(Picture for problem above.)

Find the value of y. Be sure to keep the exact value (use square root and don’t round your answer).

(Picture For Problem Above.)Find The Value Of Y. Be Sure To Keep The Exact Value (use Square Root And

Answers

Answer 1

Answer:

y = 8·√3

Step-by-step explanation:

From the drawing of the right triangle, we have;

The length of the opposite leg to the given 60° (reference) angle = 12

The length of the adjacent leg to given 60° (reference) angle = x

The length of the hypotenuse side = y

By trigonometric ratios, we have;

[tex]sin(Reference \, Angle) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]

Therefore, we have;

[tex]sin(60^\circ) = \dfrac{12}{y}[/tex]

From the value of sin(60°), we have;

[tex]sin(60^\circ) = \dfrac{\sqrt{3} }{2}[/tex]

[tex]\therefore y= \dfrac{12}{sin(60^\circ) } = \dfrac{12}{\dfrac{\sqrt{3} }{2} } = \dfrac{2 \times 12 \times \sqrt{3} }{{{3} } } = \dfrac{24 \times \sqrt{3} }{{{3} } } = 8 \cdot \sqrt{3}[/tex]

y = 8·√3

[tex]\left(x= \dfrac{12}{tan(60^\circ) } = \dfrac{12}{{\sqrt{3} } } = 4\cdot \sqrt{3} \right)[/tex]


Related Questions

what is the perimeter of figure B ?

Answers

Answer:

35 for perimeter of b

122.5 for perimeter of a

Step-by-step explanation:

To find the perimeter, you add all of the values of the outside of the shape together. Since 12+9+9+5 = 35, the answer is 35.

Okay, so what you have to do is set up a proportion for a to b. To do that, you have to have a fraction where a is the numerator and b is the denominator. 7/2 equals x/35. Then cross multiply

7*35 = 2x

x = 122.5 :)

Answer:

The perimeter is 35.

Step-by-step explanation:

To find perimeter, add all the sides together.

9 + 9 + 5 + 12 = 35

The perimeter is 35.

For all values of x,
f(x) = 2x - 3
and
g(x) = x2 + 1
a) Find fg(x).
Simplify and give your answer in the form ax2 + b
b) Find gf(x).
Simplify and give your answer in the form ax2 + bx + c
I DONT NEED THE ANSWER TO A, I JUST NEED B

Answers

Answer:

The composition g(f(x)) is:

[tex]g(f(x))=4x^{2}-12x+10[/tex]

Step-by-step explanation:

b) g(f(x)) is a function composition.

So we will have:

[tex]g(f(x))=(f(x))^{2}+1[/tex]

[tex]g(f(x))=(2x-3)^{2}+1[/tex]

[tex]g(f(x))=4x^{2}-12x+9+1[/tex]

[tex]g(f(x))=4x^{2}-12x+10[/tex]

Here:

a is 4

b is -12

c is 10

I hope it helps you!

use the following values for x {-1 ,0 , 1 , 2 } for the function f{x} = 4x+3 to make a function table

please help me , and thanks

Answers

Answer:

f(x)= -1

f(x)= 3

f(x)= 7

f(x)= 11

Step-by-step explanation:

You need to add the values of x into the function

f(x)= 4(-1) + 3

f(x)= 4(0) + 3

f(x)= 4(1) + 3

f(x)= 4(2) + 3

The square root of 5 , has a decimal expansion that does not end or repeat. To which set of numbers does it belong?

A. rational
B. Natural
C. Integer
D. Irrational

Answers

Answer:

Irrational numbers is correct.

The required square root of 5 is an irrational number.

Given that,
The square root of 5, has a decimal expansion that does not end or repeat. To which set of numbers does it belong is to be determined.

What is a rational number?

In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.

What are irrational numbers?

An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.

Here,
√5 = 2.2360679775..
Which is an irrational number.

Thus, the required square root of 5 is an irrational number.

Learn more about rational numbers here:

https://brainly.com/question/17450097

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Amy is dressing a mannequin for a store window to show off a
new line of men's clothing. Amy can choose from 4 different T-
shirts and 2 styles of jeans. How many different ways can Amy
dress the mannequin?

Answers

Answer:

8

Step-by-step explanation:

4 different shirts would be 4 combinations. You can have one of each of the jeans on the mannequin, giving 4x2=8.

Answer:

8

Step-by-step explanation:

Rewrite the number in standard notation.
8 times 10 ^8

Answers

Answer:

80

Step-by-step explanation:

8 times 10 equals 80

8*10 = 80

Answer:

800000000

Step-by-step explanation:

multiple 8 by 10^8 or 100000000

Sugar Rounds Donut Shop offers 2 free donuts with every 20 purchased donuts. Sweet Delights Donut Shop offers 3 free donuts with every 30 purchased donuts. Which donut shop offers a greater ratio of free donuts to purchased donuts?

Answers

Answer:

there the same ratio because there both offering the same ratio of of there number

3x10=30 ratio : 10

2x10=20 ratio: 10

Step-by-step explanation:

LOOK AT PIC PLS THX!! I WILL TRY TO GIVE BRAINLIEST TO RIGHT ANSWRR

Answers

Answer:

240 ounces

Step-by-step explanation:

y'know you could just look this up lol

Answer:

240 oz

Multiply pounds by 16

15 × 16 = 240

Rewrite using a single positive exponent.
8
.8
-3

Answers

Answer: .8
Explanation: I hope this helps you !

2+5.67890654321678-5432

Answers

-5,424.3 ...............

Use this number line to help you answer the question. What is the opposite of 4? 30 points

Answers

Answer:

The opposite of 4 is -4

Step-by-step explanation:

Hope this helps.

the owner of a food cart sells an average or 120 frozen treats per day during the summer ​

Answers

Answer:

uhhh ok

Step-by-step explanation:

The straight line y = 3x +2 intersects the curve y = 2x^2 + 7x-11 at two points. Find the coordinates of these two points Give your answers correct to 2 decimal places.

Answers

Given:

The equation are

[tex]y=3x+2[/tex]

[tex]y=2x^2+7x-11[/tex]

To find:

The coordinates of intersection points.

Solution:

We have,

[tex]y=3x+2[/tex]          ...(i)

[tex]y=2x^2+7x-11[/tex]           ...(ii)

From (i) and (ii), we get

[tex]3x+2=2x^2+7x-11[/tex]

[tex]0=2x^2+7x-11-3x-2[/tex]

[tex]0=2x^2+4x-13[/tex]

If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then by quadratic formula:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

In the equation [tex]0=2x^2+4x-13[/tex], we have [tex]a=2,b=4,c=-13[/tex].

Using quadratic formula, we get

[tex]x=\dfrac{-4\pm \sqrt{4^2-4(2)(-13)}}{2(2)}[/tex]

[tex]x=\dfrac{-4\pm \sqrt{16+104}}{4}[/tex]

[tex]x=\dfrac{-4\pm \sqrt{120}}{4}[/tex]

Now,

[tex]x=\dfrac{-4+\sqrt{120}}{4}[/tex] and [tex]x=\dfrac{-4-\sqrt{120}}{4}[/tex]

[tex]x=1.7386[/tex] and [tex]x=-3.7386[/tex]

[tex]x\approx 1.74[/tex] and [tex]x\approx -3.74[/tex]

Putting x=1.74 in (i), we get

[tex]y=3(1.74)+2[/tex]

[tex]y=5.22+2[/tex]

[tex]y=7.22[/tex]

Putting x=-3.74 in (i), we get

[tex]y=3(-3.74)+2[/tex]

[tex]y=-11.22+2[/tex]

[tex]y=-9.22[/tex]

Therefore, the coordinates of the intersection points are (1.74, 7.22) and (-3.74,-9.22).

two angles of a quadrilateral are 67 and 100. what is the sum of the other two angles

Answers

Answer:

93

Step-by-step explanation:

can someone help i have several questions like this i also need the work shown

Answers

Answer:

x = 8

Step-by-step explanation:

Create the expression:

10(x + 10) = 9(9 + 11)

Do PEMDAS (Parenthesis):

10(x + 10) = 9(20)

Do PEMDAS (Multiplication):

10x + 100 = 180

Cancel out:

10x + 100 = 180

        -100   -100

10x = 80

Simpilfy:

x = 8

PLS HELP DUE AT MIDNIGHT

Answers

60yooooooooooooooooooooo

Answer:

m<BDC = 60 degrees

Step-by-step explanation:

m<EBD is 120, m<EBC = 180 (it's a straight angle) so m<DBC = 180-120= 60 degrees.

All angles in a triangle add up to 180. 60+60+x=180. 180-120=x=60.

Calculate the geometric mean of 12 and 20

Answers

Answer:

The Geometric mean of two numbers is the square root of their product.

Given numbers are 12,20.

Geometric mean = √(12*20)

= √240.

= 15.49.

= 15.5.

The geometric mean of 12 and 20 is 4√15.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 3 + 3x + 4y = 7 is an expression.

We have,

The geometric mean of a and b is √(ab).

Now,

a = 12 and b = 20

so,

The geometric mean of 12 and 20.

= √(12 x 20)

= √240

= 4√15

Thus,

The geometric mean of 12 and 20 is 4√15.

Learn more about expressions here:

https://brainly.com/question/3118662

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Connor invested $8,000 in an account paying an interest rate of 82% compounded
monthly. Henry invested $8,000 in an account paying an interest rate of 8 %
compounded daily. After 5 years, how much more money would Henry have in his
account than Connor, to the nearest dollar?

Answers

Answer:

Connor would have $83.37 more than Henry.

Step-by-step explanation:

Connor:

Initial investment= $8,000

Interest rate= 8.2% = 0.082/12= 0.00683

Number of periods= 12*5= 60 months

Henry:

Initial investment= $8,000

Interest rate= 8% = 0.08/365= 0.00022

Number of periods= 365*5= 1,825 days

To calculate the future value, we need to use the following formula on each investment:

FV= PV*(1+i)^n

Connor:

FV= 8,000*(1.00683^60)

FV= $12,035.35

Henry:

FV= 8,000*(1.00022^1,825)

FV= $11,951.98

Difference= 12,035.35 - 11,951.98= $83.37

Connor would have $83.37 more than Henry.

1.
Find the value of x in the parallelogram below.
*
65
Enter each line of work as an equation.

Answers

Answer:

x+65=180(being cointerior angle)

x=180-65

x=115

sos please help how to do this

Answers

Answer:

±√7

Step-by-step explanation:

[tex]3 {x}^{2} + 7 = 28 \\ 3 {x}^{2} = 21 \\ {x}^{2} = 7 \\ x = \sqrt{7} [/tex]

A kg sugar cost $1.40 a kg of socks cost $0.55 what is the total price of two KG of sugar and two KG of salt

Answers

One kg of sugar = $1.40 so two kg of sugar equals $1.40 + $1.40 = $2.80

One kg of salt cost $0.55, so two kg of salt costs $0.55 + $0.55 = $1.10

To find the total price, add the cost of 2kg of sugar plus 2kg of salt together.

Total price = $2.80 + $1.10
Total price = $3.90

What is the function
X
- 1
0
1
2
3
у
-1
-0.5
0
0.5
1
The table represents
a linear function.
Write the function.
y=

Answers

Answer:

Step-by-step explanation:

x                y               Difference (d)

-1              -1                       -

0             -0.5             -0.5 - (-1) = 0.5

1                 0               0 - (-0.5) = 0.5

2              0.5              0.5 - 0 = 0.5

3                1                 1 - 0.5 = 0.5

There is a common difference (d) = 0.5

Therefore, table represents a linear function.

Let the equation of the linear function is,

y = mx + b

Here, m = Slope and b = y-intercept

Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Two points from the given table are (-1, -1) and (0, -0.5)

m = [tex]\frac{-0.5-(-1)}{0-(-1)}[/tex]

m = 0.5

Y-intercept of the line 'b' = -0.5 (Value of y at x = 0)

Therefore, equation of the line will be,

y = 0.5x - 0.5


Please help me find the value of x in the rectangle ABCD

Answers

Answer:

x = 52

Step-by-step explanation:

Hello there!

All of the angles in a rectangle are right angles

if a right angle has a measure of 90 degrees then we can find x by subtracting the given angle from 90

90 - 38 = 52 so we can conclude that x= 52

Step-by-step explanation:

Each angle in a quadrilateral is 90⁰ therefore 38⁰+x=90⁰

hence x=90⁰-38⁰ which gives you 52⁰

pleaseee help meeee i need help

Answers

Answer:

[tex] \boxed{ \boxed{{x}^{2n- 1} . {y}^{2n - 1} }}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:law of exponentPEMDAStips and formulas:[tex] \frac{ {x}^{m} }{ {x}^{n} } < = > {x}^{m - n} [/tex]let's solve:[tex] \sf use \: the \: formula : \\ \tt \frac{ {x}^{2n + 4}. {y}^{4n} }{ {x}^{5} . {y}^{2n + 1} } \\ \tt {x}^{2n + 4 - 5} . {y}^{4n - 2x - 1} [/tex][tex] \sf simplify \: subtraction : \\ \tt {x}^{2n- 1} . {y}^{2n - 1} [/tex]

Solve 56 > -7x
Thank you!

Answers

Answer:

-8 > x

Step-by-step explanation:

56 divided by -7 = -8

-8 > x

make sure to double check before turning it in!

help me pls i need you guys help

Answers

Dont open that link bro its a bot

How to prove this using trig identities?
(Tan B + Cot B)^2 = sec^2B + csc^2B

Thanks and please shows steps. I will vote best answer and helpful and do more.

Answers

Step-by-step explanation:

tanB + cotB = (sinB)/(cosB) + (cosB)/(sinB)

 

                      = (sin2B + cos2B)/[(cosB)(sinB)]

 

                       = 1/[(cosB)(sinB)]

 

                        = (1/cosB)(1/sinB)

 

                        = (secB)(cscB)

The value of 3° is
its from the chapter exponenets

Answers

Answer:

1

Step-by-step explanation:

=>. the value of 3° = 1

=> it is known to us that any number to the

power zero is equals to 1

hope it helps

Can someone pleade help me on this question 8

Answers

It’s d because it is

2 24-5what is 24 - 2x wanted to 24 - 5 exponent ​

Answers

Answer:

24-5:x2

Step-by-step explanation:

im not sure

mark brainliest if it helps

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