Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection. Which function f represents the relationship between the number of stamps (s) and the number of weeks (w)?
A.
s = f(w) = 12 + 4w
B.
w = f(s) = 12s + 4
C.
s = f(w) = 12 + 4s
D.
w = f(s) = 12w + s
E.
s = f(w) = s – 12

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

Velocity is distance divided by time, that is:

[tex]v = \frac{d}[t}[/tex]

Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:

[tex]v - v_w = \frac{2520}{4}[/tex]

[tex]v - v_w = 630[/tex]

[tex]v = 630 + v_w[/tex]

Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:

[tex]v + v_w = \frac{9450}{9}[/tex]

[tex]v + v_w = 1050[/tex]

[tex]v = 1050 - v_w[/tex]

Hence, solving for the wind's speed:

[tex]630 + v_w = 1050 - v_w[/tex]

[tex]2v_w = 420[/tex]

[tex]v_w = \frac{420}{2}[/tex]

[tex]v_w = 210[/tex]

For the plane, we have that:

v = 1050 - 210 = 840.

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A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,

x - y =1300

x = 1300 + y

Also,  at the end of the year the total interest from the two investments was $1270. Therefore, we can write,

0.13x + 0.07y = 1270

Substitute the value of x from the above,

0.13(1300 + y) + 0.07y = 1270

169 + 0.13y + 0.07y = 1270

0.20y = 1101

y = 5505

substitute the value of y in the first equation,

x - y = 1300

x = 6805

Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.

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Answer:

(-4, -5)

Step-by-step explanation:

-3x + 4y = -8

+

3x + y = -17

= 5y = -25 = y = -5

-3x + 4(-5) = -8

-3x - 20 = -8

-3x = 12

x = -4

The length QT is 36 units

The attached image represents the missing information in the question

From the image, we have:

RQ =QT

Substitute known values

5x + 1 = 3x + 15

Evaluate the like terms

2x = 14

Divide by 2

x = 7

Substitute x = 7 in QT = 3x + 15

QT = 3 * 7 + 15

Evaluate

QT = 36

Hence, the length QT is 36 units

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Using the Factor Theorem, the polynomials are given as follows:

1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]

2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Item a:

The parameters are:

[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]

Item b:

The roots are:

[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

Item 3:

The roots are:

[tex]x_1 = x_2 = 3, x_3 = -2[/tex]

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

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Answer:

Step-by-step explanation:

The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]

Domain of a function refers to the values or range of input values of a function for which the function exists in real.

In this problem the given function is

[tex]y=\sqrt{(x+6)}-7[/tex]

Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.

So, for existence of function it is must to

[tex]x+6\geq0[/tex]

[tex]x\geq-6[/tex]

Hence the domain of the given function is given by [tex]x\geq-6[/tex]

Hence the correct option is (B).

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Answer:

x

Step-by-step explanation:

[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]

Answer:

There were 42 fewer students who chose Football than Hockey.

Step-by-step explanation:

Fraction of students who chose Hockey

= 1 - [tex]\frac{1}{6}[/tex] - [tex]\frac{1}{3}[/tex]

= [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] units = 21

 1 unit = 42

No. of students who chose Football

= 2 units ([tex]\frac{2}{6}[/tex])

= 84 students

No. of students who chose Hockey

= 3 units ([tex]\frac{3}{6}[/tex])

= 126 students

Difference between no. of students who chose Football and Hockey

= 126 - 84

= 42 students

∴There were 42 fewer students who chose Football than Hockey.

Answer:

y^-1= x +8

Step-by-step explanation:

this may be helpful for you

Answer:

Perimeter = 2(l + b)

= 2(x + 5x³ + 4 - x²)

= 2x + 10x³ + 8 - 2x²

= 10x³ - 2x² + 2x + 8

Hence, ur answer is the first option.

Answer:

A.

Step-by-step explanation:

L = x

W = 5x³ + 4 - x²

P = 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

P(x) 10x³ - 2x² + 2x + 8

L = x

W = 5x³ + 4 - x²

P= 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

= P(x) 10x³ - 2x² + 2x + 8

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

In this problem, the function is given by:

y = 2x² + 25x + 3.

Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

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Answer:

6.25, -75.13

Step-by-step explanation:

it just is

Answer:

Look down my answer↓:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function

Answer: 59

Step-by-step explanation:

The measure of an arc is equal to the measure of the central angle intercepted by it.

The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

The regression equation is given as;

y = 7.36x - 14,354.33

In 2008, the value of x is

x = 2008

So, we have:

y = 7.36 * 2008 - 14,354.33

Evaluate

y = 424.55

Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

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The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000.

We have given that,

The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.

The regression equation is given as

y = 7.36x - 14,354.33

In 2008, the value of x is

x = 2008

So, we have y = 7.36 * 2008 - 14,354.33

Evaluate y = 424.55

Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

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Answer:

A, D, E

Explanation:

It's right on edge lol

Answer:

1. F

2. F

3. T

4. F

5. F

6. T

7. T

8. F

9. F

10. T

Step-by-step explanation:

1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.

2. They do not lie on the same line.

3. Points A, B, C, D all lie in the same plane therefore making them coplanar.

4. Points X, Y do not lie in the same plane as A, B.

5. Point X does not lie in the same plane as C, D, B

6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.

7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.

8. Plane AXY cannot be defined as point X and Y are not in a plane.

9. Lines AB and CD cannot both be in a different plane.

10. Both rays sum up to equal Line XY.

Answer:

Step by step explanation:

Given that,

[tex]f(x) = {x}^{2} [/tex]

[tex]g(x) = x - 1[/tex]

Solution:

Solving for (f•g)(x):

[tex] = f(x) \cdot g(x)[/tex]

Now substitute the given values.

[tex] = x {}^{2} \cdot(x - 1)[/tex]

[tex] = x {}^{2} (x - 1)[/tex]

Apply distributive property:

[tex] = (x ^{2} \cdot x) - x {}^{2} \cdot 1[/tex]

Hence,f•g(x) will be [tex] x {}^{3} - x {}^{2}[/tex].

Answer:

$9

Step-by-step explanation:

Let, the price of pencils is x, and the price of rulers is y.

4x+2y=8.....(i)

2x+4y=10......(ii)

From eq(i),

2(2x+y)=8

2x+y=4

y=4-2x eq(iii)  .....put in eq(ii)

2x+4(4-2x)=10

2x+16-8x=10

-6x=10-16

x=-6/-6

x=1 put in eq (iii)

y=4-2(1)

y=2

Now, the price of 3 rulers and 3 pencils = 3x+3y=3(1)+3(2)

=9

Please give me brainlist.

The percentage change in G is 21 %

Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.

It is given that

G = ab

when a is increased by 10% the new a will be = 1.1 a

When b is increased by 10% the new b will be 1.1 b

So,

G' = 1.1a *1.1 b

G' = 1.21 ab

G' = 1.21

(G' - G)*100/G = (1.21-1)*100/1

The percentage change is 21 %

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A function assigns the values. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?

A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.

B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.

C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.

D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.

If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.

Hence, the correct option is D.

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Answer:

Important- not urgent

Step-by-step explanation:

The research paper is important but since Brandon has two weeks to decide it is not urgent.

The probability notation for the probability of choosing a green marble is P(G)

This is simply defined as the extent to which something is likely to occur.

The probability that an event will occur is given as the ratio of the number of favorable outcomes to the total number of outcomes.

Probability notation is a symbol used in indicating the probability of an occurring event. Since our focus is on the probability of obtaining a green marble, then the probability notation will be P(G). This is illustrated below:

P(G) = nG / nT

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Answer:One of the factors of the given expression is (2h + 1).

Step-by-step explanation:

ed

Answer:

C on edge 23

Step-by-step explanation:

because i said so

Answer:

6.871 decimeters

Step-by-step explanation:

687.1 square centimeters = 6.871 square decimeters

1 dm² = 100 cm²

Answer:

6.871

Step-by-step explanation:

calculator

Answer:

All its side lengths are equal

(and all the agle of 60°)

Step-by-step explanation:

What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .​

X = 6

Y = (-6)