Solve for x and y. 30-60-90 triangles

Solve For X And Y. 30-60-90 Triangles

Answers

Answer 1

Answer:

[tex]x = 3[/tex][tex]y=3\sqrt{3}[/tex]

Step-by-step explanation:

From the given right-angle triangle

The angle = ∠60°

The adjacent to the angle ∠60° is x.The opposite to the angle ∠60° is y.

The hypotenuse = 6

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = x and hypotenuse = 6

cos 60° = x / 6

6 × cos 60° = x

x = 3

Thus, the value of x is:

x = 3

And using the trigonometric ratio

sin 60° = opposite / hypotenuse

substituting opposite = y and hypotenuse = 6

[tex]sin\:60^{\circ }\:=\:\frac{y}{6}\:[/tex]

[tex]y=6\:\times\:sin\:60^{\circ }[/tex]

   [tex]=6\times \frac{\sqrt{3}}{2}[/tex]                   ∵ [tex]\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}[/tex]

   [tex]=3\sqrt{3}[/tex]

Therefore, the value of y is:

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

Summary:

[tex]x = 3[/tex][tex]y=3\sqrt{3}[/tex]

Related Questions

Find the gradient of the line drawn bellow

Answers

We need a picture of the problem

5 + 5?

(hint: look at how many points you'll get)

Answers

10!!!!!!!!!!!!!!!!!!!!

Can someone please help me with this, and give a thorough explanation?

Answers

Answer: x=68

Step-by-step explanation:

A. It’s asking what the last test must have to be (x) for all five tests to average out to an 80. This can be represent by:

(95+76+77+84+x)/5=80

The first four numbers are the existing test scores and x is the score you need. This is all divided by five so that you can find the average of all of these added together, which will equal 80, because that’s the grade you’re trying to get. Next, just solve for x:

= 95+76+77+84+x=80(5)

= 332+x=400

X=68

B. I got 74 for this one by using the same process as in part a, but I divided the left side by six and multiplied x by two: (95+76+77+84+2x)/6=80

But I’m not completely positive about this answer. A is definitely right though

10(1.05)^x growth or decay

Answers

Answer:

growth

Step-by-step explanation:

Highest common factor of 308 and 420

Answers

GCF of 308 and 420 is 28

Answer:

hcf, ( 308; 420) = 28 = 2^2 × 7: greatest ( highest ) common factor ( divisor ), calculated.

Plz halp need an answer right away!

Answers

Answer:

20.56 cm

Step-by-step explanation:


[tex] - 2x - 4y = 10 \\ 2x + 4y = - 10[/tex]
please find the point of intersection​

Answers

Answer:

They are the same slope

Step-by-step explanation:

When you convert both equations you get y=-[tex]\frac{1}{2\\}[/tex]x-[tex]\frac{5}{2}[/tex]

what does-25=1/3n-10 equal

Answers

Answer:

-45

Step-by-step explanation:

add 10 to -25, then divide 1/3 to that answer, which is -15. and you get -45

Answer: N=-45

Step-by-step explanation: Solve for n by simplifying both sides of the equation, then isolating the variable.

Pleaseeeeee help. Picture attached

Answers

Answer:

Option C

Step-by-step explanation:

Given expression is [tex]y^{-\frac{4}{3}}[/tex].

Exponent of this expression is [tex](-\frac{4}{3})[/tex].

Option (A)

[tex]-\frac{4}{3}y[/tex]

Since, exponents and coefficients of both the expressions are different.

They are not equivalent.

Option (B)

[tex]-(\sqrt[3]{y})^4=-(y^{\frac{1}{3}})^4[/tex]

            [tex]=-y^{\frac{4}{3}}[/tex]

Here, exponent is with positive notation [tex](+\frac{4}{3})[/tex] while in the original expression it is negative [tex](-\frac{4}{3})[/tex].

Therefore, both the expressions are not equivalent.

Option (C)

[tex]\frac{1}{(\sqrt[3]{y})^4}=(\sqrt[3]{y})^{-4}[/tex]

         [tex]=y^{-\frac{4}{3}}[/tex]

Both the expressions are equivalent.

Option (D)

[tex]-(\sqrt[4]{y})^3=-(y)^{\frac{3}{4}}[/tex]

Exponents of both the expressions are different.

Therefore, not equivalent.

Option (E)

[tex]\frac{1}{(\sqrt[4]{x})^3}=(\sqrt[4]{x})^{-3}[/tex]

         [tex]=y^{-\frac{3}{4}}[/tex]

Exponent of this expression is different from the original expression.

Therefore, not equivalent.

Option (C) will be the correct option.


Identify the constant of proportionality

Answers

The answer is #2. 3/2. The dot rises 3 lines and moves to the right 2 lines.

Solve the system of linear equations by substitution. 2x=y−10 x+7=y

Answers

Answer:

(-3, 4)

Step-by-step explanation:

2x = y - 10 (y = x +7) so

2x = x +7 - 10

2x = x -3

x = -3

-3 + 7 = y

4 = y

Step-by-step explanation:

2x = y - 10 and x + 7 = y.

By Substitution,

2x = (x + 7) - 10.

=> 2x = x - 3, x = -3.

Therefore y = (-3) + 7 = 4.

The pair of solutions are x = -3, y = 4.

Please need answers please

Answers

Answer:

13

Step-by-step explanation:

-(-13) = 13

Answer:

13

Step-by-step explanation:

a - times - is a + so there you go I would use photo math if I was you

What is the standard form of 2x2x2x2x2?​

Answers

Answer:

The standard enthalpy of formation is the energy that would be involved if one mole of the substance were to be formed from its elements that were at standard conditions of temperature and pressure which are 25 degrees C and one atm pressure.

Step-by-step explanation:

The standard form of the given expression 2 × 2 × 2 × 2 × 2 is 2⁵.

The expression is given as follows:

2 × 2 × 2 × 2 × 2

When simplifying repeated multiplication of the same number, we use exponents as a concise representation.

The exponent denotes how many times the base is multiplied by itself. In this case, 2 is multiplied five times (2 × 2 × 2 × 2 × 2).

So, it is equal to 2⁵.

In this form, the base (2) is raised to the power of the number of times it is multiplied (5).

Thus, the standard form of 2 × 2 × 2 × 2 × 2 is 2⁵.

Learn more about the standard form here :

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simplify: 45÷3+2×8-12+30​

Answers

[tex] \bold{\underline{Solution}}[/tex]

[tex]{\bold{\underline{\underline{Given}}}}[/tex]

[tex]45÷3+2×8-12+30[/tex]

[tex] {\bold{ \underline{lets \: begin - : }}}[/tex]

Now,

Solve,,

[tex] \small\bold{simpify}[/tex]

[tex]45 \div \: 3 + 2 \times 8 - 12 + 30 \\ \\ = 15 + 16 - 12 + 30 \\ \\ = 15 + 16 - 12 + 30 \\ \\ = 49[/tex]

Division → Multiplication → Addition →Subtraction .

BODMAS stand for

B stand for bracketO stand for ofD stands for divisionM stand for multiplicationA stand for addition addition S stand for subtraction

Answer :

49 is the answer.

Solution :

Using BODMAS rule.

B = Bracket O = Of D = Division M = Multiplication A = AdditionS = Subtraction

First dividing.

>> 45 ÷ 3 + 2 × 8 - 12 + 30

>> 15 + 2 × 8 - 12 + 30

Now multiplying 2 into 8,

>> 15 + 16 - 12 + 30

Adding 15 and 16,

>> 31 - 12 + 30

Now,

>> 19 + 30

>> 49

I NEED HELP PLEASE !!!!

Answers

Answer: de

Step-by-step explanation:

Find the sum.
(12p+ 9) + (4p - 3)
A. 12p+ 6
B. 16p+6
C. 16p+ 12
D. 16p - 6
SUBMIT

Answers

Answer:

B. 16p+6

Step-by-step explanation:

Answer:

B . 16p + 6

Step-by-step explanation:

12p + 9 + 4p -3

collect like terms

(12p + 4p) + (9 - 3)

16p + 6

Which expression is equivalent to
–4(2r)?

Answers

Answer:

is it -8r

Step-by-step explanation:

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Use pi = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answers

Answer:

We can say that volume of cylinder (452.16) is greater than volume of cone (301.44).

Step-by-step explanation:

Diameter of cylinder = 8 inches

Diameter of cone = 8 inches

Height of cylinder = 9 inches

Height of cone = 18 inches

We need to find the relationship between the volume of this cylinder and this cone.

First we will find volume of the cylinder

The formula used is: [tex]Volume=\pi r^2h[/tex]

We have

Diameter of cylinder = 8 inches

Radius = d/2 = 8/2 = 4 inches.

Height of cylinder = 9 inches

Putting values and finding volume

[tex]Volume=\pi r^2h\\Volume=3.14\times (4)^2 \times 9\\Volume=452.16[/tex]

So, Volume of cylinder = 452.16 inches³

Now, we will find volume of the cone

The formula used is: [tex]Volume=\pi r^2\frac{h}{3}[/tex]

We have

Diameter of cone = 8 inches

Radius = d/2 = 8/2 = 4 inches.

Height of cone = 9 inches

Putting values and finding volume

[tex]Volume=\pi r^2\frac{h}{3}\\Volume=3.14 \times (4)^2 \times \frac{18}{3}\\Volume=3.14 \times (4)^2 \times 6\\Volume=301.44[/tex]

So, Volume of cone = 301.44 inches³

Now, comparing volume of both cylinder and cone.

Volume of cylinder = 452.16 inches³

Volume of cone = 301.44 inches³

We can say that volume of cylinder (452.16) is greater than volume of cone (301.44).

What is 1200% as a simplified fraction>

Answers

Answer:

Step 1: Write down the percent divided by 100 like this: 1200% = 1200 / 100. Step 2: Multiply both top and bottom by 10 for every number after the decimal point: As 1200 is an integer, we don't have numbers after the decimal point. So, we just go to step 3.

Answer:

12/1 or 12

Step-by-step explanation:

Are 2(x + 1) and 2x + 1 equivalent expressions? explain.

I’m not in a hurry, take your time.

Answers

Answer:

Yes

Step-by-step explanation:

When you simplify 2(x+1). [MULTIPLY]

It comes 2x+1 so it is equivalent to 2x+1

Yes,  2(x + 1) and 2x + 1 are equivalent algebraic expression.

Given that,
To determine whether the  2(x + 1) and 2x + 1 are equivalent expressions.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let
y = 2 (x + 1) - - - - - -(1)
z = (2x + 1)  - - - - -  (2)

from equation1
y = 2 (x + 1)
using the PEMDAS rule, applying operation on the parenthesis 1st as distributive property,
now,
y = 2x + 1
Since the outcome of the equation is equal to equation 2.

Thus, 2(x + 1) and 2x + 1 are equivalent algebraic expression.

Learn more about simplification here:
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4 The triangles shown are similar. Find y.

Answers

180 degrees is equal to a triangle if we add 111 and 32 degrees it will get 143 degrees so we should subtract 143 from 180 degrees it will get 37

I need help with this question

Answers

Answer:

98 in.^2

Step-by-step explanation:

The lateral area is the sum of the areas of the 3 rectangular sides.

The triangular sides are the bases.

lateral area = 7.2 in. * 5 in. + 3 in. * 5 in. + 9.4 in. * 5 in.

lateral area = 36 in.^2 + 15 in.^2 + 47 in.^2

lateral area = 98 in.^2

square root of 479/90
a question that is hard for me. I dont have my calculator

Answers

Answer:

the answer is 0.24317854031 hope this helps have a nice day please give me brainliest:))

Step-by-step explanation:

Answer:

0.24317854031

Step-by-step explanation:

1. Open your browser

3. Search up: square root of 479/90

4. Copy paste answer

5. Need I say more?

2(−5x+4)+4x−5=-3 i need help

Answers

2(-5x4)×4x-5=-3 its going to be x=1

The population of a city is modeled by the exponential function ƒ (x​) = 689,254 · 2.40.014x​, where x is the number of years after 2000. In what year will the city's population exceed one million?

Answers

Answer:

2036

Step-by-step explanation:

Given the population of a city is modeled by the exponential function

ƒ (x​) = 689,254 · 2.4e^0.014x​, where x is the number of years after 2000

In order to determine the year that the city's population will exceed one million, we will substitute f(x) = 1,000,000 and find x first as shown:

1,000,000 = 689,254  2.4e^0.014x​,

1000000/689,254  = 2.4e^0.014x​,

1.4508 = 2.4e^0.014x​,

1.4508 /2.4 = e^0.014x​,

0.6045 = e^0.014x​,

Apply ln to both sides

ln 0.6045 = lne^0.014x​,

-0.5033 = 0.014x

x = -35.95

Since x cannot be negative, lets say x ≈ 36years

This means that the population will exceed one million after about 36 years. The year it will exceed this amount will be 2000+36 = 2036

Note that the exponential equation used was not correctly written but the same calculation can be employed for any exponential functions you might have.

One equation in a system of equations is y=4x-5 write a second equation to complete the system if the solution to the system is (3,7) PLSSS BE QUICK :))

Answers

Answer:

4y = -x + 31

Step-by-step explanation:

Given that one equation in a system of equations is y = 4x - 5 write a second equation to complete the system if the solution to the system is (3,7)

Since the solution of the system is (3, 7), that means the two lines of equations meet or intersect at point X = 3 and Y = 7

Let assume that the two equations are perpendicular to each other. Then, there slope can be expressed as

M1M2 = -1

Where M1 = 4

Find M2

4M2 = -1

M2 = -1 / 4

Using general linear equation

Y = MX + C

Let's find C by substituting Y, X and M2

7 = -1 /4( 3 ) + C

7 = -3/4 + C

C = 7 + 3/4

C = 31/4

Substitute C back into the equation

Y = -1/4X + 31/4

4y = -x + 31

Therefore, the second equation is

4y = -x + 31

33 POINTS! Find the area of the shape.

Answers

Answer:

The Answer is 41 cm.

Step-by-step explanation:

You have to add each side.

I read it wrong my anwser is wrong

Answer:

103.96

Step-by-step explanation:

justt solved it

3.5
Think About the Process Karen purchased a DVD player on sale. The original selling price was
$175.90. The sale price was $149.62. What is the first step in finding the percent markdown? Find
the percent markdown.

Answers

It doesn’t s 19% I hope this helps bye

PLZ HELP!!!! I HAVE A BAD GRADE IN MATH

Answers

Answer:

me too

Step-by-step explanation:

Answer: i think this question is asking for y=1/3x - 1

Which is the mathematical symbol. HELP ASAP

Answers

Answer:

I would think D

Step-by-step explanation:

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