A farmer has a large field that is x feet in length. He wants to fence in a rectangular section in the middle of the field, leaving a length of 100 feet of open field beyond each end of the fenced rectangle. He also wants the width of the fenced-in space to be 100 feet less than its length, as shown in the diagram.
Find the equation in standard form for the area of the fenced-in section in terms of the length of the field.
(area = length • width)

The radius of the cylinder is 8 inches.

Given,

In one design being considered for the container shaped like a cylinder, the container will have a height of 12 inches.

We need to find the radius of the container to the nearest 10th of an inch.

A cylinder is a three-dimensional solid that has two parallel bases joined by a curved surface, at a fixed distance.

The volume of a cylinder is given by:  π r² h.

The relation between the radius of the base and the height of a cylinder is that the ratio between the radius of the base and the height of a cylinder is 2:3.

We have,

The container will have a height of 12 inches.

The container is like a cylinder.

Height of the cylinder = 12 inches.

Using the relationship between radius and height of a cylinder.

= Radius: Height

= 2 : 3

Let radius be 2x and height be 3x.

We have,

Height = 3x = 12 inches.

Radius = 2x

Find the value of x.

3x = 12 inches

x = 12 / 3 inches

x = 4 inches.

Now,

Put x = 4 inches in radius =2x.

Radius = 2x

Radius = 2 x 4

Radius = 8 inches.

Thus the radius of the cylinder is 8 inches.

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Answer:

i don't know i think its 20 in my opnian

Step-by-step explanation:

i don't know sorry

Answer:

$8,888

Step-by-step explanation:

if he makes $35,876, then to find out the amount he has left, you jsut need to take away the expenses which would be $26,988. When you do the math, he has $8,888 left.

Answer:

The wife earns $95,000.

man they save up they can get a Rolls-Royce i wonder what there job is cause i want it. lol PLS GIVE ME BRAINLIEST

Answer:

Step-by-step explanation:

\(\sqrt{- i} =\sqrt{(-1)i} =\sqrt{i^2i} =i\sqrt{i}\)

The most appropriate choice for differentiation will be given by

h'(3) = 24.02

h''(3) = \(210.48\)

What is differentiation?

Differentiation is the process in which instantaneous rate of change of function can be calculated based on one of its variables.

Here,

h(x) = tan(4x + 8)

h'(x) = \(\frac{d}{dx} (tan(4x + 8))\)

       = \(sec^2(4x + 8)\frac{d}{dx}(4x + 8)\)

       = \(4sec^2(4x + 8)\)

h'(3) =

\(4sec^2(4\times 3 + 8 )\\4sec^220\\24.02\)

h''(x) =

\(\frac{d}{dx}(4sec^2(4x + 8))\\4\times 2sec(4x + 8)\times \frac{d}{dx}(sec(4x + 8))\\8sec(4x + 8)sec(4x+8)cosec(4x+8)\times\frac{d}{dx}(4x + 8)\\32sec^2(4x + 8)cosec(4x +8)\)

h''(3) =

\(32sec^2(4\times 3+8)cosec(4\times 3+8)\\32sec^220cosec20\)

\(210.48\)

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Answer:

47.2 meters

Step-by-step explanation:

For a right triangle, the following relation holds

\(\tan \theta = \dfrac{Opposite\;side}{Adjacent\;side}\)

where opposite side is the leg opposite angle θ and adjacent side is the other leg adjacent to angle θ

We are given
θ₁ = 55.1°    angle of elevation to base of lighthouse

θ₂ = 56.5°  angle of elevation to top of lighthouse

Let x be the height of the base from sea level

Let y be the height of the top from sea level

Therefore x - y = height of the lighthouse from the top of the cliff

Given these we can come up with two equations

\(\tan(55.1^\circ) = \dfrac{x}{610} \cdots[1]\\\\\tan(56.5^\circ) = \dfrac{y}{610} \cdots[2]\\\)

From equation 1:
\(\tan(55.1^\circ) = \dfrac{x}{610} \\\\x = 610 \times \tan(55.1^\circ)\\\\\)

From equation 2
\(\tan(56.5^\circ) = \dfrac{y}{610} \\\\y = 610 \times \tan(56.5^\circ)\)

The height of the lighthouse is therefore x - y
x - y  \(x - y = 610 \times \tan56.5^\circ) - 610 \times \tan55.1^\circ \\\\= 610(\tan56.5^\circ - \tan55.1^\circ)\\\\= 47.1949\;7 meters\)

Therefore, rounded to the nearest tenth, the height of the lighthouse from the top of the cliff is 47.2 meters

Answer:

200

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(120^{2}\) + \(160^{2}\) = \(c^{2}\)

14400 + 25600 = \(c^{2}\)

40000 = \(c^{2}\)

\(\sqrt{40000}\) = \(\sqrt{c^{2} }\)

200 = c

Jesus love you.

Answer:

9.75 dollars

Step-by-step explanation:

13/4=3.25x3=9.75

Answer:

The answer is $9.75

Step-by-step explanation:

take $13 and divide by 4 to get the unit price, then you multiply by 3 to get what you want to know..

= $9.75

Answer:

Step-by-step explanation:

You want to write exponential functions through the given points.

The exponential function ...

  f(x) = a·b^x

will have the values ...

Using these relations we can write the function from the table values:

  f(x) = 10400·(2600/10400)^x

  f(x) = 10400·(1/4)^x

Then your table is ...

  \(\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}\)

Using the given points in the exponential function form, we have ...

   4.32 = a·b^1

   59.71968 = a·b^4

Dividing the second equation by the first, we find ...

  59.71968/4.32 = b^3   ⇒   b = 2.4

Using this in the first equation, we get ...

  4.32 = a·2.4   ⇒   a = 1.8

The equation of the function is ...

  g(x) = 1.8·2.4^x

The exponential function ...

  y = a·b^x . . . . . . a > 0, b > 0

will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.

Sarah's belief is incorrect.

Answer:

\(\textsf{1.} \quad f(x)=10400(0.25)^x\)

     (-1, 41600)  and  (3, 162.5)

\(\textsf{2.} \quad g(x)=1.8(2.4)^x\)

3.   Sarah is incorrect.

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}\)

The y-intercept is when x = 0.  

Therefore, from inspection of the given table, the y-intercept is 10400:

\(\implies a=10400\)

Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:

\(\implies 2600=10400b^1\)

\(\implies 2600=10400b\)

\(\implies b=\dfrac{2600}{10400}\)

\(\implies b=0.25\)

Therefore, the equation of the function is:

\(\boxed{f(x)=10400(0.25)^x}\)

Find the value of x when f(x) = 41600:

\(\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}\)

Find the value of f(x) when x = 3:

\(\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}\)

Therefore, the completed table is:

\(\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}\)

Given points:

Substitute the given points into the exponential formula g(x) = abˣ

\(\implies ab=4.32\)

\(\implies ab^4=59.71968\)

To find b, divide the equations:

\(\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}\)

\(\implies b^3=13.824\)

\(\implies b=\sqrt[3]{13.824}\)

\(\implies b=2.4\)

Substitute one of the points and the found value of b into the equation and solve for a:

\(\implies 2.4a=4.32\)

\(\implies a=\dfrac{4.32}{2.4}\)

\(\implies a=1.8\)

Therefore, the equation of the function is:

\(\boxed{g(x)=1.8(2.4)^x}\)

Sarah is incorrect.  For an exponential function in the form a · bˣ:

Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

\(x_1 = -4, x_2 = 5, x_3 = 12\)

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:

6

Step-by-step explanation:

We have y ∝ x which is another way of saying y varies directly with x

We can rewrite the direct proportion relation y ∝ x as y = k.x where k is a constant - the constant of proportionality

So y = kx or x = y/k

using y and x values know, we can solve for k and then solve for any x given y

We have

y = 37.4 =  k (17)

Therefore k = (37.4/17) = 2.2

To find x given y = 13.2, use the second equation
x = y/k = 13.2 / 2.2 =  6

From the given numbers, 2.6628, 4.17183 and √9 are the rational numbers.

Rational numbers are the numbers that are in the form of p/q where q is not equal to zero that is q≠0. Rational numbers can be expressed as a fraction where both numerators and denominator are whole. When these fractions are further divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal

Irrational numbers are numbers that cannot be written as simple fractions but can be written in decimal form. It has endless non-terminating digits after the decimal point.

Now according to the question ,

i) √3300 = 57.4456…. as it has endless non-terminating digits after the decimal point. It is an irrational number.

ii) 2.6628 is a rational number as it has a terminating decimal.

iii) 4.137183 is also a rational number as it has terminating decimal.

iv) √9 = 3 is a rational number as it is a perfect square and can be written as fraction.

v) 9.327925…. is a irrational as it has endless non-terminating digits after the decimal point.

Hence 2.6628, 4.17183 and √9 are the rational numbers.

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Answer:

I hope I am right or close

Step-by-step explanation:

I believe He would get an 32,000 commission!

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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Answer:

The expected value of lateness \(\frac{7}{20}\) hours.

Step-by-step explanation:

The probability distribution of lateness is as follows:

  Lateness             P (Lateness)

  On Time                     4/5

1 Hour Late                  1/10

2 Hours Late                1/20

3 Hours Late                1/20​

The formula of expected value of a random variable is:

\(E(X)=\sum x\cdot P(X=x)\)

Compute the expected value of lateness as follows:

\(E(X)=\sum x\cdot P(X=x)\)

         \(=(0\times \frac{4}{5})+(1\times \frac{1}{10})+(2\times \frac{1}{20})+(3\times \frac{1}{20})\\\\=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20}\\\\=\frac{2+2+3}{20}\\\\=\frac{7}{20}\)

Thus, the expected value of lateness \(\frac{7}{20}\) hours.

An expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment.

Expected value of lateness is  \(\frac{7}{20}\) hours.

Let us consider, P(x) is represent that probability of lateness and x represent number of hours late.

So, below a table is formed.

         x       0             1            2           3

      P(x)      4/5         1/10      1/20       1/20

From formula of expected value,

        E(x) = ∑ x P(x)

\(E(x)=(0*\frac{4}{5} )+(1*\frac{1}{10} )+(2*\frac{1}{20} )+(3*\frac{1}{20} )\\\\E(x)=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20} \\\\E(x)=\frac{7}{20}\)

So, expected value of lateness is 7/20 hours.

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The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of the line's general form is:

y = MX + c

Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).

Determine the line's slope:

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2-2) / (2+7 )

Slope= -4/9

The y-intercept is determined as follows:

y = MX + c

2 = -4/9x 2+c

c = -8/9

The lines' equation:

y = MX + c

y = -4/9x - 8/9

Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

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Answer:

m=0

Step-by-step explanation:

the slope is calculated using two points on the line and the formula

m = (y2 - y1) ÷ (x2 - x1)

where

x1 and y1 are the coordinates of point 1

x2 and y2 are the coordinates of point 2

for example, you can take

point 1 = (x1;y1) = (-2;3)

point 2 = (x2;y2) = (-1;3)

then your slope is

m = (3 - 3) ÷ (-1 - (-2)) = 0

notice that x1 is always at the left of x2 on the x axis

and it makes sense that your slope is 0 because for each x your y is the same

the inverse of F(x)=2x-4 is f^-1(x) = (x + 4) / 2.

In simple terms, the inverse function takes the output of the original function and gives you the original input back. So, if you input 2 into the original function, you get 6 as the output. If you input 6 into the inverse function, you get 2 as the output.

I hope this helps!

Answer:

f^-1(x)=( x + 4 ) / 2  

Step-by-step explanation:

by putting f(x) = y , we got the x in y i.e. x = (y+4)/2.

then replace y with x, we get the inverse of function f(x).

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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True, the diameter = twice the radius

Answer:

O (-4,1)

I hope I helped you^_^

Answer:

5.356

Step-by-step explanation:

You add everything in parentheses then subtract that by 0.08.

Answer:

x=3

Step-by-step explanation:

AB+BC>AC

2x + 3 + x + 1 > x + 10

we correct like terms

2x + x + 3 + 1> x+ 10

3x + 4> x + 10

3x - x > 10-4

2x > 6

divide both sides by 2

2x÷2 > 6÷2

x = 3

The trigonometry ratio values are tan(50) = 1.19 and cos(70) = 0.34

This can be calculated using a calculator

So, we have

tan(50) = 1.19 and cos(70) = 0.34

This can be calculated using a calculator

So, we have

sin(84) = 0.9945 and tan(75) = 3.7321

Here, we make use of the laws of cosines and sines

So, we have

cos(X) = 15/17 = 0.8824

sin(C) = 36/45 = 0.8

Here, we make use of the laws of tangents and sines

So, we have

tan(?) = 6/13 = 0.4615

? = 24.77

sin(?) = 41/59 = 0.6949

? = 44.01

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