Rachel is having chocolate cake for dessert. The cake is 12 inches in diameter and she plans to cut it into 12 pieces. What is the area of each slice of Rachel's cake?
Answers
The area of each slice of the cake is 3π square inches
How to find the area of a circle?The cake is 12 inches in diameter. The cake top is circular.
Therefore, the area of a circle is as follows;
area of a circle = πr²
where
r = radiusTherefore,
r = diameter / 2
r = 12 / 2
r = 6 inches
Hence,
area of a circle = π × 6²
area of a circle = 36π
area of each sliced cake = 36π / 12
area of each sliced cake = 3π square inches
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Related Questions
18. A tennis player uses up 800 calories every hour. In 1 hour and 15 minutes, how many calories does this player use? (A) 900 (B) 1000 (C) 1100 (D) 1200
Answers
An hour = 60 minutes,
60/4= 15 minutes
The tennis player uses 800 calories, so 800/4 =200 calories
1 hour 15 minutes= 60 minutes + 15 min.
= 800 cal. + 200 cal.
=1000calories
1. How do you prove congruence through transformations?
2. How do you prove triangle congruence using congruency postulates? Give a general explanation of what the S and A stand for. Please name each of the postulates and what the letters stand for.
Answers
One can prove congruence through transformation if they have the same shape and size.
The congruency postulates include:
SSS - Side-Side-SideSAS - Side-Angle-SideASA- Angle-Side-AngleAAS - Angle-Angle-SideRHS - Right angle-Hypotenuse-SideWhat is congruence?In geometry, it should be noted that two figures are congruent if they have the same shape and size.
In this case, if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
One can prove triangle congruence using congruency postulates by using the SSS theorem( side side side theorem).
It should be noted that the congruence postulate is used to illustrate that the triangles are equal.
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what time 2 equals 25
Answers
Answer:
the answer to "2 times what equals 25?" is 12.5.
Use method of subtitution, will give brainliest, 20 pts
Answers
Answer:
x=3
y = -2
Step-by-step explanation:
2x+5y = -4
y = x-5
We want to use substitution
In the first equation, every time we see y, substitute x-5
2x + 5( x-5) = -4
Distribute
2x + 5x -25 = -4
Combine like terms
7x -25 = -4
Add 25 to each side
7x -25+25 = -5+25
7x = 21
Divide each side by 7
7x/7 = 21/7
x=3
Now we can find y
y = x-5
y = 3-5
y = -2
The answer is x = 3, y = -2 or (3, -2).
We are given that :
2x + 5y = -4y = x - 5Let us substitute the 2nd equation's value of y in the 1st equation.
2x + 5(x - 5) = -42x + 5x - 25 = -47x = 21x = 3Now, substitute for x in the 2nd equation.
y = 3 - 5y = -2At the beginning of the summer, sarah has $250. she takes a summer job and saves $150 per week. felicia has $1,650 at the beginning of the summer. she travels during the summer and spends $200 per week. at the end of which week do sarah and felicia have the same amount of money?
Answers
Answer:
Week 4
Step-by-step explanation:
Victoria has $250 and saves $150 each week, hence have increments $150 each week
250+150 (first week)
= 400
second week = 400 + 150 = 550
third week = 550 + 150 = 700
fourth week = 700 + 150 = $850
Felicia on the other hand has $1,650 and spends $200 each week, hence has decrements of $200 each week.
1650+200 (first week)
= 1450
second week = 1450 - 200 = 1250
third week = 1250 - 200 = 1050
fourth week = 1050 + 200 = $850
A regular octagon has an apothem measuring 10 in. and a perimeter of 66.3 in. a regular octagon has an apothem with length 10 centimeters and a perimeter of 66.3 inches. what is the area of the octagon, rounded to the nearest square inch?
Answers
331.5 inches² is the area of the octagon, rounded to the nearest square inch.
What is octagonal in shape?
In geometry, an octagon is a polygon that has 8 sides and 8 angles. All the sides are joined end to end to form the shape of the octagon. The sum of the interior angles of an octagon is equal to 180 degrees.Solving for an area of a regular octagon, we can make use of the formula shown below:
Area = 1/2 × apothem × perimeter
In this problem, the following values were given such as:
Apothem = 10 inches
Perimeter = 66.3 inches
Put the values in the formula
Area = 1/2 × 10 × 66.3
Area = 331.5 inches²
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Answer: C). 332 in.2
Step-by-step explanation:
on edg
Select the correct answer. what is the completely factored form of this expression? 3x2 − 17x − 28 a. (3x 4)(x 7) b. (3x 4)(x − 7) c. 3x2 − 17x − 28 d. (3x2 4)(x − 7)
Answers
Answer:
A. (3x + 4)(x-7)
Step-by-step explanation:
3x times x = 3x^2
3x times -7 = -21x
4 times x = 4x
4 times -7 = -28
-21x + 4x = -17x
3x^2 - 17x - 28
define ratio (maths short definition)
Answers
Answer:
division
Step-by-step explanation:
ratio compares 2 numbers by dividing them
example
2 out of 3 dentists like gum
2 ÷ 3 = .67 = 67%
so you can say
67% of dentists like gum
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.
Given the functions f(x) = –4ˣ + 5 and g(x) = x³ + x² – 4x + 5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
Answers
Answer:
f(x) is an exponential functiong(x) is a polynomial function of degree 3Key common features: same domain, both have one x-intercept and one y-intercept.Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-4^x+5\\g(x)=x^3+x^2-4x+5 \end{cases}[/tex]
Function f(x)This is an exponential function.
An exponential function includes a real number with an exponent containing a variable.
x-intercept (when y = 0):
[tex]\begin{aligned}f(x) & = 0\\\implies -4^x+5 & =0\\ 4^x &=5\\\ln 4^x &= \ln 5\\x \ln 4 &= \ln 5\\x&=\dfrac{ \ln 5}{\ln 4}\\x&=1.16\:\: \sf(2\:d.p.)\end{aligned}[/tex]
Therefore, the x-intercept of f(x) is (1.16, 0).
y-intercept (when x = 0):
[tex]\begin{aligned}f(0) & = -4^{0}+5\\& = 1+5\\& = 6\end{aligned}[/tex]
Therefore, the y-intercept of f(x) is (0, 6).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow 5[/tex]
Therefore, there is a horizontal asymptote at y = 5 which means the curve gets close to y = 5 but never touches it. Therefore:
Domain: (-∞, ∞)Range: (-∞, 5)Function g(x)This is a polynomial function of degree 3 (since the greatest exponent of the function is 3).
A polynomial function is made up of variables, constants and exponents that are combined using mathematical operations.
x-intercept (when y = 0):
There is only one x-intercept of function g(x). It can be found algebraically using the Newton Raphson numerical method, or by using a calculator.
From a calculator, the x-intercept of g(x) is (-2.94, 0) to 2 decimal places.
y-intercept (when x = 0):
[tex]\begin{aligned}g(0) & = (0)^3+(0)^2-4(0)+5\\& = 0+0+0+5\\& = 5 \end{aligned}[/tex]
Therefore, the y-intercept of g(x) is (0, 5).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow - \infty[/tex]
Therefore:
Domain: (-∞, ∞)Range: (-∞, ∞)Conclusion
Key features both functions have in common:
One x-intercept (though not the same)One y-intercept (though not the same)Same unrestricted domain: (-∞, ∞)Consider the function . find the vertical asymptote(s) of f(x). x = 0, –9 x = –9 x = 0, 9 x = 9
Answers
The vertical asymptote of f(x) is (A) x = 0, –9.
What is a function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.To find the vertical asymptote of f(x):
The vertical asymptotes of a function are the zeroes of the denominator of a rational function
The function is given as: [tex]f(x) = \frac{(x-9)}{(x^{3} -81x)}[/tex]
Set the denominator to 0:
[tex]x^{3} -81x=0[/tex]Factor out x:
[tex]x(x^{2} -81)=0[/tex]Express 81 as 9^2:
[tex]x(x^{2} -9^{2} )=0[/tex]Express the difference between the two squares:
[tex]x(x-9)(x+9)[/tex]Split, [tex]x=0[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].
Solve for x:
[tex]x=0\\[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.
(See attachment for the graph of f(x))
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The complete question is given below:
Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).
A) x = 0, –9
B) x = –9
C) x = 0, 9
D) x = 9
A hydrogen atom has one positively charged proton and one negatively charged electron.
Write an addition equation to represent how their charges combine to make the overall charge of the atom.
Answers
The addition equation to represent how their charges combine to make the overall charge of the atom is + 1 + - 1 = 0
How to write equation to represent charges of atom?A hydrogen atom has one positively charged proton and one negatively charged electron.
An atom of every elements has an electron(negatively charged) and positively charge(proton) part.
An atom as a whole is electrically neutral if the number of proton and electron are equal. They will cancel each other to make the atom neutral.
Therefore, the addition equation to represent how their charges combine to make the overall charge of the atom is as follows;
+ 1 + - 1 = 0
1 positively charged proton plus single negatively charged electron = zero(neutral)
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Please help!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
Answer:
6
Step-by-step explanation:
Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.
[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]
The length of AC is simply x, therefore 6
The graph below shows the speed of a car that is driven through a town and then on a major highway. During which of the following time intervals was the car stopped at a traffic light?
Answers
Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
When is a car stopped at a traffic light?When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.
In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
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PLEASE HELP IM STUCK ON THIS
Answers
Pick 2 coordinates:
I choose first & last one (0,15) & (8-9)
Change in y is 24
(15--9 = 24)
Change in x is 8
(0 - 8) = - 8
24/-8 = - 3
So, slope = - 3
Hope this helps!
Answer:
-3
Step-by-step explanation:
The formula to find the slope is (change in y)/(change in x). In other words, rise over run.
If we look at the data, we can see that the x and y value changes.
x value: 0 --> 2 --> 4 --> 6 --> 8
y value: 15 --> 9 --> 3 --> -3 --> -9
When y changed from 15 to 9, the x changed from 0 to 2.
y: 15 --> 9
x: 0 --> 2
There was a difference of -6 in the y and a difference of 2 in the x.
At the top, I wrote that the slope was (change in y)/(change in x)
With -6 and 2 we found, we can say that the slope is -6/2.
If we simplify this answer, we end up with -3.
So -3 is the slope of the data.
Samuel is arranging books in shelves at their library. He has 80 books to arrange he needs to put the same number of books on each shelf, and he needs to use all of the books. Between 9, 10 and 11 shelves, which is his best choice for the number of shelves that he can use?
(Show the solution and do not use Division (optional) and use the Divisibility rules of numbers)
Answers
Answer:
10 shelves
Step-by-step explanation:
out of the other choices, 10 is most suitable to divide with 80
Using the following table determine the probability a person tests positive who does not actually have Tuberculosis.
Answers
Using it's concept, the probability a person tests positive who does not actually have Tuberculosis is:
c. 49/148.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 198 + 98 = 296 people who test positive, which is the number of total outcomes, and of those, 98 do not have the disease, which is the number of desired outcomes. Hence the probability is given by:
p = 98/296 = 49/148.
Which means that option c is correct.
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The probability a person tests positive who does not actually have Tuberculosis is 1/100
How to determine the probability a person tests positive who does not actually have Tuberculosis?The probability is given as:
The probability a person tests positive who does not actually have Tuberculosis.
This is a conditional probability, and it can be calculated using
P = n(Tests positive | Does not have Tuberculosis)/n(Does not have Tuberculosis)
Using the given table of values, we have:
P = 98/9800
Evaluate the quotient
P = 1/100
Hence, the probability a person tests positive who does not actually have Tuberculosis is 1/100
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How many lines of symmetry does a regular pentagon have?
4
4
5
5
6
6
7
7
Answers
Answer:
5 line of symmetry
Step-by-step explanation:
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
[tex]m = m \\ \frac{97 - 68}{2 - 1} = \frac{134 - 97}{3 - 2} \\ 29 = 37 \\ this \: function \: is \: non \: linear[/tex]
Since the only two other options are quadratic and given that it must satisfy one of them i will assume the following general form of the function.[tex]f(1) = 68 \: \: \: f(2) = 97 \: \: \: \: f(3) = 134 \\ f(x) = ax {}^{2} + bx + c[/tex]
Substitute in the first function any point.[tex]f(1) = 68 \\ 7.8(1) {}^{2} - 2.9(1) + 67.1 = 68 \\ 7.8 - 2.9 + 67.1 = 68 \\ 72 = 68 \\ this \: is \: false[/tex]
I'm pretty sure something is wrong with the givenFind the solution to the system of equations: x 3y = 7 and 2x 4y = 8 1. isolate x in the first equation: 2. substitute the value for x into the second equation: 3. solve for y: 4. substitute y into either original equation: 5. write the solution as an ordered pair:
Answers
Two or more equations using the same variable are referred to mathematically as a "system of linear equations." These equations' solutions serve as a representation of the intersection of the lines.
According to the given information:Two equations are presented here:
1) x + 3y = 7
2) 2x + 4y = 8
First, in the first equation, we want to isolate x:
x + 3y = 7
x = 7 -3y
In order to create an equation that depends just on the variable y, we must now b) swap it out in the second equation.
2x + 4y = 8
2(7 - 3y) + 4y = 8
The value of y is now determined by solving this equation in step (c).
14 - 6y + 4y = 8
14 - 2y = 8
-2y = 8 - 14 = -6
y= 6/2= 3
d) With the value of y now available, we can change the equation we obtained in step a) by substituting it.
x = 7 - 3y
x = 7 - 3*3 = 7 - 9 = -2
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I understand that the question you are looking for is:
Find the solution to the system of equations, x + 3y = 7 and 2x + 4y = 8.
1. Isolate x in the first equation: x = 7 − 3y
2. Substitute the value for x into the second equation: 2(7 − 3y) + 4y = 8
3. Solve for y:
14 − 6y + 4y = 8
14 − 2y = 8
−2y = −6
y = 3
4. Substitute y into either original equation: x = 7 − 3(3)
5. Write the solution as an ordered pair:
HEY PLEASE HELP ASAP
Answers
Answer:
[tex]\dfrac{8y-43}{(y-1)(y-8)}[/tex]
Explanation:
[tex]\rightarrow \dfrac{5}{y-1} +\dfrac{3}{y-8}[/tex]
make the denominators similar
[tex]\rightarrow \dfrac{5(y-8)}{(y-1)(y-8)} +\dfrac{3(y-1)}{(y-8)(y-1)}[/tex]
Join both the fraction
[tex]\rightarrow \dfrac{5(y-8)+3(y-1)}{(y-1)(y-8)}[/tex]
simplify the expression
[tex]\rightarrow \dfrac{5y-40+3y-3}{(y-1)(y-8)}[/tex]
[tex]\rightarrow \dfrac{8y-43}{(y-1)(y-8)}[/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{5}{y - 1} + \cfrac{3}{y - 8} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{5(y - 8) + 3(y - 1)}{(y - 1)(y - 8)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{5y -40 + 3y - 3}{y {}^{2} - y - 8y + 8} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{8y -43}{y {}^{2} - 9y + 8} [/tex]
A basketball is shot into the air. its height is represented by the polynomial equation h(t) = –16t2 35t 5, where h is the height of the basketball at t seconds. what is the height of the basketball at 0.5 seconds?
Answers
The height of the basketball at 0.5 seconds will be = 26.5
What is a polynomial equation?A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.
Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.
According to the given equation if we put value in it we will follow the following steps -
[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]
Therefore, the height of the basketball at 0.5 s will be 26.5
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Answer:
Is the question supposed to be (1.5), if so then the answer would be 21.5
Step-by-step explanation:
ht=-16t^2+35t+5
h(1.5)=-16(1.5)^2+35(1.5)+5
=21.5
Geometry: fill in the blanks (ASAP!! It’s urgent)
Answers
5. m∠C = 95°
6. m∠C = 70°
7. The other acute angle in the right triangle = 70°
8. m∠C = 70°
9. m∠C = 60° [equilateral triangle]
10. Measure of the exterior angle at ∠C = 110°
11. m∠B = 70°
12. m∠Z = 70°
What are Triangles?A triangle is a 3-sided polygon with three sides and three angles. The sum of all its interior angles is 180 degrees. Some special triangles are:
Isosceles triangle: has 2 equal base angles.Equilateral triangle: has three equal angles, each measuring 60 degrees.Right Triangle: Has one of its angles as 90 degrees, while the other two are acute angles.5. m∠C = 180 - 50 - 35 [triangle sum theorem]
m∠C = 95°
6. m∠C = 180 - 25 - 85 [triangle sum theorem]
m∠C = 70°
7. The other acute angle in the right triangle = 180 - 90 - 25 [triangle sum theorem]
The other acute angle = 70°
8. m∠C = 180 - 55 - 55 [isosceles triangle]
m∠C = 70°
9. m∠C = 60° [equilateral triangle]
10. Measure of the exterior angle at ∠C = 50 + 60
Measure of the exterior angle at ∠C = 110°
11. m∠B = 115 - 45
m∠B = 70°
12. m∠Z = 180 - 35 - 75
m∠Z = 70°
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Add 77 -10 with its additive inverse.
Answers
Answer: 77 - 10 = 67, and the additive inverse of 77 - 10 is 77 + 10. 77 + 10 = 87.
Hope this helps! This question was kind of confusing for me, because I didn’t understand why you said to add 77 - 10… is this is the incorrect answer sorry your question was worded weird
Urgent!!!!!!!!!!!!!!!!!!
Answers
9 Left triangle VMR - 0.5 (6)(3)
24 + 9 = 33
Prove this please
Optional Math
Cos2A =
[tex] \frac{( \cot\alpha - \tan\alpha ) }{( \cot\alpha + \tan\alpha ) } [/tex]
Answers
Step-by-step explanation:
proof from r.h.s to l.h.s
(cot(a)-tan(a))(cot(a)+tan(a))
cot(a)=cos(a)/sin(a)
tan(a)=sin(a)/cos(a)
(cot(a)-tan(a))=cos(a)/sin(a) - sin(a)/cos(a)
=cos²(a)-sin²(a)/sin(a)cos(a)
from trigonometry identity cos²(a)-sin²(a)=cos2(a)
so we have cos2(a)/sin(a)cos(a)
(cot(a)+tan(a))=cos(a)/sin(a) +sin(a)/cos(a)
=cos²(a)+sin²(a)/cos(a)sin(a)
from trigonometry identity cos²(a)+sin²(a)=so we have 1/cos(a)sin(a)
(cot(a)-tan(a)) ÷(cot(a)+tan(a))
=cos2(a)/cos(a)sin(a) ÷ 1/cos(a)sin(a)
=cos2(a)/cos(a)sin(a) * cos(a)sin(a)
=cos2(a)
proved
urgent please help!!
Answers
Answer:
14cm.
Step-by-step explanation:
X is the hypotenus, 7√3 is the opposite and the other side is the adjacent. Choose sin from (soh, cah, toa) because you have to find 'H' (hyp) and opposite is given. Hence, sin 60= 7√3 over x. Cross multiply and you'll get x * sin 60= 7√3. Make x the subject of formula and 14 will be the answer.
Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
Answers
There are 59 integer solutions
Such questions are best solved by writing cases and calculating the total number of cases. So beginning with
1) x = -3. The possible combinations are as follows:-
-3 2 13
-3 3 12
-3 4 11
-3 5 10
-3 6 9
-3 7 8
-3 8 7
-3 9 6
-3 10 5
-3 11 4
10 combinations
2) x = -2
-2 2 12
through
-2 11 3
10 combinations
3) x = -1
-1 2 11
through
-1 10 3
9 combinations
4) x = 0
0 2 10
through
0 9 3
8 combinations
as we can see from the pattern at x =1 we get 7 combinations, at x =2 we get 6 combinations, at x=3 we get 5 combinations and at x =4 we get 5 combinations.
Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.
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3x 2y = 4 2x - y = 5 this system of equations has no solution. has one solution. is coincident.
Answers
Answer:
no solution
Step-by-step explanation: because if it has no variables that are the same it has no solution.
how many terms are there in the series 7+21+15+19+.....+79?
anybody can answer these .
Answers
Answer:
7+21+15+19+.....+79
Here 21 be replaced by 11.
Now., common diffrence btw terms , d = 11-7 = 4
first term , a = 7
Last term , l = 79
number of terms = ( a + l ) ÷ d
=( 7 + 79 ) ÷ 4 = 86 ÷ 4 = 21.5 { It cannot be in decimal }
There's some mistake in the terms you provided please check your question again...
Given u=2i-9j and v=-5i+7j, what is u•v?
Answers
The value of the vector will be -53. The correct option is C.
What are vectors?In mathematics and physics, the term "vector" is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.
The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of integers of equal length and outputs a single number.
The given vectors are u=2i-9j and v=-5i+7j, the dot product of the vectors will be calculated as below:-
u.v = ( 2i-9j ).( -5i+7j)
u.v = -10i² + 17 (i.j) -45(i.j) -63j²
Substitute i² = 1, j² = 1 and (i.j) = 0 in the above equation.
u.v = -10 + 63
u.v = 53
Therefore, the value of the vector will be -53. The correct option is C.
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