What are the domain and range of the real-valued function f(x) = -3-√√4x - 12?

Trigonometric ratio in option (c) tan C will not have the same value as sin A.

Trigonometric functions are defined as the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given a right angled triangle ABC given below.

ABC angle is 90° and angle ACB is 45°.

Then angle BAC = 180° - (90° + 45°) = 45°

Since two angles are equal, it is an isosceles triangles.

So opposite sides to the equal angles are equal.

AB = BC

AC is the hypotenuse.

Sin A = Opposite side / Hypotenuse = BC / AC

(a) Cos A = Adjacent side / Hypotenuse = AB / AC = BC / AC

(b) Sin C = AB / AC = BC / AC

(c) Tan C = Opposite side / Adjacent side = AB / BC = BC / BC = 1, not equal to Sin A

(d) Cos C = BC / AC

Hence the option (c) is not equal to sin A.

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Answer:

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Where r is the radius of the circle.

Plugging in the value for the radius of the Earth, we have:

Circumference = 2π(6371 km) = 12,742 km

So the length of the rope, assuming it makes a perfect circle around the Earth, would be 12,742 km = 2π(6371) kilometers.

Step-by-step explanation:

The velocity of the apple, to the nearest hundredth, when it hit the ground is equal to 13.35 meters per seconds.

In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.

From the information provided about an apple that fell off a branch of the tree, a function that models the velocity of the apple include the following:

Velocity = (19.8d)^{1/2}

Where:

d represents the distance in meters.

Velocity = (19.8 × 9)^{1/2}

Velocity = (178.2)^{1/2}

Velocity = 13.35 meters per seconds.

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The population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

percentage, a relative value indicating hundredth parts of any quantity.

First, we can find the population of chickadees by multiplying the population of phoebes by 0.7 (100% - 30%):

Population of chickadees = 0.7 x 12,000 = 8,400

Next, we can find the population of blue jays by multiplying the population of phoebes by 0.3:

Population of blue jays = 0.3 x 12,000 = 3,600

Therefore, the population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

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The answer is B. 18

When solving similar triangles, you must set up a proportion. We do not know what the other two lengths are for side AB, but we can still solve another way. For side AC, we can set up a proportion of 33/44. We're going to take AM and put that over the total. The total length of side AB is 24, and we're going to use x for AL.

33/44 = x/24

Once finished solving the proportion, you are left with 18

The missing length of triangle is 18.

What exactly is a triangle?

Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorised into three categories based on its sides, namely:

A triangle is categorised into three categories based on its angles, namely:

Now,

As these triangles are similar that means

we can find the proportion of sides from given sides and

from that find x.

So, here  AC/AM=AL/AB

44/33=24/x

AL=24*33/44

AL=18

Hence,

            The missing length AL of triangle is 18.

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Answer: 75%

Step-by-step explanation: To calculate,

(0.1 x 100) + (0.3 x 80) + (0.2 x 95) + (0.4 x 75) = 83%

Note that in order to solve the above, we had to assume a start date for the construction. Hence, by March 2022​, a total number of liters supplied is 3,380,000 liters.

To solve the problem, we need to know how many weekdays are in March 2022. March 2022 has 23 weekdays (31 days - 4 Saturdays - 4 Sundays).

Since the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays, we can assume an average of 14 water tankers per weekday. Therefore, the total number of water tankers to be supplied on weekdays in March 2022 would be:

14 water tankers/day x 23 weekdays = 322 water tankers

On Saturdays, the company has to supply a minimum of 4 water tankers. Since there are 4 Saturdays in March 2022, the total number of water tankers to be supplied on Saturdays in March 2022 would be:

4 water tankers/day x 4 Saturdays = 16 water tankers

Therefore, the total number of water tankers to be supplied in March 2022 would be:

322 water tankers (weekdays) + 16 water tankers (Saturdays) = 338 water tankers.

Assuming each water tanker carries a load of 10,000 liters, the total volume of water supplied to the construction site in March 2022 would be:

338 water tankers x 10,000 liters/tanker = 3,380,000 liters

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Full Question:

The company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Assuming the start month for the construction was February 2022, Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022​

The lowest values of x are;

1. x = 1/2, x = 2/4, x = 3/6

2. x = 14, 15, 16

From the information given, we have that;

10-3x > 8

collect the like terms, we get;

-3x > 8 - 10

subtract the values

-3x > -2

Make 'x' the subject

x > 2/3

5x-27 > 7x

collect the like terms

5x - 7x> 27

subtract the like terms

-2x> 27

Make 'x' the subject

x > -27/2

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Step-by-step explanation:

(x-2)(x-2)-4x

x²-2x-2x +4-4x

x²-4x-4x +4

x²-8x+4

Answer:

 4x - (x - 2)² = 4x - x² + 4 = 3x + 4

Step-by-step explanation:

The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units

The radius of the base = 4 units

The length of the side of the square = 2x

The area of the square = a^2

Where a is side of the square

The area of the square = (2x)^2

= 4x^2

The equation of the circle is

x^2 + y^2 = 16

x^2 = 16 - y^2

The area = 4(16 - y^2 )

= 64 - 4y^2

The volume of the square

V = [tex]\int\limits^a_b {A(y)} \, dy[/tex]

= [tex]\int\limits^4_0 {64-4y^{2} } \, dy[/tex]

= 64×4 - 4×(4^3/3)

= 256 - 256/3

= 512/3 cubic units

Therefore, the volume of the solid is 512/3 cubic units

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The required graph has been attached below which represents the given linear equation y = (2/5)x - 4.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To plot the graph of y = (2/5)x - 4, you can follow these steps:

Choose a range of values for x that you want to plot. For example, you can choose x values from -10 to 10.

Substitute the x values into the equation to find the corresponding y values. For example, if x = -10, then y = (2/5)(-10) - 4 = -8.

Plot the ordered pairs (x, y) on a coordinate plane. For example, if x = -10 and y = -8, plot the point (-10, -8) on the plane.

Repeat this process for several x values to plot additional points.

Connect the points with a straight line to obtain the graph of the equation y = (2/5)x - 4.

Note that the graph should be a straight line with a slope of 2/5 and a y-intercept of -4.

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The question seems incomplete, the correct question would be as:

How to plot the graph of y = (2/5)x — 4?

The critical value strategy entails deciding whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true in order to determine whether something is "likely" or "unlikely."

How do you determine the rejection zone and the crucial value?

The rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it. The rejection area, for the right-tailed test, for instance, is any value bigger than the critical value, or c 1 .

To execute any hypothesis test, the critical value technique entails four specific phases, which are as follows:

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D because none of the inputs (x) are repeated. All the others have the same input with two or more different outputs.

Step-by-step explanation:

we need to remember 2 things for right-angled triangles (which we need to use to find the sides of the rectangle, so that we then can calculate the area) :

1. Pythagoras

a² + b² = c²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.

2. geometric mean theorem

height = sqrt(p×q)

with p and q being the segments of the baseline the height is splitting it into. in our case MA and AL.

so, to get the length of the rectangle (PL) we use Pythagoras :

PL² = 6² + 8² = 36 + 64 = 100

PL = 10 units

to get PM we first need to get ML. and for that we need to get MA.

6 = sqrt(MA × 8)

36 = MA × 8

MA = 36/8 = 4.5 units

that means ML = 8 + 4.5 = 12.5 units

and again Pythagoras

ML² = PL² + PM²

12.5² = 10² + PM²

156.25 = 100 + PM²

56.25 = PM²

PM = 7.5 = 7.5 units

so, the area of the rectangle is

10 × 7.5 = 75 = 75.00 units²

to "round" to the nearest hundredth.

Answer is B. 
y= 2x -3 y= -2x + 1

step by step

First I found the y intercepts at (red line) -3 and (green line) +1.

There is only one answer that shows these two y intercept values.

 To double check this answer, I checked the slope of each line. The red line has a slope of 2 and the green line has a slope of -2.

Slope was found on the graph finding rise over run and compared to the number next to x in the equations.

See attached graph.

Answer: the first box is does not the 2st box does  i hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-2, 3) (2, -1)

(-1 - 3)/(2 + 2)= -4/4 = -1

m = -1

does

does not

y - 3 = -1(x + 2)

y - 3 = -x - 2

y = -x + 1

Option 1

The lengths of the pieces are 1ft and 9ft

From the information given, we have that;

The shorter side = x

The longer side of the board = 6 +3x

The total length = 10

Substitute the values, we have;

x + 6 + 3x = 10

collect the like terms

x + 3x = 10 -6

Add or substract the like terms, we have;

4x = 4

Now, make 'x' the subject of formula by dividing by 4, we get;

4x/4 = 4/4

x = 1 ft

The longer side = 9ft

Hence, the values are 1 and 9

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Answer:

D. Machines, vehicles, furniture, and appliances are not considered liabilities. Liabilities are obligations or debts that a business owes to others. They are usually in the form of loans or accounts payable and represent money that must be paid in the future.

Machines, vehicles, furniture, and appliances are assets, which are resources that a business owns and that have monetary value. Assets can be sold to generate cash or used to produce goods or provide services. While assets can be used to secure loans, they do not represent a debt or obligation that must be paid in the future like a liability

Answer:

D

Step-by-step explanation:

current liability is money owed to suppliers in the form of accounts payable . Current liabilities are typically settled using current assets, which are assets that are used up within one year.

There were 375 adult tickets sold and 316 student tickets for the school play.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the number of student tickets would be x and the number of adult tickets would be y

As per the question, we have a system of equations:

x + y = 691   ....(i)

x = y - 59     ....(ii)

Substitute the value of x = y - 59 in equation (i),

y - 59 + y = 691

2y = 691 + 59

2y = 750

y = 375

Substitute the value of y = 375 in equation (ii), and solve for x:

x = 375 - 59

x = 316

Thus, there were 375 adult tickets sold.

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The complete question would be as:

A total of 691 tickets were sold for the school play. There were 59 fewer student tickets sold than adult tickets. How many adult tickets were sold?

The single payment 2 years from now will be of $13,287.26

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given that money earns 7.74% compounded quarterly, a payment of $2,070 due 2 years ago, but not paid, and $300 today.

To calculate investments or debts with compound interests.

Where:

V(n) is the value of the debt after n years,

R is the annual interest rate,

t is the number of times the debt is going to be compounded annually,

n is the number of years the debt is going to be compounded,

P is the principal amount being owed.

we know that the debt will be cancelled in 2 years from now. Therefore we have that n = 2 for both debts, because after the 2rd year the debts.

Then you have that t = 4, because the debt is compounded quarterly.

We can add up the two principals $2,070 + $300 = $2,370 to make it our value P, so P = 9000.

And finally we have that R = 7.74.

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 2,370 / (1 + 7.74/365)(365)^(2)

P = $13,287.26

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The proportional relationship used to find the distance that the train will travel after m minutes is given as follows:

d = 0.12m.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Considering that when the input is of 5, the output is of 0.6, the constant of the relationship in this problem is given as follows:

k = 0.6/5

k = 0.12.

Hence the equation is given as follows:

d = 0.12m.

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The boat has a top speed of approximately 29.7 miles per hour and a displacement of approximately 73,934 metric tons.

Answer:

[tex]29.9[/tex] miles per hour

[tex]73482[/tex] metric tons

Step-by-step explanation:

We are given:

top speed of 26 knots

displacement of 81,000 tons

It is asking us to convert knots to miles per hour.

It is asking us to convert tons to metric tons.

We can use conversion factors to complete the unit conversions.

1 knot (kt) = 1.15077945 miles per hour (mph)

1 ton = 0.907185 metric tons

Numerical Evaluation

Lets convert our top speed.

We can set up an equation like this

[tex]\frac{1}{1.15077945} =\frac{26}{x}[/tex]

Lets solve for [tex]x[/tex].

Cross multiply.

[tex]1x=26*1.15077945[/tex]

Evaluate [tex]26*1.15077945[/tex].

[tex]26*1.15077945 =29.9202657[/tex]

Round to the nearest tenth.

[tex]29.9[/tex] miles per hour

Lets convert our displacement.

We can set up an equation like this

[tex]\frac{1}{0.907185 } =\frac{81000}{x}[/tex]

Lets solve for [tex]x[/tex].

Cross multiply.

[tex]1x=81000*0.907185[/tex]

Evaluate [tex]81000*0.907185[/tex].

[tex]81000*0.907185=73481.985[/tex]

Round to the nearest tenth.

[tex]73482[/tex] metric tons

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Any line of the form:

y = (3/2)x + b

Is perpendicular to the given line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is -1.

Here we want to find a line perpendicular to:

2x + 3y = 10

We can rewrite this as:

3y = 10 - 2x

y = (10/3) - (2/3)*x

Then the slope of the perpendicular line must be such that:

a*(-2/3) = -1

a = 3/2

Then any line of the form:

y = (3/2)*x + b

Is perpendicular to the given line.

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The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

from the given data we get,

The categories are mutually exclusive, so we have ...

P(≥21) = P(21-30) +P(31-40) +P(41-50)

           = 45% +19% +15%

 P(≥21) = 79%

           =0.79

The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.

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Given expression q=p+7

Expression can be defined as contains one or more variables and constants with one or more arithmetic operators.

Simply put the p values in the expression. solve it and get the q values.

q=p+7 in the place of p submit p=0

q=0+7

q=7

q=p+7  in the place of p submit p=2

q=2+7

q=9

q=p+7  in the place of p submit p=3

q=3+7

q=10

Therefore, The values of q are 7,9,10

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The missing numbers are:

7,9 and 10 when 0, 2, and 3 respectively.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An equation,

q = p + 7.

Substituting the values of p:

When p = 0,

q = 0 + 7

q = 7.

When p = 2,

then q = 9.

And when p = 3,

q = 10

Therefore, all the required values are given above.

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The linear equation that passes through the two given points is:

y = (5/8)*x + 19/8

We want to find the equation of a line that passes through (1, 3) and (9, 8).

Remember that the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂) is given by the equation:

slope = (y₂ - y₁)/(x₂ - x₁)

Here we know the two points (1, 3) and (9, 8).

Then the slope is:

slope = (8 - 3)/(9 - 1) = 5/8

We can write the line as:

y = (5/8)*x + b

To  find the value of b,we can evaluate in one of the given points, for example, if we use (1, 3) then we will get:

3 = (5/8)*1 + b

3 = 5/8 + b

3 - 5/8 = b

24/8 - 5/8 = b

19/8 = b

The linear equation is:

y = (5/8)*x + 19/8

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Answer:

c

Step-by-step explanation:

trust me

The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.

The system of equations that represent the information in the question is:

a + b = 20,000 equation 1

0.07a + 0.08b = 1540 equation 2

Where:

a = amount invested in the account that earns 7% interest

b = amount invested in the account that earns 8% interest

The elimination method would be used to solve the equations.

Multiply equation 1 by 0.07

0.07a + 0.07b = 1,400 equation 3

Subtract equation 3 from equation 2

0.01b = 140

Divide both sides of the equation by 0.01

b = 140/ 0.01

b = 14,000

Substitute for b in equation 1:

a + 14,000 = 20,000

a = 20,000 - 14,000

a = 6,000

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Answer:

the solution is done in the given picture..

thank you