[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=81\pi \end{cases}\implies 81\pi =\pi r^2\implies \cfrac{81\pi }{\pi }=r^2\implies 81=r^2 \\\\\\ \sqrt{81}=r\implies \boxed{9=r}~\hspace{10em}\stackrel{\textit{diameter = twice the radius}}{18}[/tex]
[tex]
A=81\pi \\
A=\pi r^2 \\
81\pi=\pi r^2\Longrightarrow r^2=81
radius=\sqrt{81}=\boxed{9} \\
diameter=2radius = 2\cdot9=\boxed{18}
[/tex]
Please Help
Calculate the side lengths a and b to two decimal places.
A. a = 11.40 and b = 13.38
B. a = 11.71 and b = 15.56
C. a = 4.18 and b = 3.15
D. a = 10 and b = 14
The side length of the triangle are as follows:
a = 11.71 and b = 15.56
How to find the side of a triangle?The side of a triangle can be found using sine rule or cosine rule depending on the sides and angles given in a triangle.
Therefore, the sides a and b can be found in the triangle using sine rule as follows:
a / sin A = b / sin B = c / sin C
b / sin 110 = 7 / sin 25°
cross multiply
b sin 25 = 7 sin 110°
b = 7 sin 110° / sin 25
b = 6.5778483455 / 0.42261826174
b = 15.5625174507
b = 15.56 units
Let's find a as follows:
a / sin 45 = 7 / sin 25
a sin 25 = 7 sin 45
a = 7 sin 45 / sin 25
a = 4.94974746831 / 0.42261826174
a = 11.7108376716
a = 11.71 units
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Math
Can someone please explain what I need to do here to find answer?
Thanks
Answer:
C
Step-by-step explanation:
First of all their is an easier way solving this 2l/ + l^2
but how you need it is c because the base is 100 and each face is 40 how 10x8=80 80/2=40
simplify the expression (x^19 times y^21) divided by (x^2 times y^6)^2
Answer:
[tex]x^{15}.y^{9}[/tex]
Step-by-step explanation:
[tex]\frac{x^{19} . y^{21}}{(x^2. y^6)^2} \\\\Here\,\, exponent\,\, rules\,\, will\,\, be\,\, used.\\First\,\, multiply\,\, power\,\, of \,\,2\,\, with\,\, denominator \,\,exponents\\\\\frac{x^{19} . y^{21}}{x^4. y^{12}}\\If \,\, same\,\, bases\,\, are\,\, divided\,\, then\,\, their\,\, exponents\,\, are \,\,subtracted\,\,\\\\x^{19-4}.y^{21-12}\\\\x^{15}.y^{9}[/tex]
Please help me (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;)
Answer:
Frequency is the number of times that roll occurred.
Ex: 7 occurred 5 times...... 5 goes in the frequency column.
Draw a line with a negative slope
What you did in the graph was correct. Essentially, all you have to do to achieve a negative slope is either make the rise negative or the run negative (make sure not to do both, as the negatives would cancel out and make a normal line)
Solving equations (algebra). Thank you!
Answer:
[tex]\large\boxed{\dfrac{1}{x^2}+x^2=23}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{1}{x}+x\right)^2=25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\left(\dfrac{1}{x}\right)^2+2(x\!\!\!\!\diagup)\left(\dfrac{1}{x\!\!\!\!\diagup}\right)+x^2=25\\\\\dfrac{1}{x^2}+2+x^2=25\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{x^2}+x^2=23[/tex]
The value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex] is [tex](a+b)^2 = a^2 +b^2 +2ab[/tex].
Given that if [tex](\frac{1}{x } +x)^2[/tex] = 25 then find the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] .
To find the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] by using the algebraic identity and follow the steps:
Apply the algebraic identity to the given equation, that is :
[tex](a+b)^2 = a^2 +b^2 +2ab[/tex]
Given that :
[tex](\frac{1}{x } +x)^2=25[/tex]
Expand the LHS by using mentioned algebraic identity:
[tex]\frac{1}{x^2 } +x^2+2x\times\frac{1}{x} =25[/tex]
On cancelation of the variable x in third term of the LHS gives:
[tex]\frac{1}{x^2 } +x^2+2=25[/tex]
Subtract by 2 on both sides, gives:
[tex]\frac{1}{x^2 } +x^2=23[/tex]
Therefore, the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex] is
[tex](a+b)^2 = a^2 +b^2 +2ab[/tex]
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what would the vertices be?
The vertices of a triangle are also called the points. Every triangle has 3 vertices. In this case, they are given.
A(-4,4)
B(-4,8)
C(0,4)
I graphed these points for you :)
a cylinder with a diameter of 24 inches and a height of 8 inches has the same volume as a cone with a diameter of 12 inches. what is the height of the cone?
Answer:
The height of the cone is 97 in
Step-by-step explanation:
Equate the formulas for the volume of a cylinder and that of a cone:
Vol-Cyl Vol-Cone
πr²h = (1/3)πr²h
Now cancel out items that are the same on both sides (π):
r²h = (1/3)r²h
Now substitute the given values for both solids:
(12 in)²(8 in) = (1/3)(6 in)²(h-cone)
1152 in³
Then (h-cone) = -------------------- = 97 in
12 in²
The height of the cone is 97 in
Answer:
96 in
Step-by-step explanation:
Use the function rule. Find y for x = 1, 2, 3, and 4. y = x – 5
-y = 4, 3, 2, 1
-y = 6, 7, 8, 9
-y = –5, –4, –3, –2
-y = –4, –3, –2, –1
Answer:
is the fourth one
Step-by-step explanation:
just replace x with the numbers given
and then work it out.
y=x-5
y=1-5=-4
y=2-5=-3
and so on
hope this helps
For this case we have a function of the form [tex]y = f (x)[/tex]where:
[tex]f (x) = x-5[/tex]
We must find the values of "y" when [tex]x = 1,2,3,4[/tex]
Then, keeping in mind that different signs are subtracted and the sign of the major is placed:
[tex]x = 1\\f (1) = 1-5 = -4\\So, y = -4[/tex][tex]x = 2\\f (2) = 2-5 = -3\\So, y = -3[/tex][tex]x = 3\\f (3) = 3-5 = -2\\Thus, y = -2[/tex][tex]x = 4\\f (4) = 4-5\\f (4) = - 1\\Thus, y = -1[/tex]Answer:
Option D
what is the answer for
an=an–1+1
‘an’ could represent any number
Simplify the expression to get an = an + 0, or an = an.
This means that a number is equal to itself, which is true for all numbers.
Are the triangles similar why or why not
Answer:
Yes
Step-by-step explanation:
Yes because all three sides have the same ratio
Use the Distributive and Commutative properties to determine
whether each pair of expressions is equivalent for all values of x.
a. 3x + 7x and 10x
b. 5x and 5x – 10x c. 4(1 + 2x) - 3x and 5x + 4 d. 5 - 3(2 – 4x) and -1 + 12x
Answer:
a. equivalent
b. not equivalent
c. equivalent
d. equivalent
Step-by-step explanation:
a. 3x +7x = (3+7)x = 10x . . . equivalent to 10x
__
b. 5x -10x = (5 -10)x = -5x . . . not equivalent to 5x
__
c. 4(1 +2x) -3x = 4·1 +4·2x -3x = 4 +(8 -3)x = 4 +5x = 5x +4 . . . equivalent to 5x +4
__
d. 5 -3(2 -4x) = 5 -3·2 -3(-4x) = 5 -6 +12x = -1 +12x . . . equivalent to -1 +12x
Evaluate the expression:
1/3 (4x3) + 2^3
Answer:
12
Step-by-step explanation:
1/3 (12) +8
4+8= 12
Answer:
12
Step-by-step explanation:
we can use PEMDAS to find the solution to the expression, PEMDAS stands for:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
we look at the expression and we see parentheses, so we solve whats inside of the parentheses
(4 x 3) = 12
1/3 (12) + 2³
now, we solve for the exponents in the expression
2³ = 2 x 2 x 2 = 8
1/3 (12) + 8
now we multiply the terms in the expression that need to be multiplied.
1/3 x 12 = 4
4 + 8
we have no division in the expression, so we skip that step and move onto addition, which will be our last step as there is no subtraction in the expression either
4 + 8 = 12
our answer to the expression is 12
Find the volume of a rectangular prism that is 8 inches high, 12 inches long, and 5 inches wide.
A
360 in.³
B
480 in.³
C
420 in.³
D
240 in.³
Answer: B.
Length x width x height
Whenever you're finding the volume of a quadrilateral, you multiply the base x width x height of the shape. In this case, you have all three of those elements.
First I substituted those numbers into their spots in the expression (it doesn't matter which you multiply first, since multiplying is commutative).
8 x 12 x 5 = 480
Your answer is 480 square inches.
What is the name of the Platonic solid shown below
Answer:
C.
Step-by-step explanation:
A hexahedron has 6 equal sides. Like the cube shown.
The name of the platonic solid shown is hexahedron.
What are different types of solids?Tetrahedron - A tetrahedron, also referred to as a triangle pyramid, is a polyhedron with four triangular faces, six straight edges, and four vertex corners in geometry.
Hexahedron - Any polyhedron with six faces is called a hexahedron.
Octahedron - An octahedron is a polyhedron with eight faces in geometry.
Dodecahedron - In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces
The figure given in the question has clearly six flat faces and hence according to the definitions it is a hexahedron.
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Problem:
Emilia bought 8 t-bone steaks for $55.92. Each steak was the same price. How much did Emilia pay for a
steak?
$447.36
B
$6.99
C
$6300
$63.92
$47.92
End
Session
Answer:
The answer would be B $6.99. With this problem you would need to divide the total cost by 8 to get the price for a single steak.
Step-by-step explanation:
Raj fully simplified the polynomial and then put it in standard form with the last term being 6y3. 2x2y + 8x3 – xy2 – 2x3 + 3xy2 + 6y3 What is the first term of the polynomial Raj ended up with? 6x3 8x3 2xy2 3xy2
Answer: First option.
Step-by-step explanation:
To simplify the polynomial [tex]2x^2y + 8x^3 - xy^2 - 2x^3 + 3xy^2 + 6y^3[/tex] you need to add the like terms, then you get:
[tex]=2x^2y+6x^3+2xy^2+6y^3[/tex]
Now, you know that Raj put this polynomial in standard form with the last term being 6y³, this means that he ordered it in descending order of "x" power and in ascending order of "y" power:
[tex]=6x^3+2x^2y+2xy^2+6y^3[/tex]
You can observe that the first term of the polynomial that Raj ended up with, is:
[tex]6x^3[/tex]
Answer:
The answer would b A
The temperature of a chemical reaction ranges between 20 degrees Celsius and 160 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during an 8-hour period. What is a cosine function that models this reaction?
Answer:
The cosine function that models this reaction is:
[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]
Step-by-step explanation:
The general cosine function has the following form
[tex]y = Acos(bx) + k[/tex]
Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.
[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.
k is the vertical displacement.
The maximum temperature is 160 and the minimum is 20. Then the amplitude A is:
[tex]A =\frac{160-20}{2}\\\\A= 70[/tex]
The reaction completes a cycle in 8 hours
Then the period is 8 hours.
Thus:
[tex]\frac{2\pi}{b}=8\\\\ b=\frac{2\pi}{8}\\\\ b=\frac{1}{4}\pi[/tex]
The function is:
[tex]y = 70cos(\frac{1}{4}\pi x)+k[/tex]
when [tex]t=0[/tex] y is minumum therefore [tex]y=-cos(x)[/tex]
So
[tex]y = -70cos(\frac{1}{4}\pi x)+k[/tex]
Now we substitute [tex]t = 0[/tex] in the function and solve for k
[tex]20 = -70cos(0)+k\\\\k=20+70\\\\k=90[/tex]
Finally
[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]
help me you get branliest 100 points and 5-star rating plus a thanks
Answer:
Step-by-step explanation:
Step 1: Additive inverse
Step 2: Additive identity
Step 3: Addition property of equality
22 is D
Find the center and radius of the circle x2 - 22x + y2 + 20y =4
Answer:
x² - 22x + y² + 20y = 4
x² - 22x + 121 + y² + 20y + 100 = 225
(x - 11)² + (y + 10)² = 15²
Center: (11, -10)
Radius: 15
Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. Kelly ran at an average speed of 8 miles per hour.
When will Ava and Kelly be 3/4 mile apart?
The answer is:
It will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.
Why?To calculate how long after they start they will be 3/4 miles apart, we need to write two equations.
So, writing the equations, we have:
Calculations for Ava:
We have the following information,
[tex]v_{Ava}=6mph[/tex]
Then, writing the equation,
[tex]x_{Ava}=x_{o}+v_{Ava}*t[/tex]
[tex]x_{Ava}=x_{o}+v_{6mph}*t[/tex]
Calculations for Kelly:
We have the following information,
[tex]v_{Kelly}=8mph[/tex]
We need to calculate when Kelly will be 3/4 miles apart of Ava, so, it's position will be the Ava's position plus 3/4 miles.
Then, writing the equation,
[tex]x_{Ava}+0.75miles=x_{o}+v_{Kelly}*t[/tex]
[tex]x_{Ava}+0.75miles=x_{o}+v_{8mph}*t[/tex]
Now, substituting Ava's speed into the second equation, we have:
[tex]x_{o}+6mph*t+0.75miles=x_{o}+8mph*t[/tex]
[tex]6mph*t+0.75miles=+8mph*t[/tex]
[tex]8mph*t-6mph*t=0.75miles[/tex]
[tex]2mph*t=0.75miles[/tex]
[tex]t=\frac{0.75miles}{2mph}=0.375hours[/tex]
Hence, we have that it will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.
Have a nice day!
Answer:
So what the other guy said in minutes was 22.5 minutes
Step-by-step explanation:
6 cm
4 cm
10 cm
Note: Figure is not drawn to scale.
What is the volume of the pencil holder?
A.
240 cubic centimeters
OB. 60 cubic centimeters
C.
120 cubic centimeters
D.
200 cubic centimeters
The volume of the pencil holder with dimensions 6 cm, 4 cm, and 10 cm is 240 cubic centimeters, as calculated using the formula for the volume of a rectangular prism.
Explanation:To calculate the volume of a rectangular pencil holder with the given dimensions of 6 cm, 4 cm, and 10 cm, the formula for the volume (V) of a rectangular prism should be used, which is:
V = length × width × height
Substitute the given measurements into the formula:
V = 6 cm × 4 cm × 10 cm = 240 cm³
Therefore, the volume of the pencil holder is 240 cubic centimeters.
What is the maximum of the sinusoidal function?
Answer:
The maximum of y = sin x is 1. The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function.
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
you and your best friend are going out for ice cream there are 7 different flavors issues from what is the approximate probability that you both choose chocolate ice cream
The approximate probability that both you and your friend will choose chocolate ice cream from seven different flavors is 1/49, or approximately 0.020408.
We are looking to find the probability that both you and your friend choose chocolate ice cream from a selection of 7 different flavors. Since the choice of ice cream is independent for each person, we can calculate the probability of both events occurring by multiplying the probability of each event occurring individually.
The probability that one person chooses chocolate ice cream is 1 out of 7, or approximately 0.142857. To find the probability that both you and your friend choose chocolate ice cream, we multiply the individual probabilities:
Probability of you choosing chocolate: 1/7
Probability of your friend choosing chocolate: 1/7
Combined probability: 1/7 x 1/7 = 1/49
Therefore, the approximate probability that both you and your friend choose chocolate ice cream is 1/49, or approximately 0.020408.
Find the roots of the equation below. 7x^2 + 1 = 0
Answer:
7x2-1 = 0
Step-by-step explanation:
Add 1 to both sides of the equation :
7x2 = 1
Divide both sides of the equation by 7:
x2 = 1/7 = 0.143
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 1/7
Answer:
Step-by-step explanation:
Rewrite 7x^2 + 1 = 0 as 7x^2 = - 1, and then as x^2 = -1/7.
Taking the square root of both sides, and remembering that the square root of a negative number is imaginary, we get:
i√7
x = ±i(1/7) = ± ----------
7
Points are plotted at (-2, 2), (-2, -4), and (2, -4). A fourth point is drawn such that the four points can be connected to form a rectangle. What is the area of this rectangle?
8 square units
12 square units
16 square units
24 square units
Answer:
24
Step-by-step explanation:
4x6 = 24
-2 and 2 are 4 apart
2 and -4 are 6 apart
Answer:
24 square units
Step-by-step explanation:
find the amount at 6% simple interest of rs 1200 due in 9 month
STEP 1: Convert interest rate of 2% per 6 months into rate per year.
rate per year = rate per 6 month⋅2=2%⋅2=4%
STEP 2: Convert 9 months into years.
9 months =
9
12
years=0.75 years
STEP 3: Find principal by using the formula
I=P⋅i⋅t
, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
In this example I = $15, i = 4% and t = 0.75 years, so
I
P
P
P
=P⋅i⋅t
=
I
i⋅t
=
15
0.04⋅0.75
=500
Final answer:
To calculate the amount at 6% simple interest on Rs 1200 for 9 months, apply the simple interest formula. Convert time to years, calculate the interest, then add it to the principal to find the total amount due, which is Rs 1254.
Explanation:
To find the amount at 6% simple interest on Rs 1200 due in 9 months, you can use the simple interest formula:
Simple Interest = Principal × Rate × Time
We have the Principal (P) as Rs 1200, the Rate (R) as 6% per annum (or 0.06 when expressed as a decimal), and the Time (T) as 9 months. The rate is given per annum but we have in months so, we need to convert the time to years. There are 12 months in a year, so 9 months is ⅓ or 0.75 years.
Now, let's calculate the simple interest (SI):
SI = 1200 × 0.06 × 0.75 = Rs 54
Total Amount = Principal + Simple Interest
Total Amount = 1200 + 54 = Rs 1254
Therefore, the total amount due at the end of 9 months would be Rs 1254.
Find the surface area of the figure. Round your answer to the nearest hundredth if necessary.
This may be what you're looking for:
Evaluate. 7P2 this is premutations and i dont get it
Answer:
[tex]\large\boxed{_7P_2=42}[/tex]
Step-by-step explanation:
[tex]_nP_k=\dfrac{n!}{(n-k)!};\ n!=1\cdot2\cdot3\cdot...\cdot n\\\\\text{We have:}\\\\_7P_2=\dfrac{7!}{(7-2)!}=\dfrac{7!}{5!}=\dfrac{5!\cdot6\cdot7}{5!}=6\cdot7=42[/tex]
The permutation 7P2 calculates the number of ways to arrange 2 items from a set of 7. It is found using the formula nPr = n! / (n-r)!, resulting in 42 different arrangements.
The student is asking about how to calculate a permutation, specifically 7P2. Permutations are used to determine the number of ways to arrange a subset of items from a larger set, where the order does matter. To compute 7P2, we use the formula for permutations, which is nPr = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to arrange.
To evaluate 7P2, we plug in 7 for n and 2 for r, which gives us: 7P2 = 7! / (7-2)! 7P2 = 7! / 5! 7P2 = (7 x 6 x 5!) / 5! 7P2 = 7 x 6 7P2 = 42
Therefore, there are 42 different ways to arrange 2 items from a set of 7.
Solve the equation using the zero product property -2x(5x-2)=0
X=0,2/5
X=0,2
X=0,-2/5
X=0,-2
Answer:
A
Step-by-step explanation:
Given
- 2x(5x - 2) = 0
Equate each factor to zero and solve for x
- 2x = 0 ⇒ x = 0
5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]
Solutions are
x = 0, x = [tex]\frac{2}{5}[/tex]