The largest area that can be enclose in straight wall is 2450 m².
What is meant by the largest area?Having to maximize or decrease a geometric figure's measurements, area, or volume is a special example of a geometry word problem.Let 'x' be the length of rectangle.
Let 'y' be the width rectangle.
Perimeter = 140 meters
2x + y = 140
y = 140 - 2x
Area = xy
Put the value of y in area.
Area = x(-2x + 140)
Area = -2x² + 140x
Differentiating the area with respect to x.
dA/dx = -4x + 140
Put dA/dx = 0 to get the critical point.
-4x + 140 = 0
x = 140/4
x = 35
Largest area at x = 35.
y = 140 - 2x
y = 140 - 2×35
y = 70
Area = xy
Area = 70×35
Area = 2450 m²
Thus, the largest area that can be enclose in straight wall is 2450 m².
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help me please please please 33333
n?
8) 2y = 6x²-x+3
2y=6x
8
sy=-15
linear or nonlinear
Answer: I would say non linear. I have done problems like these before and anytime there is an exponent in the equation it always ends up being non linear. Also remember for it to be linear it most form a straight line that passes through the origin.
Step-by-step explanation:
Identify the correct command to find the derivative ofywith respect toxof the following equation:y=4x∧4−3x∧2+6x+14dydx=polyder([4,0,−3,6],14)dydx=polyder([4,0,−3,6,14])dydx=polyder(4,0,−3,6,14)dydx=polyder([4,−3,6],14) Explanation: When taking the derivative of a polynomial, the coefficients of the polynomial must be arranged in decending powers, being careful to specify zero for missing terms. The constant (i.e.,xto the zero power) is included in the array of coefficients.
The derivative of the given polynomial equation is 16x³ - 6x + 6.
We are given an equation. The equation represents a polynomial in one variable. The degree of the polynomial is four; hence, it is called biquadratic. We need to find the derivative of the given polynomial. The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
The equation is given below.
y = 4x^4 - 3x² + 6x + 14
dy/dx = (d/dx)(4x^4 - 3x² + 6x + 14)
dy/dx = (d/dx)(4x^4) - (d/dx)(3x²) + (d/dx)(6x) + (d/dx)(14)
dy/dx = [4*4x^(4 - 1)] - [3*2x^(2 - 1)] + [6*1x^(1 - 0)] + [14*0x^(0 - 1)]
dy/dx = 16x³ - 6x + 6
Hence, the derivative of the given polynomial equation is 16x³ - 6x + 6.
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for each of the following determine the n -unit percent change. the 19-unit percent change is 45 %. what is the 17-unit percent change? % the 16-unit percent change is 43 %. what is the 12-unit percent change? % the 20-unit percent change is -25 %. what is the 18-unit percent change? % the 5-unit percent change is -50 %. what is the 8-unit percent change?
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
Given, that
The 19-unit percent change is 45 %
Now, 1-unit percent change is 45/19
17-unit percent change is (45/19)×17%
= 40.26%
The 16-unit percent change is 43 %
Now, 1-unit percent change is 43/16
12-unit percent change is (43/16)×12%
= 32.25%
The 20-unit percent change is -25%
Now, 1-unit percent change is -25/20
18-unit percent change is (-25/20)×18%
= -22.5%
The 5-unit percent change is -50 %
Now, 1-unit percent change is -50/5
8-unit percent change is (-50/5)×8%
= -80%
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
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6y^2 + 7y - 20= 0
solve this quadratic equation using a multiplication frame.
y= -4/3=-1.333
y= 5/2=2.500
verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same
The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram
The statement is
"The median and altitude of an isosceles triangle can be same"
Draw an isosceles triangle ABC with BD = CD,
Draw a line segment AD perpendicular to the side BD
Here AD is the height of the triangle which is the altitude of the triangle
From the figure we can see that the length of BD = length of CD
Where D is the mid point of the line BD.
Therefore the line AD is the median of the triangle
Hence, The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram
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Factorise the following
4x²-25y²
Answer:
= (2x + 5y) * (2x - 5y)
Step-by-step explanation:
4x²-25y²
= (2x)² - (5y)²
= (2x + 5y) * (2x - 5y)
Answer:
[tex]\huge\boxed{\sf (2x + 5y)(2x - 5y)}[/tex]
Step-by-step explanation:
Given expression:[tex]4x^2-25y^2[/tex]
Both of the terms are perfect squares.
[tex](2x)^2-(5y)^2[/tex]
Using formula: a² - b² = (a + b)(a - b)= (2x + 5y)(2x - 5y)
[tex]\rule[225]{225}{2}[/tex]
If a person spins a six-space spinner and then flips a coin, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the spinner outcomes and H, T for the coin outcomes.
The sample space is S={__}
(Use a comma to separate answers as needed.)
Answer:
Step-by-step explanation:
If one spins a six-space spinner and then flips a coin, then the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
As per the question statement, a person spins a six-space spinner and then flips a coin,
And we are required to determine the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes.
Now, on spinning a six-space spinner, any one of the 6 faces will come as outcomes, and if these outcomes are denoted by (1, 2, 3, 4, 5, 6).
And after spinning the six-space spinner, if one flips a coin, either of "heads" face or "tails" face will come as outcome, which can be denoted by {H, T}.
Therefore, If one spins a six-space spinner and then flips a coin successively as mentioned above, every possible outcome of the spinner will be accompanied by one of two the possible outcomes the coin. Hence, the sample space (S) of possible outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
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PLEASE HELP I WILL GIVE BRAINLY!!!Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions LC)
Rewrite 30 - 6x³ using a common factor.
O2(15-3x³)
O 2x(15-3x²)
O6(5-6x³)
O6x(5-x²)
Answer:
(15-3x³) is the answer.
Step-by-step explanation:
2*15-2*3x³
which is 30-6x³.
White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 7:3
The ratio of the number of white circles to the number of white squares is 2:7
The ratio of the number of black circles to the number of black squares is 1:2
Work out what fraction of all the shapes are circles.
Give your answer as a fraction in its simplest form.
(Hint: Fractions can be written in the form a/b. eg [tex]\frac{5}{28}[/tex] would be written as 5/28)
The fraction of all the circles in the shapes is 23/90
How to calculate the fraction of all the shapes are circles?Given that the:
Ratio of the number of white shapes to the number of black shapes is 7:3
Ratio of the number of white circles to the number of white squares is 2:7
Ratio of the number of black circles to the number of black squares is 1:2
Total share for both white and black shape = 7+3 = 10
share for white shape = 7/10 and share for black shape = 3/10
Total share for white circles and white squares = 2+7 = 9
share for white circles = 2/9 and share for white squares = 7/9
Total share for black circles and black squares = 1+2 =3
share for black circles = 1/3 and share for black squares = 2/3
White circles will take 2/9 of white colors i.e. 2/9 x 7/10 = 14/90 = 7/45
Black circles will take 1/3 of black colors i.e. 1/3 x 3/10 = 3/30 = 1/10
Fraction of circles = 7/45 + 1/10
= 14+9/ 90
= 23/90
Therefore, the fraction of all the shapes that are circles is 23/90
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Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
How far apart are the cars 1.5 hours after they start moving?
Answer:
3s - 7.5 milesStep-by-step explanation:
GivenThe speed of car1 is s,The speed of car2 is 5 less than s,Time is 1.5 hrs.SolutionDistance equation:
Distance = speed * timeIf cars move in opposite directions their speeds add up, then the distance between them after 1.5 hours is:
(s + s - 5)*1.5 = (2s - 5)*1.5 = 3s - 7.5Answer:
After 1.5 hr, they are 3s - 7.5 mi away.
Step-by-step explanation:
Forming the expression,
→ 1.5 × (s + s - 5)
Now the required solution will be,
→ 1.5 × (s + s - 5)
→ 1.5 × (2s - 5)
→ 1.5(2s - 5)
→ 3s - 7.5
Hence, answer is 3s - 7.5 miles.
A shopkeeper buys a dress for 40$ she sells it for 48$
Workout the percentage increase in the price of the dress.
Please help now
Given a point (5,-6) and slope m = -2
Write the Point-Slope Equation of the line.
Please give me a great explanation and explain like your talking to a baby please. Thanks :)
Answer:
y+6 =-2(x-5)
Step-by-step explanation:
The question is asking for the equation of the line
The equation for point-slope form is always written as y-y₁=m(x-x₁)
y₁ and x₁ are the points given to you in this order (x₁, y₁)
so x₁=5 and y₁=-6
Now you plug in all the numbers you have into the point slope form
y- (-6)= -2(x-5)
When you subtract a negative (a double negative you get a positive)
y+6=-2(x-5)
Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).
Notes:
For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be
y-2=-2(x-1)
What is a,b,c and day
[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]
Answer:
A = 13 B = 3 C = -7 D = -12
Step-by-step explanation:
Just insert the x values for a, b, c, and d. for example if we were to find a.
The x value for a is -3 so we would put -3 in place of x in the equation.
-5(-3) - 2
Remember: Two negative numbers multiplied with each other equal a positive.
15 - 2 = 13
a bank wishes to estimate the mean credit card balance owed by its customers. the population standard deviation is estimated to be $300. if a 98% confidence interval is used and an margin of error of $75 is desired, how many customers should be sampled?
Using a 98% confidence interval, the total number of customers that should be sampled is 87.
What exactly is sample size?The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.
Given,
Standard deviation σ=300
Confidence level: 0.98
Maximum allowable error: ε=75
The critical value is calculated using the standard normal table at the level of significance (0.02)
The critical value in this case is 2.326.
Sample size is calculated by,
n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²
n=((2.326)²×(300)²)/(75)²
n=86.564≈87
Therefore, the required sample size is 87.
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Please help me!!!!!!!!!
Answer:
-6
Step-by-step explanation:
The value of [tex]b[/tex] is the same as the value of [tex]y[/tex] when [tex]x=0[/tex].
Find h in the parallelogram shown.
h= ? ft
The required value of h is 5.29 ft in the parallelogram shown.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
As per the given figure, the dotted lines create a triangle, and the hypotenuse of that triangle is the opposite base of the parallelogram, indicating that it is likewise 8 feet long.
The base of the newly made triangle is one of the parallelogram's diagonals, which is 6 feet long.
According to Pythagorean's theorem, we have
h² + 6² = 8²
h² + 36 = 64
h² = 28
h = √28
h = 5.29
Thus, the required value of h is 5.29 ft.
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Answer:
4
I did the i-ready, hope this helps! :)
Find value of x. Show steps.
A theatre contains 439 seats and the ticket prices for a recent play were $48 for adults and $28 for children. if the total proceeds we $15,852 for a sold-out matinee, how many of each type of ticket were sold?
The theatre sold 178 adult tickets and 261 children tickets for the play.
It is given that the total number of seats is 439 seats.
There are two types of tickets available- children and adults.
The price for adult tickets is $48 and that for children is $28.
Let the number of adult tickets sold be x
Let the number of children's tickets sold be y.
The show was a sold-out
Hence,
x + y = 439 [1]
48x + 28y = 15852 [2]
From equation [1] we get
x = 439 - y
putting this result in equation [2] gives us
48(439 - y) + 28y = 15852
or, 21072 - 48y + 28y = 15852
or, -20y = - 5220
or, y = -5220/ -20
or, y = 261
Therefore,
x + 261 = 439
or, x = 439 - 261
or, x = 178
Hence, 178 adult tickets were sold and 261 children's tickets were sold.
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What is the surface area of the cuboid below? Remember to give the correct units.
Answer:
surface area=2(lb+lh+bh)
surface area=2(9)(4)+(9)(12)+(4)(12)
surface area=384cm2
HELP!!
If a₁ = 3 and an
-
= (an-1)2 + 1 then find the value of a4.
The required value of a₄ is 10,202 to the given recursive formula.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given recursive formula in the question as:
aₙ = (aₙ ₋₁ )² + 1 ....(i)
And, a₁ = 3
Substitute the value of a₁ = 3 in equation (i), and solve for n = 2
a₂ = (a₁)² + 1
a₂ = (3)² + 1
a₂ = 9 + 1 = 10
Substitute the value of a₂ = 10 in equation (i), and solve for n = 3
a₃ = (10)² + 1
a₃ = 100 + 1 = 101
Substitute the value of a₃ = 101 in equation (i), and solve for n = 4
a₄ = (101)² + 1
a₄ = 10,201 + 1
a₄ = 10,202
Therefore, the required value of a₄ is 10,202.
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state how the 2 triangles are congruent?? SSS and SAS HELP ASAPPP??
The two triangles are congruent by SAS criterion.
What is SAS criterion?According to this standard, two triangles are said to be congruent if their two sides are equal to the sides of another triangle and their respective angles are also equal. The "Side-Angle-Side" triangle congruence theorem is referred to as the SAS Criterion.According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides and the included angle of another triangle.Verification:
Let's carry out an exercise to demonstrate SAS's validity. AB=PQ, BC=QR, and ∠B=∠Q are given. To demonstrate: ΔABC≅ΔPQRPlacing the triangle ABC over the triangle PQR will cause B to fall on Q and the AB side to coincide with the PQ side.Point A falls on point P because AB=PQ.The side BC will fall along the side QR since ∠B=∠Q.Point C is in line with point R since BC=QR. As a result, BC and QR coincide, while AC and PR coincide.ΔABC will therefore match ΔPQR. Consequently, ΔABC ≅ ΔPQR. This exemplifies the SAS congruence criterion.To learn more about SAS criterion, refer to https://brainly.com/question/22472034
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the honda civic hybrid gets 46 miles per gallon in city driving and 51 mpg in highway driving. the car is driven 621 miles in 13 gallons of gasoline. how many miles were driven in the city and how many were driven on the highway?
The distance driven in city is 386.4 miles and same in highway is 213.6 miles.
Let the distance driven in city be x and driven in highway be y.
Now given that the mileage in city is 46 miles per gallon and in highway same is 51 miles per gallon.
The car is driven 621 miles in 13 gallon.
So suitable system of linear equations in two variables to solve this is,
x+y = 621 ……(1)
x/46+y/51 = 13 …….(2)
From (2) we get,
51x+46y = 30498
5x+46(x+y) = 30498
5x+46*621 = 30498
5x = 30498-28566
5x = 1932
x = 386.4
So from (1) we get,
y = 621-x = 621-386.4 = 213.6
Hence the car drove 386.4 miles in city and 213.6 miles in highway.
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in a one-tailed hypothesis test (lower tail), the z test statistic is determined to be -1.9. the p-value for this test is
The p-value for this z test statistic is equal to 0.0287.
What is a null hypothesis?A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the z test statistic?The z test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x represents the sample mean.μ represents the mean.σ represents the standard deviation.n represents the number of hours.In this scenario, the z test statistic for a one-tailed hypothesis test (lower tail) is equal to -1.9. Therefore, by using a t-distribution and z-score calculator for a normal distribution, the p-value for this test is given by:
P-value = P(t > -1.9)
P-value = 0.0287.
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What is the y-intercept of the function y = log4 (2x+64) +3?
Answer:
(0, 6)
Step-by-step explanation:
Given function:
[tex]y=\log_4(2x+64)+3[/tex]
The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.
Therefore, to find the y-intercept, substitute x = 0 into the function:
[tex]\implies y=\log_4(2(0)+64)+3[/tex]
[tex]\implies y=\log_4(64)+3[/tex]
Rewrite 64 as 4³:
[tex]\implies y=\log_4(4)^3+3[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies y=3\log_4(4)+3[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies y=3(1)+3[/tex]
[tex]\implies y=3+3[/tex]
[tex]\implies y=6[/tex]
Therefore, the y-intercept of the given function is (0, 6).
tickets for a community theater cost $11 for each main floor seat and $6 for each balcony seat. there are 400 seats on the main floor, and these seats were sold out for the evening performance. the total revenue from ticket sales was $5060. how many balcony seats were sold?
The number of balcony seats sold is 110
Finding Unknown quantity using Linear equation:
The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.
Here we have
Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.
There are 400 seats on the main floor, which are sold out for the evening performance
The total revenue from ticket sales was $5060.
Here we don't know the number of balcony seats.
Let us assume that number of balcony seats = x
Then total revenue = 400(11) + 6x = 5060
=> 4400 + 6x = 5060
=> 6x = 5060 - 4400
=> 6x = 660
=> x = 110
Therefore,
The number of balcony seats sold = 110
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a sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies? responses 15.1 15.1 15.3 15.3 16.3 16.3
The mean sleep time is 16.54 hours per day for newborn babies
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."It is a statistical idea with significant financial implications. The idea is applied in a number of financial areas, such as business appraisal and portfolio management, although not exclusively.acc to our question-
z-score = (x - μ)/σ, where x is the score , μ is the mean and σ is thestandard deviationA sleep time of 15.9 hours per day for a newborn babyx = 15.9 hoursAt the 10th percentile of the distribution of sleep times for all newborn babiesThat means we want to find z-score corresponding to 0.1 (10/100 = 0.1)By using the normal distribution tablez = -1.28The standard deviation is 0.5 hourσ = 0.5Substitute these values in the rule above-1.28 = (15.9 - μ)/0.5Multiply both sides by 0.5-0.64 = 15.9 - μAdd μ to both sides-0.64 + μ = 15.9add -0.64 to both sidesμ = 15.9 + 0.64 = 16.54The mean sleep time is 16.54 hours per day for newborn babies.
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Please help! I need help solving this final problem for geometry.
graph y =-x+7
pls help i was gone when we did this
the slop is -1 and the y-intercept is (0,7)
What is vertex?An element of a line is a line segment.A line segment that can be extended endlessly is known as a ray.An angle is created when two line segments or rays cross one another.A vertex is created by definition whenever two lines come together to produce an angle.Thus, we can state that a vertex is formed when two line segments or rays intersect.acc to our question-
plot a point on the y- axis line at 7. Then go right 7 units and down 7 unitsHence,the slop is -1 and the y-intercept is (0,7)
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You measure containers for international shipments. The height of the standard container is 6 feet and 7 inches. Which of the following is closest to its height in meters?