Factor these polynomials

f(x) = x^2 - 8

f(x) = 25x^2 -12

The interval of convergence of the Maclaurin series of (A)-1 is x≈P(x)=x

The concept of Maclaurin series states that the function is just the part of Taylor series of the function if in the Taylor series the center is taken as c = 0 then the Taylor series is called Maclaurin series.

Here we need to find the the interval of convergence of the Maclaurin series.

Let us consider  x up to n=3. and the function is x.

Then the Maclaurin series is given by

Find the 1st derivative: f(1)(x)=(f(0)(x))′=(x)′=1

valuate the 1st derivative at the given point: (f(0))′=1

Find the 2nd derivative: f(2)(x)=(f(1)(x))′=(1)′=0

Evaluate the 2nd derivative at the given point: (f(0))′′=0

Find the 3rd derivative: f(3)(x)=(f(2)(x))′=(0)′=0 (steps can be seen here).

Evaluate the 3rd derivative at the given point: (f(0))′′′=0

Now, use the calculated values to get a polynomial:

f(x)≈0/0! x⁰ + 1/1! x¹ + 0/2! x² + 0/3! x³

Finally, after simplifying we get the final answer:

=> f(x)≈P(x)=x

Therefore the Taylor (Maclaurin) series of x up to n=3 is x≈P(x)=x

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We are not given the radius of the circle or any other relevant data, so I assumed the radius of the circle r=5

Answer:

The y-coordinate of Q is 3

Step-by-step explanation:

Circles and Lines

The figure below shows a circle of radius r=5 and a segment that goes from the center of the circle to a point of the circumference, where x=4.

We can find the y-coordinate of that point by using Pithagora's theorem:

\(r^2=x^2+y^2\)

Solving for y:

\(y^2=r^2-x^2\)

\(y^2=5^2-4^2\)

\(y^2=25-16=9\)

\(y=\sqrt{9}=3\)

The y-coordinate of Q is 3

Answer:

Acute

Step-by-step explanation:

All triangles have to have a acute or it would be to big

Answer:

yes it is because its a triangle and its acute

Answer:

Step-by-step explanation:

19. sin (35) = 4/x

    x = 4/sin (35) = 6.97

Option C

20. sin(40) = x/7

x = 7* sin(40) = 4.50

Answer:

Step-by-step explanation:

a)  (0, 12)

b)  12

P = 12 x 1.4⁰ = 12

c) P = 12 x 1.4³ ≈ 33 rabbits

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

Answer:

Step-by-step explanation:

Refer to attached

Find the y-intercept:

Find the x-intercepts:

We have vertices of the triangle at:

Base of the triangle is:

Height of triangle:

The area is:

Answer:

7.5 unite square

Step-by-step explanation:

someone already explained so i will just tell you the steps. I deeply apologize for the inconvieence, grammer mistakes, and lack of showing work.

step 1.

find the x- and y intercepts

step 2.

find the vertexes

step 3.

pug the points onto the cordiante plane

s

Answer: 2.5

Step-by-step explanation:

Answer:

2 1/2

Step-by-step explanation:

Do keep change flip. Make 2 an improper fraction by making it 2/1. Change the division symbol to a multiplication symbol. Flip 4/5 to 5/4. The equation you should have is 2/1x5/4.  2x5=10 1x4=4. the fraction you should have is 10/4. 10 divided by 4 =2.5. the fraction you should have now is 2 2/4. Simplify 2 2/4 to 2 1/2.

Step-by-step explanation:

51x + 23y = 116 ……….. (i)

23x + 51y = 106 ………… (ii)

Subtracting (ii) from (i)

28x – 28y = 10

28(x – y) = 10

⇒ (x – y) = 10/28 = 5/14

The solution of the expression x- y is 5/14.

Given Equation:

Equation 1: 51x + 23y = 116

Equation 2: 23x + 51y = 106

Now, multiply 23 in equation 1 and 51 in equation 2 gives

Equation 3: 1173x + 529y = 2,668

Equation 4: 1173x + 2601 y = 5406

Solving the Equation 1 and (3) gives

2601y - 529y = 5406 - 2668

2072y= 2738

y = 37/28.

Substituting the value of y= 37/28 in Equation 1 gives

51x + 23(37/28)= 116

51 x= 2397/28

x= 47/28

So, the value of x-y

= 47/28 - 37/28

= 10/28

= 5/14

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Answer:

25.50 is the final price

Step-by-step explanation:

First find the new price at 15% off

59.99 * 15%

59.99 * .15

9.00

Subtract 9 dollars from the price

59.99-9.00

50.99

Now take 50% off

50.99 * 50%

50.99*.50

25.50

50.99-25.50

25.50

Answer:

yes it is 604892÷4=151,223

Step-by-step explanation:

(a) The average rate of change of h on the interval (40000, 55000) is given by the formula:

(h(55000) - h(40000)) / (55000 - 40000) = (13200 - 15500) / (55000 - 40000) = -2200 / 15000 = -0.147

This value is the average rate of change of the car's value per mile driven.

(b) The best possible estimate of h'(55000) is given by the formula:

[h(70000) - h(55000)] / (70000 - 55000) = (11100 - 13200) / (70000 - 55000) = -2100 / 15000 = -0.14

This estimate suggests that the rate of change of the car's value per mile driven at 55000 miles is around -0.14 dollars per mile.

(c) h'(30000) is expected to be greater than h'(80000) because the rate of change of a function at a lower value of the independent variable is typically greater than the rate of change at a higher value of the independent variable. This is because as the independent variable (miles driven) increases, the dependent variable (value of the car) is decreasing at a slower rate.

(d) The long-term behavior of the function V = h(m) is that the value of the car decreases as the number of miles driven increases. The long-term behavior of h'(m) is that the rate of change of the car's value per mile driven decreases as the number of miles driven increases, meaning that the decrease in value is happening at a slower rate. Practically speaking, this means that the value of the car decreases more quickly when it is new and decreases more slowly as it gets older and has more miles on it

Answer:

Parent function is g(x) = x² a quadratic

Step-by-step explanation:

quadratic; translation down 4 units  

-4 means the vertex will move down 4

The transformation of the parent function that represents translation down 4 units. Therefore, quadratic; translation down 4 units.

The given function is g(x)=x²-4.

A parent function is the simplest function that still satisfies the definition of a certain type of function. For example, when we think of the linear functions which make up a family of functions, the parent function would be y = x. This is the simplest linear function.

Quadratic; translation down 4 units:

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)² + k, where a ≠ 0.

The transformation of the parent function that represents translation down 4 units. Therefore, quadratic; translation down 4 units.

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Answer:

7400

Step-by-step explanation:

Answer:

7400

Since

3256 + (74×56)

3256 + 4144

7400

Answer:

11

Step-by-step explanation:

just put the values in for the variables

5(3)(1) - 4(1)

15(1) - 4(1)

15 - 4

11

(Brainliest pleaseee)

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

-7 is the lowest number, since it is a negative. The absolute value of -2, or |-2|, is 2 making it the second lowest. 3 comes next. The absolute value of 4.5 is 4.5, being the greatest number.

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

First, let's find -2 and |4.5| .

Absolute value of a number is its distance from 0. Remember, absolute value is always zero or positive.

Now, let's use a number line to order the numbers. Numbers to the left are less than numbers to the right.

The values in order from least to greatest is as follows: -7, |-2|, 3, |4.5|.

==================================================

Work Shown:

\(\displaystyle \lim_{x \to 3} \frac{f^2(x)-4}{f^2(x)-f(x)-2}\\\\\\\displaystyle \lim_{x \to 3} \frac{(f(x)-2)(f(x)+2)}{(f(x)-2)(f(x)+1)}\\\\\\\displaystyle \lim_{x \to 3} \frac{f(x)+2}{f(x)+1}\\\\\\\displaystyle \frac{f(3)+2}{f(3)+1}\\\\\\\displaystyle \frac{2+2}{2+1}\\\\\\\displaystyle \frac{4}{3}\\\\\\\)

Notes:

In step 2, I used the difference of squares rule to factor the numerator. The denominator can be factored through trial and error. The key here is the f(x)-2 terms that show up in each. Those factors cancel in step 3.

Afterward, we apply the substitution rule, \(\displaystyle \lim_{x \to a} f(x) = f(a)\), so basically I plugged in x = 3. Then evaluated f(3) = 2 due to the point (3,2).

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

5/6

Step-by-step explanation:

1/2x3= 3/6

1/3x2=2/6

3/6+2/6=5/6

Answer:

54 is the answer

have a great dayyyy

Answer:

there are 64 feet in18 yards

Step-by-step explanation:

1 yard equals 3 feet

Answer:  2,175 divided by 12 will give you 181.25.

The measure of the arc or angle is:

m∠NLM = 60 deg

From the given figure, line LN is the diameter. Thus, the measure of arc LN is 180° (semicircle).

Thus, we can say:

arc NM + arc ML = 180°

(3x + 21) + (8x + 16) =  180°

11x + 37 = 180

11x = 180 - 37

11x = 143

x = 143/11

x = 13

arc NM = 8x + 16

put x = 13:

arc NM = 8(13) + 16 = 120°

Recall that:

The measure of inscribed angle is half the measure of its intercepted arc. That is:

m∠NLM = 1/2 * 120°

m∠NLM = 60°

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Answer:

20

Step-by-step explanation:

Because 21.50 x 20 =430

and 18 x 20 = 360

then you add 70 to 360 and you get 430

so Katrina would have to order 20 shirts from each company in order for the cost to be the same.

Answer: 2

Step-by-step explanation:

The best first step in solving m–2(m–4)≤3m for m will be A. Distribute -2 through the parentheses.

It should be noted that an inequality simply means a relation between the expressions that are unequal.

It should be noted that the best first step in solving m–2(m–4)≤3m for m will be to distribute -2 through the parentheses.

This is important in order to have variables of m and then solve accordingly.

In conclusion, the best option is A.

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Answer:

10.74666666666667 per quart

Step-by-step explanation3 divided 36.24

Answer:

5/28.

Step-by-step explanation:

3/7 * 5/12

= (3*5) / (7*12)

= 15/84

= 5/28.