Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.

3x^2−30x=−2

Answer:

a

Step-by-step explanation:

Answer:

The top box:  3

The middle box:  2

The bottom box:  1

Step-by-step explanation:

In order to fill out the yellow boxes we have to use the equation above the table, and plug in the x values, and so we get...

If x = 2, then

y = x + 1

y = 2 + 1

y = 3

If x = 1, then

y = x + 1

y = 1 + 1

y = 2

If x = 0, then

y = x + 1

y = 0 + 1

y = 1

Answer:

58-(14)2

58-28

30

Step-by-step explanation:

Answer:

35 million

Step-by-step explanation:

20000000×70%=35million

Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. The correct option is D, 38 millon.

Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.

It is given by the formula,

A = P(1+r)ⁿ

where, A is the value after n period of time, P is the initial amount, and,

r is the rate of increment or decrement.

Given that On the first day of a song's release, it had 20 million streams. Also, the number of streams increases by 10% per day. Therefore, it can be said that the number of streams is compounding. Thus, the number of streams on the seventh day will be,

Number of streams = 20 (1+0.10)⁷ million

                                 = 20 × 1.9487 million

                                 = 38.974 million

                                 = 38 million

Hence, the number of streams there will be on the seventh day is 38 million.

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9. The value of x is 7

10. In the figure  x = 10

11. The relationship is that their sum is 180 degrees

This relationship is known as the Same-Side Interior Angles Theorem.

12. The statement is true.

Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal

14 < 3 = 94 degrees

9. The value of x is solved using the knowledge of corresponding angles are equal

< A = < B

4x = 3x + 7

x = 7

10. In the figure < 3 and < 6 are alternate internal angles which is equal

7x - 10 = 5x + 10

7x - 5x = 10 + 10

2x = 20

x = 10

11. The relationship between the interior angles on the same side is that their sum is 180 degrees

This relationship is known as the Same-Side Interior Angles Theorem. It is a fundamental concept in geometry and is used to solve problems involving parallel lines and transversals.

12. The statement is true.

Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal

13. The measure of w is solved using the idea of vertical angels

w + 85 = 148

w = 148 - 85

w = 63

14. The mistake is that < 5 is not corresponding angle to < 2

The correct solution is < 3 = < 5 alternate internal angles

< 3 + 86 = 180 supplementary angles

< 3 = 180 - 86

< 3 = 94 degrees

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The probability that the buyer waits more than 10 minutes is 0.0271

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

Probability function:

fy(y)=0.2e^(-0.2y), y ≥ 0

The inequality expression y ≥ 0 means that

The value of y is atleast 0

The probability that the buyer waits more than 10 minutes means that

y = 10

So, we have the following representation

y = 10 in fy(y)=0.2e^(-0.2y)

Substitute the known values in the above equation, so, we have the following representation

fy(10)=0.2e^(-0.2 * 10)

Evaluate the exponents

fy(10)=0.2 * 0.13533528323

Evaluate the products

fy(10) = 0.0271

Hence, the probability is 0.0271

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Answer:

Success or failure

Step-by-step explanation:

In a binomial experiment, each trial is independent of each other, and each trial will end up either succeeding or failing. Both outcomes cannot occur at the same time, so the outcomes are mutually exclusive.

Answer:

Step-by-step explanation:

4/mx

The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

<95141404393>

Answer:

-5

Step-by-step explanation:

Simplify f(x)

\(f(x)=x^5-5x^4-17x^3+85x^2+16x-80\\f(x)=x^4(x-5)-17x^2(x-5)+16(x-5)\\f(x)=(x^4-17x^2+16)(x-5)\\f(x)=(x^2-16)(x^2-1)(x-5)\\f(x)=(x-4)(x+4)(x+1)(x-1)(x-5)\)

Therefore, \(x=4,-4,-1,1,5\) are the roots of the polynomial \(f(x)\), which makes option 3 the best choice.

The system of equations is.

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

And the solutions are y = 50 and x = 10.

Let's define the two variables:

With the given information we can write two equations, then the system will be:

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

Now let's solve it.

We can isolate x on the first  to get:

\(\text{x} = 60 - \text{y}\)

Replace that in the other equation to get:

\(15\times(60 - \text{y}) + 10\text{y} = 800\)

\(-2\bold{y} = 900 - 800\)

\(-2\bold{y} = 100\)

\(\text{y} = \dfrac{100}{-2} = \bold{50}\)

Then \(\bold{x=10}\).

Therefore, the solutions are y = 50 and x = 10.

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for every input there is exactly one output

Step-by-step explanation:

Answer:

75 child tickets and 100 adult tickets were sold.

Step-by-step explanation:

Given that adult tickets cost $ 6 and children's tickets cost $ 2, knowing that 175 tickets were sold for $ 750, to determine how many child tickets were sold the following calculation must be performed:

2 x 175 = 350

750 - 350 = 400

6 - 2 = 4

400/4 = 100

175 - 100 = 75

100 x 6 = 600

75 x 2 = 150

Therefore, 75 child tickets and 100 adult tickets were sold.

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Its 7 add 7 to each number to prove

The volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

What is frustum of pyramid?

The top of a conventional pyramid is removed to create the frustum, which is a pyramid. It is known as a truncated pyramid for this reason. The height of a pyramid is represented by the letter h and is the distance from its base to its summit. Similar to it, it has two bases and a slant height indicated by the letter "s" (top and bottom).

We are given frustum of a pyramid with square base of side 22, square top of side 13 and height 20.

We know that volume of frustum of pyramid(V) = h(b^2 + a^2 + ab)/3

We are given b = 22, a = 13 and h = 20

From this, we get

⇒V = h(b^2 + a^2 + ab)/3

⇒V = 20(22^2 + 13^2 + 22*13)/3

⇒V = 20(484 + 169 + 286)/3

⇒V = 20(939)/3

⇒V = 20*313

⇒V = 6260 cubic units

Hence, the volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

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Answer:

Input work is the work done on a machine as the input force acts through the input distance. This is in contrast to output work which is a force that is applied by the body or system to something else. Output work is the work done by a machine as the output force acts through the output distance.Jan 15, 2020 hwgsvsd d jxvsd

dvsud sgsgs hsysvdudbd dvyd dhsgtsjd vsytwgsud gsyfwuyebdbhys. dusgcejd b

Step-by-step explanation:

Count the number of times you have to move the decimal point to the right until it is to the right of the 1st nonzero number.

a) You have to move the decimal point 11 times until it gets to the right of the 1st nonzero number, which is 7. You then rewrite this number as

\(7.2×10^{-11}\)

The exponent of 10 is a negative number because you moved the decimal point to the right.

b) Similarly, you have to move the point 9 times to the right so the answer is

\(9.5×10^{-9}\)

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Answer:

x = 9 and y = 15

Step-by-step explanation:

this is the answer because each side is equivalent to the parallel line so y would be whatever is across from it

Answer:

y=15

x=9

Step-by-step explanation:

they are parallel and equal to the opposite sides

Answer:

2(3x + 6)

Step-by-step explanation:

For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.

Given information:

Cost of Guatemalan coffee = $11/lb

Cost of the other coffee = $5/lb

Desired cost of the blend = $8/lb

Total weight of the blend = 6 pounds

To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:

\((x \times 11 + (6 - x) \times 5) / 6 = 8\)

In this equation, \((x \times 11)\) represents the cost of the Guatemalan coffee in the blend, and\(((6 - x) \times 5)\) represents the cost of the other coffee in the blend.

The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.

Now, let's solve the equation for x:

(11x + 30 - 5x) / 6 = 8

6x + 30 = 48

6x = 48 - 30

6x = 18

x = 18/6

x = 3

Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.

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Answer:

$40.00 is the answer

Step-by-step explanation:

also can you mark me as a brainlist if you get a chance

Answer: $40.00

Step-by-step explanation:

12 is 30% of 40

Answer:

The answer is "Option b"

Step-by-step explanation:

In Model 1:

\(\to SSR = 11600 \times 2 = 23200\\\\\to SST = 23200 + 37200 = 60400\\\\\to R^2 = \frac{23200}{60400}\)

         \(= 0.384106\)

In Model 2:

\(\to SSR = 11650 \times 4 = 46600\\\\\to SST = 46600 + 13800 = 60400\\\\\to R^2 = \frac{46600}{60400} \\\\\)

         \(= 0.771523\)

The Additional variation value:

\(= 0.771523 - 0.384106 \\\\ = 38.74\%\)

Answer: - 3/8

Step-by-step explanation:

The intersection of two regular pentagons can be a square. Option D

A pentagon is known as a geometrical shape with five sides and five angles.

The sum of all the interior angles for a regular pentagon is 540 degrees.

Properties of a pentagon:

Pentagons intersect to form a kite- shaped region which could also be an equilateral or square

Thus, the intersection of two regular pentagons can be a square. Option D

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Yes, because for each input there is exactly one output. Therefore, the relation represented by the mapping diagram is a function.

To determine if the relation represented by the given mapping diagram is a function, we need to check if each input (x value) has exactly one output (y value) associated with it.

From the given mapping diagram, we can see that:

The input value -3 is associated with the output value 0.

The input value -1 is associated with the output value 2.

The input value 1 is associated with the output value 0.

The input value 3 is associated with the output value 2.

The input value 5 is associated with the output value 5.

As we can see, each input value has exactly one output value associated with it. Therefore, the relation represented by the mapping diagram is a function.

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