the history of pi and it’s importance to geometry!!!!!!
Answer:
Famous mathematician Archimedes of Syracuse did the first calculation of pi around 250 BC. Without pi, we cannot calculate the ratio of the circumference of a circle to its diameter. Pi is made up of 31.4 trillion digits. Within pi, you can find your birthday, social security number, and every word ever if put into alphabetic values (1=a, 2=b, etc). You can get your entire life story from beginning to end just from pi!
hope this helps:)
H. e. l. p MeEe
plss
Step-by-step explanation:
here you go hope it helps you
A large rectangular prism is 5 feet long, 3 feet wide, and 4 feet tall. A small rectangular prism is 2.5 feet long, 1.5 feet wide, and 2 feet tall.
How many small prisms would it take to fill the large prism?
Write your answer as a whole number or decimal. Do not round.
Answer:
2 small prism could fit.
Step-by-step explanation:
the large prism is 4 feet tall, 5 feet long, And 3 feet wide. So it would take to small prism to fit because the small prism is 2 feet tall, 2.5 feet long, And 1.5 feet long. Do you see it the small prism is exactly half the size of the large prism there the large prism could fit two small prism with in its self.
Roberta grows pea plants, some in shade and some in sun. she picks 8 plants of each type at random and
records the heights.
shade plant heights (in.) 7 12 7 10 8 12 8 8
sun plant heights (in.) 19 24 21 22 23 19 20 20
express the difference in the means as a multiple of their ranges.
the difference in the means is times the ranges.
Which of the following equations are NOT linear equations? Select all that apply.
(Choose 2)
(btw the answers are impossible to write so if you know what im talking abt then thats good)
The linear equations are 6x + y = 5, x + 2 = −8, y = 1, and y = −2/3x + 3. Then the correct options are A, B, E, and G.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
If the power of the variable is one then the equation will be a linear equation.
The equations are given below.
A. 6x + y = 5, this is the linear equation.
B. x + 2 = −8, this is the linear equation.
C. 2x² + 3x − 8 = 19, this is not a linear equation.
D. 3 + 8 = 11, this is not a linear equation.
E. y = 1, this is the linear equation.
F. 4x³ = 32, this is not a linear equation.
G. y = −2/3x + 3, this is the linear equation.
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A system of equations is shown below
2x+y=9,x+3y=-13
Which sequence of operations would produce the correct x- or y-value of the solution to this system of equations?
a)multiply the first equation by 3 and add the result to the second equation to eliminate y and solve for x
b)multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x
c)multiply the second equation by 9/13 and add the result to the first equation to eliminate the constant and solve for x and y
d) multiply the second equation by –1 and add the result to the first equation to eliminate x and solve for y
The sequence of operations is multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x. The correct option is - b)
Solving a system of equations by EliminationFrom the question, we are to determine the sequence of operations that would produce the correct x- or y-value of the solution to the given system of equations
The given systems of equations are
2x+y=9
x+3y=-13
First, multiply the first equation by -3That is
-3 × (2x+y=9)
-6x-3y=-27
Now, add to the second equation-6x-3y=-27
+(x+3y=-13)
-----------------
-5x = -40
Thus, we can solve for x
These sequence of operations will enable us to eliminate y and solve for x
Hence, the sequence of operations that would produce the correct x- or y-value of the solution to the system of equations is multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x. The correct option is - b)multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x
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pls help 50 points for reward.
Answer:
-2
Using the slope formula (y1-y2)/(x1-x2), the slope of the line is (-10-8)/(9-0), which is equal to (-18)/9= -2.
Slope
m=y2-y1/x2-x1m=8+10/0-9m=18/-9m=-2Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a decimal to the nearest hundredth.
Answer:
The probability as a decimal to the nearest hundredth is 0.550.55.
Step-by-step explanation:
61 cash, 5 debit card, and 45 credit card.
\color{steelblue}{61}+5+45=
61+5+45=
\,\,\color{indianred}{111}
111
There were a toal of 111 customers. 61 paid with cash.
Probability the next customer will pay with cash:
\frac{\color{steelblue}{61}}{\color{indianred}{111}}=
111
61
=
\,\,0.549549...
0.549549...
\approx
≈
\,\,0.55
0.55
Round to the nearest hundreth
The probability that the next customer will pay with cash is 0.55.
What is the formula for probability?Probability is the ratio of the number of favorable events divided by the total outcome.
We have, given that, Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.
The total number of payments is,
61+45+5=111.
We have to find the probability that the next customer will pay with cash as a decimal to the nearest hundredth.
The number of the favorable outcome for the customer will pay with cash is 61, and the total number of outcomes is 111.
Therefore, the probability is,
P(A)=61/111
P(A)=0.5495.
Therefore, the probability of the nearest hundredth is 0.55.
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100 points. bee fast
Jalen says that the height, radius, and diameter of a cone lie entirely on the base of the cone. What is Jalen’s error? The height does not lie on the base because it is perpendicular to the base. The radius does not lie on the base because it contains the center of the base. The diameter does not lie on the base because it contains a radius of the circle. The base does not contain the height, the radius, or the diameter because it is a circle.
Answer:
The height does not lie on the base because it is perpendicular to the base.
For Questions 2-5, determine whether each expression is a polynomial:
(Questions are in image)
Answer:
2. Polynomial
3. Not a polynomial
4. Polynomial
5. Polynomial
Step-by-step explanation:
Find the area of the blue shaded region
Step-by-step explanation:
Area of shaded region= area of rectangle- area of semi-circle
Area of rectangle= l×b
=6×4
=24 in²
Area of semi-circle=[tex]\frac{\pi r^{2} }{2}[/tex]
= [tex]\frac{\pi (2)^{2} }{2}[/tex]
= 6.28 in²
Area of shaded region= area of rectangle- area of semi-circle
= 24-6.28
=17.72 in²
The half-life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.
Answer:
442.302 kg
Step-by-step explanation:
amount = 487 (1/2)^(t/36) where t is the number of days.
if t = 5
amount = 487(.5)^(5/36)
= 442.302 kg
Will mark branlyest (Polynomial Functions)
1. Find the zeros: 2x^2 + 12x + 18 = 0
A . {-3}
B .{3}
C .{-9}
D.{-3,3}
2. Find the x-intercepts: 2r^2 = 5r + 3
A. {-1/2,3}
B.{-1/2,-3
C.{1/2,3}
D.{1/2,-3}
Answer:
1. A
2. A
Step-by-step explanation:
Question 1
1 Factor out the common term 2.
2(x^2+6x+9)=0
2 Rewrite x^2+6x+9 in the form a^2+2ab+b^2a, where a=x and b=3.
2(x^2+2(x)(3)+3^2)=0
3 Use Square of Sum: (a+b)^2=a^2+2ab+b^2(a+b).
2(x+3)^2=0
4 Divide both sides by 2.
(x+3)^2=0
5 Take the square root of both sides.
x+3=0
6 Subtract 3 from both sides.
x=-3
Question 2
1 Move all terms to one side.
2r^2-5r-3=0
2 Split the second term in 2r^2-5r-3 into two terms.
2r^2+r-6r-3=0
3 Factor out common terms in the first two terms, then in the last two terms.
r(2r+1)-3(2r+1)=0
4 Factor out the common term 2r+1.
(2r+1)(r-3)=0
5 Solve for r.
r=-1/2,3
just please help 6 through 8 thank you please help me its a homework but i really dont get it that much please help me
Problem 6
It's not clear what the instructions are, but I'm assuming your teacher wants you to rationalize the denominator.
If so, then we could have these steps
[tex]\sqrt{\frac{3\text{x}}{7}}\\\\\frac{\sqrt{3\text{x}}}{\sqrt{7}}\\\\\frac{\sqrt{3\text{x}}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\frac{\sqrt{3\text{x}*7}}{(\sqrt{7})^2}\\\\\frac{\sqrt{21\text{x}}}{7}\\\\[/tex]
In the third step, I multiplied top and bottom by [tex]\sqrt{7}[/tex] so that the denominator can get rid of the square root.
Answer: [tex]\frac{\sqrt{21\text{x}}}{7}\\\\[/tex]======================================================
Problem 7
We'll follow the same idea for this problem.
[tex]\sqrt{\frac{5m^2}{2}}\\\\\frac{\sqrt{5m^2}}{\sqrt{2}}\\\\\frac{\sqrt{5m^2}*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{5m^2*2}}{(\sqrt{2})^2}\\\\\frac{\sqrt{10m^2}}{2}\\\\\frac{\sqrt{10}*\sqrt{m^2}}{2}\\\\\frac{m\sqrt{10}}{2}\\\\[/tex]
Where m is nonnegative.
In the second to last step, I split up the root so I could use the rule [tex]\sqrt{x^2} = x \text{ when } x \ge 0[/tex]
Answer: [tex]\frac{m\sqrt{10}}{2}\\\\[/tex]======================================================
Problem 8
[tex]\sqrt{\frac{12\text{x}^3}{5}}\\\\\frac{\sqrt{12\text{x}^3}}{\sqrt{5}}\\\\\frac{\sqrt{12\text{x}^3}*\sqrt{5}}{\sqrt{5}*\sqrt{5}}\\\\\frac{\sqrt{12\text{x}^3*5}}{(\sqrt{5})^2}\\\\\frac{\sqrt{60\text{x}^3}}{5}\\\\\frac{\sqrt{4\text{x}^2*15\text{x}}}{5}\\\\\frac{\sqrt{4\text{x}^2}*\sqrt{15\text{x}}}{5}\\\\\frac{\sqrt{(2\text{x})^2}*\sqrt{15\text{x}}}{5}\\\\\frac{2x\sqrt{15\text{x}}}{5}\\\\[/tex]
where x is nonnegative.
Answer: [tex]\frac{2x\sqrt{15\text{x}}}{5}\\\\[/tex]Need help with this. Find the value of x
Answer:
x=72.4
Step-by-step explanation:
Since we have an angle that is facing a known side, we are able to use sine
Step 1- Prepare your equation: sin(∅°)=opposite/hypotenuse
Step 2- Substitute: sin(28°)=34/x
Step 3- Calculate: use a graphing calculator to solve the equation, make sure to have the answer to degrees not radians
Step 4- Answer: 72.4 by calculator
ur wlcm :)
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in order to make a specific shade of green paint a panter mixes 1 1/2 quarts of blue paint 2 cups of green paint and 1/2 gallion of white paint how much of each collor is needed to make 100 cups of this shade of green paint
Answer:
37.5 cups of blue
12.5 cups of green
50 cups of white
Can anybody help me with this please!!
Answer:
C. Complementary angles
Step-by-step explanation:
Since it's mentioned that <DAB is 90 degrees then that means that <BAE is also 90 degrees and since angles A and B are the only angles in <BAE, it means that Angle A and B are complimentary
Write an algebraic expression for each of the statements below.
Answer:
D) 3x + 7y = 49
E) x / 3 = 9
F) 2x + 4
Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x i)(x – 2) f(x) = 3(x 4)(x – i)(x i)(x – 2)
The polynomial function with leading coefficient of 3 and root -4, i, and 2 all with multiplicity of 1 is f(x) = 3(x+4)(x-i)(x+2)
Polynomial function
The Leading coefficients are the numbers written in front of the variable with the largest exponent.
Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.
The multiplicity is the number of times a given factor appears in the factored form of the equation of a polynomial.
Therefore, the polynomial f(x) = 3(x+4)(x-i)(x+2) has a root -4 , 1 and -2.
The leading coefficient is 3. The multiplicity is all one.
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Answer:
d
Step-by-step explanation:
please help! this is due soon and im a bit confused
Who is faster, the snowboarder or the skier? Explain how you know who is faster.
PLEASE YALL I NEED HELP AND FAST
The answer is that skiers are faster by 20%, with the top speed ever recorded on a ski coming in at 250kph, while the top speed recorded on a snowboard is 200kph. If we want to discuss which sport is cooler, then we can have a lively conversation! The Basics Of Biomechanics
Find the area of the complex figure.
Answer:
1863M
Step-by-step explanation:
split into smaller rectangles
(31 * 23) * 2 = 713 *2 = 1426
31-12 = 19
19 * 23 = 437
1426 + 437
Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 5. If the volume of rectangular prism B is 5125 km°, find the volume of rectangular prism A, the preimage
The volume of the rectangular prism A, the preimage is 41km^3
How to determine the volume?The given parameters are:
Volume B = 5125km^3
Scale factor, k = 5
The volume of B is calculated using:
B = A * k^3
So, we have:
5125 = A * 5^3
Divide both sides by 5^3
A = 41
Hence, the volume of rectangular prism A, the preimage is 41km^3
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Which description best describes parallel lines?
O A. Lines that are not in the same plane and will never intersect
O B. Lines that lie in the same plane but will never intersect
0
C. Lines that intersect at a right angle
0 D. Lines that intersect
• A bag contains 5 orange, 3 yellow, and 5 black marbles. What are the odds of picking an orange marble?
Answer:
The odds will be 5/13.
Step-by-step explanation:
There are 13 marbles total in this situation. 5 orange, 3 yellow and 5 black (5+3+5) will give us 13 as our overall total. Now, because we have 5 orange marbles available, we'll write this as a 5/13 odds/ chance of picking an orange marbles because it is how many orange marbles are present over how many marbles there are total.
Also! You can't simplify this any further, thus you'd have 5/13 odds.
What is the measure (in radians) of central angle \thetaθtheta in the circle below?
Enter an exact expression.
Answer:
1 radians
Step-by-step explanation:
Here,
Arc length ( l ) = 8π cm
Radius ( r ) = 8 cm
To find : Angle θ ( in radians )
Formula : -
θ = l / r
θ = 8π / 8
θ = 1π
Note : -
Radians is denoted by " π ".
If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)? startfraction (5 x) over x endfraction startfraction 1 over (5 x) endfraction 5 (startfraction 1 over x endfraction) 5 (5 x)
The composition of the two given functions is:
(k°h)(x) = 1/5x
How to get the composition of the functions?
Here we have the functions h(x) = 5x and k(x) = 1/x.
We want to get (k°h)(x), which is equal to:
k(h(x))
Then we have:
k(h(x)) = 1/h(x)
Replacing h(x) we get:
k(h(x)) = 1/h(x) = 1/(5x)
So the composition is just one over 5x.
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Jason is planning on retiring after 25 years of employment. For the last three years he
has made $60,000; $56,000; and $58,000. His employer offers a defined benefit plan
in which the annual pension is calculated as the product of the final three-year
average salary, the number of years of service, and a 2.25% multiplier. What will
Jason's monthly pension be?
O $27,187.50
O $2,812.50
O $32,625
O $2,718.75
Jason's monthly pension is the product of the final three-year average salary is $32,625. Then the correct option is C.
What is a monthly pension?Jason is planning on retiring after 25 years of employment.
For the last three years he has made $60,000; $56,000; and $58,000.
His employer offers a defined benefit plan in which the annual pension is calculated as the product of the final three-year average salary, the number of years of service, and a 2.25% multiplier.
Then Jason's monthly pension will be
[tex]\rm Monthly \ pension = \dfrac{(60,000+56,000+58,000)}{12} \times 2.25\\\\Monthly \ pension = 14500 \times 2.25\\\\Monthly \ pension = \$ \ 32,625[/tex]
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Evaluate each expression.
6! =
3! - 2!=
61/
3!
=
Answer:
6! = 720
3! - 2! = 4
6! ÷ 3! = 120
Step-by-step explanation:
I used a calculator. ^v^
Billy has 10 bouncy balls. His brother has 30 bouncy balls. He washed 10 of his and 10 of his brother. How many bouncy balls do they have left?
Answer:
20
Step-by-step explanation:
10 + 30 = 40
40 - 10 = 30
30 - 10 = 20
answer is 20
Answer:
20 bouncy Balls!
Step-by-step explanation:
10+30 - 20 = 20