Katrina buys a 66-ft roll of fencing to make a rectangular play area for her dogs. Use 2(l+w) = 66 to write a function. for the length, given the width. Graph the function. What is a reasonable domain for the situation? Explain. The function f(w) = gives the length as a function of the width. (Simplify your answer.)​

Answer:

A.  (x - 80)² = -320(y = 20)

B.  Focus:  (80, -60)

     Directrix:  y = 100

     Axis of symmetry:  x = 80

Step-by-step explanation:

If the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:

Standard form of a parabola with a vertical axis of symmetry:

[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute one of the x-intercepts and the vertex into the formula and solve for p:

[tex]\implies (0-80)^2=4p(0-20)[/tex]

[tex]\implies (-80)^2=4p(-20)[/tex]

[tex]\implies 6400=-80p[/tex]

[tex]\implies p=-80[/tex]

Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:

[tex]\implies (x-80)^2=4(-80)(y-20)[/tex]

[tex]\implies (x-80)^2=-320(y-20)[/tex]

Given:

[tex]\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}[/tex]

Answer:

  4

Step-by-step explanation:

You want the 8th term of the geometric sequence 512, 256, 128, ....

The formula for the n-th term of a geometric sequence is ...

  an = a1×r^(n-1)

where a1 is the first term (512), and r is the common ratio (1/2).

Then the 8th term is ...

  a8 = 512(1/2)^(8-1) = 512/128 = 4

The eighth term of the sequence is 4.

Answer:

340%

Step-by-step explanation:

119000/35000

Answer:

exterior angle = 139°

(I'm using "X" instead of "2")

to find the exterior angle, find the interior angle first and then use the straight line.

interior angle = 180° therefore,

75° + 64° + X = 180

139° + X = 180°

X = 180° - 139°

X = 41° (not the answer)

a straight line = 180°

X = 41°

Y - the exterior angle

41° + Y = 180°

Y = 180° + 41°

Y = 139°

hope this is clear :)

The number of division that will take place when the chocolate factory a machine takes a 1 kg block of chocolate is 100.

From the information, in the chocolate factory a machine takes a 1 kg block of chocolate and then divides it into rectangles each weight 10g.

It is important to note that:

1000 grams = 1 kilograms

Therefore, since the chocolate is divided into 10g, this will be:

= Total grams / 10 gram

= 1000g / 10g

= 100

Therefore, there will be 100 division.

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Complete question

In a chocolate factory a machine takes a 1 kg block of chocolate. It then divides it into rectangles each weight 10g. How many division will take place?

The points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.

What is a graph of a function?

A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f could also be defined as the graph of the equation y = f(x).

The given function is

                               [tex]f(x)=\frac{8-x}{x^2-7x+12}\\\\\[/tex]

Now we put f(x) = 3, we get

                             [tex]3=\frac{8-x}{x^2-7x+12}\\\\\\\3x^2-21x+36=8-x\\3x^2-20x+24=0\\[/tex]

Solving we get

                                x=5.09717

                                 x=1.5695

So the points on the graph of the given function at the value f(x)=3 would be x=5.0971 and x=1.5695.

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The dimensions of the rectangular paint of perimeter 104.09 inches are given as follows:

The perimeter of any polygon, including a rectangle, is given by the sum of all the lengths of the outer edges of the figure.

Hence, for a rectangle of height h and width w, the perimeter is given by twice the sum of these dimensions, hence it is given as follows:

P = 2(h + w).

In this problem, the perimeter has the value given as follows:

P = 104.09 inches.

Hence:

2(h + w) = 104.09

h + w = 104.09/2

h + w = 52.045 inches.

The painting is 5.72 inches taller than it is​ wide, hence:

h = 5.72 + w.

Then the height is obtained as follows:

5.72 + w + w = 52.045

2w = (52.045 - 5.72)

w = (52.045 - 5.72)/2

w = 23.16 inches.

Then the height of the rectangular painting is given as follows:

h = 5.72 + w = 5.72 + 23.16 = 28.88 inches.

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The preparation of a schedule of cash receipts for J. Lo's Clothiers covering the fourth quarter from October through December is as follows:

Fourth Quarter Cash Receipts        October    November   December

Month of sale (30%)                         $18,000       $16,500      $24,000

Following month (60%)                     42,000        36,000         33,000

Total cash receipts                         $60,000      $52,500      $57,000

A cash receipts schedule is a financial document that specifies how a business expects to collect cash from its credit sales customers based on the sales budget.

The cash collection formula can be established using the company's past collection patterns.

                     September

Credit Sales (actual) $ 70,000

Fourth Quarter                  October   November   December

Credit Sales                     $60,000     $55,000      $80,000

Cash Receipts:

Month of sale (30%)        $18,000       $16,500      $24,000

Following month (60%)    42,000        36,000         33,000

Total cash receipts        $60,000      $52,500      $57,000

Cash receipts in October = $60,000 ($60,000 x 30% + $70,000 x 60%)

Cash receipts in November = $52,500 ($55,000 x 30% + $60,000 x 60%)

Cash receipts in December = $57,000 ($80,000 x 30% + $55,000 x 60%)

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Considering the definition of a line, the equation of the line that passes through the point (-2, 1) and has a slope of 1/3 is y= 1/3x + 5/3.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Substituting the value of the slope m, you get:

y= 1/3x + b

Replacing the value of the point in previous expression, the value of the ordinate to the origin b can be obtained:

1= 1/3× (-2) + b

1= - 2/3 + b

1 + 2/3= b

5/3= b

Finally, the equation of the line is y= 1/3x + 5/3.

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Answer:

Coefficient is 7, variable is z

Step-by-step explanation:

Answer:

The average rate of change is: -4

Step-by-step explanation:

So to solve this we just need to plug our numbers into the formula. We are using the formula f(b) - f(a)b - a where “a” and “b” are our numbers. So we are given the intervals x=2 and x=5. When we see that we can rewrite it as (2,0) and (5,0). This is because when it is telling us just “x” we know “y” (the second number in the parentheses) is 0. So just plugging in the numbers we get: (-(5)2+3(5)+1)-(-(2)2+3(2)+1)(5 - 2). Solving it we get -4.

You have to multiply 3/8 by 9 and then you get your answer which is 3.375

Answer:

x = 1

Step-by-step explanation:

Given:

g(x) = 4x - 4

To Find:

x when g(x) = 0

[tex] \rm \implies 4x - 4 = 0 \\ \\ \rm \implies 4x - 4 + 4 = 0 + 4 \\ \\ \rm \implies 4x = 4 \\ \\ \rm \implies \cancel{\frac{4}{4}} x = \cancel{ \frac{4}{4} } \\ \\ \rm \implies x = 1[/tex]

Answer:

Step-by-step explanation:

They're both linear graphs, so they both follow the formula y = mx + b.

The y-intercept is when the graph crosses the y-intercept, so when x = 0.

First graph:

Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-3-(-1)}{-3-0} =\frac{-2}{-3} =\frac{2}{3}[/tex]

y-intercept(b): (0, -1)

Second graph:

Slope(m): [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-4-2}{-3-0} =\frac{-6}{-3} =2\\[/tex]

y-intercept(b): (0, 2)

Answer:

512

Step-by-step explanation:

A common multiple is defined as a whole number, a shared multiple of each set of numbers. The multiples common to two or more numbers are called the common multiples of those numbers.

OML I just gave u the answer do I need to put this in simple terms for you since u don't understand - 2 to the power of 3 x 3 is 512 and that is not a whole number a common multiple is defined as a whole number and for 512 to be an integer it has to be a whole number. UNDERSTAND NOW???

Answer:

option 4

Step-by-step explanation:

Use distributive property: a(b +c) = (a*b) + (a*c).

Multiply each term of (-x - 5) by (-3).

  -3( -x  - 5) = ( -3* -x) + (-3*-5)

                  = ( 3x ) + ( 15)

                  = 3x + 15

⇒Note I am going to solve them step by step for you to understand.

1.

[tex]3(x)+3(5)=3x+5\\3x+15=3x+5\\3x-3x=5-15\\no\\solution[/tex]

since 0≠-10

2.

[tex]-3(x)-3(-5)=-3x-15\\-3x+15=-3x-15\\-3x+3x=-15-15\\0\neq -30\\no\\solution[/tex]

3.

[tex]3(-x)+3(5)=8-x\\-3x+15=8-x\\\\-3x+x=8-15\\-2x=-7\\\frac{-2x}{-2} =\frac{-7}{-2} \\x=\frac{7}{2}[/tex]

4.

[tex]-3(-x)-3(-5)=3x+15\\3x+15=3x+15\\3x-3x=15-15\\0=0\\[/tex]

Note there is no certain value for x as any value you insert as x can make the whole equation true.

No solution is the answer for Q4

The number pattern for the missing numbers is 1,2,1,1,2,3,2,1,1,2,3,4,3,2,1,1,2,3,2,1,2,2

A pattern of numbers formed with a definite rule is called sequence

How to find a number pattern?

In every number patter, first term of this number pattern is 1; and the terms after the first term are obtained by adding, subtracting or multiply by 1 to the previous term.

1+1=2

2-1=1

1*1=1

1+1=2

2+1=3

3-1=2

2-1=1

1*1=1

.1*1=1

1*1=1

2+1=3

3+1=4

4-1=3

3-1=2

2-1=1

1*1=1

1+1=2

2+1=3

3-1=2

2-1=1

1+2=2

2*1=2

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We get the expression with the powers as

a) x⁻³.x⁵= x²

b) m⁻³:m⁶= m⁻⁹

c) a⁻⁷.a⁻²= a⁻⁹

d) (m⁻³)⁻²= m⁶

Given that,

We have to find the power of the expressions.

a) x⁻³.x⁵

Bases are equal so powers must be added.

x⁻³⁺⁵

x²

b) m⁻³:m⁶

It is in ratio that means

m⁻³/m⁶

We can take the m⁶ to numerator

m⁻³.m⁻⁶

Bases are equal so powers must be added.

m⁻³⁻⁶

m⁻⁹

c) a⁻⁷.a⁻²

Bases are equal so powers must be added.

a⁻⁷⁻²

a⁻⁹

d) (m⁻³)⁻²

Powers are multiplied

m⁶

Therefore, We get the expression with the powers as

a) x⁻³.x⁵= x²

b) m⁻³:m⁶= m⁻⁹

c) a⁻⁷.a⁻²= a⁻⁹

d) (m⁻³)⁻²= m⁶

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Answer:

Either 15 or -1 see below

Step-by-step explanation:

I am not sure if you menat n = 2 or n = -2

n= 2

4n + 7  Subtitute in 2 for n

4(2) + 7

8 + 7

15

n = -2

4n + 7y

4(-2) + 7

-8 + 7

-1

For the given graph , slope of the line is equal to  ( 1 / 2 ).

As given in the question,

Form the given graph,

Scale is given by,

On x-axis each unit of the graph represent 1 unit.

On y- axis each unit of the graph represent 1 unit.

Consider two coordinates from the line of the graph,

( x₁ , y₁ ) = ( 1, 2 )

( x₂ , y₂ ) = ( 3, 3 )

Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )

 Substitute the value in the formula of the slope we get,

Slope of the line = ( 3 - 2 ) / ( 3 - 1 )

⇒ Slope of the line = 1 / 2

Therefore, for the given graph , slope of the line is equal to  ( 1 / 2 ).

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Answer:

70

Step-by-step explanation:

8 - 1 = 7

7 x 10 = 70

He used 70 sheets.

Answer:

The slope is 4 and the equation is y = 4x + 18

Step-by-step explanation:

Okay, so you start by solving for the slope. The formula for slope is

m = y1-y2 over x1-x2 (it looks lke a fraction)

then you plug in your coordinates, so it becomes:

m = 7-3 over -4 - (-4) which then you get your slope as 4, but because it has to be perpendicular, the slope becomes -1/4. this is because the slope has to be the reciprocal and the opposite sign to be perpendicular.

Then, you can continue to create the equation by using point-slope form, which is y - y1 = m (x-x1)  (y1 and x1 are from the coordinates btw)

so the point-slope equation is:

y - 3 = -1/4 (x + 4)

y - 3 = -1/4x - 1

   +3            +3

y = -1/4x + 2 (this is your equation in slope - intercept form)

I hope this helps!!

Setting up a system of equation, the number of small boxes shipped is 13 and large box shipped is 6

System of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Let;

We can represent this using equations;

35x + 60y = 815 ...eq(i)

x = 7 + y ... eq(ii)

Solving equation (i) and (ii)

x = 13, y = 6

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Answer:

x = 3/2 and -4/3

Step-by-step explanation:

[tex] \rm \implies 6 {x}^{2} - x - 12 = 0 \\ \\ \rm \implies 6 {x}^{2} - 9x + 8x - 12 = 0 \\ \\ \rm \implies 3x(2x - 3) + 4(2x - 3) = 0 \\ \\ \rm \implies (2x - 3)(3x + 4) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: \: and \: \: 3x + 4 = 0 \\ \\ \rm \implies 2x = 3\: \: and \: \: 3x = - 4 \\ \\ \rm \implies x = \frac{3}{2} \: \: and \: \: x = - \frac{4}{3} [/tex]

The area of the semicircle is A = 1187.9 cm².

The area of a circle with a radius of r is A = πr².

Given that, the diameter of the semicircle is 55 cm.

The radius of the semicircle is,

r = 55/2

The area of a semicircle is given by,

A = (1/2)πr²

Substitute the values,

A = (1/2)π(55/2)²

A = 1187.9

Hence, the area of the semicircle is A = 1187.9 cm².

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As per the concept of system of linear equations, the maximum revenue of this basket ball match is $3.4

Linear equation:

Linear equation refers the one variable is an equation in which there is only one variable present. And it is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.

Given,

A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $10 the average attendance has been 28000. When the price dropped to $7, the average attendance rose to 33000. Assume that attendance is linearly related to ticket price.

Here we need to find the ticket price would maximize revenue.

In order to find the ticket price for the maximum revenue,

We have to identify the details from the given question,

Total seating capacity = 66,000

When ticket price $10 then the attendance 28,000

When ticket price $7 then the attendance 33,000

Let us consider the x be the maximum revenue ticket price.

Now, to solve this we have to find the slope for the equation,

That is,

=> m = (33000 - 28000)/(7 - 10)

=> m = 5000/-3

=>  m = -5000/3

=> m = 1666.6

Then the revenue equation is written as,

=> y = (10 - x) * (28,000 + 1666.6x)

=> y = 280000-11334x-1666.6x²

If we plot the this function into the graph, then we get the graph like the following.

Therefore, the solution of the graph is 3.4.

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Simple interest of $325 was accrued on a principal of $26,000.00 for a period of 0.25 years (13 weeks) at a rate of 5% per year, bringing the total amount due to $26,325.00 (principal plus interest).

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay additional interest on the interest that has already accrued.

Here,

A = $26,325.00

I = A - P = $325.00

A is equal to P(1 + rt).

The first step is to convert R percent to r a decimal, which is equal to R/100 = 5%/100 = 0.05 per year.

For ease, let's convert time to years: 13 weeks / 52 weeks / year = 0.25 years.

How to resolve our equation

A = 26000(1 + (0.05 × 0.25))  = $26,325.00

Simple interest accrued on a principal of $26,000.00 at a rate of 5% per year for 0.25 years (13 weeks) totaling $26,325.00 (principal plus interest).

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Answer:

S: {11}

Step-by-step explanation:

Hello!

Solve the inequality for n by isolating the variable.

The solution for n is all values less than 14, so 11 would work.

Answer:

========================

The difference between two consecutive integers is 1.

A) x + (x + 1) + (x + 2) = 42,

B) x + (x + 2) + (x + 4) = 42

C) (x minus 1) + x + (x + 1) = 42

D) (x minus 2) + x + (x + 2) = 42

E) x + 2 x + 3 x = 42

Answer:

x + (x + 1) + (x + 2) = 42

(x minus 1) + x + (x + 1) = 42

Step-by-step explanation:

Integer: A whole number that can be positive, negative, or zero.

Consecutive integer:  Integers that follow each other in order.

Let x be an integer.

Consecutive integers of x are one more or one less than each other in order.

This equation represents 3 consecutive integers as each value is one more than the previous value.

This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.

This equation represents 3 consecutive integers as each value is one more than the previous value.

This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.

This equation does not represent 3 consecutive integers as each value is x more than the previous value.