Javier wants to inscribe a circle inside of the triangle ABC shown in the following figure. He begins by constructing the angle bisectors of angles A and B and finding their intersection at point D.

If Javier is trying to inscribe a circle inside of triangle ABC in as few steps as possible, which of the following steps would be the best step for him to take next?

1) Construct the perpendicular line from point D to the line BC.

2) Find the altitude from point C.

3) Use the distance from D to any of the triangle's vertices to set the width of the compass.

4) Construct the angle bisector of angle C.


Thank you :)

Final answer:

A variable is a name assigned to a quantity that can take on various values, and is used by mathematicians, economists, and statisticians in different contexts to represent data or elements of an equation.

Explanation:

A variable is the name given to a quantity that may assume a range of values. Mathematicians and economists often use variables in equations to represent different aspects of a problem or scenario. For example, in the equation of a line, commonly expressed as y = mx + b, the variables are 'x' and 'y'. Here, 'x' typically represents values on the horizontal axis, and 'y' represents values on the vertical axis, while 'b' is the y-intercept, and 'm' is the slope of the line. To understand how an equation with variables functions, we can look at a numerical example.

In statistics, variables can also refer to characteristics or measurements that can be determined for each member of a population. These variables can be numerical or categorical. A numerical variable, such as 'X' representing the number of points earned by a math student, allows for mathematical calculations like averaging. A categorical variable, like 'Y' indicating a person's political party affiliation, places individuals into categories and doesn't lend itself to mathematical operations like averaging.

The standard deviation decreases and the sampling distribution becomes more normal as the sample size increases in x bar distribution.

The variability of the x bar distribution changes as the sample size increases. As the sample size increases, the standard deviation of the sampling distribution of the means will decrease, approaching the standard deviation of X. The sampling distribution of the mean becomes more normal as the sample size grows, showing less variability.

To find the difference in weight between the Newfoundland and the Springer Spaniel, subtract the weight of the Springer Spaniel from the weight of the Newfoundland.

To find the difference in weight between the Newfoundland and the Springer Spaniel, we need to subtract the weight of the Springer Spaniel from the weight of the Newfoundland. The Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. So, we first need to find the weight of a Cocker Spaniel by subtracting 7,590 grams from the weight of the Springer Spaniel. We then add this weight to the weight of the Newfoundland to get the final answer. Let's calculate:

We can now substitute the given values into these equations and solve.

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Answer:

a = 0.75

b= 0.4375

d= 0.6

e=0.175

f= 2.55

Step-by-step explanation:

By simple division method, the following answers can be calculated:

a.

=[tex]\frac{3}{4}[/tex]

=0.75

b.

= [tex]\frac{7}{16}[/tex]

=0.4375

d.

= [tex]\frac{3}{5}[/tex]

=0.6

e.

= [tex]\frac{7}{40}[/tex]

=0.175

f.

=[tex]\frac{51}{20}[/tex]

=2.55

Thus, the answer are :

a = 0.75

b= 0.4375

d= 0.6

e=0.175

f= 2.55

Answer:

A.0.75 B.0.4375 C. 14.4 D. 0.6 E. 0.175 F. 2.55

Step-by-step explanation:

Answer:

Option 1 - Division Property of Equality

Step-by-step explanation:

Given : If  [tex]4x=20[/tex], then x=5.

To find : Which property justifies this statement?

Solution :

The equation is  [tex]4x=20[/tex]

To make variable separate we have to remove 4 which is in multiple of variable x.

So, We divide both side by 4,

Applying division property of equality,

We can divide both sides of an equation by the same number and preserve equality.

[tex]\frac{4x}{4}=\frac{20}{4}[/tex]

[tex]x=5[/tex]

Therefore, The property justifies the statement is 'Division Property of Equality'.

So, Option 1 is correct.

To find the balance after 3 years in a savings account with $12,000 and a 3.5% interest rate compounded monthly, we can use the formula for compound interest.

To find the balance after 3 years, we can use the formula for compound interest:

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

where:

Plugging in the given values:

The formula gives us:

A = $12,000(1 + 0.035/12)^(12*3)

Calculating this expression will give us the balance after 3 years.

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The simplification of the given expression is 0.6i.

Complex numbers are those numbers that contain the imaginary and the real part.

A Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

where r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Usually the simplification involves proceeding with the pending operations in the expression.

We need to simpify the 0.4i - i

= i(0.4-1)

= 0.6i

Therefore, the simplification of the given expression is 0.6i.

Learn more about cube root of complex numbers here:

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Answer:

B 3 times

C. 4 times

Step-by-step explanation:

For Tristan to  jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.

Considering the options given

A. 2 * 7/10 = 1.4 miles (this is not within the range)

B. 3 * 7/10 = 2.1 miles (this is within the range)

C. 4 * 7/10 = 2.8 miles (this is within the range)

D. 5 * 7/10 = 3.5 miles (this is not within the range)

Answer: 500

Step-by-step explanation:

Since,  The monthly salary is modeled by the function,

f(c) = 250 c + 500.

According to the question,

Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars.

In the given function c is a variable.

Thus, c must show the number of cars.

Thus, the base pay must be free from any variable.

In the above expression 500 is free from the variable c therefore, 500 is the base pay of Adam.

⇒ f(c) is the total earning by Adam after selling a car.

If he Does not sell any car then c=0,

f(0) = 250×0+500 = 500

Therefore, if he does not sell any car then his earning is 500.

Answer:  [tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]

Step-by-step explanation:  Given that

[tex]\sin\theta=-\dfrac{1}{2}[/tex] and [tex]\theta[/tex] lies in Quadrant III.

We are to find the value of [tex]\tan \theta.[/tex]

We will be using the following trigonometric identities:

[tex](i)~sin^2\theta+\cos^2\theta=1,\\\\(ii)~\dfrac{\sin\theta}{\cos{\theta}}=\tan \theta.[/tex]

We have

[tex]\tan\theta\\\\\\=\dfrac{\sin\theta}{\cos\theta}\\\\\\=\dfrac{\sin\theta}{\pm\sqrt{1-\sin^2\theta}}\\\\\\=\pm\dfrac{-\frac{1}{2}}{\sqrt{1-\left(\frac{1}{2}\right)^2}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\\=\pm\dfrac{1}{\sqrt3}.[/tex]

Since [tex]\theta[/tex] lies in Quadrant III, so tangent will be positive.

Thus,

[tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]

the answer would be 6 i did my calculations on paper then misplaced it but checked answer and it said 6

56×10= 560 so the answer is 560

The answer 108 degrees.

Answer: [tex]108^{\circ}[/tex]

Step-by-step explanation:

The sum of all the angles in a regular polygon with sides n , is given by :-

[tex]S_n=180^{\circ}(n-2)[/tex]

Now, the sum of all the angles in a regular pentagon with 5 sides will be :-

[tex]S_5=180^{\circ}(5-2)=180^{\circ}(3)=540^{\circ}[/tex]

We know that all the interior angles of a regular polygon are equal .

Therefore, the measure of each interior angle in a pentagon is given by :-

[tex]x=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]

Hence, the measure of each interior angle in a pentagon=[tex]108^{\circ}[/tex]

The required Integers  are 13, 15, 17

What are the Integers?

Integers are the collection of whole numbers and negative numbers.

Given that twice the three consecutive odd Integers is nine more than the largest.

Let the numbers be x , x+2 , x+4

According to question

2x = 9+x+4

x = 13

Hence the Integers are 13, 15, 17

For more references about Integers click:

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