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3 years ago

7

Simplify negative 5 minus the square root of negative 44 negative 5 minus 4 times the square root of 11 i negative 5 minus 4 i t

imes the square root of 11 negative 5 minus 2 i times the square root of 11 negative 5 minus 2 times the square root of 11 i

1 answer:

Anika [276]3 years ago

6 0

Answer:

$-5-\sqrt{-44}=-5-2\sqrt{11}i$

Step-by-step explanation:

We want to simplify:

$-5-\sqrt{-44}$

We rewrite the expression under the radical sign to obtain:

$-5-\sqrt{4\times11\times -1}$

We split the expression under the radical sign to get:

$-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}$

Recall that:

$\sqrt{-1}=i$

This implies that:

$-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}=-5-2\sqrt{11}i$

Therefore $-5-\sqrt{-44}=-5-2\sqrt{11}i$

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Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.

dedylja [7]

g(x) is basically transformed f(x). First, let's focus on f(x) graph. Notice how the graph has slope of 1 and intersect y-axis at (0,0).

Which means that our equation for f(x) is:

$\large{f(x) = x}$

Now then we focus on g(x). g(x) is f(x+k). That means if f(x) = x then f(x+k) would mean substitute x = x+k in the equation.

$\large{f(x + k) = x + k }\\ \large{g(x) = x + k}$

Next, we want to find the value of k. In the slope-intercept form or y = mx+b where m = slope and b = y-intercept. Notice the g(x) graph and see that the graph intersects y-axis at (0,4). Therefore k = y-intercept = 4.

$\large{g(x) = x + 4}$

Answer

g(x) = x+4
Therefore the value of k is 4.

3 0

3 years ago

A+2/a-5÷a+1/a2-8a+15

krok68 [10]

For $A+\frac{2}{a}-\frac{5}{a}+\frac{1}{a^2}-8a+15$

Combine the fractions $\frac{2}{a} - \frac{5}{a} \ \textgreater \ \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{2-5}{a}$

$\mathrm{Subtract\:the\:numbers:}\:2-5=-3 \ \textgreater \ \frac{-3}{a}$

$\mathrm{Apply\:the\:fraction\:rule}:\ \frac{-a}{b}=-\frac{a}{b} \ \textgreater \ -\frac{3}{a}$

Therefore our final answer is $A-\frac{3}{a}+\frac{1}{a^2}-8a+15$

Hope this helps!

3 0

2 years ago

Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to neg

Mars2501 [29]

The function is $f(x)= x^{5} -9x ^{3}$

1. let's factorize the expression $x^{5} -9x ^{3}$ :

$f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)$

the zeros of f(x) are the values of x which make f(x) = 0.

from the factorized form of the function, we see that the roots are:

-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3

(the multiplicity of the roots is the power of each factor of f(x) )

2.
The end behavior of f(x), whose term of largest degree is $x^{5}$ , is the same as the end behavior of $x^{3}$ , which has a well known graph. Check the picture attached.

(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of $x^{2}$ )

so, like the graph of $x^{3}$ , the graph of $f(x)= x^{5} -9x ^{3}$ :

"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "

7 0

3 years ago

Read 2 more answers

A swimming pool is in the shape of a rectangular prism. the pool is 4 feet deep. its length is 4 times its width. the volume of

makvit [3.9K]

First you will have to use the equation length*width*height. The just plug in 4 for the height, then since the length is 4 times longer plug in 4x, and the width would just be x. SO your equation would be 4*4x*x=6400 ft^3. Then foil it out to get 16x^2=6400, then square root 6400 which will give you80, then divide by 16 so x=5 feet^3. That is your width but you length is 4 times that amount. So for length just do 4(5)=20 feet^3

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2 years ago

Carolyn paid a mechanic x dollars per hour for a 5-hour job plus $70 for parts. The total charge was less than $320. Which equat

snow_lady [41]

Answer: should be 70+50x is less than 320

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2 years ago