How to write 5x923 in expanded form

The value of sin (α - β), where sin α = 21/29 and α is in the 2nd quadrant, and cos β = 15/17 and β is in the 1st quadrant, is calculated to be 379/493.

In trigonometry, the formula for sin (α - β) is defined as sin α cos β - cos α sin β. Given the problem, we know sin α is 21/29 and cos β is 15/17.

However, we need to determine cos α and sin β. In these cases, we use the identity sin² α + cos² α = 1, and its counterpart for β. For α being in the second quadrant, cos α would be negative. Therefore, cos α = -√(1 - (21/29)²), which simplifies to -8/29. Similarly, for β in the first quadrant (where sin β is positive), sin β = √(1 - (15/17)²), which simplifies to 8/17.

Substitute these values into the formula for sin (α - β), we have sin (α - β) = (21/29 * 15/17) - (-8/29 * 8/17) = 315/493 + 64/493 = 379/493.

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The man has 17 dimes and 7 quarters.

A system of equations was set up, using the total number of coins and their total value, to determine the quantity of each coin type.

Let's denote the number of dimes as d and the number of quarters as q. We are given two facts: (1) the man has a total of 24 coins, and (2) the total value of the coins is 345 cents. Thus we have two equations:

We can solve this system of equations to find the values of d and q.

Subtracting the first equation from the second (multiplied by 10) to eliminate the variable d:

10d + 25q = 345
-(10d + 10q = 240)
-------------------------
15q = 105

Dividing by 15 to solve for q, we get q = 7. This means the man has 7 quarters. Substituting q = 7 into the first equation:

d + 7 = 24
d = 24 - 7
d = 17

So, the man has 17 dimes.

Therefore, the man has 17 dimes and 7 quarters.

The value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

The given function is f(t)=10t²+5t+1.

We need to find the value of t for which the tangent line to the graph of f(t) has slope 1.

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.

Now, f'(t) = slope of the tangent line to the curve at the point (t, f(t)).

Given, f'(t) = 1

f(t)=10t²+5t+1

⇒f'(t)=20t+5

⇒1=20t+5

⇒20t=-4

⇒t=-4/20

⇒t=-1/5

Therefore, the value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

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Answer:

16.77

Step-by-step explanation:

MA BRAIN

The solution to the equation 4−(2x+4)=5 is x = -2.5. None of the provided suggestions x = 32, x = -52, x = -10, x = 6 are correct.

To solve for x in the equation 4−(2x+4)=5, you first simplify the expression in the parentheses, which creates the equation 4 - 2x - 4 = 5. This simplifies to -2x = 5. You then divide each side by -2 which results in x = -5/2 or x = -2.5. So the solution to this equation is not any of the provided x = 32, x = -52, x = -10, x = 6 but rather x = -2.5.

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The equation of the circle where the vertices of an inscribed square are (-9,4),(-2,5),(-8,-3),(-1,-2) is (x+5)² + (y-1)² = 25. This is found by getting the average x and y coordinates to find the center of the circle, calculating the radius, and applying it to the standard equation of a circle.

To find the equation of the circle where the vertices of an inscribed square are located at (-9,4),(-2,5),(-8,-3),(-1,-2), first, you need to find the center of the circle. In the case of a square inscribed in a circle, the center of the square is the same as the center of the circle. This can be found by averaging the x and y coordinates of the vertices of the square.

The average x-coordinate = [(-9) + (-2) + (-8) + (-1)] / 4 = -5
The average y-coordinate = [4 + 5 - 3 - 2] / 4 = 1

So, the center of the circle is at (-5, 1).

Next, you need to calculate the radius of the circle. The radius in an inscribed square is the half of the square's diagonal. Calculate the distance between two opposite vertices of the square - for example (-9,4) and (-1,-2). Apply the distance formula: √[(-1 - (-9))^2 + (-2 - 4)^2 ]. That's √[64 + 36], giving a distance of √100 = 10. As this is the diagonal of the square, the radius would be half of this, giving us a radius of 5.

Finally, the equation of the circle in its standard form (x-h)² + (y-k)² = r² can be written as (x+5)² + (y-1)² = 5².

Thus, the equation of the circle is (x+5)² + (y-1)² = 25.

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1st one -*- =+,+*- = -,-*- = +

2nd one = 0

3rd one-*-=+,+*+=+,+*+=+

4th one +*-=-,-*-=+,+*- = -

 4th one is negative

We have to round 566, such that , it has three significant figures.

→ Option 1

600=It has only one Significant figure.Zeroes which lie on right side of digit ,if there is no decimal after zeroes are not significant.

→ Option 2

570=Two Significant figure.

→ Option 3

566=Three Significant figure.

→ Option 4

500=One Significant figure.

⇒Option 3 ,which is equal to 566, is most appropriate ,among given Options, that is when this number is rounded , it has three significant figures.

Answer:

125.0600 million

[tex]\frac{6253}{50} million[/tex]

125,060,000

125 million 60 thousand

Step-by-step explanation:

It does not matter how many zeroes we add to the right end after the decimal, it does not change the value of the number.

Thus, 125.06, 125.060, 125.0600,.... all have the same values.

Similarly 125.06 can be change into the rational form

Thus, [tex]125.06=\frac{6253}{50} =\frac{12506}{100} \text{all have same values}[/tex]

We can also write the word "million" into the digits.

Thus, 125.06 million = 125,060,000 = 125 million 60 thousand

Angles are measured in degrees and their reflex measures can be obtained by adding 180 degrees to their measures.

In mathematics, an angle is a measure of the amount of turn between two lines or rays that share a common endpoint. The measure of an angle is given in degrees, and it represents the amount of rotation needed to move from one ray to the other.

The reflex measure of an angle is the sum of the angle's measure and 180 degrees. It represents the amount of rotation needed to move from one ray to the other while going in the opposite direction. For example, if an angle has a measure of 30 degrees, its reflex measure would be 30 degrees + 180 degrees = 210 degrees.

So, the relationship between the measure of an angle and its reflex measure is that the reflex measure is obtained by adding 180 degrees to the measure of the angle.

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To convert 7 quarts to gallons, divide 7 by 4, as there are 4 quarts in a gallon. The result is that 7 quarts equal 1.75 gallons.

To convert quarts to gallons, one must understand the unit equivalence between the two. One gallon is equivalent to 4 quarts. To find out how many gallons are in 7 quarts, divide the number of quarts by the number of quarts in a gallon.

Using the equivalence provided:

You would perform the following calculation:
7 quarts
4 quarts per gallon = 1.75 gallons

Therefore, 7 quarts is equal to 1.75 gallons.

Answer:

7 quarts of water is equivalent to 1.75 gallons.

Explanation:

To convert quarts to gallons, you can use the conversion factor that 1 gallon is equal to 4 quarts.

Given that the container holds 7 quarts of water, you can use the conversion factor to find out how many gallons that is:

[tex]\[ \text{Number of gallons} = \frac{\text{Number of quarts}}{4} \][/tex]

[tex]\[ \text{Number of gallons} = \frac{7 \text{ quarts}}{4} \][/tex]

[tex]\[ \text{Number of gallons} = 1.75 \text{ gallons} \][/tex]

Answer:

The track is 111 m

Step-by-step explanation:

The easiest way to calculate the meters in the track is to find the Greatest Common Divisor (GCD). This method is used to find the largest number to exactly divide both numbers 444 and 777, which are the meters both guys ran. The resulting number will give us the longest distance the track could have.

   There are various techniques used to find the GCD. One of the is to find all divisors of both numbers and then look for the biggest one they have in common.

   D 444 = { 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444 }

   D 777 = { 1, 3, 7, 21, 37, 111, 259, 777 }

   As we can see, the only divisors they have in common are 1, 3 ,37 and 111. The greatest of them is 111 ----> GCD(444,777) = 111.

   This means the track has 111 m.

(Actually, the track could have been as long as any of the other common divisors, but it wouldn't have been realistic for the track to be 1, 3 or 37 meters).