Final answer:
The third piece of wood must be longer than 9 ft but shorter than 35 ft to make a triangular garden bed with the other two pieces, adhering to the Triangle Inequality Theorem.
Explanation:
To determine the possible length of the third piece of wood to create a triangular garden bed with the other two pieces measuring 22 ft and 13 ft, we need to recall the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Conversely, the difference between these two sides must be less than the length of the remaining side.
Step 1: Identify the lengths of the two given pieces: 22 ft and 13 ft.
Step 2: To find the minimum length of the third piece, subtract the shorter piece from the longer piece, then add a small value to avoid equality (as the sum must be greater).
Minimum length > 22 ft - 13 ft => 9 ft + a small value
Step 3: To find the maximum length of the third piece, sum the lengths of the two pieces and subtract a small value (as the length must be less than the sum of the other two pieces).
Maximum length < 22 ft + 13 ft => 35 ft - a small value
So, the third piece of wood must be longer than 9 ft but shorter than 35 ft to form a triangle with the other two pieces.
consider the function f(x) = {(sinx)/x, x cannot equal 0
{k, , x = 0
In order for f(x) to be continuous at x - 0, the value of k must be..
Final answer:
For the function f(x) = (sinx)/x to be continuous at x = 0, the value of k must be 1, which is the limit of the function as x approaches 0.
Explanation:
The student is asking about the continuity of a given function at x = 0. To determine what the value of k must be for the function f(x) = (sinx)/x when x is approaching 0, we need to look at the limit of the function as x approaches 0.
Although the function is not defined at x = 0 due to division by zero, we know that the limit of (sin x)/x as x approaches 0 is 1. This can be proven using L'Hospital's rule or the squeezing theorem. Hence, for the function to be continuous at x = 0, the value of k must also be 1.
The graph of the piecewise function f(x) is shown.
What is the domain of f(x)?
{x | 1 < x < 5}
{x | 1 < x < 5}
{y | −4 < y < 1}
{y | −4 < y < 1}
Answer:
Domain is {x| 1<=x <5}
Step-by-step explanation:
The graph of the piecewise function f(x) is shown.
In the given graph of piecewise function
Domain is the set of x values for which the function is defined
first graph is from x= 1 to 3, 3 is excluded
second graph is from x= 3 to 5, 5 is excluded
So the graph of x values is from x=1 to 5 ( 5 excluded because we have open circle at 5)
Domain is {x| 1<=x <5}
For exercises 19-24, y varies directly with x
if y = 25 when x = 15, find y when x = 6.
Help me explain how to do it step by step !
A sprinter can run 279 feet in 9 seconds. Find the sprinter's unit rate of feet per second.
To find the sprinter's unit rate of feet per second, divide the total distance by the time. In this case, the sprinter's unit rate is approximately 31 feet per second.
Explanation:To find the sprinter's unit rate of feet per second, we need to divide the total distance the sprinter can run by the time it takes. In this case, the sprinter can run 279 feet in 9 seconds. So the unit rate is 279 feet divided by 9 seconds, which is approximately 31 feet per second.
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South middle school has 750?students. North middle school has 13/15 times as many students as South. Does north middle school have more or fewer than 750 students?
Answer : The north middle school have fewer than 750 students.
Step-by-step explanation:
Let the number of students in south middle school be, x
and the number of students in north middle school be, y
Given:
Number students in south middle school = x = 750
and,
North middle school has 13/15 times as many students as South. That means,
[tex]y=\frac{13}{15}\times x[/tex] ........(1)
Now put the value of 'x' in expression 1, we get:
[tex]y=\frac{13}{15}\times 750[/tex]
[tex]y=650[/tex]
Thus, number of students in north middle school = y = 650
From this we conclude that north middle school have fewer than 750 students.
Hence, the north middle school have fewer than 750 students.
Math question: Write the equation of the line with an undefined slope, passing through the point (2, 5).
The equation of a line with an undefined slope passing through the point (2, 5) can be written as x = 2.
When the slope of a line is undefined, it means that the line is vertical. In a vertical line, the x-coordinate remains constant while the y-coordinate can take any value.
So, for this line passing through the point (2, 5), the x-coordinate will always be 2, regardless of the value of y. Therefore, we can represent this line with the equation x = 2.
TRUE or FALSE.
Based only on the information given in the diagram, it is guaranteed that ΔABC ≈ ΔXYZ.
It is a true statement that it is guaranteed that ΔABC ≈ ΔXYZ in the diagram given.
Why will ΔABC equals ΔXYZ?In this context, all triangles have 180 degrees altogether in as much they have a standard size of the shape.
The triangles have the sames standard size although the letters of the angles are different.
Therefore, the statement is a true statement.
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Calculate the slope of the line given the points (2, 1) and (1, -4).
A. 1/5
B. 5
C.-3
D. none of the above
Find f(6) if f(x) = x2 ÷ 3 + x.
A function is denoted as y = f (x), where x is the argument or input of the function. This means that from f(6) follows that x= 6, and to get the answer we should replace x with 6.
f(6)=6^2÷ 3 + 6= 36÷ 3 + 6= 12+6= 18
f(6)=18
Answer:
The value of f(6) is, 18
Step-by-step explanation:
Given the function:
[tex]f(x) = x^2 \div 3+ x[/tex] .....[1]
We have to find the value of [tex]f(6)[/tex].
Put x = 6 in [1] we have;
[tex]f(6) = 6^2 \div 3+ 6[/tex]
⇒[tex]f(6) = 36 \div 3 +6[/tex]
⇒[tex]f(6) = \frac{36}{3}+6[/tex]
Simplify:
[tex]f(6) = 12 +6 = 18[/tex]
Therefore, the value of f(6) is, 18
The integer n3 + 2n is divisible by 3 for every positive integer n
prove it by math induction
is it my proof right ?
By the principle of mathematical induction, we have shown that for all positive integers n, n^3 + 2n is divisible by 3.
Proof by Induction: n^3 + 2n is divisible by 3 for all positive integers n.
Base Case:
For n = 1, n^3 + 2n = 1^3 + 2(1) = 3, which is divisible by 3.
Induction Hypothesis:
Assume that for some positive integer k, k^3 + 2k is divisible by 3. We can write this as: k^3 + 2k = 3m, where m is an integer.
Induction Step:
We need to show that (k + 1)^3 + 2(k + 1) is divisible by 3. Expanding the expression:
(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2
= (k^3 + 2k) + (3k^2 + 3k + 3)
Substituting the induction hypothesis:
= 3m + 3(k^2 + k + 1)
= 3(m + k^2 + k + 1)
Since k^2 + k + 1 is an integer (sum of three integers), and m is an integer, their sum (m + k^2 + k + 1) is also an integer. Therefore, (k + 1)^3 + 2(k + 1) is divisible by 3.
The circumference of a circle is defined to be the _________.
A. the width of the circle
B. length of the radius
C. distance around the circle
D. area of the circle
Answer:
it is the distance of a circle
Step-by-step explanation:
In a basic sine curve, where can the zeros NOT be found
Copycats copies charges $.18 for the first copy and $.12 for each additional copy what is the greatest number of copies you can get for three dollars
A $15,000, 6 percent , 50-day note ,dated November 8, is discounted at 5 percent on November 28, the proceeds of the note would be?
A. $14,936,46
b. $ 15,610,64
c. $63,54
d. $15,061,98
Answer:
D. $15061.98
Step-by-step explanation:
In order to calculate the proceeds we will using the following computation:
Principal + {Principal * Discounted rate * Frequency of a year on Maturity Date}
15,000 + {15,000 * 5% * (30/365)}
Hence, the proceeds of note would be $15,061.98
A baseball team plays in a stadium that holds 51,000 spectators. With ticket prices at $10, the average attendance had been 38,000. When ticket prices were lowered to $8, the average attendance rose to 42,000. Find the demand function (price p as a function of attendance x), assuming it to be linear?? ...?
Answer:
[tex]p(x)=-0.0005x+29[/tex]
Step-by-step explanation:
It is given that a baseball team plays in a stadium that holds 51,000 spectators.
Let x be the attendance and p be the price.
With ticket prices at $10, the average attendance had been 38,000. When ticket prices were lowered to $8, the average attendance rose to 42,000.
Assuming that the demand function is linear. It means, the demand line passes through the points (38000,10) and (42000,8).
The equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-10=\dfrac{8-10}{42000-38000}(x-38000)[/tex]
[tex]y-10=\dfrac{-2}{4000}(x-38000)[/tex]
[tex]y-10=-0.0005(x-38000)[/tex]
[tex]y-10=-0.0005x-0.0005(-38000)[/tex]
[tex]y-10=-0.0005x+19[/tex]
[tex]y=-0.0005x+19+10[/tex]
[tex]y=-0.0005x+29[/tex]
Substitute y=p(x).
[tex]p(x)=-0.0005x+29[/tex]
Therefore, the demand function is [tex]p(x)=-0.0005x+29[/tex].
(1.) decide if function f is invertible.
a) f(n) is the number of students in your calculus class whose birthday is on the nth day of the year.
b) f(x) is the volume in litters of x kilograms of water at 4 degrees celsius. ...?
what is an asymptote? ...?
The sum of two numbers is 27. the larger number is 6 more than twice the smaller number. what are the numbers?
the 6 a.m. temperatures for Four constructed days in the town of Lincoln were -12.1 Celsius -7.8 Celsius -14.3 Celsius and -7.2 Celsius what was the average 6 a.m. temperature for the four days
What are the variable terms in the expression?
6x^2 + 3xy + 4z
Answer:
[tex]6x^2,3xy,4z[/tex]
Step-by-step explanation:
We are given that an expression
[tex]6x^2+3xy+4z[/tex]
We have to find the variable terms in the given expression.
Variable term: The term which contains variable is called variable term.
Constant term:The term which does not contain variable is called constant term.
To find the variable terms we will find the terms which contains variable.
We can see that in the given expression
There are three terms which contain variables.
Hence, the variable terms are
[tex]6x^2,3xy,4z[/tex]
. Evaluate 9C5
126
24
3024
120
...?
Answer:
126 is the answer please give me brainliest.
Step-by-step explanation:
SOLVE. (2ax + 1/2 bx)2 ...?
Explanation of how to expand and simplify the given quadratic expression Hence answer is 4a²x² + abx² + 1/4b²x²,
Solve the equation: (2ax + 1/2 bx)²
Expanding the given expression:
(2ax + 1/2 bx)²
= (2ax)² + (2ax) (1/2 bx) + (1/2 bx)²
= 4a²x² + 2abx² + 1/4b²x²
= 4a²x² + abx² + 1/4b²x²
Answer: 4a²x² + abx² + 1/4b²x²
Related Rates
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.1 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
once you have that relation, then you can replace the variables by the numbers given. by similar triangles that relation is
y12=2x then differentiate both sides a thermometer is guaranteed to give a temperature no more than 1.2 degrees farenheit from the actual temperature. if thermometer reads 28 degrees farenheit, write and solve equation to find max and min temps could be
Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)
f (x) = x2 + 9x − 4 relative minimum
(x, y) =
relative maximum (x, y) =
please help me
...?
Final answer:
To find the relative minimum of the function, we first calculate its first derivative and set it to zero to find critical points. A single critical point is found at x = -9/2. Using the Second Derivative Test, we conclude that there is a relative minimum at (-9/2, -97/4) since the function's second derivative is positive, indicating the function is concave up at this point.
Explanation:
To find the relative extrema of the function f(x) = x2 + 9x − 4, we first need to determine its critical points. This is done by finding the derivative of f(x) and setting it equal to zero.
The derivative of the function, f'(x), can be calculated as follows:
f'(x) = 2x + 9
Setting the derivative equal to zero gives us:
2x + 9 = 0
x = -9/2
Now, we apply the Second Derivative Test to determine if this critical point is a relative maximum or minimum. The second derivative is:
f''(x) = 2
Since the second derivative is positive, the function is concave up at x = -9/2. Therefore, the function has a relative minimum at this point.
To find the y-coordinate, we substitute x = -9/2 into the original function:
f(-9/2) = (-9/2)2 + 9*(-9/2) − 4
Simplifying this, we get:
y = 81/4 - 81/2 - 4
y = 81/4 - 162/4 - 16/4
y = -97/4
Therefore, the relative minimum is (-9/2, -97/4). There is no relative maximum since the function is a parabola that opens upwards.
Calculate cos to two decimal places
A ball bearing is shaped like a sphere and has a diameter os 2.5 centimeters l. What is the volume contained inside the ball bearing? Use 3.14 pi. Round your answer to the nearest hundredth
The volume of the ball bearing, which is a sphere, would be approximately 8.18 cm³. This is calculated using the formula for the volume of a sphere and the given diameter, which is halved to get the radius for the calculation
Explanation:The volume of a sphere can be calculated using the formula V = 4/3 * π * r³, where r is the radius of the sphere. In this case, the diameter of the ball bearing is 2.5 cm, so the radius would be half of that (diameter/2), which is 1.25 cm. Substituting the radius value to the volume formula, we get: V = 4/3 * π * (1.25cm)³ = 4/3 * 3.14 * 1.95cm³ = approximately 8.18 cm³, rounded to the nearest hundredth.
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kelly has 4 times as many songs on her music player as Lou. Tiffany has 6 times as many songs on her music player as Lou. Altogether, they have 682 songs on their music players. How many songs does kelly have?
Ben wants to buy 2 blue sweaters for 119$ and 3 brown sweaters for 44$ each how much will ben spend on his five sweaters?
A Jeweler has 36 inches of silver chain. She needs 5 times much to make some necklaces and 3 times that amount to make some bracelets. How much does the jeweler need to make her necklaces and bracelets
Step-by-step explanation:
The students at Monroe Junior High sponsored a canned food drive. The seventh-grade class collected 129% of its canned food drive goal.
a. ABOUT how many canned foods did the seventh-graders collect if their goal was 200 cans? _____________________
b. ABOUT how many canned foods did the seventh-graders collect if their goal was 595 cans? _________________________