The maximum possible area would have a length of 24 feet and width of 12 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the length and y represent the width, hence:
Since beth has 48 ft fencing and cover 3 sides, hence:
x + 2y = 48
x = 48 - 2y (1)
Also:
Area (A) = xy
A = (48 - 2y)y
A = 48y - 2y²
The maximum area is at A' = 0, hence:
A' = 48 - 4y
48 - 4y = 0
y = 12 feet
x = 48 - 2(12) = 24
The maximum possible area would have a length of 24 feet and width of 12 feet.
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Choose the expression that represents a cubic expression. 2x 11 −3x2 − 2x 11 4x3 − 3x2 − 2x 11 5x4 4x3 − 3x2 − 2x 11
(C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
What is a cubic expression?A cubic polynomial has the generic form [tex]p(x): ax^{3} +bx^{2} +cx+d[/tex], a 0, where a, b, and c are coefficients and d is the constant, all of which are real integers. A cubic equation is one that involves a cubic polynomial.To determine which expression represents a cubic expression:
[tex]8x^{3} -7x^{2} -6x+5[/tex] is a cubic expression.The variable is x. [tex]8x^{3} -7x^{2} -6x+5[/tex] : The variable x has the highest power as 3. [tex]8x^{3} -7x^{2} -6x+5[/tex] is a polynomial.[tex]-7x+4[/tex] is a linear expression because the highest power of the variable x is 1.[tex]7x^{2} -5x+6[/tex] is a quadratic expression because the highest power of the variable x is 2.[tex]9x^{4} +8x^{3} -6x^{2} -2x+11[/tex] is a polynomial with the highest power of the variable being 4.Therefore, (C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
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The complete question is given below:
Choose the expression that represents a cubic expression.
(A) −7x + 14
(B) 7x2 − 5x + 6
(C) 8x3 − 7x2 − 6x + 5
(D) 9x4 + 8x3 − 6x2 − 2x + 11
5. (02.02 MC)
Use the graph to fill in the blank with the correct number. (1 point)
f(1) =
If i throw 20 knifes what is the probability that i will hit my assistant exactly 3 out of those twenty times?
The probability that knife will hit assistant exactly 3 out of 20 times is 0.001425.
According to the given question.
Number of times a kinfe is thrown = 20
Let p denotes the probability that knife will hits the assistant. And q denotes the probability that knife will not hit the assistant.
so,
p = 1/20
q = 1 - 1/20 = 19/20
Therefore,
The probability that knife will hit assiant exactly 3 out of 20 times
[tex]= ^{20}C_{3} ( \frac{1}{20}) ^{3} (\frac{1}{19} )^{17}[/tex]
= [tex]\frac{20!}{3!17!} (0.05)^{3} (0.0526)^{17}[/tex]
=
Hence, the probability that knife will hit assistant exactly 3 out of 20 times is 0.001425.
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Numbers that are divisible by 2 4 6 8 and 10 have to be?
Answer:
Even
Step-by-step explanation:
Select the correct answer what are the solutions to this quadratic equation 4x^2-10=10-20x
Answer:
x1 = 5-3squareroot 5/2 x2= -5+3 squareroot 5 / 2
Step-by-step explanation:
Solve the system of equations
ax+y=2a
x+ay=1+a^2
Answer:
x = 1; y = a
Step-by-step explanation:
ax+y=2a
x+ay=1+a^2
-a²x-ay=-2a²
x+ay=1+a^2
(1 - a²)x = 1 - a²
x = (1 - a²)/(1 - a²)
x = 1
a + y = 2a
1 + ay = 1 + a²
a = y
x = 1; y = a
bell canada came by my house that I just bought and installed a new wire support for one of the telphone poles on my property. the electrical code says that the support must hit the ground at a 55 degree angle..If the telephone pole is 25 feet tall. how long is the wire spport that bell just installed?
Answer:
The cable length will have to be at least 30.51936ft
Step-by-step explanation:
[tex]c= \frac{25}{ \sin( 55 ) } = 30.51936[/tex]
C = Cable
Oscar corporation is planning to construct an elliptical gate at its headquarters. the width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. the company wants to place two bright spots at the foci of the ellipse. how far from the center of the ellipse will the spots be located?
The distance from the center of the ellipse to where the spots are located will be 2 feet.
What is Distance?
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.The distance from the center of the ellipse to where the spots are located will be -
= 5 - 3
= 2 feet.
Therefore, the distance from the center of the ellipse is 2 feet.
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Lakisha’s employer pays $2,150 in health insurance and $86 in life insurance per year. she also gets $3,520 in paid time off per year. her monthly gross pay is $4,370. what are lakisha’s total job benefits per year? a. $5,756 b. $10,126 c. $52,440 d. $58,196 please select the best answer from the choices provided a b c d
Lakisha's total job benefits per year are (D) $58,196.
What are employees' benefits?Employee perks and benefits in kind are non-wage compensation provided to employees in addition to their regular income or salary. A "salary package" or "salary exchange" arrangement is one in which an employee exchanges salaries for some other type of compensation.To find Lakisha's total job benefits:
If Lakisha's employer pays $2,150 in health insurance and $86 in life insurance per year, and she also gets $3,520 in paid time off per year, then Lakisha's total job benefits per year are equal to:
Total Benefits = Health Insurance + Life Insurance + Paid Time Off + Annual Gross Pay
Total Benefits= $2,150+$86+$3,520+12($4,370)Total Benefits= $2,150+$86+$3,520+$52,440Total Benefits=$58,196Therefore, Lakisha's total job benefits per year are (D) $58,196.
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Answer The answer is D
Step-by-step explanation:
I got it correct on edg
Evaluate the integral.
√
S-
5
√x (4+5√x)²
2
dx
Substitute [tex]y=4+5\sqrt x[/tex] and [tex]dy=\frac5{2\sqrt x}\,dx[/tex]. Then the integral is
[tex]\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = 2 \int \frac{1}{(4+5\sqrtx)^2} \frac{5}{2\sqrt x} \, dx = 2 \int y^{-2} \, dy[/tex]
By the power rule,
[tex]\displaystyle \int y^{-2} \, dy = -y^{-1} + C[/tex]
so that
[tex]\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = \boxed{-\frac2{4+5\sqrt x} + C}[/tex]
Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:
A. 19 p
B. 20 p
C. 21 p
D. 18 p
Based on the fact that the number of points scored are consecutive numbers, the number of points scored by Lewis is D. 18 points.
How many points did Lewis score?Lewis is the player who scored the least amount of points as they are first in the order.
To find the total number of points scored in the game therefore, you need to assume Lewis's points based on the options, and then sum up the three numbers above it to see if they add up to 78 points.
If Lewis scored 19 points as the lowest then the total points would be:
= 19 + 20 + 21 + 22
= 82 points
If Lewis scored 20 points, the total points would be:
= 20 + 21 + 22 + 23
= 86 points
Lewis therefore scored less than 19 points.
If Lewis scored 18 points, the total is:
= 18 + 19 + 20 + 21
= 78 points
Lewis therefore scored 18 points.
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It costs $0.50 to mail a postcard to Canada and $0.60 to mail a one ounce letter to Canada. Ahmad wrote to 21 friends and spent $12.00 for postage. How many letters and how many postcards did he write?
It costs $0.50 to mail a postcard to Canada, cost of mailing a one ounce letter to Canada is $0.60 and Ahmad wrote to 21 friends and spent $12.00 for postage. This means that he wrote 15 letters and 6 postcards.
Given Information:
Cost of mailing a postcard = $0.50
Cost of mailing a letter = $0.60
Total number of friends Ahmad wrote to = 21
Total cost of postage = $12.00
Let the number of postcards written by Ahmad be x and that of letters be y.
Then, x + y = 21 ............... (1)
0.50x + 0.60y = 12 ................ (2)
Multiplying equation (1) by 0.50, we get,
0.50x + 0.50y = 10.5 ................. (3)
Subtracting equation (3) from (2), we get,
0.1y = 1.5
⇒ y = 15
From equation (1), x = 21 - y
x = 21 - 15
x = 6
Thus, Ahmad wrote 6 postcards at a mailing cost of $0.50 each and 15 letters at a mailing cost of $0.60 each.
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Which values represent solutions to cosine (startfraction pi over 4 endfraction minus x) = startfraction startroot 2 endroot over 2 endfraction sine x, where x is an element of [0, 2pi)?
The given trigonometric function consists of trigonometric values of common angles.
The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
What are trigonometric functions?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.The given function is: [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]
Where; x ∈ [0, 2·π).
We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).
[tex]cos(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}, sin(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}[/tex]Which gives:
[tex]cos(\frac{\pi }{4}-x )=\frac{\sqrt{2} }{2}. cosx+\frac{\sqrt{2} }{2}.sinx[/tex]So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]
Therefore, the possible solutions (x-values) to cos x = 0 are:
[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]
Where, n = 1, 3, 5, .., x ∈ [0, 2·π)
We get: [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
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Given f(x) = 3 and g(x) = cos(x). what is limit of left-bracket f (x) minus g (x) right-bracket as x approaches negative pi? 2 3 4 dne
Answer:
3
Step-by-step explanation:
f(x)-g(x)=3-cos(x)
when u limit it
u have
3-cos180
which is 3-0
3
Select the correct answer. the diameter of a sphere measures 10.4 inches. what is the surface area of the sphere? a. b. c. d.
The surface area of the sphere is 108.16π in². So, option b is correct.
What is the surface area of a sphere?The surface area of the sphere is calculated by the formula,
A = 4πr²
In terms of diameter - d;
A = 4π × (d/2)²
= 4π × d²/4
= πd² sq. inches
Calculation:The given sphere has a diameter d = 10.4 inches
So, the surface area of the sphere is calculated by
A = πd²
= π × (10.4)²
= 108.16 π sq. inches
So, option b is correct.
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Disclaimer: The given question on the portal is incomplete. Here is the complete question.
Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?
a. 432.64π in²
b. 108.16π in²
c. 54.08π in²
d. 216.32π in²
Answer:
Step-by-step explanation:
The surface area of the sphere is 108.16π in². So, option b is correct.
What is the surface area of a sphere?
The surface area of the sphere is calculated by the formula,
A = 4πr²
In terms of diameter - d;
A = 4π × (d/2)²
= 4π × d²/4
= πd² sq. inches
Calculation:
The given sphere has a diameter d = 10.4 inches
So, the surface area of the sphere is calculated by
A = πd²
= π × (10.4)²
= 108.16 π sq. inches
So, option b is correct.
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Disclaimer: The given question on the portal is incomplete. Here is the complete question.
Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?
a. 432.64π in²
b. 108.16π in²
c. 54.08π in²
d. 216.32π in²
Find the slope of the line grapef below
Answer:
x = 1
Step-by-step explanation:
No matter what y is, x will always be 1.
(1,-4)
(1,-3)
(1,-2)
(1,0)
(1,1)
(1,2) and so on and so on.
PLS HELP ITS MATH PLS
Answer:
y = 2x + 7
Step-by-step explanation:
When a line is parallel to another line, then the slopes of the lines are equal. If line A has an equation y = 3x + 5, then line B, parallel to line A, must also have a slope of 3. Therefore, we know that m (slope) is 2 in this case.
Next, let’s substitute the x and y coordinates and the slope value into y - y1 = m(x - x1). In this case, -4 is x1, and -1 is y1.
y - y1 = m(x - x1)
y + 1 = 2(x + 4)
Finally, simplify the equation and transform it into the slope intercept form, y = mx + b.
y + 1 = 2(x + 4)
y + 1 = 2x + 8
y = 2x + 7
As people exited a movie theater, they were informally surveyed about whether they enjoyed the movie or not.
What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.
#6 pls quick answer!!!
Answer:
ANSWER: mix 120 ml of 35% acid solution with 60 ml of 65% acid solution to obtain 180 ml 0f 45% acid solution
Step-by-step explanation:
If x = number of ml of 35% acid solution and 60 = number of ml of 65% acid solution, then x + 60 = number of ml of the mixture.
Acid content of first ingredient + acid content of second ingredient = acid content of the mixture
So, 0.35x + 0.65(60) = 0.45(x + 60)
0.35x + 39 = 0.45x + 27
12 = 0.10x
120 = x
Geometry: write formal proofs, ASAP!!!!
Answer:
By the definition of midpoints, AX and CX are congruent. By the definition of segment bisectors, X is the midpoint of BD, and therefore BX and DX are congruent. Since angle AXD and CXB are vertical angles, they are congruent by the vertical angles theorem. By SAS, triangles AXD and CXB are congruent. By CPCTC, angles A and C are congruent. By converse of alternate interior angles theorem, AD is parallel to CB.
Please help quick
[tex]y=\frac{-1}{2\sqrt{x^{3} } }[/tex]
can you put step-by-step no verbal explanation needed how I can get to
[tex]y=\frac{-2}{x\sqrt{x} }[/tex]
The equation y=[tex]-1/2\sqrt{x^{3} }[/tex] does not give result to y=-2/[tex]x\sqrt{x}[/tex].
Given two equations y=[tex]-1/2\sqrt{x^{3} }[/tex] and y=-2/[tex]x\sqrt{x}[/tex].
We are required to find that how the first equation will result in second equation.
Equation is like a relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c. It may be a linear equation,cubic or quadratic equation or many more depending on the power if variable.
Taking the first equation.
y=[tex]-1/2\sqrt{x^{3} }[/tex]
Interchange the power of x.
y=-1/2[tex]\sqrt{x} ^{3}[/tex]
Now multiply [tex]\sqrt{x}[/tex] three times.
y=-1/2[tex]\sqrt{x} \sqrt{x} \sqrt{x}[/tex]
Now [tex]\sqrt{x} \sqrt{x}[/tex] will result in x.
y=-1/2x[tex]\sqrt{x}[/tex]
You can see our result is not matching the second equation.
Hence the equation y=[tex]-1/2\sqrt{x^{3} }[/tex] does not give result to y=-2/[tex]x\sqrt{x}[/tex].
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Angle Sum Theorem
y = ?
Answer:
140°
Step-by-step explanation:
The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)
20 + 120 = 140
Answer:
y= 140
Step-by-step explanation:
first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.
Please give me a correct answer and the step by step explanation.
keeping in mind that the points are A(-8 , 6) and C(2 , 5), so
[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{2}{5}\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-8)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AC}}}{\left( 10 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left( \stackrel{x_1}{-8}~~+~~\frac{2}{5}(10)~~,~~\stackrel{y_1}{6}~~+~~\frac{2}{5}(-1) \right)\implies \left(-8+4~~,~~6-\frac{2}{5} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill B\left(-4~~,~~5\frac{3}{5} \right)~\hfill[/tex]
A standard deck of cards contains 52 cards. There are four suits (spades, clubs, hearts, and diamonds) and thirteen of each suit (2-10, jack, queen, king, ace). One card is selected at random from the deck. What is the probability the card selected is an Ace or a heart?
The probability of selecting an ace or a heart when one card is drawn from 52 cards is 1/52.
Given that there are 52 cards in which there are 13 cards each for spades,clubs,hearts and diamonds.
We are required to find the probability of getting an ace or a heart when one card is drawn from 52 cards.
Probability is basically the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative. The probability can be calculated through following formula:
Probability=Number of items/total number of items.
Number of hearts=13
Number of ace=4
Probability of getting an ace or a heart when one card is drawn=P(X=heart)*P(X=ace)
=13/52 * 4/52
=52/(52*52)
=1/52
Hence the probability of getting an ace or heart when one card is drawn from standard deck of cards is 1/52.
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Which equation shows the commutative property of addition? 4 3 = 3 4 1(3) = 3 (2 7) 12 = 2 (7 12) 4 0 = 4
The equation which shows the commutative property of addition is (A) 4+3=3+4.
What is the commutative property of addition?The commutative property is concerned with arithmetic operations such as addition and multiplication. It indicates that switching the order or position of two numbers while adding or multiplying them has no effect on the outcome. For example, 4 + 5 equals 9, and 5 + 4 equals 9.So,
The commutative property for addition states that, a + b = b + a .
Where a, b is any number.
The above condition is satisfied by the equation
4 + 3 = 3 + 47 = 7Therefore, the equation which shows the commutative property of addition is (A) 4+3=3+4.
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The correct question is given below:
Which equation shows the commutative property of addition?
A. 4+3=3+4
B. 1(3)=3
C. (2+7)+12=2+(7+12)
D. 4+0=4
Given: the equation of a parabola is x2 = 8y. step 4: where does the focus for the given parabola lie?
The vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
What is the vertex of a parabola?The vertex of a parabola exists as the point at the intersection of the parabola and its line of symmetry. The vertex of the parabola exists as the minimum point on the graph for a positive right-handed parabola.
Given the equation of parabola exists [tex]$x^{2}=8 y$[/tex].
[tex]$\mathrm{y}=x^{2} / 8[/tex]
General vertex form for any given parabola exists [tex]$\mathrm{y}=\mathrm{a}(x-a)^{2}+\mathrm{b}$[/tex]
where (a, b) exists the coordinates of the vertex.
For this function it exists [tex]$\mathrm{y}=1 / 8(x-0)^{2}+0$[/tex]
The vertex of the given parabola exists at (0, 0).
Therefore, the vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).
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Find the volume of the parallelepiped determined by the vertices (0, 1, 0), (1, 1, 1), (0, 2, 0), (3, 1, 2)
The volume of the parallelopiped is 1 cubic units.
In this question,
A parallelepiped is a three-dimensional shape with six faces, that are all in the shape of a parallelogram. It has 6 faces, 8 vertices, and 12 edges. The volume of a parallelepiped is the space occupied by the shape in a three-dimensional plane.
Let the parallelepiped be PQRS.
The vertices of parallelepiped are P(0, 1, 0), Q(1, 1, 1), R(0, 2, 0), S(3, 1, 2).
The volume of parallelopiped can be found by using following steps.
PQ = Q - P = (1,0,1)
PR = R - P = (0,1,0)
PS = S - P = (3,0,2)
Now, the volume of parallelopiped is
[tex]v=\left\begin{vmatrix}1&0&1\\0&1&0\\3&0&2\end{vmatrix}[/tex]
The determinant the matrix is
⇒ 1(2-0) - 0(0-0) + 1(0-3)
⇒ 1(2) - 0 + (-3)
⇒ 2 - 3
⇒ -1
Hence we can conclude that the volume of the parallelopiped is 1 cubic units.
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Given the data cleanup problem of removing 0 values from a data set, the ____ algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.
The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.
According to the statement
We have given that the there is a algorithm which is used to data cleanup problem of removing 0 values from a data set, and scans a list from left to right and copies every legitimate value into a new list.
and we have to explain about that algorithm.
So,
Here we given that the algorithm copies and paste the values in the new files then
the algorithm is called the copy over algorithm.
So, The copy over algorithm is a a single specimen of something that occurs in a multiple edition, such as a book, article, etc. a matter to be reproduced in print or an imitation or reproduction of an original.
So, The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.
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Which linear inequality will not have a shared solution set with the graphed linear inequality? y < five-thirdsx – 2 y < negative five-thirdsx 1 y > five-thirdsx 2 y > negative five-thirdsx 2
The inequality will not have a shared solution set with the graphed linear inequality is y > five-thirds x + 2.
Linear inequalities are inequalities that involves at least one linear algebraic expression, that is, a polynomial of degree 1.Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.
y < five-thirds x – 2. The inequality will have a shared solution set with the graphed linear inequality. y < negative five-thirds x - 1. The inequality will have a shared solution set with the graphed linear inequality.y > five-thirds x + 2. The inequality will not have a shared solution set with the graphed linear inequality. y > negative five-thirds x + 2. The inequality will have a shared solution set with the graphed linear inequalityHence, the inequality will not have a shared solution set with the graphed linear inequality is y > five-thirds x + 2.
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Answer:
C
Step-by-step explanation:
answer is C
Which term is not possible in the domain of a sequence?
The term that is not possible in the domain of a sequence is:
-5
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexed of the terms, starting at 0 and going until the nth term.
For example, suppose we have the following sequence: 3, 5, 7, ...
The term with index 0 is 3.The term with index 1 is 5.The term with index 2 is 7.From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:
-5.
Which is the only negative number of the options.
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