Find all intersection points of the parabola y = x^2 and the circle with a radius √6 and center at (0,4).

The degree and the independent term of each of the following polynomials include the following;

Degree of P(x) is 4.

Independent term of P(x) is 7.

Degree of Q(x) is 3

Independent term of Q(x) is 1.

In Mathematics, a polynomial function simply refers to a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

Generally speaking, the degree of a polynomial function is sometimes referred to as an absolute degree and it is the greatest exponent (leading coefficient) of each of its term.

Additionally, the independent term is a number that isn't accompanied by any variable i.e it is a constant.

P(x) = 2x⁴ - 2x³ - 3x² + 7; degree = 4 and independent term = 7.

Q(x) = -x³ + 5x²-3x + 1; degree = 3 and independent term = 1.

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Complete Question:

Write the degree and the independent term of each of the following polynomials.

If the market requires a return of 15% on assets of this risk, the stock should be selling for $3.92.

We can calculate the stock price using the dividend discount model with the following formula: "Stock Price = Dividend / (Required Rate of Return - Dividend Growth Rate)".

Data:

Dividend =  $0.50

Increase its dividend by 2% per year.

The next dividend (D1) can be calculated as:

D1 = D0 x (1 + Dividend Growth Rate)

D1 = $0.50 x (1 + 0.02)

D1 = $0.51

Using these values, we can calculate the stock price as follows:

= $0.51 / (0.15 - 0.02)

= $0.51 / 0.13

= $3.92.

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Check the picture below.

Answer:

C.  ∠B ≅∠E

Step-by-step explanation:

Since ΔJAB ≅ ΔFED, their corresponding angles are congruent.

Therefore:

Given that m∠BJA = 52° and m∠EDF = 65°, then:

Therefore, m∠ABJ = 65°.

Interior angles in a triangle sum to 180°. Therefore:

⇒ m∠JAB + m∠BJA + m∠ABJ = 180°

⇒ m∠JAB + 52° + 65° = 180°

⇒ m∠JAB + 117° = 180°

⇒ m∠JAB = 63°

As m∠JAB = m∠FED, then m∠FED = 63°.

Since ΔJAB ≅ ΔFED, their corresponding sides are congruent.

Given that AB = 10 inches, then ED = 10 inches.

Therefore, the statement that is not true is:

Answer:

87.9646 millimeters.

Step-by-step explanation:

The circumference (C) of a circle is given by the formula:

C = πd

Where d is the diameter of the circle and π (pi) is a mathematical constant approximately equal to: 3.14159.

In this case, the diameter of the circle is given as 28 millimeters, so we can substitute this value into the formula to find the circumference:

C = πd = π(28 mm) = 87.9646 mm (rounded to 4 decimal places)

Therefore, the circumference of the circle is approximately 87.9646 millimeters.

The height of the rectangle is approximately 15.5 inches.

Let's call the height of the rectangle "h". We know that the width is 47 inches longer than the height, so the width can be expressed as "h + 47".

We can use the Pythagorean theorem to solve for the height. The Pythagorean theorem states that for a right triangle with legs of length "a" and "b" and hypotenuse of length "c", a^2 + b^2 = c^2.

In this case, we can consider the rectangle to be a right triangle, with the height as one leg, the width as the other leg, and the diagonal as the hypotenuse. So we can write:

h^2 + (h + 47)^2 = 65^2

Simplifying this equation gives:

2h^2 + 94h - 1476 = 0

We can solve for "h" using the quadratic formula:

h = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = 94, and c = -1476. Plugging these values into the quadratic formula gives:

h = (-94 ± sqrt(94^2 - 4(2)(-1476))) / 4

Simplifying this expression gives:

h = (-94 ± sqrt(10084)) / 4

h = (-94 ± 100.42) / 4

h = -48.6 or 15.42

Since the height of the rectangle cannot be negative, we can discard the negative solution. Therefore, the height of the rectangle is approximately 15.5 inches.

The concept Pythagoras theorem is used here to determine the length of the hypotenuse. It is an important theorem which explains the relation between the sides of a right angled triangle. The length of hypotenuse is

According to Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. The sides of this triangle have been named perpendicular base and hypotenuse.

Hypotenuse² = Perpendicular² + Base²

9² + 4² = 97

√97 = 9.84 cm

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Your question is incomplete most probably your full question was:

What is the length of the hypotenuse of the triangle when x=9 now and other side y = 4.

The price of each shirt she bought is $3.16

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

Store credit = $39.58

Items = 4

Amount spent = 52.22

The price of each shirt (x) she bought is calculated using

4 * x + Store credit = Amount spent

So, we have

4x + 39.58 = 52.22

Evaluate

x = 3.16

Hence, the price of each shirt she bought is 3.16

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The symbols that would complete the inequality for the range include the following:

-2 ≤ y < 5.

c is less than or equal to.

d is less than.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Based on the information provided about the graph of this function, we can reasonably infer and logically deduce that the domain and range can be written as follows:

Domain = {-4, 4} or -4 < x ≤ 4.

Range = {-2, 5} or -2 ≤ y < 5.

In conclusion, the missing symbols are "less than or equal" to and "less than" respectively.

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Complete Question:

Use the drop downs to determine which symbols would complete the inequality for the range. −2 ___(c)___ y ___(d)___ 5 (c) (d) On a coordinate plane, a graph of an image with a curve and straight line has 2 points. A closed circle appears at (negative 4, negative 2) and an open circle appears at (4, 5).

The amount of money that will be in the account after 10 years is: $1297.70

The formula for solving compound interest is expressed as:

A = P(1 + r/n)^(nt)

where:

A is Accrued amount (equal to principal added to interest)

P is the Principal amount

r is the annual nominal interest rate expressed as a decimal

R is termed as the annual nominal interest rate which is expressed as a percentage

r is equal to R/100

n is the number of the compounding periods per unit of the time

t is the time which is expressed in decimal years

We are given:

r = 0.0375

n = 2 times per year

t = 10 years

P = $895

Thus:

A = 895(1 + 0.0375/2)^(2 * 10)

A = $1297.70

Thus, that is the money that will be in the account after a period of 10 years

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The summation ∑₁¹²⁴(29a₁ - 13b₁)  = -30

Suppose that ∑₁¹²⁴a₁ = -10 and  ∑₁¹²⁴b₁ = -20. We desire to compute the following ∑₁¹²⁴(29a₁ - 13b₁), we proceed as follows.

So, the summation ∑₁¹²⁴(29a₁ - 13b₁)

Expanding the brackets, we have that

∑₁¹²⁴(29a₁ - 13b₁) = ∑₁¹²⁴29a₁ -  ∑₁¹²⁴13b₁)

= 29∑₁¹²⁴a₁ -  13∑₁¹²⁴b₁

Given that ∑₁¹²⁴a₁ = -10 and  ∑₁¹²⁴b₁ = -20.

So, substituting the values of the variables into the equation, we have that

∑₁¹²⁴(29a₁ - 13b₁) = 29∑₁¹²⁴a₁ -  13∑₁¹²⁴b₁

= 29(-10) - 13(-20)

= -290 + 260

= -30

So, ∑₁¹²⁴(29a₁ - 13b₁)  = -30

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Answer:   [1/5x-4+2y]+[2/5x+5-4y] simplifies to 3/5x - 2y + 1.

Step-by-step explanation:

To simplify the given expression, we need to combine like terms.

The like terms are the ones with the same variable parts.

Let's first simplify the expression inside the brackets separately:

[1/5x-4+2y] = 1/5x + 2y - 4

[2/5x+5-4y] = 2/5x - 4y + 5

Now, we can combine the simplified expressions:

[1/5x + 2y - 4] + [2/5x - 4y + 5]

= 1/5x + 2y - 4 + 2/5x - 4y + 5

= (1/5 + 2/5)x + (2y - 4y) - 4 + 5

= 3/5x - 2y + 1

Therefore, [1/5x-4+2y]+[2/5x+5-4y] simplifies to 3/5x - 2y + 1.

The function that is most likely increase exponentially is f(x). Because it eventually exceeds g(x)

To determine which function is most likely increasing exponentially, we need to compare the rate at which the two functions are increasing.

Looking at the table, we can see that as x increases, f(x) increases at a faster rate than g(x). In fact, f(x) eventually exceeds g(x) for x values greater than or equal to 5. This suggests that f(x) is increasing at an exponential rate.

On the other hand, g(x) is increasing at a much slower rate than f(x). Although g(x) is also increasing, it does not appear to be increasing exponentially. In fact, g(x) will never exceed f(x), because f(x) grows at a faster rate.

Therefore, the function that is most likely increase exponentially is f(x).

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The factorized form of the quadratic equation is:

4(x - 3)*(x + 0.25) = 0

The quadratic equation is 4x² - 11x -3 = 0

To do that, we need to find the zeros, so let's use the quadratic formula:

[tex]x = \frac{11 \pm \sqrt{(-11)^2 - 4*4*-3} }{2*4} \\\\x = \frac{11 \pm 13 }{8}[/tex]

Then the two roots are:

x = (11 + 13)/8 = 3

x = (11 - 13)/8 = -2/8 = -0.25

Then the factorized form is:

4(x - 3)*(x + 0.25) = 0

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Answer:

Step-by-step explanation:

hello :

6x  the greatest common factor from the polynomial.

 12x² + 30x

The volume of the figure created is 98 cubic units.

Given that:

A triangle with coordinates (0,0), (0, 7), and (6,0) is rotated 360 degrees about the x-axis.

A cone is formed when a triangle rotates. Then the volume created is calculated as,

V = 1/3 x 7² x 6

V = 49 x 2

V = 98 cubic units

The volume is 98 cubic units.

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Answer:

Ohe repainted the right strap.

The choice between Hometown National Bank and Freedom Bank depends on usage. Should you use out-of-network ATMs with regularity, the former may be favored due to its lower ATM charge. Otherwise, if these visits are sporadic, the latter might reign superior in regards to its maintenance fee.

Still, no financial institution can be deemed unequivocally better. Additional variables influencing this decision could include the frequency of out-of-network ATM travel, one's account balance, as well as any supplementary services each establishment may supply.

In order to safeguard yourself against fees, consider utilizing in-network ATMs, mobile banking, or taking advantage of cashback options offered when making purchases from retailers.

By calculating total fees for each bank, estimating monthly out-of-network ATM activity, and factoring in other services and one's individual preferences, it is possible to determine which establishment best suits your needs.

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Using function notation on the table, we can say that:

f(3) = -2

When f(x) = -5, x = 4

Function notation is defined as a way of expressing a relationship between two variables.

From the given table, we see that:

when x = -6, f(x) = 8

when x = 7, f(x) = 3

when x = 4, f(x) = -5

when x = 3, f(x) = -2

when x = -5, f(x) = 12

Thus, we can say that:

f(3) = -2

When f(x) = -5, x = 4

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Answer:

If the shoes are 20% off, then the sale price of the shoes will be:

67 - 0.20 * 67 = 67 - 13.40 = 53.60

So the sale price of the shoes is $53.60.

If the sales tax is 5%, then the tax on the shoes will be:

0.05 * 53.60 = 2.68

So the tax on the shoes is $2.68.

To find the total price of the shoes including tax, we need to add the sale price of the shoes and the tax:

53.60 + 2.68 = 56.28

Therefore, the total price of the shoes, including tax, is $56.28.

Answer:

$56.28

Step-by-step explanation:

1. Find the shoes' sale price.

The shoes are 20% off. We will find the new price by first finding 20% of $67.

An easy way to do it:

10% of 67 = 6.7
20% of 67 = 13.4

to double the percentage of the first equation, double the answer.

Now that we know 20% of 67 we can take away 20% from it:

67 - 13.4 =53.6

Money uses 2 decimal points so we will add a 0 at the end of the result.

The price of the shoes with only the sale is $53.60.

2. Add sales tax

First find out 5% of $53.60.

An easy way to do it:

10% of 53.60 = 5.360

5% of 53.60 = 2.68

to half the percentage of the first equation, half the answer.

Now that we know the price of the tax we can add it to our shoe price. With the sale the shoe costs $53.60 and we will add our tax:

53.60 + 2.68 = 56.28

Add your units:

Answer:2^4=4x-4 would be the answer

Step-by-step explanation: You would exponentiate both sides

Answer:

The local minima are 1 and -2

The values at which the function f has a local minimum are -3 and 4

Step-by-step explanation:

Main Concepts:

Brief side-discussion about local vs global minimums

Concept 1. What a Local minimum is

Concept 2. Where a local minimum is at

Brief side-discussion:  a Local minimum  vs  Absolute or Global minimum

A local minimum is the height of any "low" point on a continuous section of the function where all of the points "near" it are higher.

In contrast, an Absolute minimum (sometimes called a "global minimum"), is the lowest height the function ever reaches.

Concept 1. What a Local minimum is

This problem is asking about local minimums, of which there are two:

"The Local minimum value" itself IS the height of the point (the "y"-value).

The point on the left has coordinates (-3,1), and the point on the right has coordinates (4,-2).

So, the local minima are 1 and -2

Concept 2. Where a local minimum is at

The minima are different from "The values AT which the function has a local minimum" which is the input (or, "x"-value) that will produce that output when put into the function.

So, the values at which the function f has a local minimum are -3 and 4

The answer to the given energy is  5096327.2 J

Remember that Joule is a derived unit of energy which is equal to the energy transferred to an object when a force of one newton acts on that object in the direction of its motion through a distance of one meter

m = 1 tonelada = 1000 kg

h = 500 m

v = 50 km / hr = 13.88 m / s

9 = 10 m / s²

Ep = ?

Ec = ?

The given formula Formula

Ep = m g h = 1000 kg X 10 m / s² X 500 m =  5000000 Joule

Ec = m V² / 2 = 1000 kg X (13.88 m / s)² / 2 = 96327.2 Joule

Et = Ep  +   Ec  =  5000000 J    +   96327.2 J = 5096327.2 J

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Answer:

20%  (D)

Step-by-step explanation:

The numbers as an integer or not are:

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

7/10 - yes or no

-6/1 - yes or no

-30.18 - yes or no

7 - yes or no

-76 - yes or no

integers are numbers without decimal point (including 0)

Using the above as a guide, we have the following:

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12π inches is the circumference of the given circle with a diameter of 12 inches.

The circumference of a circle can be found using the formula C = π*d, where d is the diameter of the circle.

If the diameter of the circle is 12 inches, then the circumference is:

C = π* d

C = π * 12 inches

C = 12π inches

So, the circumference of the circle in terms of π is 12π inches.

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The tires of Julián's bicycle must take 620 turns to go from his house to school.

The circumference of the tire can be calculated using the formula C = πd, where d is the diameter of the tire.

C = πd = π(45cm) ≈ 141.37cm

To find out how many turns the tires must take, we need to divide the total distance by the distance covered by one revolution of the tire:

Number of turns = Distance / Circumference

Number of turns = 877m / (141.37cm/100cm/1m)

Number of turns ≈ 620.09

Therefore, the tires of Julián's bicycle must take approximately 620 turns to go from his house to school.

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The inequality that represents the situation is w ≥ 32.

To graph the inequality, we first need to solve it for w:

3/4w ≤ 24

We can isolate w by multiplying both sides by 4/3 (which is the reciprocal of 3/4), remembering to reverse the inequality because we're multiplying by a negative number:

w ≥ 24 × 4/3

w ≥ 32

So the solution to the inequality is w ≥ 32.

To graph this, we draw a number line and put a closed circle at 32 (because the inequality includes "equal to"), and shade to the right of 32 to represent all the values that satisfy the inequality given in the attached image.

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Breanna and Qasim must contribute $22,583.39 per year for eight years to have enough money to pay for their daughter's university education.

To determine the yearly contribution required for Breanna and Qasim, we need to use the present value formula for an annuity.

The formula is:

PV = C * ((1 - (1 + r)⁻ⁿ) / r)

Where PV is the present value of the annuity, C is the annual contribution, r is the annual interest rate, and n is the number of years.

First, we need to calculate the present value of the contributions that Breanna and Qasim make for the first eight years. We can use the formula:

PV = C * ((1 - (1 + r)⁻ⁿ) / r)

Where C is the annual contribution, r is the annual interest rate, n is the number of years, and PV is the present value of the contributions.

We know that the annual contribution is the same for each of the eight years, so we can simplify the formula to:

PV = C * (((1 - (1 + r)⁻ⁿ) / r))

The present value of the contributions is equal to the future value of the withdrawals five years after the last contribution. We can use the future value formula for an annuity to calculate this:

FV = R * ((1 + r)ⁿ - 1) / r

Where FV is the future value, R is the annual withdrawal, r is the annual interest rate, and n is the number of years.

We know that the future value of the withdrawals is $51,100 per year, the interest rate is 4%, and the number of years is 5.

FV = 51,100 * ((1 + 0.04)⁵ - 1) / 0.04 = $246,387.19

This is the present value of the contributions that Breanna and Qasim make over the first eight years. We can now solve for the annual contribution required using the present value formula:

PV = C * (((1 - (1 + r)⁻ⁿ) / r))

$246,387.19 = C * (((1 - (1 + 0.04)⁻⁸) / 0.04))

C = $22,583.39

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there are 120 different ways a sequence of 10 coin flips can consist of exactly 3 heads and the rest tails.

To solve this problem, we can use the formula for combinations. The number of ways to choose k items from a set of n items is given by the formula n choose k, which is written as C(n,k) or sometimes as nCk.

In this case, we want to choose 3 heads from a set of 10 coin flips. The number of ways to do this is C(10,3) = 120.

Once we have chosen the 3 heads, the remaining 7 flips must all be tails. There is only one way to arrange 7 tails, since they are all the same.

Therefore, the total number of sequences that consist of exactly 3 heads and the rest tails is 120.

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