Determine whether the equation defines y as a function of x

Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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To find f(g(x)), we substitute g(x) in place of x in the function f(x).

f(g(x)) = f(5x/(1-x)) = (5x/(1-x)) / (5 + (5x/(1-x))) = 5x / (1-x+5-5x) = 5x / 6 - 4x/6 = x/6

To find g(f(x)), we substitute f(x) in place of x in the function g(x).

g(f(x)) = g(x/(5+x)) = (5(x/(5+x))) / (1 - (x/(5+x))) = 5x / (5+x-x) = 5x/5 = x

Therefore, f(g(x)) = x/6 and g(f(x)) = x.

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Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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the answer it is 2  

ok

9514 1404 393

Answer:

  N = 5; only one rate is possible

Step-by-step explanation:

The values of the sets of chips are ...

  12 +9N +8N^2 +4N^3

and

  2 +N +N^3 +N^4

We want to find N such that the difference in value is zero:

  N^4 -3N^3 -8N^2 -8N -10 = 0

A graphing calculator can show us the roots. There is only one positive real root to this equation: N = 5.

The exchange rate N is 5. Only one rate is possible.

Answer:

C

Step-by-step explanation:

Answer:

$2000

Step-by-step explanation:

The profit is the money earned by the store, meaning in this case, it's 32%. 32 percent of an amount is equal to 640. Set up an equation: 0.32(x) = 640, where x is the total money earned including the profit. x is solved to be 2000 dollars.

The function y = |x| is called a modulus function. The solution of the given modulus equations are as (1) x = 1 / 6 and - 1 / 6, (2) x = 1, (3) x = -10 / 9 and 2 / 15 and (4) x = -3, 5, 1 and 9.

A modulus function gives the magnitude of a number. The modulus of a number is positive for both a negative and a positive number.

The given equations are solved one by one as follows,

(1)

|3x - 1| - |2x +5 - (5 - x)| = 0

It can be written as,

|3x - 1| - |3x| = 0

⇒ |3x - 1| = |3x|

There can be four cases for the above equation which are as follows,

(i) 3x - 1 = 3x

It has no solution.

(ii) -(3x - 1 ) = 3x

⇒ x = 1 / 6

(iii) 3x - 1 = -3x

⇒ x = -1 / 6

(iv) -(3x - 1 ) = -3x

It has no solutions.

(2)

|2(x + 1) - 4| = |2 - 2(2 - x)|

It can be simplified as,

|2x - 2| = |2x - 2|

There can be four cases for the above equation which are as follows,

(i) 2x - 2 = 2x - 2

It has no solution.

(ii)2x - 2 = -(2x - 2)

⇒ x = 1

(iii) -(2x - 2) = 2x - 2

⇒ x = 1

(iv) -(2x - 2) = -(2x - 2)

It has no solution.

(3)

|(x - 2) / 4| - 1 / 3 = x

It can be simplified as,

|(x - 2) / 4| = x + 1 / 3

There can be two cases for the above equation which are as follows,

(i) (x - 2) / 4 = x + 1 / 3

⇒ x - 2 = 4x + 4 / 3

⇒ x - 4x = 4 / 3 + 2

⇒ x = -10 / 9

(ii) (x - 2) / 4 = -(x + 1 / 3)

⇒ x - 2 = -4x - 4 / 3

⇒ 5x = 2 - 4 / 3

⇒ x = 2 / 15

(4)

1 /2 |x - 3| - 1 = |x - 3| + 2

It can be simplified as,

|x - 3| = 2|x - 3| + 6

There can be four cases for the above equation which are as follows,

(i) (x - 3) = 2(x - 3) + 6

⇒ -(x - 3) = 6

⇒ x = -3

(ii) (x - 3) = -2(x - 3) + 6

⇒ 3(x - 3) = 6

⇒ x = 5

(iii) -(x - 3) = 2(x - 3) + 6

⇒ -3(x - 3) = 6

⇒ x = 1

(iv)  -(x - 3) = -2(x - 3) + 6

⇒ (x - 3) = 6

⇒ x = 9

Hence, the value of x for the given equations are as, (1) x = 1 / 6 and - 1 / 6, (2) x = 1, (3) x = -10 / 9 and 2 / 15 and (4) x = -3, 5, 1 and 9.

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Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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Answer: 8 servings

Step-by-step explanation:

1/2 cup + 1/2 cup = 1 cup

                                              >  1 cup + 1 cup = 2 cups = one pint

1/2 cup + 1/2 cup = 1 cup

if 4 servings go in one pint then 8 servings goes in 2 pint

Answer:

8 cups/servings.

Explanation:

Can't explain further more because I'm not good in explaining things yet I'm sure that's the correct answer.

Answer:

2 (4+x)

Step-by-step explanation:

4 + x     is  the sum of four and a number 'x'   now multiply by 2

2  ( 4+ x)

Answer:

\( {x}^{ - \frac{5}{3} } = \frac{1}{ {x}^{ \frac{5}{3} } } = \frac{1}{ \sqrt[3]{ {x}^{5} } } \)

Answer:

Sorry It is verry blerd

Step-by-step explanation:

sorry pic more please

The triangles ABC and DBE are similar by the SAS similarity theorem

The measure of the side lengths AC is 16 units

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and DBE

These triangles have the following measures

This means that the triangles are similar by the SAS similarity theorem

Using the SAS similarity theorem, we have the following equation

(x + 1)/12 = (x + 5)/15

Cross multiply the equation

15x + 15 = 12x + 60

So, we have

3x = 45

Divide by 3

x = 15

This means that

x + 1 = 15 + 1 = 16

x + 5 = 15 + 5 = 20

Hence, the measure of the side lengths are 16 and 20 units

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Answer:

Hey! So basically, 7 1/2 x 2 = 15 and 15 x 3 = 45

Hope this helped! :D

Answer: 3x-x+2=4

Step-by-step explanation:

You can put this solution on YOUR website!

running distance is 9(t3+0.5)

biking distance is 16 (2(t3+0.5))=16(2t3+1)

swimming distance is 2.5t3

9t3+4.5+32t3+16+2.5t3=64

43.5t3=43.5

t3=1 hour

He biked for 3 hours (48 miles)

He ran for 1.5 hours (13.5 miles)

He swam for 1 hour (2.5 miles)

He covered 62 miles in 5.5 hours of activity.

Answer:

He swam for 1 hour (2.5 miles)

Step-by-step explanation:

The relation between time, speed, and distance is,

distance = speed × time

Answer:

Answer 60 degrees

Step-by-step explanation:

70-10 60-5 55+7 62-2 60

a. The shape of the distribution is normal, by the Central Limit Theorem.

b. The mean is of: 0.23.

c. The standard error is of: 0.125, meaning that the sample proportions differ by around 0.125 from the mean of 0.23.

d. The probability is of: 0.2877 = 28.77%.

By the Central Limit Theorem, as each sample has at least 10 successes and at least 10 failures, the shape of the distribution is normal.

For each sample, the mean and the standard error are given as follows:

Hence for the distribution of differences, the mean and the standard error are given as follows:

Using the z-score formula, the probability that the difference is greater than 30 is one subtracted by the p-value of Z when X = 0.3, hence:

Z = (0.3 - 0.23)/0.125

Z = 0.56

Z = 0.56 has a p-value of 0.7123.

1 - 0.7123 = 0.2877 = 28.77%.

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Answer:

1,4,3,2,5

Step-by-step explanation:

Let P and Q be two complex numbers such that

P = a+bi

Q = c+di

Where a,b,c,d are real numbers and i = sqrt(-1).

This means i^2 = -1.

-------------------

Adding P and Q means

P+Q = (a+bi)+(c+di)

P+Q = a+bi + c+di

P+Q = (a+c) + (bi+di)

P+Q = (a+c) + (b+d)i

As you can see, we just add the corresponding components together.

-------------------

Subtraction is a similar story.

P-Q = (a+bi)-(c+di)

P-Q = a+bi - c-di

P-Q = (a-c) + (bi-di)

P-Q = (a-c) + (b-d)i

We subtract the corresponding components

-------------------

Multiplication is a bit more complicated.

We'll use the FOIL rule

P*Q = (a+bi)*(c+di)

P*Q = a*c + a*di + bi*c + bi*di

P*Q = a*c + ad*i + bc*i + bd*i^2

P*Q = a*c + ad*i + bc*i + bd*(-1)

P*Q = a*c + ad*i + bc*i - bd

P*Q = (ac - bd) + (ad*i + bc*i)

P*Q = (ac - bd) + (ad + bc)i

Unfortunately multiplication isn't as simple as addition or subtraction, but we can at least make a tidy formula for it. You could also use the box method to visually organize the terms into a table to help multiply out P and Q.

Answer:

because they have different stepa

The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².

The side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²

= 75.69 cm²

Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²

Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².

In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².

Total surface area = surface area of the cube + surface area of the cylinder

Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²

Total surface area ≈ 583.31 cm²

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Answer:

Absolute, relative, absolute, relative, relative

Step-by-step explanation:

Absolute location is the coordinates or address of something- it is exact.

Relative location is the location in reference to something else. For example, Mexico is south of the US compares the location of Mexico to the location of the US.

Answer:

1st: absolute

2nd: relative

3rd: absolute

4th: relative

5th: relative

Step-by-step explanation:

Absolute location provides a deeper, more drawn out description, while relative tends to usually use other buildings, landmarks, or other interesting things to point out the direction.

Absolute: (44 degrees N, 19 degrees W), 104 Lovers Lane.

Relative: East off the street of Mcdonalds, Across the street from the Cinema.

Answer:

0.9009

Step-by-step explanation:

Let X be the event that Current will flow

Let Y be the event that the first relay which is 1 is closed

Thus, we can say that every element of Y is in X, but X possesses more elements. Thus, Y ⊂ X.

Thus, we can say that;

P(X ∩ Y) = P(Y)

Thus, given that current flowed, the probability that relay 1 functioned will be expressed as;

P(Y | X) = (P(Y ∩ X))/P(X)

From earlier, we saw that P(X ∩ Y) = P(Y). Thus;

P(Y | X) = P(Y)/P(X)

From the question, P(Y) = 0.9

Since there are 3 relays, then we have;

P(X) = 1 - 0.1³ = 0.999

Thus;

P(Y | X) = 0.9/0.999

P(Y | X) = 0.9009

The  probability that relay 1 functioned is 0.9009

Let us assume X be the event that Current will flow

And,

Let us assume Y be the event that the first relay

So,  Thus, Y ⊂ X.

Now

P(X ∩ Y) = P(Y)

The probability that relay 1 functioned should be

P(Y | X) = (P(Y ∩ X)) ÷ P(X)

From earlier, we saw that P(X ∩ Y) = P(Y).

So,

P(Y | X) = P(Y) ÷ P(X)

Now

P(X) =\(1 - 0.1^3\) = 0.999

So,

P(Y | X) = 0.9  ÷0.999

P(Y | X) = 0.9009

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Answer:

D

Step-by-step explanation:

In scientific notation, the number that is being multiplied by the power of ten must be greater than or equal to 1 and less than 10. This eliminates options B, C, and E. The rest of the options are all 5.79 times something. To find that something, we can do 5,790,000 / 5.79 = 1000000 = 10⁶. This means that the answer is D.