1 Select the correct answer. What is the simplified form of this expression? (-3x² + 4x) + (2x²-x-11)
a. -x2 + 5x − 11
b. -x² + 3x - 11
c. -x² + 3x + 1
d. -x2 + 5x + 11
Blynomials: Mastery Test
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The first four terms of the sequence generated by g_(1)=(1)/(2) g_(n)=6g_(n-1), for all integers n>=2 are (1/2), 3, 18, and 108.

The first four terms of the sequence generated by g_(1)=(1)/(2) g_(n)=6g_(n-1), for all integers n>=2 are (1/2), 3, 18, and 108.

To find the first four terms of the sequence, we can use the given formula and plug in the values for n.

For the first term, n=1, so we use the formula g_(1)=(1)/(2) to get the first term, which is (1/2).

For the second term, n=2, so we use the formula g_(n)=6g_(n-1) and plug in the value for n and the value of the first term for g_(n-1):

g_(2)=6g_(2-1)=6g_(1)=6(1/2)=3

For the third term, n=3, so we use the same formula and plug in the value for n and the value of the second term for g_(n-1):

g_(3)=6g_(3-1)=6g_(2)=6(3)=18

For the fourth term, n=4, so we use the same formula and plug in the value for n and the value of the third term for g_(n-1):

g_(4)=6g_(4-1)=6g_(3)=6(18)=108

Therefore, the first four terms of the sequence are (1/2), 3, 18, and 108.

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Answer: -2x = 16

Step-by-step explanation:

The answer is -2x = 16.

We start by isolating the -2x on one side of the equation. To do this, we must subtract 3x from both sides of the equation. This gives us -2x = 4 - 3x. We then add 3x to both sides of the equation to give us -2x + 3x = 4. Since 3x + (-3x) = 0, we are left with -2x = 16.

Answer:

x=8

Step-by-step explanation:

12 -3x=4+ (-2x)

12-3x=4-2x add 12 to both sides

-3x=-2x-8 add 2x to both sides

-x=-8 divide both sides by 1

x=8

let me know if this helped :)

Answer:

The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:

For x² - 3x + 2 = 0:

a = 1, b = -3, c = 2

x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2

x = 1 or x = 2

For x² + x + 2 = 0:

a = 1, b = 1, c = 2

x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2

x = (-1 ± i√7) / 2

Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:

(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))

The simplified expressions are: (a) z = 1/4, (b) 3z^2, (c) -4z, and (d) 3z^2.

To simplify each expression by performing the indici, we need to follow the order of operations and combine like terms. Here are the steps for each expression:

(a) z + 3z = 1
First, we need to combine the like terms on the left side of the equation. Since both terms have the variable z, we can add them together:
4z = 1
Next, we need to solve for z by isolating the variable on one side of the equation. We can do this by dividing both sides of the equation by 4:
z = 1/4

(b) z * 3z
To simplify this expression, we just need to multiply the two terms together:
3z^2

(c) -z - 3z
To simplify this expression, we need to combine the like terms. Since both terms have the variable z, we can add them together:
-4z

(d) (-z)(-3z)
To simplify this expression, we just need to multiply the two terms together. Remember that a negative times a negative is a positive:
3z^2

So the simplified expressions are: (a) z = 1/4, (b) 3z^2, (c) -4z, and (d) 3z^2.

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The probability that a person chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).

Typically, the probability is defined as the ratio of favourable events to all other outcomes in the sample space. The formula for probability of an occurrence is P(E) = (Number of favourable outcomes) (Sample space).

The formula is as follows:

P(AorB) = P(A)+P(B)-P(AandB)

where A and B are two events.

Then, we have:

P(A) = 30/60 = 1/2 (since 30 out of 60 students go for extra help)

P(B) = 22/60 (since 22 out of 60 students study at home only)

Using the formula, we can then find:

P(AorB) = P(A)+P(B)-P(AandB)

= 1/2 + 22/60 - 0

= 5/6

Hence, the probability that someone chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).

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It is true that v1 + 2v2, v2 + 2v3, v4 is also a basis for V.

Suppose that v1, v2, v3, v4 is a basis for vector space V. A basis for a vector space is a set of vectors that are linearly independent and span the entire vector space. In other words, any vector in the vector space can be written as a linear combination of the basis vectors.

In this case, the vectors v1 + 2v2, v2 + 2v3, and v4 are linear combinations of the original basis vectors v1, v2, v3, and v4. Therefore, they are also linearly independent and span the entire vector space V. As a result, the set {v1 + 2v2, v2 + 2v3, v4} is also a basis for V.

In general, any set of vectors that are linearly independent and span the entire vector space can be considered a basis for that vector space. Therefore, it is true that v1 + 2v2, v2 + 2v3, v4 is also a basis for V.

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Step-by-step explanation:

Seven people are in the pool who each have expected payouts of $8,600 for the year. One more person is added to the pool whose expected payout is $14,000 per year. How much is the average expected payout for each member of the group of eight? Expected Payout for each member of the group is $​

The correct symbol in the expression is 95/56 < 2 5/7

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

95/56 and 2 5/7

Convert the improper number to a mixed number

So, we have the following representation

1 39/56 and 2 5/7

By comparison;

1 39/56 is less than 2 5/7

So, the inequality symbol is a less than inequality

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Answer:

0.40 or 40% is shaded

Step-by-step explanation:

There are 40 shaded out of the 100 squares. Therefor, .40 is the answer

The values of sec x, csc x, and cot x are:

sec x = sqrt(61)/6

csc x = -sqrt(61)/5

cot x = -6/5

What is the Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right-angled triangle.

We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the terminal side and the x- and y-axes. Then, we can use the definitions of the trigonometric ratios to find the values of sec x, csc x, and cot x.

Let r be the length of the hypotenuse:

r = sqrt(6^2 + (-5)^2) = sqrt(61)

Then, we have:

cos x = adjacent/hypotenuse = 6/sqrt(61)

sin x = opposite/hypotenuse = -5/sqrt(61)

From these, we can find:

sec x = hypotenuse/adjacent = sqrt(61)/6

csc x = hypotenuse/opposite = -sqrt(61)/5 (Note that csc x is negative because sin x is negative in the third quadrant)

cot x = adjacent/opposite = -6/5

Hence, the values of sec x, csc x, and cot x are:

sec x = sqrt(61)/6

csc x = -sqrt(61)/5

cot x = -6/5

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Answer:

a = 1

Step-by-step explanation:

6a + 5a + 1 = 12

Subtract one to both side leaving a by itself.

6a + 5a = 12 - 1

Now simply by add or subtracting, multiply or dividing.

11a = 11

Divide 11 to both side leaving a = ?

a = 1

Answer:

a= 1

Step-by-step explanation:

6a + 5a + 1 = 12

(-1) + 6a + 5a +1 = 12 -1

6a + 5a = 11

11a = 11

11a/11 = 11/11

a= 1

Answer:

To find the ratio of boxes of pens ordered to boxes of pencils ordered, we need to divide the number of boxes of pens by the number of boxes of pencils:

24 boxes of pens ÷ 15 boxes of pencils = 8/5

Therefore, the ratio of boxes of pens ordered to boxes of pencils ordered is 8:5.

The correct answer is (C) 8:5.

Answer:

C. 8:5

Step-by-step explanation:

pens: 24

pencils: 15

pens : pencils

24 : 15 = 8 : 5

2a + 2h

(a) Simplifying, we get f(a+h)−f(a)/h = (a+h)2−2(a+h)+3 − (a2−2a+3) / h = (2a+2h)h/h = 2a + 2h.

(b) We now use the definition of the derivative to compute f'(a) = limh→0 (2a + 2h) = 2a.

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Answer:

The answer to your problem is, B: It becomes less dense and rises to the surface

Step-by-step explanation:

Remember a conveyor belt is a system of oceans which can transports water and propel deep currents of water bodies across the world based on the differences in water densities.

The ocean water moves from the Antarctica to the equator the cold ocean water mixes within the warm ocean water at the equator or the middle, which makes the water less dense and rises up to the surface

Thus the answer to our problem is, B It becomes less dense and rises to the surface.

Answer:

p^(2(s-t)^2)/(s+t)

Step-by-step explanation:

We can simplify this expression by using the properties of exponents:

((p^r)/(p^s))^(r+s) ((p^2)/(p^t))^(s+t) ((p^t)/(p^r))^(r+t)

= (p^(r+s-s))^r (p^(2s-2t))^s (p^(t-r+r))^t / (p^(r+s-r))^r (p^(2t-2s))^s (p^(r-t+t))^t

= p^r p^(2s-2t)s p^t / p^r p^(2t-2s)s p^t

= p^r / p^r * (p^(2s-2t))^(s/(s+t)) / (p^(2t-2s))^(s/(s+t))

= p^r / p^r * p^((2s-2t)s/(s+t)) / p^((2t-2s)s/(s+t))

= p^0 * p^(2s^2-2st-2ts+2t^2)/(s+t)

= p^(2s^2-2st-2ts+2t^2)/(s+t)

= p^(2(s-t)^2)/(s+t)

Therefore, ((p^r)/(p^s))^(r+s) ((p^2)/(p^t))^(s+t) ((p^t)/(p^r))^(r+t) simplifies to p^(2(s-t)^2)/(s+t).

The composition of the two given rational functions is another rational function, [tex]g(f(x)) = 1/((x+3)^2)[/tex].

The composition of two functions, f(x) and g(x), is denoted as g(f(x)) and is defined as the function that results from applying g(x) to the output of f(x). In other words, the composition of two functions is the function that results from plugging one function into another function.

To find the composition [tex]g(f(x))[/tex], we need to substitute the expression for [tex]f(x)[/tex] into the expression for [tex]g(x)[/tex] wherever we see an "x".

Given that [tex]f(x)=(1)/(x+3)[/tex] and [tex]g(x)=x^2[/tex], the composition [tex]g(f(x))[/tex] can be found as follows:

[tex]g(f(x)) = g((1)/(x+3)) = ((1)/(x+3))^(2) = (1^(2))/((x+3)^(2)) = 1/((x+3)^(2))[/tex]

Therefore, the composition [tex]g(f(x)) = 1/((x+3)^2)[/tex].

In conclusion, the composition of the two given rational functions is another rational function, [tex]g(f(x)) = 1/((x+3)^2)[/tex].

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The next term in the sequence would be -31.

What is Sequence ?

A sequence is a list of numbers or objects that follow a specific pattern or rule. Each number in the sequence is called a term, and the terms can be finite or infinite.

A. {31, 26, 21, 16, 11,...}

To find the common difference (d) between consecutive terms in the arithmetic sequence, we can subtract any term from the term that comes after it. For example, we can subtract 26 from 31 to get:

31 - 26 = 5

Similarly, we can subtract 21 from 26, 16 from 21, and so on:

26 - 21 = 5

21 - 16 = 5

16 - 11 = 5

Since the differences between consecutive terms are all the same, we can conclude that the common difference is d = 5.

To find the next term in the sequence, we can add the common difference (d = 5) to the last term (11):

11 + 5 = 16

Therefore, the next term in the sequence would be 16.

B. {-45, -38, -31, -24, . . .}

To find the common difference (d) between consecutive terms in the arithmetic sequence, we can subtract any term from the term that comes after it. For example, we can subtract -38 from -45 to get:

-45 - (-38) = -7

Similarly, we can subtract -31 from -38, -24 from -31, and so on:

-38 - (-31) = -7

-31 - (-24) = -7

Since the differences between consecutive terms are all the same, we can conclude that the common difference is d = -7.

To find the next term in the sequence, we can add the common difference (d = -7) to the last term (-24):

-24 - 7 = -31

Therefore, the next term in the sequence would be -31.

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Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]9(2 - x) = 3x - 6 \\ 18 - 9x = 3x - 6 \\ 18 + 6 = 3x + 9x \\ 24 = 12x \\ x = 2[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 2 !

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:if what im getting at is correct, 8000  cm for the part a then that means part b is probably in conversion of that to 80 m

Step-by-step explanation:

if what i think may be correct 1:1000 means that 8 cm would be 8000 then, if it wants to know the real length in meters then it would have to be converted making it 80 meters

___________________________________________________

Hope this is correct

Answer:

A) 8000 cm

B) 80m

Step-by-step explanation:

A) 1:1000 is 0.001 times that by 1000 you get 8 x 1000=8000

=8000cm

B) we know that in cm the ship size is 8000cm converting cm to meter is basically

8000÷100= 80meters

Answer:

20.5 in.

Step-by-step explanation:

Just divide 82 by 4 to get the answer since  1 inch equals to 4 feet.

To find the missing quantity, we will plug in the given values into the formula for simple interest and solve for the unknown variable. The formula for simple interest is I = Pxrxt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given:
P = $4000
r = 8% = 0.08
t = 3 years

Plugging in the given values into the formula, we get:

I = $4000 x 0.08 x 3

Simplifying the equation, we get:

I = $960

Therefore, the missing quantity is the interest, I, which is equal to $960.

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The given sequence is A(n) = 6.3 + (n-1)(5).

To find the 6th term of the sequence, we substitute n = 6 into the formula:

A(6) = 6.3 + (6-1)(5)

A(6) = 6.3 + 25

A(6) = 31.3

Now, to find the 5th term of this sequence, we need to substitute n = 5 into the formula:

A(5) = 6.3 + (5-1)(5)

A(5) = 6.3 + 20

A(5) = 26.3

Therefore, the 5th term of the 6th term of the sequence A(n) = 6.3 + (n-1)(5) is 26.3.

The scale factor of dilation for the given shape are:

For A : (0,0)

For B : (2,2)

For C : (2,2)

Magnification is defined as the ratio of the size of the new image to the size of the old image. The center of expansion is a fixed point in the plane. A dilation transform is defined based on the scale factor and dilation center. If the scale factor is greater than 1, the image will be stretched. 

Formula: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Solution:

Given, A = A' = (0,0)

           B= (2,2) , B' = (4,4)

           C=(3,2) , C' = (6,4)

Scale factor for A = (0,0), it is because that's the center of dilation.

Scale factor for B = (4/2 , 4/2) = (2,2)

Scale factor for C = (6/3 , 4 /2) = (2,2)

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40000000

Step-by-step explanation:

ezy Peasy lemon squeeze

Answer:40,000,000

Step-by-step explanation:

its just like 2 divided by 8 which is 4 then just add all your zeros

Answer:

-1

Step-by-step explanation:

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The partial derivatives of f with respect to u and v at (u,v) = (-2, -2) are ∂f/∂u(-2,-2) = 224 and ∂f/∂v(-2,-2) = -1056.

To evaluate the partial derivatives ∂f/∂u and ∂f/∂v at (u,v) = (-2, -2) using the Chain Rule, we need to find the derivatives of f with respect to x, y, and z, and then multiply them by the derivatives of x, y, and z with respect to u and v.

First, let's find the derivatives of f with respect to x, y, and z:
∂f/∂x = 3x^2
∂f/∂y = z^2
∂f/∂z = 2yz

Next, let's find the derivatives of x, y, and z with respect to u and v:
∂x/∂u = 2u
∂x/∂v = 1
∂y/∂u = 1
∂y/∂v = 2v
∂z/∂u = 4v
∂z/∂v = 4u

Now, we can use the Chain Rule to find the partial derivatives of f with respect to u and v:
∂f/∂u = (3x^2)(2u) + (z^2)(1) + (2yz)(4v)
∂f/∂v = (3x^2)(1) + (z^2)(2v) + (2yz)(4u)

Finally, we can plug in the values of u and v to find the partial derivatives at (u,v) = (-2, -2):
∂f/∂u(-2,-2) = (3((-2)^2 + (-2))^2)(2(-2)) + ((4(-2)(-2))^2)(1) + (2((-2)+(-2)^2)(4(-2)))
= (3(0)^2)(-4) + (16^2)(1) + (2(2)(-8))
= 0 + 256 - 32
= 224

∂f/∂v(-2,-2) = (3((-2)^2 + (-2))^2)(1) + ((4(-2)(-2))^2)(2(-2)) + (2((-2)+(-2)^2)(4(-2)))
= (3(0)^2)(1) + (16^2)(-4) + (2(2)(-8))
= 0 - 1024 - 32
= -1056

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There are 6 people in a group. Their names are selected randomly and they act independently. The probability that the first person arriving has the same name as 1 or more people is 0. The probability that there are people in the group with the same name is 98.46%.

The probability that the initial arrival shares a name with one or more others is 0 percent. This is because the first person arriving has no one to compare their name with, so there is no chance that they will have the same name as someone else.

The probability that there are people in the group with the same name can be calculated using the formula

P(same name) = 1 - P(different names).

The probability of everyone having different names is calculated by multiplying the probabilities of each person having a different name from the previous person. This can be represented as

(6/6) * (5/6) * (4/6) * (3/6) * (2/6) * (1/6) = 0.0154.

Therefore, the probability of there being people in the group with the same name is 1 - 0.0154 = 0.9846 or 98.46%.

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Sabrina needs to buy at least 8 pairs of socks to get free shipping, so the inequality will be x ≥ 8.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Sabrina needs to buy at least 100 dollars worth of items to get free shipping, and she already has a 70 dollar sweatshirt in her cart.

Let x be the number of pairs of socks she needs to buy.

Each pair of socks costs 4 dollars, so the cost of x pairs of socks is 4x dollars.

To get free shipping, the total cost of her items must be at least 100 dollars.

Therefore, we can write the inequality -

70 + 4x ≥ 100

Subtracting 70 from both sides, we get -

4x ≥ 30

Dividing both sides by 4, we get -

x ≥ 7.5

Since Sabrina cannot buy a fraction of a pair of socks, she needs to buy at least 8 pairs of socks to meet the minimum spending requirement for free shipping.

Therefore, the solution to the situation is x ≥ 8.

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The likelihood function for a sequence of coin tosses x1, . . . , xn with P[H] = p is given by:

L(p) = P(x1, . . . , xn | p) = P(x1 | p) * P(x2 | p) * . . . * P(xn | p)

Using the notation that 1 denotes H and 0 denotes T, we can write the likelihood function as:

L(p) = p^k * (1-p)^(n-k)

where k is the number of heads in the sequence and n-k is the number of tails.

To find the maximum likelihood estimate for p, we need to take the derivative of L(p) with respect to p and set it equal to zero:

dL(p)/dp = k*p^(k-1)*(1-p)^(n-k) - (n-k)*p^k*(1-p)^(n-k-1) = 0

Solving for p, we get:

p = k/n
Therefore, the maximum likelihood estimate for p is the number of heads in the sequence divided by the total number of tosses.

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