Mr. Rogers is designing the layout for a new floor of his office. His new layout will have 8 workstations in one row, with the side length of each workstation being 2 feet longer than the side length (s) of the workstations in the existing layout. He writes this expression to help him design the layout.

8(s + 2)

Which algebraic expression is equivalent to this expression?

A.
8s + 16
B.
8s + 2
C.
8s + 10
D.
s + 16

Answer:

1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant

2. The polynomial is easier to evaluate when it is written in Horner form:

 f(x) = ((x -4)x +1)x +6

To show that 2 is a zero, we want to find f(2):

 f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0

 f(2) = 0, so 2 is one of the zeros of this function

3.  Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...

 x = 2 (from above), x = 3, x = -1 (from our factorization)

4. In factored form, the polynomial can be written ...

 f(x) = (x +1)(x -2)(x -3)

The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).

The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.

There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.

\(\stackrel{\textit{\huge P~\hfill E~\hfill M~\hfill D~\hfill A~\hfill S}}{\cfrac{3.5(3.7-2.2)}{4(-1.75)}\implies \cfrac{3.5(1.5)}{4(-1.75)}\implies \cfrac{5.25}{4(-1.75)}\implies \cfrac{5.25}{-7}\implies -0.75}\)

sin(x+pi)=-sin(x)=sin(-x)=cos(pi/2)

cos (x+pi)=-cos(x)

So according to the question:

cos(pi/2 +x)=cos(x)

Using the solution of cos, obtain:

(pi/2) + x = 2pi +- (x)

case#1: (pi/2) + x = 2pi + (x)

But here, the value of x is canceled, just

case#2: (pi/2) + x = 2pi - (x)

answer------------>>>>>>>>> x=pi-pi/4

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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When the following code section runs, the value of the variable y will be -2.

Given that,

We have to find when the following code section runs, what value will the variable y have? Assume the following input values:

The code mentioned above is explained in the section below.

Here, x=5, n=0, and the input values are 1–6.

So, x>3 is true.

Control will go to second if block and input y and z.

Now y=1 and z=2 and n=1

Next control goes to if(x) since x>0 which is true.

Now z=3 and x=4 and y=0 and n=0

Her n==0 so r=z- ++x => 3- (5) =>-2.

Hence r=-2

Therefore, the variable r=-2 is the output for the code.

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Answer:

174

Step-by-step explanation:

thanks for the help guys

1) y = (5/2)√(3), x = 5/2, and 5, 2) y = 2i 3√(2), 4√3 and x = 2i√6 are radicals in simplest form.

In mathematics, an equation is a statement that shows that two expressions are equal to each other. An equation typically consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equals sign (=).

Equations are used to represent mathematical relationships and to solve problems in a variety of fields, including physics, engineering, economics, and finance. They can be linear or non-linear, and they may involve one or more variables.

Using the Pythagorean theorem in right triangle ABC, we have:

AC² = AB² + BC²

5² = y² + x²

x² = 25 - y²

Since angle BCA = 60 degrees, we know that:

tan(60) = y/x

√(3) = y/x

y = x√(3)

Substituting this into the equation x² = 25 - y², we get:

x² = 25 - 3x²

4x² = 25

x = √(25/4) = 5/2

And y = x√(3) = 5/2 ×√(3)

Therefore, AB = y = (5/2)√(3), BC = x = 5/2, and AC = 5.

Using the Pythagorean theorem in right triangle DEF, we have:

DF² = DE² + EF²

x² = y² + (4√3)²

x² = y² + 48

Since angle DEF = 60 degrees, we know that:

tan(60) = y/x

√(3) = y/x

y = x√(3)

Substituting this into the equation x² = y² + 48, we get:

x² = 3x² + 48

2x² = -48

x = √(-24) = 2i √(6)

And y = x √(3) = 2i√(18) = 2i 3√(2)

Therefore, DE = y = 2i 3√(2), EF = 4√3 and DF = x = 2i√6.

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Answer:

8^2+12x

Step-by-step explanation:

4x(2x+3)

=4x times 2x+4x times 3

=4 times 2xx+4 times 3x

Answer:

8x^2 +12x

Step-by-step explanation:

Step 1) Multiply each term in the parentheses by 4x

4xx2x+4xx3

Step 2) Calcuate the product

8x^2 +12x

Answer: 211,500

Step-by-step explanation:

Just took the quiz

The equation of the parabola is\((y + 6)^2 = 4(x - 13)\), where the vertex is (13, -6) and the distance between the directrix and focus is 14.

To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).

We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.

We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.

Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.

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Answer:

-2/3

Step-by-step explanation:

The range is virtually the answer to the question,

"In which interval can find all y-values of the function".

So you look at the y-axis and see that your function begins with \(y=-5\) (including -5 because of the dot on the graph) and ends at including \(y=-1\).

So the interval notation is,

\(y\in[-5,-1]\)

But you are asked to specify the set notation of the interval, to do so first rewrite the interval using inequality operators, say we find some y in between (and including) -5 and -1,

\(-5\leq y\leq-1\)

To specify that this is a set use curly bracelets and a bar,

\(\{y\mid-5\leq y\leq-1\}\).

The y before bar is a step function and everything followed after the vertical bar is the range of the step function.

Hope this helps.

Using it's concept, it is found that the range of f(x) is given by:

{y|-5 <= -y <= -1}

The range of a function is the set that contains all possible output values. In a graph, it is given by the values of y, that is, the values of the vertical axis.

In the function described by this graph, the vertical axis assumes values between -1 and -5, inclusive, hence the range is given by:

{y|-5 <= -y <= -1}

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Answer: 8/30

Because I left the sink on ran away and left the room

On Wednesday, there is a higher (0.7395) likelihood that both managers will be accessible than on Monday (0.7216).

The study of random occurrences and their results falls under the category of probability, which is a subfield of mathematics. A number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty, is used to express the likelihood of an event happening. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. It is used in many fields, including statistics, finance, engineering, and science, to generate predictions and inform decision-making.

given

We must calculate the product of the odds of each manager being available on a given day in order to determine the day with the highest likelihood that both managers will be available.

The likelihood that both managers will be accessible on Monday is 0.82 x 0.88, or 0.7216.

The likelihood that both managers will be accessible on Wednesday is 0.87 x 0.85 = 0.7395.

Therefore, the solution is option C: Wednesday. On Wednesday, there is a higher (0.7395) likelihood that both managers will be accessible than on Monday (0.7216).

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The total measure of all the angles in a triangle is 180°.

Since there is already a 90° angle, the other 2 angles must also add up to 90°.

The only answer that fits is x = 9.

Check:

9x7 = 63°

3x9 = 27°

Add up = 90°

:)

C (x=18)

is your answer

A statement that you believe to be true but have not proved to be true is called a conjecture.

Hence, Option C is the correct answer.

Answer:

6

Step-by-step explanation:

b+4=10

  -4 .-4

b=6

Answer:

b= 6

Step-by-step explanation:

subtract the answer (10) by the remaining 4, (so 10-4) which equals 6

Answer:  The second description is correct for the absolute value of x

Main details: Horizontal line from 0 to the dot 6 ticks to the left, and 6 written above the line

Step-by-step explanation: breaking it down:

A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. The first part is the same in all of the descriptions

A dot is shown on a point at 6 tick marks to the left of 0. This represents -6 on the number line.

Above the number line, a bracket is shown extending from a point at 6 tick marks to the left of zero to 0. This shows the distance between 0 and -6. Important. Absolute value is the distance between two numbers

A horizontal line is shown between the brackets, This is the measuring line 6 units long.

and 6 is written on the line. Important. It is a plain number, no negative or positive! Absolute value is just that.

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

Answer:

The area of the quarter circle = 346.19 miles²

Step-by-step explanation:

If the perimeter of a quarter circle = 74.97 miles

r + r + 1/4 * 2pi*r = 74.97 miles

2r + 1/2r * pi = 74.97

Multiply left and right of the = sign by 2 gives...

2 * ( 2r + 1/2 * r * pi ) = 74.97 * 2

( 4r + 2/2* r * pi ) = 149.94

r * ( 4 + 3.14 ) = 149.94

r * ( 7.14 ) = 149.94

7.14 * r = 149.94

Divide left and right of the equal sign by 7.14

7.14 / 7.14 * r = 149.94 / 7.14

r = 149.94 / 7.14

r = 21 miles

Area full circle = r² * pi

21² * pi

441 * pi

We need to calculate a quarter part of the area of the full circle, so

1/4 * 441 * pi

110.25 * pi

110.25 * 3.14

= 346.185, which rounded to the hundreth gives.

The area of the quarter circle = 346.19 miles²

Answer: 346.19 miles²

Step-by-step explanation:

Perimeter (P) of the quarter circle is the curve + both sides.

Perimeter of the curve

\(\dfrac{1}{4}C=\dfrac{1}{4}2\pi\cdot r\\\\\\.\quad =\dfrac{\pi \cdot r}{2}\)

Perimeter of the sides

2 sides = 2r

Perimeter = curve + both sides

\(74.97=\dfrac{\pi \cdot r}{2}+2r\\\\\\2(74.97)=\pi \cdot r+2(2r)\\\\\\149.94=\pi r+4r\\\\\\149.94=r(\pi +4)\\\\\\\dfrac{149.94}{\pi +4}=r\\\)

Find the Area

\(\dfrac{1}{4}A=\dfrac{1}{4}\pi\bigg(\dfrac{149.94}{\pi+4}\bigg)^2\\\\\\.\quad =\dfrac{1}{4}3.14\bigg(\dfrac{149.94}{3.14+4}\bigg)^2\\\\\\.\quad =\dfrac{1}{4}3.14(21)^2\\\\\\.\quad =\large\boxed{346.185}\)

Answer:

3c-6

Step-by-step explanation:

One day is c-2 so we need to multiply by 3. We get 3(c-2) or 3c-6.

Tip: use the variables/numbers in the problem to form an equation. Then, simplify.

Answer:

the total surface area of the prism is 374.8 cm^2.

Step-by-step explanation:

Since the cross-section is an equilateral triangle of side 6 cm, the area of the triangle is:

A = 1/2 * base * height = 1/2 * 6 cm * 5.2 cm = 15.6 cm^2

where 5.2 cm is the height of the equilateral triangle.

The total surface area of the prism consists of the area of the two equilateral triangles and the area of the three rectangular faces. The area of each rectangular face is the product of its length and width.

The length of the prism is 20 cm and the width of each rectangular face is 6 cm, so the area of each rectangular face is:

A_rect = length * width = 20 cm * 6 cm = 120 cm^2

Therefore, the total surface area of the prism is:

A_total = 2 * A_tri + 3 * A_rect

= 2 * 15.6 cm^2 + 3 * 120 cm^2

= 374.8 cm^2

Hence, the total surface area of the prism is 374.8 cm^2.

The measure of the largest exterior angle of the polygon in discuss is; 100°.

It follows from the task content that the measure of the largest exterior angle of the polygon be determined.

Since the sum of all exterior angles of a polygon is equal to 360°;

x° + 4x° + 5x° + 7x° + 9x° + 10x° = 360°

36x° = 360°

x = 10

Therefore, it follows that the measure of the largest exterior angle is; 10x° = 10(10)° = 100°.

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Question asked:Jacob and Sarah are saving money to go on a trip. They need at least $1975 in order to go. Jacob mows lawns and Sarah walks dogs to raise money. Jacob charges $25 each time he mows a lawn and Sarah charges $15 each time she walks a dog. The number of dog walks that Sarah has scheduled is no more than four times the number of lawns Jacob has scheduled to mow. Sarah will walk at least 50 dogs.Write a set of constraints to model the problem, with x representing the number of lawns mowed and y representing the number of dogs walked.

My answer:

They need at least $1975. Jacob charges $25 each time he mows a lawn and Sarah charges $15 each time she walks a dog.

25x + 15y ≥ 1975

The number of dog walks that Sarah has scheduled is no more than four times the number of lawns Jacob has scheduled to mow.

y ≤ 4x

Sarah will walk at least 50 dogs.

y ≥ 50

Answer:

k > −7

Step-by-step explanation:

1 Subtract 6k6k from both sides.

9k+3-6k>-189k+3−6k>−18

2 Simplify  9k+3-6k9k+3−6k  to  3k+33k+3.

3k+3>-183k+3>−18

3 Subtract 33 from both sides.

3k>-18-33k>−18−3

4 Simplify  -18-3−18−3  to  -21−21.

3k>-213k>−21

5 Divide both sides by 33.

k>-21/3

6 Simplity 21/3 to 7.

k>-7

Hope This Helps.

Answer:

k > -7

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    9*k+3-(6*k-18)>0  

Step by step solution :

STEP  1:

Pulling out like terms

1.1     Pull out like factors :

  3k + 21  =   3 • (k + 7)  

Equation at the end of step  1:

STEP 2:

2.1    Divide both sides by  3  

Solve Basic Inequality :

2.2      Subtract  7  from both sides

           k > -7

Inequality Plot :

2.3      Inequality plot for

        3.000 X  + 21.000  >  0

One solution was Made :

k > -7

HOPE THIS HELPS!

PLEASE MARK BRAINLIEST IF THIS HELPED YOU LEARN! :)

Answer:

59,475,643

Step-by-step explanation:

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

The answer is 2.1 m squared

Answer:

The salesperson's commission for this month is: $4116.75

Step-by-step explanation:

Given

Current month's paid invoice's total = $49,900

Commission =  8.25% = 0.0825

To determine

What is the salesperson's  commission for this month?

The salesperson's  commission for this month can be determined by multiplying the invoice's total i.e. $49,900 with the commission percentage of 0.0825.

Thus,

Commission amount =  49,900 × 8.25%

                                  =  49,900 × 0.0825           ∵  8.25% = 0.0825  

                                  = $4116.75

Therefore, the salesperson's commission for this month is: $4116.75