Berti is the Shape Factory's top employee. She has received awards every month for having the top sales
figures so far for the year. If she stays on top, she will receive a $5000 bonus for excellence. She currently has
sold 16, 250 shapes and continues to sell 340 per month.
EMPL
Since there are eight months left in the sales year, Sarita is working hard to catch up. While she has only sold
8,830 shapes, she is working overtime and on weekends so that she can sell 1, 082 per month. Will Sarita
catch up with Berti before the end of the sales year? If so, when?

The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

Given,

We have to expand the given polynomials and simplify them.

1. The polynomial: (a² - 3a)²

Here,

The polynomial is in the form of (a - b)²

So,

(a - b)² = a² - 2ab + b²

Then,

(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²

(a² - 3a)² = a⁴ - 6a³ + 9a²

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.

a = 1, b = -6 and c = 9

[tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex] = [tex]\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}[/tex] = [tex]\frac{6(+-)\sqrt{36 - 36} }{2}[/tex] = [tex]\frac{6(+-)\sqrt{0} }{2}[/tex] = (6±0) / 2

= 6/2 = 3

Then,

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) = 3

So,

(a² - 3a)² = 3a²

2. The polynomial: (1/2x³ + 6x)²

Here, the polynomial is in the form (a + b)²

(a + b)² = a² + 2ab + b²

Here,

(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²

(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

a = 1/4, b = 6 and c = 36

Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex]

= [tex]\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}[/tex] = [tex]\frac{-6(+-)\sqrt{36-36} }{1/2}[/tex] = (-6±0) / (1/2) = -6 × 2 = -12

Therefore,

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

Here,

(1/4x⁴ + 6x² + 36) = -12

Then,

(1/2x³ + 6x)² = -12x²

That is,

The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

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Using the relation between velocity, distance and time, it is found that:

a. The equation used to find the distance of the flowerbed from the​ hive is: d = 540 feet per minute x 1.6 minutes.

b. The distance of the flower bed from the hive is: 864 feet.

Velocity is given by the distance divided by the time, as follows:

v = d/t

In the context of this problem, we have that:

The times are as follows:

The sum of this times is of 22 - 18 = 4 minutes, hence:

[tex]t_1 + t_2 = 4[/tex]

During the first step, that is, from hive to flowerbed, the velocity is 1.5 times greater than during the second step, thus the second time is 1.5 times the first time, that is:

[tex]t_2 = 1.5t_1[/tex]

Then the first time is calculated as follows:

[tex]1.5t_1 + t_1 = 4[/tex]

[tex]2.5t_1 = 4[/tex]

[tex]t_1 = \frac{4}{2.5}[/tex]

[tex]t_1 = 1.6[/tex]

The velocity during this time was of 9 feet per second = 540 feet per minute, for 1.6 minutes, hence the equation is:

d = v x t

d = 540 feet per minute x 1.6 minutes.

d = 864 feet.

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Vertical angles are : 1 and 6

supplementary angles : 1 and 2

linear pair : angle 4 and 8

adjacent angles: 21 and 22

A supplementary angle is an angle that, when added to another angle, results in a total angle measure of 180 degrees. In other words, if two angles are supplementary, the sum of their angle measures will be equal to 180 degrees.

For example, if angle A measures 100 degrees, its supplementary angle B would measure 80 degrees, since 100 + 80 = 180. Conversely, if angle B measures 120 degrees, its supplementary angle A would measure 60 degrees, since 120 + 60 = 180.

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A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate

31.4π units

10π units

31.4 units ​

we know that

the circumference of a circle is equal to

we have

pi=3.14

r=5 units

substitute

the exact value is 10pi units

the approximate value (assume pi=3.14)

C=31.4 units

so

order from most accurate to least accurate is

10π units

31.4 units

31.4π units

Answer: The perimeter of the triangle is 69 cm.

Step-by-step explanation:

Let us consider the side of the triangle be 3x ,4x and 5x.

According to the question,

The longest side of the triangle be 30 cm.

. 5x=30cm

x=6 cm

So the side of the triangle are 18cm ,24 cm and 30 cm.

The perimeter of the triangle is the sum of sides of the triangle.

so perimeter is =15+24+30=69 cm



The algebraic expression is equivalent to the expression below is 36x+110

According to the Distributive Law, multiplying a number by a collection of numbers is equivalent to performing each multiplication independently.

For instance, given the standard expression C(D + E). Using the distributive law;

C(D + E) = CD + DE

Using this rule to the given expression shown below;

11(4x + 10) - 8x

Apply the distributive property;

11(4x + 10) - 8x

11(4x) + 11(10) - 8x

44x + 110 - 8x

Collect the like terms

44x + 110 - 8x

44x-8x+110

36x+110

This gives the resulting equation of the linear function after expansion

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Answer:

It would be MOP is adjacent

Step-by-step explanation:

Part A

Explanation: Count the number of leaves.

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

Part B

Reason:

Look at the largest stem (9) and the largest leaf of this largest stem (5).

This forms the largest value of 95.

The smallest value is 41 since it corresponds to the smallest stem and smallest leaf.

The term "min" and "max" are often used here.

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

Part C

Explanation:

The data set is

41, 52, 57, 58, 65, 66, 70, 75, 78, 80, 81, 95

There are n = 12 items in this set.

Splitting in half gets us n/2 = 12/2 = 6.

The item in slot 6 is 66, and the next item over is 70.

The midpoint of these values is the median. (66+70)/2 = 68.

This midpoint rule only applies if n is even.

To find the range, we subtract the largest and smallest items.

range = max - min = 95 - 41 = 54

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

Part D

Reason:

The stem 8 doesn't have a leaf of 5 attached to it.

It only has the leaves 0 and 1 to form the numbers 80 and 81.

Answer:

A = {KL}

Step-by-step explanation:

The subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}

It is a branch of mathematics that deals with the occurrence of a random event.

The sample space of this experiment consists of all possible ways of choosing two names from a group of three.

Since the order in which the names are chosen does not matter, the size of the sample space is given by the number of combinations of 3 things taken 2 at a time, which is 3.

The three possible outcomes are: {JK, JL, KL}.

If we want to find the complement of the event in which Joe plays in the first match, we need to find the outcomes in which Joe does not play in the first match.

There are two such outcomes: JL and KL.

Therefore, the subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}

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The expression -3.1^4x * -3.1^2x + 7 has an equivalent of 887.503681x^2 + 7

From the question, the expression is given as

-3.1^4x * -3.1^2x + 7

Evaluate the exponents in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 92.3521x * 9.61x + 7

Evaluate the products in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 887.503681x^2 + 7

Hence, the equivalent expression of -3.1^4x * -3.1^2x + 7 is 887.503681x^2 + 7

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When QP bisects DQL, then the angles DQP and angle PQL is 23°.

Given that,

In the picture we can see the diagram,

The QL  line is there and the QD line.

QP line bisect the angles DQL

The angle DQP is 5x-7

The angle PQL is 11+2x

We have to find the x value and the angles DQP and PQL.

We know,

From the bisection we can say the angle are equal to each other

The angle DQP=The angle PQL

5x-7=11+2x

5x-2x=11+7

3x=18

x=18/3

x=6

Substitute x value in angles DQP and angle PQL.

The angle DQP=5x-7=5(6)-7=30-7=23°

The angle PQL=11+2x=11+2(6)=11+12=23°.

Therefore, the angles DQP and angle PQL is 23°.

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Answer: $29.10

Step-by-step explanation:

1. Make a table, like the one shown in the image. You will need the item, its price, and how many are being bought.

2. Multiply the price and quantity of each item that is being bought.

3. Add all of the products together. This should get you the final price.

My steps are in the image. Hope this helps!

We are given the following absolute value equation

Let us solve the problem then we will compare it with the given solution.

Now we will solve for the positive and negative sign separately

Comparing it with the given solution, there is an error on the left-hand side step 2. (the sign of 38 should be positive but in the figure, it is shown negative)

Now let us substitute the obtained x values into the original absolute value equation and check if they satisfy the equation.

For x = -4:

Hence, x = -4 is a valid solution.

For x = -38:

Hence, x = -38 is not a valid solution.

The above is an example of an extraneous solution.

An extraneous solution is a solution that we get during the process of solving an equation but it is not really the solution meaning that it does not satisfy the equation!

Therefore, x = -4 is the only solution to the given equation.

The function f(x) = 600(0.75)^x. is a decay function by 25%

The equation of the function is given as

f(x) = 600(0.75)^x.

The above function is an exponential function

An exponential function is represented as

y = ab^x

When f(x) = 600(0.75)^x. and y = ab^x are compared, we have

b = 0.75

The value of b in this case is the factor

Also if b is less than 1, then the function is a decay function

0.75 is less than 1

So, the function represents a decay function

The decal percentage is then calculated as

Decay = 1 - b

So, we have

Decay = 1 - 0.75

Evaluate

Decay = 25%

Hence, the function is a decay function

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The 'x' and 'y' variables are highlighted in the box

Answer:

x = 7

y = 15

Step-by-step explanation:

Disclosure:  After I had completed my answer, I found that Answerwell had already posted a solution.  It is more straightforward than my approach.  While the answers are the same, I'm still adding mine because 1) I worked hard on it, and 2) it illustrates there can be different ways of reaching a solution.

See attached worksheet.

Answer:

the length of AB is 9

Step-by-step explanation:

an isosceles triangle is a type of triangle i which two of its sides are equivalent(equal). let AB=AC=x

perimeter=22

                  perimeter=AB+AC+BC

                                22=x+x+4

                                 22-4=2x

                                      18/2=2x/2

                                           9=x

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

Explanation:

A hand of two pairs is when we have 2 cards of the same value, and another 2 of the same value, then the fifth card is something else entirely.

An example hand is:

-------------

We use the nCr formula since order doesn't matter.

C(n,r) = (n!)/(r!*(n-r)!)

For any suit, there are n = 13 cards. We make r = 2 selections for each of the two pair.

C(n,r) = (n!)/(r!(n-r)!)

C(13,2) = (13!)/(2!*(13-2)!)

C(13,2) = (13!)/(2!*11!)

C(13,2) = (13*12*11!)/(2!*11!)

C(13,2) = (13*12)/(2!)

C(13,2) = (13*12)/(2*1)

C(13,2) = (156)/(2)

C(13,2) = 78

There are 78 ways to select which two ranks will be chosen to represent each of the two pair.

Let's say one of the ranks of the two pair is a king. There are n = 4 kings and we select r = 2 of them. That gives C(4,2) = 6 ways to select those two kings. We'll also have 6 ways to select the other two cards in the other pair.

Therefore, we have 78*6*6 = 2808 ways to pick the first four cards that consist of the two pair (eg: 2 kings and 2 queens).

-----------------

So far we've considered just the two pairs. We have one card left to select. There are 13-2 = 11 cards of any particular suit that weren't part of the two pair. There are 4 suits to pick from, which means we have 11*4 = 44 cards to pick from for that fifth and final slot.

-----------------

Summary so far:

That gives 2808*44 = 123,552 different two pair hands possible.

This is out of C(52,5) = 2,598,960 hands

Divide those two values to get the final answer

(123,552)/(2,598,960) = 0.04753901560624

This then rounds to 0.04754 as the final answer.

The equation relating T to H is H = 45 - 7T.

Temperature simply means the degree of hotness and coldness in a body.

In this case, they find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface.

Let T = the temperature (in Celsius).

Let H = the height above the surface (in kilometers).

The equation will be:

H = 45 - (7 × T)

H = 45 - 7T

The axes aren't given and can't be graphed.

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The parallel between 2 highlights is called eduidistand

Answer:

1. 5ft

2. 2ft

3. 2ft

4. 1ft

Step-by-step explanation:

In linear equation,  that price of shorts before discount was $25

What in mathematics is a linear equation?

Assume that the price of shorts after the discount is x

Total payment = price of shorts + taxes

We know that:

total payment = $21

taxes = 5% = 0.05 of the price

This means that:

21 = x + 0.05x

21 = 1.05x

x = $20

Therefore, the price of the shorts is $20 after the discount

Now, we will get the price of the shorts before the discount:

Assume that the price of shorts before discount is y

We know that:

The discount was 20%

This means that Jennifer paid:

100% - 20% = 80% of the price of the shorts

Therefore:

80% of the price = $20

0.8y = 20

y = $25

This means that price of shorts before discount was $25.

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The movies for the movie marathon can be chosen in 120  different ways .

In the question ,

it is given that

total number of movies = 10 movies

number of movies that need to be played in specific order = 7 movies .

we have to find how many different ways can the movies be selected for the movie marathon .

we can solve this with Combination ,

where n = 10  and r = 7

So C(n,r) =  C (10,7)

= 10! / (3! * 7! )

= (10*9*8*7!)/(3! * 7! )

= ( 10*9*8) / (3*2 )

= 10 * 3 * 4

= 120 ways .

Therefore , The movies for the movie marathon can be chosen in 120  different ways .

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Answer:

[tex]y=\frac{3}{2}x+5[/tex]

Step-by-step explanation:

[tex]-6x+4y=20 \\ \\ 4y=6x+20 \\ \\ y=\frac{3}{2}x+5[/tex]

Answer:

Step-by-step explanation:

35-27=8

Answer:22.85%

Step-by-step explanation:

27 - 35

|35|

× 100% =

-8

35

× 100 = -22.8571428571% (decrease)

If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.

Let the equation be AB + BC = AC

substitute the values in the above equation, we get

AB + x + 3 = 34

simplifying the value of x,

Subtract A B from both sides AB + x + 3 - AB = 34 - A B

x + 3 = 34 - AB

Subtract 3 from both sides,

x + 3 - 3 = 34 - AB - 3

x = -AB + 31

Plug in this value of x into the line segments to find BC and AC.

Where, BC = x + 3

substitute the value of x in the above equation, we get

BC = [-AB + 31 ] + 3

BC = -AB + 34

Then, AB + BC = AC

x = -AB + 31

AB = 31/x

Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,

BC = x + 3, and AC = 34, then AB = 31/x.

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Graph is attached below.

Given,

y = 2x - 4

We have to draw a graph according to this

Here,

x E {-2; "-1;" 0; 1; 2}:

Image is attached.

How to draw a graph?

First, label and draw your X and Y axes at a straight angle. Axis Y is vertical, whereas axis X is horizontal. Write the scale for each axis down the line and mark the junction as 0, then draw a line. Calculate the values of Y for various values of X after drawing the axes.

So, the graph is given below.

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Answer:  [tex](h\circ m)(2) = 6[/tex]

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

Explanation:

The notation [tex](h \circ m)(2)[/tex] refers to function composition

It's the same as writing [tex]h(m(2))[/tex]

According to

m = {(3,4), (2,-2), (-2,6), (5,8)}

We have m(2) = -2 since x = 2 leads to m(x) = -2

Then the output -2 is treated as the input of the outer function h(x)

Looking through

h = {(1,5), (-2,6), (4, -3), (6,9)}

shows that h(-2) = 6

Therefore, [tex]h(m(2)) = h(-2) = 6, \ \text{ and } \ (h\circ m)(2) = 6[/tex]

Optionally we can write out a table like shown below.

The row highlighted shows the input x = 2 leading to m(x) = -2, which is then plugged into h(x) to get 6 as the final output. Think of it like a chain of dominoes.

Given

To fill the blanks.

Now,

The grpah of f(x)=tanx is given as,

Therefore, from the graph,

Then,

Also,

For x=0, tan(0)=0.

Therefore, the y-intercept is (0,0).

The points for the function f(x)=tanx is,

Since

Then, the points of the graph y=tanx is,

Hence, the answer should be in the order,

i)

ii)

iii)

Answer:

x ≈ 3.33

Step-by-step explanation:

given y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition y = 6 , x = 10

6 = [tex]\frac{k}{10}[/tex] ( multiply both sides by 10 )

60 = k

y = [tex]\frac{60}{x}[/tex] ← equation of variation

when y = 18 , then

18 = [tex]\frac{60}{k}[/tex] ( multiply both sides by k to clear the fraction )

18k = 60 ( divide both sides by 18 )

k = [tex]\frac{60}{18}[/tex] ≈ 3.33 ( to 3 significant figures )