The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 150, hence:
Area = length × width = x × y
150 = xy
y = 150/x
A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:
Amount of fencing needed (P) = x + x + y + y + y = 2x + 3y
Amount of fencing needed (P) = 2x + 3(150/x) = 2x + 450/x
To minimize the amount of fencing needed, dP/dx = 0, hence:
dP/dx = 2 - 450/x²
2 - 450/x² = 0
2 = 450/x²
2x² = 450
x² = 225
x = 15 feet
Let's find the value of y.
y = 1350/x = 1350/15 = 10 feet
Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.
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What is 12 = -4(-6x - 3)
Answer:
no solution
Step-by-step explanation:
12=-4(-6x-3)
12=24x+12
0=24x
Select all equations that are equivalent to
(6x + 2)
3
-=2(3x +14)
(Select all that apply.)
(6x + 2)
3
(6x + 2) = 2 (3x+14)
2x+3=2-(3x +14)
=-3x-12
6x + 2 = -9x-36
(6x + 2)
3
= -3x+16
Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 , the correct option is (a) and (d) .
In the question ,
it is given that
the equation is (6x+2)/3 = 2 - (3x+14)
solving the brackets on the right side of the equation ,
(6x+2)/3 = 2 - 3x - 14
(6x+2)/3 = -3x - 12 ....option(a)
On Cross Multiplying , we get
6x + 2 = 3(-3x - 12)
6x + 2 = -9x - 36 ....option(d)
Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 .
The given question is incomplete , the complete question is
Using Simplification , Select all equations that are equivalent to
(6x+2)/3 = 2 - (3x+14)
(a) (6x+2)/3 = -3x-12
(b) (6x+2) = 2 - (3x+14)
(c) 2x + 2/3 = 2 - (3x+14)
(d) 6x+2 = -9x-36
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Find the length of a using
the Pythagorean Theorem.
8
a
6
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Answer:5.3
Step-by-step explanation:
using the Pythagorean theorem 8²-6²=28 √28=5.3
5
Step-by-step explanation:
Pythagoras theorem states that
a²+b²=c²
therefore a²=b²-c²
a²=8²-6²
a=√8²-6²
=√64-36
=√28
=5.3 or approximately 5
Epsilon3 is an exoplanet with a mass of 9.43x10^27g. It has a radius of 7.6x10^8cm. What is the density of the planet? What is it made of?
The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.
How to get the density of the planet?Density is defined as the quotient between mass and volume.
Here we know that the mass is:
9.43*10²⁷g
And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:
V = 3.14*(3/4)*R³
Then in this case the volume is:
V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³
Then the density is:
D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3
For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)
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Use polynomial long division to find the quote and the remainder when 2x^3-4x^2-x+2 is divided by X+2
The quotient of the polynomial is 4x - 9 and the remainder is 20
What are Quotient and remainder?The resultant of the division is called the quotient while the Remainder is the number that is left after division.
In long division, the terms on top of the division symbol are called the quotient while that at the bottom is called the remainder.
When a division has no remainder it means that the polynomial is divisible by the divisor.
The body of the calculation is found in the attached file below.
In conclusion, the Quotient and remainder are 4x - 9 and 20 respectively.
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5
link
!!!
MULTIPLE CHOICE QUESTION
Find the distance between (-3,-4) and (2,8).
Hint: plot the points on the coordinate plane and
then use the Pythagorean Theorem.
The distance between points (-3,-4) and (2,8) is 13.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, or it follows Pythagoreans theorem.
The horizontal distance = 5
And the vertical distance = 12
The vertical and horizontal lines make a right angle when they meet,
To find distance between points, use Pythagoreans theorem,
(D)² = (5)²+(12)²
(D)² = 25 + 144
(D)² = 169
D = 13
The distance between points (-3,-4) and (2,8) is 13.
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List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The simplified form of the given fraction is, 2/3.
What is greatest common factor?
The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.
Consider, the given fraction [tex]\frac{48}{72}[/tex]
The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
So, from above the greatest common factor of 48 and 72 is 24.
Therefore,
[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]
Therefore, the simplified form of the given fraction is, 2/3.
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in a particular chi-square goodness-of-fit test, there are eight categories and 825 observations. use the 0.10 significance level. a. how many degrees of freedom are there?
By probability , 7 is degrees of freedom are there .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.It is predicated on the likelihood that something will occur. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of getting a head is 1 in 2.825 Observations and 8 categories .
Degree of freedom = k - 1
df = 8 - 1
df = 7
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If was asked to think of a number and multiply it by 2, could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, multiply it by 5 and subtract 3 from the result."
The algebraic expression of the mentioned statement will be 5x-3.
According to the question,
An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.
Let the unknown number be taken as x.
If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,
x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).
For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).
Hence, algebraically the final statement will be 5x -3.
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What is 10 and 3/4 as a decimal
Answer:10.75
Step-by-step explanation:
3/4 as a decimal is 0.75. add that to the 10 gives you 10.75
TR is the angle bisector angle ATS. The m angle RTS = (17x-5) and m angle ATS= (28x + 8). find X
Applying the definition of angle bisector, the value of x is: x = 3.
What is an Angle Bisector?An angle bisector can be defined as a ray or line that divides an angle into two parts that are congruent or equal to each other in measure.
Since TR is the angle bisector that bisects angle ATS, it implies that angle ATS is divided into equal parts.
Given the following:
Measure of angle RTS = (17x - 5)°
Measure of angle ATS = (28x + 8)°
Therefore:
Measure of angle ATS = 2(measure of angle RTS) [definition of angle bisector]
Substitute
28x + 8 = 2(17x - 5)°
28x + 8 = 34x - 10
Combine like terms
28x - 34x = -8 - 10
-6x = -18
Divide both sides by -6
-6x/-6 = -18/-6
x = 3
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Rhino poaching is a serious problem and has resulted in rhinos, particularly the black rhino, becoming an endangered species. Statistics suggest that there were 60 500 black rhinos at the beginning of 1970, but only 4 000 remained at the end of 2011. Determine the annual rate of depreciation that these statistics represent.
The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %
What is a rate of depreciation?The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.
The initial number of black rhinos in 1970 = 60,500
The number of black rhinos remaining in 2011 = 4,000
The annual rate of depreciation can be found using the formula;
[tex]FV = PV \cdot \left(1+\dfrac{r}{100} \right)^n[/tex]Where;
FV = The future value = 4,000
PV = The present value = 60,500
r = The annual depreciation rate
n = The number of years
[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]
[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]
[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]
The annual rate of depreciation is approximately 6.41%
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someone please help!
Give the numerical coefficient of the term.
xw
The numerical coefficient is _____.
Answer:
x
Step-by-step explanation:
The numerical coefficient is x.
HELP
(2, -1); m = 5/4
Answer:
part b
y + 1 = 5/4(x - 2)
part c
y - 5 = 3(x - 0) or y - 5 = 3(x)
Step-by-step explanation:
Which expression is equivalent to
94
94
310
95
94
310
(9².3³) ²₂
Answer:
Step-by-step explanation: The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
What is an integer exponent?
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The question is incomplete.
The complete question is attached in the picture, please refer picture.
We have an expression:
Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
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cook-it rice cooker has a mean time before failure of 38 months with a standard deviation of 4 months, and the failure times are normally distributed. what should be the warranty period, in months, so that the manufacturer will not have more than 7% of the rice cookers returned? round your answer down to the nearest whole number.
In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.
Define p- value.A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value. Statistical significance is commonly defined as a p-value of 0.05 or less. The sample data, test type, and sampling distribution of the test statistic under the null hypothesis are used to determine the p-value (lower-tailed test, upper-tailed test, or two-sided test).
Given,
Cook-it rice cooker has a mean time before failure of 38 months with a standard deviation of 4 months, and the failure times are normally distributed.
The 7th percentile, or X when Z has a p-value of 0.08, or X when Z = 0.4720, should serve as the warranty period.
Z = X - Mean/ standard deviation
0.472 = x - 38/4
0.472 (4) - x - 38
1.888 = x - 38
x = 39.88
x = 40
In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.
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PLSSSS HELPPPPP MEEE !!!!!
All the angles in a triangle add up to 180 degrees.
40 + x + (5x + 14) = 180
54 + 6x = 180
6x = 126
x = 21 degrees
Answer:
x=21
Step-by-step explanation:
a triangle adds up to 180 degree so to find x we will use the formula
(5x+14)+x+40=180
subtract 40 from each side so we have
(5x+14)+x=140
we have 2 terms with the same factor (x) so combine like terms
6x+14=140
subtract 14 from both sides
6x=126
divide both sides by 6
x=21
check your answer
5(21)+14
105+14=119
119+ 21+40=180
so x is equal to 21
Compute and expressed the result as a mixed fraction?
1) 2+ 3/4
Answer:
2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
2 + [tex]\frac{3}{4}[/tex]
= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number
can anyone help?????
Answer: 0
Step-by-step explanation:
Since y is 2, and it’s being multiplied by 4, you have 8 - 8 which =0
Y=2
4(2) - 8
8-8
0
Answer:
0
Step-by-step explanation:
4y - 8
Given that,
y = 2
To find the value of given expression, replace y with 2 and solve the expression.
Let us solve it now.
4y - 8
4 × 2 - 8
8 - 8
0
Find the perimeter of the triangle
HELPPPPPP
Answer: 4x + 29
Step-by-step explanation: add the like terms together.
Answer:
39 inches
Step-by-step explanation:
the triangle has all equal angles
this means it is equilateral and this also means all the sides are equal
so take 2 sides and set them equal to each other to find x
21 - x = x + 5
now solve
add x to both sides
21 = 2x + 5
subtract 5 to both sides
16 = 2x
divide everything by 2
8 = x
now flip it
x = 8
plug this is to one of the equations and multiply that by 3
8 + 5 = 13
13 * 3 = 39
that is the perimeter
The attendance at an amusement park in a month of july was 178,383.What is the attendance rounded to the nearest thousand
Answer:
178 000
Step-by-step explanation:
178 383 8 is in the thousands place...if the number next to it (3) is ≥ 5 round it up by 1 o/w leave it alone
Answer:
178,000
Step-by-step explanation:
It's 178,000 because the number in front of the 8 in 178,383 was under five so the number dropped.
Use the given vertices to graph quadrilateral TUVW and its image after a dilation centered at the origin with scale factor
k=2/3
T(9,-3), U(6,0), V(3,9), w(0,0)
Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.
As here we have scale factor=3>1.
Hence, the dilation changes the original will expand the original figure.
Hence, each of the coordinate of a figure get multiplied by 3.
Hence, the co
ordinates of the image are given as:
i.e. A(0,0) → A'(0,0)
B(2,3) → B'(6,9)
C(1,-2) → C'(3,-6)
D(-3,-3) → D'(-9,-9)
Step-by-step explanation:
this is my last question please help asap!!
The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
The correct option is (A).
What is the average rate of change of a function?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
Using function notation, we can define the Average Rate of Change of a function f from a to b as:
[tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]
The given function is [tex]g(x) = 5(2)^{x}[/tex],
Now calculating the average rate of change of function from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]
Now, calculate the average rate of change of function from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]
The jump from m = 10 to m = 40 is "times 4".
So option (A) is correct.
Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
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if the product of five and the number is increased by seven, the result is the same as eight less than three times a number
Please helppppp
Answer:
The number is -7.5
Step-by-step explanation:
Creating an equation:
5x+7=3x-8
-> 5x = 3x-15
-> 2x=-15
-> x=-7.5
Write the linear equation in the slope intercept form.
(-6,0); slope= 2/3
Answer:
Step-by-step explanation:
y=2/3x+4
a parking garage charges the rates in the table below. what is the rate of change? don’t forget your units.
2(20x8) + 2(20x3)+2(8x3)
Answer:
488
Step-by-step explanation:
2(20x8) + 2(20x3)+2(8x3)
Assuming the "x" is not a variable.
The answer is 488
However, if "x" is a variable. The equation would be
40x^8 + 56x^3
Answer:
488
Step-by-step explanation:
using BODMAS
METHOD 1.
[tex]2(20 \times 8) + 2(20 \times 3 + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) = \\ = 320 + 120 + 48 \\ = 448[/tex]
METHOD 2.
[tex]2(20 \times 8) + 2(2 \times 3) + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) \\ = 2(160 + 60 + 24) \\ = 2 \times 244 \\ =488[/tex]
a 39-inch by 104-inch piece of cardboard is used to make an open-top container by removing a square from each corner of the cardboard and folding up the flaps on each side. what size square should be cut from each corner to get a container with the maximum volume? enter the area of the square and do not include any units in your answer.
According to the solving the area of the square is 68.0625.
What's a square's area?As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.
According to the given data:The box formed after cutting the square from each corner will have the dimensions as,
length = 104 - 2x, width = 39 - 2x, height = x.
∴ volume of the box = length × width × height
∴ v = (104 - 2x)(39 - 2x)(x) -----(i)
∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])
∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])
∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
let f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x -----(ii)
To, find x for which f(x) is maximum,
⇒we should apply second derivative test ,
According to this test, first we should find critical points at which f'(x) = 0.
then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.
∴ let us consider, f'(x) = 0.
now, f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056. -----(iii)
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)
⇒ f'(x) = 0.
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0
⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a ; where a = 3, b = -143, c = 1014.
∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3
∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.
∴ x = [tex]\frac{143 + 91}{6}[/tex] , x = [tex]\frac{143 - 91}{6}[/tex]
⇒ x = 39, 8.25
the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.
Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]
∴ Area = 68.0625
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HALF SOLVED PLEASE HELP