Find the equation of the line below… Please I really need help! :)

Find The Equation Of The Line Below Please I Really Need Help! :)

Answers

Answer 1
y = mx + c

m = y/x

m = - 2/1
= -2

y = -2 + 9


Related Questions

factor tree 50 and 75 math

Answers

Answer:

2 x 25 (50)

3 x 25 (75)

Step-by-step explanation:

Which statement best describes sqrt 125

Answers

Answer:

11.18

The square root of 125 is 11.18.

Hope this helps have a great day! ♣

2. Jaden ordered 3 sodas for $1.08 each, 2 hamburgers for $2.30 each, and 1
large fry for $4.25. Write an expression you can use to calculate the total
cost for the order. Use the variables s, h, and fas needed.
Answers:
1: 1.08s+2h+4.25f
2: 6f
3: 3s+2h+1f
4:7.63f

Answers

Answer:

It’s the first one because the letters or variables represent how many of each Is worth so you could calculate these by using this equation .

The expression that can be used to calculate the total cost for Jaden's order is 3s + 2h + 1f

Here's an explanation of each variable in the expression:

s represents the cost of each soda, which is $1.08.

h represents the cost of each hamburger, which is $2.30.

f represents the cost of the large fry, which is $4.25.

To calculate the total cost, we multiply the cost of each item by the quantity and sum them up:

3s represents the total cost of 3 sodas ($1.08 each)

2h represents the total cost of 2 hamburgers ($2.30 each)

1f represents the cost of 1 large fry ($4.25)

By adding these three terms together, we get the total cost for Jaden's order.

Therefore, the expression 3s + 2h + 1f correctly represents the total cost for the order.

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A student purchased groceries at the following prices: $1.01,$3.46,$5.84, and $7.38. What was the average price (in dollars)? Round your answer to the nearest cent. QuEST10N 10 : The formula for wimple interest is I=Prt, where I= interest, Pa peincipal, rw rate, and f= time. Which of the following would be an equivalent formula rearranged for rate? If = t divided by P I None of the options are correct. r=1 divided by P t r=P divided by t1 outsTion11 The sum of three numbers is 170 . If the first number is 50 and the third number is twice the second number, what is the socond number?

Answers

Step 1: The average price is $4.17.

Step 2: To calculate the average price, we need to find the sum of all the prices and divide it by the total number of items. In this case, the student purchased groceries at the prices of $1.01, $3.46, $5.84, and $7.38.

Summing up these prices, we get $1.01 + $3.46 + $5.84 + $7.38 = $17.69.

Since there are four prices, we divide the sum by 4 to find the average price: $17.69 / 4 = $4.4225.

Rounding this to the nearest cent, the average price is $4.42.

Step 3: The average price of the groceries purchased by the student is $4.17. This is calculated by summing up the individual prices and dividing the sum by the total number of items. The average price is commonly used as a measure to understand the typical or representative value of a set of prices.

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Write equation line that passes through (2,2) and is parallel to line y=3x+9

An equation of parallel line is y=___

Answers

Answer:

Step-by-step explanation:

The slope is in the given line. It is the number in front of the x which is 3.

So far what you have is

y = 3x + b

Now use the point to find b

x = 2

y = 2

Substitute

y = 3*2 + b

2 = 6 + b

2 - 6 = b

b = - 4

y = 3x - 4

Please help no need for step by step just the answer will help

Please help no need for step by step just the answer will help

Answers

Answer:

I think it is 5, -2.5

Step-by-step explanation:

use this https://www.meracalculator.com/graphic/midpoint.php

show that 21^n, n €N can never ends with 0,2,4,6 and 8​

Answers

Answer:

Step-by-step explanation:

\(21 ^n = (3 \times 7)^n\)

21 has no 2 in it's prime factorization. So it can never end in 0, 2 , 4 , 6 , 8.

 OR

Odd number raise to any number is always odd, Which does not include 2, 4, 6 , 8.

So \(21^n\) does not end with 0, 2, 4 , 6 , 8.

how any units are in math

Answers

Answer:

Math is a broad field that encompasses several branches, each with its own units of measurement. Some examples of units in math include:

In geometry:- Units of length, such as meters, centimeters, and inches

Units of area, such as square meters, square centimeters, and square feet

Units of volume, such as cubic meters, cubic centimeters, and cubic feet- Units of weight or mass, such as kilograms, grams, and pounds - Units of time, such as seconds, minutes, and hours

Units of temperature, such as Celsius and

Fahrenheit

Units of angle measurement, such as degrees and radians

Units of speed or velocity, such as meters per second or miles per hour

Units of frequency, such as Hertz or cycles per second

Units of energy or work, such as joules, calories, and foot-pounds

Units of power, such as watts and horsepower

These are just a few examples of the many units used in math. The type of unit used depends on the specific problem or application.

HOPE IT HELPS

PLEASE MARK ❣️‼️ ME AS BRAINLIEST .

Question should guns be allowed to be at school for example can a security guard have a gun?

Answers

Answer: First secutitys at my school dont even have nothing but a walkie talkies in there hands but I will say this we have cops walking around inside of our school and there all armed up because obvisouly their cops so i would think not security should not have a fire arm because what happens if a old lady a securrityguard she cant move fast so I think not they would have to deal it with by hand and there walkie talkies.

Step-by-step explanation:

Answer:no because they might be part of a crime and shoot up the school like boom bang bin bot pow and 500 people drop dead like me in the bed room.

Step-by-step explanation:

Write a complete two-column proof for following information.
B
C
Given: AB = 3y - 1, BC = 7y, AC = 29
Prove: AB = 8

Answers

Hence proved that triangle   AB = 3(3) - 1 = 9 - 1 = 8.

What is triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

Given that,

AB + AC = AC

3y - 1 + 7y = 29

10y = 29 + 1 = 30

y = 30/10 = 3

Therefore, AB = 3(3) - 1 = 9 - 1 = 8.

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(1 point) 5 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible? your answer is :

Answers

There are 7776 different outcomes possible when 5 dice of different colors are rolled.

What is probability?

The ratio of favorable outcomes to the total number of outcomes of an event is said to be the probability of that event.

P(E) = n(E)/n(S)

Calculation:

It is given that, there are 5 dice with different colors.

There are 6 outcomes for each die rolling. That is the number coming up on each die when it is rolled (1, 2, 3, 4, 5, 6).

So, for five dice when rolled, the number of possible outcomes is

n = 6 × 6 × 6 × 6 × 6

⇒ n = 7776

Therefore, 7776 different outcomes are possible.

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Suppose two equally probable one-dimensional densities are of the form: p(x|ωi)∝e-|x-ai|/bi for i= 1,2 and b >0.
(a) Write an analytic expression for each density, that is, normalize each function for arbitrary ai, and positive bi.
(b) Calculate the likelihood ratio p(x|ω1)/p(x|ω2) as a function of your four variables.

Answers

The likelihood ratio can be expressed as:

p(x|ω1)/p(x|ω2) =

(b2/b1) * e^(-(x - a1) + (x - a2)/(b1*b2)) if x >= (a1+a2)/2

(b2/b1) * e^((x - a1) - (x

To normalize each density function, we need to find the appropriate normalization constants. Let's consider each density function separately:

For p(x|ω1):

p(x|ω1) ∝ e^(-|x-a1|/b1)

To normalize this function, we need to find the constant C1 such that the integral of p(x|ω1) over the entire range is equal to 1:

1 = ∫ p(x|ω1) dx

= C1 ∫ e^(-|x-a1|/b1) dx

Since the integral involves an absolute value, we can split it into two parts:

1 = C1 ∫[a1-∞] e^(-(x-a1)/b1) dx + C1 ∫[a1+∞] e^(-(a1-x)/b1) dx

Simplifying each integral separately:

1 = C1 ∫[a1-∞] e^(-x/b1) dx + C1 ∫[a1+∞] e^(-x/b1) dx

To evaluate these integrals, we can use the fact that the integral of e^(-x/b) dx from -∞ to ∞ is equal to 2b:

1 = C1 (2b1)

Therefore, the normalization constant C1 is 1/(2b1), and the normalized density function p(x|ω1) is:

p(x|ω1) = (1/(2b1)) * e^(-|x-a1|/b1)

Similarly, for p(x|ω2), we have:

p(x|ω2) ∝ e^(-|x-a2|/b2)

To normalize this function, we need to find the constant C2 such that the integral of p(x|ω2) over the entire range is equal to 1:

1 = C2 ∫ p(x|ω2) dx

= C2 ∫ e^(-|x-a2|/b2) dx

Following the same steps as before, we find that the normalization constant C2 is 1/(2b2), and the normalized density function p(x|ω2) is:

p(x|ω2) = (1/(2b2)) * e^(-|x-a2|/b2)

(b) The likelihood ratio p(x|ω1)/p(x|ω2) can be calculated as follows:

p(x|ω1)/p(x|ω2) = [(1/(2b1)) * e^(-|x-a1|/b1)] / [(1/(2b2)) * e^(-|x-a2|/b2)]

Simplifying:

p(x|ω1)/p(x|ω2) = (b2/b1) * e^((|x-a1| - |x-a2|)/(b1*b2))

We can further simplify the exponent term by considering the absolute value difference:

|x-a1| - |x-a2| =

(x - a1) + (x - a2) if x >= (a1+a2)/2

(x - a1) - (x - a2) if x < (a1+a2)/2

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A circle has a diameter of 18. The sector has a central angle of 30 degrees. What is the area of the sector?

Answers

Answer:

21.21

Step-by-step explanation:

Area of a circle is A = π r^2

Variables:

r = 18/2 = 9

θ = 30 deg

Find the area:

A = π r^2

A = π 9^2

A = 254.47

Find the area of the sector:

θ/360 * A

= 30/360 * 254.47

= 21.21

Kayl is going to invest into an account paying an interest rate of 2. 9% compounded monthly how much would Kayla need to invest to the nearest cent for the value of her account to reach 42000 in 6 years

Answers

For the given interest rate of 2.9% compounded monthly ,  principal amount need to invest by Kayla to get the value of her account $42000 in 6 years is equal to $35299.88.

As given in the question,

Let us consider principal amount 'P' invested by Kayla at the interest rate 'r' 2.9% compounded monthly .

Amount 'A' in her account received by Kayla = $42,000

Time period 't' = 6years

Compounded monthly 'n' = 12

Formula used to find principal amount compounded monthly:

A = P ( 1 + (r/12) )^nt

Substitute the value in the formula we get,

42,000 = P [ 1 + (2.9/ (100×12)) ]^6×12

⇒ 42,000 = P [ 1 + (2.9/1200)]^72

⇒ 42,000 = P [ (1200 + 2.9)/1200]^72

⇒ 42,000 = P [ 1202.9 /1200]^72

⇒ P = (42,000 × 1200^72) / 1202.9^72

⇒ P = $ 35299.88

Therefore, for the given interest rate of 2.9% compounded monthly ,  principal amount need to invest by Kayla to get the value of her account $42000 in 6 years is equal to $35299.88.

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How are the graphs of the functions f(x) = StartRoot 16 EndRoot Superscript x and g(x) = RootIndex 3 StartRoot 64 EndRoot Superscript xrelated?

The functions f(x) and g(x) are equivalent.

The function g(x) increases at a faster rate.

The function g(x) has a greater initial value.

The function g(x) decreases at a faster rate.

Answers

Answer:

A. The functions f(x) and g(x) are equivalent.

Step-by-step explanation:

Given  functions:

f(x) = √16 = √4² = 4g(x) = ∛64 = ∛4³ = 4

As we see both function are same once roots cleared.

Correct choice is A

Step-by-step explanation:

f(x) = \(\sqrt{16} = 4\) g(x) = \(\sqrt[3]{64} = 4\) f(x) = g(x) ==> 4 = 4

Soo, answer is option (A.)

Estimate σA and σB using the loan allocation deviation formula.
A. σ(A) = 12.25% ; σ(B) = 14.14%
B. σ(A) = 17.32% ; σ(B) = 20.0%
C. σ(A) = 16.33% ; σ(B) = 14.14%
D. σ(A) = 14.14% ; σ(B) = 16.33%

Answers

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Sorry if the image is blurry! Please help!

Sorry if the image is blurry! Please help!

Answers

Answer:

A. 244.93 ft sq

Step-by-step explanation: radius= 7 pi= 3.14 area for triangle= 168 area for semi-circle = 76.93.

how i got it:

area of semicircle 7 x 7 =49  49 x 3.14 = 153.86  153.86 divded by 2 = 76.93

 area of triangle: 14 x 24 = 336 336 divded by 2 = 168  168 + 76.93 = 244.93

Triangle OPQ is similar to triangle RST. find the neasure of side ST. Round to the nearest tenth if necessary

Answers

By definition, when two figures are similar, their corresponding angles are congruent (this means that they have equal measure) and the ratios of the lengths of their corresponding sides are the same.

In this case you know that the triangles shown in the picture are similar, therefore, you can set up the following proportion:

\(\frac{OP}{RS}=\frac{PQ}{ST}\)

You can identify that:

\(\begin{gathered} OP=37 \\ RS=7 \\ PQ=48 \end{gathered}\)

Therefore, you can substitute values into the proportion:

\(\frac{37}{7}=\frac{48}{ST}\)

Now you have to solve for ST:

\(\begin{gathered} (ST)(\frac{37}{7})=48 \\ \\ ST=(48)(\frac{7}{37}) \\ \\ ST\approx9.1 \end{gathered}\)

The answer is:

\(ST\approx9.1\)

im not sure of my answer so can anyone help me out on this

im not sure of my answer so can anyone help me out on this

Answers

question a: 3cm
question b: 8cm
question c: 12cm

(could be wrong)

Answer:

6 cm

13 cm

14 cm

Step-by-step explanation:

a) length of AC

= 3² + 5²

= √36

= 6 cm

b) length of BG

= 5 cm + 8 cm

= 13 cm

c) length of BF

= 6 cm + 8 cm

= 14 cm

Use the Wronskian to show that the functions y1 = e^6x and y2 = e^2x are linearly independent. Wronskian = det[] = These functions are linearly independent because the Wronskian isfor all x.

Answers

The functions y1 = e^(6x) and y2 = e^(2x) are linearly independent because the Wronskian, which is the determinant of the matrix formed by their derivatives, is nonzero for all x.

To determine the linear independence of the functions y1 and y2, we can compute their Wronskian, denoted as W(y1, y2), which is defined as:

W(y1, y2) = det([y1, y2; y1', y2']),

where y1' and y2' represent the derivatives of y1 and y2, respectively.

In this case, we have y1 = e^(6x) and y2 = e^(2x). Taking their derivatives, we have y1' = 6e^(6x) and y2' = 2e^(2x).

Substituting these values into the Wronskian formula, we have:

W(y1, y2) = det([e^(6x), e^(2x); 6e^(6x), 2e^(2x)]).

Evaluating the determinant, we get:

W(y1, y2) = 2e^(8x) - 6e^(8x) = -4e^(8x).

Since the Wronskian, -4e^(8x), is nonzero for all x, we can conclude that the functions y1 = e^(6x) and y2 = e^(2x) are linearly independent.

Therefore, the linear independence of these functions is demonstrated by the fact that their Wronskian is nonzero for all x.

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What is the value of x

What is the value of x

Answers

Answer:

The value of x is 138

98 x 63 – 32 x 69 =

Answers

Answer:

3966

Step-by-step explanation:

Use order of operations to solve this problem:

ParenthesesExponentsMultiply (Left to right)Divide (Left to right)AdditionSubraction

In your case, there are no parentheses or exponents, so we can skip right the the multiply and divide step. The first multiplication is 98*63=6174. The next step is to do 32*69=2208. Then you minus 6174-2208=3966.

Hope this helps!

Find the point on the ellipse x^2 + 2y^2 + 2xy = 18 with the greatest x - coordinate.

Answers

The point on the ellipse \(x^2 + 2y^2 + 2xy = 18\) with the greatest x-coordinate is:

Point: (√(18/5), √(18/5))

To find the point on the ellipse \(x^2 + 2y^2 + 2xy = 18\) with the greatest x-coordinate, we need to maximize the value of x.

Let's start by rewriting the equation of the ellipse in a more convenient form:

\(x^2 + 2y^2 + 2xy = 18\)

Rearranging the terms, we have:

\(x^2 + 2xy + y^2 + y^2 = 18\)

Factoring the quadratic terms, we get:

\((x + y)^2 + y^2 = 18\)

Now, we can see that this equation represents an ellipse centered at the origin (0,0). To find the point on the ellipse with the greatest x-coordinate, we need to find the point where the sum (x + y) is maximum.

To achieve this, we need to determine the maximum value for (x + y). Since the ellipse is symmetric about the origin, the maximum value of (x + y) will occur when x and y have the same value.

Let's set x = y and substitute it into the equation:

(x + x)^2 + x^2 = 18

Simplifying further:

4x^2 + x^2 = 18

Combining like terms:

\(5x^2 = 18\)

Dividing both sides by 5:

\(x^2 = 18/5\)

Taking the square root of both sides:

x = ±√(18/5)

Since we are looking for the point with the greatest x-coordinate, we take the positive square root:

x = ±√(18/5))

Now, substitute this value of x back into the equation to find the corresponding y-coordinate:

√(18/5) + y = √(18/5) + y

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the point is (u - √18, √18), where u is the value that satisfies \(u^2 + y^2 = 18.\)

What is value?

In mathematics, a value refers to a numerical or symbolic quantity that represents a specific quantity or property. Values can be numbers, variables, constants, or expressions that have a definite or assigned meaning.

To find the point on the ellipse with the greatest x-coordinate, we need to maximize the value of x while satisfying the equation of the ellipse.

The equation of the ellipse is:

\(x^2 + 2y^2 + 2xy = 18\)

To simplify the equation, we can rewrite it as:

\(x^2 + 2xy + y^2 + y^2 = 18\\\\(x + y)^2 + y^2 = 18\)

Let's define a new variable u = x + y. Substituting this into the equation, we have:

\(u^2 + y^2 = 18\)

Now, we want to maximize the x-coordinate, which is equivalent to maximizing the value of u. Since u = x + y, we need to find the maximum value of u that satisfies the equation of the ellipse.

To find the maximum value of u, we can use calculus. Taking the derivative of \(u^2 + y^2 = 18\) with respect to y, we get:

2u + 2y(dy/dx) = 0

Since we are interested in the maximum value of u, we want dy/dx to be as small as possible. Setting dy/dx = 0, we have:

2u = 0

This implies that u = 0. Substituting u = 0 into the equation \(u^2 + y^2 = 18\), we get:

\(0^2 + y^2 = 18\\\\y^2 = 18\)

y = ±√18

Now, we can substitute the value of y into the equation u = x + y to find the corresponding x-coordinate.

For y = √18, we have:

u = x + √18

x = u - √18

For y = -√18, we have:

u = x - √18

x = u + √18

Since we want to maximize the x-coordinate, we need to choose the positive square root of 18. Therefore, the point on the ellipse with the greatest x-coordinate is given by:

x = u - √18

y = √18

Thus, the point is (u - √18, √18), where u is the value that satisfies\(u^2 + y^2 = 18.\)

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Suppose a small metal object, initially at a temperature of 40 degrees, is immersed in a room which is held at the constant temperature of 70 degrees. It takes 3 minutes for the temperature of the object to reach 55 degrees. Calculate the heat transfer coefficient r, i.e. the constant of proportionality in the differential equation that describes Newton's law of cooling.

Answers

The heat transfer coefficient, r, in the differential equation that describes Newton's law of cooling for this scenario is 5.

Newton's law of cooling states that the rate of change of temperature of an object is proportional to the temperature difference between the object and its surroundings. Mathematically, this can be expressed as dT/dt = -r(T - Ts), where dT/dt is the rate of change of temperature, T is the temperature of the object, Ts is the surrounding temperature, and r is the heat transfer coefficient.

In the given scenario, the object's temperature changes from 40 degrees to 55 degrees in 3 minutes when immersed in a room held at a constant temperature of 70 degrees. We can use this information to determine the heat transfer coefficient r.

Using the formula, we have (dT/dt) = -r(T - Ts). Plugging in the values, we have (55 - 40)/(3 minutes) = -r(55 - 70). Simplifying this expression, we get 15/3 = 15r, which implies r = (15/3) = 5.

Therefore, the heat transfer coefficient, r, in the differential equation that describes Newton's law of cooling for this scenario is 5.

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a rectangular swimming pool 50 ft long, 30 ft wide, and 8 ft deep is filled with water to a depth of 6 ft. use an integral to find the work required to pump all the water out over the top. (take as the density of water lb/ft. )

Answers

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

We have,

To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.

First, let's calculate the weight of the water in the pool.

The weight of an object is given by the formula:

Weight = mass x gravitational acceleration

Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.

The volume of the pool is given by the formula:

Volume = length x width x depth

Volume = 50 ft x 30 ft x 6 ft = 9000 ft³

Now, let's calculate the weight of the water:

Weight = density x volume x gravitational acceleration

Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb

To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.

The work required to pump the water out is given by the formula:

Work = weight x height

Work = 290,400 lb x 8 ft = 2,323,200 ft-lb

Therefore,

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

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Beeswax used in making candles is produced by honeybees produce 7 pounds of honey for each pound of wax they produce. How many pounds of honey is produced if 145 pounds of beeswax

Answers

Answer:

1,015

Step-by-step explanation:

7 pounds of honey equals 1 pound of wax

So if we have 145 pounds of was, we multiply 145 by 7

145x7= 1,015

How would you describe Melody's relationship with her mother? (1 point)
• Melody's mother is supportive, but sometimes indifferent.
They have mutual understanding, but not a close bond.
O Melody's mother is supportive at home and school.
O They have a close bond, but not much mutual understanding

Answers

Answer: commensalism

Step-by-step explanation:

Melody and her mother aren't hurting each other but also aren't of the same benefit

The relationship that Melody has with her mother is that They have a close bond, but not much mutual understanding.

What is meant by a Story?

A story is a fiction or a non fiction narrative which tells us about a series of events or verse, which is narrated in such a way that it takes the interest of the reader.

Most of the fictions convey a certain moral or idea that should be taken in to our life.

Given is a story of a little girl Melody and her mother.

We can clearly seen from the story that, Melody is five year old.

She has a pet named Ollie, which is a fish.

When the fish come out of the bowl by itself, Melody was scared and screamed for help.

But non one heard.

So as a method to rescue Ollie, she put the bowl upside down to save it.

When mother sees it, she misunderstood the situation.

So the relationship between Melody and mother is close bond, but not much mutual understanding.

Hence the correct answer is option D.

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Our physics club has $20$ members, among which we have 3 officers: President, Vice President, and Treasurer. However, one member, Alex, hates another member, Bob. How many ways can we fill the offices if Alex refuses to serve as an officer if Bob is also an officer

Answers

We can fill the offices in 7146 ways if Alex refuses to serve as an officer if Bob is also an officer.

Given that we have 20 members in a physics club, and among which 3 are officers: President, Vice President, and Treasurer. One of the members, Alex refuses to serve as an officer if Bob is also an officer. The problem is to find out how many ways we can fill the offices under these circumstances.

Let's say we start by filling the post of President. This post can be filled in 20 ways.

After we have filled the President's post, we move on to the Vice-President's post. This post can be filled in 19 ways, as there are only 19 people left to choose from. Finally, we fill the Treasurer's post, which can be done in 18 ways. Thus the total number of ways we can fill the offices is equal to:$$20 \times 19 \times 18 = 6840$$Therefore, we can fill the offices in 6840 ways if Alex refuses to serve as an officer if Bob is also an officer.

In the given question, we have been given that we have 20 members in a physics club. Out of the 20 members, 3 of them are officers. We are also given that Alex does not want to serve as an officer if Bob is also an officer. We are required to find out the number of ways we can fill the offices under these circumstances.So let's say we start by filling the post of President.

There are 20 members in the club, and hence 20 ways in which we can select the President. After we have filled the post of the President, we move on to the Vice-President's post. But here we have to keep in mind that Alex does not want to serve as an officer if Bob is also an officer. So, let's consider two cases:

Bob is not selected as the PresidentIn this case, Bob is available for selection as the Vice President. Therefore, we can select the Vice President in 19 ways. After this, we can select the Treasurer in 18 ways.

Hence the total number of ways in which we can select the officers when Bob is not selected as the President is equal to:$$20 \times 19 \times 18 = 6840$$.

Bob is selected as the President.In this case, Bob is not available for selection as the Vice President. Therefore, we can select the Vice President in 18 ways (as we can't select Bob). After this, we can select the Treasurer in 17 ways (as we can't select Bob and the Vice President). Hence the total number of ways in which we can select the officers when Bob is selected as the President is equal to:$$1 \times 18 \times 17 = 306$$.

Therefore, the total number of ways in which we can fill the offices when Alex refuses to serve as an officer if Bob is also an officer is equal to the sum of the two cases:$$6840 + 306 = 7146$$Thus, we can fill the offices in 7146 ways if Alex refuses to serve as an officer if Bob is also an officer.

We can fill the offices in 7146 ways if Alex refuses to serve as an officer if Bob is also an officer.

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if in 7 years, sam would be 2 times old as she was 3 years ago. what is sams present age?

Answers

Answer

Sam is 13 years old

Step-by-step explanation:

He is 13 years old.

13+7=20

13-3=10

10x2=20

Answer: 13

Step-by-step explanation:

We can represent this in an algebra equation

(x+7)=2(x-3)

(x+7)=2x-6

(x+7)=2x-6

-2x    -2x

-x+7=-6

-7       -7

-x= -13

/-1    /-1

x=13

Match the polynomial expression on the left with the simplified version on the right.
(y + 5)²
(y - 5)(y + 5)
A
2-10
²-25
²+25
²-10y-25
²+10y + 25
Pls answer quick

Match the polynomial expression on the left with the simplified version on the right.(y + 5)(y - 5)(y

Answers

The simplified version of first expression is  y² + 10y + 25 and  simplified version of second expression is  y²  – 25

The first polynomial expression on the left is (y + 5)²

= y² + 2×y×5 + 5² (using the formula (a + b)² = a² + 2ab + b²)

= y² + 10y + 25

The second polynomial expression on the left is (y + 5)(y – 5)

= y(y – 5) + 5(y – 5)

= y² – 5y + 5y – 25

= y²  – 25

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The complete question is given below :

The polynomial expression on the left is (y + 5)², and the simplified version on the right for this polynomial is y² + 10y + 25.

The polynomial expression on the left is (y – 5)(y + 5), and the simplified version on the right for this polynomial is y² – 25.

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