he length of a rectangular field is 90m and its breadth is 32m. find the length of the wire needed to fence the field

Answer: w = -6

Step-by-step explanation:

-30 = 3(w + 6) + 5w

-30 = 3w + 18 + 5w

-30 = 8w + 18

-48 = 8w

w = -6

Hope this helps

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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Having simplified the above equation, the solution to the expression x = 10³⁰

We can simplify the equation using logarithmic rules

1/5 log x - log 1000 = 3

log\(x^{1/5}\) - log 1000 = 3

log (\(x^{1/5}\) /1000) = 3

\(x^{1/5}\) /1000 = 10³

\(x^{1/5}\)= 1000  * 10³

\(x^{1/5}\) = 10⁶

x = (10⁶)⁵

x =  10³⁰

Therefore, the solution to the equation is x = 10³⁰

Note that the logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be increased to obtain x is the logarithm of a number x to the base b. For example, since 1000 = 10³, 1000's logarithm base 10 is 3, or log₁₀ = 3.

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Answer:

2/3

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

25×53

Applying the fractions formula for multiplication,

=2×55×3

=10/15

Simplifying 10/15, the answer is

=2/3

Answer: 0.514285714286 ≈

Step-by-step explanation: 18/35 is already in the simplest form. It can be written as 0.514286 in decimal form

Let's recall what are the symbols

We were told that angle AEc and angle DEF are vertical angle.

When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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Answer:

sas means side angle side

aa means angle angle

asa means angle side angle

sss means side side side

hope it helps you

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Answer:

Proved: AC = BD

Step-by-step explanation:

The complete question related to this with diagram can be found at toppr website.

Given: O is the mid point of AB and CD

Find attached the diagram

∠COA = ∠BOD (vertical angles are equal)

∠AOD = ∠COB (vertical angles are equal)

For ∆AOC

AC + OC + OA = 180° (sum of angles in a triangle)

For ∆DOB

DB + OB + OD = 180° (sum of angles in a triangle)

OC = OD (sides are equal)

OA = OB (sides are equal)

Since both ∆AOC and ∆DOB are equal to 180°, AC = DB.

DB = BD

Proved: AC = BD

By solving a simple product we will see that 12% of 45 is equal to 5.4

If we have a number N and we want to take a percentage P of that number, the operation we need to do is:

new number = N*(P/100%)

Here the original number is N = 45 and the percentage is 12%, then we need to solve:

new number = 45*(12%/100%) = 5.4

Then the 12% of 45 is equal to 5.4

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Consider the quadratic equation:

\(\(x^2-8x=3\)\)

To complete the square of the above quadratic equation, we need to follow the below steps.

Move the constant term from the left side of the equation to the right side.

\(\(x^2 - 8x + \underline{16}= 3 + \underline{16}\)\)

Complete the square by adding the square of half of the coefficient of x to both sides of the equation.

\(\(x^2 - 8x + 16 = 19\)\)

The left-hand side of the equation becomes

\(\((x-4)^2\).\)

This is the square of the binomial, which is always the result of completing the square. Substituting

\(x^2-8x=3\)

for the left side of the equation gives us

\(\((x - 4)^2 = 19\)\)

Therefore, this equation will look like \((x-4)^2=19\) after completing the square on the left side.

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Answer:

1 is multipy the last term by 1/6

2 is geometric because you multiply by 2 every time.

3 is arithmitic sequence because you subtract 20 every time

Step-by-step explanation:

1. Use the Pythagorean Theorem since this is a right triangle:

a^2 + b^2 = c^2

4^2 + b^2 = 9^2

b^2 = 9^2 - 4^2

b = √ 65

b = 8

answer : 8

Answer:

45

Step-by-step explanation:

Because 15 plants is 25% of 60 plants

Hope it helps :)

The number of smartphones the vendor buys is 21 and the number of tablet computers the vendor buys is 15.

What are Simultaneous Equations?

Let the number of smartphones be x and the number of tablet computers be y.

Given that the vendor buys 36 smartphones and tablet computers for $28,065.

\(x+y=36\)    -----(1)

\(\implies y= 36-x\)    -----(2)

It is also given that smartphone costs $895 and a tablet computer costs $618.

\(\implies 895x+618y=28065\)   -----(3)

Now, substituting (2) in (3), we get

\(895x+618(36-x)=28065\\\implies 895x+22248-618x=28065\\\implies 277x+22248=28065\)

Simplifying, we get

\(277x=28065-22248\\\implies 277x=5817\\\implies x=21\)

So, the number of smartphones the vendor buys is 21.

\(y=36-x\\\implies y=36-21\\\implies y=15\)

So, the number of tablet computers the vendor buys is 15.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

12x9

Step-by-step explanation:

12x9 equals ____ square units

The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67

In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.

By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.

In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:

=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).

If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.

If the owner counted 7 trees in the first square, the formula would be

=> (7 / 70) x (2500 / 12) = 16.67.

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Complete Question:

To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.

7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5

Answer:

2469 x 2/3= 1646

personally, I solve it by dividing the 2469 by 3 to get 1/3.

2469/3= 823

then, double it to get 2/3.

823x2= 1646

Answer:

B.18

Step-by-step explanation:

2+1+3

3+3=6

6+5=11

11+7=18

Answer:

108 degrees

Step-by-step explanation:

an arithmetic progression means that there is a constant inbetween all of the angles. Since the smallest angle is 12 degrees, ( i just guessed and checked) and came up with the angles :

12, 60, 108

these have a constant of 48

Answer:

108°

Step-by-step explanation:

Since the angles are in arithmetic progression , then the angles are

a + a + d + a + 2d

a is the first term and d the common difference

Sum the angles and equate to 180 with a = 12

a + a + d + a + 2d = 180

12 + 12 + d + 12 + 2d = 180 , that is

36 + 3d = 180 ( subtract 36 from both sides )

3d = 144 ( divide both sides by 3 )

d = 48

Then the largest angle is

a + 2d = 12 + 2(48) = 12 + 96 = 108°

Answer:

the answer to this is C. 129 cm

The following option describes the two functions correctly: The number of boxes that can be packed by Ryan and Daniel each decreases over time. Daniel's function has a greater rate of change than Ryan's function, indicating that Daniel can pack fewer boxes per hour. Option D is correct, that is, the number of boxes that can be packed by Ryan and Daniel each decreases over time.

Daniel's function has a greater rate of change than Ryan's function, indicating that Daniel can pack fewer boxes per hour.

A function is a rule that specifies a relationship between two quantities. It is a mapping from one set of inputs to another set of outputs that are consistent with certain rules. A function can be described using variables, equations, or graphs, among other things. A function has three components: an input, an output, and a rule that specifies the relationship between the input and the output.

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Answer: 9.88

​​​​​​​​​​​​​​​​​​​

Answer

9.88

Step-by-step explanation:

the tenth place is the first decimal place, hundredth is the second decimal place, the thousandth place is the third decimal place, etc...

Answer:

Both pass there all higher the 50%

Answer:

a)

\(( \frac{h}{g} )(x) = \frac{h(x)}{g(x)} = \frac{ - 7 + 3 {x}^{2} }{7 - 3x} \)

\(( \frac{h}{g}) (4) = \frac{h(4)}{g(4)} = \frac{ - 7 + 3( {4}^{2}) }{7 - 3(4)} = \)

\( \frac{ - 7 + 3(16)}{7 - 12} = \frac{ - 7 + 48}{ - 5} = - \frac{41}{5} = - 8.2\)

b) 7 - 3x ≠ 0, so x ≠ 7/3.

7/3 (2 1/3) is not in the domain of h/g.

Answer:

\(\textsf{(a)}\quad \left(\dfrac{h}{g}\right)(4)=\boxed{-\dfrac{41}{5}}\)

\(\textsf{(b)}\quad \textsf{Value(s) that are NOT in the domain of $\dfrac{h}{g}$\;:}\;\;\boxed{\dfrac{7}{3}}\)

Step-by-step explanation:

Given functions:

\(\begin{cases}h(x)=-7+3x^2\\g(x)=7-3x\end{cases}\)

\(\hrulefill\)

To find the value of (h/g)(4), we need to evaluate the function h(x) divided by g(x) at x = 4.

\(\begin{aligned}\left(\dfrac{h}{g}\right)(4)&=\dfrac{h(4)}{g(4)}\\\\&=\dfrac{-7+3(4)^2}{7-3(4)}\\\\&=\dfrac{-7+3(16)}{7-3(4)}\\\\&=\dfrac{-7+48}{7-12}\\\\&=\dfrac{41}{-5}\\\\&=-\dfrac{41}{5}\end{aligned}\)

Therefore, (h/g)(4) is equal to -41/5.

\(\hrulefill\)

To find the values of x that are not in the domain of (h/g), we need to consider the restrictions imposed by the division operation.

The division (h/g) is undefined when the denominator g(x) equals zero. Therefore, we must exclude any x-values that would make the denominator zero.

Set g(x) to zero and solve for x:

\(\begin{aligned}g(x)&=0\\\\\implies 7-3x&=0\\\\7&=3x\\\\3x&=7\\\\x&=\dfrac{7}{3}\end{aligned}\)

Therefore, x = 7/3 is not in the domain of (h/g).

Given:

The vertices of the rectangle ABCD are A(-3,4), B(-1,4), C(-1,-1) and D(-3,-1).

It is reflected over the line x=2.

To find:

The vertices of the image A'B'C'D'.

Solution:

If a figure is reflected over the line x=a, then

\((x,y)\to (-(x-a)+a,y)\)

\((x,y)\to (-x+a+a,y)\)

\((x,y)\to (-x+2a,y)\)

The rectangle ABCD is reflected over the line x=2. So, the rule of reflection is

\((x,y)\to (-x+2(2),y)\)

\((x,y)\to (-x+4,y)\)

Using this rule, we get

\(A(-3,4)\to A'(-(-3)+4,4)\)

\(A(-3,4)\to A'(3+4,4)\)

\(A(-3,4)\to A'(7,4)\)

Similarly,

\(B(-1,4)\to B'(5,4)\)

\(C(-1,-1)\to C'(5,-1)\)

\(D(-3,-1)\to D'(7,-1)\)

The vertices of image are A'(7,4), B'(5,4), C'(5,-1) and D'(7,-1).

Note: All options are incorrect or not in proper format.