Snooker is a kind of pool or billiards played on a 6-foot-by-12-foot table. the side pockets are halfway down the rails (longside)
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6
Find the distance, to the nearest tenth of an inch, diagonally across from the corner pocket to side pocket ...?
1. Use the function described below to answer questions 1 - 4.
Yvonne invested $4,000 in a savings account which pays 3.5% interest compounded annually. Use the formula A = P(1 + r)t, where P is the principal, r is the interest rate, and t is the time in years.
What is the percent of increase as a decimal? Do not round.
2. Approximately, how much money will Yvonne have in 4 years? Round to the nearest cent.
3. Approximately, how much money will Yvonne have in 8 years? Round to the nearest cent.
4. Approximately, how many years will it take for Yvonne to double her money? Write the number of years only.
5. Alex buys a top of the line computer. He did not realize that the computer would lose value so fast. If his computer cost $1800.00 and it depreciates at a rate of 45% each year, in how many years will it be worth less than 1/3 of what he paid for it?
Find the perimeter of △ABC with vertices A(−4, 3), B(1, −5), and C(−4, −5). Round your answer to the nearest hundredth.
What fraction is £1 of 13p?
.
Are the two triangles below similar?
Triangles ABC and DEF are shown. Angle A measure 30 degrees, angle C measure 65 degrees, side AC measures 14, side AB measures
Yes, because there are two pairs of congruent corresponding angles
No, because there are not two pairs of congruent corresponding angles
Yes, because the corresponding sides are proportional
No, because the corresponding sides are not proportional
Answer:
The correct answer is A. Yes, because there are two pairs of congruent corresponding angles.
Step-by-step explanation:
This is because to prove that two triangles are congruent, you need at least two pairs of corresponding angles.
Also, the degrees 30, 65, and 85 is equal to 180 degrees.
Hope this helps!
Find a solution with theta in radians (of possible)
1. tan(theta)
3. 3cos(theta)
5. tan(5(theta)+7
...?
If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
The maximum volume of the box is:
1000 cm³
Step-by-step explanation:Let x be the length of the square base
and h be the height(h) of the box.
As we know that the length(l) and width(w) of the box is same( since the base is in the shape of square)
As we know that the surface area of box is given by:
[tex]Surface\ Area=2(lw+wh+hl)\\\\\\i.e.\\\\\\Surface\ Area=2(x^2+xh+xh)\\\\\\Surface\ Area=2(x^2+2hx)[/tex]
We are given surface area of box=600 cm²
Hence,
[tex]2(x^2+2hx)=600\\\\i.e.\\\\x^2+2xh=300\\\\i.e.\\\\h=\dfrac{150}{x}-\dfrac{x}{2}[/tex]
The volume of box is given by:
[tex]Volume(V)=l\times w\times h\\\\\\Volume=x^2h\\\\\\Volume=x^2(\dfrac{150}{x}-\dfrac{x}{2})[/tex]
Hence,
[tex]V=150x-\dfrac{x^3}{2}[/tex]
Now, for maxima or minima we have derivative equal to zero.
[tex]i.e.\\\\\\\dfrac{dV}{dx}=0\\\\\\i.e.\\\\\dfrac{d}{dx}(150x-\dfrac{x^3}{2})=0\\\\\\i.e.\\\\\\150-\dfrac{3x^2}{2}=0\\\\\\i.e.\\\\\\150=\dfrac{3}{2}x^2\\\\\\x^2=100\\\\\\i.e.\\\\\\x=\pm 10[/tex]
Now,
[tex]\dfrac{d^2V}{dx^2}=\dfrac{-6x}{2}\\\\\\=-3x[/tex]
Now, as we know if for a given x
[tex]\dfrac{d^2V}{dx^2}<0[/tex]
then that x is a point of maxima.
Hence, when we put x=10 we get: [tex]\dfrac{d^2V}{dx^2}<0[/tex]
Hence, x=10 is a point of maxima
Also, the value of V at x=10 is:
[tex]V=150\times 10-\dfrac{(10)^3}{2}\\\\\\V=1500-\dfrac{1000}{2}\\\\\\V=1500-500\\\\V=1000\ cubic\ cm.[/tex]
Hence, the maximum volume of the box is:
1000 cm³
How many points are used to define a plane?
A. zero
B. one
C. two
D. three
Answer:
it will be D
Step-by-step explanation:
Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use?
If ΔABC and ΔGEF are congruent by the ASA criterion, which pair of angles must be congruent?
Answer:
it should be CAB and GEF
Step-by-step explanation
A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. What is the measure of the angle subtended by the arc?
What is the explicit rule for this geometric sequence? 2, 6, 18, 54, …
Answer:
A term at position n can be expressed as \[2*3^{n-1}\]
Step-by-step explanation:
The given geometric sequence is 2, 6, 18, 54, …
Starting term = 2
Second term = 6
So second term is 3 times the first term.
Similarly, Third term = 18
This is 3 times the second term, that is , 3 * 6
Fourth term is is 54.
This is 3 times the third term, that is , 3 * 18
Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]
where n represents the position of the term in the sequence.
Solve for the indicated variable
A= bh/2, solve for b
Answer:
b = 2A/have a nice day :)
The required simplified solution for b for the given expression is b=2A/h.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
A = bh/2
Isolate the variable B, and multiply both sides by 2/h,
2A/h = b
So
b = 2A/h
Thus, the required simplified solution for b for the given expression is b=2A/h.
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Which of the following statements describes the absolute value of a number "a"?
A) The opposite value of a number "a" can be represented by the absolute value of a number "a."
B) Given |a|, "a" is always positive
C) The distance from the number "a" to 0 on a number line can be represented by the absolute value of a number "a."
D) The positive value of a negative number "a" can be represented by the absolute value of a number "a."
Oscar needs to ship 14 rock cds, 12 classical cds, and 8 pop cds. he can only pack only one type of cd in each box and he must pack the same number of cds in each box. what is the greatest number of cds oscar can pack in each box?
Answer:
2
Step-by-step explanation:
Oscar needs to pack only one type of cd in each box and he must pack the same number of cd's in each box.
To solve this problem we would need to find the greatest common factor of the numbers given; the numbers that we have are 14, 12, 8.
First we are going to find the factors of all these three numbers:
14 = 1 x 2 x 7
12 = 1 x 2 x 2 x 3
8 = 1 x 2 x 2 x 2
The common factors of these three numbers are bolded:
14 = 1 x 2 x 7
12 = 1 x 2 x 2 x 3
8 = 1 x 2 x 2 x 2
We can see that the common factors are 1 and 2. The biggest of them is 2.
Therefore, the greatest number of cd's Oscar can pack in each box is 2
Since 2 is common to them all, hence the greatest number of cds oscar can pack in each box is 2 CDs
Given the number of cars needed to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs
In order to get the greatest number of cds oscar can pack in each box, we will have to calculate the GCF of each value as shown:
The prime factors of each value is as shown
14 = 2 * 7
12 = 3 * 2 * 2
8 = 2 * 2 * 2
From the factors, we can see that only 2 is common to them all, hence the greatest number of CDs oscar can pack in each box is 2 CDs
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Two numbers are in a ratio of 3:6 their sum is 63 find the bigger number
To find the bigger number in the given ratio of 3:6 with a sum of 63, simplify the ratio to 1:2, assign a variable to the smaller number, and solve for the larger one. The bigger number is found to be 42.
Explanation:To find the bigger number when two numbers are in a ratio of 3:6 and their sum is 63, first simplify the ratio to its lowest terms. The ratio 3:6 simplifies to 1:2, since both terms can be divided by 3. Let's assign the variable x to the smaller number, which corresponds to the '1' part of the ratio. Therefore, the bigger number is twice the smaller one, so it can be represented as 2x.
The sum of the two numbers is given by the equation x + 2x = 63. Combine like terms to get 3x = 63. Dividing both sides by 3 gives x = 21. Since 2x represents the bigger number, we have 2x = 2 imes 21 = 42.
Hence, the bigger number in this ratio is 42.
PLEASE HELP ASAP!!!!!!!!!!
Use the table below to answer this question:
x y
0
2
1
−1
2
−6
Find the average rate of change for the given function from x = 0 to x = 2.
2
4
−4
1
how to find the hypotnuse
Final answer:
To find the hypotenuse of a right triangle, apply the Pythagorean theorem: a² + b² = c². After squaring the lengths of the two other sides and adding them together, take the square root of the sum to get the length of the hypotenuse, which is approximately 10.3 units in the example provided.
Explanation:
To find the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be written as the equation a² + b² = c². To solve for the hypotenuse, you would rearrange the equation to c = √(a² + b²).
For example, if the legs of a right triangle measure 9 and 5 units:
First, square both of the leg lengths: 9² = 81 and 5² = 25.Add these two values together: 81 + 25 = 106.Take the square root of the sum: √106 ≈ 10.3 units.Thus, the hypotenuse would measure approximately 10.3 units, where we use three significant figures for precision in measurement.
how many 5/6s are in 3 and 1/3
How many x-intercepts are there in y = –3x2 + 4x + 4
If BC bisects the angle ACD, then B is the midpoint of AD.
A. True
B. False
Answer:
It’s true
Step-by-step explanation: just took the test
Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?
9 is 35 percent of what number
HELP ME- 15 points
Jaycee is writing a coordinate proof to show that the diagonals of a rectangle bisect each other. She starts by assigning coordinates to a rectangle. Then she uses these coordinates to write the coordinates of the midpoint of each diagonal. She finds that the midpoints of the diagonals have the same coordinates, so the diagonals must bisect each other.
What are the coordinates of the midpoint of the diagonals of the rectangle?
Enter expressions in the box for the coordinates of the midpoint.
(__,__)
The coordinates of the midpoint of the diagonals of a rectangle are found by averaging the x-coordinates and the y-coordinates of the endpoints of the diagonals. Because of the properties of a rectangle, the midpoint will be the same for both diagonals, confirming that the diagonals bisect each other. The midpoint's coordinates are ((x1+x2)/2, (y1+y2)/2).
Explanation:To find the coordinates of the midpoint of the diagonals of a rectangle, you must first know the coordinates of the rectangle's vertices. Suppose the rectangle has vertices at (x1, y1), (x1, y2), (x2, y1), and (x2, y2). Without loss of generality, let (x1, y1) and (x2, y2) be the endpoints of one diagonal and (x1, y2) and (x2, y1) be the endpoints of the other diagonal.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found by averaging each of the x-coordinates and the y-coordinates of the endpoints. Thus, the midpoint M1 has coordinates ((x1+x2)/2, (y1+y2)/2). Similarly, the midpoint M2 for the other diagonal has coordinates ((x1+x2)/2, (y2+y1)/2). Because of the properties of a rectangle, these midpoints will be the same, confirming that the diagonals bisect each other.
Therefore, the coordinates of the midpoint of the diagonals of a rectangle are ((x1+x2)/2, (y1+y2)/2).
24 plus something =120÷3
15 POINTS. Find the total area (in terms of K) of the prism. Place "K" last in your formula.
T.A. =
Please tell me what to put in the blanks, how the question asks
AB = BC
Angle BDC = 37½°
CBD =
Answer:
[tex]\angle CBD=105^{\circ}[/tex]
Step-by-step explanation:
We have been given a diagram. We are asked to find the measure of angle CBD using given diagram.
We can see that in triangle ABD two angles measure 60 degree. Using angle sum property of triangle, we can find measure of triangle angle ADB as:
[tex]\angle A+\angle B+\angle D=180^{\circ}[/tex]
[tex]60^{\circ}+60^{\circ}+\angle D=180^{\circ}[/tex]
[tex]120^{\circ}+\angle D=180^{\circ}[/tex]
[tex]120^{\circ}-120^{\circ}+\angle D=180^{\circ}-120^{\circ}[/tex]
[tex]\angle D=60^{\circ}[/tex]
Since all angles of triangle ABD are equal, so it is an equilateral triangle and its all sides will have same measure.
[tex]AB=BD=AD[/tex]
We have been given segment AB is equal to segment BC. Now, we will get:
[tex]AB=BD=AD=BC[/tex]
In triangle BCD sides two sides (BD and BC) are equal, so it is an isosceles triangle.
We know that angles corresponding to equal sides of an isosceles triangle have equal measure, so measure of angle BDC will be equal to angle BCD.
[tex]\angle BDC=\angle BCD=37\frac{1}{2}^{\circ}[/tex]
Now, we will use angle property of triangle to find measure of angle CBD as:
[tex]\angle CBD+\angle BCD+\angle BDC=180^{\circ}[/tex]
[tex]\angle CBD+37\frac{1}{2}^{\circ}+37\frac{1}{2}^{\circ}=180^{\circ}[/tex]
[tex]\angle CBD+\frac{75}{2}^{\circ}+\frac{75}{2}^{\circ}=180^{\circ}[/tex]
[tex]\angle CBD+\frac{150}{2}^{\circ}=180^{\circ}[/tex]
[tex]\angle CBD+\frac{150}{2}^{\circ}-\frac{150}{2}^{\circ}=180^{\circ}-\frac{150}{2}^{\circ}[/tex]
[tex]\angle CBD=\frac{360}{2}^{\circ}-\frac{150}{2}^{\circ}[/tex]
[tex]\angle CBD=\frac{210}{2}^{\circ}[/tex]
[tex]\angle CBD=105^{\circ}[/tex]
Therefore, the measure of angle CBD is 105 degrees.
The leather of marshalls rectangular poster is 2 times its width. if the perimeter is 24 inches, what is the area of the poster
A circular walkimg path has a diameter of 45 yards. what is the circunference of the walking path
steve has 276 slides in carousels. each carousel holds 75 slides. how many carousels will be completely filled?
Steve can completely fill 3 carousels with his 276 slides as each carousel holds up to 75 slides.
Explanation:Based on the provided data, Steve has 276 slides and each carousel holds up to 75 slides. To find out how many carousels can be completely filled, we have to divide the total number of slides by the number that each carousel holds.
So, the calculation would be: 276 (total slides) divided by 75 (slides each carousel can hold).
276 ÷ 75 equals about 3.68. Since we cannot have a fraction of a carousel, we round the number down to the nearest whole number. Hence, Steve can completely fill 3 carousels with his slides.
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