MATHEMATICS HIGH SCHOOL

5tanx-2cotx+1=0...... .

Answers

Answer 1

Answer:

Step-by-step explanation:

5(tanx)^2 -2 +tanx=0

let tanx=y

5y^2 + y-2=0

y=0.5403 or y= -0.7403

tanx=0.5403

x=arctan(0.5403)

x=28.38°

tanx=-0.7403

x=arctan(-0.7403)

x=143.49°

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The points on a number line correspond to

Answers

the points on a number line correspond to; real numbers

Write this mixed number 6 4/7 as an improper faction in simplest form

Answers

it is 46/7 you could multiply 6x7 and then add 4 = 46/7

46/7. You do 7 times 6 and get 42. 42+4 is 46.
So 46/7 is the answer.
~JZ

Find the cardinal number of the set C = {x | 25 < x ≤ 50}, where ℤ denotes the set containing all integers. A) 26 B) 24 C) 25 D) 27

Answers

Answer:

The correct answer is A.

Final answer:

The cardinal number of the set C = {x | 25 < x ≤ 50}, containing integers greater than 25 and up to (including) 50 is 25 as it represents the total number of integers within these conditions.

Explanation:

The set C = {x | 25 < x ≤ 50} denotes the set of all integers that are greater than 25 and less than or equal to 50. When we calculate these values, we get the numbers 26 through to 50. This gives us a total of 25 different values (or integers). So, the Cardinal number of the set C, which stands for the number of elements in the set, is 25. Therefore, the correct option is C) 25.

The set C = {x | 25 < x ≤ 50} represents all values of x that are greater than 25 and less than or equal to 50. We can count the number of integers within this range to find the cardinal number of the set.

Step 1: Subtract the lower bound from the upper bound and add 1: 50 - 25 + 1 = 26

Therefore, the cardinal number of the set C is 26.

Learn more about Cardinal Numbers here:

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Use an inequality symbol (<, >, =, ≤) to compare −3 + 7 _____ −10 − 2 A. > B. < C. = D. ≤

Answers

By using the concept of inequality, the solution for the correct inequality used between the given numbers is,

$(- 3 + 7 ) > (- 10 - 2)$

Used the concept of inequality, which states that,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that,

Compare the numbers (- 3 + 7) and ( - 10 - 2).

Now, to compare the numbers we can solve each side,

(- 3 + 7) = - 3 + 7

= 7 - 3

= 4

(- 10 - 2) = - 10 - 2

= - 12

So, by the definition of positive and negative numbers, we get,

4 > - 12

As positive numbers are always greater than negative numbers.

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A would be the best choice because -3 + 7 is 4 and -10 - 2 is -12.

How many 2.5 inch by 6 inch tiles will fit on a back splash that is 2.5 feet tall and 8 feet long?

Answers

Area of each of the tiles = (2.5 * 6) inches^2
   = 15 inches^2
Now we have to get down to the case of the backsplash
1 feet = 12 inches
Then
Length of the back splash = 8 feet
   = (8 * 12) inches
   = 96 inches
Height of the back splash = 2.5 feet
   = (2.5 * 12) inches
   = 30 inches
Then
Area of the back splash = ( 30 * 96) inches^2
   = 2880 inches^2
So
The number of tiles required to fit in the back splash = 2880/15
   = 192
So 192 tiles will be required to fit in the back splash. I hope the procedure is clear enough for you to understand.

Final answer:

Convert the back splash dimensions to inches. Calculate the areas of the back splash and a tile. Then divide the total area of the back splash by the tile area to get the number of tiles required, which is 192 tiles.

Explanation:

To determine the number of tiles needed, we first need to convert the dimensions of the back splash from feet to inches since the size of the tiles is given in inches. So, the back splash is 2.5 feet tall equal to 30 inches (because 1 foot = 12 inches and 2.5x12 = 30) and it is 8 feet long which is 96 inches (because 1 foot = 12 inches and 8x12 = 96).

Next, we calculate the area of the back splash by multiplying the length by the height which is 2880 square inches (30 inches x 96 inches = 2880).

Then, we find the area of a tile by multiplying the length and the width of the tile: 2.5 inch x 6 inch which equals 15 square inches.

Finally, we divide the total area of the back splash by the tile area to get the number of tiles required. So, 2880 square inches / 15 square inches equals 192 tiles.