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3 years ago

1. Name a pair of angles for each of the following. (Lesson 1)

Mathematics

1 answer:

gtnhenbr [62]3 years ago

7 0

Answer:

I can't see the angle.

Step-by-step explanation:

I can't see the angle.

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Which answer best describes the complex zeros of the polynomial function?

marysya [2.9K]

Answer-

D. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location.

Solution-

The given polynomial is,

$f(x)=x^3-x^2+6x-6$

The zeros of the polynomials are,

$\Rightarrow f(x)=0$

$\Rightarrow x^3-x^2+6x-6=0$

$\Rightarrow x^2(x-1)+6(x-1)=0$

$\Rightarrow (x^2+6)(x-1)=0$

$\Rightarrow (x^2+6)=0,(x-1)=0$

$\Rightarrow x=\sqrt{-6},\ x=1$

$\Rightarrow x=1,\ \pm \sqrt6i$

Therefore, this function has only one real zero i.e 1 and two nonreal zeros i.e ±√6i . The graph of the function intersects the x-axis at exactly one location i.e at x = 1

3 0

3 years ago

Please help me im crying over this question

denis23 [38]

Answer:

y = 2x - 2

Step-by-step explanation:

y= mx+b

m= slope

b= y-intercept (point on line where x= 0.... or the point where the line hits the y-axis)

Determine slope by using slope formula or by counting boxes

By counting boxes, you can see that each point is 2 units up, 1 unit right (2/1)

the slope is 2

the point where the line is touching the y-axis is (0, -2)

m = slope = 2

b = y-intercept = -2

y = 2x + (-2) OR y = 2x -2

5 0

3 years ago

How many times does the graph of the function below interect or touch the x-axis? y=-2x^2+3x+5

Andrei [34K]

Answer:

Two times at (-1,0) and (2.5,0)

Step-by-step explanation:

When the graph intersects or touches x-axis, y is equal to 0

so y = -2x^2 + 3x + 5

=> 0 = -2x^2 + 3x + 5

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

so a = -2

b = 3

c = 5

substitute in the formula

x = [-3 +/- √(3^2 - 4x-2x5)]/2(-2)

x = [-3 +/- √(9 + 40)]/(-4)

x = [-3 +/- 7]/(-4)

x1 = (-3 + 7)/(-4) = 4/-4 = -1

x2 = (-3 - 7)/(-4) = -10/-4 = 5/2 = 2.5

so the graph has two x-intercepts (-1,0) and (2.5,0), therefore it intersects x-axis two times

7 0

3 years ago

( -3/4 + 4/3) + i =0 Show your work. (Please help)

Effectus [21]

Answer:

i = -7/12

Step-by-step explanation:

(-3/4 + 4/3) + i = 0

(-9/12 + 16/12) + i = 0

7/12 + i = 0

i = -7/12

6 0

3 years ago

Read 2 more answers

I tell you these facts about a mystery number, $c$: $\bullet$ $1.5 < c < 2$ $\bullet$ $c$ can be written as a fraction wit

makkiz [27]

Answer:

Possible answer: $\displaystyle c = \frac{16}{10} = \frac{8}{5} = 1.6$ .

Step-by-step explanation:

Rewrite the bounds of $c$ as fractions:

The simplest fraction for $1.5$ is $\displaystyle \frac{3}{2}$ . Write the upper bound $2$ as a fraction with the same denominator:

$\displaystyle 2 = 2 \times 1 = 2 \times \frac{2}{2} = \frac{4}{2}$ .

Hence the range for $c$ would be:

$\displaystyle \frac{3}{2} < c < \frac{4}{2}$ .

If the denominator of $c$ is also $2$ , then the range for its numerator (call it $p$ ) would be $3 < p < 4$ . Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than $2$ .

To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)

$\displaystyle \frac{3}{2} = \frac{2 \times 3}{2 \times 2} = \frac{6}{4}$ .

$\displaystyle \frac{4}{2} = \frac{2\times 4}{2 \times 2} = \frac{8}{4}$ .

At this point, the difference between the numerators is now $2$ . That allows a number ( $7$ in this case) to fit between the bounds. However, $\displaystyle \frac{1}{c} = \frac{4}{7}$ can't be written as finite decimals.

Try multiplying the numerator and the denominator by a different number.

$\displaystyle \frac{3}{2} = \frac{3 \times 3}{3 \times 2} = \frac{9}{6}$ .

$\displaystyle \frac{4}{2} = \frac{3\times 4}{3 \times 2} = \frac{12}{6}$ .

$\displaystyle \frac{3}{2} = \frac{4 \times 3}{4 \times 2} = \frac{12}{8}$ .

$\displaystyle \frac{4}{2} = \frac{4\times 4}{4 \times 2} = \frac{16}{8}$ .

$\displaystyle \frac{3}{2} = \frac{5 \times 3}{5 \times 2} = \frac{15}{10}$ .

$\displaystyle \frac{4}{2} = \frac{5\times 4}{5 \times 2} = \frac{20}{10}$ .

It is important to note that some expressions for $c$ can be simplified. For example, $\displaystyle \frac{16}{10} = \frac{2 \times 8}{2 \times 5} = \frac{8}{5}$ because of the common factor $2$ .

Apparently $\displaystyle c = \frac{16}{10} = \frac{8}{5}$ works. $c = 1.6$ while $\displaystyle \frac{1}{c} = \frac{5}{8} = 0.625$ .

8 0

3 years ago

Read 2 more answers