Find the area of an equilateral triangle with a radius 6 square root of 3. Leave your answer in simplest radical form
Final answer:
The area of the equilateral triangle with a radius of 6√3 is 27√3 square units.
Explanation:
An equilateral triangle has all three sides equal in length and all three angles equal to 60 degrees. In this case, the radius of the circumscribed circle is given as 6√3. This radius is equal to the length of the side of the equilateral triangle.
To find the area of an equilateral triangle, we can use the formula A = (sqrt(3)/4) * s^2, where s is the length of the side of the triangle.
Substituting the given value of the radius into the formula, we have:
A = (sqrt(3)/4) * (6√3)^2 = (sqrt(3)/4) * 108 = 27sqrt(3).
Therefore, the area of the equilateral triangle is 27sqrt(3) square units.
which ratio is proportional to 10/24
A 20/36
B 5/8
C 35/84
D 5/6
Answer:
C 35/84
Step-by-step explanation:
The given ratio is less than 1/2. Only one answer choice is less than 1/2: 35/84.
__
The given ratio reduces to 5/12. The reduced ratios of the answer choices are ...
A 5/9
B 5/8
C 5/12 . . . . your answer
D 5/6
A ball is kicked upward with an initial velocity of 56 feet per second. The ball's height h (in feet) can be expressed as a function of time t (in seconds) by the equation h = -16t2 + 56t. How much time does the ball take to return to the ground?
A) 1.75 seconds
B) 2.50 seconds
C) 2.75 seconds
D) 3.50 seconds
Answer:
D) 3.50 seconds
Step-by-step explanation:
You are interested in the positive value of t such that h=0. Substituting 0 for h, we get ...
0 = -16t^2 +56t
0 = -16t(t -3.5) . . . . . factored form
The product is zero when the factors are zero. Here, the factor of interest is ...
0 = t-3.5
3.5 = t . . . . . add 3.5 to both sides
The ball takes 3.5 seconds to return to the ground.
Final answer:
The ball takes D. 3.5 seconds to return to the ground.
Explanation:
To find the time it takes for the ball to return to the ground, we need to set the height function h equal to 0 and solve for t.
So, we have the equation -16t^2 + 56t = 0.
Factoring out t, we get t(-16t + 56) = 0.
Setting each factor equal to 0, we find that t = 0 or t = 3.5.
Since time cannot be negative, we disregard the t = 0 solution.
Therefore, the ball takes 3.5 seconds to return to the ground.
A five-sided solid has the numbers 1, 2, 3, 4, and 5. What is the probability of rolling two five-sided number solids and getting a sum of either a 3 or an 8?
A. 6/625
B. 9/625
C. 6/25
D. 1/5
Answer:
The answer is D. 1/5 hopefully this helps!
The town of Goodland, Kansas, claims that it has one of the world's largest easels. It holds an enlargement of a van Gogh painting that is 24 feet wide. The original painting is 58 cm wide and 73 cm tall. If the reproduction is similar to the original, what is the height of the reproduction to the nearest foot?
The length of a rectangle is 4 inches less than twice its width. if the area of the rectangle is 70 square inches, what are its dimensions?
Fill in the missing numbers to complete the factorization. Some of the numbers could be negative. Type the numbers in increasing order.
x 3 + 2x 2 - x - 2 = (x +
Answer:
[tex]x^3+2x^2-x-2=(x+1)(x-1)(x+2)[/tex]
Step-by-step explanation:
We have given equation : [tex]x^3+2x^2-x-2=(x+[/tex]
To find : the missing numbers
We have given that missing numbers complete the factorization
so, we find the factors of the given equation
[tex]x^3+2x^2-x-2=0[/tex]
with the help of graph(attached) we find the roots of the equation or you can also take help of hit n trial method.
Roots of the equation are = 1,-1,-2
therefore the factors are (x+1)(x-1)(x+2)
and the missing terms are the factors of the equation = (x+1)(x-1)(x+2)
Answer:
[tex](x-1)>(x+1)>(x+2)[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^3+2x^2-x-2[/tex]
Factorizing the above equation, we get
[tex](x+1)(x^2+x-2)[/tex]
[tex](x+1)(x^2+2x-x-2)[/tex]
[tex](x+1)(x(x+2)-1(x+2))[/tex]
[tex](x+1)(x-1)(x+2)[/tex]
which is the required factorized form of the given equation.
Now, the numbers in increasing order are:
[tex](x-1)>(x+1)>(x+2)[/tex]
At the end of the calendar year, the a/p department creates _____ forms for non-incorporated individuals paid over $600.00
Answer:
The Form 1099-MISC
Step-by-step explanation:
At the end of the calendar year, the a/p department creates 1099 MISC forms for non-incorporated individuals paid over $600.00
The Form 1099-MISC is an IRS tax return document used to give miscellaneous payments made to non employees like contractors etc, during the calendar year. This is recorded when at least $600 in services, rents and other payments are made.
The weight of 8 science books is 28 pounds. what is the weight of 11 science books?
Answer:
Weight of 11 books =38.5 pounds
Step-by-step explanation:
Weight of 8 science book = 28 pounds
Weight of 11 science books = ?
If 8 science books -----------------------28 pounds
then 11 science books ---------------------?
Cross multiplying, we have
Weight of 11 books = (11 * 28)/8
= 308/8
= 38.5 pounds
Liams entire school is traveling by bus to the new aquarium there are 665 boys and 473 girls in liams school if each bus can hold 45 students how many buses will be needed.
The equation √7-x=x 5 has two possible solution.
Answer:
What is the extraneous solution of the equation? Answer: x= -9
What is the true solution of the equation? Answer: x= -2
This is the correct answer.
Hoped this helped!
Someone help me with these problems ASAP
what is 32 percent of 60
one horsepower is equal to how many foot pounds of work per second
in the fraction 3/5 which statement best describes the denominator
Solve for w.
2w=12-4w
Simplify your answer as much as possible.
Solve the equation. (enter your answers as a comma-separated list.)2^−125x = (0.5)^x − 5
What is an equation for the line with slope 2/3 and y-intercept 9?
Answer:
[tex]y=\frac{2}{3}x+9[/tex]
Step-by-step explanation:
We can describe a line using the following equation :
[tex]y=ax+b[/tex]
Where ''a'' and ''b'' are real numbers.
In the equation, the number ''a'' is the slope of the line. If we want a line with slope [tex]\frac{2}{3}[/tex] ⇒
[tex]y=\frac{2}{3}x+b[/tex]
The intersection of a line with the y-axis can be calculated replacing [tex]x=0[/tex] in the equation ⇒
[tex]y=(\frac{2}{3}).(0)+b\\y=b[/tex]
The interception is the real number ''b''. We want that interception to be 9
⇒
[tex]y=\frac{2}{3}x+9[/tex] is the equation of the line with slope [tex]\frac{2}{3}[/tex] and that intersects the y-axis at the point [tex](0,9)[/tex]
How many square feet of outdoor carpet will need for this hole
Answer:
[tex]Area=63 square foot[/tex]
Step-by-step explanation:
The dimensions of the outdoor carpet which is rectangle in shape are:
L=6 ft and w=12 ft.
The dimensions of the indoor carpet that is triangle in shape are:
b=3 ft and h=9 ft.
Now, area of the outdoor= Area of the green region-Area of triangular region
[tex]Area=l{\times}b-\frac{1}{2}{\times}b{\times}h[/tex]
[tex]Area=6(12)-\frac{1}{2}{\times}3{\times}6[/tex]
[tex]Area=72-9[/tex]
[tex]Area=63 square foot[/tex]
Thus, the area of the outdoor carpet is 63 square foot.
Simplify but do not evaluate. 2 to the power of 3 times 2 to the power of 4.
A certain small factory employs 98 workers of these 10 recieve a wage of 150 dollars per day and the rest recieve 85.50 dollars a day to the management a week is equal to 6 working days how much does the factory pay out for each week
Answer:
The factor payout for each week is $54144. Below is the explanation
Step-by-step explanation:
Given:
There are 98 employs
10 of them receive $150 per day
88 of them receive $85.50 per day.
There are 6 working days in a week.
To find:
Let's find the wage per week by multiplying the wage per day by the number of people and the number of days in a week.
10 of them receive $150 per day.
So, they will receive $150*10*6
Which is simplified as $9000.
88 of them receive $85.50 per day
So, they will receive $85.50*88*6
Which is simplified to $45144.
So, the sum of wages for both would be $9000+$45144.
Add them together, which gives $54144.
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Find the midpoint of the following segment created by these pairs of endpoints: (0, 1), (0, 5)
1: (1, 5)
2: (0, 2.5)
3: (0, 3)
4: (5, 1)
Eleven less than a number is more than seventeen in number form
Of the students in ms. dancer's class, 6 walk to school. this represents 30% of her students. how many students are in ms. dancer's class?
What is 2576 divided by 3?
2576 divided by 3 is equal to 859 with a remainder of 2.
Explanation:When dividing 2576 by 3, you can divide each digit individually. Start with the first digit, 2. Since 2 is less than 3, you can't divide it evenly, so you move to the next digit. The next digit is 5. With 5, you can divide it evenly by 3, which gives you 1. Now, subtract 3 from 5, which gives you 2. Bring down the next digit, which is 7. The new dividend is 27. Divide 27 by 3, which gives you 9 with no remainder. Finally, bring down the last digit, which is 6. The new dividend is 26. Divide 26 by 3, which gives you 8 with a remainder of 2. So, 2576 divided by 3 is equal to 859 with a remainder of 2.
Sarah's age is five less than twice her sister's age. Sarah is fifteen years old.
Which equation could you use to solve for the age of Sarah's sister?
2x - 5 = 15
2(15) - 5 = x
15 = 5 - 2x
15 - 5 = 2x
Robyn opened a bank account to save her birthday money. it was paying 3.75% interest. then the interest rate went up by 0.65%. how much is her new interest rate?
the height of a football in the air t seconds after it is thrown can be modeled by the function y=-16t^2+96t+3, where y are measured in feet and t is time. What is the maximum height that the football reaches? How long did it take the football to reach the maximum height? At what times will the football be above the ground at 122 feet?
The maximum height the football reaches is 147 feet, and it takes 3 seconds for the football to reach that height. To determine when the football is above 122 feet, the equation is set equal to 122 and solved for time t.
To find the maximum height reached by the football, we need to determine the vertex of the parabolic function given by y = -[tex]16t^2[/tex] + 96t + 3. Since the coefficient of [tex]t^2[/tex]is negative, the parabola opens downwards, and the vertex will give us the maximum height.
To find the time at which the maximum height occurs, use the formula t = -b/2a, where a is the coefficient of [tex]t^2[/tex] and b is the coefficient of t.
In this equation, a = -16 and b = 96, so t = -96/(2 x -16) = 3 seconds. Plugging this back into the original equation gives us the maximum height: y = -16[tex](3)^2[/tex] + 96(3) + 3 = 147 feet.
To determine when the football is above 122 feet, we set the equation equal to 122 and solve for t:
122 = -[tex]16t^2[/tex] + 96t + 3. We simplify and solve the quadratic equation, which may yield two possible times, one during the ascent and one during the descent of the football's path.
The population of a town increases at the rate of 1% each year. today the town’s population is 8,500. what will the population be in five years?
Population of the town after 5 years = 8933.59.
What is Population growth rate?Population growth rate is defined as the change in the size of the population with respect to the time.
The growth rate is usually written as the ratio of the annual increase or decrease in population to the entire population of that year.
The formula for finding the future population is,
P(F) = P(R) [ 1 + r]ⁿ , where
P(F) = Future population
P(R) = Present population
r = Growth rate
n = Number of years
From the question, we have
P(R) = 8500, r = 1% = 0.01 and n = 5
Substituting these values in the main equation,
P(F) = 8500 [ 1 + 0.01 ]⁵
P(F) = 8500 × 1.01⁵
P(F) = 8933.59
Hence, the population of the town after 5 years if the rate of increase in population is 1% = 8933.59
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Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
According to the given information, quadrilateral RECT is a rectangle.
By the definition of a rectangle, all four angles measure 90°.
Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the Converse of the Same-Side Interior Angles Theorem.
Quadrilateral RECT is then a parallelogram by definition of a parallelogram.
Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent.
Therefore, one can say that segment ER is congruent to segment CT.
Segment TR is congruent to itself by the Reflexive Property of Equality.
The _______________ says triangle ERT is congruent to triangle CTR.
And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.