Color of car. a. Qualitative/Ordinal b. Qualitative/Nominal c. Quantitative/Discrete d. Quantitative/Continuous

28 = (45 + KL)/2

56 = 45+ KL

KL = 56-45

KL = 11

the volume of the hole would be  3 * 6 * 4 =72 cubic feet.

 However, since it is a hole, there would be no dirt in it.

Consider the equation [tex] x^6+6x^3+5=0 [/tex].

First, you can use the substitution [tex] t=x^3 [/tex], then [tex] x^6=(x^3)^2=t^2 [/tex] and equation becomes [tex] t^2+6t+5=0 [/tex]. This equation is quadratic, so

[tex] D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1 [/tex].

Then you can factor this equation:

[tex] (t+5)(t+1)=0 [/tex].

Use the made substitution again:

[tex] (x^3+5)(x^3+1)=0 [/tex].

You have in each brackets the expression like [tex] a^3+b^3 [/tex] that is equal to [tex] (a+b)(a^2-ab+b^2) [/tex]. Thus,

[tex] x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1) [/tex]

and the equation is

[tex] (x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0 [/tex].

Here [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex] and you can sheck whether quadratic trinomials have real roots:

1. [tex] D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25} <0 [/tex].

2. [tex] D_2=(-1)^2-4\cdot 1=1-4=-3<0 [/tex].

This means that quadratic trinomials don't have real roots.

Answer: [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex]

If you need complex roots, then

[tex] x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2} [/tex].

The function F(x) = (6x-2)/5 is an example of a rational function.

The function F(x) = (6x-2)/5 is an example of a rational function. A rational function is a function that can be expressed as the quotient of two polynomial functions, where the denominator is not equal to zero.

In this case, the function F(x) has a numerator of 6x-2 and a denominator of 5. Both the numerator and denominator are polynomial functions since they involve multiplication, addition, and subtraction of terms with x.

Therefore, the function F(x) = (6x-2)/5 is indeed a rational function, so the correct answer is True.

The function F(x) = (6x-2)/5 is an example of a rational function because it can be expressed as a ratio of two polynomials.

Function F(x) = (6x-2)/5 is an example of a rational function because it is a ratio of two polynomials. The numerator, 6x-2, is a linear polynomial, and the denominator, 5, is a constant polynomial.

To determine if a function is rational, we check if the function can be expressed as a quotient of two polynomials. In this case, F(x) is a ratio of a linear polynomial, 6x-2, and a constant polynomial, 5.

Therefore, the statement is True.

Answer: [tex]121.73\text{ feet per second}[/tex]

Step-by-step explanation:

Given : The speed of a  baseball pitcher  = 83 mph

or  83 miles per hour

Since , we know that

1 mile= 5280 feet

1 hour = 3600 seconds

Then,  83 miles per hour = [tex]\dfrac{\text{83 mile}}{\text{1 second}}=\dfrac{83\times5280\text{ feet}}{1\times3600\text{ seconds}}[/tex]

[tex]\approx121.73\text{ feet per second}[/tex]

Hence, the speed of the ball in feet per second = [tex]121.73\text{ feet per second}[/tex]

12 sixteen notes have a nice day

-2/x+1

the / is a fraction symbol xxx

Answer:

Step-by-step explanation:

Given is a piecewise graph.

From the graph we find that the domain is [-3,1]

From [-3,-1) the line is slant passing through (-3,0)(-2,1)

Slope  =change in y/change in x = 1

Equation is y = x+3

Thus the function is x+3 for -3≤x<-1

and                          5, -1≤x≤1

B is correct :

5 1/4 = 21/4

2 2/7=16/7

21/4x7/16=147/64=2 19/64

The quadratic equation that can be used to determine the thickness of the border, x is 4x² + 216x - 684 = 0

Which quadratic equation can be used to determine the thickness of the border, x?

From the question, we have the following parameters that can be used in our computation:

Length = 72

Width = 36

Border = x

Area = 3276

The area can be represented as

Area = (Width + 2x) * (Length + 2x)

Substitute the known values into the equation

(36  + 2x) * (72 + 2x) = 3276

Expand

4x² + 216x + 2592 = 3276

So, we have

4x² + 216x + 2592 - 3276 = 0

4x² + 216x - 684 = 0

Hence the quadratic equation is 4x² + 216x - 684 = 0

By setting up a proportion based on the similar triangles formed by Peter's line of sight and the analogous line from the top of the house to the mirror, we find that the house is 25 feet tall.

According to the Law of Reflection and the information provided, we have two similar triangles: one formed by Peter's eyes, the mirror, and the point on the ground directly below his eyes, and the other formed by the top of the house, the mirror, and the point on the ground directly below the top of the house.

The first triangle has a height of 5 feet (Peter's eye level) and a base of 6 feet (the distance from Peter to the mirror). The second triangle's height is what we are trying to find (height of the house), and its base is 30 feet (distance from the house to the mirror).

Because the triangles are similar, the ratios of their corresponding sides are equal. So, we can set up the following proportion:

Height of Peter's eyes / Distance to mirror = Height of the house / Distance to mirror from house

5 feet / 6 feet = Height of the house / 30 feet

Now, cross-multiply to solve for the height of the house:

5 feet * 30 feet = Height of the house * 6 feet

Height of the house = (5 * 30) / 6

Height of the house = 150 / 6

Height of the house = 25 feet

Therefore, the height of the house is 25 feet.

Answer:

First,you need to convert 307km/hr into 85.2 meter per second.The formula for finding time is the distance divided by the speed.So,the answer is 10809 second,about 3 hours.

When the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.

It is given that when Newton was 14 years old , his fathers age was 41 yrs.

We have to find out that at what age of Newton his fathers age will be reversed again ?

Solve for the value of x ;  10 x - 14 = 12x - 28 ?

The value of x will be 7.

Let's assume the tens place as x and one's place as y.

The actual number will be ; 10 x + y.

Reverse numbers pairs can be written as (10x+y) and (10y+x).

As the age of Newton's father is 41 yrs when he is 14 yrs old , so we have ;

(10x+y) - (10y+x) = 41–14 = 27

Hence , we can say that the age difference between Newton and his father is 27 years. This age difference will be same forever.

So ;

(10x+y) - (10y+x) = 27

and we have to find all values of x and y that will satisfy this equation.

⇒ (10x+y) - (10y+x) = 27

⇒ 9x - 9y = 27

⇒ x - y = 3

For all x’s and y’s who have their difference as 3 will answer the question. For example , (4,1) (5,2) (6,3) (7,4) (8,5) …. and so on.

Since Newton's father age today is 41 yrs.

The next age to satisfy the condition is 52 yrs.

This makes Newton’s age to be 52 - 27 = 25 which is the reverse of 52.

So , the answer of the question is that Newton should be of 25yrs , for his age to be the reverse of his father’s age.

Thus , when the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.

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Answer:

B

Step-by-step explanation:

no

Answer:

0.33 and 6.07

Step-by-step explanation: