What is the slope of the line tangent to the curve 3y2 - 2x2 = 6 - 2xy at the point (3,2)?

Answer:

If you round, he runs 7 meters in a second.

436.8  m 62.08 s

x m 1 s

(436.8 X 1) / 62.08 = 7.03 m/s

7.03 m 1 s

y m 1/10 s

(7.03 X 0,1 ) /1 = 0,703 m

Step-by-step explanation:

To find Andy's running speed, divide distance by time, adjusting for decimals by multiplying both the divisor and dividend by powers of 10, shifting the decimal point to simplify division.

To calculate Andy's running speed, you would divide the distance he ran (436.8 meters) by the time it took (62.08 seconds). When you divide or multiply decimals by powers of 10, the decimal point is shifted. For instance, if we multiply or divide a number like 1.9436 by 10, 100, or 1000, our decimal point moves to the right or left accordingly. If dividing by 10, it moves one place to the left; by 100, two places; by 1000, three places,  turning our number into 0.19436, 0.019436, and 0.0019436 respectively. The same principle applies to Andy's calculation, where the numbers would be easier to handle if we removed the decimal points by multiplying both the divisor and dividend by the same power of 10. Consequently, when dividing 436.8 by 62.08, we can multiply both by 100 to remove the decimal and divide 43680 by 6208, ultimately giving the same answer but with much simpler arithmetic.

To solve the system of equations xy = 6x + 12 and yy = x + 47, we can rearrange the equations, isolate one variable, and substitute it into the other equation. Then, solve for the variables. The solution is x = 282 / (270 - y) and y = (270 - xy) / 6.

To solve the given system of equations,

xy = 6x + 12
yy = x + 47

We can start by rearranging the equations:

xy - 6x = 12
yy - x = 47

Next, we can isolate one variable in terms of the other variable and substitute it into the other equation:

x = (yy - 47)
xy - 6(yy - 47) = 12

Simplifying the equation:

xy - 6yy + 282 = 12

Combining like terms:

-6yy + xy = -270

Now, we can solve this equation for y in terms of x:

y = (270 - xy) / 6

Re-substituting the value of y back into one of the original equations:

(270 - xy) / 6 * x = 47

Simplifying and solving for x:

270x - xy = 282

x(270 - y) = 282

x = 282 / (270 - y)

So, the solution to the system of equations is:

x = 282 / (270 - y)
y = (270 - xy) / 6

Answer:

Area and Side length of a rhombus.

Step-by-step explanation:

1. Area and side length of a rhombus - This is least proportional as they are inversely proportional.

2. Distance and time when speed is constant is proportional.

Distance = speed x time

When speed is constant, the distance increases with respect to speed.

3. Total cost and the number of movie tickets purchased.

As the number of tickets purchased increases, the cost also increases.

4. Hours worked and money earned

When the number of hours increases, the money earned also increases.

The probability of Mark hitting the bull's-eye on the fourth shot, assuming he misses the first three times, is 8.64%. This is calculated as the product of the probabilities of each event occurring independently.

This is indeed a problem related to probability, particularly, this pertains to the concept of an independent event in statistics. Mark's success in shooting an arrow accurately to the target is an independent event because the outcome of one shot doesn't affect the outcome of other shots.

In Mark's case, he hits the bull's-eye about 40% of the time, i.e. his success rate P(Success) is 0.40 and his failure rate P(Failure) is 0.60. Since the question asked about the probability of him hitting the bull's-eye on the fourth shot, we should look at the first three shots being failures and only the fourth being a success.

This leads us to the calculation: P(FFFH) = P(F) x P(F) x P(F) x P(H) = (0.60)*(0.60)*(0.60)*(0.40) = 0.0864 or 8.64% chance.

So, there's an 8.64% chance that Mark will hit the bull's-eye on the fourth shot given that he misses the first three.

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The probability that Mark hits the bull's-eye on his fourth shot, given he typically hits the bull's-eye 40% of the time, is 0.0864 or 8.64%

The problem is about the probability that Mark hits the bull's-eye on the fourth shot given that he hits the bull's-eye about 40% of the time. In these cases, for the first three shots, he should not hit the bull's-eye (probabilty of 60%) and on the fourth trial, he should hit the bull's-eye (probability of 40%). Therefore, we multiply the individual probabilities together to find the answer.

Step 1: Find the probability that he does not hit the bull's-eye in the first three trials. This is (0.6)*(0.6)*(0.6) = 0.216.

Step 2: Find the probability that he hits the bull's-eye on the fourth trial. This is simply 0.4.

Step 3: Multiply the two probabilities together to find the final answer. This gives us 0.216*0.4 = 0.0864.

So, the probability that Mark hits the bull's-eye on the fourth shot is 0.0864, or 8.64%.

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Answer:

Option B) 719 ways

Step-by-step explanation:

Given that you are sending your friend a coded message by rearranging the letters in the word “STRIKE.” That is, your code can be any arrangement of the letters in the word “STRIKE” except one, “S-T-R-I-K-E.”

This means any code we can send using the given letters without strike.

There are 6 different letters and order matters for coding i.e. st is different from ts

Hence no of ways of arranging strike in different ways

[tex]= 6!= 6*5*4*3*2*1\\= 720[/tex]

We must subtract the arrangement strike from this as strike is not allowed.

Hence total number of different ways we code this message

=720-1 =719 ways

Answer: B. The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Step-by-step explanation:

Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

We can see that a scale factor (2) is used in the above rule.

Rigid motions do not use any scale factor.

The transformation that uses scale factor to transforms figure is dilation.

And Dilation is not rigid motion because it does not produce congruent images.

Hence,  The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Answer:

[tex]\frac 15[/tex]

Step-by-step explanation:

Hello!

We can convert it into slope intercept form: [tex]y = mx + b[/tex]

The slope is [tex]\frac15[/tex].

Finding the slope of a line from its equation depends on the equation's form. If it's already in slope-intercept form (y = mx + b), the coefficient of x (m) is the slope. If not, rewrite it to that form by isolating y. Alternatively, use the point-slope form (y - y1 = m(x - x1)) with a known point on the line and solve for m. Remember, the slope tells you how much the line rises/falls per unit move to the right. For the equation in the image, the slope is 1/5.

• Using the slope-intercept form: This is the most straightforward way to find the slope if the equation is already in slope-intercept form, which is y = mx + b. In this form, the slope (m) is the coefficient of the x term. For example, if the equation is y = 2x + 3, the slope is 2.

• Using the standard form: If the equation is not in slope-intercept form, you can first rewrite it in slope-intercept form. To do this, you need to isolate the y term. For example, if the equation is 3x + 2y = 6, you would first subtract 3x from both sides to get 2y = -3x + 6. Then, you would divide both sides by 2 to get y = -3/2x + 3. Once the equation is in slope-intercept form, you can find the slope as described in the first method.

• Using the point-slope form: The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. To find the slope using this form, you need to plug in the coordinates of a point on the line. For example, if the equation is y - 2 = 3(x - 1), and you know that the point (3, 7) is on the line, you can plug in x = 3 and y = 7 to get 5 = 3(2). Solving for m, you get m = 5/3.

The slope of a line tells you rise over run, or how much the line goes up or down for every unit it goes to the right. A positive slope means the line goes up as you move to the right, a negative slope means the line goes down as you move to the right, and a zero slope means the line is horizontal.

In the image, the equation is -15 - x = -5y. To find the slope using the slope-intercept form, we need to rewrite the equation so that y is isolated on one side. We can do this by adding x and dividing both sides by -5:

y = (1/5)x + 3

Therefore, the slope of the line is 1/5.

Answer:

B. 238.95 is correct

Step-by-step explanation:

Nper = 11*2 = 22 (indicates the period over which interest payments are made)

PMT = 1000*10.3%*1/2 = 51.5 (indicates sem-annual interest payments)

PV = 1000*95% = 950 (indicates the current selling price of the bonds)

FV = 1000 (indicates the face value of bonds)

Rate = ? (Indicates YTM)

YTM = Rate(Nper,PMT,PV,FV)*2 = Rate(22,51.5,-950,1000)*2 = 11.098% or 11.10%

Answer is 11.098% or 11.10%.

Answer:

R  ~ D,

S  ~  E,

T  ~  B,  and

Q  ~  C

208 is 65 percent of 320.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction, To change the percentage to a fraction, just put the percentage number in the numerator and 100 in the denominator.

We can write a percentage in the form of fraction as well.

For example :- 10%, 78%, 56%, 98%

Given that, what is percent of 320 is 208,

Using the concept of percentage,

Divide 208 by 320 and multiply it by 100

= 208 / 320 x 100

= 0.65 x 100

= 65%

Hence, 208 is 65 percent of 320.

Learn more about percent, click;

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The sentence 'The quotient of 2 and the sum of a number and 1' can be represented as an algebraic expression 2 / (x + 1).

To convert the given statement into an algebraic expression, let's first identify the components of the statement. 'A number' is represented as x. 'The sum of a number and 1' can be written as (x + 1). 'The quotient of 2 and...' signifies division by 2.

Therefore, based on the above definitions, we can represent 'The quotient of 2 and the sum of a number and 1' as 2 / (x + 1).

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Answer:

Step-by-step explanation:

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

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

8x²+4xy-8xy-4y²=

8x²-4y²-4xy

Factorise term

4(2x²-y²-xy)

PLEASE MARK BRAINLIEST.

Answer:  The correct option is (B) [tex]1\dfrac{1}{2}.[/tex]

Step-by-step explanation:  Given that Alice had [tex]4\dfrac{1}{4}[/tex] pounds of walnuts at the beginning of the week. At the end of the week, she had [tex]2\dfrac{3}{4}[/tex] pounds.

We are to find the quantity of walnuts that she had used.

We have

The quantity of walnuts that Alice has is

[tex]q_1=4\dfrac{1}{4}=\dfrac{17}{4}~\textup{pounds}[/tex]

and the quantity of walnut that she had at the end of the week is

[tex]q_2=2\dfrac{3}{4}=\dfrac{11}{4}~\textup{pounds}.[/tex]

Therefore, the quantity of walnut that she has used is given by

[tex]Q=q_1-q_2=\dfrac{17}{4}-\dfrac{11}{4}=\dfrac{6}{4}=\dfrac{3}{2}=1\dfrac{1}{2}.[/tex]

Thus, the required quantity of walnut that she has used is [tex]1\dfrac{1}{2}~\textup{pounds}.[/tex]

Option (B) is CORRECT.

To find the smallest poster area with a fixed printed area of 388 square centimeters, calculate optimized values for the width and height of the printed area, considering the margins, and derive the poster's dimensions by adding the margins to these values.

To find the dimensions of the poster with the smallest area given a fixed printed area, we should first determine the dimensions of the printed area. We know that the printed area is 388 square centimeters and that the margins do not change. Let's denote the width of the printed area as w and the height as h.

The area of the printed material is given by Area = w × h = 388 cm². The total width of the poster would be w + 2×(8 cm) (since there are two side margins), and the total height would be h + 2×(4 cm) (since there are top and bottom margins).

To minimize the area of the poster, we need to minimize the function for the total area of the poster A(w,h) = (w + 16)(h + 8). As the printed area is fixed, we can express h in terms of w using h = 388/w and substitute this into the function to get A(w) = (w + 16)((388/w) + 8).

Taking the derivative dA/dw and setting it to zero, we find the optimal value for w, and consequently, we calculate h. The dimensions of the poster that minimize the total area can then be determined by adding the margins to these optimized values of w and h.

The simplified version of the polynomial 3+4p to the second power -5p - 3p to the second power + 4p - 8 is p to the second power - p - 5 which corresponds to answer choice C.

The problem you're asking about is a simplification of a polynomial. We can combine like terms in the polynomial which is a basic skill in algebra. The polynomial you provided is 3+4p to the second power -5p - 3p to the second power + 4p - 8

To solve this, we combine similar variables and constant separately. So, we add 4p to the second power and - 3p to the second power which will give us p to the second power. Next, we add -5p to +4p which results in -p. Finally, adding the constants 3 and -8 gives us -5. Therefore, the simplified polynomial becomes p to the second power - p - 5. Thus, the correct answer is option C.

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