Define the domain and range of the function and state whether it is one-to-one, onto, both or neither.

According to the figure:-

We know that Sin∅=P/H

Hence Sinx°=13/25

[tex] { \sin}^{ - 1} \frac{25}{13} = X°[/tex]

Answer:

[tex] \frac{271}{100} [/tex]

Step-by-step explanation:

hopefully it makes sense

:)

The decimal 2.71 can be written as the simplified fraction as 271/100.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

The given number is 2.71.

We can write 2.71 as 2.71 / 1, since any number divided by 1 is the number itself.

Multiplying both numerator and denominator of 2.71 / 1 with 100, we get,

(2.71 × 100) / (1 × 100)

= 271/100

This cannot be simplified further since 271 is a prime number.

Hence the simplified fractional form of 2.71 is 271/100.

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Answer:

-20

Step-by-step explanation:

Hi

The value of the expression is a decimal -17.33.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

0.3x = -5 - (-0.4 - (-0.6))

0.3x = -5 - (-0.4 + 0.6)

0.3x = -5 - 0.2

0.3x = -5.2

x = -5.2/0.3

x = -17.33

Thus,

The value of x is -17.33.

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Answer:

The answer is 200000 milligrams

Hope that helped you

Answer:

212

Step-by-step explanation:

[tex]3( {3}^{3}) +2 ( {10}^{2} ) - 15[/tex]

[tex]3(9) + 2(100) + 15[/tex]

[tex]27 + 200 - 15[/tex]

[tex]212[/tex]

Answer:

hence the required midpoint of the given line is (9,5)

Answer:

[tex]( \frac{6 + 2}{2} +\frac{12 + 8}{2}) = ( \frac{8}{2} + \frac{20}{2} ) = (4 \: comma10)[/tex]

The answer is :(4, 10)

Answer:

q is 4

Step-by-step explanation:

[tex]gradient = \frac{y_{2} - y_{1} }{x _{2} - x _{1} } \\ [/tex]

let gradient of the line joining (4, q) to (6, 5) be x

let gradient of the line joining (0, 0) to (4, q) be y

[tex]y = 2x[/tex]

therefore:

[tex]( \frac{q - 0}{4 - 0} ) = 2( \frac{5 - q}{6 - 4} ) \\ \\ \frac{q}{4} = \frac{2(5 - q)}{2} \\ \\ \frac{q}{4} = 5 - q \\ \\ q = 4(5 - q) \\ q = 20 - 4q[/tex]

collect like terms:

[tex]q + 4q = 20 \\ 5q = 20 \\ q = \frac{20}{5} \\ \\ q = 4[/tex]

Let,

As we know,

then,

→ [tex]\frac{q-0}{4-0} = 2(\frac{5-q}{6-4} )[/tex]

      [tex]\frac{q}{4} = \frac{2(5-q)}{2}[/tex]

      [tex]\frac{q}{4} = 5-q[/tex]

By applying cross-multiplication, we get

      [tex]q = 4(5-q)[/tex]

      [tex]q = 20-4q[/tex]

By adding "4q" both sides, we get

[tex]q+4q= 20-4q+4q[/tex]

     [tex]5q = 20[/tex]

       [tex]q = \frac{20}{5}[/tex]

       [tex]q = 4[/tex]

Thus the above value is correct.

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Step-by-step explanation:

Add all the data and divide by 2 to get your median

The median of the data set 8, 8, 14, 15, 15, 15.4, 17, 23, 38.5 will be 15.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The data set is given below.

17, 8, 23, 14, 15, 38.5, 8, 15.4

Arrange the data in ascending order, then we have

8, 8, 14, 15, 15, 15.4, 17, 23, 38.5

The number of the term will be 9, then the median will be

Median = (n + 1) / 2

Median = (9 + 1) / 2

Median = 10 / 2

Median = 5th term

5th term that is 15.

The median of the data set 8, 8, 14, 15, 15, 15.4, 17, 23, 38.5 will be 15.

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Answer:

56

Step-by-step explanation:

show your work

Answer:

adding by 13

Step-by-step explanation:

subtract 54-41

13.54 g/mL = (100 g)/v

==>   v = (100 g)/(13.54 g/mL) = 7.39 mL

The volume of 100 grams of mercury is 7.38 mL when the density of mercury is 13.54 g/mL.

To calculate the volume of 100 grams of mercury, we can use the density formula:

Density = Mass / Volume

We are given the density of mercury as 13.54 g/mL, and we want to find the volume in mL.

Volume = Mass / Density

Substituting the given values:

Volume = 100 g / 13.54 g/mL

Simplifying the division:

Volume= 7.38 mL

Therefore, the volume of 100 grams of mercury is 7.38 mL.

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Answer:

182

Step-by-step explanation:

First, we can say that ∠ACB and ∠BCF are opposite angles because they are not next to each other and are formed by intersecting lines. Therefore, ∠ACB = ∠BCF

Next, angles correspond with the side opposite of it. This means that, for example, ∠ACB corresponds with line AB and ∠BCF corresponds with line BF. Because ∠ACB and ∠BCF are equal and the triangles are similar, we can say that their corresponding sides have a ratio with each other. Similarly, ∠CAB corresponds to CB, ∠ABC corresponds to AC, ∠CWV corresponds to CV, and ∠CVW corresponds to CB.

Because the triangle CVW is isosceles, we can say that the angles whose corresponding sides are equal are equal as well, so ∠CAB = ∠ABC and ∠CVW = ∠CVW. Next, because ∠ACB and ∠BCF are equal and correspond to each other, and the other two angles in each triangle are equal to each other, we can say that the other two angles must be equal. Another way of putting this is like this:

Say that x = ∠CAB. Then,

∠CAB + ∠ABC + ∠ACB = 180

x + x + ∠ACB = 180

2x + ∠ACB = 180

subtract ∠ACB from both sides

180 - ∠ACB = 2x

Similarly, if y = ∠CWV,

180 - ∠WCV = 2y. Therefore, 2y=2x and y=x, so ∠CAB = ∠ABC = ∠CWV = ∠CVW.

Given this, we can say that sides CV and CW correspond with BC and AC. This means that the ratio between, for example, CV and BC is equal to the ratio between CW and AC. Therefore,

CV/BC = CW/AC

84/182 = 84/?

Filling in the blank, 84/182 is equal to 84/182, so ? = 182

Answer:

I think it's D.................

Answer:

Step-by-step explanation:

x = first number

x + 2 = second number

x + 4 = third number

5(x + 2) = 6 + 2x + 2 ( x + 4)

5x + 10 = 6 + 2x + 2x +8

5x - 4x = 14 - 10

x = 4

The first number (x) = 4

The second number ( x + 2) = 4 + 2 = 6

The third number (x + 4) = 4 + 4 = 8

Answer:

2x + 2x +2 + 2x +4 = 6x +6 =Sum

5 * (2x +2) = 2 * (2x + 2x +4) +6

10x + 10 = 8x + 8 + 6

2x = 4

x = 2

So the numbers are:

2x or 4

2 x + 2 = 6

2x + 4 = 8

Double-Check

5 * 2nd integer = 30

2 *  (1st + 3rd integers) = 24

30 is 6 more than 24

Success!!!

Step-by-step explanation:

Answer:

Concept:

Intersecting lines are lines that overlap upon only one point. The number of lines can be two or more.

Intersecting lines can intersect at any angle.

Solve:

There are in total four intersecting points in the given figure.

As we can see from the figure, any two lines would intersect each other

Therefore, 2 pairs of intersecting lines can be any pairings of lines that are not in the same orientation.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

The above given statement is true

Answer:

This is called a bisector.

Answer:

C

Step-by-step explanation:

all whole numbers can be written as fractions that is over 1

Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.

Given that:

[tex]C(t) = \frac{-10t^2 + 50t}{t^2 + 4t + 3 }[/tex]

(a): The domain of the function

Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.

t, cannot take negative values (i.e. it is not possible to have a negative time).

The least possible value of t is 0

So, the domain of the function based on the context is:

[tex]t \ge 0[/tex]

(b) The greatest concentration of the medication

From the graph (see attachment), the maximum y-value is 5.

Hence, the greatest concentration of the medication is 5 mg/L

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A function assigns the values. The greatest concentration of the medication that a patient will have in their body is when the time is t=1.

A function assigns the value of each element of one set to the other specific element of another set.

A.) Given the function of the concentration of medication in the body as to[tex]C(t)=\ \frac{\left(-10t^{2}+50t\right)}{t^{2}+4t+3}[/tex] where t is the time. Since the time can not be negative, therefore, the domain of the function is t≥0.

B.) The graph of the function can be plotted as shown below. Now, the greatest concentration of the medication that a patient will have in their body is when the time is t=1.

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Answer:

[tex] = (4x + 8)(2x - 12) \\ = ( {8x}^{2} - 48x + 16x - 96) \\ = (8 {x}^{2} - 32x - 96) \\ = 8( {x}^{2} - 4x + 12)[/tex]

Answer:

\begin{gathered} = (4x + 8)(2x - 12) \\ = ( {8x}^{2} - 48x + 16x - 96) \\ = (8 {x}^{2} - 32x - 96) \\ = 8( {x}^{2} - 4x + 12)\end{gathered}

=(4x+8)(2x−12)

=(8x

2

−48x+16x−96)

=(8x

2

−32x−96)

=8(x

2

−4x+12)

Answer:

120°

Step-by-step explanation:

The protractor shows that ∠AOE is 120°. If A started from the left, then it would be 60°.

Answer:

120

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

p^-8q^-20 * p^8q^-10

=q^-30

=1/q^30

Answer:

the slope is 5

and the intercept is 0

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(7)

(25x + 8) and (9x + 2) are adjacent angles and sum to 180° , then

25x + 8 + 9x + 2 = 180 , that is

34x + 10 = 180 ( subtract 10 from both sides )

34x = 170 ( divide both sides by 34 )

x = 5

Then

9x + 2 = 9(5) + 2 = 45 + 2 = 47

(7y + 5) and (9x + 2) are vertical angles and are congruent , so

7y + 5 = 47 ( subtract 5 from both sides )

7y = 42 ( divide both sides by 7 )

y = 6

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

(8)

(11x - 24) and (7x + 30) are vertical angles and are congruent, so

11x - 24 = 7x + 30 ( subtract 7x from both sides )

4x - 24 = 30 ( add 24 to both sides )

4x = 54 ( divide both sides by 4 )

x = 13.5

Similarly

(17y - 4) and (5y + 38) are vertical angles and congruent , then

17y - 4 = 5y + 38 ( subtract 5y from both sides )

12y - 4 = 38 ( add 4 to both sides )

12y = 42 ( divide both sides by 12 )

y = 3.5

Answer:

[tex]5x + 6y = 42[/tex]

Step-by-step explanation:

Hope it is helpful....