Use the function y= 3/4x-1 to answer parts (a) & (b) below:

a. Find the equation of the inverse function of the given function using only algebra.

b. Using the coordinate grid, show how you can find the inverse function of the given function without using algebra. Then explain in at least one complete sentence how you know you found the correct inverse function based on your graph.

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer:

To find the equation of the line containing the segment DE, we can use the coordinates of D and E to find the slope:

slope = (change in y) / (change in x) = (0 - 3) / (4 - 2) = -3/2

We can use the point-slope form of the equation of a line, using either D or E as the point:

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

Simplifying this equation, we get:

y = (-3/2)x + 6

Similarly, to find the equation of the line containing the segment EF, we can find the slope using the coordinates of E and F:

slope = (change in y) / (change in x) = (-2 - 0) / (1 - 4) = 2/3

Using either E or F as the point, we can write the equation in point-slope form:

y - 0 = (2/3)(x - 4)

Simplifying, we get:

y = (2/3)x - (8/3)

To find the equation of the line containing the segment TV, we can find the slope using the coordinates of T and V:

slope = (change in y) / (change in x) = (0 - 3) / (-2 - 0) = 3/2

Using either T or V as the point, we can write the equation in point-slope form:

y - 3 = (3/2)(x - 0)

Simplifying, we get:

y = (3/2)x + 3

Finally, to find the equation of the line containing the segment VW, we can find the slope using the coordinates of V and W:

slope = (change in y) / (change in x) = (-2 - 0) / (1 - (-2)) = -2/3

Using either V or W as the point, we can write the equation in point-slope form:

y - 0 = (-2/3)(x - (-2))

Simplifying, we get:

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

Answer:

are reflection across the y-axis and translation 2 units right.

Step-by-step explanation:

Taking into account the zeros of a quadratic function, the time of the rocket when it is in the air is equal to 1.5 seconds.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

The zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

A rocket launched with height function h(t)= -16t²+ 24t

where

Time for which rocket is in the air given by h(t) = 0, so:

0= -16t²+ 24t

where:

Solving:

[tex]x1=\frac{-24+\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]

[tex]x1=\frac{-24+\sqrt{24^{2}} }{2x(-16)}[/tex]

[tex]x1=\frac{-24+24 }{2x(-16)}[/tex]

[tex]x1=\frac{0 }{-32}[/tex]

x₁= 0

and

[tex]x2=\frac{-24-\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]

[tex]x2=\frac{-24-\sqrt{24^{2} } }{2x(-16)}[/tex]

[tex]x2=\frac{-24-24}{2x(-16)}[/tex]

[tex]x2=\frac{-48}{-32}[/tex]

x₂= 1.5

Therefore, the time of the rocket in the air is 1.5 seconds.

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Answer:

a₂₆ = 248

Step-by-step explanation:

to find the 26th term substitute n = 26 into the explicit formula

a₂₆ = 14 + 9(26) = 14 + 234 = 248

The theoretical probability of each section is 1/8, since there are 8 equal-sized sections on the spinner. To find the theoretical frequency, we multiply the theoretical probability by the total number of spins:

Theoretical frequency = (1/8) x 450 = 56.25

We can then calculate the experimental probability for each section by dividing the frequency by the total number of spins:

Experimental probability = Frequency/Total number of spins

Using this formula, we can calculate the experimental probabilities for each section:

Part 1: Experimental probability = 58/450 ≈ 0.129

Part 2: Experimental probability = 52/450 ≈ 0.116

Part 3: Experimental probability = 39/450 ≈ 0.087

Part 4: Experimental probability = 77/450 ≈ 0.171

Part 5: Experimental probability = 50/450 ≈ 0.111

Part 6: Experimental probability = 43/450 ≈ 0.096

Part 7: Experimental probability = 60/450 ≈ 0.133

Part 8: Experimental probability = 71/450 ≈ 0.158

To find the number with the greatest difference between the theoretical and experimental probability, we can calculate the difference between the two probabilities for each section:

Part 1: |0.125 - 0.129| = 0.004

Part 2: |0.125 - 0.116| = 0.009

Part 3: |0.125 - 0.087| = 0.038

Part 4: |0.125 - 0.171| = 0.046

Part 5: |0.125 - 0.111| = 0.014

Part 6: |0.125 - 0.096| = 0.029

Part 7: |0.125 - 0.133| = 0.008

Part 8: |0.125 - 0.158| = 0.033

As we can see, the greatest difference between the theoretical and experimental probability is for Part 4 with a difference of 0.046. This indicates that the experimental frequency for Part 4 is significantly different from the theoretical frequency, which may suggest that the spinner is biased towards that section.

Answer: -3x+y

Step-by-step explanation:

This is a subtraction problem and "from" means it's the 1st number so

(2x+7y) - (5x + 6y)       be careful to distribute negative

2x +7y - 5x -6y

-3x+y

To find the simplest expression when (5x + 6y) is subtracted from (2x + 7y), we subtract the coefficients of like terms. This gives us -3x + y as the final result.

The expression represents the difference when (5x + 6y) is subtracted from (2x + 7y) can be found using the properties of addition and subtraction for algebraic expressions. We will combine like terms to simplify.

So, Subtract (5x + 6y) from (2x + 7y), it's like saying (2x + 7y) - (5x + 6y) this will give us:

-3x + y is the final expression in the simplest form.

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The ratio of the number of sweets that Amber has to the number of sweets that Callum has is 16:9.

A quantitative comparison of two or more quantities that shows their relative sizes is called a ratio.

In terms of how many times one is greater or less than the other, it describes the relationship between the two quantities.

Let's assume that Amber and Bethan bought x number of sweets, then Callum and David also bought x number of sweets.

According to the problem, Amber and Bethan share the sweets in the ratio 2:1. Therefore, Amber has (2/3)(x) sweets and Bethan has (1/3)(x) sweets.

Also, Callum and David share the sweets in the ratio 3:5. Therefore, Callum has (3/8)(x) sweets and David has (5/8)(x) sweets.

Now, we can find the ratio of the number of sweets that Amber has to the number of sweets that Callum has as follows:

Amber/Callum = [(2/3)(x)]/[(3/8)(x)] = (16/9)

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The solution of compound interest problem using formula of amount  is

Anna have$2,734 more money than  Hudson.

Compound interest is a type of interest in which the interest gained is added to the principal sum before the interest for the subsequent period is calculated using the updated total sum. In other words, in addition to the initial principal, the accumulated interest from prior periods is also taken into account for calculating interest. As a result, as time passes, the interest earned increases, increasing the total amount earned or due. Savings accounts, loans, and investments frequently use compound interest.

For continuous compounding, the formula is:

A = Pe^(rt)

Where:

A = the amount after t years

P = the principal amount

r = the annual interest rate (as a decimal)

t = the time in years

For daily compounding, the formula is:

A = P(1 + r/n)^(nt)

Where:

A = the amount after t years

P = the principal amount

r = the annual interest rate (as a decimal)

n = the number of times compounded per year

t = the time in years

Using these formulas, we can calculate the amount that Anna and Hudson will have after 10 years, and then find the difference between them.

For Anna's investment:

r = 8.5% = 0.085 (as a decimal)

t = 10 years

P = $69,000

A = Pe^(rt) = 69000 * e^(0.085*10) = $156,794.63

For Hudson's investment:

r = 8 3/8% = 8.375% = 0.08375 (as a decimal)

n = 365 (daily compounding)

t = 10 years

P = $69,000

A = P(1 + r/n)^(nt) = 69000(1 + 0.08375/365)^(365*10) = $154,060.52

Therefore, the difference between the two amounts is:

$156,794.63 - $154,060.52 = $2,734.11

So Anna will have approximately $2,734 more in her account than Hudson after 10 years.

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The crucial t-value is determined to be 1.734 using a t-table with 19 degrees of freedom and a significance threshold of 0.05 for a one-tailed test.

A type of statistical hypothesis known as a null hypothesis claims that a certain collection of observations has no statistical significance. The viability of hypotheses is evaluated using sample data. known as "zero" at times and represented by the letter H0. The assumption made by researchers is that there is a relationship between the variables. The null hypothesis, on the other hand, asserts that such a connection does not exist. Although it might not seem significant, the null hypothesis is an important part of research.

We may run a one-tailed t-test for the standard deviation to test the hypothesis that the standard deviation of heights of major-league baseball players is less than 2.7 inches.

The following formula may be used to get the sample standard deviation of the players' heights among the 20 chosen at random:

where n is[tex]s = 1/(n-1) * \sum(x' - x)^2 = 1/(20-1) * (1.83-1.755)^2 + ... + (1.9-1.755)^2 = 0.0414[/tex] the sample size, xi is the player's height at position i, and x is the average player's height in the sample.

The test statistic may then be calculated as follows:

[tex]t = (n-1) * s^2 / \sigma ^2 = 19 * 0.0414^2 / 2.7^2 = 0.197[/tex]

The crucial t-value is determined to be 1.734 using a t-table with 19 degrees of freedom and a significance threshold of 0.05 for a one-tailed test.

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Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.

Exponents, usually referred to as powers and indices, are a type of mathematical operation that requires increasing a base number to a specific exponent. You can multiply the minimum amount by itself a given number of times using the exponent. For instance, the number 2 raised toward the power of 3 (printed as 23) is equivalent to 2 x 2 x 2, which is 8. Exponents are frequently employed in scientific notation, algebra, and other areas of mathematics to express extremely big or extremely small integers.

given

The distributive property of multiplication is used to multiply out the expression when expanding (x+2y) in ascending powers of x.

[tex](x + 2y) = x + 2yx^0[/tex]

By remembering that every number raised to the power of zero equals 1, we may simplify the second term. We thus have:

(x + 2y) = x + 2y(1) (1)

When we multiply the expression, we get:

(x + 2y) = x + 2y

Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.

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The equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

A linear equation has the formula y = mx + b, where x and y are variables, m is the angle of the line's slope, and b denotes the y-intercept (the location where the line crosses the y-axis). On a graph, this equation represents a straight line.

The y-intercept of a linear equation, which is determined by the value of b, is first plotted on a graph. The slope is then used to determine further points along the line. How much y changes for each unit of x is indicated by the slope. For instance, if the slope is 2, then y grows by 2 for every unit increase in x.

Given that, a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.

Let us suppose number of minutes = x.

Then,

Cost = 0.75 + 0.15(x - 3)

hence, the equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

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The complete question is:

Answer:

half-life ≈ 2.74

Step-by-step explanation:

One formula we can use for half life is,

N(t) = No * (1/2)^(t / t_1/2), where

We already know that N(t) = 28, No = 128, the base is 1/2, and t is 6.  Thus, we must solve for t_1/2 using the following equation:

28 = 128 * (1/2) ^ (6 / t_1/2)

(28 = 128 * (1/2) ^ (6 / t_1/2) / 128

0.21875 = (1/2) ^ (6 / t_1/2)

ln (0.21875) = ln (1/2 ^ (6 / t_1/2))

ln (0.21875) = 6 / t_1/2 * ln (1/2)

(ln ( 0.21875) = 6 / t_1/2 * ln (1/2)) / ln (1/2)

ln (0.21875) / ln (1/2) = 6 / t_1/2

[tex]\frac{ln(0.21875)}{ln(1/2)}=\frac{6}{t_{1/2} }\\ \\ t_{1/2}*ln(0.21875)=6*ln(1/2)[/tex]

(t_1/2 * ln (0.21875) = 6 * ln (1/2)) / ln (0.21875)

t_1/2 = (6 * ln (1/2) / ln (0.21875)

t_1/2 = 2.736420983 hours

t_1/2 = 2.74 hours

The only real difference between the longer number and the rounded number is that the longer answer gives a more exact answer when you plug it in, but the rounded answer seems to make more sense to write:

Result when plugging in exact answer for t_1/2:

N (2.736420983) = 128 (1/2) ^ (6 / 2.736420983) = 28

Result when plugging in rounded answer for t_1/2:

N (2.74) = 128 (1/2) ^ (6 / 2.74) = 28.05564116

20.49 trillion is 412.25% larger than 4.00 trillion.

To calculate the percentage increase of a value from an initial value to a final value, you can use the following formula:

increase in percentage = ((final value - initial value) / initial value) x 100%

Percentage increase is useful in a variety of contexts, including: Finance, Sales, Economics, Science, Education. Percentage increase is a useful tool for measuring growth or change over time and comparing different values.

To find the percentage increase, we first need to calculate the difference between the two numbers:

20.49 trillion - 4.00 trillion = 16.49 trillion

Next, we can divide the difference by the original amount (4.00 trillion) and multiply by 100 to get the percentage increase:

(16.49 trillion / 4.00 trillion) * 100 = 412.25%

Therefore, 20.49 trillion is 412.25% larger than 4.00 trillion.

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Answer:

x = -3

Step-by-step explanation:

We know that,

[tex]\sf a^x*a^y=a^{x+y}\\\\(a^x)^y=a^{xy}\\\\\frac{a^x}{a^y} =a^{(x-y)}[/tex]

Accordingly,

[tex]\sf \frac{(7^{10})^2}{7^4} =\frac{7^9*7^{10}}{7^x} \\\\\sf \frac{7^{10*2}}{7^4} =\frac{7^{9+10}}{7^x} \\\\\sf \frac{7^{20}}{7^4} =\frac{7^{19}}{7^x}\\\\7^{20-4}=7^{(19-x)}\\\\16=19-x\\\\16-19=x\\\\-3 =x[/tex]

Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways

Answer:

Step-by-step explanation

A=bh for a parallelogram.  The diagram is flipped(turn your paper)

b=9

h=6.7

A=(9)(6.7)=60.3 in²

The amount of money in the account after 17 years, to the nearest dollar, would be $76,956.

What is the formula for the future value?

The formula for the future value of an investment with continuous compounding is [tex]A = Pe^{(rt)}[/tex] where A is the future value, P is the principal (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the number of years.

Putting in the given values,

[tex]A = 52000 \times e^{(0.021 \times 17) }\\ A ≈ 76,956.18[/tex]

Therefore, the amount of money in the account after 17 years, to the nearest dollar, would be $76,956.

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The solution to the inequality, 4 - 2x ≥ 10, is x ≤ -3.

The graph is shown below.

To graph the solution to the inequality given, we have to first of all solve for the possible values of x in the given inequality.

Given the inequality,  4 - 2x ≥ 10, we have:

4 - 2x ≥ 10

Subtract 4 from both sides:

4 - 4 - 2x ≥ 10 - 4

-2x ≥ 6

Divide both sides by -2:

-2x/-2 ≤ 6/-2

x ≤ -3

This means that the values of x are equal to -3 or less than -3.

The graph below shows the solution.

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For the frequency distribution table;

1. The total number of observation is 24.

2. The width of each class is 11

3. The midpoint of the second class is 26

4. The model class is 65-75

5. The class limits of the next class is 76-86

For the frequency distribution table,

1. Total observation is the sum of the frequency:

2 + 3 + 5 + 6 + 0 + 8 = 24

2. The width is the first limit lower class - first limit of upper class.

21-10 = 11 or 32-21 = 11

3. The midpoint of class 2 is 21 + 31 = 52/2 = 26

4.   The class with the highest frequency is the model class      

5. Next class lower limit = 75 + 1 = 76

   Next class upper limit = 75 + 11 = 86

Use the frequency distribution to complete parts (a) through (e).

                                                                               Class            Frequency

a) Determine the total number of observations. 10-20               2

b) Determine the width of each class.                 21-31                 3

c) Determine the midpoint of the second class. 32-42               5

d) Determine the modal class (or classes).          43-53               6

e) Determine the class limits of the next class    54-64                0

if an additional class were to be added.             65-75               8

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The value of x is 31/64 or 0.484375 and the value of 61/64 is given by adding the value of 29/64 and 31/64 which is 0.9375.

To convert a fraction to a decimal, you need to divide the top number by the bottom number. Here are the steps to follow:

1. Fraction should be written as numerator (top) divided by denominator (bottom).

2. Divide the numerator by the denominator using long division or a calculator.

3. Keep dividing until you get a decimal that terminates or repeats.

a) The given equation is

       [tex]\frac{61}{64} = \frac{29}{64} + x[/tex]

       [tex]\frac{61}{64} - \frac{29}{64} = x[/tex]

       [tex]x = \frac{31}{64}[/tex]

b) Now 31/64 = 0.484375 and given that 29/64 = 0.453125

Hence from the equation 61/64 = 29/64 + 31/64 = 0.453125 + 0.484375

= 0.9375.

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Answer:

sinA =9/41. CosA=40/41

Step-by-step explanation:

in right triangles, the sine, cosine and tangent represent ratios of the sides of a triangle. Sine of an angle is the ratio of the side opposite the angle divided by the hypotenuse and the cosine of the angle is side adjacent (touching) the angle divided by the hypotenuse.

The value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

here, we have,

The values of the angels will be calculated by using the trigonometry property.

Sin A = Perpendicular / Hypotenuse

Sin A = 9 /41

Cos A = Base / Hypotenuse

Cos A =  40 / 41

Therefore the value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

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The solution of given trigonometric Problem by using formula of sine , cosine , tangent is part A 1)cos-1(12/13) 2)∅=cos-1(2/3) 3)sin-1(4/13)

part B 1)13.75 unit 2) 8.112 unit 3) 5.5 unit

Trigonometry is a branch of mathematics that deals with the study of relationships between angles and sides of triangles. It primarily focuses on the properties and functions of angles, and how they can be used to calculate the measurements of sides and angles in a triangle.

Part A

1)In the given ΔACB  Right angle at ∠C

for find ∅ we use

          cos∅=B/H

          cos∅=AC/AB

          cos∅=12/13

           ∅=cos-1(12/13)

2)      cos∅= AC/AB

          ∅=cos-1(6/9)

           ∅=cos-1(2/3)

3)       sin∅=CB/AC

             ∅=sin-1(4/13)

Part-B

      1)   cos37°=11/x

              4/5=11/x

                x=55/4

                  x=13.75 unit

2)         tan32°=x/13

          0.624=x/13

          x= 8.112 unit

3)       cos 60°=x/11

         1/2= x/11

           x=11/2

            x=5.5 unit

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Answer:

Step-by-step explanation:

Therefore, the height of the tower is approximately 121.4 meters.

The point (2, 7) belongs to the solution region of the system of inequalities.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The system of inequalities given is:

y > 1.5x + 4

y > -x + 6

One point that belongs to the solution region of this system of inequalities is (2, 7).

To check if this point satisfies the system of inequalities, we can substitute the values of x and y into each inequality:

For the first inequality, y > 1.5x + 4, we have:

7 > 1.5(2) + 4

7 > 7

This is true, so the point (2, 7) satisfies the first inequality.

For the second inequality, y > -x + 6, we have:

7 > -(2) + 6

7 > 4

This is also true, so point (2, 7) satisfies the second inequality.

Therefore, points (2, 7) belong to the solution region of the system of inequalities.

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The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.

1. Let's calculate the probability of selecting a blue disk

We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is = 3/8

2. Let's calculate the probability of selecting the blue disk labeled with number 2 =

We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is = 1 /3

3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:

Probability of selecting a 2 given that a blue disk is selected =

3/8 x  1/3 = 3/24 = 1/8

Thus,it is correct to state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.

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Full Question:

See attached image.

Answer: 20,493

Step-by-step explanation:

%45 off of $37,260 is the same as (45 x 45) / 100 which equals to: 16,767

Then do: 37,260 - 16,767 = 20,493

And there you have it! Hope this helps!!

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - 2~~)^2 + (~~7 - 1~~)^2} \implies d=\sqrt{( 3 )^2 + ( 6 )^2} \\\\\\ d=\sqrt{ 9 + 36 } \implies d=\sqrt{ 45 }\implies d\approx 6.7[/tex]

x = -1 is a root of the polynomial only if C = 3.

We want to have x = -1 as a root of the polynomial, then we just need to solve:

f(-1) = 0

this is:

2(-1)³ - 4(-1)² - 3(-1) + C  =0

-2 - 4 + 3 + C = 0

-3 + C = 0

C = 3

Tha must be the value of C.

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Answer:

Step-by-step explanation:

8 points

Answer:

Step-by-step explanation:

Formula for trapezoid:

A=[tex]\frac{1}{2}[/tex](b1 + b2)h

1.  b1=5    b2=23  h=12

A=1/2(5+23)12

=168