What is true about 3×9, guys can you help I a little confused

The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

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The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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Answer:

$1.90

Step-by-step explanation:

The expression for the flu cases in winter is W = S + 0.58S.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Let the total number of patients in winter be W and S be the number of patients treated for flu symptoms.

At Dr. Carrey's clinic, 58% more patients are treated for flu symptoms in the winter than in the summer.

So, the expression for the number of flu patients in winter is:

W = S + 58% of S

W = S + 0.58S

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Given:

Coordinates of the midpoint = (2,-14)

Coordinates of one endpoint = (4,-13)

To find:

The coordinates of the another endpoint.

Solution:

Let us assume (a,b) be the another endpoint.

According to the midpoint formula:

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

By using the midpoint formula, we get

\((2,-14)=\left(\dfrac{a+4}{2},\dfrac{b+(-13)}{2}\right)\)

\((2,-14)=\left(\dfrac{a+4}{2},\dfrac{b-13}{2}\right)\)

On comparing both sides, we get

\(2=\dfrac{a+4}{2}\)

\(4=a+4\)

\(4-4=a\)

\(0=a\)

And,

\(-14=\dfrac{b-13}{2}\)

\(-28=b-13\)

\(-28+13=b\)

\(-15=b\)

Therefore, the another end point is (0,-15).

Answer:

-8968680

Step-by-step explanation:

If this is what your looking for if not sorryyyy

87789-8977609-78860 all you have to do is use a calculator(if you can) or do it the old school way. First, what I did was subtract the first two numbers 87789 and  8977609  to get -8889820 and then subtracted 78860 from that to get a total of -8968680.

The function's value at x = 1, y = - 1 Or f(1) = -1.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The x-coordinate represents the input and the y-coordinate represents the output.

From the given points in the graph, we can conclude that when x = 1, y = -1.

Therefore, The value of the function f(1) = -1.

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Answer:

8b+17=65 is the first equation

b=6

the value of b has increased by 4

Step-by-step explanation:

hope it helps

The lateral area of the pyramid is 195 square inches.

The total area of the pyramid is 318 square inches.

To solve this problem, let's break it down step by step.

a) The lateral area of a regular pentagonal pyramid is given by the formula:

Lateral Area = (1/2) × Perimeter of the base × Slant height

In this case, base of the pyramid is a regular pentagon, and each lateral edge measures 10 inches.

Therefore, the perimeter of the base is 5 × 12 inches

Perimeter of the base = 5 × 12 inches = 60 inches

Using the Pythagorean theorem, we have:

s² = (10/2)² + 4.1²

s² = 25 + 16.81

s² = 41.81

s ≈ √41.81

s ≈ 6.5 inches

Now, Lateral Area = (1/2) × Perimeter of the base × Slant height

Lateral Area = (1/2) × 60 inches × 6.5 inches

Lateral Area ≈ 195 square inches (rounded to the nearest tenth)

Therefore, the lateral area of the pyramid is 195 square inches.

b) The area of the base of a regular pentagonal pyramid is given by the formula:

Base Area = (1/2) × Perimeter of the base × Apothem

Base Area = (1/2) × 60 inches × 4.1 inches

Base Area ≈ 123 square inches

and, Total Area = Lateral Area + Base Area

Total Area ≈ 195 square inches + 123 square inches

Total Area ≈ 318 square inches

Therefore, the total area of the pyramid is 318 square inches.

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Considering the definition of an inequality, the maximum number of days that Ariana can rent the car while staying within her budget is 5 days.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "x" the number of days that Ariana can rent the car, the inequality in this case is

30.42x + 0.06×450 ≤200

Solving:

30.42x + 27 ≤200

30.42x ≤200 - 27

30.42x ≤173

x ≤173÷ 30.42

x≤ 5.687

Finally, the maximum number of days is 5 days.

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The point of concurrency of the angle bisectors is called the incenter. The incenter is the center of the incircle of a triangle, which is the largest circle that can be inscribed within the triangle.

The center present in the largest circle that can be inscribed in the triangle is defined as incircle. It is in the equal distance from all the sides present in the triangle , which makes it unique comparing to others.

The line that bisects the angle which is also called as angle bisector is one of the method to find the incenter. It divide the entire triangle into three triangles of same area and length. The triangle includes three bisectors to each angle.

These bisectors are intersected at the same point in the triangle , which is also termed as incenter of the triangle. This is because the incenter is in equal distance from each of the every side of the triangle, and this makes the angle bisectors to divide the triangle into parts which makes the incenter equidistant from all three sides of the triangle.

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A t-test with a level of significance of 0.05 results in a test statistic of -2.09, indicating a significant difference between the population mean for the math scores and the population mean for the EBRW scores.

To test for a difference between the population mean for the math scores and the population mean for the ebrw scores, we can conduct a two-sample t-test.

Using a calculator or software, we can find that the sample mean for math scores is 520.5 and the sample mean for ebrw scores is 485.5.

The sample size is n = 12 for both groups.

The sample standard deviation for math scores is s1 = 48.50 and for ebrw scores is s2 = 87.63.

Using a level of significance of 0.05, and assuming unequal variances, we can find the test statistic as:

t = (520.5 - 485.5) / sqrt((\(48.50^2/12\)) + (\(87.63^2/12\)))

t = 0.851

Rounding to two decimal places, the test statistic is 0.85.

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The probability that a friend of yours is jogging in place when you enter the express exercise circuit at a random time is 1/3, and the probability that your friend will be on the weight machines is also 1/3.

To determine the probabilities, we need to consider the duration of each activity relative to the total cycle time. The total cycle time is the sum of the durations for the weight machines (90 seconds), jogging in place (60 seconds), and aerobics (30 seconds), which gives a total of 180 seconds.

The probability that your friend is jogging in place is determined by dividing the duration of jogging (60 seconds) by the total cycle time (180 seconds), resulting in a probability of 1/3.

Similarly, the probability that your friend is on the weight machines is found by dividing the duration of using the weight machines (90 seconds) by the total cycle time (180 seconds), which also yields a probability of 1/3.

In summary, if you enter the express exercise circuit at a random time, the probability that your friend is jogging in place is 1/3, and the probability that your friend will be on the weight machines is also 1/3. This assumes that the activities are evenly distributed within the cycle, with equal time intervals allocated for each activity.

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Answer:

have  a nice day! you are loved!

Step-by-step explanation:

Answer: A= pp popo

Step-by-step explanation:

Answer: a = 22

Step-by-step explanation:

(2a + 3) +(6a +1 ) = 180

8a + 4 = 180

     -4      -4

8a = 176

8       8

a = 22

They are supplementary angles, so they add up to 180 degrees.

13.50<= 1.20c + 3 is the inequality

We can see that it costs her $3 in addition to the $1.20 she receives for each task she completes, which is "C," for a total of $13.50.

Start by deducting her initial investment ($3) from the total ($13.50) to find the solution. By doing this, you'll discover that Janie needs to earn $10.50 in order to meet her goal, and since she receives $1.20 for EVERY chore, you'll also want to determine how many chores it will take her to reach that amount. You can calculate this by simply dividing $10.50 by $1.20, which gives you the total number of tasks she must complete, which is 8 and third tasks.

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14/99

Select 1 marble; the chance that it is white is 4/12. Select a 2nd marble; the chance that it is white is 3/11. Select a 3rd; the chance it is white is 2/10. Select a 4th; the chance it is red is 8/9. Select a 5th; the chance it is red is 7/8. The chance of getting this specific set of 5 marbles in this order is (4/12)×(3/11)×(2/10)×(8/9)×(7/8)=(2×7)/(11×10×9).

This specific set could occur in the permutation of 5 things taken 5 at a time where 3 are identical (white), and the other 2 are also identical (red). The formula for this is 5!/(3!2!)=10.

Combining the chance of getting white, white, white, red, red with the number of ways 3 white and 2 red could have been distributed in the draw of 5 marbles gives the answer:

{(2×7)/(11×10×9)}×10=14/99

A similar process will show that the chance of getting 5 red marbles is 7/99; 4 white and 1 red is 1/99; 2 white and 3 red is 42/99; and 1 white and 4 red is 35/99.

The equation of line that passes through (4,2)

3x-4y-4 = 0

A line is a geometry object characterized under zero width object that extends on both sides. An straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called an straight line.

Given,

Line l₁ passes through point (4,2)

Equation of the line l₁ passing through a point (x', y') ≡ (4, 2), if its slope is m₁:

y-y' = m₁(x-x')

y-2 = m₁(x-4)     --------- (a)

Line l₂ passes through the points (x₁, y₁) ≡(-2,2) and (x₂, y₂) ≡ (2,5)

Slope of line l₂ (m₂) = (y₂-y₁)/(x₂-x₁)

⇒m₂ = (5-2)/(2-(-2))

⇒m₂ = 3/4

since l₁ and l₂ are parallel

then slope of l₁ will be equal to l₂

⇒ m₁ = m₂

⇒ m₁ = 3/4

Putting value of m₁ in equation (a)

y-2 = 3/4(x-4)

⇒ 4y-8 = 3x-12

⇒ 4y+4 = 3x

⇒ 3x-4y-4 = 0

Hence, the equation of straight line is 3x-4y-4 = 0.

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The approximate total area of the three 30°-60°-90° triangles used in Isabelle's tile floor pattern, with a longer leg length of 24 inches, is approximately 518.9 square inches when rounded to the nearest tenth.

To calculate the area of a 30°-60°-90° triangle, we need to know the length of one of its legs. In this case, the longer leg of each triangle is given as 24 inches.

The area of a 30°-60°-90° triangle can be calculated using the formula A = (1/2) * base * height, where the base is the longer leg and the height is the shorter leg.

In a 30°-60°-90° triangle, the ratio of the longer leg to the shorter leg is 2:1. Therefore, the shorter leg can be found by dividing the longer leg by 2, giving us 24/2 = 12 inches.

Using the formula for the area of a triangle, we can calculate the area of each triangle as (1/2) * 24 * 12 = 144 square inches.

Since Isabelle is using three triangles in her design, the total approximate area would be 144 * 3 = 432 square inches.

Therefore, the approximate total area of the three 30°-60°-90° triangles in Isabelle's tile floor pattern, with a longer leg length of 24 inches, is approximately 432 square inches when rounded to the nearest tenth.

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Answer:

13.6 and 2.18 AND 1.36 and 21.8

Step-by-step explanation:

Answer:

b is the answer

Step-by-step explanation:

this might help you out..

Answer: 15/7 2 1/7

Step-by-step explanation: First divide 8x-3=x+12 Then add 3 to both sides.

8x=x+15 Subtract x from both sides. 7x=15 Then divide again so 7/7 and 15/7. If you simplify it become 2 1/7

Answer:

x = 15/7

Step-by-step explanation:

Reduce the fraction with 2

8x - 3 = x + 12

Move variable to the left-hand side and change its sign

8x - x - 3 = 12

Move constant to the right-hand side and change its sign

8x - x = 12 + 3

collect like terms

7x = 12 + 3

Add the numbers

7x = 15

Divide both sides of the equation by 7

Solution: x = 15/7

Alternate form

x = 2 1/7, x = 2.142857

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

the price of the shirt without discount is 75,000 pesos

Step-by-step explanation:

The computation of the price of the shirt without discount as follows:

There is a discount of 20%

And the person pays 60,000 pesos after considering the discount

So, the price without discount is

= 60,000 pesos ÷ 0.80

= 75,000 pesos

hence, the price of the shirt without discount is 75,000 pesos

The correct expansion of (3x – 2)(2\(x^2\) + 5) is 3x • 2\(x^2\) + 3x • 5 + (–2) • 2\(x^2\) + (–2) • 5. Thus, option A is the right answer to the given question.

To expand an expression of multiplication of two variables to two variables is done as follows:

1. We take the first term of the first expression which in this case is 3x

2. We multiply it by the first term of the second expression. In this case, we get 3x • 2\(x^2\).

3. Subsequently we multiply the first term with further terms and add them. In the given case, the expression we get is 3x • 2\(x^2\) + 3x • 5

4. Then we take the second term of the first expression and repeat the above steps and add it to the existing equation.

We get x • 2\(x^2\) + 3x • 5 + (–2) • 2\(x^2\) + (–2) • 5 as the answer.

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Answer:

10q^2+3q

Step-by-step explanation:

All you have to do is combine like terms I think

(I haven't done this stuff in ages so I'm most likely wrong)

Answer:

10q^2+3q

Step-by-step explanation:

2q^2 +3q +8q^2

Combine like terms

10q^2+3q

to minimize the time it takes to reach the island, the visitor has to run 15 km west of the tent to first get to the closest point of the shoreline to the island before swimming across to the island.

Here we have;

Location of island = 15km west

Location of tent = 2 km south of point on shoreline

Running speed of visitor = 8 km/h

Swimming speed = 1 km/h

Distance of island from tent = \(\sqrt{15^2 +2^2}\) = 15.13

Since, time = distance/speed, it will take 15.13/1 hours or 15.13 hours to swim directly to the island.

However if the visitor first runs to the closest point on the shoreline to the island, then swims across to the island, it will take;

15/8 Hr + 2/1 hr = 31/8 hours or 3.875 hours only.

Therefore, to minimize the time it takes to reach the island, the visitor has to run 15 km west of the tent to first get to the closest point of the shoreline to the island before swimming across to the island.

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