sec theta = 11/4, cot theta < 0

The values of x in both equations are 1/26 and 1/50, respectively

The equations are linear equations.

So, the variable can be calculated by simply dividing both sides by the coefficient

Using the above as a guide, we have the following computations:

Part A: (26)x = 1

Divide both sides by 26

x = 1/26

Part B: (50)x = 1

Divide both sides by 50

x = 1/50

Hence, the values of x in both equations are 1/26 and 1/50, respectively

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Answer:

Step-by-step explanation:

Part A: If (26)x = 1, what is the value of x? Explain your answer. 

The value of x is 0. Anything to the 0 power = 1. So I had to figure out what times 6 would = 0. Anything times 0 = 0. Hence x = 0 because 6 x 0 = 0 and 2^0 =1.

Part B: If (50)x = 1, what are the possible values of x? Explain your answer.

X could be any number because anything times 0 = 0. In order for the answer to be 1, I had to figure out how to keep 5 to the 0 power. Since anything times 0 = 0, it doesn't matter what number x is, because anything times 0 =0. 

In order to find out how many albums will fit in the box, divide the total height of the box by the thickness of one album. This resulted in a total of 64 albums.

The problem involves determining the number of record albums that can be stacked into a box with a height of 12 inches. Each album is 3/16 of an inch thick. To find the number of albums, you will need to divide the total height of the box, which is 12 inches, by the thickness of one album.

Here is the calculation: 12 ÷ (3/16) = 12 ÷ 0.1875 = 64.

Therefore, you can fit 64 albums in a 12-inch high box. Remember, this involves simple division and understanding of fractions and their decimal equivalents.

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divide 25 1/2 by 6

25 1/2 = 51/2

51/2 / 6 =

51/12 = 4 1/4

each piece is 4 1/4 feet long

since the line is vertical ( both x coordinates are -2)

the equation of the line is x=-2

The decreasing linear relationship is shown in table 1. The correct option is A.

The linear relation is defined as the variation of the variables by a constant factor with the different values of variables x and y.

The given table is,

X    Y

4     10

7     17

10   18

13   22

The linear relation will be calculated as:-

y = kx

k = y / x

k = 10 / 4 = 2.5

k = 17 / 7 = 2.42

k = 18 / 10

k = 1.8

k = 22 / 13 = 1.69

The slope will be,

m = ( 17 - 10 ) / ( 7 - 4 ) = 7 / 3

Therefore, table 1 depicts the decreasing linear relationship. A is the correct answer.

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the answer is all trapezoids have one pair of parallel sides.

Answer:

  (D)  3x +6 ≤ 3

Step-by-step explanation:

Since there is a solid dot at x=-1, the inequality must include "≤", which eliminates the first two choices.

You can check x=-1 in each of the remaining choices to see which results in the "equal to" case.

  2(-1) +5 ≤ 1 . . . . . choice C

  3 ≤ 1 . . . . . . . . . . .not true

__

  3(-1) +6 ≤ 3 . . . . . choice D

  3 ≤ 3 . . . . . . . . . . true; the "equal to" case we're looking for

Answer: 10/3 or 3 1 /

Step-by-step explanation:

First ywould turn the 1 1/3 cups into an improper fraction. That makes the math a little easier. 1 1/3 = 4/3. You know that 4/3 cups makes two dozen cookies. So, if you take half of 4/3 which is 2/3 that is how many cups it takes to make one dozen. Then to find how many cups it would take to make 5 dozen just multiply 2/3 by 5 to get 10/3 or 3 1/3

The exact perimeter of pentagon JKLMN could not be calculated without the lengths of its sides. One would add the lengths of all sides for a polygon, while for a rectangle, such as a town square, the perimeter formula is twice the sum of its length and width.

To calculate the perimeter of a pentagon, you need to add the lengths of all its sides. Unfortunately, the specific lengths of the sides of pentagon JKLMN were not provided, so I cannot calculate the exact perimeter. However, I can explain how you would find the perimeter if the side lengths were known. If you have the coordinates of the vertices, you can use the distance formula to find the lengths of the sides between each pair of vertices. Then you would add those lengths together to find the total perimeter. On the other hand, if the pentagon is regular (all sides and angles are equal), you would just multiply the length of one side by 5.

You also provided an example of calculating the perimeter of a rectangle which has a formula of perimeter = 2(length + width). If we use this formula with the given dimensions of the town square, the perimeter would be 2(39.2 meters + 17.5 meters) = 2(56.7 meters) = 113.4 meters.

To find the approximate perimeter of pentagon JKLMN, we add up the given lengths of its sides. Using the information provided, we can estimate that the approximate perimeter of the pentagon is 840,000 km.

The perimeter of a polygon is the sum of the lengths of its sides. To find the approximate perimeter of pentagon JKLMN, we need to know the lengths of all its sides.

Since we are not given the lengths of the sides directly, it is not possible to compute the exact perimeter. However, we can use the information provided to find the approximate perimeter.

Using the given information, we know that the perimeter of the pentagon is approximately equal to 200,000 km + 100,000 km + 300,000 km + 240,000 km. Evaluating this expression gives us an approximate perimeter of 840,000 km.

Therefore, the correct answer is D. 40.62 units.

Final answer:

To find out the number of marbles Ben has, we set up equations based on the information given, solve for Jerry's marbles (J), and then use that to solve for Ben's marbles (B). Ben has 172 marbles.

Explanation:

Let's denote the number of marbles Jerry has as J, and the number Ben has as B. According to the problem, Ben has one more marble than three times the number of marbles Jerry has, so we can write this relationship as B = 3J + 1. Together, Ben and Jerry have a total of 229 marbles, which gives us the equation B + J = 229.

Now, we can substitute the expression for B from the first equation into the second equation to solve for J:

Now that we know Jerry has 57 marbles, we can find out how many marbles Ben has:

Therefore, Ben has 172 marbles.

to change the temperature from -13 on Saturday to -4 on Sunday, you would need to add 9 degrees ( -13 + 9 = -4 )

 so you need the equation that would also = 9

-4 + 13 = 9

-4 - (-13) = 9

-4 -13 = -17

4 +(-13)= -9

 there are 2 equations that equal the correct change in temperature, but since both temperatures are negative ( -13 & -4)

 the correct equation would also contain 2 negative numbers

 so correct equation should be: -4-(-13) =

Three of the numbers are correctly written in scientific notation. For the two that are not, we rewrite them correctly.

A. 4.51x10-2: This number is correctly written in scientific notation.

B. 0.789x105: This number is not correctly written in scientific notation. To rewrite it correctly, we move the decimal point to the right so that there is only one non-zero digit to the left of the decimal point. This gives us 7.89x104.

C. 31.5x102: This number is correctly written in scientific notation.

D. 3.008x10-8: This number is not correctly written in scientific notation. To rewrite it correctly, we move the decimal point to the left so that there is only one non-zero digit to the left of the decimal point. This gives us 3.008x10-9.

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To add fractions 1/9 and 5/6, find the least common denominator, convert each fraction to have this denominator, then add the numerators while keeping the denominator the same. The resulting fraction is 17/18.

The first thing you need to do to add fractions 1/9 and 5/6 is to find a common denominator. Since we can only add numerators with the same denominator, we must convert these fractions so that they have the same bottom number. The least common denominator (LCD) for 9 and 6 is 18.

So, we convert 1/9 by multiplying both its numerator and denominator by 2, to get 2/18. Similarly, we convert 5/6 by multiplying both its numerator and denominator by 3, to get 15/18. Now we can add the numerators:

2/18 + 15/18 = 17/18

Remember, we never add the denominators; they remain the same. After finding a common denominator and converting each fraction, we add the numerators together to get the final result.

Final answer:

To add 1/9 and 5/6, find a common denominator, convert each fraction to an equivalent fraction with this denominator, and then add the numerators. The least common multiple of 9 and 6 is 18, leading to 1/9 + 5/6 = 17/18 after conversion and addition.

Explanation:

The first thing you need to do to add the fractions 1/9 and 5/6 is to find a common denominator. A common denominator is necessary because you can only add fractions directly when they share the same denominator. To find a common denominator, you can often multiply the denominators together, but it's better to find the least common multiple (LCM) of the two denominators to simplify the process.

Once the common denominator is found, you convert each fraction to an equivalent fraction with this common denominator. Then, you add the numerators while keeping the denominator the same. The denominators are never added together. If the result is an improper fraction, you may have to simplify it or convert it to a mixed number.
Using our given fractions, the LCM of 9 and 6 is 18. Therefore, 1/9 can be converted to 2/18 and 5/6 to 15/18. Adding these gives 2/18 + 15/18 = 17/18.

The reflection of the point (-2,5) across the x-axis results in the point (-2,-5), as reflecting a point across the x-axis involves changing the sign of the y-coordinate while keeping the x-coordinate the same.

In mathematics, reflecting a point across the x-axis involves changing the sign of the y-coordinate while keeping the x-coordinate the same. To find the reflection of the point (-2,5) across the x-axis, we simply change the sign of the y-coordinate from positive 5 to negative 5, while keeping the x-coordinate -2 the same. Thus, the point (-2,5) reflects across the x-axis to (-2,-5).

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