Eva and Archer, the Magnificent Math Kitties are wanting to find the coefficients a, b, and c so that the graph of f(x) = ax^2 + bx + c passes through the points (1,2), (-1,6), and (2,3). Eva says we can set up a system of equations to solve this problem, but Archer says that we can't since we have a quadratic function and not a linear function? Who is right? If Eva is correct, set up and use Gaussian Elimination to solve this augmented matrix. Hint: Eva is usually correct.

Answer:

y - 3 = 5/3(x - 6)

General Formulas and Concepts:

Algebra I

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Point-Slope Form: y - y₁ = m(x - x₁)  

Step-by-step explanation:

Step 1: Define

Point (9, 8)

Point (6, 3)

Step 2: Find slope m

Step 3: Write function

Slope m = 5/3

Point (6, 3)

The effective interest method is used to amortize the bond premium. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond. The journal entry for bond issuance is as follows: Dr. Cash 205,000, Dr. Premium on Bonds Payable 5,000, Cr. Bonds Payable 210,000

The effective interest method is a method of amortizing bond premium or discount that takes into account the time value of money. The effective interest is the interest that would be earned if the bond were purchased at its market value and held to maturity. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond.

The journal entry for bond issuance records the proceeds from the sale of the bonds, the premium on bonds payable, and the bonds payable. The proceeds from the sale of the bonds are equal to the face value of the bonds plus the premium.

The premium on bonds payable is a liability that represents the excess of the issue price of the bonds over their face value. The bonds payable account is a long-term liability that represents the amount that the company owes to the bondholders.

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Answer:

\(m=\frac{-1}{2}\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

\(m=\frac{-3-(-1)}{2-(-2)}\)

\(m=\frac{-3+1}{2+2}\)

\(m=\frac{-2}{4}\)

\(m=\frac{-1}{2}\)

Answer:

B

Step-by-step explanation:

Answer:

Scale factor = 1/2

Step-by-step explanation:

Explanation:

    A scale factor is a number you multiply the dimensions of a shape by to get the image. Because figure B has half the length and width, we can conclude the scale factor is 1/2.

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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Answer:

Primera pregunta: es el Jueves 21 de mayo

Segunda pregunta: Viajaría el 11 de abril

40 días en total si se cuenta desde el momento que tomo el vuelo.

Step-by-step explanation:

The required difference of the polynomial functions is -9s^2 + 4s - 2

Given the following difference of polynomial expressed as:

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

We are to find the difference

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

Expand

–6s^2 + 12s – 8 - 3s^2 - 8s + 6

Collect the like terms

–6s^2- 3s^2 + 12s - 8s - 8 + 6

-9s^2 + 4s - 2

Hence the required difference of the polynomial functions is -9s^2 + 4s - 2

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complete question

Find each difference.

(–6s2 + 12s – 8) – (3s2 + 8s – 6) =

–9s2 + 4s – 14

–9s2 + 4s – 2

–9s2 + 20s – 14

–9s2 + 20s – 2

The steps to construct an equilateral triangle inscribed in a circle are as shown above.

A polygon is a plane figure that is bound by three or more line segments that join at the vertices. Polygons can be constructed through a series of steps using various tools such as a compass, a straight edge, and a protector. Given the problem in step 2 to construct regular polygons inscribed in a circle, let us construct an equilateral triangle inscribed in a circle as follows:Step-by-step construction of an equilateral triangle inscribed in a circle by hand using a compass and straightedge:Step 1: Draw a circle of radius r and label the center O. Step 2: Construct a line segment that passes through the center O of the circle, and let the line segment be labeled AB. Step 3: Place the compass on point A and draw an arc that intersects circle O at point C. Without adjusting the compass, place the compass on point B and draw another arc that intersects circle O at point D. Step 4: With the same radius from Step 3, place the compass on point C and draw an arc that intersects line AB at point E. Step 5: Place the compass on point D and draw another arc with the same radius from Step 3 that intersects line AB at point F. Step 6: Draw a line segment from point C to point F and another line segment from point D to point E. The line segments CF and DE should intersect at point G.Step 7: Draw a line segment from point G to point O.

Finally, triangle CEF is the desired equilateral triangle inscribed in the circle O.A screenshot of the construction is as follows:Answer: The steps to construct an equilateral triangle inscribed in a circle are as shown above.

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let s = speed in still water

let c = rate of the current

then

(s-c) = effective speed up-stream

and

(s+c) = effective speed down-stream

Write a distance equation for each way; dist = time * speed

5/6*(s-c) = 5

1/2 *(s+c) = 5

Now we get rid of the fractions

5(s-c)=30

s + c = 10

5s - 5c = 30

s + c = 10

siplifying:

s - c = 6 (1)

s + c = 10 (2)

adding:

2s = 16, then s = 8

8 mph is the boat speed in still water

According with (2):

8 + c = 10, then c = 2

2 mph is the speed of the current

Answer:

(-2, -4)

Step-by-step explanation:

Start at point O which has coordinates (0, 0). Go 2 units left. Go 4 units down. Now you are at point I.

Answer: (-2, -4)

Answer: 1,004.8 cubic meters (choice D)

Work Shown:

V = (1/3)*pi*r^2*h

V = (1/3)*3.14*8^2*15

V = 1,004.8

The number of cruise passengers must there have been in 2017 is  26.7 million.

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

\(\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}\)

Multiplying both sides by 100;

\(\begin{aligned}&\frac{106.7 x}{100} * 100=28.5 * 100 \\&106.7 x=2850\end{aligned}\)

Dividing both sides by 106.7;

\(\frac{106.7 x}{106.7}=\frac{2850}{106.7}\)

x = 26.7

Therefore, the number of cruise passengers in 2017 must have ranged from 26.7 million.

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Answer:

The notation "f(x)" is exactly the same thing as "y"

Step-by-step explanation:

The effect of using f(x) instead of y is that it allows us to talk about f.

If we have an equation relating X to Y then that's a relationship between rwo nimbers.

For example if you have that y=

\(y = {x}^{3} \)

...then that means that X and Y are some numbers obeying that equation

Answer:

See below

Step-by-step explanation:

All other parabolas are transformations of \(y=x^2\)

Transformations include:

Answer:

amount invested in the account that earns 10% interest  = Rs 3500

amount invested in the account that earns 8% interest  =Rs 5500

Step-by-step explanation:

Two equations can be derived from the question

x + y = 9000 equation 1

0.08x + 0.1y = 790 equation 2

x = amount invested in the account that earns 8% interest

y =  amount invested in the account that earns 10% interest

multiply equation 1 by 0.08

0.08x + 0.08y = 720 equation 3

subtract equation 3 from 2

0.02y = 70

divide both sides of the equation by 0.02

y = 70 / 0.02

y = 3500

Substitute for y in equation 1

x + 3500 = 9000

x = 9000 - 3500 = 5500

Answer:

145000x2

=answer

then

answer×2

= final answer

Answer:

580,000 people

Step-by-step explanation:

First, find out how many times the population will double. Divide the number of years by how long it takes for the population to double.

48÷24=2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

145,00022=580,000

That calculation could also be written with exponents:

145,000 x 2^2=580,000

After 48 years, the population will be 580,000 people.

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

1 3/4

Step-by-step explanation:

Left Improper Conversion =

2 × 10

1 × 10

+

1/10

Left Improper Fraction =

21/10

Right Improper Conversion =

1 × 5

1 × 5

+

1/5

Right Improper Fraction =

6/5

Divide =

21/10

÷

6/5

Multiply =

21

10

X

5/6

Answer =

105/60

Greatest Common Divisor (GCD) =15

Divide by GCD =

105 ÷ 15

60 ÷ 15

Answer (Simplified) =

7/4

Answer (Mixed) =1 3/4

I hope this helps you

Statistical analysis will provide the answer to this question. In order to carry out a statistical analysis, the One Proportion applet was used with 100 repetitions to see if the toast landed buttered side down a majority (more than 50%) of the time.

When we drop a piece of buttered toast on the floor, is it just as likely to land buttered side up as buttered side down? Statistical analysis will provide the answer to this question. In order to carry out a statistical analysis, the One Proportion applet was used with 100 repetitions to see if the toast landed buttered side down a majority (more than 50%) of the time. Suppose that 7 of the last 10 times we dropped toast, it landed buttered side down. Then, we would like to know whether there is statistical evidence that the true proportion of the time the toast lands buttered side down is greater than 50%. We will use the following hypotheses: H0: p = 0.5 (the true proportion is 50%)

Ha : p > 0.5 (the true proportion is greater than 50%)

The test statistic is: z = (7 - 5) / (sqrt((0.5 * (1 - 0.5)) / 10)) = 0.89443

The p-value is: Prob(Z > 0.89443) = 1 - 0.31286 = 0.68714

Since the p-value is greater than 0.05 (or the significance level we are using), we fail to reject the null hypothesis H0. That is, we do not have enough evidence to claim that the true proportion of the time the toast lands buttered side down is greater than 50%. Hence, it seems that the toast does not follow any rules and there is no justification to say that it is just as likely to land buttered side up as buttered side down. The One Proportion applet showed no statistical evidence that the toast fell buttered side down a majority of the time. The hypothesis test failed to reject the null hypothesis H0 which suggests that the true proportion is 50%.

Therefore, No justification exists to say that it is just as likely to land buttered side up as buttered side down when we drop a piece of buttered toast on the floor. This is because the toast does not follow any rules, and statistical evidence suggests that we do not have enough evidence to claim that the true proportion of the time the toast lands buttered side down is greater than 50%. In addition, a One Proportion applet was used to test this hypothesis with 100 repetitions and found that there was no statistical evidence that the toast fell buttered side down a majority of the time. Therefore, it is uncertain how often the toast lands buttered side down.

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer:

let the numbers be x and y then by given conditions:

x + y = 10 ….. eq 1

and

xy = 9….. eq 2

from eq 2. y = 9/x

put this in eq. 1

x + 9/x = 10

x + 9= 10x

x = 1

now,

xy = 9put value of x

y = 9

Step-by-step explanation:

Hope it is helpful....

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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The total attendance at the food festival from 2014 to 2017 is 16648.

It should be noted that a graph is simply used in Mathematics to illustrate the information given for a data.

In this case, the graph shows the attendance for the years that are given. Therefore, the total attendance at the food festival from 2014 to 2017 will be:

= 2118 + 3391 + 4785 + 6354

= 16648

The attendance is 16648.

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DM is congruent to line CM because CDM is congruent to triangle CBM using the SAS congruence criteria for triangles.

Draw a diagram of the rectangle ABCD with M as the midpoint of AB. Draw lines CM and DM ( refer to the attached image). Since AB is a line segment, we know that AM is congruent to MB (because M is the midpoint of AB). Since ABCD is a rectangle, we know that AB is parallel to CD, and AD is parallel to BC. Thus, we have two pairs of parallel lines: AB and CD, and AD and BC.

Using the fact that opposite sides of a rectangle are congruent, we have CD = AB. Now, we have a pair of congruent sides (DM and CM) that are opposite each other in triangle CDM and CBM respectively. We also have another pair of congruent sides (CD and AB) that are opposite each other in both triangles. Finally, we know that the angle CMD is congruent to the angle CMB because they are vertical angles. By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle CDM is congruent to triangle CBM.

Therefore, line DM is congruent to line CM by SAS congruence criteria.

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Answer:

594

Step-by-step explanation:

54 * 11 = 594

54 Is the quotient of 11 and 594 because 594 divided by 11 is 54.

(sorry if this is incorrect, i may had misinterpreted the question)

Answer:

Step-by-step explanation:

54 is the quotient of 11 and a number

Let the number be x

The number is 11/54

Answer:

24.01 is the answer.....

Hope it helps!!!

Answer:

John is growing at a faster rate.

Step-by-step explanation:

John grew 6 inches in 2 years, while Dave grew 7 inches in 4 years. We can expect John to grow another 3 inches by 2011, making John 49 inches tall in 2011. We can expect Dave to grow about another 7 inches by 2011, since another 4 years has passed. This seems reasonable enough...