Answer:
The answer is
y = 6
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.
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.
name the property used in each equation. then find the value of n.
2.) 1·n=8
3.) 28·n=0
4.) 0+n=22
5.) 1/4·n=1
Someone help me with these problems ASAP
graph the fraction 1/2 on the number line.
the number of equally sized spaces needed between 0 and 1 is ?
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!
in the fraction 3/5 which statement best describes the denominator
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]
What are the coordinates of the vertex for f(x) = 2x^2 + 4x + 9?
(−2, 4)
(−1, 7)
(1, 15)
(2, 9)
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
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?
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?
one horsepower is equal to how many foot pounds of work per second
Which transformations map the strip pattern onto itself
Answer: a horizontal translation and a 180 rotation
Step-by-step explanation:
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.
Which term describes a rate in which the second quantity is 1?
unit rate
percent
proportion
ratio
Hillary wants to go on the latin club trip to italy it cost 2730 for the trip the trip is 30 weeks away and she wants to make equal weekly payments how much money altogether does hillary need to pay at the end of week eight
A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x + 162 square inches.
Which could be the dimensions of the rectangular piece of cloth when it is unfolded? Remember, the area of a rectangle can be determined using the formula A = lw.
we need to factor the expression
[tex] x^{2} + 27x + 162 [/tex]
Equate to zero the expression
[tex] x^{2} + 27x + 162=0 [/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex] x^{2} + 27x =-162 [/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex] x^{2} + 27x +182.25=-162+182.25 [/tex]
[tex] x^{2} + 27x +182.25=20.25 [/tex]
Rewrite as perfect squares
[tex] (x+13.5)^{2}=20.25 [/tex]
[tex] (x+13.5)=(+/-)4.5 [/tex]
[tex] x1=-13.5+4.5= -9 [/tex]
[tex] x2=-13.5-4.5= -18 [/tex]
Hence
[tex] x^{2} + 27x + 162 =(x+9)*(x+18) [/tex]
Remember that the area of the rectangle is equal to
[tex] A=L*W [/tex]
therefore
the answer is
the dimensions of the rectangular piece of cloth could be
[tex] L=(x+18)\ inches\\ W=(x+9)\ inches [/tex]
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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Simplify but do not evaluate. 2 to the power of 3 times 2 to the power of 4.
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
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!
Solve the equation. (enter your answers as a comma-separated list.)2^−125x = (0.5)^x − 5
what is 32 percent of 60
The function p(t) represents the value of a new car t years after it was manufactured.
p(t)=24,525(0.94)^t
What does the value 0.94 represent in this situation?
The value of the car increases by 94% each year.
The value of the car decreases by 94% each year.
The value of the car is 0.94 times the value of the car the previous year.
The initial value of the car is 0.94.
Answer:
The value of the car is 0.94 times the value of the car the previous year.
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.
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?
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.
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]
Eleven less than a number is more than seventeen in number form