounts Wednesday. Rachelle processed 24 accounts Monday, 18 accounts Tuesday, and 11 accounts Wednesday. Who has processed the most accounts this week, and by how many
Answers
Answer:
Luisa processed the most accounts this week, by 1.
Step-by-step explanation:
Luisa:
15 on Monday, 22 on Tuesday and 17 on Wednesday.
So a total of 15 + 22 + 17 = 54.
Rachelle:
24 on Monday, 18 on Tuesday, 11 on Wednesday.
So a total of 24 + 18 + 11 = 53.
Who has processed the most accounts this week, and by how many?
54 - 53 = 1, so Luisa processed the most accounts this week, by 1.
helllpplll pleaseeeeee
Answers
Answer:
Step-by-step explanation:
area of bottom of round pan = πr² = 9π in² ≅ 28.27 in²
area of bottom of rectangular pan = 10×2 = 20 in²
area of bottom of round pan is greater than area of bottom of rectangular pan by about 8.27 in²
Can you help me find the area of the shaded region in the picture of the shape I have attached below?
Answers
The area of the shaded region is equal to 32.44 m²
How to evaluate for the area of the shaded regionThe unshaded region is circle with a radius of 2 m, so to get the area of the shaded region, we subtract the area of the circle from the area of the rectangle as follows:
area of rectangle = 9 m × m = 45 m²
area of the circle = 22/7 × 2m × 2m
area of the circle = 12.56 m²
area of the shaded region = 45 m² - 12.56 m²
area of the shaded region = 32.44 m²
Therefore, the area of the shaded region is equal to 32.44 m².
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Terrance's garden is 3/ 5 yard by 1 2/ 5 yards. Each square is 1/ 5 yard long. He needs to know the area so he can buy the right amount of fertilizer. What is the area of his garden?
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Answer:
brain
Step-by-step explanation:
Shhdhskwoqoqpqpqlqlqlqlalalsmmsmsmznzhxhfhrsq
Answers
Answer:
C=14π
Step-by-step explanation:
C=2πr
14 is the diameter. radius is half of diameter. r=7
C=2π(7)
C=14π
Please help this question is asking about the volume of a hemisphere and cylinder?
Answers
Answer:
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