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The GCF (greatest common factor) of the first two terms of the polynomial 3p^(3)+9p^(2)+5p+15 is 3p^(2). This is because both terms have a common factor of 3p^(2) that can be factored out.

The GCF of the last two terms of the polynomial is 5. This is because both terms have a common factor of 5 that can be factored out.

Therefore, the polynomial can be factored as follows:

3p^(2)(p+3) + 5(p+3)

Now, we can factor out the common factor of (p+3) to get the final factored form of the polynomial:

(3p^(2)+5)(p+3)

So, the GCF of the first two terms is 3p^(2) and the GCF of the last two terms is 5.

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Answer: $135

Step-by-step explanation:

    We know that:

         Selling price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]

    Using the given cost price and loss%, we can solve.

         Selling Price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]

         Selling Price = (100 - 10)([tex]\frac{\text{150}}{100}[/tex])

         Selling Price = (90) * (1.5)

         Selling Price = $135

    This means the selling price of the dress is $135.

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.

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Function Family: quadratic

Domain: all real numbers

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

y-int: (0,0)

Answer:

Step-by-step explanation:

the answer is eitehr b or a

Answer: y > 2/5x - 4

Step-by-step explanation:

The slope intercept form is y = mx + b

To get the inequality to that, we have to get y alone.

Starting:

2x - 5y < 20

Subtract 2x from each side leaves you:

- 5y < -2x + 20

Dividing by -5 leaves you:

(Remember that when dividing by a negative in an inequality, the sign flips.)

y > 2/5x - 4

Hope this helps!

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.

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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.

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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.

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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.

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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.

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The correct statement about the functions f(x) and g(x) include the following: B. f(x) has a steeper slope than g(x).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m of g(x) = (1 - (-3))/(0 - (-2))

Slope, m of g(x) = 4/2

Slope, m of g(x) = 2.

Slope of f(x) = 3. Therefore, 3 is greater than 2.

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The area of the shaded shape WXZY s equal to 381.4 cm².

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = θπr²/360

Where:

In order to determine the area of the shaded shape WXZY, we would have to subtract the area of sector OYZ from the area of the sector OWX.

Area of sector OWX = 75 × 3.14 × 32²/360 = 669.87 cm²

Area of sector OYZ = 75 × 3.14 × 21²/360 = 288.49 cm²

Area of shaded shape WXZY = Area of sector OWX - Area of sector OYZ

Area of shaded shape WXZY = 669.87 cm² - 288.49 cm²

Area of shaded shape WXZY = 381.4 cm².

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Elena plans on running a total of 5 miles.

Mile, any of several distance measurements, such as the statutory mile (5,280 ft) (1.609 km). It comes from of the Romans lire passus, also referred as the "1000 steps," which was equal to 5,000 Romans feet. Unit of length is a related topic. See all relevant material The "old London" mile was eight furlongs when it was first established in 1500.

The term mille passus, which translates to "a hundred paces" in Latin and meant a length of 1,000 rates of speed or 5,000 Rome feet, was originally used by the Romans. It is equivalent to around 1,480 metres, or 1,618 contemporary yards.

We are aware that she has covered 2 miles, or 40% of a total distance, in her run thus far:

[tex]2=0.4x[/tex]

To find x,

[tex]2=0.4x[/tex]

[tex]x=\frac{2}{0.4}[/tex]

[tex]x=5[/tex]

Therefore, Elena plans to run a total distance of 5 miles.

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The value of x is 18 and y is 16. The solution has been obtained by using concept of similar triangles.

If two triangles have the same number of corresponding sides and corresponding angles, they are said to be similar. Similar figures are objects that have the same shape but various sizes, like two or more figures.

We are given that in ΔABC and ΔBDC,

∠ABC ≅ ∠BDC  (right angles)

BC ≅ BC  (common side)

∠ACB ≅ ∠BCD (common angle)

So,  ΔABC ≅ ΔBDC.

We know that in similar triangles, the ratio of the corresponding sides is same.

So,

AC / BC = BC / CD

Now, by substituting the given values in the relation, we get,

⇒18/a = a/16

We are given proportion as x/a = a/y.

On comparing both, we get

x = 18 and y = 16

Hence, the value of x is 18 and y is 16.

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Answer:

First, we need to calculate Danielle's commission on the merchandise she sold:

Commission = 7.25% of $4,100 = 0.0725 x $4,100 = $296.25

Next, we need to calculate her total earnings for the week:

Total earnings = Base salary + Commission

Total earnings = $725 + $296.25

Total earnings = $1,021.25

Therefore, Danielle earned $1,021.25 last week.

Answer:

1,021.25

Step-by-step explanation:

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.

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Answer:

working on it

Step-by-step explanation:

(a) (6, H, 7) is not a possible outcome because the sum of the two numbers rolled on the number cube cannot be 7 if the first number rolled is 6.

(b) (T, 3, 4) is a possible outcome because the first outcome is tails, the second outcome is 3, and the third outcome is 4.

(c) (6, H, 6, T) is not a possible outcome because the third outcome cannot be both 6 and T at the same time.

(d) (1, T, 1) is a possible outcome because the first and third outcomes are both 1 and the second outcome is tails.

(e) (H, H, 3) is not a possible outcome because the third outcome cannot be 3 if the first two outcomes are both heads.

What is Probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

Since each of the three people orders a different flavor, the first person has 6 choices, the second person has 5 choices (since one flavor has already been chosen), and the third person has 4 choices (since two flavors have already been chosen). The total number of outcomes is the product of these numbers:

6 × 5 × 4 = 120

Therefore, there are 120 possible outcomes.

(part 1) There are 10 options for the first digit, 9 options for the second digit (since one digit has already been chosen), and 8 options for the third digit (since two digits have already been chosen). The total number of combinations is the product of these numbers:

10 × 9 × 8 = 720

Therefore, there are 720 possible locker combinations.

(part 2) If you absolutely choose 9 as your first digit, then there are only 9 options for the first digit. The second and third digits can still be any of the remaining 9 digits (since digits cannot repeat). Therefore, the number of possible combinations is:

1 × 9 × 8 = 72

The theoretical probability of getting HH on two coin flips is (1/2) × (1/2) = 1/4 = 0.25. The experimental probability of getting HH after 100 trials is 25/100 = 0.25. Since the experimental probability is equal to the theoretical probability, we can say that the experimental probability of getting HH is equal to the theoretical probability.

The possible outcomes of rolling a standard number cube are 1, 2, 3, 4, 5, and 6. The possible outcomes of flipping a coin are heads (H) or tails (T).

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The expression (122two _ 202three)_ 1001three can be evaluated by breaking it down into its constituent parts.

Expression in math is a combination of numbers, symbols, and/or operations that represent a mathematical statement. Expressions can be used to calculate values, solve equations, and to model real-world problems. Expressions can be simple or complex and can range from basic arithmetic operations to more complex functions and equations. Expressions are an essential part of mathematics and are used to represent equations, formulas, and even solutions to complex problems.

The first part, 122two, is a number and can be evaluated to 122. The second part, 202three, is also a number and can be evaluated to 203. The third part, 1001three, is also a number and can be evaluated to 1002. Taking the evaluation of each part (122, 203 and 1002), the overall expression (122two _ 202three)_ 1001three can be evaluated to 121.

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Answer:

80

Step-by-step explanation:

we will write an inequality of 1.50x + 130 =250

We subtract 130 from each side, so we have

1.50x=120

Now we divide by 1.50 on each side

X=80.

She gets $114 to work at grocery store for 6 hours and $200 at the nursery.

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute.

We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Eli has two summer jobs. During the week he works in the grocery store, and on the weekend he works at a nursery. He gets paid $20 per hour to work at the grocery store and $17 per hour to work at the nursery.

14 hours at the grocery store and 9 hours at the nursery? How much does he earn if he works

Therefore, She gets $114 to work at grocery store for 6 hours and $200 at the nursery.

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The correct classification for the expression 2x+2 is a Linear binomial.(3)


A monomial is an algebraic expression with only one term. A binomial is an algebraic expression with two terms. A trinomial is an algebraic expression with three terms.

A quadratic expression is an expression with a term that has a degree of 2. A linear expression is an expression with a term that has a degree of 1.

In the given expression, 2x+2, there are two terms (2x and 2) so it is a binomial. The highest degree of the terms is 1 (in the term 2x), so it is a linear expression. Therefore, the correct classification for the expression is a Linear binomial.

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complete question

Classify 2x+2 in one of the following

1.Quadratic monomial

2.Linear monomial

3.Linear binomial

4.Quadratic trinomial

The series converges.

To test the series 3 + 3/5 + 3/5^2 + 3/5^3 + … =∑n=0[infinity] 3/5^n,

we can use the ratio test.

Specifically, we can look at the ratio of each successive term.

Let an+1/an = 3/5n+1/3/5n = 1/5. Since this is less than 1, the series converges.

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Some of the questions to ask grade 12 students on a questionnaire about taking a gap year after school​ are:

A questionnaire refers to a set of questions or items used to collect information about respondents' attitudes, experiences, or opinions. Questionnaires can be used to collect both quantitative and qualitative data. Questionnaires are widely used in market research, as well as social and health sciences.

As the researcher's study focus on semester taken after high school and prior to post-secondary education, such questionnaire involve will focus on variables on the student gap year.

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Answer:

Step-by-step explanation:

x = number of small boxes

x-4 = number of large boxes

total number of eggs in the large boxes = 12(x-4) = 12x - 48

total number of eggs she buys = 6x + 12x - 48 = 18x - 48 = 6(3x - 8)

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.

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The answer is x=26.

To solve the equation x-5=21 using the addition property of equality, we need to isolate the variable x on one side of the equation. The addition property of equality states that if we add the same value to both sides of an equation, the equation will remain true.

Step 1: Add 5 to both sides of the equation to cancel out the -5 on the left side.
x-5+5=21+5

Step 2: Simplify both sides of the equation.
x=26

Step 3: Check the solution by substituting the value of x back into the original equation.
26-5=21
21=21

The solution checks out, so the answer is x=26.

In conclusion, the solution to the equation x-5=21 using the addition property of equality is x=26.

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