Jacob found a computer game that was on sale at 20% off its original price. Which expression below will find the sale price, s, of the computer game, if p represents the original price of the product?

18.614 because a=πh(r^2)/3 pretty sure thats the formula but the answer is correct  

The approximate diameter of the pile of sand in the cone that sand was dumped in is 9.30 feet.

A cone is a 3-dimensional object that consists of a ciruclar base and a vertex. The diameter is twice the length of the radius.

Radius = √[volume / (1/3 x π x height)]

√[136 / (1/3 x 22/7 x 6)]

√[136 / 6.29 = 4.65

Diameter = 4.65 x 2 = 9.30 feet

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Answer:

[tex]m\angle DEC=91^o[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite

so

[tex]m\angle DEC=\frac{1}{2}[arc\ AB+arc\ DC][/tex]

substitute the given values

[tex]m\angle DEC=\frac{1}{2}[39^o+143^o][/tex]

[tex]m\angle DEC=\frac{1}{2}[182^o][/tex]

[tex]m\angle DEC=91^o[/tex]

Answer: 23

Step-by-step explanation:

let x=no. of students in both classes

no. of students in anatomy = 34

no. of students in anatomy only= 34 -x

no. of students in physics= 37

no. of students in physics only=37-x

48 = 34-x + 37-x + x

48 = 34 - x + 37

48 = 71 - x

x = 71 - 48

x = 23

Therefore the number of students in both classes are 23

Final answer:

To find the number of students in both the anatomy and physics classes, we can use the concept of sets and intersection. The number of students in both classes is 23.

Explanation:

To find the number of students in both the anatomy and physics classes, we can use the concept of sets and intersection. Let's assume A represents the set of students in the anatomy class, B represents the set of students in the physics class, and U represents the universal set of all students.

According to the given information, |A| = 34, |B| = 37, and |U| = 48.

The number of students in both classes can be found by using the formula:

|A ∩ B| = |A| + |B| - |U|

Substituting the values, we get:

|A ∩ B| = 34 + 37 - 48

|A ∩ B| = 71 - 48

|A ∩ B| = 23

Therefore, there are 23 students in both the anatomy and physics classes.

Answer:The number of yards of Chris's ribbon are neither purple nor green is 1.625 yards

Step-by-step explanation:

Chris has a total of 3 2/3 yards of ribbon. Converting 3 2/3 yards to improper fraction, it becomes 11/3 yards. Chris has 7/8 yards of purple ribbon. He also has 1 1/6 yards of green ribbon. Converting to improper fraction, it becomes 7/6 yards of green ribbon.

The total length of purple and green ribbon that Chris has would be 7/8 + 7/6 = (21+28)/24 = 49/24

The number of yards of Chris's ribbon are neither purple nor green is 11/3 - 49/24 = (88 - 49)/24

= 39/24 = 1.625 yards

Answer: he would need to ride at least 13.3 miles

Step-by-step explanation:

The total amount that Grant needs to make in a day is greater than or equal to $15.

He has an agreement with Brian to rent the bike for $35.00 a night.

He charges customers $3.75 for every mile he transports them. If he transports the customers over x miles, his total revenue would be

3.75 × x = 3.75x

Profit = revenue - cost. Therefore,

his profit would be

3.75x - 35

Therefore,

3.75x - 35 ≥ 15

3.75x ≥ 15 + 35 = 50

x ≥ 50/3.75

x ≥ 13.3

Answer:

length of the pretty side  and length of the side oppositte to the pretty side  =   37.91 ft

length of the other two sides  = 27.52 ft

Step-by-step explanation:

The mathematical problem is:

Max A = b1*h

subject to: 35*b1 + 18*(2*h + b2) <= 3000

Where

A: area of the garden

b1: length of the pretty side

b2: length of the side oppositte to the pretty side

h: length of the other two sides

Replacing with b1 = b2 and taking only the equality sign in the restriction (in the maximum all the money will be spent), we get:

35*b1 + 18*(2*h + b1) = 3000

35*b1 + 36*h + 18*b1 = 3000

53*b1 + 36*h = 3000

b1 = 3000/53 - (36/53)*h

Substituing in Area's formula  

A = (3000/53 - (36/53)*h)*h

A = (3000/53)*h - (36/53)*h^2

In the maximum, the derivative of A is equal to zero

dA/dh = 3000/53 - 2*(36/53)*h =

3000/53 - 72/35*h = 0

h = (3000/53)*(35/72)

h = 27.52 ft

then,

b1 = 3000/53 - (36/53)*27.52

b1 = 37.91 ft =b2

The dimensions of the garden that give Mr. Rogers the maximum area are approximately: Length (L) = 28.3 feet and Width (W) = 41.7 feet.

To find the dimensions of Mr. Rogers's garden that will give him the maximum area while staying within his budget, we need to set up and solve a problem involving optimization with constraints.

First, let's define the variables:

The cost of fencing:

The total cost of fencing can be expressed as follows:

[tex]35L + 18(2W + L) = 3000[/tex]

Simplifying this equation:

[tex]35L + 36W + 18L = 3000[/tex]
[tex]53L + 36W = 3000[/tex]

To find the dimensions that maximize the area, we need to express the area in terms of one variable and use calculus to find the maximum. Let's solve for one variable in terms of the other. We'll solve for [tex]W[/tex]:

[tex]53L + 36W = 3000[/tex]
[tex]36W = 3000 - 53L[/tex]
[tex]W = \frac{3000 - 53L}{36}[/tex]

Now, express the area [tex]A[/tex] as a function of [tex]L[/tex]:

[tex]A = L \cdot W[/tex]
[tex]A = L \left(\frac{3000 - 53L}{36}\right)[/tex]
[tex]A = \frac{3000L - 53L^2}{36}[/tex]

To find the maximum area, we take the derivative of [tex]A[/tex] with respect to [tex]L[/tex] and set it to zero:

[tex]\frac{dA}{dL} = \frac{3000 - 106L}{36}[/tex]

Set the derivative to zero and solve for [tex]L[/tex]:

[tex]\frac{3000 - 106L}{36} = 0[/tex]
[tex]3000 - 106L = 0[/tex]
[tex]106L = 3000[/tex]
[tex]L = \frac{3000}{106}[/tex]
[tex]L \approx 28.3[/tex]

Now we use this value of [tex]L[/tex] to find the corresponding value of [tex]W[/tex]:

[tex]W = \frac{3000 - 53 \times 28.3}{36}[/tex]
[tex]W \approx \frac{3000 - 1499.9}{36}[/tex]
[tex]W \approx \frac{1500.1}{36}[/tex]
[tex]W \approx 41.7[/tex]

The probability of a player winning depends on whether balls are replaced after each draw. With replacement, the probabilities remain constant and A has a higher chance of winning (9/20) compared to B and C (11/40 each). Without replacement, the probabilities change after each turn and require complex computation.

This is a probability problem involving sequence of events. The outcome is dependent on whether the balls are replaced or not after each draw.

For case a), if each ball is replaced after being drawn, the probabilities for A, B, and C stay constant each round. There are 4 white balls out of 12 total, so the probability of drawing a white ball is 4/12 = 1/3. Because the players draw successively and stop once a white ball is drawn, we need to consider the rounds of draws. For A to win, a white ball needs to be drawn on the 1st, 4th, 7th turns, and so on. For B to win, a white ball needs to be drawn on the 2nd, 5th, 8th rounds, and so forth. Similar logic applies to player C. Using geometric distribution to compute these, we have [tex]P(A) = 1/3 * (2/3)^0 + 1/3 * (2/3)^3 + 1/3 * (2/3)^6 +... = 9/20.[/tex] Applying similar logic to players B and C, we get P(B) = P(C) = 11/40. (Note that the sum of P(A), P(B), and P(C) = 1, which verifies our calculation is correct.)

For case b), if the balls are not replaced after each draw, the probability changes after each turn. Initially the probability of drawing a white ball is 4/12 = 1/3, then it becomes 4/11, 4/10, and so forth if a white ball is not drawn, and 3/11, 3/10, and so forth if a white ball is drawn. Therefore a recursive method computing the probability is needed in this case and the calculation could be quite complicated depending on when we stop the game.

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Answer:

12

Step-by-step explanation:

Number of students in Bobby's class = 30

40% of the students have blue eyes.

It means 40 out of 100 students will have blue eyes.

Then we have to find how many out of 30 students will have blue eyes.

Let us take the number of blue-eyed students out of 30 to be x.

Then:

[tex]\frac{40}{100}=\frac{x}{30}\\x=\frac{40}{100}\times30\\x=12[/tex].

Hence 12 out of 30 students will have blue eyes.

Answer:

14

Step-by-step explanation:

48 - 6 = 42

42 divided by 3 = 14.

Mr. Kim's daughter is 14 years old.

Mr. Kim's daughter is 14 years old. This was determined by setting up the equation 48 = 3x + 6 and solving for x step-by-step, which resulted in x = 14.

To find Mr. Kim's daughter's age, we can set up an equation based on the problem statement.

Let's denote the daughter's age by x.

According to the problem, Mr. Kim's age is 6 more than 3 times his daughter's age. This can be written as:

48 = 3x + 6

We need to solve for x step-by-step:

Subtract 6 from both sides of the equation:

48 - 6 = 3x

Simplify the left side:

42 = 3x

Divide both sides by 3:

[tex]\frac{42}{3}[/tex] = x

Simplify the right side:

x = 14

Therefore, Mr. Kim's daughter is 14 years old.

In parallelogram ABCD, opposite sides AB and DC are both 8 units long, and AD and BC are both 5 units long.

To show that quadrilateral ABCD is a parallelogram, we need to demonstrate that both pairs of opposite sides are congruent. We can do this by finding the lengths of the opposite side pairs and showing that they are equal.

Let's denote the points as follows:

- A, B, C, D are the vertices of the quadrilateral ABCD.

- AB and DC are opposite sides, and AD and BC are opposite sides.

Given that AB = 8 units and AD = 5 units, we need to find the lengths of DC and BC.

Since ABCD is a parallelogram, opposite sides are congruent. Therefore, DC = AB = 8 units.

To find BC, we know that BC = AD = 5 units.

Thus, we have:

- AB = DC = 8 units

- AD = BC = 5 units

Since both pairs of opposite sides are congruent, quadrilateral ABCD is a parallelogram.

The length of BC is 5 units.

In the given case, The length of BC is 8 units.

To show that quadrilateral ABCD is a parallelogram, we need to demonstrate that both pairs of opposite sides are congruent.

Let's denote the lengths of the sides as follows: AB, BC, CD, and DA.

 Given that ABCD is a parallelogram, we know that opposite sides are equal in length.

Therefore, we can equate the lengths of AB to CD and BC to DA.

 Let's assume that the length of side AB (and thus CD, since they are opposite and equal) is given as 8 units.

We are asked to find the length of side BC (which will be equal to the length of side DA).

 Since we do not have any additional information such as angles or diagonals, we cannot calculate the length of BC directly.

However, if we are given that ABCD is a parallelogram, then by definition, the lengths of opposite sides are equal.

Therefore, without loss of generality, we can state that the length of BC is also 8 units, which is equal to the length of AB.

 Thus, we have shown that both pairs of opposite sides are congruent:

AB = CD = 8 units

BC = DA

Since AB = 8 units and AB = CD, it follows that CD = 8 units.

Similarly, since AB = CD and AB = 8 units, by the properties of a parallelogram, BC must also be equal to 8 units.

 Therefore, the length of BC is 8 units, confirming that quadrilateral ABCD is indeed a parallelogram.

when you multiply $1.59 by 5 you get $7.95

when you multiply $1.87 by 2 you get $4.74

so when you subtract them you get $3.21

Answer:

t=2.83

Step-by-step explanation:

Linear Approximation Of Functions

The equation of a line is given by

[tex]y=y_o+m(x-x_o)[/tex]

Where m is the slope of the line and [tex](x_o,y_o)[/tex] are the coordinates of a point through which the line goes.

Given a function B(t), we can build an approximate line to model the function near one point. The value of m is the derivative of B in a specific point [tex](t_o, B_o)[/tex]. The equation becomes

[tex]B(t)=B_o+B'(t_o)(t-t_o)[/tex]

Let's collect our data.

[tex]B'(t)=8e^{0.2cost},\ B_o=B(2.2)=4.5[/tex]

Let's find the required values to build the approximate function near [tex]t_0=2.2[/tex]. We evaluate the derivative in 2.2

[tex]B'(2.2)=8e^{0.2cos2.2}=7.11[/tex]

The function can be approximated by

[tex]B(t)=4.5+7.11(t-2.2)[/tex]

Once we have B(t), we are required to find the value of t, such that

[tex]B(t)=9[/tex]

Or equivalently:

[tex]4.5+7.11(t-2.2)=9[/tex]

Rearranging

[tex]\displaystyle t-2.2=\frac{9-4.5}{7.11}[/tex]

Solving for t

[tex]\displaystyle t=\frac{9-4.5}{7.11}+2.2[/tex]

[tex]\boxed{t=2.83}[/tex]

We find the equation of the linear approximation at t=2.2 using B(2.2) and B'(2.2). We then solve this equation for t when the linear approximation equals 9. This gives us the time at which the linear approximation estimates B(t) = 9.

To solve for the time when the linear approximation gives an output of 9, we need to find the equation of the tangent line (i.e., the linear approximation) at t = 2.2. The linear approximation to a function at a particular point is given by the formula L(t) = f(a) + f'(a)*(t-a), where f is the function, a is the point, and f' denotes the derivative of the function.

Given that B(2.2) = 4.5 and B'(t) = 8e0.2cos(t), we can substitute these into the linear approximation formula to get L(t) = 4.5 + 8e0.2cos(2.2)*(t-2.2).

Next, we solve this equation for t when L(t) = 9: 9 = 4.5 + 8e0.2cos(2.2)*(t-2.2). Solving the equation for t gives the time at which the linear approximation estimates B(t) = 9.

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Answer:

Option C. The company built a total of 40 skateboards the week its office was relocated

Step-by-step explanation:

Let

s ----> the total number of skateboards

w ---> the number of weeks

we have

[tex]s(w)=4w+40[/tex]

This is the equation of the line in slope intercept form

where

The slope is [tex]m=4\ \frac{skateboard}{week}[/tex]

The y-intercept is [tex]b=40\ skateboard[/tex]

Remember that

The y-intercept is the value of the function s when the value of variable w is equal to zero

In the context of the problem

The company built a total of 40 skateboards the week its office was relocated

Answer:

Cost of 1 gallon of Regular gasoline is $2.45 and  Cost of 1 gallon of Premium gasoline is $2.90.

Step-by-step explanation:

Let the Cost of Regular gasoline be 'x'.

Let the Cost of Premium gasoline be 'y'.

Given:

Amount of regular gasoline bought yesterday = 2 gallons

Amount of premium gasoline bought yesterday = 3 gallons

Total Cost of yesterday = $13.60

Now we know that Total Cost of yesterday is equal to sum of Amount of regular gasoline bought yesterday multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought yesterday multiplied by Cost of premium gasoline.

Framing in equation form we get;

[tex]2x+3y=13.60 \ \ \ \ equation\ 1[/tex]

Also Given:

Amount of regular gasoline bought today = 3 gallons

Amount of premium gasoline bought Today = 4 gallons

Total Cost of Today = $18.95

Now we know that Total Cost of Today is equal to sum of Amount of regular gasoline bought Today multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought Today multiplied by Cost of premium gasoline.

Framing in equation form we get;

[tex]3x+4y=18.95 \ \ \ \ equation\ 2[/tex]

Now Multiplying equation 1 by 3 we get;

[tex]2x+3y=13.60\\\\3(2x+3y)=13.60\times3\\\\6x+9y= 40.80 \ \ \ \ \ equation\ 3[/tex]

Now Multiplying equation 2 by 2 we get;

[tex]3x+4y=18.95\\\\2(3x+4y)=18.95\times2\\\\6x+8y= 37.90 \ \ \ \ \ \ equation\ 4[/tex]

Subtracting equation 4 from equation 3 we get;

[tex](6x+9y)- (6x+8y)= 40.80-37.90\\\\6x+9y-6x-8y= 2.9\\\\y=\$2.90[/tex]

Substituting the value of y in equation 1 we get;

[tex]2x+3y=13.60\\\\2x+3\times2.90 =13.60\\\\2x+8.7=13.6\\\\2x=13.6-8.7\\\\2x=4.9\\\\x=\frac{4.9}{2} =\$2.45[/tex]

Hence Cost of 1 gallon of Regular gasoline is $2.45 and  Cost of 1 gallon of Premium gasoline is $2.90.

Answer:

It takes 3.5 hours for the second plane to catch the first plane.

Step-by-step explanation:

From the information given:

To find when the second plane catches the first plane, the distances of both planes must be equal.

We can use Distance = Rate x Time.

Let t be the time.

Distance of the first plane = Rate x Time = [tex]300\cdot t + 350[/tex]

Distance of the second plane = Rate x Time = [tex]400\cdot t [/tex]

Distance of the second plane = Distance of the first plane

[tex]400\cdot t=300\cdot t + 350[/tex]

Solving for t.

[tex]100\cdot t = 350[/tex]

t = 3.5 hours

It takes 3.5 hours for the second plane to catch the first plane.

The distance travelled by the two planes is an illustration of a linear function.

It will take the second plane 3.5 hours to catch up with the first plane

Let t represent time and d represent distance

The distance traveled by the first plane is represented as:

[tex]\mathbf{d_1 = 350 + 300t}[/tex]

The distance traveled by the second plane is represented as:

[tex]\mathbf{d_2 = 400t}[/tex]

Both planes will be at the same distance, when d1 = d2.

So, we have:

[tex]\mathbf{400t = 350 + 300t}[/tex]

Subtract 300t from both sides

[tex]\mathbf{400t - 300t = 350}[/tex]

Subtract

[tex]\mathbf{100t = 350}[/tex]

Divide both sides by 100

[tex]\mathbf{t = 3.50}[/tex]

Hence, it will take the second plane 3.5 hours to catch up with the first plane

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Answer:

Domain: {-4, -3, 1 }

Step-by-step explanation:

As we know that domain of a relation basically consists of all the first elements or x-coordinates of order pairs.

As the relation is : {(-4, 3), (-4, 4), (-3, 1), (1, 1)}

So,  

         Domain: {-4, -3, 1 }

Note: We can not duplicate an element when we determine the domain of any relation. As -4 was present in first and second order pairs i.e. (-4, 3), (-4, 4). But, we have to write it only once when we write the domain of any relation.

So, the domain will be listed as:

                                       Domain: {-4, -3, 1 }

Keywords:  domain, relation

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The second hand of a clock is 8 cm long what is the distance of the tip of the second hand travel in 10 minutes

Answer:

The distance travelled by tip of second hand in 10 minutes is 502.4 cm

Solution:

Length of second hand = 8 cm long

In one revolution it travels a circumference of  a circle of which radius is 8 cm

The circumference of circle = [tex]2 \pi r[/tex]

[tex]c = 2 \times \pi \times 8 = 16\pi[/tex]

We are aksed to find the distance of the tip of the second hand travel in 10 minutes

Second hand complete 1 revolution in 1 minute.

Therefore, in 10 minutes it revolves 10 revolution,

In 1 revolution tip of second covers = 16π

Hence distance travelled is given as:

[tex]\rightarrow 16 \pi \times10 = 160 \pi[/tex]

We know that π is a constant equals to 3.14

[tex]\rightarrow 160 \pi = 160 \times 3.14 = 502.4[/tex]

Thus the distance travelled by tip of second hand in 10 minutes is 502.4 cm

Answer:

502.4

Step-by-step explanation:

To calculate the number of different sandwich combinations at a sandwich shop, one multiplies the basic sandwich configurations (3 types of sandwiches on 2 types of bread, totaling 6) by the possible topping combinations (2^6 = 64, including the option of no toppings), resulting in 384 different sandwich combinations.

The question revolves around combinatorial mathematics, focusing on calculating the number of different sandwich combinations available at a sandwich shop with a given set of ingredients. The shop offers three types of sandwiches (ham, turkey, and chicken), each of which can be ordered on either white bread or multi-grain bread. Additionally, customers can add any combination of the six available toppings to their sandwiches. To calculate the total number of possible sandwich combinations, one would need to consider the choices for the type of sandwich, the bread, and the combinations of toppings.

For the sandwich and bread choices, since there are three types of sandwiches and two types of bread, there are a total of 3 * 2 = 6 basic sandwich configurations. For the toppings, since customers can choose any combination of the six available toppings, including the option of having no toppings at all, the total number of topping combinations can be calculated using the formula for combinations of a set: 2n, where n is the number of items (toppings) to choose from. Therefore, there are 26 = 64 possible topping combinations.

The total number of different sandwich combinations available can be calculated by multiplying the basic sandwich configurations by the topping combinations, which gives 6 * 64 = 384 different sandwich combinations. This calculation showcases the versatility of the menu and the vast array of options available to customers at the sandwich shop.

Let's say:

Ham sandwich: H

Turkey sandwich: T

Chicken sandwich: C

White bread: W

Multigrain bread: M

The representation using set notations would be:

[ (H,W), (H,M), (T,W), (T,M), (C,W), (C,M) ]

Complete question is here:

Represent the sample space using set notation.A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each sandwich can be ordered with white bread or multi- grain bread.

Answer:

The  gluten ratio in micrograms per milliliter is 13 µg/mL.

Step-by-step explanation:

Consider the provided information.

It is given that the food has a gluten ratio of [tex]13 \frac{mg}{L}[/tex].

Now we need to convert gluten ratio in micrograms per milliliter

To convert mg to micro grams use the information shown below:

1 mg = 1000 micro-grams.

1 L = 1000 milliliter

Now, substitute 1 mg = 1000 micro-grams and 1 L = 1000 milliliter in the above ratio.

[tex]13( \frac{1000 \ micro-grams}{1000 \ milliliter} )= 13( \frac{micro-grams}{milliliter})[/tex]

Hence, the  gluten ratio in micrograms per milliliter is 13 µg/mL.

Answer:

the answer is 4μm to the power of⁻1

Step-by-step explanation:

khan academy said

Answer:

Step-by-step explanation:

miles left to travel=51-15=36

more days required=36/9=4 days.

Answer: it will take 4 more days before DeAndre finishes

Step-by-step explanation:

DeAndre is 15 miles into a 51-mile backpacking trip in the wilderness. This means that he has already covered 15 miles and the total number of miles is 51. Number of miles left is 51 - 15 = 36 miles.

DeAndre can hike 9 miles per day. The number of days that it will take him to cover 36 miles would be 36/9 = 4 days

Answer:

[tex]P(S|\bar{C} ) = 0.1739[/tex]

Step-by-step explanation:

We define the probabilistic events how:

S: Today is snowing

C: The class is canceled

If it is snowing, there is an 80% chance that class will be canceled, it means

P( C | S ) = 0.8  conditional probability

If it is not snowing, there is a 95% chance that class will go on

[tex]P( \bar{C} | \bar{S}) = 0.95[/tex]

and P(S) = 0.05

We need calculate

[tex]P( S |\bar{C} ) = \frac{P(\bar{C} | S) P(S)}{P(\bar{C})}[/tex]

[tex]P(\bar{C}) = P( \bar{C}|S)P(S) + P( \bar{C}|\bar{S})P(\bar{S})[/tex]

How

[tex]P(C | S) = 0.8[/tex]  then  [tex]P( \bar{C} | S) = 0.2[/tex]

[tex]P (\bar{C})[/tex] = (0.2)(0.5) + (0.95)(0.5)

                                =0.575

[tex]P(S |\bar{C} ) = \frac{(0.2)(0.5)}{(0.575)}[/tex]

[tex]P(S|\bar{C} ) = 0.1739[/tex]

Answer:

The answer to your question is x³ + 11² + 30x

Step-by-step explanation:

Data

       x = 0; x = - 5; x = 6

Process

1.- Equal the zeros to zero

      x₁ = 0; x₂ + 5 = 0; x₃ + 6 = 0

2.- Multiply the results

      x(x + 5)(x + 6) = x [ x² + 6x + 5x + 30]

3.- Simplify

                             = x [ x² + 11x + 30]        

4.- Result

                             = x³ + 11² + 30x

The polynomial equation with zeros at x = 0, x = -5, and x = 6 is x^3 - x^2 - 30x.

To find a polynomial equation with zeros at x = 0, x = -5, and x = 6, you would use the relationship between zeros and factors of a polynomial. Each zero corresponds to a factor of the polynomial; for x = 0, the factor is x, for x = -5, the factor is (x + 5), and for x = 6, the factor is (x - 6). Therefore, the polynomial equation that has these zeros can be constructed by multiplying these factors together.

The result is the polynomial equation:

f(x) = x(x + 5)(x - 6)

Expanding this product gives:

f(x) = x³ - x² - 30x

Answer:

  A(2, 2)

Step-by-step explanation:

I find it useful to graph the given points. The center of rotation is at the place where the perpendicular bisectors of BB' and CC' meet. That point is ...

  A =  (2, 2).

__

The graph shows you the slope of BB' is 1, so its perpendicular bisector will have a slope of -1. The midpoint of BB' is (2-2, 6+2)/2 = (0, 4). This is the y-intercept of the line, so the perpendicular bisector of BB' has equation ...

  y = -x +4

The slope of CC' is -1/3, so its perpendicular will have a slope of -1/(-1/3) = 3. The midpoint of CC' is (4+1, 3+4)/2 = (5/2, 7/2). In point-slope form the equation of the perpendicular bisector of CC' is ...

  y -7/2 = 3(x -5/2)

  2y -7 = 3(2x -5) . . . . multiply by 2

  2(-x+4) -7 = 3(2x -5) . . . substitute for y

  -2x +1 = 6x -15 . . . . .eliminate parentheses

  16 = 8x . . . . . . . . . . add 2x+15

  x = 2 . . . . . . divide by 8

  y = -2+4 = 2 . . . . from the equation for y

The intersection of the perpendicular bisectors of BB' and CC' is the center of rotation:

  A = (2, 2)

Final answer:

The coordinate of vertex A is (2, 2), found by equating B' to (y, x) and using the given B' coordinates.

Explanation:

To find the coordinates of vertex A, we can use the properties of a rotation. A 90° counterclockwise rotation about a point involves switching the coordinates and negating the y-coordinate. Let's denote the coordinates of A as (x, y). After the rotation, A becomes B', so we have:

B' = (y, x)

From the given coordinates of B' (–2, 2), we can equate:

y = 2

-2 = -x

Solving these equations, we find that x = 2. Therefore, the coordinates of vertex A are (2, 2). So, Maggie's image graph depicts a 90° counterclockwise rotation about vertex A (2, 2) of triangle ABC.

Answer:

A) 210

B) 357

C) 267

Step-by-step explanation:

A) Among 7 games, we can first choose 3 wins, and then among remaining 4 games, we can choose 2.

To calculate the possibility, we will use Combination.

[tex]C(7,3)*C(4,2) = 35 *6 = 210[/tex]

B) Player A can get 4 points with the following cases:

4 wins and 3 loses

3 wins, 2 draws and 2 loses

2 wins, 4 draws and 1 lose

1 win and 6 draws

Indeed, these cases matches for Player B too to get 3 points.

So again, we will use Combination to calculate the possibility.

[tex]C(7,4) + C(7,3)*C(4,2) + C(7,2)*C(5,4) + C(7,1) = 357[/tex]

C) Here, we need to find two possibilities after 6 games and add them, while Player A has 3 points and wins the 7th game, and Player A has 3.5 points and draws the 7th game.

[tex][C(6,3)+C(6,2)C(4,2)+C(6,1)C(5,4)+C(6,6)] + [C(6,3)C(3,1)+C(6,2)C(4,3)+C(6,1)] =[20+90+30+1]+[60+60+6]=141+126=267[/tex]

The transformation T could be translation, rotation, reflection, or dilation, altering the position, orientation, or size of the triangle.

The transformation T mapping triangle XYZ to triangle X'Y'Z' could be any of the basic rigid transformations in geometry: translation, rotation, reflection, or dilation.

- A translation involves shifting the entire triangle by a certain distance in a certain direction without changing its orientation or shape.

- A rotation rotates the triangle around a fixed point (e.g., the origin or a specific vertex), altering its orientation but maintaining its shape and size.

- A reflection flips the triangle across a line (e.g., the x-axis, y-axis, or an arbitrary line), producing a mirror image with reversed orientation.

- A dilation scales the triangle uniformly, either enlarging or shrinking it while maintaining its shape and proportions.

To determine which transformation T specifically represents, additional information is needed, such as the coordinates of the vertices X, Y, Z and X', Y', Z', or any constraints or properties of the transformation provided. Each type of transformation has distinct characteristics that can be identified through geometric properties and transformations of coordinates.

Answer:

The correct option is

If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.

Step-by-step explanation:

Given:

RS ≅ SQ

∠PSR ≅ ∠PSQ = 90°

To Prove:

point P is equidistant from points R and Q

i.e PR ≅ PQ

Proof:

In  ΔPSR  and Δ PSQ

PS ≅ PS                         ……….{Reflexive Property}

∠PSR ≅ ∠PSQ = 90°     …………..{Measure of each angle is 90° given}

RS ≅ QS                         ……….{Given}

ΔPSR  ≅ ΔPSQ  ….{By Side-Angle-Side Congruence test}

∴ PR ≅ PQ .....{Corresponding Parts of Congruent Triangles}

i.e point P is equidistant from points R and Q    .......Proved

Answer:

f(x) = 8x⁴-8x²+1

Step-by-step explanation:

I will assume that f(cos θ) = cos(4θ). Otherwise, f would not be a polynomial. lets divide cos(4θ) in an expression depending on cos(θ). We use this properties

cos(4θ) = cos(2 * (2θ) ) = cos²(2θ) - sin²(2θ) = [ cos²(θ)-sin²(θ) ]² - [2cos(θ)sin(θ)]² = [cos²(θ) - ( 1 - cos²(θ) ) ]² - 4cos²(θ)sin²(θ) = [2cos²(θ)-1]² - 4cos²(θ) (1 - cos²(θ) ) = 4 cos⁴(θ) - 4 cos²(θ) + 1 - 4 cos²(θ) + 4 cos⁴(θ) = 8cos⁴(θ) - 8 cos²(θ) + 1

Thus f(cos(θ)) = 8 cos⁴(θ) - 8 cos²(θ) + 1, and, as a result

f(x) = 8x⁴-8x²+1.

Question:

A construction company needs to remove 24 tons of dirt from a construction site. They can remove 3/4 tons of dirt each hour. How long will it take to remove dirt

Answer:

It takes 32 hours to remove the dirt

Step-by-step explanation:

Given:

Total amount dirt to be removed =   24 tons

Dirt that can removed in one hour =  3/4 tons

To Find:

Time taken to remove all the dirt =?

Solution:

Let the time taken to remove the dirt from the company be x.

Then

x =  [tex]\frac{ \text { total amount of dirt in the company}}{\text{ amount of dirt removed in one hour}}[/tex]

Substituting the given values , we get

x = [tex]\frac{24}{\frac{3}{4}}[/tex]

x = [tex]24\times \frac{4}{3}[/tex]

x = [tex] \frac{96}{3}[/tex]

x= 32

Answer:38 t-shirts

Step-by-step explanation:

P=30t-640 main street

p=25t-450 broad street

30t-640=25t-450

30t-25t-640=-450

5t-640+640=-450+640

5t/5=190/5

t=38

enjoy

Answer:the total number of milkshake that the ice cream shop sold that day is 120

Step-by-step explanation:

Let x represent the total number of

vanilla milkshakes that the ice cream shop sold that day.

The ice cream shop sold 48 vanilla milkshakes in a day which is 40% of the total number of milkshake sold that day. It means that

40/100 × x = 48

0.4 × x = 48

0.4x = 48

x = 48/0.4 = 120