Answer:
the answer is d. Cr= 2 pi
Step-by-step explanation:
The correct answer that is not equivalent to the formula for the circumference of a circle is: Cr = 2pi. (Option D).
How to get the Circumference of a Circle?To prove the options, it is important to test the formulas given:
In option A, C over r equals 2 times pi:
C/r = 2 * pi
This equation is equivalent to the formula for the circumference of a circle, C = 2 * pi * r, as you can simply multiply both sides by 'r' to get the standard formula.
In Option B, C over pi equals 2 times r:
C/pi = 2 * r
This equation is equivalent to the formula for the circumference of a circle as pi can be multiplied on both sides
In Option C, C over the quantity of r times pi equals 2:
C / (r * pi) = 2
This equation is equivalent to the formula for the circumference of a circle since you can multiply both sides by (r * pi) to get C = 2 * (r * pi).
In option D, This equation is not equivalent to the formula for the circumference of a circle. It is missing the division by 'r' on the right side of the equation.
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Solve the problem.
Find all values of k so that the given points are\sqrt {29} units apart. (-5, 5), (k, 0)
Choose the right answer
a. 3, 7
b. 7
c. -3, -7
d. -7 ...?
Final answer:
The values of k that ensure the points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex]units apart are -3 and -7, derived using the Pythagorean theorem and algebraic manipulation.
Explanation:
To find all values of k so that the points (-5, 5) and (k, 0) are \(\sqrt{29}\) units apart, we use the distance formula derived from Pythagoras’ theorem, which is[tex]d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]. Here, [tex]\(x_1 = -5\), \(y_1 = 5\), \(x_2 = k\), and \(y_2 = 0\). Substituting the given values, we get:[/tex]
[tex]\(\sqrt{29} = \sqrt{(k + 5)^2 + (0 - 5)^2}\)[/tex]
Squaring both sides to eliminate the square root gives:
[tex]29 = (k + 5)^2 + 25[/tex]
Subtracting 25 from both sides, we get:
[tex]4 = (k + 5)^2[/tex]
Therefore, \(k + 5 = \pm2\), which simplifies to:
[tex]\(k + 5 = 2\) giving \(k = -3\)[/tex]
[tex]\(k + 5 = -2\) giving \(k = -7\)[/tex]
The values of k are -3 and -7, so the correct option is c. -3, -7.
The correct answer is option (c) -3, -7.
How is it so?
To find the values of k such that the given points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex] units apart, use the distance formula between two points in a plane:
[tex]\[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given that the distance between the points is [tex]\(\sqrt{29}\)[/tex], we have:
[tex]\[ \sqrt{(k - (-5))^2 + (0 - 5)^2} = \sqrt{29} \][/tex]
[tex]\[ \sqrt{(k + 5)^2 + 5^2} = \sqrt{29}[/tex]]
[tex]\[ \sqrt{k^2 + 10k + 25 + 25} = \sqrt{29} \][/tex]
[tex]\[ \sqrt{k^2 + 10k + 50} = \sqrt{29} \][/tex]
Squaring both sides to eliminate the square root:
[tex]\[ k^2 + 10k + 50 = 29 \][/tex]
[tex]\[ k^2 + 10k + 21 = 0 \][/tex]
Solve this quadratic equation
[tex]\[ k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Where a = 1, b = 10, and c = 21.
[tex]\[ k = \frac{-10 \pm \sqrt{10^2 - 4 \cdot 1 \cdot 21}}{2 \cdot 1} \][/tex]
[tex]\[ k = \frac{-10 \pm \sqrt{100 - 84}}{2} \][/tex]
[tex]\[ k = \frac{-10 \pm \sqrt{16}}{2} \][/tex]
[tex]\[ k = \frac{-10 \pm 4}{2} \][/tex]
[tex]\[ k = \frac{-10 + 4}{2} \] or \( k = \frac{-10 - 4}{2} \)[/tex]
[tex]\[ k = \frac{-6}{2} \] or \( k = \frac{-14}{2} \)[/tex]
[tex]\[ k = -3 \] \:or \( k = -7 \)[/tex]
So, the correct answer is option (c) -3, -7.
Evaluate -2x 2 y, if x = -3 and y = -1.
-12
-18
18 im thinking this one
12
Your school has a $1200 grant to buy books and magazine subscriptions for the school library. The avarage cost of magazine subscription is $30. Your school decided to spend $870 on books and the remaining amout on magazine subscriptions. How many subscriptions can the school buy?
Heathers desk is 3 feet long about how long is it in meters
Shane measured 457 ml of water in a beaker. olga measured 3 times as much water. how much water did they measure altogether
How many miles is it from honolulu to turtle bay?
The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.
Explanation:The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.
It's important to note that the actual distance traveled may vary depending on the specific route taken and any detours or alternate paths chosen.
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30inches increased by 30 percent
A parallelogram has a base that measures 5 units and a height that measures (x + 6) units. The area of this parallelogram is 20 square units. What must be the value of x?
Choose one answer.
a. x=4
b. x=-2
c. x=5
d. x=15
To solve for 'x' in the parallelogram area equation, we multiplied the given base (5 units) by the height (x + 6 units) and set it equal to the given area (20 square units). After simplifying, we found that x must be -2 to satisfy the equation 5x + 30 = 20.
Explanation:The question presented is a typical algebra problem where we need to find the value of 'x' in the context of the area of a parallelogram. The base of the parallelogram is given as 5 units and its height is given as (x + 6) units, with the total area given as 20 square units. Since the formula for the area of a parallelogram is base × height, we can set up the equation 5 × (x + 6) = 20 to find the value of x.
Now, we will solve for x:
Multiply the base by the height: 5(x + 6) = 20.Distribute the 5: 5x + 30 = 20.Subtract 30 from both sides to solve for x: 5x = -10.Divide both sides by 5 to find x: x = -2.Hence, the correct answer is b. x=-2.
Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC. (See figure.)
The [tex]x[/tex] coordinates of the point A is [tex]\boxed{\bf 0}[/tex].
The [tex]x[/tex] coordinates of the point B is [tex]\boxed{\bf 0}[/tex].
The [tex]x[/tex] coordinates of the point C is [tex]\boxed{\bf 10}[/tex].
Further explanation:
Given:
The coin labeled as A lies on the [tex]y[/tex]-axis.
The coin labeled as B lies on the origin.
The coin labeled as C lies on the [tex]x[/tex]-axis.
The distance of the point B and C is [tex]10\text{ cm}[/tex].
Concept used:
The point which lies on the [tex]x[/tex]-axis, the value of its [tex]y[/tex]-coordinate is [tex]0[/tex].
The point which lies on the [tex]y[/tex]-axis, their [tex]x[/tex]-coordinate is [tex]0[/tex].
The coordinate of the origin is [tex](0,0)[/tex].
Calculation:
The coin labeled as A lies on the [tex]y[/tex]-axis therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].
The coin labeled as B lies on the origin therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].
The distance from point B to the point C is [tex]10\text{ cm}[/tex] and the coin labeled as C lies on the x axis it means that the [tex]x[/tex]-coordinate of the point is [tex]10[/tex].
Therefore, the [tex]x[/tex] coordinate of the point A is [tex]0[/tex].
The [tex]x[/tex] coordinate of the point B is [tex]0[/tex].
The [tex]x[/tex] coordinate of the point C is [tex]10[/tex].
Learn more:
1. Coordinate of the point : https://brainly.com/question/1286775
2. Equation: https://brainly.com/question/1473992
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Coordinate geometry, x-axis, y-axis, x-coordinate, y-coordinate, coin, square, three corners, three identical coins.
7 square yards is equal to how many square meters? A. 2.58 square meters B. 3.50 square meters C. 5.85 square meters D. 14.25 square meters C. 5.85 square meters
Final answer:
To convert 7 square yards to square meters, you multiply by the conversion factor, resulting in approximately 5.85 square meters. Hence, the correct answer is C. 5.85 square meters.
Explanation:
7 square yards is equal to how many square meters? To convert square yards to square meters, you can use the conversion factor 1 square yard = 0.83612736 square meters. Therefore, to convert 7 square yards to square meters:
7 sq yards * 0.83612736 sq meters/sq yard = 5.85289152 sq meters
When rounding to two decimal places, this is approximately 5.85 square meters. So, the correct answer would be C. 5.85 square meters.
Will upvote and tip
A smart phone costs $149.99 before tax. The tax on the smart phone is 7%.
What is the total cost of the smart phone?
Round your answer to the nearest cent.
Answer/Step-by-step explanation:
149.99+(149.99*0.07)=160.4893. Round to $160.49
Two angles of a triangle measures of 70° and 85° which is not the measure of an exterior angle of the triangle
What is the solution to the linear equation?
2/3x –1/2 = 1/3 +5/6 x
A. x=-5
B. x= - 1/6
C.x= 1/6
D. x=5
Answer:
A) -5
Step-by-step explanation:
What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.
The solution to the system of equations are ±2i and ±i
Quartic equationsGiven the quartic equation
x^4 + 3x^2 + 2 = 0
Let u = x^2 to have:
(x^2)^2 + 3x^2 + 2 = 0
u^2 + 3u + 2 = 0
Factorize
u^2 + u +2u + 2 = 0
u(u + 1) + 2(u + 1) = 0
(u + 2)(u + 1) = 0
u = -2 or -1
If u = x^2
-2 = x^2
x = √-2
x = 2i
Similarly
If u = x^2
-1 = x^2
x = √-1
x = i
Hence the solution to the system of equations are ±2i and ±i
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Final answer:
To solve the equation x^4 + 3x^2 + 2 = 0 using u substitution, substitute x^2 for u and solve the quadratic equation. The resulting solutions in the complex number system are x = i, -i, √2i, and -√2i. There are no real solutions for this equation.
Explanation:
The solutions of the equation x4 + 3x2 + 2 = 0 can be found using u substitution. First, let's substitute u for x2, which transforms the original equation into the form u2 + 3u + 2 = 0. This is a quadratic equation, and we can solve it using the quadratic formula or by factoring. Factoring (u + 1)(u + 2) = 0, we get the solutions for u as u = -1 and u = -2. Since u is a substitute for x2, we then solve for x.
For u = -1, the equation x2 = -1 has no real solutions because the square of a real number cannot be negative. However, in the complex number system, the solutions are x = i and x = -i, where i is the square root of -1.
For u = -2, the equation x2 = -2 also has no real solutions, but the complex solutions are x = √2i and x = -√2i.
Therefore, the full set of solutions for the original equation are x = i, -i, √2i, and -√2i.
All real numbers that are less then -3 or greater then or equal to 5
Identify the temperature that is halfway between 0 degrees fahrenheit and 10 degrees fahrenheit
State the y-coordinate of the y-intercept for the function below.
ƒ(x)=x^3-x^2-x+1 ...?
Answer:
1
Step-by-step explanation:
Answer is 1 for Apex Precal
What are the factor pairs of 23?
What is the exact value of the expressions the square root of 180. − the square root 125. + the square root of 5.? Simplify if possible.
A) 2the square root of 2.
B) 12the square root of 2.
C) 2the square root of 5.
D) 12the square root of 5.
Answer:
[tex]2\sqrt{5}[/tex]
C is the correct option.
Step-by-step explanation:
The given expression is [tex]\sqrt{180}-\sqrt{125}+\sqrt{5}[/tex]
In order to simplify the expression, we find the factors.
180 =6 ×6×5
125 = 5 ×5×5
Hence, we can rewrite the expression as
[tex]\sqrt{6\times6\times5}-\sqrt{5\times5\times5}+\sqrt{5}[/tex]
We can further write this expression as
[tex]\sqrt{6^2\times5}-\sqrt{5^2\times5}+\sqrt{5}[/tex]
Now, we can use the rule [tex]\sqrt{x^2}=x[/tex]
[tex]6\sqrt{5}-5\sqrt{5}+\sqrt{5}[/tex]
Finally, we can combine these like terms
[tex]2\sqrt{5}[/tex]
Hence, C is the correct option.
which of the following is the correct factorization of the polynomial below?
27x^3+64
a) (3x+4)(9x^2-12x+16)
b) (9x+8)(3x^2-16x+8)
c) (3x^2+8)(9x-16x+8)
d) the polynomial is irreducible
...?
Answer:
a) (3x+4)(9x^2-12x+16)
Step-by-step explanation:
Which of the following statements is true?
A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
According to the Wall Street Journal, 14,200,000 videotape copies of Walt Disney's Fantasia have
been sold to date. Write that number in scientific notation.
A. 1.42 × 10^7
B. 1.42 × 10^6
C. 142 × 1,000,000
D. 142 × 10^7
This table shows the input and output values for an exponential function f(x)
What are the ratios of outputs for any two inputs that are 1 apart?
A. 1/2
B. 4
C. 1/8
D. 2
x −3, −2, −1, 0, 1, 2, 3
f(x) 1/256, 1/64, 1/16, 1/4, 1, 4, 16
Answer:
B. 4
Step-by-step explanation:
This table that shows the input and output values for an exponential function f(x) is,
x -3 -2 -1 0 1 2 3
f(x) 1/256 1/64 1/16 1/4 1 4 16
Taking [tex]x=2[/tex] and [tex]x=3[/tex] as input (because they are 1 apart), the ratio of output is,
[tex]=\dfrac{f(3)}{f(2)}[/tex]
[tex]=\dfrac{16}{4}[/tex]
[tex]=4[/tex]
Answer:
The correct answer is B. 4
Step-by-step explanation:
is triangle EFG is congruent to triangle STU , what can you conclude about angle E, angle S, angle F and angle T
If triangle EFG is congruent to triangle STU, the following statements are true:
* Angle E = angle S.
* Angle F = angle T.
* Side EF = side ST.
* Side FG = side TU.
* Side EG = side SU.
If triangle EFG is congruent to triangle STU, then we can conclude that the following pairs of angles are congruent:
* Angle E is congruent to angle S.
* Angle F is congruent to angle T.
This is because congruent triangles have corresponding angles that are congruent.
We can also conclude that the following pairs of sides are congruent:
* Side EF is congruent to side ST.
* Side FG is congruent to side TU.
* Side EG is congruent to side SU.
This is because congruent triangles have corresponding sides that are congruent.
Therefore, the following statements are true:
* Angle E = angle S.
* Angle F = angle T.
* Side EF = side ST.
* Side FG = side TU.
* Side EG = side SU.
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PLEASE HELP!
A 20in. by 24in. photo is reduced so that the length (the longer dimension) is 15in.
What is the width of the reduced photo?
A: 11in
B: 12.5 in
C: 13.5 in
D: 18in
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
Dimensions of the photo is given by
[tex]20\ in.\ by\ 24\ in.[/tex]
According to question, the photo is reduced so that the longer dimension is 15 inch.
So, Let the width of the reduced photo be x.
So, it becomes,
[tex]\frac{20}{x}=\frac{24}{15}\\\\x=\frac{15\times 20}{24}\\\\x=12.5\ in.[/tex]
So, the width of the reduced photo is 12.5 inch.
Hence, Option 'B' is correct.
HELPPPPPPPPPPPPP
(3 pt)
Which number sentences show ways to solve the problem?
The 9 members of a conservation club purchased a total of 45 tree saplings. Each member bought the same number of trees to plant in the community. Each tree cost $15. How much did each member pay for the trees?
Choose all answers that are correct.
A.
15 × 9 = 135 and 135 – 75 = 60
B.
3 × 15 = 45 and 45 + 15 = 60
C.
45 ÷ 9 = 5 and 5 × 15 = 75
D.
45 × 15 = 675 and 675 ÷ 9 = 75
Evaluate.
2^3+4⋅2−7
A.1
B.5
C.9
D.36
What is the Quadratic Formula?
Kenneth is inviting people to his parents' anniversary party and wants to stay at or below his budget of $6,000 for the food. The cost will be $40 for each adult's meal and $15 for each child's meal.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of adults
y = the number of children
A movie theater charges $11 for each adult and $6 for each ticket. one day, they sold 163 tickets and made $1578. How many of each ticket did they sell?
The movie theater sold 117 adult tickets and 46 child tickets.
Explanation:To solve this problem, we can set up a system of equations. Let's say the number of adult tickets sold is x and the number of child tickets sold is y. We can then write two equations based on the given information:
x + y = 163 (equation 1, representing the total number of tickets sold)11x + 6y = 1578 (equation 2, representing the total amount earned)We can solve this system of equations by either substitution or elimination. Let's use elimination:
Multiply equation 1 by 6 to make the coefficients of y in both equations equal:6x + 6y = 978
Subtract equation 1 from equation 2 to eliminate y:(6x + 6y) - (11x + 6y) = 978 - 163
-5x = -585
Divide by -5:
x = 117
Substitute x back into equation 1 to find y:117 + y = 163
y = 163 - 117
y = 46
Therefore, 117 adult tickets and 46 child tickets were sold.