2. What is the circumference of the circle?
e) 26π cm²
g) 6767 cm²
f) 52π cm²
h) 1697 cm²
Answers
Answer:
26π cm
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = πd ( d is the diameter )
= π × 26
= 26π cm
▶︎◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◀︎
[tex]Hello[/tex] [tex]There![/tex]
We are looking for the circumference of the circle.
It's not hard, I promise! I will take you through a few steps, and we'll find the answer.
Are you ready? Then let's begin...:)
[tex]Procedure:[/tex]
First, we need a formula for the circumference. We can't find the circumference without a formula!
· Luckily, there is a formula for the circumference:
⇒ [tex]C=\pi d}[/tex]
Whoa. What's that?!
No worries, I'll clarify everything in a moment. :)
We are looking for the circumference.
In this formula, what stands for the circumference?
That's right, [tex]C[/tex].
Now, what is this: [tex]\pi[/tex]?
This letter stands for pi - a constant in maths that comes in handy when we're searching for the circumference of a circle (or area).
It has an infinite number of digits after the decimal point, and these digits never repeat!
You might be thinking, "Oh no! Are we really going to use that infinite number?!"
The answer is "No". Mostly, we use 3.14 for [tex]\pi[/tex], because these are the first three digits of pi, but since we aren't asked to use 3.14 for pi, we just press the [tex]\boxed{\pi }[/tex] button on our calculator.
Whew!
And then last but not least, we see "d". This isn't a constant, this is the diameter.
Checking our provided information, we see that the diameter is 26 cm.
Now, we substitute 26 for d:
[tex]\bold{C=\pi (26)}[/tex]
[tex]\bold{C=\pi *26}[/tex]
And now all we have to do is type these numbers into our calculator, and find the answer:
[tex]\bold{C\approx81.7\:cm}[/tex]
Hooray! We've found the circumference!
But wait - why isn't 81.7 an option?
Because what we need to do is write it in terms of pi, which is even easier, because we just substitute 26 for d:
[tex]\bold{C=\pi *26}[/tex]
➢ Rearrange the order of the terms:
[tex]\bold{C=26\pi \:cm}[/tex]
▲ Circumference
Now there's another thing - why are all four options with units squared?
Circumference isn't measured in units squared, the area is!
▶︎ Incase you need the area, here it is:
[tex]\bold{A=\pi r^{2}}[/tex]
A=Area (what we're looking for)
[tex]\pi[/tex] = pi
Here we have a new variable - it's r, which is the radius.
Do you see that [tex]^2[/tex] next to r? It means that r is squared, or multiplied by itself.
You might be thinking, "But we don't have the radius!"
If we have the diameter, finding the radius is a piece of cake, because we divide the diameter by 2:
[tex]\bold{26\div2}[/tex]
[tex]\bold{13}[/tex]
Now we substitute 13 for r and evaluate:
⇒ [tex]\bold{A=\pi (13)^{2}}[/tex]
13 times itself is 169:
⇒ [tex]\bold{A=169\pi \:cm^{2}}[/tex]
Whew! We're finally done!
hope it's helpful!wishing you a great day!
[tex]Greetings![/tex]
--
Related Questions
Pls help me classify this asap?!!
Answers
What is the equation of the following line? Be sure to scroll down first to see all answer options .
Answers
Answer:
f
Step-by-step explanation:
your welcome
Verify whether x ≤ 3 is the solution to the inequality 7x ≥ 20x - 39.
Answers
Answer:
Yes, it is correct.
Step-by-step explanation:
7x≥20x-39
39≥13x
x≤39/13
x≤3
Four friends are sharing 5 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
Answers
Answer:
each friend will get 5/4 or 1.25 cups of lemonade
Step-by-step explanation:
5 divide by 4 since there are 4 friends.
so 5/4 of the lemonade will be shared by each friend.
Step-by-step explanation:
each friend would get 1.25 cups each
A mouse climbs up a well of 86 meters. It advances 14 meters during the night, but during the day it retreats 2. The mouse will reach the surface on the day:
Answers
Step-by-step explanation:
we assume day and night are equally long.
and the mouse will start at night of day 1.
then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).
so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).
with a starting value of 14 (the first night).
so, we are getting an arithmetic sequence
an = an-1 + c
c = 12 in our case.
a1 = 14
a2 = a1 + 12 = 14+12 = 26
a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38
an = a1 + (n-1)×12 = 14 + 12(n-1)
at what n will it reach 86 ?
86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n
84 = 12n
n = 7
so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answers
[tex]\bf Blue \ Color \ Line : y = x^2[/tex]
If you are going to make it open from downwards. The function should be negative : -(x)²If the graph moves 10 units downwards. : y = (x)² - 10If you are going to move the graph horizontally 2 units left. : y = (x+ 2)²When added all together:
[tex]\bf Black \ color \ Line: y=-\left(x+2\right)^{2}-10[/tex] = Final answer.
The graph below shows the solution to which system of inequalities?
O A. x< 1 and yz x
B. x< 1 and y>x
C. y≤ 1 and y>x
D. y< 1 and yzx
Answers
Answer:
y < 1 and y > x
Step-by-step explanation:
Let's find each equation without any inequalities first.
We have a dotted line at y = 1
Now, a dotted line represents exclusivity, and hence; it should not include the = sign
Therefore, the answer is y < 1 and y > x
The polynomial function f(x) = 3x5 – 2x2 7x models the motion of a roller coaster. the roots of the function represent when the roller coaster is at ground level. which answer choice represents all potential values of when the roller coaster is at ground level? begin by factoring x to create a constant term. 0, plus-or-minus one-seventh, plus-or-minus1, plus-or-minus three-sevenths, plus-or-minus3 0, plus-or-minus one-third, plus-or-minus1, plus-or-minus seven-thirds, plus-or-minus7 plus-or-minus one-seventh, plus-or-minus1, plus-or-minus three-sevenths, plus-or-minus3 plus-or-minus one-third, plus-or-minus1, plus-or-minus seven-thirds, plus-or-minus7
Answers
The root of the polynomial function f(x) = 3x⁵ - 2x² + 7x is 0
How to determine the roots of the equation?The polynomial function is given as:
f(x) = 3x⁵ - 2x² + 7x
Set the function to 0
3x⁵ - 2x² + 7x = 0
Factor out x
x(3x⁴ - 2x + 7) = 0
Divide both sides by (3x⁴ - 2x + 7)
x = 0
Hence, the root of the equation is 0
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Answer:
B
Step-by-step explanation:
cause math
This table shows the relationship between x and y.
Answers
The radius of a semicircle is 9.1 centimeters. What is the semicircle's perimeter?
Answers
Answer:
46.77 cm
Step-by-step explanation:
Perimeter of the semicircle = Circumference + 2r
πr + 2r = r (π + 2)9.1 (3.14 + 2)9.1 (5.14)46.77 cmConvert the fractions to decimals
Answers
Answer:
0.333333...
Step-by-step explanation:
2/6 = 1/3 = 0.33333...
You can divide on paper or on a calculator 2÷6 or 1÷3 to find this. If you are allowed to use a calculator and your calculator has F>D and D>F buttons they are for converting decimals and fractions back and forth. On paper, you are doing like a long division calculation. Put 2 inside the little dividing frame and put 6 on the outside. Or 1 inside and 3 outside. See image.
Using two or more complete sentences, describe how to find the general rule for the geometric sequence with a4=3 and a6=3/16. In your final answer, include all of your calculations.
Answers
The steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.
What is geometric sequence?
Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
It can be given as,
[tex]a_n=a_1r^{n-1}[/tex]
Here, a₁ is the first term of the sequence and r is the common ratio.
The fourth term and sixth term given in for the geometric sequence are 3 and 3/16. For the fourth term,
[tex]a_4=a_1r^{4-1}\\3=a_1r^3[/tex] ...1
For the sixth term,
[tex]a_6=a_1r^{6-1}\\\dfrac{3}{16}=a_1r^5[/tex] ....2
On solving, we get, a₁=192 and r=1/4. Thus, the geometric sequence can be given as,
[tex]a_n=a_1r^{n-1}\\a_n=192\times\dfrac{1}{4}^{n-1}[/tex]
Hence, the steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.
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The volume of this rectangular prism is 2,016 cubic millimeters. What is the value of y?
Answers
Answer:
y = 12 mm
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 2,016 mm³l = 14 mmw = 12 mmh = y mmSubstitute the values above and solve for y:
2,016 = 14 × 12 × y
2,016 = 168y
2,016/168 = 1395v/168
12 = y
Final answer: 12 mm
Hope this helps!
please please help!!! see attached questions I WILL VENMO YOU ( i’m not sure if the first one is right)
Answers
Answer:
Your first answer is correct.
Second question: 300 ft.
Step-by-step explanation:
2nd problem, create a proportion.
[tex]\frac{220}{x}=\frac{305}{416} \\305x = 91520\\\frac{305x}{305}= \frac{91520}{305} \\x=300[/tex]
Augustus is trying to make chocolate milk. He has made a 10% chocolate milk solution (this means that the solution is 10% chocolate and 90% milk). He has also made a 25% chocolate milk solution. Unfortunately, the 10% solution is too weak, and the 25% solution is way too chocolaty. He has a whole lot of the 10% solution, but he has only 30 gallons of the 25% solution. How many gallons of 10% solution should he add to the 25% solution to make a mixture that is 15% chocolate?
Answers
Answer:
60 gallons
Step-by-step explanation:
The amount of 10% solution he should add can be found by writing an equation for the total amount of chocolate in the mix.
__
Let x represent the amount of 10% solution that Augustus needs to add to the 30 gallons of 25% solution. The amount of chocolate in the resulting 15% mix is ...
0.10x +0.25(30) = 0.15(x +30) . . . . gallons of chocolate in the mix
0.10(30) = 0.05x . . . . . . . . subtract 0.10x +0.15(30)
60 = x . . . . . . . . . . . . divide by 0.05
Augustus should add 60 gallons of the 10% solution to make a 15% mixture.
Given the pyramid, calculate the SURFACE AREA and VOLUME. (please help ASAP)
Answers
Simplify the expression.
-81 ÷ (-9)
Please help
Answers
Answer:
-81/-9
both minus will be cut so
81/9
9
Step-by-step explanation:
the answer is 9
2 x{15 plus[24-(1.5 x2)]}
Answers
Answer:
72.
Step-by-step explanation:
2 x{15 plus[24-(1.5 x2)]}
Using PEDMAS:
= 2 x {15 + [24-(3)]}
= 2 x (15 + 21)
= 2 x 36
= 72.
What is the rate of change from 4 to 8?
Answers
Answer:
the rate of change from 4 to 8 is 4
Step-by-step explanation:
you can find this by subtracting the first number from the secone number and if the two numbers were in a diffrent order being 8 and 4 the answer would still be 4 because when you subtract 8 from 4 you ger-4 but with rate of change you always use the absolute value
hope this helped
I need help pleaseeeeee I do not know what to do here
Answers
Answer:
[tex]A = 256[/tex]
Step-by-step explanation:
Since the hexagon is regular, we know that all of the side lengths are equal. We can find the length of the sides by solving for [tex]l[/tex] in the formula for the area of a hexagon:
[tex]A = \frac{3\sqrt{3}}{2}l^2\\384\sqrt{3} = \frac{3\sqrt{3}}{2}l^2\\384 = \frac{3}{2}l^2\\256 = l^2\\16 = l[/tex]
Now that we have the side length, we can find the area of the square:
[tex]A = l^2\\A = 16^2\\A = 256[/tex]
Answer:
256 in²
Step-by-step explanation:
Area of a Hexagon (To find side length)
A = 3√3 x l² x 1/2384√3 = 3√3 x 1/2 x l²256 = l²l = 16 inArea of square
Area = (Side length)²Area = (16)²Area = 256 in²In a company, 85% of the workers are women. If 390 people work for the company who aren't women, how many workers are there in all?
Answers
Answer:
2210
Step-by-step explanation:
390 =15%
390*3 = 130=5%
130*17=2210
If the first number is increased by 7 and the second number is reduced by 6 times, the sum of these numbers is 29.
If the first number is reduced by 5 and the second number is increased 2 times, the difference between the second and first number is 9.
Find these numbers.
Answers
Answer:
First number = 20
Second number = 12
Explanation:
Let the 1st number be x
Let the 2nd number be y
=====================
Condition 1
[tex]\sf \rightarrow x + 7 + \dfrac{y}{6} = 29[/tex]
[tex]\rightarrow \sf x=-\dfrac{y}{6}+22[/tex]
=====================
Condition 2
[tex]\rightarrow \sf 2y - (x - 5) = 9[/tex]
[tex]\rightarrow \sf x = 2y -4[/tex]
=====================
Substitute equations
[tex]\rightarrow \sf -\dfrac{y}{6}+22 = 2y-4[/tex]
[tex]\rightarrow \sf y=12[/tex]
=====================
Find value of 1st number
[tex]\rightarrow \sf x = 2y - 4[/tex]
[tex]\sf \rightarrow x = 2(12) - 4[/tex]
[tex]\rightarrow \sf x = 20[/tex]
What is the value of y on question 7
Answers
The value of y in the given question will be y = -2x + 26.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The value of y will be calculated as:-
Given the equation :-
4y - 2x = 12
y = x / 2 + 12
Now for two perpendicular lines, the product of the intercepts is -1
m₁ x m₂ = -1
So the new intercept will be
m₂ = -1 / m₁ = -1 / 1 / 2 = -2
So new equation will be
y = -2x + c
2 = -2 x 12 + c
c = 26
So the equation will be:-
y = -2x + 26
Therefore the value of y in the given question will be y = -2x + 26.
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Susan bought gas for her car,the gas cost 2.79 per gallon susan bought 15.4 gallons,what was the total cost for susans gas
Answers
in a class of 32 students there are 8 girls who played basket ball and 5 boys who did not
Answers
(a) 12 boys play basketball
(b) See figure 2 below
==========================================================
Explanation:
Part (a)
You are on the right track so far when you wrote the partial table.
There are 15 girls in the class, and 8 girls that play basketball. That must mean 15-8 = 7 girls do not play basketball.
Focusing on the first row only, we'll have 7 go in the second column and 15 go in the third column. The first row is filled out entirely.
There are 32 students and 15 girls. This means there are 32-15 = 17 boys. We'll write 17 at the end of the second row.
The other missing value of this row is 17-5 = 12 to represent the number of boys who play basketball. This is because of the 5 boys that don't play basketball.
To fill out the missing items in the third row, add the columns straight down.
We have 8+12 = 20 basketball players and 7+5 = 12 people who do not play basketball. Notice how 20+12 = 32 along the bottom row to help confirm the correct values.
Check out figure 1 to see the entire two-way frequency table.
We see that there are 12 boys that play basketball.
------------------------------------------------
Part (b)
The previous part detailed how to set up the two-way frequency table.
For this part, we'll be creating the two-way relative frequency table. The keyword "relative" means that we'll divide each item by the grand total 32.
For instance, in the first row & first column we have 8/32 = 0.25; do the same with the other values. Do not round. The reason for this is because each decimal item is a terminal decimal, meaning the digits stop at some point. If your teacher instructs you to round, then be sure to follow those instructions of course.
Check out figure 2 so you can see the two-way relative frequency table.
A result like 0.25 in the first row & first column tells us that 25% of the class is a girl and plays basketball.
PLEASE PLEASE HELP ME
Answers
A rhombus is a quadrilateral whose all sides are of equal length. The measure of the ∠QPR is 42°.
What is a Rhombus?A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other.
The diagonals of a rhombus intersect each other at 90°. Therefore, the measure of ∠QTR can be written as,
∠QTR = 90°
(6y+6) = 90°
6y = 90 - 6
6y = 84
y = 14
Also, the diagonals of the rhombus divide the angle into two equal angles, therefore,
∠QPR = ∠SPR
∠QPR = 3y
∠QPR = 3(14)
∠QPR = 42°
Hence, the measure of the ∠QPR is 42°.
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If (product ) > 20 then (product) - 27 else if (product) < 10, then (product) + 2 else (product) - 6
Answers
AnsweB i think
Step-by-step explanation:
A triangle has side lengths of 7 inches, 12 inches, and c inches. Enter values to write an inequality that describes the possible values for c, the length of the third side of the triangle.
Answers
Answer:
The inequality is: 5<c<19
Length of third side "c" can have values greater than 5 but less than 19
Solution:
Given that,
Length of two sides of triangle are 7 inches and 12 inches respectively
Let the length of third side be "c"
The Triangle Inequality Theorem, states that, the sum of the lengths of any two sides of a triangle is greater than the length of the third side
So we get a inequality as:
Case 1:
Sum of length of two sides of triangle > length of third side
Rewrite,
Case 2:
Let 12 inches be the length of third side
Sum of sides of length 7 and c > 12
Therefore from case 1 and case 2,
Which can be combined,
Therefore the possible values of "c" are:
"c" can have values greater than 5 but less than 19
It is recommended that one fire extinguisher be available for every 6,000 square feet inside a building. a school superintendent is working to determine the number of fire extinguishers needed for a school building that has a floor plan with 132,000 square feet. let the variable x represent the number of fire extinguishers.
Answers
How to solve for b? Do you need another variable?
Answers
Answer:
No there are 180 degrees on a line
Step-by-step explanation:
180
115-
065
65°