The radius of the circle with a circumference of 12.56 inches is 2 inches, calculated using the formula C = 2πr and rearranging it to find the radius.
Explanation:The circumference of a circle is given by the formula C = 2πr, where C stands for the circumference and r stands for the radius of the circle. The value of π (pi) is approximately 3.14159. Given the circumference of the circle as 12.56 inches, you can find the radius by rearranging the equation to r = C / (2π).
Now, let's calculate the radius using the given circumference:
r = 12.56 inches / (2 × 3.14159)
r = 12.56 inches / 6.28318
r = 2 inches
Therefore, the measure of the radius of the circle is 2 inches, which corresponds to option A.
To find the measure of the radius of the circle given its circumference, we can use the circumference formula of a circle, which is:
\[ C = 2 \pi r \]
Where \( C \) is the circumference, \( \pi \approx 3.14159 \), and \( r \) is the radius of the circle.
Now, we know the circumference (\( C \)) is 12.56 inches. We can solve for the radius (\( r \)) by rearranging the formula:
\[ r = \frac{C}{2 \pi} \]
Plugging the given circumference into the equation, we get:
\[ r = \frac{12.56}{2 \times \pi} \]
\[ r = \frac{12.56}{2 \times 3.14159} \]
\[ r = \frac{12.56}{6.28318} \]
\[ r = 2 \]
Rounding the result to two decimal places as may be required for some comparisons, we still get \( r = 2.00 \) inches.
Therefore, the measure of the radius of the circle is 2 inches, which corresponds to option A.
Solve the equation x/4+1=-6
the answer is x = -28
Help asap please i don't know the answer lol
Answer:
H
Step-by-step explanation:
The parallel line BC divides the sides AD and AE in proportion, that is
[tex]\frac{AB}{BD}[/tex] = [tex]\frac{AC}{CE}[/tex], that is
[tex]\frac{2}{3}[/tex] = [tex]\frac{AC}{4}[/tex] ( cross- multiply )
3AC = 8 ( divide both sides by 3 )
AC = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex], hence
AE = AC + CE
= 2 [tex]\frac{2}{3}[/tex] + 4 = 6 [tex]\frac{2}{3}[/tex] → H
HELP!! With the question
Answer:
-x^2+21x+18/ x^3-x^3-16x-20
Step-by-step explanation:
-x^2+21x+18/ (x-5)(x^2+4x+4)
= -x^2+21x+18/ x^3+4x^2+4x-5x^2-20x-20
= -x^2+21x+18/ x^3-x^2-16x-20
At 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. At 10:15 a.m., there are 8 cells in the bottle. At what time will there be 64 cells in the bottle?
at 10:30 there will be 64 bacteria
Answer:
At 10:20 a.m., there will be 16 cells in the bottle.
At 10:30 a.m. there will be 64 cells in the bottle .
Step-by-step explanation:
The measures of two sides of a triangle are given. If P is the perimeter, find the measure of the third side.
c = 2x + 3. The third side of the triangle is 2x + 3.
The key to solve this problem is using the perimeter of a triangle equation which is P = a + b + c, where a, b, and c are the sides of the triangle.
We know that the perimeter P = 3x² + 7x, let's suppose a = 6x - 7, b = 3x² - x + 4, and c is the unknow.
Clearing c from the equation:
c = P - (a + b)
c = 3x² + 7x - (6x - 7 + 3x² - x + 4)
c = 3x² + 7x - 6x + 7 - 3x² +x - 4
Grouping the equal terms:
c = 3x² - 3x² + 7x + x - 6x + 7 - 4
c = 0 + 8x - 6x + 3
c = 2x + 3
Find the values of x in this equation: x – 15 x = 2 . A. -7, 3 B. -5, 2 C. -7, 5 D. -2, 5 E. -3, 5
Answer:
Step-by-step explanation:
The given expression is x- [tex]\frac{15}{x}[/tex] = 2
and we have to solve this for the value of x,
( x- [tex]\frac{15}{x}[/tex]) = (2)
[tex]\frac{x^{2}-15 }{x} =2[/tex]
x² - 15 = 2x
x² - 2x - 15 = 0
x² - 5x + 3x - 15 = 0
x ( x-5 ) + 3(x - 5) = 0
( x+3 )( x-5 ) = 0
( x+3) = 0
x = -3
or ( x- 5 ) = 0
x = 5
Therefore, x = -3 and 5 will be the solution.
Option E is the answer.
Triangle ABC is isosceles. What is true about the measure of angle B?
Is it equal to the measure if angle C
In an isosceles triangle, the measure of the vertex angle (Angle B in this case) is equal to the measure of the other base angle. This is because in an isosceles triangle, the angles opposite the equal sides are also equal.
Explanation:In an isosceles triangle ABC, Angle B, the angle between the two sides of equal length, is known as the vertex angle. The two base angles of an isosceles triangle are always equal. Therefore the measure of Angle B will be equal to the measure of Angle C. This property comes from the fundamental characteristics of an isosceles triangle, where two sides are of equal length and the angles opposite these equal sides are also equal.
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What is the range for this set of data?
7, 15, 12
Answer:
The answer would be eight.
Step-by-step explanation:
The range is the difference between the largest and smallest number you need to make sure you have them in order or it won’t work.
Answer:
the answer is eight
Step-by-step explanation:
Solve the system of equations. 2x + 3y = 1 5x + 2y = 8 What is the solution?
Answer:
(2,-1)
Step-by-step explanation:
The solution of the system of equations 2x + 3y = 1 and 5x + 2y = 8 is x = 2 and y = -1.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.
And simultaneous equation is the system of equation.
Given:
System of equations,
2x + 3y = 1, {equation 1}
And 5x + 2y = 8. {equation 2}
To find the solution:
Multiply 5 to the equation 1 and multiply 2 to the equation 2.
And then subtract the equation 2 to the equation 1.
We get,
11y = -11
y = -1
And 2x = 4
x = 2
Therefore, the solution is x = 2 and y = -1.
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What is the length of segment AB?
A coordinate plane is shown. Point A is located at 0, 12, and point B is located at 5, 0. The two points are connected by a line segment.
Answer:
length of segment AB is 13
OR
AB = 13
Step-by-step explanation:
Use the Pythagorean Theorem with c being the length of segment AB.
a^2 + b^2 = c^2
5^2 + 12^2 = c^2
169 = c ^2 (square root both sides to get c by itself)
13 = c
Help solve please !
Answer:
[tex]\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]
Step-by-step explanation:
The given logarithmic expression;
[tex]3\log_2x-(\log_23-\log_2(x+4))[/tex]
Expand the parenthesis:
[tex]3\log_2x-\log_23+\log_2(x+4)[/tex]
Use the product rule on the last two terms;
[tex]\log_aM+\log_aN=\log_aMN[/tex]
[tex]3\log_2x-\log_23(x+4)[/tex]
[tex]3\log_2x-\log_23(x+4)[/tex]
Apply the power rule:
[tex]\log_2x^3-\log_23(x+4))[/tex]
We now apply the quotient rule of logarithms:
[tex]\log_aM+\log_aN=\log_a(\frac{M}{N})[/tex]
[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{x^3}{3(x+4)})[/tex]
Or
[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]
2y +6=3y+8
Verify it and explain step by step?
Write an equation to match each graph:
f
Looking at the shape, you should be able to tell immediately that this will be an absolute value function. Noticing that it is both 1 over and 1 up, you will get the equation y = - | x + 1 | + 1
Answer:
y=-|x+1|+1
Step-by-step explanation:
In circle K, what is the value of x?
(5x)
I think 5x represents 90 degrees.
5x = 90
x = 90/5
x = 18
ANSWER
[tex]x = 18 \degree[/tex]
EXPLANATION
A semicircle subtends an angle of 90° at the circumference.
From the diagram, the semicircle subtends an angle of (5x)° at the circumference.
We equate this angle to 90° and solve for x.
This implies that,
[tex]5x = 90 \degree[/tex]
Divide both sides by 5.
[tex]x = \frac{90}{5} [/tex]
[tex]x = 18 \degree[/tex]
Please help me
A(-3, 6) and B(0, 6), what are the coordinates of point P that lies on segment AB, such that AP:PB = 2:1?
Answer:
(-1,6)
Step-by-step explanation:
P= 1A + 2B
AP + PB
= 1(-3,6) + 2(0,6)
3
= (-3,6) + (0,12)
3
= (-3 + 18)
3
= (-1,6)
HELP!!!!!!!
Consider the function:
f(x) =
What are these values?
Answer:
f(-3) = -5/2
f(-1) = 3/2
f(3) = 3/4
Step-by-step explanation:
To find the values, we just have to replace by the values given (-3, -1, 3). Since there are different definitions of the function depending on the range of x, we just have to pick the right one before replacing x by its value.
x = -3
When x ≤ -1, the function is 7/2 + 2x
So, x = -3 is certainly ≤ -1, so....
f(-3) = 7/2 + 2 (-3) = 7/2 - 6 = 7/2 - 12/2 = -5/2
x = -1
When x ≤ -1, the function is 7/2 + 2x
So, we do the same calculation:
f(-1) = 7/2 + 2 (-1) = 7/2 - 2 = 7/2 - 4/2 = 3/2
x = 3
When x ≥ 3, the function is defined as: (1/4)x or x/4. So,
f(3) = 3/4
The output values of f(-3), f(-1), and f(3) in the piece-wise function are -5/2, 3/2, and 3/4 respectively.
To determine the output value of f(-3), f(-1), and f(3) in the piece-wise function, we simply plug in the values of x in the piece that is within the domain.
To solve for f(-3), plug x = -3 into the piece with the domain of x ≤ -1:
f( x ) = 7/2 + 2x
Pug in x = -3:
f( -3 ) = 7/2 + 2(-3)
f( -3 ) = -5/2
To solve for f(-1), plug x = -1 into the piece with the domain of x ≤ -1:
f( x ) = 7/2 + 2x
Pug in x = -1:
f( -3 ) = 7/2 + 2(-1)
f( -3 ) = 7/2 - 2
f( -3 ) = 3/2
To solve for f(3), plug x = 3 into the piece with the domain of x ≥ 3:
f( x ) = (1/4)x
Pug in x = 3:
f( 3 ) = (1/4) × 3
f( 3 ) = 3/4
Therefore, the values for f(-3), f(-1), and f(3) are -5/2, 3/2, and 3/4 respectively.
Determine in which direction the parabola below opens. y=-4x^2+8x+12
Down
The formula for a quadratic equation is y = ax^2 + bx + c. In this case, a = -4, b = 8, and c = 12. The direction of the parabola can be determined by a. If a is positive, the parabola opens upwards, and if a is negative, the parabola will open downwards.
Please help, What is tan B? a. 8/17 b. 15/8 c. 15/17 d. 8/15
tan <B is 16/30 which is 8/15
Answer:
Step-by-step explanation: It’s gotta be b or c.
Please help ASAP!!!!!
Answer: OPTION C
Step-by-step explanation:
Complete the square:
Having the equation in the form [tex]ax^2+bx=c[/tex], you need to add [tex](\frac{b}{2})^2[/tex] to both sides of the equation:
You can identify that "b" in the equation [tex]x^2+6x=5[/tex] is:
[tex]b=6[/tex]
Then:
[tex](\frac{6}{2})^2=3^2[/tex]
Add this to both sides:
[tex]x^2+6x+3^2=5+3^2[/tex]
Rewriting, you get:
[tex](x+3)^2=14[/tex]
Solve for "x":
[tex]x+3=\±\sqrt{14}\\\\x+3=\±\sqrt{14}\\\\x=\±\sqrt{14}-3[/tex]
Then, the solutions are:
[tex]x=-3+\sqrt{14}\ or\ x=-3-\sqrt{14}[/tex]
Which of the following values of x is in the solution set of 2|x + 4| > 14?
Answer:
-12
Step-by-step explanation:
What is the constant term in the expression 2xy - 5x2 - 7x + 9?
Answer:
9?
Step-by-step explanation:
on a 6-sided die, what is the probability of rolling an even number that is not 4
ANSWER
[tex]P(4)'= \frac{1}{3} [/tex]
EXPLANATION
The sample space of rolling a 6-sided die is
{1,2,3,4,5,6}
The even numbers apart from 4, are
{2,6}
The probability of rolling an even number that is not 4 is
[tex]P(4)'= \frac{2}{6} = \frac{1}{3} [/tex]
Use the graph. HELP NEEDED!!! Answer choices are below.
A. [-3,4]
B. [-2,0]
C. [0,4]
D. [-3,-2]
ANSWER
A. [-3,4]
EXPLANATION
We want to determine from the graph the interval on which
[tex]f(x) \geqslant 0[/tex]
This refers to the interval on which the the graph lies on or above the x-axis.
This interval is from x=-3 to x= 4
The correct choice is A. [-3,4]
Can you plz help me answer this question
Answer:
the answer is 77
Step-by-step explanation:
46.20 divided by 60 cents = 77
Explain whether or not the following equation is a quadratic function in vertex form. y = 4(x - 2)^2 + 6.
Your explanation should be at least 3 - 4 sentences and include at least 5 of the following words/phrase:
-squared term
-constant term
-quadratic function
-coefficient
-vertex form
-y variable
Answer:
Yes, the following equation is a quadratic function in vertex form
Step-by-step explanation:
we know that
The quadratic function of the vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2} +k[/tex]
where
(h,k) is the vertex of the parabola
If the coefficient a is > 0 ----> the parabola open upward (vertex is a minimum)
If the coefficient a is < 0 ----> the parabola open downward (vertex is a maximum)
in this problem we have
[tex]y=4(x-2)^{2} +6[/tex]
The squared term contain the x-coordinate of the vertex
[tex]h=2[/tex]
The constant term is the y-coordinate of the vertex
[tex]k=6[/tex]
The vertex is the point (2,6)
The coefficient is equal to
[tex]a=4[/tex] ----> open upward (vertex is a minimum)
Jarred sells dvds. His inventory shows that he has a total of 3500 dvds. He has 2342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of dvds.
Answer:
x = classic
x + 2342 = contemporary
3500 = x + (x +2342)
3500= 2x + 2342
and then you would just solve the equation, but it does not ask for a solution
Step-by-step explanation:
x = classic
x + 2342 = contemporary
3500 = x + (x +2342)
3500= 2x + 2342
Answer: Jared has a total of 3500 dvds of two types, contemporarys and classics.
we also know that Jared has 2342 more contemporary dvds than classics.
Now, how we write this as system of equations?
if x is the number of classics, and y the number of contemporarys, then:
1) x + y = 3500
and
2) y - x = 2342
this is the system of equations, but just for fun we can solve it!
in the second equation we can leave y alone in the right side ande get: y = 2342 + x, and then replace it in the first equation.
x + y = 3500
x + (2342 + x) = 3500
2*x = 3500 - 2342 =1158
x = 1158/2 = 579
So Jared has 579 classic titles.
then:
y + x =3500
y + 579 = 3500
y = 3500 - 579 = 2921
And Jared has 2921 contemporary titles.
For the function y=tan theta which angle measure has the same values as 2pi/3
tan(theta)=tan(pi+theta)
So your answer would be 5pi/3
Answer:
The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]
Step-by-step explanation:
[tex]tan(\theta)=tan(\pi+\theta)[/tex]
[tex]tan(\theta)=tan(\pi+\theta)[/tex]
so, here [tex]\theta=\frac{2\pi}{3}[/tex]
[tex]tan(\frac{2\pi}{3})=tan(\pi+\frac{2\pi}{3})[/tex]
[tex]tan(\frac{2\pi}{3})=tan(\frac{5\pi}{3})[/tex]
Hence, The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]
what is the solution to the equation x/2-4=6
Answer
x = 20
Explanation
Multiply the entire equation by 2 to get rid of the fraction.
x/2 * 2 = x
-4 * 2 = -8
6 * 2 = 12
Now, we have:
x - 8 = 12
To complete, add 8 to both sides
x = 20
For this case we must find the value of "x" of the following equation:
[tex]\frac {x} {2} -4 = 6[/tex]
So:
We add 4 sides of the equation:
[tex]\frac {x} {2} = 6 + 4\\\frac {x} {2} = 10[/tex]
We multiply by 2 on both sides of the equation:
[tex]x = 20[/tex]
Thus, the value of the variable x is 20
Answer:
[tex]x = 20[/tex]
The ratio 60 : 48 in its simplest form
Answer:
5 : 4
Step-by-step explanation:
To simplify the ratio , find the greatest common factor of 60 and 48, then divide both parts of the ratio by it
the greatest common factor of 60 and 48 is 12, hence
60 ÷ 12 : 48 : 12 = 5 : 4 ← in simplest form
30:24 = 10:8 = 5:4
Step-by-step explanation:
First divide them by 2
then divide the answer (30:24) with 3
then divide the answer with 2
And the answer comes as 5:4
kumar is saving to buy a bicycle that costs $375.25. so far he has saved $295.25. How much more money does he need
Answer:
80
Step-by-step explanation:
Kumar needs only $80 to buy bicycle.
What is subtraction?Subtraction is mathematic operation. Which is used to remove terms or objects in expression.
Given, bicycle costs $375.25.
And so for he has saved $295.25
To find the rest of money, we subtract the total cost to a saved money.
required money = $375.25 - $295.25 = $80
Therefore, he needs only $80 to buy a bicycle.
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