The area of the small triangle is 10.5 meters squared and the area of the larger triangle is 94.5 meters squared. If the altitude of the large triangle is 9, what is the altitude of the smaller triangle?

12 sixteen notes have a nice day

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.

Answer:

10.90

Step-by-step explanation:

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.

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

Answer:

14x+23y=65

Step-by-step explanation:

let cds=x and dvds=y

14x+23y=65

Answer:

1

Step-by-step explanation:

There are a total of 16+25 = 41 students that own hamsters.

There are a total of 16+24 = 40 students that own dogs.

This is a difference of 41-40 = 1.

Answer: 1

Step-by-step explanation:

Total number of students that own hamsters 16+25 = 41.

Total of students that own dogs 16+24 = 40.

To get how many more students own hamsters than dogs, we find the difference;

That is 41-40 = 1.

Good luck

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]

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].

Answer:

Even

Step-by-step explanation:

A function is said to be even function if we put -x instead of x and we get the same result of both function. i.e. f(-x) = f(x)

A function is said to be odd function if we put -x instead of x and we get the result as negative of that function. i.e. f(-x) = -f(x)

Now we have function, f(x) = [tex]f(x) = \frac{2}{x^{2}}[/tex]

Now putting -x in place of x

[tex]f(-x) = \frac{2}{(-x)^{2}}\\ = \frac{2}{x^{2}} = f(x)[/tex]

Hence, given function is an Even function.

-2/x+1

the / is a fraction symbol xxx

Answer:

0.33 and 6.07

Step-by-step explanation:

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

28 = (45 + KL)/2

56 = 45+ KL

KL = 56-45

KL = 11

B is correct :

5 1/4 = 21/4

2 2/7=16/7

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