Answer:
Step-by-step explanation:
Comment
The first thing you should notice once you have read it, is there is a plus sign required. That means you are likely to get a binomial (two different things that won't reduce or combined).
So what you get is
18*g + 5
Notice where the place sign is. It is between 18g and 5. The result cannot be simplified any further.
Answer
18g + 5
please help me this has to be just a fake question 98 points
[tex] \frac{7}{4} - 9 \div .08 + \frac{4}{5} - 7 \times .8[/tex]
Let's try solving the problem using the order of operations method, otherwise known as PEMDAS.
[tex]\begin{tabular}{c | l}Order of Operation & Required Operation \\\cline{1-2}1 & Parentheses () \\2 & Exponents e^{x} \\3 & Multiplication \times \\4 & Division \div \\5 & Addition + \\6 & Subtraction -\end{tabular}[/tex]
We are given this question :
[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 7 \times .8}[/tex]
Since there are no parentheses or exponents, let's multiply.
[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 5.6}[/tex]
The next step is to divide.
[tex]\mathrm {\frac{7}{4} - 112.5 + \frac{4}{5} - 5.6}[/tex]
After that, add.
[tex]\mathrm {\frac{7}{4} - 112.5 + 0.8 - 5.6}[/tex]
[tex]\mathrm {\frac{7}{4} - 111.7 - 5.6}[/tex]
Finally, subtract the remaining terms.
[tex]\mathrm {1.75 - 111.7 - 5.6}[/tex]
[tex]\mathrm {-109.95 - 5.6}[/tex]
[tex]\mathrm {-115.55}[/tex]
The final answer is -115.55.
I hope this helped solve the problem.
Good luck on your studies!
Answer:
-115.55
Step-by-step explanation:
7/4 -9÷ .08 + 4/5 -7 * .8
I would change fractions to decimals
1.75 - 9 ÷ .08 +.8 -7 * .8
Now using pemdas, multiply and divide from left to right
1.75 -112.5 +.8 -7 * .8
1.75 -112.5 +.8 -5.6
Now add and subtract from left to right
-110.75+.8 -5.6
-109.95-5.6
-115.55
Mya has ballet lessons every sixth day and swimming lessons every fourth day. Today she has both lessons. In how many days will Mya have both lessons on the same day again?
Mya would have both lessons on the same day again on the 12th day.
In how many days would they have the classes on the same day again?In order to determine when they would have the both lessons on the same day, the common multiple of 6 and 4 has to be determined. A multiple of a number is the product of an integer and that number. A common multiple is the multiple that is common to two or more numbers.
Multiple of 6 = 6, 12, 28, 24, 30, 36,
Multiple of 4 = 4, 8, 12, 16, 20, 24, 28
Common multiple = 12
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HELPPPPP: An ipod cost $200. Ivy is going to save money for the ipod by babysitting for $15 per week. Ivy already has $32 saved. Write an inequality that can be used to find the minimum number of weeks Ivy must babysit to earn enough to buy an ipod.
To form an equation from a word problem, we can recognize variables and operations from keywords.
Solving the QuestionLet the number of weeks be a.
We're given:
Goal amount is $200 at minimumMoney earned is $15aCurrent amount is $32Because $200 is the minimum account required, we know that the amount earned must be greater than or equal to 200.
[tex]200\leq[/tex]
Our current savings and money can be calculated by adding 15a and 32:
[tex]200\leq15a+32[/tex]
Answer[tex]200\leq15a+32[/tex]
Bernie owns Bernie’s Bike Shop and is advertising his company by
taking his logo and placing it around town on different sized signs. After creating a few signs, he
noticed a relationship between the amount of ink he needs for his logo and the size of the sign.
1. The table below represents some of the signs Bernie has created and the relationship
between the amount of ink needed versus the size of the sign. Complete the information
below to help Bernie see this relationship
From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:
f(x) = x²Domain = 2, 3, 4, 15 and x.Range = 4, 9, 16, 225 and x².What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.
By critically observing the table (see attachment), we can logically deduce that relationship between the amount of ink and the size of the sign is modeled by this function:
f(x) = x²
From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:
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A rotating sprinkler head sprays water as far as 20 feet. the head is set to cover a central angle of . what area of grass will be watered?
The area of the grass that will be watered is given by 800/9 pi ft^2.
What is the area of a circle?
Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, etc. Area of Circle = πr2 or πd2/4, square units. where π = 22/7 or 3.14.The area of a circle of radius r is given by:
A = πr²
In this problem, a rotating sprinkler head sprays water as far as 20 feet, hence the radius is of r = 20 ft.
It covers a central angle of 80º, while an entire circle has 360º, hence the area of grass that will be watered corresponds to 80/360 = 2/9 of the area of the circle.
Hence the watered area in ft² is given by-
A = 2/9 π × (20)²
= 800π/ 9
Therefore, the area of the grass that will be watered is given by 800/9 pi ft^2.
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What is NOT another name for Q?
A. line LQ←→
B. line RG←→
C. line LG←→
D. line RL←→
The line that is not another name for Q is RL
How to determine the line that is not another name for Q?For a line to represent the point Q, the following must be true:
The line must start from any pointAnd the line must go through point QUsing the above highlights,
The line LQ starts from L and extends through QThe line RG starts from R and extends through QThe line LG starts from L and extends through QThe line RL starts from R and does not extend through QHence, the line that is not another name for Q is RL
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factor this:
18x^2+39x-15
Steps for Factoring:
1) Find CM (common factor) for the expression: 3
Factor out 3 =>
[tex]3(6x^{2}+13x-5)[/tex]
2)Factor the above expression by grouping:
The expression needs to be written as [tex]6x^{2} + ax+ bx -5[/tex]
a and b should add up to 13 and multiply up to -30 (6 × -5)
By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)
3) Now we can rewrite [tex](6x^{2}+13x-5)[/tex] as [tex](6x^{2} -2x)+(15x-5)\\[/tex]
Factor out 2x in the first group and 5 in the second group:
[tex]2x(3x-1)+5(3x-1)\\[/tex]
As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)
(3x-1) (2x+5)
The answer is 3(3x-1) (2x+5)
Hope it helps!
2. Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary
f(x)=-0.5x+2
g(x)=x³-5x² + 3
The points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
How to solve the system of equations?Given:
f(x) = -0.5x+2
g(x) = x³ - 5x² + 3
The point of intersection exists the point where f(x) = g(x)
x³ - 5x² + 3 = - 0.5x + 2
x³ - 5x² + 3 + 0.5x - 2 = 0
x³ - 5x² + 0.5x + 1 = 0
Factorize and estimate the value of x
Let x = 0.53 and 4.85
substitute the value of x = 0.53
f(0.53) = -0.5(0.53) + 2
f(0.53) = -0.265 + 2
f(0.53) = 1.375
If x = 4.85
f(4.85) = -0.5(4.85) + 2
f(4.85) = -2.425 + 2
f(4.85) = -0.245
Therefore, the points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
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Use the root test to determine the convergence or divergence of the series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] 1 nn n = 1
The root test is Divergent, for given [infinity] 1 nn n = 1.
The foundation take a look at to research the restrict of the nth root of the nth time period of your collection. Like with the ratio check, if the restrict is less than 1, the series converges; if it is extra than 1 (together with infinity), the series diverges; and if the restrict equals 1, you analyze not anything.
The root check this collection is divergent. again, there is not too much to this series. therefore, with the aid of the root take a look at this collection converges clearly and hence converges. notice that we needed to maintain the absolute cost bars at the fraction until we would taken the limit to get the sign accurate
Root test requires you to calculate the value of R the usage of the components under. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent.
explanation:
If tan is series
if Lim n root (1) = l
if l =<1 than it is convergent
if l = > 1 than it is divergent
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Find the rectangular coordinates of the point with spherical coordinates (rho,θ,ϕ) : (4,π6,2π3)
The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.
I’m going to assume that your values are in the form of:
(r,θ,z)=(4,6π,2π/3)
where
(r,θ)are the polar coordinates of the point’s projection in the xy-plane
z is the usual z-coordinate in the Cartesian coordinate system
Now solving for Cartesian coordinates:
x=rcosθ=4cos(6π)=4(0.86)=3.44
y=rsinθ=4sin(6π)=2
Now for spherical transformation, note that:
(ρ,θ,ϕ)
ρ is the distance between P and the origin
θ is the same angle used to describe the location in cylindrical coordinates
ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π
OK, now that we have that out of the way, let’s compute:
ρ=r2+z2 = 5
θ=θ=6π
ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad
The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.
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Can someone explain step by step how to do this problem? Thanks! Calculus 2
Answer:
1.314 MJ
Step-by-step explanation:
As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.
There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.
The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.
Mass of waterThe mass of the water being raised is the product of the volume of the cone and the density of water.
The cone volume is ...
V = 1/3πr²h . . . . . . for radius 2 m and height 8 m
V = 1/3π(2 m)²(8 m) = 32π/3 m³
The mass of water in the cone is then ...
M = density × volume
M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg
Center of massThe center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.
Easy WayThe discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...
W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J
Hard Way
As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.
V(y) = (32π/3)(y/8)³
The differential volume at height y is the derivative of this:
dV = π/16y²
The work done to raise this volume of water to a height of 10 m is ...
(9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J
The total work done is the integral over all heights:
[tex]\displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}[/tex]
It takes about 1.31 MJ of work to empty the tank.
a section of a circle has both endpoints on the circle. what is the section of the circle called
Answer:
ChordStep-by-step explanation:
What is chord?A chord is a straight line that connects two points on a curve. An arrangement of three or more notes that blend harmoniously when played together.
A section of a circle has both endpoints on the circle. Chords are the sections of a circle.
Therefore, the final answer is "chords".
I hope this helps, let me know if you have any questions.
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A trapezoid has bases with lengths of 1.5 yards and 4 yards. The height is 12 yards. What is the area of the trapezoid?
A) 24 square yards
B) 27 square yards
C) 33 square yards
D) 66 square yards
The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?
92
8,655
212,520
1,573,210
There are 8855 ways in which a 4-member committee be formed from 23 members
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The number of ways that a 4-member committee be formed from 23 members is:
Number of ways = 23! / [(23 - 4)!4!] = 8855 ways
There are 8855 ways in which a 4-member committee be formed from 23 members
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Answer:
The answer is 212,520.
Step-by-step explanation:
This is a permutation, not a combination. So, we need to follow the formula
[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]
Plug in the numbers and solve:
[tex]nP_{r}= \frac{23!}{(23-4)!}[/tex]
[tex]nP_{r}= \frac{23!}{19!}\\[/tex]
[tex]nP_{r}= \frac{25,852,016,738,884,976,640,000}{121,645,100,408,832,000}[/tex]
[tex]nP_{r}= 212,520[/tex]
Because 212,520 is an answer choice, this is the correct answer.
If f(x) = x/3 and g(x)=1/x find f(x)-g(x)
A.
x-1/3-x
C. 1/3
B. x²-3/3x
D. 3-x²/3x
Please select the best answer from the choices provided
Answer:
x^2-3/3x
Step-by-step explanation:
x/3-1/x=x*x-1*3/3*x
=x^2-3/3x
Use an appropriate half-angle formula to find the exact value of the expression. cos(22. 5°)
The value of given trigonometric value cos(22. 5°) is 0.387.
According to the statement
we have given that the trigonometric value and we have to find the exact value of that given value with the help of the half angle formula.
So, For this purpose, we know that the
The half angle formulas are used to find the exact values of the trigonometric ratios of the angles like 22.5°.
So,
The given value is :
cos(22. 5°)
Then the value of cos half angle formula is
[tex]cos (theta/2) = +- sqrt((1-cos theta) / 2)[/tex]
then
The value of θ/2 is 22.5 degree.
And θ is 22.5*2
θ = 45 degree
and cos 45 degree is 1/squareroot 2
And by this the value of given value become is
[tex]cos 22.5 = +\sqrt{((\sqrt{2} -1)/(2 \sqrt{2} )) } = + 0.3827[/tex]
So, The value of given trigonometric value cos(22. 5°) is 0.387.
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Find the area of a circle if i) radius is 21cm ") diameter is 28cm
Answer:
i) 441π cm² ≈ 1385.4 cm²
ii) 196π cm² ≈ 615.8 cm²
Step-by-step explanation:
The areas of circles with radius 21 cm or diameter 28 cm can be found using the appropriate area formula.
i)The formula for the area of a circle based on its radius is ...
A = πr²
When the radius is 21 cm, the area is ...
A = π(21 cm)² = 441π cm² ≈ 1385.4 cm²
ii)The formula for the area of a circle based on its diameter is ...
A = (π/4)d²
When the diameter is 28 cm, the area is ...
A = (π/4)(28 cm)² = 196π cm² ≈ 615.8 cm²
Answer:
Before multiplying by pi. 441π cm²
After multiplying by pi. 1384.74 cm²
Step-by-step explanation:
The formula for area of a circle is πr².
r=radius
Square the radius.
21²=441
If they want the answer in this form: 441π cm². If not, then use 3.14 for π.
441*3.14=1384.74
The answer is 1384.74 cm².
Hope this helps!
What is the value of the variable intresult, given: int a = 3, b = 2, c = 10, intresult; intresult = c *b;
The integer value of the given integers is 20.
According to the statement
we have given that the some integers values like a = 3, b = 2, c = 10 and we have to find the intresult = c *b it means integer result = c *b
So, For this purpose we know that the
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
And here integer a = 3 and b = 2 and c = 10 and we have to find the value of c *b then
intresult = c *b
Substitute the values in it then
intresult = 10 *2
intresult = 20.
So, the intresults is 20 from the given numbers.
Hence, The integer value of the given integers is 20.
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Algebra 3, in the excercise size the graphs to determine the functions domain and range, x and y intercepts if any, and the functions values indicated below the graphs
Answer:
Read explanation
Step-by-step explanation:
I answered another one of your questions just like this in detail so I'll keep this one shorter.
Domain: (-∞, 0]
Range: (-3,∞)
x-intercept: Approximately -3.75
y=intercept: -3
Jane gained 25 points in the first round of a game. In the second round she lost 40 points and
on the third round she gained 10 points. Write and evaluate an expression to find how many
points Jane gained or lost.
Jane lost 5 points in the game.
Given that, Jane gained 25 points in the first round of a game. In the second round, she lost 40 points and in the third round, she gained 10 points.
We need to write and evaluate an expression to find how many points Jane gained or lost.
What are integers?An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Now, for the given situation we can write an expression as follows:
25 – 40 + 10
=25 + 10 + ( -40 )
=35 -40= -5
Therefore, Jane lost 5 points in the game.
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At Eva’s restaurant, 2/3 of the dishes on the menu are vegetarian. Of the vegetarian dishes, 1/10 are pasta dishes. What fraction of the dishes on the menu are vegetarian pasta?
Answer:
1/15 of the dishes on the menu are vegetarian pasta.
Step-by-step explanation:
1/10 of 2/3 of all dishes are vegetarian pasta.
1/10 of 2/3 of all = 1/10 * 2/3 * 1 = 2/30 = 1/15
if i get 6 gems every 2 minutes and 30 seconds how many gems will i have after one hour?
Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.
How many gems will I have after one hour?Given that;
6 gems are gotten every 2 minutes and 30 secondsLets convert 2min to second; 2min = ( 60 × 2 )sec = 120secHence 6 gems are gotten every 120sec and 30 seconds
Hence 6 gems are gotten every 150seconds
Next we convert 1 hour to seconds
1 hour = ( 60 × 60 × 1 )sec = 3600sec
Now,
6 gems can be gotten every 150seconds
x gems can be gotten every 3600 seconds
x = ( 6 × 3600 ) / 150
x = 21600 / 150
x = 144 gems
Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.
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What is 3.172 rounded to the nearest tenth?
3.2
3.3
3.7
3.8
Answer: 3.2
Step-by-step explanation: 3.2 is the answer because the number 7 is higher than 5. so the number 1 goes up by one, which that equals 3.2
If one earthquake is 20 times as intense as another how much latger is its magnitude on the richter scale?
The magnitude of the larger earthquake is about 1.3 greater than the magnitude of the smaller earthquake.
In physics, significance is defined actually as “distance or quantity.” It depicts the absolute or relative course or size wherein an object moves within the sense of motion. it's miles used to express the scale or scope of something. In physics, importance normally refers to distance or quantity.
Magnitude is described as big in size or very vital. An example of value is the depth of the Grand Canyon. An instance of importance is the dimensions of the trouble of world hunger. (geology) A measure of the amount of energy launched by using an earthquake, as indicated on the Richter scale.
The magnitude is more than a few that characterizes the relative size of an earthquake. value is primarily based on the measurement of the maximum movement recorded with the aid of a seismograph.
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show that xcosec^2x = cotx - d/dx xcotx
The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.
In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.
To prove, we go by the right-hand side of the equation:
cot x - d/dx x.cot x.
We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.
cot x - {x. d/dx(cot x) + cot x. d/dx(x)}
= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}
= cot x + x. cosec²x - cot x
= x. cosec²x
= The left-hand side of the equation.
Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.
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ratio and proportion
1. there are 24 green cars and 48 white cars in a parking lot.
i) find the ratio of green cars to white cars.
ii) what can you say about them?
Based on the given tast content; the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars.
Ratio and proportionNumber of green cars = 24Number of white cars = 48Ratio of green cars to white cars = 24 : 48
= 24 / 48
= 1 / 2
Ratio of green cars to white cars = 1 : 2
Therefore, the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars
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The number of students from there sections of class 6 are 32,3640. find minimum number of books required for their class library . so, that they can be equally distributed among the students of three sections?
The minimum number of books required to be equally distributed among the students are 1,440 books.
What is LCM?The smallest feasible multiple of two or more numbers is found using the LCM method. LCM is an abbreviation for least common multiple. The LCM of two numbers is divisible by both of them. The LCM of 6 and 8 is 24, for example. As a result, 24 is divisible by both 6 and 8.To find the minimum required books so that they can be equally distributed:
The number of students in three sections of class 6th are 32, 36, and 40.
Now, find the LCM od 32, 36, and 40.
The LCM od 32, 36, and 40 will be 1,440.
Therefore, the minimum number of books required to be equally distributed among the students are 1,440 books.
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HELP ME ASAP!!! I WILL GIVE MANY POINTS and
The 8 cm circle radius and the location of the circle X gives the following values;
(a) tan(<XAB) = -(r - 8)/(2•r + 4) = (8 - r)/8
Which gives;
r = (8 - 4)÷2 = 2(b) <XAB is approximately 0.644 radians
(c) The area of the shaded region is approximately 3.107 cm²
Which method can be used to analyze the figure?8 × (8 - r) = 0.5 × 16 × (8 + r) × sin(A)
(8 - r) = (8 + r) × sin(A)
sin(A) = (8 - r)÷(8 + r)
(8 - r)² = 8² + (8 + r)² - 2×8×(8 + r)×cos(A)
16×(8 + r)×cos(A) = (8² + (8 + r)²) - (8 - r)²
Which gives;
cos(A) = ((8² + (8 + r)²) - (8 - r)²) ÷ (16×(8 + r))
cos(A) = (2•r + 4)/(r + 8)
tan(A) = ((8 - r)÷(8 + r))/( (2•r + 4)/(r + 8))
tan(A) = -(r - 8)/(2•r + 4) = (8 - r)/8
(8 - r)/(2•r + 4) = (8 - r)/8
8 = 2•r + 4
2•r + 4 = 8
Therefore;
r = (8 - 4)÷2 = 2(b) sin(A) = (8 - r)÷(8 + r)
sin(A) = (8 - 2)÷(8 + 2) = 0.6
Therefore;
<XAB = <A = arcsin(0.6) ≈ 0.644 rad
<XAB in degrees ≈ 36.87°
Angle at sector PXQ = 180° - 2 × (36.87°) ≈ 106.26°
Area of sector PXQ ≈ (106.26°/(360°)) × π × 2²
(106.26°/(360°)) × π × 2² ≈ 3.71
Area of sector APO ≈ (36.87°/(360°)) × π × 8² ≈ 20.59
Area of triangle AXB = 8 × (8-2) = 48
The shaded area is therefore;
48 - (2×20.59 + 3.71) ≈ 3.107
The area of the shaded region, A ≈ 3.107Learn more about the trigonometric ratios here:
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a) The radius of the small circle is 2 centimeters.
b) The measure of the angle XAB is approximately equal to 51.340°.
c) The area of the shaded region is approximately equal to 2.423 square centimeters.
How to analyze a system formed by three semicircles and a circle
In this question we must analyze a geometrical system formed by three semicircles and a circle. The small circle touches the two side semicircles tangentially at points P and Q and the uppermost section of it also tangent to the central semicircle (point R).
(a) Therefore, we have to solve the following system of equations:
8² + h² = (8 + r)² (1)
h + r = 8 (2)
By (2) in (1):
8² + (8 - r)² = (8 + r)²
32 · r = 64
r = 2
The radius of the small circle is 2 centimeters.
(b) The measure of the angle XAB is found by trigonometric functions:
tan m ∠ XAB = OX / AO
tan m ∠ XAB = 10 / 8
m ∠ XAB ≈ 51.340°
The measure of the angle XAB is approximately equal to 51.340°.
(c) The area of the shaded region if the area of the triangle AXB minus the areas of the three circular sections, that is:
A = 0.5 · (16 cm) · (10 cm) · sin 51.340° - (51.340° / 180°) · π · (8 cm)² - 0.5 · (77.320° / 180°) · π · (2 cm)²
A ≈ 2.423 cm²
The area of the shaded region is approximately equal to 2.423 square centimeters.
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In the figure, ABCDEF is a regular hexagon. △ BDF is drawn by joining the
alternate vertices. Show that △ BDF is equilateral
Answer:
Step-by-step explanation:
Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.
ProofAB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon
∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon
ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence
FB ≅ BD ≅ DF . . . . CPCTC
ΔBDF is equilateral . . . . definition of equilateral triangle
If two 12-sided dice are rolled what is the probability that both numbers will be even?
Answer:
probability result of sample space would result in 12/144
Step-by-step explanation:
as result there is 12 numbers on each dice, blth have exact same numbers, resulting in 144 combinations ti be thrown as sample space event outcome wluld be;
1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12
2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12
3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8 3/9 3/10 3/11 3/12
4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 3/9 4/10 4/11 4/12
5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10 5/11 5/12
6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8 6/9 6/10 6/11 6/12
7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8 7/9 7/10 7/11 7/12
8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12
9/1 9/2 9/3 9/4 9/5 9/6 9/7 9/8 9/9 9/10 9/11 9/12
10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12
11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12
12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12
giving 12 matching numbers in a 144 possible rolled outcome
mathematic formula would be P(A) = n(A)/n(S)
As P(A)= probabolity of event A
n(A)= number of favouravle outcome
n(S)= total number of outcome in sample space
giving
12=2/144=0,0138888889