simplify the following quadratic expressions
1) 2x^2 -3x -9
2) 3x^2 +5x +2​

Answer:

P = 12.50 + 1.25t

Step-by-step explanation:

To find an equation to represent the price of a pizza, we need to first figure out the original price of a pizze.
Since the price is 16.25 dollars, and there are 3 toppings, each of which cost 1.25, the original price would be:

16.25 - 3(1.25) = 12.50

Thus, we can represent the cost of a pizze with toppings as:
P = 12.50 + 1.25t, where P = Price and t = amount of toppings.

Hope this helps!

Answer:

D 3.5

Step-by-step explanation:

Replace values in the equation with values given. Calculate.

Answer:

D: 3.5

Step-by-step explanation:

Answer:

27x^3+3x^2+9x

Step-by-step explanation:

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

Case 2

The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)

Case 3

We need to add + 64 to both sides. (Correct choice: B)

Case 4

We need to add + 16 to both sides. (Correct choice: C)

In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:

Case 2

x² - 14 · x + 48 = 0

x² - 14 · x + 49 = 1

(x - 7)² = 1

x - 7 = ± 1

x = 7 ± 1

The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.

Case 3

x² - 16 · x = - 21

x² - 16 · x + 64 = 64 - 21

(x + 8)² = 43

The first step consists in adding both sides by + 64.

Case 4

x² - 8 · x = 0

x² - 8 · x + 16 = 16

(x - 4)² = 16

The first step consists in adding both sides by + 16.

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Answer:

Step-by-step explanation:

Since the first 730 days were under 6% compounded daily and the last 401 days were under 8% compounded daily, the final future value of the loan in the sum of $6,155.27 agrees with Dylan's calculations of what he owed Paul.

The final future value combines two separate calculations using an online finance calculator.

The first computation determines the future value based on a present value of $5,000 at 6% for 730 days.

The final computation determines the future value based on a present value of $5,637.43 at 8% for 401 days.

$5,000 for 730 days at 6% Compounded Daily:

N (# of periods) = 730 days

I/Y (Interest per year) = 6%

PV (Present Value) $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $5,637.43

Total Interest = $637.43

$5,637.43 for 401 days at 8% Compounded Daily:

N (# of periods) = 401 days

I/Y (Interest per year) = 8%

PV (Present Value) = $5,637.43

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $6,155.27

Total Interest = $517.84

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The factored form of the trinomial x² + 17x + 72 is ( x + 8 )( x + 9 ).

Given the trinomial in the question;

x² + 17x + 72

To factor, find a pair of integers whose product is 72 and whose sum is 17.

Considering the trinomial x² + 17x + 72;

8 and 9 are the two integers whose product is 72 and whose sum is 17.

Now, write the factored form using these integers

( x + 8 )( x + 9 )

Therefore, the factored form is ( x + 8 )( x + 9 ).

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The computation is that the width is 21.5 feet and the height is 12.5.

Let the height = h

Let the width = (3 × h) - 16 = 3h - 16

Therefore, the dimensions will be:

h + 3h - 16 = 34

4h = 34 + 16

4h = 50

Divide

h = 50/4

h = 12.5

Therefore width = 3h - 16 = 3(12.5) - 16

= 37.5 - 16

= 21.5

The width is 21.5 feet and the height is 12.5.

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The component vector of F parallel to the ramp is approximately 382.2i - 153.2j.



First, we need to find the weight of the boat and trailer that is distributed on each wheel. Since the weight is evenly distributed, we can simply divide the total weight by 2:

440 lb / 2 = 220 lb

Next, we need to find the component vector of the weight parallel to the ramp. To do this, we will use trigonometry and break the weight vector into its x and y components.

Let's start with the y component. The weight vector is acting perpendicular to the ramp, so we need to find the component that is parallel to the ramp. To do this, we can use the sine function:

sin(21°) = y / 220 lb

y = 220 lb * sin(21°) = 75.9 lb

So the y component of the weight vector parallel to the ramp is -75.9 lb (negative because it is acting downwards).

Now, let's find the x component. Again, we need to find the component of the weight vector that is parallel to the ramp, so we can use the cosine function:

cos(21°) = x / 220 lb

x = 220 lb * cos(21°) = 202.9 lb

So the x component of the weight vector parallel to the ramp is 202.9 lb.

Finally, we can put these components together to get the component vector of the weight parallel to the ramp:

Fpar = 202.9i - 75.9j

Rounding to one decimal place, we get:

Fpar = 382.2i - 153.2j

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Answer:

16 : 28

Step-by-step explanation:

If 12 out of the 28 pupils are female, we can calculate the number of males by subtracting the number of females from the total number of pupils.

28 - 12 = 16

So, there are 16 males in the class. Now, we know that the ratio of males : total is 16 : 28.

I hope this helps! Have a lovely day!! :)

(brainliest is much appreciated!!)

Answer:

give they guy brainliest

Step-by-step explanation:

because hes right

In a nutshell, to solve exponential equations by rewriting the base, we either use the change of base formula or convert the bases to make them the same.

One method to solve exponential equations by rewriting the base is the change of base formula. It is as follows:

If a is a positive number not equal to one, and x and y are any positive numbers, then:
\(- a^(loga(x)) = x and

- loga(xy) = loga(x) + loga(y).\)
Thus, we can rewrite exponential equations with any base by using logarithms of any base.
Another way to rewrite exponential equations is to make sure the bases are the same. For instance, we can convert \(2^x = 64 to base 2:

2^x = 64

2^x = 2^6  (since 64 = 2^6)

x = 6\)
So, x = 6 is the solution to\(2^x = 64.\)

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Answer:

1.D

2.C

3.C

4.B

Step-by-step explanation:

mark me as brainliest

Answer: -1.12, -1^(1/2), 1^(1/8), 1^(1/2), 1^(2/3), 1.12

Step-by-step explanation:

Starting with the smallest:

-1.12

-1^(1/2) (which is equal to -1)

1^(1/8) (which is equal to 1)

1^(1/2) (which is equal to 1)

1^(2/3) (which is equal to 1)

1.12

Therefore, the numbers in order from smallest to largest are: -1.12, -1, 1, 1.12.

Answer:

\(1.445 \times {10}^{3} \)

Step-by-step explanation:

\((1.7 \times {10 }^{4} )(8.5 \times {10}^{ - 2} ) = 14.45 \times {10}^{2} = 1.445 \times {10}^{3} \)

Therefore, the range of the middle 50% of these data is 16.  range = 16.

To find the range of the middle 50% of data, we need to first find the quartiles.

Let's start by sorting the data:10, 10, 20, 26, 30

The median is the middle value when the data is arranged in order, which in this case is 20.

To find the first quartile (Q1), we need to find the median of the lower half of the data:10, 10, 20

This gives us a median of 10, since there are an even number of values,

we take the average of the two middle values.

To find the third quartile (Q3), we need to find the median of the upper half of the data:20, 26, 30

This gives us a median of 26.

So our quartiles are:

Q1 = 10Q2 (median) = 20Q3 = 26

Now we can find the range of the middle 50% of data.

The middle 50% of data is the range between Q1 and Q3.

So, we need to find the range between 10 and 26:26 - 10 = 16

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Answer:

The answer is 1800.

Step-by-step explanation:

3/540 = 10/x

3x = 540 × 10

x = 5400/3

x = 1800

A circle has a center at point A ( 3, − 1 ) and a point on the circle is located at R ( 5,4 ).  The location of S is (1, -6).

To find the location of S on the diameter RS, we need to first find the midpoint of RS, which will be the center of the circle. Then we can find the coordinates of S by using the distance formula.

The midpoint of RS is the average of the coordinates of R and S:

((5 + x)/2, (4 + y)/2)

Since the midpoint is the center of the circle, it has the same coordinates as point A:

((5 + x)/2, (4 + y)/2) = (3, -1)

We can solve this system of equations for x and y:

(5 + x)/2 = 3

(4 + y)/2 = -1

Solving for x and y, we get:

x = 1

y = -6

Therefore, the location of S is (1, -6).

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The data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.

The mean is a measure of central tendency that represents the average value of a set of numbers. There are different types of means, including the arithmetic mean , the geometric mean , and the harmonic mean.

The spread of data refers to the variability or dispersion of a set of values. It provides information about how spread out or clustered the data is. A set of data can have a high or low spread, depending on the range of values and how they are distributed.

In the given question,

The spread of a data set refers to how much the individual data points in the set vary from each other. There are several measures of spread that are commonly used, including the range, variance, and standard deviation.

To find the spread of the data set {4, 2, 6, 10, 8, 0}, we can calculate the range, which is the difference between the maximum and minimum values in the set. The maximum value in the set is 10, and the minimum value is 0, so the range is:

Range = maximum value - minimum value = 10 - 0 = 10

Therefore, the spread of the data set is 10.

In other words, the data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.

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Answer:

Its 6

Step-by-step explanation:

Did the test

Answer:

C. t = 3/5

Step-by-step explanation:

\(10t + 4 - 2t = 2 - 2(t - 4)\)

\(4 + 8t = 2 - 2t + 8\)

\(4 + 8t = 10 - 2t\)

\(4 + 10t = 10\)

\(10t = 6\)

\(t = .6 = \frac{3}{5} \)

Answer:

x-4

Step-by-step explanation:

The product of one and a number x is 1x which is basically x.

Four less than x is x-4.

The value of g(f(-5)) is 5.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x)= |2x+ 9|

Now, g(f(-5))

f(-5) = |2(-5)+9|

       = |-10 + 9|

       = |-1|

       = 1

and, g(f(-5)) = g(1)

So, from the graph we can see that the value of g(1) is 5.

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A sample of 20 body temperatures has a mean of 98.3 °F and a standard deviation of 24 °F. We need to construct a 98% confidence interval estimate for the standard deviation of body temperature for all healthy humans.

To construct the confidence interval estimate, we will use the chi-square distribution. The formula for the confidence interval is:

CI = [(n-1)*s^2 / chi-square upper , (n-1)*s^2 / chi-square lower]

Here, n represents the sample size (20), s represents the sample standard deviation (24 °F), and chi-square upper and chi-square lower are the critical values from the chi-square distribution corresponding to a 98% confidence level and degrees of freedom (n-1). By looking up the critical values, we can calculate the confidence interval estimate for the standard deviation.

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Answer:

B. 12

Step-by-step explanation:

Edges are the straight lines

Answer:

5/10

Step-by-step explanation:

The isolated value of h is found to be V/πr²

The three-dimensional solid shape of a cylinder is made up of two parallel bases connected by a curved surface. These bases have the shape of a spherical disc. The axis of the cylinder is a line drawn through the centre or connecting the centres of two circular bases. The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr²h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the component.

According to given formulae:

V=πr²h

On dividing both side with πr² we get

⇒V/πr²=πr²h/πr²

(Solving R.H.S)

⇒h=V/πr²

Therefore, the value of h in the given question is V/πr²

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The highlighted part of the circle is an inscribed angle.

Given that a circle is centered at O.

From the provided diagram,

A circle is centered at O.

YH is the diameter of the circle.

BK is the tangent of the provided circle at K.

And a secant of the circle BR.

As per the given choices,

Tangent: the line BK is tangent to a given circle.

center: the center of the circle is at O.

Central angle: ∠ROH.

Inscribed angle: ∠OYR.

An inscribed angle is the angle that an arc at any point on the circle subtends.

Therefore, an inscribed angle is ∠OYR.

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One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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