The minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle and (r) is the radius of the circle.
A company produces circular drink coasters. the equation which represents the size of a coaster is,
[tex]x^2+ y^2 = 18.0625[/tex]
The units are in the inches. This equation can be written as,
[tex]x^2+ y^2 = \dfrac{289}{16}\\x^2+ y^2 =\left( \dfrac{17}{4}\right)^2[/tex]
Compare it with the equation of the circle, we get,
[tex]h=0\\k=0\\r=\dfrac{17}{4}\rm\; in[/tex]
The radius of the circular coaster is 17/4. The diameter of it is,
[tex]d=2\times\dfrac{17}{4}\\d=\dfrac{17}{2}\rm \; in[/tex]
Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.
[tex]a=d=\dfrac{17}{2}\rm\; in[/tex]
The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,
[tex]A=a^2\\A=\left(\dfrac{17}{2}\right)^2\\A=72.25\rm\; in^2[/tex]
Thus, the minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
Learn more about the equation of circle here;
https://brainly.com/question/1506955
Write your answer as a fraction or as a whole
6
cm
4.
m
ол
52
cm
52 cm
62 cm
Answer:
Perimeter=25
Step-by-step explanation:
HOPE THIS HELPS YOU
om
9) A dog bowl has a
diameter of 17 inches. Find
the radius, area, and
circumference of the dog
bowl.
D in
Radius:
Area:
Cirum foron
Answer:
Radius: 8.5 inches
Area ≈ 226.98
Circumference ≈ 53.42
Step-by-step explanation:
2πr = formula for circumference of a circle
πr² = formula for area of a circle
radius of a circle = (1/2)d
please help me? it is school related i promise
Answer:
$96.25
Step-by-step explanation:
In the morning, this worker was in for a total of 4 hours. Since the wage is $11/hr, we have to multiply 4 by 11.
11 * 4 = 44
In the afternoon, they worked for 4 hours and 45 minutes. Now, we have to multiply 4 3/4 (which is the fraction form of 4 hours and 45 mins) by 11.
11 * 4 3/4 = 52.25
Now, to find the total pay, we add together both the morning and afternoon pays.
44 + 52.25 = 96.25
Therefore, the total pay is $96.25
I hope this helps!! Have a lovely day!! :)
Answer:
$96.25
Step-by-step explanation:
Hours worked in the morning = 12:00 - 8:00
= 4 hours
Hours worked in the afternoon = 17:30 - 12:45
= 4 hours 45 minutes
Total hours worked = 4:00 + 4:45
= 8 hours 45 minutes
[tex]=8\dfrac{45}{60} \ hours\\\\= 8\dfrac{3}{4}\\\\\\= \dfrac{35}{4} hours[/tex]
Wage = [tex]\dfrac{35}{4}*11[/tex]
= $96.25
PLIS DOY CORONA Y TODO ESO PERO PORFAA AHORITaaaaaaaaaaaaaaaaaaaaa
no te vallas :(
Answer:
n=5 x=6
Step-by-step explanation:
2n+1 +n = 16
3n+1 =16
3n=15
n=5
2x+x+x+1 =25
4x+1=24
4x=24
x=6
please help i need the answer to this question -5x-48=-7(x+8)
Please help!
what polynomial must be added to
−5x^3 + 4x − 3 so that the sum is x^2 − x − 1?
Let the number to be added be A
Now,
[tex]\begin{gathered}\implies\quad \sf −5x^3 + 4x − 3 + A = x^2 − x − 1 \\\end{gathered} [/tex]
Transposing (−5x³+ 4x − 3 ) to other side-
[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 -( −5x^3 + 4x − 3) \\\end{gathered} [/tex]
Remember if there is a -ve sign before a bracket the signs of whole of the terms changes on opening bracket
[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 + 5x^3 - 4x + 3\\\end{gathered} [/tex]
Putting like terms together -
[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 - x -4x +3 -1 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 -5x +2 \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Therefore, 5x³+x²-5x +2 should be added to −5x³+ 4x − 3 to get x²− x − 1
evaluate the expression when x = -6: x^2 + 7x + 8
Answer:
2
Step-by-step explanation:
Basically you plug in -6 where all the x's are.
(-6)² + 7(-6) + 8, Multiply -6 * -6 (AKA (-6)²)
36 + 7(-6) + 8, Multiply 7 by -6
36 - 42 + 8, Add 36 + 8
44 - 42, Subtract
2
A ball is dropped from a height of 9 m. Each time it strikes the ground it bounces vertically to a height that is 2/3 of the preceding height. Find the total distance the ball will travel if it is assumed to bounce infinitely often. show all work.
Answer:
The answer i 9
Step-by-step explanation:
If the ball bounces 2/3 of the height of 9, and a 1/3 of 9 is 3, then 6 is the answer.
Suppose that 16 inches of wire costs 48 cents at the same rate ,how many inches of wire can be bought for 39 cents?
draw a triangle ABC with vertices A(4,2), B(3,5)and C(6,5) on a graph paper. Reflect it on X=Y and show the image on the same graph paper.
Answer:
not sure if its correct but let me know if its incorrect
thank you !
Which expression converts startfraction pi over 4 endfraction radians to degrees?
Using the degree and radian relation π/4 radian equals 45°.
Given angle =π/4 radian
What is the relation between radian and a degree?π radian equals 180 degrees means 1 radian equals 180/π degree or we can say 1-degree equals π/180 radian.
Since, 1 radian equals 180/π degree.
So, π/4 radian =180/π * π/4 degree.
π/4 radian = 45°.
So, π/4 radian equals 45°.
Therefore, using the degree and radian relation π/4 radian equals 45°.
To get more about angles visit:
https://brainly.com/question/25770607
What is the length of a line segment with endpoints 3, 2, and -3, -4, in
the simplest radical form
[tex] \qquad \qquad \qquad\large\overbrace{\underbrace{\underline{ \boxed{ \sf \:Answer }}}}[/tex]
Let's use distance formula :
[tex]\qquad \sf \dashrightarrow \: \sqrt{(3 - ( - 3)) {}^{2} + (2 - ( - 4) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(3 - ( - 3)) {}^{2} + (2 - ( - 4)) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {6}^{2} + {6}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {6}^{2}(1 + 1) } [/tex]
[tex]\qquad \sf \dashrightarrow \: 6\sqrt{ 2 } \: \: units[/tex]
Find the area of the figure
Answer:
C. 418 cm²
Step-by-step explanation:
Rectangle
= s × s
= 19 × 19
= 361 cm²
Triangle
= 1/2 × 6 × 19
= 57 cm²
361 + 57 = 418 cm²
So, therefore your answer is 418 cm²
*HELP ASAP I WILL GIVE U BRAINLEAST* (20 POINTS)
You have inherited $8000 from your grandfather. Knowing that you will soon be going to college you decide to invest your money into an account that has an 8% interest rate that is compounded quarterly. How much money will you have in your account after 5 years?
a) Exponential growth or decay:
b) Identify the initial amount:
c) Identify the growth/decay factor:
d) Write an exponential function to model the situation:
e) “Do” the problem:
Answer:
a) exponential growth b) 8000 c) 1.02 d) f(x) = 8000(1+.05/4)^(4)(5) e) $11887.58
Step-by-step explanation:
This situation is exponential growth because the money will be increasing over time. The initial amount is the amount invested in the beginning so in this case 8000. The growth factor is found by 1+r/n where r is the rate and n is the number of compounds per year so 1 + .08/4 where the r is expressed as a decimal and compounding quarterly means 4 times per year. The function is modeled by f(x) = P(1 +r/n)^nt. Evaluating the function gives f(x) = 8000(1 + .08/4)^(4*5).
10 in.
Based on the measures shown, could the figure be a
parallelogram?
(x + 5) in.
(2x-3) in.
O Yes, one pair of opposite sides could measure
10 in., and the other pair could measure 13 in.
O Yes, one pair of opposite sides could measure
10 in, and the other pair could measure 8 in.
O No, there are three different values for x when each
expression is set equal to 10
O No, the value of x that makes one pair of sides
congruent does not make the other pair of sides
congruent
(x + 2) in
Answer: (1)
Step-by-step explanation:
if TSA of cuboid box is 486 cmsquare find its volume
Answer:
It has 6 faces, So, each face has an area = 486/6 = 81 sq cm. Side of the cube =√81= 9 cm. Hence, volume of the cube = 9^3 = 729 cm^3.Jul 18, 2019
Step-by-step explanation:
Hope it's help
There's a mistake in your question it's not T.S.A of cuboid it is T.S.A of cube . Because it's not possible to find the length , breadth and height of cuboid without giving only it's Total Surface Area .
Question : -If TSA of cube box is 486 cm square , find its volume .
Given : -Total Surface Area ( T.S.A ) of cube is equal to 486 cm square .To Find : -Volume of cubeConcept : -For solving such types of questions we must have knowledge of faces of shapes and formula for surface areas and volumes of three dimensional shapes .
Formula Used : -Area of square = side²Volume of cube = a³Solving Question : -We know that cube have 6 faces . So area of each faces is equal to :
[tex] \rightarrow \: \cancel\frac{486}{6} \: cm \: sq.[/tex]
Now , dividing 486 by 6 :
[tex] \rightarrow \: 81 \: cm \: sq.[/tex]
Therefore , each square faces of cuboid have area of 81 cm square .
Now , We know that area of square :
Side ²s² = 81s = √81s = 9 cmTherefore , side/edge of cube is of 9 cm ..
Now , finding volume of cube :
We know that volume of cube is equal to ,
a³9³9 × 9 × 981 × 9729 cm³Therefore , volume of cube is 729 cm³ .
#Keep LearningHow can you decompose the composite figure to determine its area? as two semicircles and a rectangle as two circles and a rectangle as a circle and a square as two semicircles and a trapezoid.
The composite figure can be decomposed to two semicircles and a rectangle so as to find the area.
What is an area?Area is the amount of space occupied by a two dimensional shape or object.
The area of a composite figure can be decomposed to smaller figures so as to find the area.
The composite figure can be decomposed to two semicircles and a rectangle so as to find the area.
Find out more on area at: https://brainly.com/question/25292087
Answer:
A. as two semicircles and a rectangle
Step-by-step explanation:
i did it
How many students are in Mr. Gatlin’s class?How did you know? Justify your reasoning..
Answer:
where is the full question?
Step-by-step explanation:
find the missing side length.
Use the formula shown:
6^2 + 2.5^ = c^2
36 + 6.25 = c^2
42.25 = c^2
Take the square root of both sides:
c = 13/2 as a fraction or 2.5495 as a decimal (round off as needed)
the following set of coordinates represent which figure (1,1) (5,3) (7,7) (3,5)
rectangle
rhombus
parallelogram
square
Answer:
It should be a rhombus :)
Help me Please?
I will give brainliest to the first one that answers
This is my algebra 1 and i dont understand it
Answer:
f(9.5) = 558.02.
Step-by-step explanation:
Because it is an exponential function, it can be written: y = (a)(b)^x
Now substitute in the two known points:
72 = (a)(b)^7.5 and
2 = (a)(b)^4 : => since 2 = (a)(b)^2 divide the left side by 2 and the right by (a)(b)^2
72/2 =[(a)(b)^7.5]/[(a)(b)^4]: => the (a) cancels out and b becomes b^(7.5–4)
36 = b^3.5: => To isolate b take the 3.5 root of both sides
{3.5 root}(36) = {3.5 root}(b^3.5)
2.783927 = b
Now to solve for a
2 = (a)(b)^4 => 2 = (a)(2.783927)^4 => 2 = (a)(60.066375) divide both sides by 60.066375 0.0332965 = a
Equation: y = (0.0332965)(2.783927)^x
Now plug in 9.5 for x
(0.0332965)(2.783927)^9.5 = 558.0178525 = 558.02
I dont understand what this is really telling me. can someone explain?
Answer:
B
Step-by-step explanation:
It's where the line goes over the x line
Answer:
B,
Step-by-step explanation:
The zeros are the x values where the graph crosses the horizontal x-axis.
These are at x = 0 and x = 5.
help please.. write the equation of the blue line using slope-intercept form (y=mx+b)
y = mx + p
p = - 7 since the line cuts the y-axis in -7
and m the slope ?
we choose 2 points (-2 ; 0) and (0 ; - 7)
we move of 2 units towards the left to go down of 7 units
=> m = - 7/2
y = - 7/2x - 7
or
y = -3,5x - 7
PLEASE HELP! DUE TODAY! TY!
Use the diagram to find the value of x and the measure of Arc MR. (MR) =(3x+19)° and (LK) =189°
Work:
x =
(MR) =
Answer: x=12, (MR)=55
Step-by-step explanation:
The exponential function f(x) has a positive coefficient, a base of 0.6, and a horizontal asymptote at y = 3. If g(x) = 2(x - 3), which statement is true? A. The function f(x) represents exponential growth, and the function g(x) represents exponential decay. B. The function f(x) represents exponential decay, and the function g(x) represents exponential growth. C. The functions f(x) and g(x) both represent exponential growth. D. The functions f(x) and g(x) both represent exponential decay.
Answer:i don’t know the answer the answer but it’s f
Step-by-step explanation:
Use an equation to solve.
What is 60% of 400?
Answer:
240 :)
Step-by-step explanation:
400 x 0.60 = 240
Have a great day!
Please rate and mark brainliest!!
Answer:
240
Step-by-step explanation:
HELP PLEASE. Check picture. I have tried but cannot seem to get it.
Answer:
[tex]884^{-7}[/tex]
Step-by-step explanation:
Start by simplifying the denominator of the fraction. When multiplying exponents of the same base, you can add the exponents. This is also known as the product rule.
[tex]a^x\cdot a^y=a^{x+y}[/tex]
["a" is the base, and "x" and "y" are the exponents]
Using this we find...
[tex]884^{58}\cdot884^{46}=884^{58+46}=884^{104}[/tex]
When dividing exponents of the same base, you can subtract the exponents. This is also knows as the quotient rule.
[tex]a^x\div a^y=a^{x-y}[/tex]
Using this we find...
[tex]\frac{884^{97}}{884^{104}}=884^{97-104}=884^{-7}[/tex]
Answer:
[tex]884^{-7[/tex]
Step-by-step explanation:
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Before we begin solving, let's review a few rules of exponents.
If an exponent is multiplying with another exponent and their bases are the same, you can simply add the exponents.If an exponent is dividing with another exponent and their bases are the same, you can simply subtract the exponents.≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
⇒ [tex]\dfrac{884^{97} }{884^{58} \times 884^{46} }[/tex]⇒ [tex]\dfrac{884^{97} }{884^{58 + 46}}[/tex] [#1]⇒ [tex]\dfrac{884^{97} }{884^{104}}[/tex]⇒ [tex]884^{97 - 104[/tex] [#2]⇒ [tex]\boxed{884^{-7}}[/tex]≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Help me on this question please!
[tex]\huge\fcolorbox{blue}{red}{Answer}[/tex]
════════════════════
[tex]\frac{ x }{ 3 } +6-2x=-6[/tex]
[tex]x+18-6x=-18 [/tex]
[tex]-5x+18=-18 [/tex]
[tex]-5x=-18-18 [/tex]
[tex]-5x=-36 [/tex]
[tex]x=\frac{-36}{-5} [/tex]
[tex]x=\frac{36}{5} [/tex]
[tex]= 7 \frac{1}{5}[/tex]
[tex]= 7.2[/tex]
So the answer is [tex]x = 7.2[/tex] or [tex]= 7.2[/tex]
══════════════════════
Step-by-step explanation:
#Carry on learning
What is the resulting equation when the expression for y in the second equation is substituted into the first equation?
3x + y = 1
y=6 - 4x
Ox+6y=1
Ox+6=1
Ox -X + 6 = 1
7X+6=1
Hello!
Let's solve this question with the information given to us in the question.
We were given two equations:
3x + y = 1
y = 6 - 4x
The question asks us to plug in our 2nd equation into the "y" variable of the first equation.
Plug in and solve:
3x + y = 1
Substitute "6 - 4x" for y
3x + 6 - 4x = 1
Simplify
-x + 6 = 1
Therefore, your answer would be the -x + 6 = 1 choice in your answer box.
Answer: -x + 6 = 1
A mom shared $490 between her 2 daughters in the ratio of 4 : 3 respectively. Calculate how much money is the larger share?
Step-by-step explanation:
let ratio be 4x and 3x
sum : 490$
4x+3x = 490
7x=490
x=490/7
Hence x = 70
first daughter gets = 4x =4 x 70 = 280
second daughter gets =3x = 3x 70 = 210
first daugter gets the larger share