Find the exact value of tan sin
5
13

The simplified value of the expression 5/6 - 7/2 - 5/3 is -13/3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

5/6-7/2-5/3

Convert the mixed fractions to improper fractions

So, we have

5/6 - 7/2 - 5/3

Evaluate the product of the numerators and the denominators in the above expression so that the denominators are the same

So, we have

5/6 - 7/2 - 5/3 = 5/6 - 21/6 - 10/6

Take the LCM of the denominators in the above expression

So, we have

5/6 - 7/2 - 5/3 = (5 - 21 - 10)/6

Evaluate the difference of the numerators in the above expression

So, we have

5/6 - 7/2 - 5/3 = -26/6

Simplify the above fraction

So, we have

5/6 - 7/2 - 5/3 = -13/3

Hence, the simplified value of the expression 5/6 - 7/2 - 5/3 is -13/3

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Answer:

16

Step-by-step explanation:

there is 2 underground and 14 above so 2 + 14 = 16

Answer: 135

Step-by-step explanation:

313 - 178 = 135

Answer:

40m² + 57mn - 27n²

Step-by-step explanation:

(8m - 3n)(5m + 9n)

each term in the second factor is multiplied by each term in the first factor, that is

8m(5m + 9n) - 3n(5m + 9n) ← distribute both parenthesis

= 40m² + 72mn - 15mn - 27n² ← collect like terms

= 40m² + 57mn - 27n²

Based on the mapping diagram shown, the function f(g(13)) is equal to 32.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

In Mathematics, there are different types of function and these include the following;

From the mapping diagram shown, g(13) is equal to 16 and f(g(13)) ⇒ f(16) would be equal to 32.

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The required grade resistance of car to the uphill movement is -2.9 degrees.

A 3000Lb Car traveling uphill has a grade resistance of -110 pounds. with the help of a  tangent function to estimate the angle of the grade.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Here,
Weight of car = 3000 Lb
grade of resistance = -110
Now,
Angle of the grade = tan⁻¹(-110 / 3000)
The angle of the grade =  tan⁻¹(-0.05)
The angle of the grade = -2.9

Thus, the required grade resistance of the car to the uphill movement is -2.9 degrees.

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Answer:

(2) 21 years old

Step-by-step explanation:

The volume of water in liters the pool holds is 68.4 liters.

Given, we know that 12 buckets of water is needed to fill the swimming pool.

Pool surface area is calculated by multiplying length by breadth. The volume in cubic meters is calculated by multiplying that by the average depth. Due to the fact that there are 7.5 gallons in every cubic foot, you can convert your results to gallons to get the pool volume.

one bucket holds 1.5 gallons .

There are approximately 3.8 liters in 1 gallon.

Therefore, the volume of the swimming pool = ?

12 buckets holding how many gallons of water = each bucket containing 1.5 gallons × total number of buckets

= 1.5 × 12

= 18

Therefore, total volume of water in the swimming pool = total gallons of water × liters in one gallon

= 18  × 3.8

= 68.4 liters

Hence we get the total volume of the swimming pool as 68.4 liters.

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Answer:

280 minutes

Step-by-step explanation:

The new distance travelled is 2.5 times larger than the previous (35/14 = 2.5), therefore, the new time needed to be travelled would also be 2.5 times larger than the original time taken.

[tex]112 \times 2.5 = 280[/tex]

Answer:

it will take her 280 minutes to travel 35 miles

Step-by-step explanation:

miles per hour = miles / hours

or in this case, miles / minutes

[tex]\frac{14 miles}{112 minutes}[/tex]

divide both the top and bottom by 112

[tex]\frac{0.125 miles}{1 minute}[/tex]

= 0.125 miles per minute

35 miles

[tex]35 / 0.125[/tex] = 280

280 minutes

Answer: A

Step by step explanation:

Hence , the rock will be 3 meters from ground level in 4.55 seconds.

It is given that  rock is thrown upward with a velocity of 12 meters per second from the top of a 50 meter high cliff, and it misses the cliff on the way back down.

Using newton's equation s = ut + 1 /2 at² + s₀

where v₀ is velocity and s₀ is the height above ground when thrown, then we have

Putting u = 12 , a = -g = - 9.8 m/s² , s = 3 , s₀ = 50

 3 = 12t + 1 / 2 (-9.8)t² + 50

 0 = 12t - 4.9t²+ 47

4.9t² -12t - 47 = 0

Putting a = 4.9 , b = -12 , c = -47 in quadratic formula , we get

    t = -(-12) ± √(-12)²-4(4.9)(-47) / 2(4.9)

      = 12 ± √144 + 921.2 /9.8

       = 12 ± √1065.2 /9.8

        = 12 ± 32.63/9.8

         = 44.63/9.8

          = 4.55 s

We will consider only positive value as time cannot be in negative

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Answer: 22.8571428571 hours

Step-by-step explanation:

Answer:

28.30282671

Step-by-step explanation:

Step 1: Find the mean.

Step 2: For each data point, find the square of its distance to the mean.

Step 3: Sum the values from Step 2.

Step 4: Divide by the number of data points.

Step 5: Take the square root.

The area covered by region 1 is 16 units and that by region 2 is 15 units.

Given the area of a square be 1unit.

So. the number of block completely covered = a

number of block that are coverered approximately half = b .

So, total area covered = 1*a + 0.5 * b

for figure 1.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 8.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 8

= 12 + 4

= 16units

for figure 2.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 6.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 6

= 12 + 3

= 15units

Therefore, the area covered in region 1 is 16 unit and the area covered in region 2 is 15 unit.

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The area covered by region 1 is 16 units and that by region 2 is 15 units.

Given the area of a square be 1unit.

So. the number of block completely covered = a

number of block that are coverered approximately half = b .

So, total area covered = 1*a + 0.5 * b

for figure 1.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 8.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 8

= 12 + 4

= 16units

for figure 2.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 6.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 6

= 12 + 3

= 15units

Therefore, the area covered in region 1 is 16 unit and the area covered in region 2 is 15 unit.

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Correct conclusion for statement : When a number is divisible by 9, the number is divisible by 3 is "the number is divisible by 3".

What is statement and conclusion ?

The statement and conclusion section is basically a logical reasoning section, in which a statement is given followed by a few conclusions from which you are supposed to choose the one that makes the most sense logically after the statement.

The statement provided is:

When a number is divisible by 9, the number is divisible by 3.

The general form of a conditional statement in if-then form is :

p → q

This implies that if p, then q.

The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.

The if-then form of the provided statement is:

If a number is divisible by 9, then the number is divisible by 3.

So, the conclusion is:

"the number is divisible by 3"

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Answer: A (then the number is divisible by 3)

Step-by-step explanation: did it on edge

Answer:

x=30 degrees

Step-by-step explanation:

both triangles are congruent therefor x will be the same as angle BAD

that's, she pays $4.48 for eggs.. that simple means that orange is also the same amount of the egg,,,

$4.48×3=$13.44

i.e X=$13.44

Answer:

f = -15

Step-by-step explanation:

f/5 - 12 = -15

    +12  |  +12

f/5 = -3

*5  |  *5

f = -15

Answer:

The total amount of the new coffee mixture would be:

8 + 12 = 20 (pounds)

The price of 20 pounds of coffee mixture would be:

8(9.2) + 12(5.5) = 139.6 (dollars).

Therefore, the average price would be:

139.6/20=6.98 (dollars).

Answer: $6.98 per pound.

The algebraic expression for the verbal phrase, "7 more than a number b" is translated as: b + 7.

A mathematical statement that is made up of operation signs (-, +), any variable (letters representing unknown quantity or number that varies), and numbers is referred to as an algebraic expression.

Algebraic expression are simplified or short form of translated phrases.

Let us represent the unknown number in the phrase as b.

"7 more than" means "+ 7".

Thus, the verbal phrase, "7 more than b" would be translated into an algebraic expression as:

b + 7.

Therefore, the algebraic expression for the verbal phrase, "7 more than a number b" is translated as: b + 7.

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Answer:

1897612903782531117or9×

The correct answer is C. Exponential growth. As the function given f(x) = ½ • (5)ª is in exponential form, its range f(x) will increase for any input x.

The given function is defined as;

f(x) = ½ • (5)ª

As, the function is written in the exponent form or power form , its is said to be exponential function.

Now, for any increasing value of x, the value of function will also increase but with increasing difference.

Thus, the function is termed as the exponential growth function.

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The amounts of the three parts of the investment are $6000, $10000, and $18000.

The total amount invested = $34000

We know that the amount was split into three parts, let the parts be x, y, z

then, x + y + z = 34000 //Equation 1

interest of any part after a year = the amount of the part times it's interest

interest of first part after a year = x* 0.08 // 8% = 8 / 100 = 0.08

interest of second part after a year = y * 0.06

interest of third part after a year = z * 0.09

we know that the total interest earned by the total investment = $2700

i.e, 0.08x + 0.06y + 0.09z = 2700 // Equation 2

Guven that interest from the first investment was 4 times the interest from the second.

i.e, 0.08x = 4 * 0.06y

= x = 3y // substituting this relation in the above eauations

x + y + z = 34000 //Equation 1

3y + y + z = 34000

= 4y + z = 34000 //Equation 3

0.08x + 0.06y + 0.09z = 2700 // Equation 2

= 0.08(3y) + 0.06y + 0.09z = 2700

=0.3y + 0.09z = 2700 // simplyfying the equation by multiplying with 100

= 30y + 9z = 270000 // Equation 4

Solving 3 and 4 equations;

36y + 9z = 306000 //Equation 3 multiplied by 9 to make it simple to solve with equation 4

30y + 9z = 270000

6y = 36000

y = 36000 / 6 = 6000// second part of the investment

x = 3y = 3 * 6000 = 18000 // first part of the investment

z = 34000 - (x + y) // from equation 1

z = 34000 - 24000 = 10000 // third part of the investment.

Therefore, the amounts of the three parts of the investment are $6000, $10000, and $18000.

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According to the inequality, the number of the cells of the knives the need is a 10 cells.

According to the statement

We have to find that the inequality for the knives which are need to buy.

So, For this purpose, we know that the

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

From the given information:

Everyone is order some new supplies for the restaurant where he works the restaurant needs at least 587 knives there are currently 387 nice if it set on cell contains 20 knives

Then

Number of the knives they need = 587 knives

Number of the knives present = 387

Number of the knives they need = 587 - 387

Number of the knives they need = 200

Then

The cell contains knives = 20 knives

Then

The number of the cells they need = 200/20

The number of the cells they need = 10 cells.

If s is the number of the cells of the knife needs then inequality become

s > 10.

So, According to the inequality, the number of the cells of the knives the need is a 10 cells.

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Answer:

9.92

Step-by-step explanation:

Hope this help you!!

6 hundreds+ 30 ones = 630

630 + 2 tenths+ 4 hundredths + 6 thousandths=

Answer:The answer is the first one multiply both sides of the equation by -1/3

Step-by-step explanation:please give brainliest.

1) The derivative of the function g(x) = (3x - 5)/(x - 2) at a = 1 is; g'(1) = -1

2) The derivative of the function f(x) = √(3x - 4) at a = 2 is; 3/(2√2)

1) We want to find the derivative of the function g(x).

g(x) = (3x - 5)/(x - 2)

g'(x) = -1/(x - 2)²

Thus;

g'(1) = -1/(1 - 2)²

g'(1) = -1

2) We want to find the derivative of the function f(x).

f(x) = √(3x - 4)

f'(x) = 3/(2√(3x - 4))

f'(2) = 3/(2√(3(2) - 4))

f'(2) = 3/(2√2)

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