Let f be the function defined by f(x) = 4x^3 - 5x + 3. Which of the following is an equation of the line tangent to the graph of f at the point where x = -1 ?

Answer:

asking all these questions why you asking all these questions

Step-by-step explanation:

Step-by-step explanation:

2.39 x 10^5 = 239000

239000 / 6 = 39833.333

39834 men

Answer:18

Step-by-step explanation:

Replace

2(2x2+5)

Solve in parentheses

2x2+5

4+5

9

Now multiply 9 by 2

2(9)

18

Answer:

18

Step-by-step explanation:

x(2x + y) =

2(2 ⋅ 2 + 5) =

2(4 + 5) =

2(9) =

18

hope this helps :)

Answer:

Step-by-step explanation:

a) To express -35/49 in standard form, we need to write it in the form a/b, where a and b are integers with no common factors other than 1 and b is positive. To do this, we can divide both the numerator and denominator by their greatest common factor (GCF). The GCF of 35 and 49 is 7, so:

-35/49 = (-1)(35/7) ÷ (7/7) = (-1)(5/1) ÷ (7/1) = -5/7

Therefore, -35/49 in standard form is -5/7.

b) To express 24/-12 in standard form, we follow the same procedure. The GCF of 24 and 12 is 12, so:

24/-12 = (24/12) ÷ (-12/12) = 2 ÷ (-1) = -2

Therefore, 24/-12 in standard form is -2.

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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If Carla plans to invest $9,000 for 10 years and  Better Bank offers a 10 year CD at an annual rate of 4% using simple interest. then investment will be worth $12600 .

What is simple interest?

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

Given that Carla plans to invest $9,000 for 10 years. Better Bank offers a 10 year CD at an annual rate of 4% using simple interest.

We know

A= PRT+ P =P(RT+1)

Where

A = Final amount,

P = Principal amount=9000

R = Annual interest rate in decimal form=0.04

t = Time in years=10

Final amount can be calculated as

\(&A=\$ 9000(1+0.04 \times 10) \\\\&A=\$ 9000(1+0.4) \\\\&A=\$ 9000(1.4) \\\\&A=\$ 12600\\\)

If Carla plans to invest $9,000 for 10 years and  Better Bank offers a 10 year CD at an annual rate of 4% using simple interest. then investment will be worth $12600 .

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To find the volume of the smallest cube-shaped box that can contain the pyramid, we need to first determine the length of the smallest edge of the box. Since the base of the pyramid is a square, the smallest edge of the box will be the diagonal of the square base of the pyramid.

Using the Pythagorean theorem, we find that the diagonal is:√(10² + 10²) = √200 = 10√2 inches Thus, the length of each edge of the smallest cube-shaped box that can contain the pyramid will be 10√2 inches. The volume of a cube is given by the formula

V = s³, where s is the length of one of its edges. Therefore, the volume of the box will be:(10√2)³ = 1000√8 cubic inches To simplify this expression, we can use the fact that √8 = √(4 · 2) = 2√2. Thus, the volume of the box is:1000√8 = 1000 · 2√2 = 2000√2 cubic inches Therefore, the volume of the smallest cube-shaped box that can contain Eric's pyramid is 2000√2 cubic inches, or approximately 2827.43 cubic inches to two decimal places.

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Answer:

D

Step-by-step explanation:

Factor
this is how is should be
x + 2 = 0
=> x = -2
x - 3 = 0
=> x = + 3

Answer:

C. These lines are perpendicular

Step-by-step explanation:

Answer:

C. the lines are perpendicular

Step-by-step explanation:

you can tell right away they're perpendicular because the slope gets flipped and changed the sign for in the second equation

2/3 going to -3/2 or vice versa means they are perpendicular

if they had the same slope they would have been parallel

Answer:

5

Step-by-step explanation:

divide 10 by 2

Answer:

There are 5 boys in the class

For the given quadratic function, the coefficient b is equal to 12.

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The question gives some points of the quadratic function, see below.

  x  f(x)

−10  24

−9  17

−8  12

−7  9

−6  8

−5  9

−4  12

From the given data you can find the coefficients by solving the system linear equation.

You can write a system linear equation using the points: (-10,24) ,(-9,17) and (-8,12) for example. Then, you have three equations:

100a-10b+c=24 (1)

81a-9b+c=17    (2)

64a-8b+c=12   (3)

Isolate the coefficient a, you have \(a=\frac{24+10b-c}{100}\). Replacing the variable a in equations 2 and 3, you have:

\(81* \frac{24+10b-c}{100}-9b+c=17 (2) \\\\ 64* \frac{24+10b-c}{100}-8b+c=12 (3)\)

Simplifying, you can rewrite it as:

\(\frac{-90b+19c+1944}{100}=17 (2) \\ \frac{-40b+9c+384}{25}=12 (3)\)

Next step, you should isolate the coefficient b from the previous equation 2. You have:

\(\frac{-90b+19c+1944}{100}=17\\ \\ -90b=1700-19c-1944\\ \\ -90b=-244-19c\\ \\ b=-\frac{-244-19c}{90} = \frac{244+19c}{90}\)

\(b=\frac{(244+19c)}{90} (4)\)

Replacing the variable b in the previous equation 3, you have:

\(\frac{-40*\frac{244+19c}{90}+9c+384 }{25} =12\\\). Multiplying both sides by 25, you find the coefficient c:

\(\frac{25*(-40(\frac{244+19c}{90})+9c+384)}{25}=12*25\\ \\ -40(\frac{244+19c}{90})+9c+384=300\\ \\ -4(\frac{244+19c}{9})+9c+384=300\\ \\ (\frac{-976-76c}{9})+9c+384=300\\ \\ -976-76c+81c+3456=2700\\ \\ -76c+81c=2700+976-3456\\ \\ 5c=220\\ \\ c=44\)

From the previous equation 4, you finally find the coefficient b. See below.

\(b=\frac{244+19c}{90} \\ b=\frac{244+19*44}{90}\\ \\ b=\frac{244+836}{90}\\ \\ b=\frac{1080}{90}\\ \\ b=12\)

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Answer:

Step-by-step explanation:

2000 * .125/12 = $20.83

at $100 remaining balance = $1920.81

at $75 remaining balance   = $1945.81

x = 3

y = 2

To evaluate the expression, just replace the given values of the variables into the equation, as follows:

4*x + 2*y

4*3 + 2*2

12 + 4 = 16

Answer:

0,3

Step-by-step explanation:

enter in a graphing calculator see where you hits 0

Answer:

the answer is 0,3

Answer:

2.5

Step-by-step explanation:

\(y=20(0.5)^3\\\)

\(y=20(0.125)\)

\(y=2.5\)

Hope this helped! :)

We can use the formula for gravitational potential energy (GPE) to find the height at which Jessie is off the ground:

GPE = mgh

where m is the mass of the object (in kg), g is the acceleration due to gravity (9.8 m/s² on Earth), h is the height (in meters) above some reference point where the GPE is defined.

In this case, we know that Jessie has a mass of 50 kg and 4,900 joules of GPE. Plugging these values into the formula, we get:

4900 = (50 kg)(9.8 m/s²)(h)

Solving for h, we get:

h = 4900 J / (50 kg x 9.8 m/s²)

h = 10 meters

Therefore, Jessie is 10 meters off the ground at the point where she has 4,900 joules of GPE.

Answer:

10 meters

Step-by-step explanation:

P.E = mgh

4900 = 50 × 9.8 × h

4900 = 490 × h

h = 10 m

Answer:

(x+14)+(x+3)=

Step-by-step explanation:

1. Expand my multiplying the numbers in parentheses by The GCF, (On the side of the parentheses, (7x2=14), (3x1=3), and switch those numbers with the new, expanded numbers with the old, smaller numbers (Don't forget to remove the GCF)

By the Comparison Test, the series ∑arctan(n)/n converges. Therefore, the correct option is b) converges.

The given series is ∑arctan(n)/n. We can use the Comparison Test to determine whether the series converges or diverges.Let an = arctan(n)/n.

In this case, we compare the given series to the p-series with p = 1. Since p = 1 is the boundary between a convergent and a divergent series, we use the Comparison Test.

Let bn = 1/n. Since 0 ≤ arctan(n)/n ≤ 1/n for all n, we have an ≤ bn for all n. So, by the Comparison Test, the series ∑arctan(n)/n converges.

We can use the Comparison Test to determine whether the series converges or diverges.

Let an = arctan(n)/n. In this case, we compare the given series to the p-series with p = 1.

Let bn = 1/n. Since 0 ≤ arctan(n)/n ≤ 1/n for all n, we have an ≤ bn for all n.

So, by the Comparison Test, the series ∑arctan(n)/n converges. Therefore, the correct option is b) converges.

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a) The initial amount a is 16,000.

b) The percent rate of change is 5%, the growth factor is 1.05.

c) The number of students enrolled after one year, based on the above growth factor, is 16,800.

d) The completion of the equation y = abˣ to find the number of students enrolled after x years is y = 16,000(1.05)ˣ.

e) Using the above exponential growth equation to predict the number of students enrolled after 22 years shows that 46,804 are enrolled.

An exponential growth equation shows the relationship between the dependent variable and the independent variable where there is a constant rate of change or growth.

An exponential growth equation or function is written in the form of y = abˣ, where y is the value after x years, a is the initial value, b is the growth factor, and x is the exponent or number of years involved.

a) Initial number of students enrolled at the college = 16,000

Growth rate or rate of change = 5% = 0.05 (5/100)

b) Growth factor = 1.05 (1 + 0.05)

c) The number of students enrolled after one year = 16,000(1.05)¹

= 16,800.

d) Let the number of students enrolled after x years = y

y = abˣ

y = 16,000(1.05)ˣ

e) When x = 22, the number of students enrolled in the college is:

y = 16,000(1.05)²²

y = 46,804

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The number of students enrolled at a college is 16,000 and grows 5% each year. Complete parts (a) through (e).

a) The initial amount a is ...

b) The percent rate of change is 5%, what is the growth factor?

c) Find the number of students enrolled after one year.

d) Complete the equation y = ab^x to find the number of students enrolled after x years.

e) Use your equation to predict the number of students enrolled after 22 years.

The equation of the inequality graph with dashed line

The equation of the inequality graph with solid line

Using the slope intercept form of the straight line which is of the form

y = mx + c

The slope, m is the ratio of the change in the output to the change in the input. This is given by the formula

m = (y₀ - y₁) / (x₀ - x₁)

Slope calculation using the points (0, -4) and  (2, 0)

m = (-4 - 0) / (0 - 2)

m = 2

y intercept, c from the graph

c = -4

applying inequality representations

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the solid line graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

y intercept, c from the graph

c = 4

The equation of the line is y = -x + 4

Solid lines indicate an equality in the inequality, while shading over the line indicates a greater than

hence y ≥ -x + 4

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(a) The expression for the image distance, di, for a concave mirror can be found using the mirror equation:

1/do + 1/di = 1/f

where do is the object distance, f is the focal length, and di is the image distance.

To find f, we can use the formula:

f = r/2

where r is the radius of curvature.

Substituting the given values, we get:

f = 19.1/2 = 9.55 cm
do = 5.7 cm

Now, we can solve for di:

1/5.7 + 1/di = 1/9.55

1/di = 1/9.55 - 1/5.7

di = -16.13 cm

Note: the negative sign for di indicates that the image is virtual and upright.

(b) Numerically, the image distance, di, is -16.13 cm.

(c) This is a virtual image.

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Answer:

y = (0,-2)

Step-by-step explanation:

change in y/ change in x.

-4/4 ---> slope is -1

plug x and y coordinates AND SLOPE into y=mx+b

-3= -4/4(1)+b

-3= -1 +b

-2=b

Answer:

ok look at comments for answers

Step-by-step explanation:

Answer:

24. -3, -1, 0, +1, +3

25. -4, -3, -2, +1, +2

26. -1, 0, +5, +7, +8

27. -7, -4, 0, +2, +3

28. -3, -2, -1, +4, +6

29. -11, -7, -4, +1, +3

:)

Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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After answering the presented question, we can conclude that The equation number of trials is predetermined: We're going to roll the dice 20 times.

An equation is a statement in mathematics that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). For example, 2 + 3 = 5 is an equation because the expression on the left-hand side (2 + 3) is equal to the expression on the right-hand side (5).

Equations are used in many areas of mathematics, science, and engineering to describe relationships between quantities and to solve problems. For example, equations are used to model physical phenomena, such as the motion of objects, the behavior of fluids, and the propagation of waves. They are also used in finance, statistics, and many other fields to analyze data and make predictions.

In this case, the random variable X reflects the number of times a specific number appears after rolling a 20-sided die 20 times.

To see if this situation fits the binomial distribution model, we must look at the four conditions listed below:

The trials are impartial: Each throw of the dice is distinct from the others.

There are just two possibilities: Each roll can produce one of the 20 numbers or none at all.

The likelihood of success is constant: The probability of rolling a given number on a 20-sided dice is the same for each roll.

The number of trials is predetermined: We're going to roll the dice 20 times.

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An initial amount of $725,000, an APR of 6.25%, and a desired time frame of 22 years, the monthly withdrawal amount would be approximately $4,491.95.

To calculate the monthly withdrawal amount that would completely exhaust your savings in 22 years, we can use the present value of an ordinary annuity formula. The present value (PV) represents the initial amount you have, the interest rate per period (i) is the monthly interest rate, and the number of periods (n) is the total number of months.

Here's the step-by-step calculation:

Convert the APR to a monthly interest rate:

Monthly interest rate (i) = Annual interest rate / Number of compounding periods per year

i = 6.25% / 12 = 0.0625 / 12 = 0.00521 (rounded to 5 decimal places)

Determine the total number of periods:

Total number of periods (n) = Number of years * Number of compounding periods per year

n = 22 * 12 = 264

Use the present value of an ordinary annuity formula to calculate the monthly withdrawal amount (PMT):

PMT = PV / [(1 - (1 + i)^(-n)) / i]

In this case, PV = $725,000

PMT = $725,000 / [(1 - (1 + 0.00521)^(-264)) / 0.00521]

Calculate the monthly withdrawal amount using a financial calculator or spreadsheet software:

PMT ≈ $4,491.95 (rounded to the nearest cent)

Therefore, you can withdraw approximately $4,491.95 per month to completely exhaust your savings in 22 years assuming monthly compounding.

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If the distance is 45 miles and speed of both cyclist is 14 and 16 miles per hour then they will take time of 1.5 hour to meet.

Given First cyclist is riding at 14 miles per hour and second at 16 miles per hour. The distance is 45 miles.

We know that speed is the distance covered by an object in a particular period of time.

Speed=distance/time.

It is expressed as kilometers per hour or miles per hour, etc.

If both riders are riding towards each other then the speed will be 16+14 =30 miles per hour.

Distance=45 miles.

Time =distance/speed

=45/30

=1.5

Hence if first cyclist is riding at 14 miles per hour and second is riding at 14 miles per hour and the distance is 45 miles then they will meet after 1.5 hours.

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A regular linear regression model is statistically helpful in providing a good fit to the information that can be used to make precise predictions about new information agendas.

A linear regression model is useful when the explanation of a significant amount of variation of the dependent variable utilizes one or more independent variables. The usability of a linear regression model can be comprehended by examining various statistical measures for instance

R-squared value of 1 shows that all of the changes in the dependent variable are elaborated by the independent variable, Hence, an R-squared value of 0 points that none of the variations is elaborated

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Answer:

5300.

If you're rounding to the nearest hundred you look at the tens place. If its 5 or over you go up. So in this case we'll raise the 2 to a 5 because 6 is above 5.

Answer:

2x

Step-by-step explanation:

i think this is correct, I'm not 100% sure that it is because the question was a little confusing.

ANSWER:

It would be 6x^3.

PRIOR NOTE:

For this question, it's slightly unclear regarding the formatting with it, but in here I'm going to assume that you've asked what is:

-2x * 3x * -x

when simplified. If it was something else, then the final answer would be different.

BACKGROUND:

To start, when multiplying two terms together, the variable will become squared or to the second power. For example:

2x * 2x = 4x^2

PROCESS:

With this question, it is asking for -2x * 3x * -x, though lets just start with the -2x * 3x part:

-2x * 3x = -6x^2

Now, finishing it off with the * -x part.

-6x^2 * -x = 6x^3

It goes to the third power, because now you have multiplied 3 x's together. The answer is also now positive since a negative * a negative = a positive.

With this, the final answer is 6x^3.