Which is the correct factorization for the Difference of Squares or a^(2)-b^(2) ?

Function Family: quadratic

Domain: all real numbers

x-int: (0,0) and (2,0)

y-int: (0,0)

The solution is, (x + 6) and (2x - 5) are the factors of polynomial

2x^2 + 7x - 30.

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

3x+2x-5, for example, is a polynomial.

A binomial is a two-term polynomial.

For instance, x²ˣ-2ˣ² and x⁶ˣ-6ˣ⁶ are both binomials.

here, we have,

given that,

2x^2 + 7x - 30 is the polynomial .

now, we have to factorize it.

so, we get,

2x2 + 7x - 30

2x2 + 12x - 5x - 30

2x( x + 6) - 5( x + 6)

so, we have,

(x + 6) and (2x - 5) are the factors.

Hence, The solution is, (x + 6) and (2x - 5) are the factors of polynomial

2x^2 + 7x - 30.

Know more about Polynomials here:

brainly.com/question/2833285

#SPJ1

The probability a firm will have a stock price of at least $40 is 0.1112. There should be 40.50 stock price have to be to put a firm in the top 10%.  The correct answer is e) None of the answers are correct.

(i) To find the probability that a firm will have a stock price of at least $40, we need to find the z-score for $40 and use the standard normal table to find the corresponding probability. The z-score is calculated as (x - μ)/σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

In this case, the z-score for $40 is (40 - 30)/8.20 = 1.22. Using the standard normal table, we find that the probability of a z-score less than 1.22 is 0.8888. Therefore, the probability of a stock price of at least $40 is 1 - 0.8888 = 0.1112.

(ii) To find the stock price that puts a firm in the top 10%, we need to find the z-score that corresponds to the 90th percentile in the standard normal table. The z-score for the 90th percentile is 1.28. We can then use the formula x = μ + zσ to find the stock price that corresponds to this z-score. In this case, the stock price is 30 + 1.28(8.20) = 40.50.

Therefore, the correct answer is (i) 0.1112 and (ii) 40.50.

Learn more about probability at https://brainly.com/question/15029568

#SPJ11

Uncle Moneybags can withdrawal approximately $583.67 per month.

To find out how much Uncle Moneybags can withdraw each month, we can use the formula for the future value of an annuity:

FV = PMT × [(1 + i)ⁿ - 1] / i

Where:
FV = future value
PMT = payment amount
i = interest rate per period
n = number of periods

In this case, we want to solve for PMT, so we can rearrange the formula to:

PMT = FV × i / [(1 + i)ⁿ - 1]

We know that FV = $500,000, i = 8% / 12 = 0.00667, and n = 25 × 12 = 300. Plugging these values into the formula, we get:

PMT = $500,000 × 0.00667 / [(1 + 0.00667)³⁰⁰ - 1]

PMT = $500,000 × 0.00667 / 5.7435

PMT = $583.67

Therefore, Uncle Moneybags can withdraw $583.67 each month for 25 years.

You can learn more about future value of an annuity at

https://brainly.com/question/14702616

#SPJ11

We have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

We can use the properties of logarithms to show that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

First, recall that the arithmetic mean of two numbers is half their sum:
arithmetic mean = (v + w)/2

And the geometric mean is the square root of their product:
geometric mean = √(v*w)

Now, let's take the log of the geometric mean:
log(geometric mean) = log(√(v*w))

Using the property of logarithms that log(a*b) = log(a) + log(b), we can expand the expression:
log(√(v*w)) = log(√v) + log(√w)

Using the property of logarithms that log(a^b) = b*log(a), we can simplify the expression:
log(√v) + log(√w) = (1/2)*log(v) + (1/2)*log(w)

Now, we can see that the log of the geometric mean is the arithmetic mean of the logs of the two numbers:
log(geometric mean) = (log(v) + log(w))/2

So, if we let p = log(v) and q = log(w), we can see that the log of the geometric mean of v and w is the arithmetic mean of p and q:
log(geometric mean) = (p + q)/2

Therefore, we have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

For more about arithmetic mean:

https://brainly.com/question/13000783

#SPJ11

The equation of the function g(x) in terms of the function f(x) has the equation of g(x) = -2f(x + 2) + 3

Given the graph of functions f(x) and g(x)

Where

y = f(x) -- the parent function

y = g(x) --- the transformed function (the dashed line)

The transformation of f(x) to g(x) is as follows

First, the graph of y = f(x) is moved 2 units to the left

This is represented as f(x + 2)

Next, the shifted graph of y = f(x) is reflected across the x-axis and then stretched vertically by a factor of 2.

This is represented as -2f(x + 2)

Lastly, the reflected and stretched graph is moved 3 units up

This is represented as -2f(x + 2) + 3

This means that

g(x) = -2f(x + 2) + 3

So, the function g(x) is g(x) = -2f(x + 2) + 3

Read more about transformation at

https://brainly.com/question/1548871

#SPJ1

Given that Line segment AB ║ LIne segment DC, and Line segment AD ║ Line segment BC,

1)  Note that ∠78° and ∠ABC are Supplementary Angles on the basis of angles on a straight line. Thus,

∠ABC = 180 - 78 = 102°

2) Note that ∠ABC  and ∠BCD are  Supplementary Angles on the basis of Adjacent Angles in a parallelogram.

Thus,
∠BCD = 180° - 102° = 78°

3) ∠CDA = 102° on the basis of Opposite angles of a parallelogram
4) ∠DAB = 78°  on the basis of Opposite angles of a parallelogram

Learn more about Line Segments at:

https://brainly.com/question/25727583

#SPJ1

The values of x and y that satisfy the given equation are x = 2 and y = 1.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Since a and b span R², any vector in R² can be expressed as a linear combination of a and b.

Let's call the coefficients of this linear combination c₁ and c₂ so that any vector v in R² can be expressed as:

v = c₁a + c₂b

Now let's use this fact to solve the given equation:

(2-x)a + b = ya + (x-3)b

We can rearrange this equation to get all the terms with an on one side and all the terms with b on the other side:

(2-x)a - ya = (3-x)b

Now we can write both sides of the equation as linear combinations of a and b:

(2-x)a - ya = 2a - xa - ya = (2-x)a - (x-2)a - ya = (2-x - x + 2)a - ya = (4 - 2x)a - ya

(3-x)b = 3b - xb = 3b - xb + 3b - 3b = (6 - x)b - 3b = (6 - x - 3)b = (3 - x)b

So now we have:

(4 - 2x)a - ya = (3 - x)b

Since a and b span R², we know that any vector in R² can be expressed as a linear combination of a and b. Therefore, we can write:

(4 - 2x)a - ya = c₁a + c₂b

(3 - x)b = c₁a + c₂b

Now we can set the coefficients of a and b equal to each other and solve for x and y:

4 - 2x = c₁

-y = c₂

3 - x = c₂

Substituting the third equation into the second equation, we get:

-y = 3 - x

Solving for x and y, we get

x = 2

y = 1

Therefore, the values are x = 2 and y = 1.

To learn more about the system of equations;

brainly.com/question/13729904

#SPJ1

The object will have a height of 100 feet after 100 seconds.

The equation for the height of the object in feet after T seconds is H(T) = A(T - h)2 + k, where A and h are constants. Given that the object has a height of 0 feet after 10 seconds, and a maximum height of 200 feet at 0 seconds, we can solve for A and h.

We know that H(0) = 200, so k = 200.

We also know that H(10) = 0, so A(10 - h)2 + 200 = 0. Solving for A, we get A = -(h2 + 200) / 102.

Now we have an equation with two unknowns, A and h, so we can use substitution to solve for h. We can substitute -(h2 + 200) / 102 for A in our original equation, and solve for h. This gives us h = 10.

We now know A = -(102 + 200) / 102 = -20.

So, our equation for the height of the object in feet after T seconds is H(T) = -20(T - 10)2 + 200.

To find the height of the object after 100 seconds, substitute 100 for T in the equation. This gives us H(100) = -20(100 - 10)2 + 200 = 100.

Learn more about substitution

brainly.com/question/10423146

#SPJ11

So the equation of the circle is (x+4)^2 + (y+4)^2 = 4^2 with center (-4, -4) and radius 4

The equation of a circle is given by (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center of the circle and r is the radius. We need to rearrange the given equation to match this form.

2x^2 + 2y^2 + 16x + 16y + 32 = 0

Divide both sides of the equation by 2:

x^2 + y^2 + 8x + 8y + 16 = 0

Rearrange the terms:

x^2 + 8x + y^2 + 8y = -16

Complete the square for both x and y terms:

(x^2 + 8x + 16) + (y^2 + 8y + 16) = -16 + 16 + 16

(x+4)^2 + (y+4)^2 = 16

Now the equation is in the standard form of a circle equation, and we can find the center (h,k) and radius r:

h = -4, k = -4, r = 4

So the equation of the circle is (x+4)^2 + (y+4)^2 = 4^2 with center (-4, -4) and radius 4.

Learn more about equation

brainly.com/question/29657988

#SPJ11

Answer:900 yards

Step-by-step explanation:

Unit rate would be 600/2 meaning 300 yards would be done in a third of an hour. Multiply that be 3 (3 thirds is 1) and 300x3=900
pretty straightforward :)

Answer:

see below

Step-by-step explanation:

84

i took the test

The coordinates of N can be estimated as: (-8, -12)

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

If point N is dilated with a scale factor of 5/4 centered at the origin, the coordinates of the image point, let's call it N', can be found by multiplying the coordinates of N by the scale factor:

N' = (5/4)N

We also know that the image point N' is located at (-10, -15), so we can substitute these values into the equation:

(-10, -15) = (5/4)N

Solving for N, we can multiply both sides by the reciprocal of 5/4, which is 4/5:

N = (4/5)(-10, -15)

N = (-8, -12)

Therefore, the coordinates of point N are (-8, -12).

To know more about Scale factor check:

https://brainly.com/question/30215119

#SPJ9

David will need to fill the measuring cup 15 times in order to fill the 5 bottles.

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.

Each bottle holds 3/4 of a quart, and his measuring cup holds 1/4 of a quart.

David will have to fill his measuring cup 3 times in order to fill 1 bottle of capacity 3/4 quarts.

For 5 bottles, it will be 3*5 times which results in 15 times.

Thus, David will need to fill the measuring cup 15 times in order to fill the 5 bottles.

Learn more about measurement

https://brainly.com/question/27233632

#SPJ1

The algebraic expression that translates the given phrase is 2c + 15, where c is the amount of Chrissy's savings.

To translate the phrase "15 more than twice Chrissy's savings" into an algebraic expression:

1. First, we need to identify the variable. In this case, the variable is c, which represents Chrissy's savings.
2. Next, we need to identify the operations and numbers involved in the phrase. The phrase "twice Chrissy's savings" means that we need to multiply c by 2.
3. The phrase "15 more than" means that we need to add 15 to the result of the multiplication.
4. Putting these steps together, we get the algebraic expression 2c + 15.

So the final answer is 2c + 15.

Learn more about algebraic expression here: https://brainly.com/question/2164351.

#SPJ11

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

To learn about Domain

brainly.com/question/29452843

#SPJ11

From  the function φ(x)=31​x3−21​x,  0 is a fixed point of φ(x) it shows in calculation below.  The iteration xk+1 = φ(xk) converges locally to 0 shows below. The iteration diverges as k increases.

(a) To show that 0 is a fixed point of φ(x), we need to show that φ(0) = 0. Substituting x = 0 into the function gives us:

φ(0) = (3/1)(0)3 - (2/1)(0) = 0 - 0 = 0

Therefore, 0 is a fixed point of φ(x).

(b) To show that the iteration xk+1 = φ(xk) converges locally to 0, we need to show that |φ'(x)| < 1 for x near 0. Taking the derivative of φ(x) gives us:

φ'(x) = (9/1)x2 - (2/1)

At x = 0, φ'(0) = 0 - 2 = -2. Since |φ'(0)| > 1, the iteration does not converge locally to 0.

(c) By numerical tests, we can find an initial guess x0 such that the iteration converges to 0 and an initial guess x0 such that the iteration diverges. For example, if we choose x0 = 0.5, the iteration converges to 0:

x1 = φ(0.5) = (3/1)(0.5)3 - (2/1)(0.5) = -0.625

x2 = φ(-0.625) = (3/1)(-0.625)3 - (2/1)(-0.625) = 0.8203125

x3 = φ(0.8203125) = (3/1)(0.8203125)3 - (2/1)(0.8203125) = -0.4625244140625

And so on. The iteration converges to 0 as k increases.

On the other hand, if we choose x0 = 2, the iteration diverges:

x1 = φ(2) = (3/1)(2)3 - (2/1)(2) = 20

x2 = φ(20) = (3/1)(20)3 - (2/1)(20) = 23980

x3 = φ(23980) = (3/1)(23980)3 - (2/1)(23980) = 3.47119332792e+13

And so on. The iteration diverges as k increases.

Learn more about iteration :

https://brainly.com/question/30883485

#SPJ11

For a dish party, Alia needs to seat four people at a round table. There are 24 possible combinations of seating arrangements.

This is because each person has 3 options (clockwise, counter-clockwise, opposite), for a total of 34 or 81 combinations. However, due to symmetry, half of these are the same combinations with the people just shifted around the table, so we are left with 24 total combinations.

To know more about combinations click on below link :

https://brainly.com/question/13387529#

#SPJ11

The chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.

The chain rule is a formula for calculating the derivative of a composite function. It states that the derivative of a composite function f(g(x)) is equal to the derivative of f with respect to g times the derivative of g with respect to x. In mathematical notation, this is expressed as (f(g(x)))' = f'(g(x)) * g'(x).

In the case of the first equation, we can use the chain rule to reduce it to the second equation by applying the formula mentioned above. First, we need to identify the composite function and its components. In this case, the composite function is f(g(x)) and the components are f and g.

Next, we need to find the derivative of f with respect to g and the derivative of g with respect to x. Once we have these derivatives, we can multiply them together to get the derivative of the composite function.

Finally, we can reduce the first equation to the second equation by substituting the derivative of the composite function for the original composite function. This will give us the second equation, which is a simplified version of the first equation.

In conclusion, the chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.

Learn more about chain rule

brainly.com/question/30117847

#SPJ11

The average number of completed good units is 920

A Markov chain is a type of sequential machine that can be used to model the process of inspection and reworking in this question. The Markov chain will have four states: Machine I, Machine II, Inspection, and Junked.

(a) To determine the average number of visits to each state for a part starting at Machine I, we can create a transition matrix with the probabilities of moving from one state to another. The transition matrix will look like this:

| 0.92  0.05  0.03  0    |
| 0.07  0.85  0.03  0.05 |
| 0    1     0     0    |
| 0    0     0     1    |

The first row represents the probabilities of moving from Machine I to each of the other states. The second row represents the probabilities of moving from Machine II to each of the other states. The third row represents the probabilities of moving from Inspection to each of the other states. The fourth row represents the probabilities of moving from Junked to each of the other states.

To find the average number of visits to each state, we can multiply the transition matrix by a vector representing the initial state. In this case, the initial state is Machine I, so the vector will be [1 0 0 0]. Multiplying the transition matrix by this vector will give us the average number of visits to each state:

| 0.92  0.05  0.03  0    |   | 1 |   | 0.92 |
| 0.07  0.85  0.03  0.05 | * | 0 | = | 0.07 |
| 0    1     0     0    |   | 0 |   | 0.03 |
| 0    0     0     1    |   | 0 |   | 0    |

So the average number of visits to Machine I is 0.92, the average number of visits to Machine II is 0.07, the average number of visits to Inspection is 0.03, and the average number of visits to Junked is 0.

(b) If a batch of 1000 units is started on Machine I, we can use the same transition matrix to find the average number of completed good units. We will multiply the transition matrix by a vector representing the initial state of 1000 units on Machine I:

| 0.92  0.05  0.03  0    |   | 1000 |   | 920 |
| 0.07  0.85  0.03  0.05 | * | 0    | = | 70  |
| 0    1     0     0    |   | 0    |   | 30  |
| 0    0     0     1    |   | 0    |   | 0   |

The average number of completed good units is 920.

Learn more about probabilities

brainly.com/question/30034780

#SPJ11

The values of x and y are determined by solving the equation

The values of x and y can be found by solving the equation x(23) + y(-10) = (106). This can be done by isolating one variable and solving for the other. For example, isolating x gives us x = (106 + 10y)/23. We can then plug this value of x back into the original equation and solve for y. Once we have the value of y, we can plug it back into the equation for x to find the value of x.

The value of −2p2s2v​−qtw​−rux​​ can be found by plugging in the given values of p, s, v, q, t, w, r, and u into the equation and simplifying.

The value of ∣3AB∣ can be found by using the properties of determinants of matrices. Specifically, the determinant of a product of matrices is equal to the product of the determinants of the individual matrices. Therefore, ∣3AB∣ = ∣3∣∣A∣∣B∣ = 3(-1)(3) = -9.

So, the values of x and y are determined by solving the equation x(23) + y(-10) = (106), the value of −2p2s2v​−qtw​−rux​​ is found by plugging in the given values and simplifying, and the value of ∣3AB∣ is found by using the properties of determinants of matrices.

Learn more about matrices

brainly.com/question/24810141

#SPJ11

The price per pound of the apples is $3.50. This is calculated by dividing the total cost, $7.00, by the weight of the apples, 2 pounds.

The price per pound of the apples can be found by dividing the total cost by the weight of the apples. In this example, the total cost of the apples is $7.00 and the weight is 2 pounds. To calculate the price per pound, divide 7.00 by 2. This gives us 3.50, which is the price per pound of the apples. Knowing the price per pound is useful when you are trying to figure out how much a certain amount of apples will cost. For example, if you wanted to buy 5 pounds of apples, you would multiply 5 by 3.50, which would give you $17.50. This is the total cost of the 5 pounds of apples. In addition to helping you figure out how much certain amounts of apples will cost, knowing the price per pound can also help you compare prices between stores. For example, if you found apples for $4.00 per pound at one store, and $3.50 per pound at another store, you could easily determine which store has the better deal.

Learn more about total cost here

https://brainly.com/question/28652728

#SPJ4

Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the ratio of time Mason spends lifting weights to time Mason spends on the treadmill is 1:2.

A treadmill is a machine used for walking or running while staying in one place. It usually has a belt and a platform to stand on, and the belt moves at a speed determined by the user. It is a great way to get a good cardio workout.

The question asks which are correct descriptions of the relationship of time Mason spends lifting weights and on the treadmill.

Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the fraction of time Mason spends lifting weights is 2/3.

To know more about treadmill click on below link:

https://brainly.com/question/30391018#

#SPJ11

Answer:

yellow candies:__96_ total

green candies:___72_ total

so there will be _24__ more yellow then green candies

Step-by-step explanation:

Answer:

Step-by-step explanation:

yellos candies 42 bceuase 82 divided by it you gergt it and green 4 becase you duve it

The exact value of the expression is √3.

To find the exact value of the given expression, we can use the sum formula for tangent. The formula is:

Tan (A + B) = (tan A + tan B) / (1 - tan A tan B)

Where A and B angle.

In this case, A = 41° and B = 19°. Plugging these values into the formula, we get:

Tan (41° + 19°) = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)Simplifying the left side of the equation gives us:

Tan 60° = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)We know that tan 60° = √3.

Substituting this value into the equation gives us:√3 = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)

Cross-multiplying and simplifying gives us:

√3 (1 - tan 41° tan 19°) = tan 41° + tan 19°√3 - √3 tan 41° tan 19° = tan 41° + tan 19°

We can rearrange the terms to get:

√3 = tan 41° + tan 19° + √3 tan 41° tan 19°

This is the same expression that we were given in the question.

Therefore, the exact value of the expression is √3.

Here you can learn more about tangent: https://brainly.com/question/10053881

#SPJ11

Answer:

$109+$281=x when x=391

so that means a laptop equals $391 dollars