Fill in the table for the function.

Answer:15620, 15491, 15096, 15076

Step-by-step explanation:

Answer:

2+2=4, not 6

Step-by-step explanation:

The graph of y = x2 –7x +12 is a parabola with x-intercepts at: {-3 and -4, or 3 and 4} and a vertex that is the: the x-intercepts are 3 and 4

The vertex is the lowest point on the curve

we know that

The equation of a vertical parabola in vertex form is equal to

y = a [tex](x-h)^{2}[/tex] + k

where

(h,k) is the vertex of the parabola

if a>0 -----> then the parabola opens upward (a vertex is a minimum)

if  a<0 -----> then the parabola opens downward (a vertex is a maximum)

In this problem we have

y = [tex]x^{2}[/tex] - 7x +12

a = 1

so

the parabola opens upward (a vertex is a minimum)

Find the x-intercepts of the quadratic equation

Equate the equation to zero

y = [tex]x^{2}[/tex] - 7x +12

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}[/tex] - 7x = -12

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]x^{2}[/tex] - 7x + 12.25 = -12 + 12.25

[tex]x^{2}[/tex] - 7x + 12.25 = 0.25

Rewrite as perfect squares

[tex](x-3.5)^{2}[/tex] = 0.25

square root on both sides

(x - 3.5) = (+/-) 0.5

x =3.5(+/-) 0.5

x = 3.5+0.5=4

x = 3.5-0.5=3

therefore

the x-intercepts are 3 and 4

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a variety of seemingly unrelated mathematical descriptions, all of which may be shown to define the same curves.

One definition of a parabola includes a line and some extent  (the focus) (the directrix). The directrix isn't the main focus. The locus of points therein plane that is equally spaced apart from the directrix and the focus is known as the parabola. A right circular conical surface and a plane parallel to a different plane that is tangential to the conical surface intersect to form a parabola, which is additionally known as a conic section.

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Answer:

-4

Step-by-step explanation:

We can use the slope formula: [tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]

this formula is really just representing: [tex]\frac{\Delta y}{\Delta x}\\[/tex] or in other words, change in y/change in x

The slope formula is calculating that difference by subtracting the y and x-values.

By just looking at the tables we can easily see that from x=6 to x=8 there is a change in 2

and from y=-16 to y=-24 there is a change in -8

So plugging this into the slope formula we get [tex]\frac{-8}{2}=-4[/tex]

Answer:

8

Step-by-step explanation:

hope i help

Answer:

8 is the gcf

welcome

a) The coordinates of P and Q are; P = (0 , 4) , Q = ( -3 , 0).

b) The graph of  points P and Q is plotted.

c) The line 3y - 4x = 12 for values of x from -3 to 3 is drawn.

The equation of line is given as;

3 y - 4 x = 12

a) To calculate the coordinates on the line are P and Q.

Let x = 0  

3 y - 4 × 0 = 12

3 y + 0 = 12

y = 4

So, points P = (0 , 4)

Now, For y = 0;  

3 × 0 - 4 × x  = 12

0 -  4 × x  = 12

x = - 3

So, points Q = ( -3 , 0)

Thus, points are P = (0 , 4) , Q = ( -3 , 0)

b) points P and Q on the graph.

The graph of the points P and Q for the coordinates of  P = (0 , 4) , Q = ( -3 , 0) is plotted.

c) Draw the line 3y - 4x = 12 for values of x from -3 to 3.

The straight line for the values of  x are drawn.

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The expression that represents “5 more than the difference of 15 and 7 is (15 - 7) + 5 and the value will be 13.

It should be noted that an expression is used to show the relationship that exists between the variables that are illustrated.

In this case, it should be noted that we wat to know the expression that represents “5 more than the difference of 15 and 7.

This will be:

= (15 - 7) + 5

= 13.

Therefore, the expression that represents “5 more than the difference of 15 and 7 is (15 - 7) + 5 and the value will be 13.

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The equation which can be used to solve for y, the length of the room according to the task content are;

According to the task content, the equations which can be used to solve for y, the length of the room according to the task content is to be determined.

Since the width of the room is 5 feet less than the length of the room.

Therefore, length = y and width = (y -5).

The area of the rectangle is therefore;

y (y -5) = 750

Therefore, the required equations are; 750 - y(y-5) = 0.

Or; y² - 5y = 750.

Or; (y + 25)(y – 30) = 0.

Therefore, the equation which can be used to solve for y, the length of the room according to the task content are;

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The slope intercept form is given as  y = 2x + 6

The general expression for slope intercept form is given as:

                   y = mx + c

where, m = slope

             c = intercept

The formula for slope intercept form when we have been given the coordinates of a point and slope is given as :

           [tex](y-y_{1}) = m(x-x_{1})[/tex]      (1)

where ([tex]x_{1} , y_{1})[/tex] = the coordinates of a point

               m = slope of the line

putting the required values in equation (1) we get

            (y - 4) = 2(x- (-1))

            (y - 4) = 2(x+1)   [As (-)*(-) = +]

             y - 4 = 2x + 2

              y = 2x + 2 + 4

              y = 2x + 6

Thus the slope intercept form is y = 2x + 6

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Answer: 1.66

For next time you can use calculator

Answer:

1.666

Step-by-step explanation:

5/6 × 2=5/3

=1.6666...

or you can use your calculator

Answer:

[tex]\frac{7}{1}[/tex]

Step-by-step explanation:

Answer:

7/1

Step-by-step explanation:

hope this helps♡

The number of units sold decreased and it decreased by

%decrese =4.23%

This is further explained below.

Generally, the equation for is  mathematically given as

Number of sold 450 units in 2011

431 units in 2012

No of Sold units decrease, so the Percentage decreased.

[tex]\% \text { decrease } &=\frac{450-431}{450} \times 100 \\\\&=\frac{19}{450} \times 100 \\[/tex]

=4.23%

In conclusion, the percentage decrease is

%decrese =4.23%

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CQ

A vacuum cleaner dealership sold 450 units in 2011 and 431 units in 2012. Find the percent increase or decrease in the number of units sold.

Did the number of units sold decrease or increase?

What percent did it it decrease or increase?

The lengths of the 3 parts of the board x,y,z would be 7 inch, 14 inch, and 35 inch.

If 3 pieces of 56 in. board have been cut into the ratio x: y: z,

The second piece y equals 2x and,

The third piece z equals 5x.

Now calculate the value of x:

x + y + z = 56

x + 2x + 5x = 5

8x = 56

x = 7 inches

Then, 2nd piece;

2x = 2(7)

2nd piece = 14 inches.

Now, the 3rd piece;

5x = 5(7)

3rd piece = 35 inches.

As a result, the lengths of the 3 parts x,y,z are 7 inches, 14 inches, and 35 inches, respectively.

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Using an exponential function, it is found that 48 new seniors will know the winner of the homecoming king election on the fourth day.

For this problem, we have that:

An exponential function is modeled as follows:

[tex]y = ab^x[/tex]

In which:

For this problem, the parameters are given as follows:

Hence the number of seniors that know the result on day x is given by:

[tex]y(x) = 3(2)^x[/tex]

On day 4, the amount is:

y = 3 x 2^4 = 3 x 16 = 48.

48 new seniors will know the winner of the homecoming king election on the fourth day.

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Answer:

-5, 1

Step-by-step explanation:
For every [tex]a[/tex] and [tex]x[/tex], the two numbers that are [tex]x[/tex] away from [tex]a[/tex] are [tex]a - x[/tex] and [tex]a + x[/tex].

Therefore, the two numbers that are 3 away from -2 are [tex]-2 - 3 = -5[/tex] and [tex]-2 + 3 = 1[/tex]

Answer: the answer is 1/16

The  statement be rewritten as a conditional statement in if-then form as If a rectangle has 4 congruent sides, then it is a square.

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true.

Given:

The conditional statement is  A rectangle with 4 congruent sides is a square.

According to given question we have

The conditional statement is given as A rectangle with 4 congruent sides is a square.

The counterexample must satisfy the hypothesis of the conditional statement.

So, '' If a rectangle has 4 congruent sides, then it is a square.''

Therefore, the  statement be rewritten as a conditional statement in if-then form as If a rectangle has 4 congruent sides, then it is a square.

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Answer: A

Step-by-step explanation:

i took it

Answer:

9^7  

Step-by-step explanation:

9 to the 7th power

The quotient of the division (4d² + 2d - 3) ÷ (d - 7) is 4d + 30 and remainder is 207.

Dividing one polynomial by the other is very similar to dividing one number by the other.

The steps for dividing polynomials using long method are as follows:

For the given question;

Dividend  = 4d² + 2d - 3

Divisor = d - 7

Divide dividend by divisor.

= ( 4d² + 2d - 3)/(d -3)

The quotient will come as 4d + 30.

Remainder = 207.

Thus,  4d² + 2d - 3 is not completed divisible by d - 3.

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Answer:

3

Step-by-step explanation:

Because C is 1 and D is 4, so 4-1=3.

5x5=25 , 25x5= 125.

5x5=25, 25x5= 125, 125x5=625, 625x5=3125, 3125x5=15625, 15625x5= 78125.

Answer:

5^10

Step-by-step explanation:

When multiplying exponents with the same base, we add the exponents

5^3  * 5^7

5^(3+7)

5^10

= 0.45

= 9/20

= (9 x 10)/(20 x 10)

= 90/200

= (1 x 100)/(2 x 100)

= 100/200

= 9/200

= 1.25

= 5/4

= 3/2

= 63/50

It should be noted that the the characteristics of perfect square trinomial include:

A perfect square trinomial is a special polynomial consisting of three terms.

A perfect square trinomial is created by multiplying a binomial to itself.

Two of the terms in a perfect trinomial are perfect squares.

They can be used to solve quadratics by completing the square

It should be noted that a perfect square trinomial is an algebraic expression that is of the form ax² + bx + c, that has three terms.

It should be noted that it is obtained by the multiplication of a binomial with itself.

For example, it should be noted that x² + 6x + 9 is a perfect square polynomial that is obtained by multiplying the binomial (x + 3) by itself.

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What are the characteristics of perfect square trinomial

The cost of ordering 26 shirts will be 430.8 dollars.

As the name suggest piecewise a piecewise function behaves differently for different domains or we can say that a function which has different parts.

According to the question given we have to write piecewise functions for ordering custom shirts.

Here y is the cost in dollars and x is the no. of shirts and also given that a 20 dollar processing fee is need for all orders and it is our constant in the function.

For 0 to 24 shirts or when 0<x≤24 and x ∈ N.

f(x) = 17x + 20.

∴Domain of the function is (0,24] and range of the given function is [37,428]

For 25 to 49 shirts or when  25≤x≤29 and x ∈ N.

f(x) = 15.80x + 20.

∴ Domain of this function is [25,49] and range of the function is [415,794.2].

For 50+ shirts or when x≥50 and x ∈ N.

f(x) = 14x + 20.

∴ Domain of this function is [50,∞) and range of this function is [720,∞].      

Now we have to determine the total cost of ordering 26 shirts for this we'll use f(x) = 15.80x + 20 because 26 lies in the domain of this function.

∴ f(x) = 15.80x + 20 for x = 26 it will be

f(26) = 430.8 dollars.

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Answer:

C. 8x^2-5x+2=0

Step-by-step explanation:

The answer is Option C because it can only be solved by quadratic formula