Which answer choice correctly solves for x and y?

Which Answer Choice Correctly Solves For X And Y?

Answers

Answer 1

Answer:

[tex]x = 10\\y = 5[/tex]

Step-by-step explanation:

1. Approach

The easiest method to solve this problem is to use the side ratios in a special right triangle. One should start by proving that the triangle is a (30 - 60 - 90) triangle. Since the problem gives on the information that one of the sides has a measure of ([tex]5\sqrt{3}[/tex]), one can use this combination with the ratio of the sides in a special right triangle, to find the unknown side lengths.

2. Prove this triangle is a (30 - 60 - 90) triangle

One is given a right triangle. This means the triangle has a (90) degree or right angle in it. This is indicated by a box around one of the angles. One is given that the other angle in this triangle has an angle measure of (30) degrees. The problem asks for one to find the third angle measure. A property of any triangle is that the sum of angle measures in the triangle is (180) degrees. One can use this to their advantage by stating the following:

[tex](90) + (30) + (unknown) = 180\\[/tex]

Simplify,

[tex](90) + (30) + (unknown) = 180[/tex]

[tex]120 + unknown = 180\\[/tex]

Inverse operations,

[tex]120 + unknown = 180\\[/tex]

[tex]unknown = 60[/tex]

Thus, this triangle is a (30 - 60 - 90) triangle, as its angles have the measures of (30 - 60 - 90).

3. Solve for (y)

The sides ratio in a (30 - 60 - 90) triangle is the following:

[tex]n - n\sqrt{3} - 2n[/tex]

Where (n) is the side opposite the (30) degree angle, ([tex]n\sqrt{3}[/tex]) is the side opposite the (60) degree angle and finally (2n) is the side opposite the (90) degree angle. The side (y) is opposite the (30) degree angle. This means that it is equal to the side opposite the (60) degree angle divided by ([tex]\sqrt{3}[/tex]). Therefore, one can state the following:

[tex]\frac{5\sqrt{3}}{\sqrt{3}}=y\\5=y[/tex]

4. Solve for (x)

Using the same thought process one used to solve for side (y), one can solve for side (x). The side (x) is opposite the (90) degree angle, hence, one can conclude that it is twice the length of the side with the length of (y). Therefore, one can state the following:

[tex]x = 2y\\x = 2(5)\\x = 10[/tex]


Related Questions

In a right triangle, two sides are 12 and 13. Find the measure of the third side. Consider all cases

Answers

Answer:

Case 1

12 and 13 are legs, then find the hypotenuse.

c = [tex]\sqrt{12^2+13^2} = \sqrt{313}[/tex] ≈ 17.69

Case 2

13 is hypotenuse, 12 is a leg, find the missing leg.

b = [tex]\sqrt{13^2-12^2} = \sqrt{25} = 5[/tex]

Answer:

Solution given:

Case 1:

if base=12

hypotenuse=13

perpendicular=??

By using Pythagoras law

hypotenuse²=perpendicular²+base²

13²=perpendicular ²+12²

perpendicular ²=13²-12²

perpendicular=[tex]\sqrt{13²-12²}=\sqrt{25}=5[/tex]units

Case:2:

Case 1:

if base=12

hypotenuse=13

perpendicular=??

By using Pythagoras law

hypotenuse²=perpendicular²+base²

13²=perpendicular ²+12²

perpendicular ²=13²-12²

perpendicular=[tex]\sqrt{13²-12²}=\sqrt{25}=\bold{\large{5}}[/tex]units

Case:2:

if base=12

hypotenuse=??

perpendicular=13

By using Pythagoras law

hypotenuse²=perpendicular²+base²

hypotenuse²=13 ²+12²

hypotenuse² ²=13²+12²

hypotenuse²=[tex]\sqrt{13²+12²}=\sqrt{313}=\bold{\large{17.7}}[/tex]units

Find the number in which 8 is in tenths place.
8945.4534
456.89732
9738.45621
6875.1234

Answers

the number in which 8 is in tenth place is

6875.1234

plese mark me as braniliest

It’d be the second option: 10ths is always the point after the decimal, and in the second option 8 is after the decimal

NOW ASAP NEED FAST ANSWERRRRRRRRRRRRRRRRRRR

Answers

Answer:

C.

Step-by-step explanation:

Dis means apart and junc means join so disjunction means the "state of being disconnected".

toán lớp 8
giải bất phương trình: 2x + 2 > 4

Answers

Answer:

x>1

Step-by-step explanation:

Answer:

x>1

I hope it will help you

please find the answer
there are options given below
plz give answer asap​

Answers

Answer

33.3

Step-by-step explanation:

if u multiply the 2, and then find the ratio of them in comparison to the number under, you will find the rate decreases by 10 percent every time, the first situation it is 4/8 = 5/10, second situation is it 32/80= 4/10, and htis situation is most like 3/10, right ? so the answer would be 33.3 :)

I need help please! Will mark brainliest! (both are seprate questions!

Answers

This answer is of no 1

Step-by-step explanation:

if you want to find volume of cone you must you this formula: hπr² so 10*π(3)*r²(4)= 120ft² and

if you want to find volume of cylinder you should use this formule: πr²*h/3 =π(3)*r²(4)*h(3)/3= 12 the figure has 132 volume in totally.

75% students out of 80 are present in a test , the students absent are :

Answers

Answer:

20 students are absent

Step-by-step explanation:

75/100 × 80 = 60

If 60 were present out of the 80

80 - 60 = 20

Have a great day :)

Find the value of x for which (4/5)-4 x (4/5)-7 =(4/5)2x-1 Can some1 say this ans fast plz

Answers

Answer:

Fraction form: x = -21/4

Decimal Form: x = -5.25

Step-by-step explanation:

See the picture for steps :)

write the equation of the graph below

Answers

Answer:

Step-by-step explanation:

This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:

[tex]y=a(x-h)^2+k[/tex] and this will allow us to solve for the value of a:

[tex]6=a(6-4)^2+5[/tex] and

[tex]6=a(2)^2+5[/tex] and

6 = 4a + 5 and

1 = 4a so

[tex]a=\frac{1}{4}[/tex] and the equation is

[tex]y=\frac{1}{4}(x-4)^2+5[/tex]

Find the domain of h(x) = 2x - 9 given a range of (-7,5,11)

Answers

Answer:

D = 1,7,10

Step-by-step explanation:

-7 = 2x - 9

x = 1

5 = 2x - 9

x = 7

11 = 2x - 9

x = 10

the domain of (1,7,10)

Find the measure of KM. PLEASE PLEASE PLEASE HELP ASAP!!!!!!!!!!!!!!!
A. 7
B. 17
C. 12
D. 14

Answers

Answer:

C

Step-by-step explanation:

Given 2 secants from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant , that is

ML × KM = MN × MR, substitute values

7 × KM = 6(6 + 8)

7 KM = 6 × 14 = 84 ( divide both sides by 7 )

KM = 12 → C

Answer:

C.) 12

Step-by-step explanation:

I got it correct on founders edtell

Determine what type of model best fits the given situation: the temperature of a cup of coffee decreases by 5 F every 20 minutes.

A. liner
B. exponential
C. quadratic
D. none of these

Answers

Answer: T = -t / 4 + T0   where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature

Explanation: This is a linear equation in T and t

(-1 / 4 represents -5 deg / 20 min  = - 1 deg / 4min

If two lines represent the same line, then what is the nature of its solution?

Answers

Step-by-step explanation:

If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .

Answer:

Infinite

Step-by-step explanation:

Solution between 2 lines is considered the point of their intersection. Now, since two lines are same (not only parallel but same), it tends to have infinite solutions.

Name the property shown by the statement 2a = a2

Answers

Distributive property

screenshot if you need more words. seems to be a well illustrated and compact explanation right there

Find the missing length indicated

Answers

Answer:

x = 240

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)

x² = 144 × 400 = 57600 ( take the square root of both sides )

x = [tex]\sqrt{57600}[/tex] = 240

x = 240

Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.

let's call the 2 segments p and q.

p+q = 400

p = 144

q = 400 - 144 = 256

so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192

now the main Pythagoras with the smallest triangle to get x

x² = 192² + 144² = 36864 + 20736 = 57600

x = 240

now, FYI, why is that formula true ?

as we said, we called the segments of the long baseline p and q.

then we can the sides of the main triangle x and y.

and the height is simply h.

so, then we have for the main rectangular triangle

(p+q)² = x² + y²

and for the 2 smaller triangles

x² = p² + h²

y² = q² + h²

=>

p² +2pq + q² = p² + h² + q² + h²

2pq = 2h²

h² = pq

h = sqrt(pq)

and there you have it. just as simple as that.

The radius of a circle is 14cm. Find the radius of the circle whose area is double of the area of circle. ​

Answers

Answer:

14√2 cm

Step-by-step explanation:

Area of circle equation:

A = πr²

Let the radius of bigger circle is x.

We have:

π(14²)*2 = πx²

Solve for x:

x² = 2(14²)x = √2(14²)x = 14√2 cm

19.8cm

Step-by-step explanation:

First find area of small circle:

A = πr2

A = 22/7 x 14 x 14

A = 22 x 2 x 14

A = 616cm2

Area of bigger circle is double that of the small circle:

= 616 x 2

= 1,232 cm2

πR2 = A

22/7 x r2 = 1,232

r2 = (1,232 x 7) ÷ 22

r2 = 8624 ÷ 22

[tex] \sqrt{r ^{2} } = \sqrt{392} [/tex]

radius of bigger circle = 19.8cm

I NEED HELP JANSJEHEHSHSBSBSBSH

Answers

Answer:

The answer is a translation

Step-by-step explanation:

In Math, translation is the displacement of a shape or object from one place to another.

Since the picture shows that the shape moved from one place to the next while remaining the same size, it is translation.

Need help we will be posting questions no leaks max points

Answers

Answer:

6

Step-by-step explanation:

To find the mean you need to add up all the number & then divide it by the total number of numbers.

7+6+7+6+6+7+6+4+5= 54/9 = 6

Answer from Gauthmath

Answer:

6

Step-by-step explanation:

To get the mean, you must add all numbers and divide it by how many digits you have. So 54 (Sum of all numbers) divide by 9 (9 digits) is 6

True or False:

4x and 4x2 are like terms

Answers

Actually its false

In algebra 4x and 4x² are two different terms and are not like terms.

Must click thanks and mark brainliest

Solid #1
SA= 539 cm?
V = 2058 cm
Solid #2
SA = 704 cm?
V?

Answers

Answer:

2688 cm³

Step-by-step explanation:

2058×704/539 = 2688 cm³

One of the lengths of a leg on a right angled triangle is 15 ft the length of the hypotenuse is 17 ft find the length of the other leg

Answers

The length of the other leg should be 8ft

what is the degree of the polynomial below

Answers

Answer:

d

Step-by-step explanation:

trust me gang

Answer:

the degree is the value of the highest exponent... 4x^3 the exponent is a three

answer "D"

Step-by-step explanation:

what’s the answer for the first question? pls help i don’t have much time…

Answers

Answer and Step-by-step explanation:

1.

Since we known how much money Jane and Mark have in total, we can subtract the amount Jane has to find the amount Mark has.

750 - 175 = $575

Mark has $575.

2.

We know how many cards Jamal sold, so if we add it to the amount he still has left, we can find the original amount of cards Jamal had.

17 + 83 = 100

Jamal had 100 cards.

#teamtrees #PAW (Plant And Water)

Answer:

Mark will have $575.

Step-by-step explanation:

Take the total amount ($750) and subtract Jane's contribution ($175) to get Mark's contribution($575).

$750-$175=$575

Write an example of an equation for an exponential growth function

Answers

Answer:

f(x) = 2^x

Step-by-step explanation:

Please help me if you can...

The roof of another Green House contains clear glass panels Isosceles Trapezium in shape, all the same size and one glass panel, REGULAR HEXAGON in shape, in the middle surrounded by the Trapezium. Its walls are squares in shape.


Q1. Illustrate the above situation with the diagram (cross section of the Green house).


Q2. The 2 angles of the Isosceles Trapezium are 1050 and 750, find the other 2 angles.


Q3. How much tape does Jane require to join the roof and the walls, if the walls are in the shape of squares of side 10m.

Answers

Answer:

Q2.the 2 angles of the isoceles trapezium are 1050 and 750,find the other 2 angles.

Can sone One help me please, Thanks a lot

Answers

I don’t really understand what you mean where is the question?

Answer:m

       

Step-by-step explanation:m

Mar-Vell Studios' blockbuster movie Gray Widow: It's About Time She Got a Movie premiered last weekend simultaneously in theaters and on streaming video. On opening weekend, the total revenue from the movie was $127,265,468, with the movie making 75% more revenue in theaters than it did via streaming video. How much money did Gray Widow make in theaters on opening weekend

Answers

Answer:

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Step-by-step explanation:

75% more revenue in theaters than it did via streaming video.

The sum of the revenues is 100%.

So the theaters were responsible for the following percentage:

[tex]P = 50 + \frac{75}{2} = 50 + 37.5 = 87.5[/tex]

How much money did Gray Widow make in theaters on opening weekend?

87.5% of the total revenue, that is, 0.875 out of $127,265,468.

0.875*127,265,468 = $111,357,284.5

Gray Widow made $111,357,284.5 in theaters on opening weekend.

A 10-foot tall tree casts a 4-foot shadow. How tall is the building next to the tree if the building’s shadow is 38 feet long?

Answers

Step-by-step explanation:

It Jun glt tm my tb my tu meri of ft me rh my


Someone help me out please

Answers

Answer:

142.5

Step-by-step explanation:

π×11²×135/360

= 363π/8

= 142.5 (rounded to the nearest tenth)

Answered by GAUTHMATH

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Find (f − g)(x).


3x3 − 5x2


−x2 + 3x + 5


x2 − 3x − 5


−3x3 − 5x2

Answers

Answer:

below

Step-by-step explanation:

that's is the solution above

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