find x and y for a triangle with 60° and 30​

Hello!

The answer is: 17 ft.

Explanation:

To find this out, just divide the perimeter, and the amount of sides in a triangle, which is 3. This will only work with equilateral triangles because an equilateral triangle has all three sides the same length. Anyway, divide 51 and 3. (51 / 3 = 17) Just to make sure, you can add three 17's together, 17 + 17 + 17 = 51, the perimeter.

I hope this helped! ~Q

The length of one of side of Equilateral Triangle is 17 feet, whose perimeter is 51 feet.

An equilateral triangle's perimeter is the sum of its three sides. P = 3a.

'a' is the side of equilateral triangle.

Given that:

Perimeter of Equilateral Triangle = 51 feet

where 'a' is the side of equilateral Triangle.

As we know that all side of equilateral triangle are equal.

So, its all sides measure 'a'.

Perimeter = a +a +a

51= 3a

a= 51/3

a=17 feet.

Hence, the side of equilateral triangle measures 17 feet.

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Answer:

$4440

Step-by-step explanation:

From the question, the annual cost of the plan is $14800

The employer pays 70% 0f the cost.

⇒70/100 ×14800 =$10360

Remaining amount to pay=

14800-10360=$4440

Answer: 15+X=27

Step-by-step explanation: 15+X=27 X Represents How Much More Is Added

Answer:

-1

Step-by-step explanation:

The midline is the average of the maximum and minum.

0.5 = (y + 2) / 2

1 = y + 2

y = -1

The minimum is at y=-1.

For the given problem the value of ymin is -1.

Suppose maximum is denoted by ymax and minimum is denoted by ymin ymid represents the mid.

By mid point theorem y

mid   = (ymax + ymin)/2

Given ymid  = 0.5

         ymax  = 2

          ymin  = y

substituing values 0.5 = (2+ y)/21 = 2+yy = -1

yminimum  = -1

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Final answer:

Miryam Williams' total pay is $3,237.50.

Explanation:

To calculate Miryam Williams' total pay, we first need to calculate her commission.

Her commission is 3.5% of her total sales, which is $92,500.

Commission = 3.5% × $92,500 = $3,237.50.

Next, we need to determine if Miryam's commission exceeds $5,000.

Since her commission is $3,237.50, it does not exceed $5,000. Therefore, she does not receive the $500 bonus.

Finally, to calculate her total pay, we sum her commission and the bonus (which is $0 in this case).

Total Pay = Commission + Bonus = $3,237.50 + $0 = $3,237.50.

To find the roots of the quadratic equation -10x^2 + 12x - 9 = 0, we can use the quadratic formula:
x = \frac{-b ± \sqrt{b^2 - 4ac}}{2a}
where
a is the coefficient of x^2, which is -10,
b is the coefficient of x, which is 12,
c is the constant term, which is -9.
First, let's identify the coefficients in our equation:
a = -10
b = 12
c = -9
Next, we will calculate the discriminant (Δ) using the formula:
Δ = b^2 - 4ac
Plug in the values of a, b, and c:
Δ = (12)^2 - 4*(-10)*(-9)
Δ = 144 - 4 * 10 * 9
Δ = 144 - 360
Δ = -216
Since the discriminant is negative, the quadratic equation has two complex roots. We will still use the quadratic formula to find them:
x = \frac{-b ± \sqrt{Δ}}{2a}
Substitute b, Δ, and a into the formula:
x = \frac{-12 ± \sqrt{-216}}{2 * (-10)}
Now, let's split the square root of the negative discriminant into real and imaginary parts:
√(-216) = √(216) * √(-1) = 14.697 * i
where i is the imaginary unit such that i^2 = -1. Substituting this into our quadratic formula gives:
x = \frac{-12 ± 14.697i}{-20}
Now, divide both the real and imaginary parts by -20:
x₁ = \frac{-12}{-20} + \frac{14.697i}{-20}
x₂ = \frac{-12}{-20} - \frac{14.697i}{-20}
Simplify those equations:
x₁ = \frac{12}{20} - \frac{14.697i}{20}
x₂ = \frac{12}{20} + \frac{14.697i}{20}
Further simplify by reducing the fractions:
x₁ = 0.6 - 0.73485i
x₂ = 0.6 + 0.73485i
Therefore, the roots of the quadratic equation -10x^2 + 12x - 9 = 0 are approximately x₁ = 0.6 - 0.73485i and x₂ = 0.6 + 0.73485i.

12%*14000*3

Which is 5040

Therefore, it will have to pay back $4050

J.T. will pay back a total of $18,480 altogether.

To calculate the total amount J.T. will pay back, we can use the formula for simple interest:

[tex]\[I = P \times r \times t\][/tex]

Where:

- (I) = Interest

- (P\) = Principal amount (the initial loan amount)

- (r) = Annual interest rate (in decimal form)

- (t) = Time (in years)

Given that J.T. borrows $14,000 at an annual interest rate of 12% for 3 years, we can plug these values into the formula:

[tex][I = 14000 \times 0.12 \times 3\][/tex]

[I = 5040]

So, the total interest J.T. will pay is $5,040.

To find the total amount J.T. will pay back, we add the interest to the principal:

[Total amount = Principal + Interest]

[Total amount = 14000 + 5040]

[Total amount = 18440]

Therefore, J.T. will pay back a total of $18,480 altogether.

In summary, by using the formula for simple interest, we determined the interest amount J.T. will pay over the 3-year period, and then added it to the principal amount to find the total repayment amount.

Complete question:

A bank offers a home improvement loan with simple interest at an annual rate of 12%. J.T. borrows an amount of $14,000 to pay back over 3 years. How much will he pay back altogether? Explain how you found the total amount.

Answer:

C - 2 2/9

Step-by-step explanation:

7 1 /2 x + 3 2/ 3 = −13

Subtract 3 2/3 from each side

7 1 /2 x + 3 2/ 3 - 3 2/3 = −13 - 3 2/3

7 1/2x = -16 2/3

Change each mixed number to an improper fraction

7 1/2 = (2*7 +1)/2 = 15/2

16 2/3 = (3*16+2)/3 = 50/3

15/2 x = -50/3

Multiply each side by 2/15 to isolate x

2/15 * 15/2 x = -50/3 * 2/15

x = -100/45

Simplify

x = -20/9

Change back to a mixed number

9 goes into 20 2 times with 2 left over

x = -2 2/9

Answer:

Here, the given expression is,

  ( By the cross multiplication ),

Since, an extraneous solution is a solution, which is emerged by solving the equation but it does not satisfying the equation,

But for x = -3, the equation  follows,

⇒ x = -3 is the non-extraneous,

⇒ The given equation has only one solution x = -3 which is non-extraneous.

Step-by-step explanation:

Answer:

x = -3 is not extraneous solution.

Step-by-step explanation:

[tex]\frac{6}{x-3} =\frac{3}{x}\\Cross\,\, Multiply\\6x =3(x-3)\\6x = 3x-9\\6x-3x=-9\\3x= -9\\x=-9/3\\x=-3[/tex]

An extraneous solution is the solution that is obtained by solving the question given but does not satisfy the original equation.

In our case x = -3

Putting value back to the original equation

[tex]\frac{6}{x-3} =\frac{3}{x}\\\frac{6}{-3-3} =\frac{3}{-3}\\\frac{6}{-6} =-1\\-1=-1[/tex]

Since our original equation is satisfied so,

x = -3 is not extraneous solution.

There will be a second image that will be showing the answer

Answer:

x = -1

Step-by-step explanation:

[tex] x^2 + 2x + 5 = 4 [/tex]

Subtract the constant term.

[tex] x^2 + 2x = -1 [/tex]

Add half of the coefficient of the x-term to complete the square.

[tex] x^2 + 2x + 1 = -1 + 1 [/tex]

[tex] (x + 1)^2 = 0 [/tex]

[tex] x + 1 = 0 [/tex]

[tex] x = -1 [/tex]

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

distance between the points given from the statement:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+( y_{2}-y_{1})^{2}} \\\\d=\sqrt{(-6-0)^{2}+(-3-4)^{2}}\\ \\d=\sqrt{36+49}\\\\d=\sqrt{85}[/tex]

Answer:

Step-by-step explanation:

In a normal equation, y=mx+b, the constant of variation is the thing that "constantly" "varies" and in other words changes the same. This is the slope. In the equation, the slope is m.

-4y=8x

y=-2x

The constant of variation, aka slope, is -2

Answer: Then you should pay her 4$ one hour

Step-by-step explanation:

Employees who earn increased commissions as their sales increase are paid a progressive commission. This method incentivizes employees to work harder to sell more, as their commission rate increases with sales volume.

Employees whose rate of commission increases as their sales increase are paid a progressive commission. With this method of remuneration, the more sales an employee makes, the higher their rate of commission becomes. This strategy is popular with both economists and the general public because it effectively incentivizes employees to work harder and achieve higher sales, leading to an increase in the overall performance of the business.

For example, a salesperson may earn a 10% commission on sales up to $10,000. However, any sales beyond that might attract a 15% commission rate, encouraging the employee to sell more. Such progressive commission schemes are common in sales-driven industries like real estate and retail.

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Answer: [tex]x=2[/tex]

Step-by-step explanation:

The equation for inverse variation is:

[tex]x=\frac{k}{y}[/tex]

Where "k" is the constant of variation.

If you solve for for the constant "k", you get the form:

[tex]k=xy[/tex]

So, if [tex]xy=2[/tex] then [tex]k=2[/tex]

Knowing the value of "k", you can find the value of "x" when [tex]y=1[/tex], by substituting these values into the equation [tex]x=\frac{k}{y}[/tex].

Therefore, you get that the value of "x" when [tex]y=1[/tex] is:

[tex]x=\frac{2}{1}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

Answer:

x = - 3 with multiplicity 2

Step-by-step explanation:

f(x) = (x - 3)(x + 3)(x + 3) = (x - 3)(x + 3)²

Equating each factor to zero and solving for x

x - 3 = 0 ⇒ x = 3 with multiplicity 1

x + 3 = 0 ⇒ x = - 3

x + 3 = 0 ⇒ x = -3

Thus x = - 3 has multiplicity of 2

The fact that the factor is squared gives the multiplicity

(x + 3)³ has root - 3 of multiplicity 3

Answer:

The Correct answer is: 1/3

Step-by-step explanation:

x = 2, y = 3

(4x + 1) / 3y²

(4*2 + 1) / 3*3²

(8 + 1) / (3*9)

9 / 27

= 1/3

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3y + 2x = 1 into this form

Subtract 2x from both sides

3y = - 2x + 1 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex] → A

By rearranging the equation 3y + 2x = 1 into slope-intercept form, y = mx + b, we find that the slope of the line is -2/3. The correct answer is A.) -2/3.

The slope of the line whose equation is 3y + 2x = 1 is found by solving for y to get the line into slope-intercept form, which is y = mx + b, where m represents the slope.

Now that the equation is in slope-intercept form, we can see that the slope m is -2/3. Therefore, the correct answer is A.) -2/3.

Answer:

$24

Step-by-step explanation:

What you do is you just times 84 x 2/7 to get your answer.

84 x 2/7=$24 is your answer.

Answer:

$24

Step-by-step explanation:

To find out how much he spent on the shoes, take the amount of money he has and multiply by the fraction he spent on shoes

84 * 2/7

168/7

24

He spent 24 dollars on new shoes

Answer:

I think its C im not sure but thats what i got

Sorry If its wrong

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The inscribed angle ∠CAD is half the central angle ∠CBD.  Therefore:

35° = 1/2 ∠CBD

∠CBD = 70°

The area of a sector is:

A = (θ/360) πr²

Since r = 10:

A = (70/360) π(10)²

A = 7000π/360

A = 175π/9

Answer is B.

Answer:

1.  mean

2. mode

3. range

4. measures of central tendency

5. outliers

6. median

good luck

Step-by-step explanation:

Answer:

Mean

Mode

Range

Measures of Central Tendency

Outliers

Median

Step-by-step explanation:

Just did the USTP got a 100%

Answer:

85°

Step-by-step explanation:

Since you know that the overall angle measure for the whole shape is 540°, you can subtract the known angles measures to find the right one.

540-90

450-90

360-115

245-160

85

Answer:

C) horizontal compression and reflection across the y-axis

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The original equation is:

f(x) = 2x

The new equation is:

f(-5x) = 2(-5x)

f(-5x) = -10*x

The answer is

C) horizontal compression and reflection across the y-axis

Answer:

Step-by-step explanation: first, find y by itself by adding 2x to the other side then diving by the 5y to get y=2/5x +2! Rise 2, run 5 from your start at positive 2 on the graph and you should get line a!!!

The graph of the equation -2x + 5y = 10 has a positive slope of 2/5 and a y-intercept of 2. None of the provided options accurately describe the graph of the equation, as they indicate incorrect y-intercept values and describe the slope incorrectly.

To find which line is a graph of the equation -2x + 5y = 10, we need to identify the slope and the y-intercept of the line. To do this, we should rearrange the equation into slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept.

Rearranging the equation, we get:

5y = 2x + 10

y = (2/5)x + 2

The slope is the coefficient of x, which is 2/5, and the y-intercept is the constant term, which is 2. The line has a positive slope, and based on the slope-intercept form, it rises on the graph as the x-value increases. Therefore, option d with a positive slope and a y-intercept of 50 must have a typo since our y-intercept is 2. The correct interpretation would be that the line gradually moves upward on the graph as the x-value increases, thanks to its positive slope.

Hence, none of the provided options describe the graph of the equation -2x + 5y = 10 accurately because the y-intercept should be 2, not 50, and the slope is positive. Keep in mind that a positive slope results in an upward, not a downward, trend as x increases.

Final answer:

The conference rooms can accommodate approximately 34 attendees each, and the ballrooms can accommodate approximately 31 attendees each.

Explanation:

To find out how many attendees each room can accommodate, we need to divide the total number of attendees by the total number of rooms.

For the quarterly meeting, there are 2 conference rooms and 5 ballrooms, which can seat a total of 238 attendees. To find out how many attendees each room can accommodate, we divide 238 by 7 (2 + 5), which gives us approximately 34 attendees per room.

For the safety training event, there are 4 conference rooms and 5 ballrooms, which can seat a total of 286 attendees. Dividing 286 by 9 (4 + 5) gives us approximately 31 attendees per room.

Answer: 48

Step-by-step explanation: All you are doing is substituting x and y with the numbers it gives u then u just solve. 2 to the 4th power is 16. 4 to the 3rd power is 64 and then times .5 gives u 32. then u add and get 16+32=48

Answer:

C

Step-by-step explanation:

Quadratic model is shaped like a "U", or a parabola

Quartic model is shaped like a "W", highest degree is 4 (x^4).

Linear model is a line.

Cubic model is x^3, shaped like a curvy snake.

Looking at the graph, it clearly shows a line. So, linear model is the answer.

C is the correct answer.

Answer:

The solution to the equation 1/4 x = 5 is '' x = 20''

Step-by-step explanation:

you take ''1/4'' and multiply it by ''20'' and the answer you'll get is ''5''

The solution to the equation 1 / 4 x = 5 is found by isolating x. After multiplying both sides of the equation by 4, you find that x = 20.

The solution to your equation, 1 / 4 x = 5, can be found using the principles of algebra. This equation is asking us 'What value of x can I multiply by 1/4 to equal 5?'

The best way to find the solution is to isolate x on one side of the equation. In this case, you'll start by multiplying both sides of the equation by 4. Now your equation looks like this:

1/4 x * 4 = 5 * 4

Simplifying the equation, you'll get:

x = 20

Therefore, you can see that the solution to the equation 1/4 x = 5 is x = 20.

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Answer: x=5, y=15

Step-by-step explanation:

x= cost of a chair

y= cost of a table

The cost of each table and of each chair is x=5, y=15.

We have given that,

Five tables and eight chairs cost $115 three tables and five chairs cost $70.

Determine the cost of each table and of each chair.

A variable cost is a corporate expense that changes in proportion to how much a company produces or sells.

x= cost of a chair

y= cost of a table

Therefore, The cost of each table and of each chair is x=5, y=15.

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Using Pythagorean theorem, for the 8-feet wide picture window to pass through the 3-feet wide door, the door must be at least approximately 7.4 feet tall.

The picture window here is a rectangular sheet of glass. The longer side (8 feet) must fit through the door. The door is only 3 feet wide, which means that the 8-foot side of the window must be angled to pass through the door in vertical orientation.

To calculate the height of the door needed, consider the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of two sides (a2 + b2 = c2). Here 'a' is the width of the door (3 feet) and 'c' is the diagonal length of the window (8 feet). Solving for 'b' which represents the door's required height, we get:

b2 = c2 - a2

b2 = 82 - 32

b = sqrt(64 - 9) = sqrt(55)

Therefore, b is approximately 7.4 feet.

So the door must be at least 7.4 feet tall to pass the 8-feet picture window through it when angled vertically.

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The door needs to be approximately 21.3 feet tall for the glass to pass through.

To determine the height of the door, we need to consider that the glass is 8 feet wide. Since the door is only 3 feet wide, the glass needs to fit through a smaller opening. We can use similar triangles to find the height of the door. Let's set up a proportion:

8 / 3 = H / 8

Cross-multiplying, we get:

3H = 64

H = 64/3

Therefore, the door needs to be approximately 21.3 feet tall for the glass to pass through.

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There are 64 possible

Answer:

12

Step-by-step explanation:

3 questions times 4 answers equals 12 possible choices,

(4+4+4)