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3 years ago

What is the value of p?

Mathematics

1 answer:

AleksandrR [38]3 years ago

4 0

Answer:

A. 133

Step-by-step explanation:

Angle P is equal to the angle that is 133 because of the propertys of angles.

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Find all the zeros of <br><img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7B6x%7D%5E%7B4%7D%20%20%20-%20%20%7B7x%7D%5E%7B

Svetradugi [14.3K]

Answer:

{-1, 1/2, 2/3, 1}

Step-by-step explanation:

I find a graphing calculator to be a most useful tool for problems like this. (See attached.)

_____

First of all, observe that the constant is -2, so 0 is not a zero.

It is often useful to look at the sum of coefficients. Here, that is 0, indicating 1 is a zero.

You can divide that out, or simply continue by looking at the sum of coefficients with odd-degree terms negated. Then you have 6 +7 -4 -7 -2 = 0, indicating -1 is also a zero.

At this point, it can be useful to divide out the factors you know. The synthetic division tableaus attached show that work. First is division by (x+1), then by (x -1).

The result of doing that is the quadratic ...

6x^2 -7x +2 = 0

This can be factored ...

(6x^2 -3x) -(4x -2) = 0 . . . . . . rewrite -7x and group term pairs

3x(2x -1) -2(2x -1) = 0 . . . . . . . factor each pair

(3x -2)(2x -1) = 0 . . . . . . the factorization of the remaining quadratic

The zeros of this are the values of x that make the factors zero: 2/3 and 1/2.

The zeros of the given function f(x) are x ∈ {-1, 1/2, 2/3, 1}.

5 0

3 years ago

The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope

NARA [144]

Answer:

a) (i) $m = 2.22$ , (ii) $m = 2$ , (iii) $m = 2$ , (iv) $m = 2$ , (v) $m = 1.82$ , (vi) $m = 2$ , (vii) $m = 2$ , (viii) $m = 2$ ; b) $m \approx 2$ ; c) The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

Step-by-step explanation:

a) The slope of the secant line PQ is represented by the following definition of slope:

$m = \frac{\Delta y}{\Delta x} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}$

(i) $x_{Q} = 6.9$ :

$y_{Q} =\frac{2}{6-6.9}$

$y_{Q} = -2.222$

$m = \frac{-2.222 + 2}{6.9-7}$

$m = 2.22$

(ii) $x_{Q} = 6.99$

$y_{Q} =\frac{2}{6-6.99}$

$y_{Q} = -2.020$

$m = \frac{-2.020 + 2}{6.99-7}$

$m = 2$

(iii) $x_{Q} = 6.999$

$y_{Q} =\frac{2}{6-6.999}$

$y_{Q} = -2.002$

$m = \frac{-2.002 + 2}{6.999-7}$

$m = 2$

(iv) $x_{Q} = 6.9999$

$y_{Q} =\frac{2}{6-6.9999}$

$y_{Q} = -2.0002$

$m = \frac{-2.0002 + 2}{6.9999-7}$

$m = 2$

(v) $x_{Q} = 7.1$

$y_{Q} =\frac{2}{6-7.1}$

$y_{Q} = -1.818$

$m = \frac{-1.818 + 2}{7.1-7}$

$m = 1.82$

(vi) $x_{Q} = 7.01$

$y_{Q} =\frac{2}{6-7.01}$

$y_{Q} = -1.980$

$m = \frac{-1.980 + 2}{7.01-7}$

$m = 2$

(vii) $x_{Q} = 7.001$

$y_{Q} =\frac{2}{6-7.001}$

$y_{Q} = -1.998$

$m = \frac{-1.998 + 2}{7.001-7}$

$m = 2$

(viii) $x_{Q} = 7.0001$

$y_{Q} =\frac{2}{6-7.0001}$

$y_{Q} = -1.9998$

$m = \frac{-1.9998 + 2}{7.0001-7}$

$m = 2$

b) The slope at P (7,-2) can be estimated by using the following average:

$m \approx \frac{f(6.9999)+f(7.0001)}{2}$

$m \approx \frac{2+2}{2}$

$m \approx 2$

The slope of the tangent line to the curve at P(7, -2) is 2.

c) The equation of the tangent line is a first-order polynomial with the following characteristics:

$y = m\cdot x + b$

Where:

$x$ - Independent variable.

$y$ - Depedent variable.

$m$ - Slope.

$b$ - x-Intercept.

The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:

$-2 = 2 \cdot 7 + b$

$b = -2 + 14$

$b = 12$

The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

7 0

3 years ago

A farmer has 120 feet of

Arturiano [62]

Answer:

you could fence each side with 40 feet if fence if the side with the barn does not need fencing

8 0

3 years ago

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Please help me for my finals!! I'll do anything

oee [108]

(A)

Choice (B) is not the right answer because I

it's only 3rd order. But because f(x) goes to negative infinity when x goes to positive infinity means that the right answer is (A).

6 0

3 years ago

Solve log525 = x 2 1/2 -2

elixir [45]

Answer:

x = 1/2

Step-by-step explanation:

The equation in correct format is:

$log_{5}(25)=x$

We have to solve this logarithmic equation to find the value of x. This can be done by using the rules of logarithm i.e the power rule and same base rule shown below:

$log(a)^{b}=b \times log(a)\\\\log_{a}(a)=1$

Using these rules on our equation, we get:

$log_{5}(25)=x\\\\log_{5}(5^{\frac{1}{2} })=x\\\\ \frac{1}{2} log_{5}(5)=x\\\\ \frac{1}{2} (1)=x\\\\ x=\frac{1}{2}$

Thus the value of x would be 1/2

6 0

3 years ago

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