Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x= y=

Answer:

Step-by-step explanation:

Discount =$7000-$4900

Discount% =

[tex] \frac{2100}{7000} \times 100 \\ = \frac{210000}{7000 } \\ = \frac{210}{7} = 30[/tex]

Answer:

324π in²

Step-by-step explanation:

The surface area of a sphere = 4πr² ( r is the radius )

Calculate r using the volume (V) formula

V = [tex]\frac{4}{3}[/tex]πr³

Here V = 972π , thus

[tex]\frac{4}{3}[/tex]πr³ = 972π ( divide both sides by π )

[tex]\frac{4}{3}[/tex]r³ = 972 ( multiply both sides by 3 to clear the fraction )

4r³ = 2916 ( divide both sides by 4 )

r³ = 729 ( take the cube root of both sides )

r = [tex]\sqrt[3]{729}[/tex] = 9

Thus

surface area = 4π × 9² = 4π × 81 = 324π in²

Answer:

son

Step-by-step explanation:

son-sin

Answer:

Step-by-step explanation:

PART A:  2x^5 + 3x^2-3

It is a fifth degree polynomial because, the highest degree is 5 and it is in the standard form since, the polynomial is written in descending order i.e, from highest degree to the least

part B:

Closure property is  applicable to the subtraction of polynomials.

for example 2x^4+2x^2-5 is a polynomial and 2x^3+2x+2 is also a polynomial.

if we subtract these two polynomials, the outcome

2x^4-2x^3+2x^2-2x-7 is also a polynomial

Step-by-step explanation:

The fifth degree polynomial

x^5 + x^4 +3x²+4x+9

the three terms 3x², 4x and 9 are forming a second degree polynomial written in standard form

since it has this form :  ax²+bx+c

The closure property for real numbers means that the sum oe the substraction of two real numbers  

The substraction of two polynomials is a polynom using the closure property

Here is an example :

calculate the substraction

The result is a polynomial

Answer:

C

Step-by-step explanation:

x+4> 8

Subtract 4 from each side

x+4-4>8-4

x > 4

Open circle at 4, line going to the right

━━━━━━━☆☆━━━━━━━

▹ Answer

[tex]Solved - x > 4\\Graphed - C[/tex]

▹ Step-by-Step Explanation

x + 4 > 8

x > 8 -4

x > 4

When graphing inequalities, you have less than, greater than, less than or equal to, and greater than or equal too. When graphing an inequality with less than or greater than, you use an open circle. When graphing an inequality with less than or equal too or greater than or equal too, you used a closed circle.

Since the numbers are positive, we are going to move up the number line therefore leaving us with the answer of C.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

(x+2.4)^2+(y+4.8)^2=2025

If you'd like additional help with math or another subject, check out growthinyouth.org!

Step-by-step explanation:

Answer:

His homework isn't finished.

Step-by-step explanation:

As in this sentence: "If the trash is taken out, and Theodore is watching television, then he has finished his homework.". It says that if trash is taken out, then Theodore has not finished his homework He has just taken out the trash.

Answer:b his homework isnt finished

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Since 3^6 is only divisible by 3 and powers of 3(including 1) the gcd of 3^6 and 6^3 mus be a power of 3 hence we need to find the highest powers of 3 that divide 6^3 and that divide 3^6, which are respectively 3^3 and 3^6, hence, taking the smaller one (since we want it to divide both), our answer is 3^3=27.

Answer:

Step-by-step explanation:

Greatest common divisor is the largest positive integer that divides each integer in the given problem

6³ = (2* 3)³ = 2³ * 3³

3⁶ = 3³ * 3³

Greatest common divisor = 3³ = 3* 3* 3 = 27

Answer:

Increases

Step-by-step explanation:

It increases because, the greater the value of x the smaller the fraction is. If x was 25 the fraction would be 5/25 this makes the value of the equation 5.2. Now if x was a smaller positive number like 5. Then the fraction would be 5/5 which would cause the equation to be equal to 6.

Answer:

∠ T ≈ 23.6°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin T = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{SU}{ST}[/tex] = [tex]\frac{4}{10}[/tex] , thus

∠ T = [tex]sin^{-1}[/tex] ([tex]\frac{4}{10}[/tex] ) ≈ 23.6° ( to the nearest tenth )

Answer:

Step-by-step explanation:

The common difference (d) can be found using the first and 4th terms:

  a1 = 3

  a4 = a1 +d(4 -1)

  -9 = 3 +3d . . . . . simplify

  -3 = 1 + d . . . . . . divide by 3

  -4 = d . . . . . . . . . subtract 1

Then ...

  x = a1 + d = 3 -4 = -1

  y = x + d = -1 -4 = -5

The values of x and y are -1 and -5, respectively.

Answer: 2 minutes

Step-by-step explanation:

Given the following :

Plane A's descent :

y = -2,500x + 14,000

Plane B's Ascent :

y = 4,000x + 1,000

where y = altitude x = minute

Time to be at the same altitude :

Being at the same altitude means ;

Plane A's descent = Plane B's Ascent

-2,500x + 14,000 = 4,000x + 1,000

-2500x - 4000x = 1000 - 14000

-6500x = - 13000

x = 13000 / 6500

x = 2

x = 2minutes.

Do you know the adjustments for the graph to show the intersecting lines.

In general and here, when we have an object with a constant cross section of area A, the volume V = A L, where L is the length.

L = V / A = 330 / 55 = 6 cm

Answer: 6 cm

Answer:

[tex]\dfrac{-3}{5}[/tex]

Step-by-step explanation:

It is given that a terminal ray that passes through the point (4,-3).

x = 4

y = -3

Using Pythagoras theorem, the value of hypotenuse is

[tex]r=\sqrt{x^2+y^2}[/tex]  

[tex]r=\sqrt{(-3)^2+(4)^2}[/tex]  

[tex]r=\sqrt{9+16}[/tex]  

[tex]r=\sqrt{25}[/tex]  

[tex]r=5[/tex]

We, know that

[tex]\sin \theta = \dfrac{y}{r}[/tex]

[tex]\sin \theta = \dfrac{-3}{5}[/tex]

Therefore, the value of [tex]\sin \theta[/tex] is [tex]\dfrac{-3}{5}[/tex].

Answer:

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

because a number is always greater than, equal to, or less than another number

======================================================

Work Shown:

A = area of trapezoid RSTU

A = height*(base1+base2)/2

A = ST*(UT+RS)/2

A = 14*(5+10)/2

A = 105 square cm

-----------------------

B = area of rectangle PQWV

B = length*width

B = WV*PV

B = 7*2.5

B = 17.5 square cm

If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.

-----------------------

C = total shaded area

C = A + B

C = 105 + 17.5

C = 122.5

Answer:

Step-by-step explanation:

[tex](x + 2)(x - 3)[/tex]

Multiply each term in the first parentheses by each term in the second parentheses ( FOIL)

[tex]x(x - 3) + 2(x - 3)[/tex]

Calculate the product

[tex] {x}^{2} - 3x + 2x - 6[/tex]

Collect like terms

[tex] {x}^{2} - x - 6[/tex]

Hope this helps..

Best regards!

Answer:

Step-by-step explanation:

Given, (x+2) (x-3)

Multiply every term

(x)(x) + (2)(x) + (-3)(x) + (-3)(2)

x^2 + 2x - 3x -6

x^2 - x -6

HOPE IT HELPS :)

GOOD LUCK WITH YOUR ASSIGNMENT!

Answer:

OPtion B)

Step-by-step explanation:

Answer: Choice C)

y < (-1/5)x + 1

The boundary line is y = (-1/5)x+1 as it goes through the points shown. The boundary line is dashed or dotted, meaning that points on this boundary line are not in the solution set. So we will not have an "or equal to" as part of the inequality sign. More specifically, the inequality sign is "less than" because we shade below the boundary line. So that's how we end up with y < (-1/5)x+1.

Answer:

Rs. 924000.

Step-by-step explanation:

Cost of  house = 765000

Additional money spent on it = 115000

Total cost incurred by Ravi = 765000 + 115000 = 880000

Gain  = 5% of total cost

gain in Rs = 5/100 * 880000 = Rs. 44000

Total selling price of house = total cost incurred + profit = 880000+ 44000

Total selling price of house = Rs. 924000

Thus, Ravi got  Rs. 924000.

Answer:

x = 6.6

Step-by-step explanation:

Data obtained from the question include the following:

Angle X = 15°

Angle Y° = 23°

Side y = 10

Side x =..?

The value of side x can be obtained by using the sine rule as shown below:

x/Sine X = y/Sine Y

x/Sine 15 = 10/Sine 23

Cross multiply

x × Sine 23 = 10 × Sine 15

Divide both side by Sine 23

x = (10 × Sine 15) / Sine 23

x = 6.6

Therefore, the value of x is 6.6.

Answer: 1/2

Step-by-step explanation:

solving bracket first we get

2 - 9/6

multiplying and dividing 2 by 6 we get

12/6 - 9/6

=3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

(6-4)-9/6

= (2)-9/6

= 12/6-9/6

= 3/6

= 1/2

Answer:

[tex]2\sqrt{33}[/tex].

Step-by-step explanation:

This triangle is a 30-60-90 triangle. That means that the hypotenuse is double the length of the smaller side.

Since the smaller side measures [tex]\sqrt{33}[/tex], the hypotenuse is [tex]2\sqrt{33}[/tex].

Hope this helps!

Answer:

96

Step-by-step explanation:

3*6=18*2=36

6*10=60*2=120

10*3=30*2=60

36+60+120=

216

Answer: 216 m

Step-by-step explanation:

2(10 x 6) = 120

2(6 x 3) = 36

2(10 x 3) = 60

120 + 36 + 60 = 216

Answer:

70

Step-by-step explanation:

An easy way to do this is to simply take 360(the sum) and divide it by 5(the number of numbers) to get 72.  Thus, 72 is the middle number and the numbers are:

72

72,72,73

70,71,72,73,74

The smallest of these numbers is 70

Hope it helps <3

Hello!

Answer:

70 is the smallest number.

Step-by-step explanation:

If the sum of 5 consecutive numbers is 360, we can solve for the smallest number algebraically:

Let 'x' represent the smallest number:

and (x + 1), (x + 2), (x + 3), and (x+4) represent the other consecutive numbers:

x + (x + 1) + (x + 2) + (x + 3) + (x+ 4) = 360

Combine like terms:

5x + 10 = 360

Subtract 10 from both sides:

5x = 350

Divide both sides by 5:

x = 70. This is the smallest of the consecutive numbers.

We can check our work:

70 + 71 + 72 + 73 + 74 = 360.

Hope this helped!

Hey there! I'm happy to help!

The slope is the steepness or incline of a line. From a graph, it is known as the rise over the run between two integer values. If you have a point at (1,1) and a point at (2,2), the rise (vertical difference) between them in 1 unit, and the run (horizontal difference) is 1 unit. 1/1 is 1, so the slope of a line that passes through these points is 1. This means that for every one unit to the right it goes, it goes one unit up.

The intercepts are where the line hits the x and y axes. By looking at a graph, you can find the y-intercept by seeing on what y-value the line intersects with the y-axis, and for the x-intercept you do so with the x-axis.

The slope-intercept equation is y=mx+b. This b is the y-intercept. To find the x-intercept, you plug in the value 0 for y and solve for x. This is because the x-axis is the line y=0, so you will see where the x is if y is equal to 0.

Linear equations and functions can be written in slope intercept form (y=mx+b), standard form (Ax+By=C), and point slope form [tex]y-y_{1} =m(x-x_{1} )[/tex].

They can be graphed by finding the y and x intercepts from the equation and then connecting the points to draw the line!

Have a wonderful day! :D

Answer:

D. twice v

Step-by-step explanation:

2v

This is 2 times v or twice v

Answer:

44°

Step-by-step explanation:

The secant- secant angle y is half the difference of the measure of its intercepted arcs, that is

[tex]\frac{1}{2}[/tex](BHF - CGJ ) = y , that is

[tex]\frac{1}{2}[/tex](156 - CGH) = 56° ( multiply both sides by 2 )

156 - CGH = 112° , thus

CGH = 156° - 112° = 44°

Answer:

Yes, this function can be defined by linear model.

Step-by-step explanation:

[tex]\mathrm{Total\:=\:Fixed\:Fee\:+\:Hourly\:Rate\:\times Number\:of\:hours}[/tex]

[tex]\mathrm{Linear:}\:\:T=\:$25+30h[/tex]

Best Regards!

Answer:

The lengths 14, 24, and 26 cannot be the sides of a right triangle.  The lengths 30, 72, 78 can be the sides of a right triangle.

Step-by-step explanation:

To prove that the lengths 14, 24, and 26 cannot be the sides of a right triangle:

a=14, b=24, c=26

Pythagoreon theorem: a^2+b^2=c^2

substitute values in: 14^2+24^2=26^2

simplify: 196+576=676

simplify again: 772=676, which is not true

This proves that the lengths 14, 24, and 26 cannot be the sides of a right triangle.

To prove that the lengths 30, 72, and 78 can be the sides of a right triangle:

a=30, b=72, c=78

Pythagoreon theorem: a^2+b^2=c^2

substitute values in: 30^2+72^2=78^2

simplify: 900+5184=6084

simplify again: 6084=6084, which is true

This proves that the lengths 30, 72, and 78 can be the sides of a right triangle.

Answer:

true, true, false,false,  false,true,true,false

See explanations below

Step-by-step explanation:

If three sides can make a RIGHT triangle, then the sum of squares of the two shorter sides EQUALS the square of the third side, using the Pythatorean theorem.

Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements?

The lengths 14, 24 and 26 cannot be sides of a right triangle.

TRUE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 can be sides of a right triangle.

TRUE, A^2+B^2-C^2= 0

The lengths 14, 24 and 26 can be sides of a right triangle.

FALSE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 cannot be sides of a right triangle.

FALSE, A^2+B^2-C^2= 0

The lengths 14, 24 and 26 can be sides of a right triangle.

FALSE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 can be sides of a right triangle.

TRUE, A^2+B^2-C^2= 0

The lengths 14, 24 and 26 cannot be sides of a right triangle.

TRUE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 cannot be sides of a right triangle.

FALSE, A^2+B^2-C^2= 0

Answer:

True

Step-by-step explanation:

Real Numbers are just numbers like:

1 12.38 −0.8625  34  π (pi) 198

In fact:

Nearly any number you can think of is a Real Number

Real Numbers include:

yes   Whole Numbers (like 0, 1, 2, 3, 4, etc)

yes   Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc )

yes   Irrational Numbers (like π, √2, etc )

Real Numbers can also be positive, negative or zero.

So ... what is NOT a Real Number?

not   Imaginary Numbers like √−1 (the square root of minus 1)

are not Real Numbers

not   Infinity is not a Real Number

Mathematicians also play with some special numbers that aren't Real Numbers.

Real numbers can be represented on a number line.