5. given no other restrictions, what are the domain and range of the following funtction? f(x)=x^2-2x+2 if your in connexus and have done the algebra 2 final could you give me the awnsers

Final answer:

Zia's age is 12 and Raj's age is 15

Explanation:

To solve this problem, we can set up two equations using the given information. Let's assume Zia's age is x. Since Raj is 3 years older than Zia, Raj's age can be represented as x + 3.

The first equation is [tex]x^2 + (x + 3)^2 = 369.[/tex]

Simplifying this equation, we get [tex]x^2 + x^2 + 6x + 9 = 369.[/tex]

Combining like terms, we have [tex]2x^2 + 6x + 9 = 369.[/tex]

Next, we can rearrange the equation by subtracting 369 from both sides and combining like terms to get [tex]2x^2 + 6x - 360 = 0.[/tex]

Now, we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula. The solutions are x = -15 and x = 12.

Since age cannot be negative, Zia's age is 12 and Raj's age is 12 + 3 = 15.

To factor the quadratic expression x² -3x -40, we find that the expression factors into (x - 8)(x + 5).

The question involves factoring the quadratic expression x² -3x -40 completely. To factor this expression, we look for two numbers that multiply to -40 and add to -3. The numbers that meet these conditions are -8 and 5, since

(-8) * 5 = -40 and

(-8) + 5 = -3.

Therefore, the expression can be factored into (x - 8)(x + 5).

Solution:

we have been asked to find the average of the first n positive even numbers.

Let the firm n positive even numbers be

[tex] 2,4,6,8,10,12,.........2(n-1), 2n [/tex]

As we know that average of numbers[tex] =\frac{\text{Sum of Numbers }}{Total number of Numbers}\\ [/tex]

Required Average[tex] =\frac{2+4+6+2(n-1)+2n}{n}\\ [/tex]

Required Average[tex] =\frac{2(1+2+3+....+(n-1)+n)}{n} [/tex]

As we know the sum of first n terms[tex] =\frac{n(n+1)}{2} [/tex]

Required Average[tex] =\frac{2n(n+1)}{2n}=n+1 \\ [/tex]

Answer:

The correct option is B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]

Step-by-step  explanation:

Consider the two linear equation:

[tex]a_1x+b_1y+c_1=0\ \text{and}\ \ a_2x+b_2y+c_2=0[/tex]

The pair of linear equation has infinitely many solutions when:

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

Now consider the option.

Option a) [tex]y=-3x+4 \ \text{and}\ \ y=-3x-4[/tex]

The above equation can be written as:

[tex]y+3x-4=0 \ \text{and}\ \ y+3x+4=0[/tex]

Therefore,

[tex]\frac{1}{1}=\frac{3}{3}\neq\frac{-4}{4}[/tex]

Thus, this pair has no solution.

Now consider the option B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]

The above equation can be written as:

[tex]y+3x-4=0 \ \text{and}\ \ 3y+9x-12=0[/tex]

Therefore,

[tex]\frac{1}{3}=\frac{3}{9}=\frac{-4}{-12}[/tex]

Thus, this pair has infinitely many solution.

Hence, the correct option is B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]

A quadratic function seems to be a second-order polynomial function. Another quadratic function has the following general form:

here,

and,

The quadratic formula is obtained by completing the square on some kind of quadratic equation instead in the standard format. Because the largest power equals two, it is indeed a 2nd-degree polynomial equation.

As a result, the aforementioned response is correct.

Learn more about quadratic equation here:

https://brainly.com/question/19942005

The formula for the area of the rectangle is actually A = LW. The length of the rectangular wall is 414 yards while its width is 223 yards. To compute for its area, you just have to follow the formula:

A = 414 (223)

A = 92,322 yards^2

Therefore, the area of the wall is 92,322 square yards.

Answer:

hey the answer is 11 1/3

Step-by-step explanation:

ive taken the quiz and this is the answer 100%

To find the distance the ball traveled after it bounces off the wall, we can use the proportion 34/x = 20/16, which simplifies to x = 27.2 inches.

To find the proportion that can be used to find the distance, x, the ball traveled after it bounces off the wall, we can use the equation:

34/x = 20/16

After cross multiplying, we get:

34 × 16 = 20x

Simplifying further:

544 = 20x

Dividing both sides by 20, we find:

x = 27.2

Therefore, the distance the ball traveled after it bounces off the wall is 27.2 inches.

Answer:4

Step-by-step explanation:just did it on edge

To solve log6(x) + log6(x + 5) = 2, combine the logarithms, rewrite in exponential form, and solve the resulting quadratic equation. The solutions are x = -9 and x = 4, but since logarithms of negative numbers are undefined, the final answer is x = 4.

To solve this logarithmic equation, follow these steps:

Final Answer: x = 4.

Answer:

[tex]y=-1[/tex]

Step-by-step explanation:

We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.    

First of all, we will divide both sides of our given equation by 4.

[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]      

[tex]\frac{x^2}{4}=y[/tex]      

[tex]y=\frac{x^2}{4}[/tex]      

Now, we will compare our equation with vertex form of parabola:

[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.

We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].

Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].

Substituting the value of a in above formula, we will get:

[tex]p=\frac{1}{4*\frac{1}{4}}[/tex]

[tex]p=\frac{1}{1}=1[/tex]

We know that directrix of parabola is [tex]y=k-p[/tex].

Substituting the value of k and p in above formula, we will get:

[tex]y=0-1[/tex]

[tex]y=-1[/tex]

Therefore, the directrix of our given parabola is [tex]y=-1[/tex].

"The correct answer is B. 79.

To solve the given problem, we need to calculate 15 4/5 percent of 50. First, let's convert the mixed number to an improper fraction to make the calculation easier.

 15 4/5% as a fraction is 15 + 4/5, which can be written as 75/5 + 4/5 = 79/5.

Now, to find the percentage of 50, we multiply 50 by the fraction representing the percentage:

[tex]\[ \frac{79}{5} \times 50 = \frac{79 \times 50}{5} \][/tex]

Next, we simplify the multiplication:

[tex]\[ \frac{79 \times 50}{5} = \frac{3950}{5} \][/tex]

Now, we divide 3950 by 5:

[tex]\[ \frac{3950}{5} = 790 \][/tex]

However, since we are looking for 15 4/5 percent and not 15 4/5 times 50, we need to adjust our calculation by dividing by 100 to get the correct percentage:

[tex]\[ \frac{790}{100} = 79 \][/tex]

Therefore, the final answer is B. 79."

To graph the inequality 2x - 5y ≤ 6, plot the line 2x - 5y = 6 with a solid boundary, test a point to determine the solution region, and shade the region that satisfies the inequality, which is below and to the right of the boundary line.

To graph the inequality 2x - 5y ≤ 6, you must first draw the boundary line of the inequality. This line is created by graphing the equation 2x - 5y = 6.

Start by finding the intercepts. For the x-intercept, set y to 0 and solve for x, which gives x = 3. For the y-intercept, set x to 0 and solve for y, which gives y = -6/5. These two points can be used to draw the boundary line. Since the inequality is '≤', this line will be solid to show that points on the line satisfy the inequality.

Now you must determine which side of the line contains the solutions to the inequality. You can do this by choosing a test point that is not on the line, like (0,0). Substitute this point into the inequality: 2(0) - 5(0) ≤ 6 is true, so the area containing (0,0), which is below and to the right of the line, is the solution region. Shade this area to show all points that satisfy the inequality 2x - 5y ≤ 6.

Solution:

we are given that

In a class, every student knows French or German (or both).

15 students know French, and 17 students know German.

Suppose there are x student who knows both French and German.

Then Total number of student in the class will be [tex] (15+17-x)=32-x [/tex]

But to guess the largest possible number of student in the class we can assume x=0

Hence the largest Possible number of Student in the class=32