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34kurt
3 years ago
7

2

alt=" 3^(x+7) = 9^(x-1)" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
DaniilM [7]3 years ago
4 0
3(x + 7) = 9(x - 1)
3(x) + 3(7) = 9(x) - 9(1)
  3x + 21 = 9x - 9
<u>- 3x          - 3x     </u>
          21 = 3x - 9
        <u>+ 9         + 9</u>
         <u>30</u> = <u>3x</u>
          3      3
         10 = x
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Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
Tamiku [17]
Our quadratic polynomial function is:

f(x) = 4x^2 + 2x + 5

our linear binomial form is:
x - a = -2
hence:
a = x + 2

and so we have:
f(x) = 4x^2 + 2x + 5
f(a) = 4(x + 2)^2 + 2<span>(x + 2)</span> + 5
= 4(x^2 + 4x + 4) + 2x + 4 + 5
f(a) = 4x^2 + 18x + 25

3 0
3 years ago
The y coordinate of the vertex of f (x)=-x^2+8x+7 is f(4)
azamat

Hello there.

To answer this question, we need to remember some properties about the vertex of quadratic functions.

Let f(x)=ax^2+bx+c,~a\neq0. Its vertex can be found on the coordinates (x_v,~y_v) such that x_v=-\dfrac{b}{2a} and y_v=-\dfrac{b^2}{4a}+c, in which y_v=f(x_v).

Using the coefficients given by the question, we get that:

x_v=-\dfrac{8}{2\cdot(-1)}\\\\\\ x_v=-\dfrac{8}{-2}\\\\\\ x_v=4

Thus, we have:

y=f(x_v)=f(4)

So the statement is true, because the x coordinate of the vertex of the function is equal to 4.~~\checkmark

7 0
3 years ago
When can a parallelogram also be a kite?
Fofino [41]

9514 1404 393

Answer:

  when it is a rhombus

Step-by-step explanation:

A kite is a figure in which the diagonals are perpendicular, and one of them is bisected by the other. It will be a parallelogram if both diagonals bisect each other. Such a figure (with mutually perpendicular bisectors as diagonals) is a rhombus.

A parallelogram that is a rhombus will also be a kite.

5 0
3 years ago
How can you find the magnitude of a vector v→=
dalvyx [7]

Answer:

The magnitude of a vector is its <u>length</u>.

To calculate the magnitude of a vector in any number of dimensions, square root the sum of the squares of each dimension.

Therefore, if  \vec v=(x,y)  then its magnitude is:

|v|=\sqrt{x^2+y^2}

Similarly, if  \vec v=(x,y,z)  then its magnitude is:

|v|=\sqrt{x^2+y^2+z^2}

4 0
2 years ago
A television station shows 3 commercials every 12 minutes. At this rate, how many commercials will the station show in 84 minute
Vlad1618 [11]

Answer:

21

Step-by-step explanation:

84/12=7x3=21

4 0
3 years ago
Read 2 more answers
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