The Shredder, Inc. produces two types of paper shredders, home and office. The office model requires 6 hours to assembly and 2 finishing work units for finishing work, the home model requires 4 hours to assemble and 12 finishing work units for finishing. The maximum number of assembly hours available is 96 per day, and the maximum number of finishing hours available is 96 per day.

Let
x = the number of office model shredders produced per day and
y = the number of home model shredders produced per day.

Write the system of inequalities that represents the maximum number of shredders that can be produced in one day.

NOTE: 4 inequalities are expected.

It should be noted that the information regarding the transformation illustrates that Elena is wrong.

A point, line, or geometric figure can be transformed in a way that affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

It should be noted that the first step makes the figures be the same by size but the second step, reflection over line AE doesn't map them together.

In this case, the correct line of reflection would be a vertical line through point D.

Therefore, it should be noted that the information regarding the transformation illustrates that Elena is wrong.

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Elena gives the following sequence of transformations to show that the two figures are similar by

transforming ABCD into EFGD.

1. Dilate using center D and scale factor 2.

2. Reflect using the line AE.

Answer:

-1 6/10

is greater than

- 5/3

Step-by-step explanation:

The given statement is true.

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

(x + 2)² + (y - 2)² = 3²

Step-by-step explanation:

Equation of a circle is (x - a)² + (y - b)² = r²,

where a is the x-coordinate of the centre of the circle, b is the y-coordinate of the centre of the circle, r is the circle's radius.

So, we have (x - -2)² + (y - 2)² = 3²

subtract a minus means we add.

(x + 2)² + (y - 2)² = 3²

The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.

As per the given question, the required solution would be as:

g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.

The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.

This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.

The slope and the shape of the function will remain the same.

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The value of x is 24 and different angles of hexagon will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

An angle is a geometric shape that is defined as the amount of rotation that occurs between two straight lines or planes. Angles are measured in degrees, with 360° representing a full circle.

We need to apply the inverse tangent function to determine the angle at which the sun strikes the flagpole. We are aware that the triangle's adjacent side is 42 feet long and its opposite side is 25 feet tall (the height of the flagpole) (the length of the shadow).

Given the figure is hexagon,

the sum of angles of a hexagon is 720,

Upon adding the given angles,

mA = (7x-8)°

mB (4x+46)°

mC = (5x)

mD = (6x+12)°

mE = (x+7)°

mF = (5x-9)°

⇒ 7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720

⇒ 28x + 48 = 720

⇒ 28x = 672

⇒ x = 24

Therefore, the angles will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

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Answer:

E

Step-by-step explanation:

A linear equation is in the form of: \(y=mx+b\), where m is the slope and b is the y-intercept.

m is the slope and it's given, which is -6

b is the y-intercept and it's given, which is 9

When we plug in to the form we get:

\(y=-6x+9\)

Answer:

Step-by-step explanation:

whitch answer how do you want us to answer

Answer:

\(Height=\boxed{10\sqrt{2}} \)

\( Area =\boxed{165\sqrt{2}} \)

Step-by-step explanation:

By geometric mean theorem:

\( AC=\sqrt{25\times 8}\)

\( AC=\sqrt{5^2 \times 2^2 \times 2}\)

\( AC=5\times 2\sqrt{2}\)

\( AC=10\sqrt{2}\)

So,

\(Height=\boxed{10\sqrt{2}} \)

\( Area = \frac{1}{2} \times base\times height \)

\( \therefore Area = \frac{1}{2} \times (25+8)\times 10\sqrt{2} \)

\( \therefore Area =33\times 5\sqrt{2} \)

\( Area =\boxed{165\sqrt{2}} \)

Answer:

6 days

Step-by-step explanation:

1 L = 1000 mL

3 days = 1500 mL = 1.5 L

9 L divided by 1.5 L = 6 days

Answer: one solution I believe

Step-by-step explanation: I got 21 as my answer and that is one solution

Answer:

Step-by-step explanation:

(6)² = 5(6) + 6

36 = 30 + 6

36 = 36

The Total Probability of getting exactly two 3s in two throws is 1/36

What is Probability?

A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Solution:

Probability of Obtaining 3 in the first throw = 1/6

Since, the number of possible outcome is 11 and total outcomes are 6

Similarly the probability of getting 3 in the second throw is 1/6

Therefore, total probability = 1/6 * 1/6 = 1/36

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Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

The maximum flow for this traffic stream (vmax) is -81.95 mi/h indicating that Greenberg's model is not an accurate representation.

Greenberg's model for traffic flow is given by:

\(Q = vmaxD(1 - \frac {D}{Dj})^4)\)

where Q is the flow rate (number of vehicles per hour), D is the density (number of vehicles per mile), Dj is the jam density (number of vehicles per mile), and vmax is the maximum velocity (miles per hour).

We are given Dj = 130 veh/mi and D = 30 veh/mi when S = 30 mi/h. We can use this information to solve for vmax.

First, we need to convert the units of Dj and D to be consistent with the units of vmax. We know that:

v = S = D/t

where v is the velocity (miles per hour) and t is the time (hours). Therefore:

Dj = 130 veh/mi = 130v veh/(St) = 130v/(30t)

D = 30 veh/mi = 30v veh/(St) = 30v/(30t)

Now we can substitute these values into Greenberg's model and solve for vmax:

\(Q = vmaxD(1 - \frac {D}{Dj})^4)\)

\(Q = vmax\times(\dfrac{30v}{30t})(1 - (\dfrac{30v}{30t})/(\dfrac{130v}{30t}))^4)\)

\(Q = vmax(30v/(30t))\times(1 - (v/130)^4)\)

To find vmax, we need to find the value of v that maximizes Q. We can do this by taking the derivative of Q with respect to v and setting it equal to zero:

dQ/dv = 0

\(d/dv (vmax\times\dfrac{30v}{30t})(1 - (\dfrac{v}{130})^4)) = 0\)

\(vmax(\dfrac{30}{30t})(1 - 4\times(\frac{v}{130})^3\times(-1/130)) = 0\)

\(vmax\times(1 + 4(\dfrac{v}{130})^3) = 0\)

This equation has two solutions: vmax = 0 or (v/130)^3 = -1/4. Since vmax must be positive, the only valid solution is:

\((\dfrac{v}{130})^3 = -\frac{1}{4}\)

\(v = -( \frac{130}{2})^{(1/3)}\)

v ≈ -81.95 mi/h

This negative velocity doesn't make sense in the context of traffic flow, so we can conclude that the maximum flow for this traffic stream does not exist. This might indicate that Greenberg's model is not an accurate representation of the actual traffic flow on this roadway.

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Answer:

x = 4

Step-by-step explanation:

ΔAED  ~ ΔACB

[∠DAE = ∠BAC ( common angle ), \(\frac{AE}{AC} = \frac{AD}{AB}\) ( gives a ratio 1:2 ) ]

\(\frac{AE}{AC} = \frac{DE}{BC}\)

Since AC = 2AE  [ AC = AE + EC, But AE = EC, ∴ AC = AE + AE ]

 \(\frac{AE}{2AE} = \frac{x + 1}{4x - 6}\\\\\frac{1}{2} = \frac{x + 1}{4x - 6}\\\\\\Cross - multiplying,\\\\4x - 6 = 2 *(x + 1)\\4x - 6 = 2x + 2\\4x - 2x = 2 + 6\\2x = 8\\x = 4\)

Answer:

25%

Step-by-step explanation:

i think it is

i am sorry if wrong

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Answer:

12 girls

Step-by-step explanation:

30*(2/5)=12

Answer:

13 divided by x + 2.

Step-by-step explanation:

\(\dfrac{5 \sin 87^{\circ} + \tan 72^{\circ} - \sec 5^{\circ}}{\cot 18^{\circ}-\csc 85^{\circ}+5\cos 3^{\circ}}\\\\\\=\dfrac{5\sin\left(90^{\circ}-3^{\circ} \right) + \tan\left(90^{\circ}-18^{\circ} \right)-\sec\left(90^{\circ}-85^{\circ} \right)}{\cot 18^{\circ}-\csc 85^{\circ}+5\cos 3^{\circ}}\\\\\\=\dfrac{5\cos 3^{\circ} + \cot 18^{\circ}-\csc 85^{\circ}}{\cot 18^{\circ}-\csc 85^{\circ}+5\cos 3^{\circ}}\\\\\\=1\)

Answer:

False

Step-by-step explanation:

The probability that they both get a red apple is, 15/28

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The probability of Ed's friend grabbing a red apple is,

= 6 red apples / (2 green apples + 6 red apples)

= 6/8

= 3/4.

Then, the probability of Ed grabbing a red apple from the remaining apples is,

= 5 red apples / (2 green apples + 5 red apples)

= 5/7.

So, the probability that both Ed and his friend get a red apple is,

= 3/4 x 5/7

= 15/28

Hence, the probability is 15/28

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The coordinate of B'  after the sequence of transformations is B' = (-6, 2)

From the question, we have the following parameters that can be used in our computation:

B = (-1, 1)

The sequence of transformations is given as

When applied, we have

Translate (‒5, ‒3)

B = (-1 - 5, 1 - 3)

B = (-6, -2)

Reflect over the x-axis

B' = (-6, 2)

Hence, the image is B' = (-6, 2)

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The number expression that represents the number line is 2 + (-5) = -3 option (D) 2 + (-5) = -3 is correct.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

The number line shown in the picture.

We can frame a number expression using the number line:

2 - (-3) = 5

2 - 5 = -3

2 + (-5) = -3

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It begins at 2 and moves backward 5 before ending at -3.

Thus, the number expression that represents the number line is 2 + (-5) = -3 option (D) 2 + (-5) = -3 is correct.

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Answer:

Coordinates A and B: (1, 0) and (3, 0)

Coordinates of P: (0, 3)

Coordinates of Q: (2, -1)

Step-by-step explanation:

You're pretty much given the x-intercepts from the original equation.

y = (x - 1)(x - 3). So to get the x-intercepts (points A and B), y has to equal 0. So,

0 = (x - 1)(x - 3).

and y = 0 when x equals 1 and 3. Because anything multiplied by 0 equals 0. So substituting 1 for the value of x, for example, we get:

0 = (1 - 1)(1 - 3)

0 = 0 * (-2)

So there are your x-intercepts, points A and B.

Now,

Expand the brackets of the equation.

y = (x - 1)(x - 3) becomes

y = x^2  -  4x  + 3

You get the y-intercept (point P) by substituting 0 for the value of x. Doing so gives:

y = 0^2 - 4*0 + 3

y = 0 - 0 + 3

y = 3

So, we have our y-intercept (0, 3).

Point Q, the x-coordinate of the vertex is calculated with the equation -b/2a

Taking our expanded equation: x^2 - 4x + 3

which is of the form ax^2 + bx + c

So we find the values of a, b and c and input the values into the equation

a = 1

b = -4

c = 3

So, inputting these into the vertex equation, gives:

-(-4) / 2 * 1

4 / 2

2

So we have the x-coordinate of the vertex. Now that we know that, we can just substitute it into the expanded equation to give the y-coordinate:

y = 2^2 - 4*2 + 3

y = 4 - 8 + 3

y = -1

So there's our y-coordinate, and now we have both the x and y coordinate for the vertex, point Q. (2, -1).

Using a system of equations, for Madelyn to add a certain number of charms to her bracelet, where the cost will be the same at either jewelry shop, the number of chams would be 5.

When two or more equations are solved concurrently, they are described as a system of equations.

Another description of a system of equations is simultaneous equations.

                                       Oxford Fine    Espinoza

Unit cost per charm              $12                 $14

The cost of the bracelet      $40                $30

Let the number of charms = c

Equation 1: (Costs at Oxford Fine) 12c + 40

Equation 2: (Costs at Espinoza) 14c + 30

For the cost to be the same at either jewelry shop, Equation 1 must equal Equation 2:

12c + 40 = 14c + 30

-2c = -10

c = 5

Check:

12c + 40

12(5) + 40 = $100

14c + 30

14(5) + 30 = $100

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