Which of the following is an equation to the tangent line to the graph of (fx) = -2x+4 at 1

A) y= -2(x-1) + 2
B) y= 2(x-1) + 2
C) y= -2(x+1) + 2
D) y= 2(x-1) - 2

Please show how to find this as I really want to learn!

The general solution for Py"(t) + 9ry'(t) + 17y(t) + 3ty'(t) + 5y(t) = 0 is y(t) = c1 e^(r1t/P) + c2 e^(r2t/P), where c1 and c2 are constants and r1 and r2 are the roots found above.


15. To find the general solution for y'(t) - y(t) + 5y(t) = 0, we first need to find the characteristic equation. The characteristic equation is r - 1 + 5 = 0, which simplifies to r + 4 = 0. Therefore, the characteristic roots are r1 = -4.

The general solution for y'(t) - y(t) + 5y(t) = 0 is y(t) = c1 e^(-4t), where c1 is a constant.

16. To find the general solution for y"(t) + 3ty'(t) + 6y(t) = 0, we first need to find the characteristic equation. The characteristic equation is r^2 + 3tr + 6 = 0, which has the roots r1 = (-3t + i sqrt(3))/2 and r2 = (-3t - i sqrt(3))/2.

The general solution for y"(t) + 3ty'(t) + 6y(t) = 0 is y(t) = c1 e^((-3t + i sqrt(3))/2) + c2 e^((-3t - i sqrt(3))/2), where c1 and c2 are constants.

17. To find the general solution for Py"(t) + 9ry'(t) + 17y(t) + 3ty'(t) + 5y(t) = 0, we first need to rearrange the equation as Py"(t) + (3t + 9r)y'(t) + (17 + 5P)y(t) = 0.

Then, we find the characteristic equation, which is Pr^2 + (3t + 9r)r + (17 + 5P) = 0. The roots of this equation are given by the quadratic formula:

r1 = (-3t - 9r + sqrt((3t + 9r)^2 - 4P(17 + 5P)))/(2P)
r2 = (-3t - 9r - sqrt((3t + 9r)^2 - 4P(17 + 5P)))/(2P)

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The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)

First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).

Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).

\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)

\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)

Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)

Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.

Now, we will write the equations with the coordinates of the basis vectors of \(b'\).

\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)

Now we will write the matrix of \(A\) as follows:

\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)

Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

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Answer:

Spiders=8

Ants=12

Step-by-step explanation:

Spider(s)=8 legs

Ants(a)=6 legs

Total legs=136

Total heads=20

8s+6a=136 (1)

s+a=20 (2)

From (2)

s=20-a

Substitute 20-a into (1)

8s+6a=136

8(20-a)+6a=136

160-8a+6a=136

160-2a=136

-2a=136-160

-2a=-24

a= -24/-2

a=12

Substitute a=12 into (2)

s+a=20

s+12=20

s=20-12

s=8

37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

The area between 550 and 725 on a standardized test of educational achievement is equal to the percentage of students whose scores fall within one standard deviation (or 68%) of the mean score of 600. This can be expressed mathematically as:

Percentage = (725 - 550) / (2 * 50) = 37.5 / 100 = 37.5%

To explain in more detail, a standard deviation is a measure of the spread of a dataset around its mean value. The mean value in this case is 600, and the standard deviation is 50. Therefore, one standard deviation from the mean is calculated by subtracting or adding the standard deviation (50) from the mean (600), giving a range of 550 to 650.

Since the area in question spans across two standard deviations (550 to 725), the area is calculated by subtracting the lower range (550) from the upper range (725) and then dividing it by two standard deviations (100). This gives us the area, which is 37.5%.

To summarize, 37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

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Answer:

0

Step-by-step explanation:

Whole numbers are 0.1.2.3...  Follows that pattern forever.

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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Answer:140mph

Step-by-step explanation:

The statements that are true of Kim's flower are:

A) The function is increasing over time. The flower's height is growing by 0.75 inches every month.

B)The function is discrete. According to the information, Kim tracks the growth of the flower every two months, showing that the data points are discrete.

F) The function is nonlinear. The function is nonlinear because the growth rate is not constant. The height increases by an amount of 0.75 inches per month, which indicates a nonlinear relationship between time and height.

A function is like a rule that connects two groups of numbers.

In other words, if you give it a number, it will return a special number.

Example: f(x) = 2x, where the input value x is multiplied by 2 to produce the output value.

For instance, if we input x = 3, the function would get f(3) = 2 * 3 = 6.

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Answer:

A. To sum up the essay's key points and reasons

Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.

To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.

The ratio of cost to the quantity of visitors for $9 and four visitors is:

$9/4 visitors = $2.25/ visitors

The ratio of value to the quantity of visitors for $18 and eight visitors is:

$18/8 visitors = $2.25/ visitors

We are able to see that both ratios are equal to $2.25 per visitor.

Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.

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Answer:

DE ≈ 6.97

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos55° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{EF}{DE}\) = \(\frac{4}{DE}\) ( multiply both sides by DE )

DE × cos55° = 4 ( divide both sides by cos55° )

DE = \(\frac{4}{cos55}\) ≈ 6.97 ( to the nearest hundredth )

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

Step-by-step explanation:

Let x, y, z represent the numbers of 1-, 2-, and 3-point baskets, respectively. The given relations are ...

  x +2y +3z = 31 . . . . . . total points scored

  y -x = 5 . . . . . . . . . . . 5 more 2-point baskets than free throws

  y = 3z . . . . . . . . . . . . 3 times as many 2-point baskets as 3-point baskets

Using the second equation to write an expression for x, we have ...

  x = y -5

Substituting this and the third equation into the first, we get ...

  (y -5) +2y +(y) = 31

  4y = 36 . . . . . . . . . . . add 5, collect terms

  y = 9

  x = 9 -5 = 4

  z = y/3 = 9/3 = 3

The player made 4 free throws, 9 2-point baskets, and 3 3-point baskets.

_____

Alternate solution

The equations can be written in augmented matrix form as ...

  \(\left[\begin{array}{ccc|c}1&2&3&31\\-1&1&0&5\\0&1&-3&0\end{array}\right]\)

Row-reducing this matrix using any of a number of calculators gives (x, y, z) = (4, 9, 3), as above.

Answer:

ok

Step-by-step explanation:

Answer:

For any exponential function, f(x) = abx, the domain is the set of all real numbers. For any exponential function, f(x) = abx, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.

Hope it helps!!!!

The value of P (present worth or principal) is approximately 19209 when F is 114260, n is 15 years, and i is 14% per year. The correct option is c. 19209.

To calculate the value of P (present worth or principal), we can use the formula:

P = F / (1 + i)^n

F = 114260

n = 15 years

i = 14% per year

Plugging in the values into the formula, we have:

P = 114260 / (1 + 0.14)^15

Calculating the result:

P ≈ 19209

Therefore, the approximate value of P is 19209.

The correct option is c. 19209.

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A)the density of |x| is f(|x|) = 1/(1-0) = 1. B) the density of p|x| is f(p|x|) = 1/(p-0) = 1/p. C) the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0. D) the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

(a) To find the density of |x|, we need to consider the range of values that |x| can take. Since x is uniformly distributed on the interval (-1, 1), the absolute value of x can take values between 0 and 1. The density function of |x| is given by f(|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = 1. Therefore, the density of |x| is f(|x|) = 1/(1-0) = 1.

(b) To find the density of p|x|, we need to consider the range of values that p|x| can take. Since x is uniformly distributed on the interval (-1, 1), p|x| can take values between 0 and p. The density function of p|x| is given by f(p|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = p. Therefore, the density of p|x| is f(p|x|) = 1/(p-0) = 1/p.

(c) To find the density of -ln|x|, we need to consider the range of values that -ln|x| can take. Since x is uniformly distributed on the interval (-1, 1), -ln|x| can take values between 0 and ∞. The density function of -ln|x| is given by f(-ln|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a  = 0 and b = ∞. Therefore, the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0.

(d) To find the density of sin(x), we need to consider the range of values that sin(x) can take. Since x is uniformly distributed on the interval (-1, 1), sin(x) can take values between -sin(1) and sin(1). The density function of sin(x) is given by f(sin(x)) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = -sin(1) and b = sin(1). Therefore, the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

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Answer:

Hope it helps

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

Answer:

Theoretical A - 20%

Experimental - 24%

Theoretical B - <

Step-by-step explanation:

The theoretical probability of choosing a card with the number 2 is:

1 out of 5 cards have the number 2, so the probability of choosing a card with the number 2 is 1/5 or 0.2, which is equal to 20%.

The experimental probability of choosing a card with the number 2 is:

Out of the 400 people surveyed, 96 chose the card labeled 2. So the experimental probability is 96/400 or 0.24, which is equal to 24%.

Answer:

D, 9^4 * 8^4

Step-by-step explanation:

The rule is whenever you have multiplication inside arentheses and it is raised to a power, you distribute the power to both the number s and solve.

I confirmed D is right on a calculator also.

Answer:

D

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

15 x 12 = 180

Sheila's entertainment center has enough space for a tv with an area of 180 sqaure inches.

196 > 180

so the television will not fit  

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Answer:

£90

Step-by-step explanation:

if it decreases by 5/6 then that means that 15 is 1/6 of the total price

15*6 = 90

Answer:

Step-by-step explanation:

Replacing X with -3 ves you -2(-3) + 5 > 13. -2(-3) is 10 + 5 > 13.  10 + 5 gives you 15, which is greater than 13.

Answer:

5x+4

Step-by-step explanation: