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2 years ago

Which of the following is equivalent to the expression

Mathematics

1 answer:

alisha [4.7K]2 years ago

6 0

Answer:

i Choice A

Step-by-step explanation:

i ^ 41

we use the rule of 4 for powers of i

if you get remainder of 0 = 1

if you get remainder of 1 = i

if you get remainder of 2= -1

if you get remainder of 1 = -i

41/4 = 10 remainder 1

so i^41 = i

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I need help with these questions ( see image for question ).<br>Please show working.<br>

antiseptic1488 [7]

Answer:

k = -4 ± 2√5

Step-by-step explanation:

#22

<h3>Given </h3>

Equation x² -4x + 1 = k(x - 4) with equal roots

The value of k

<h3>Solution</h3>

<u>The equation in standard form is:</u>

x² -4x + 1 = k(x - 4)
x² - 4x - kx + 1 + 4 = 0
x² - (k + 4)x + 5 = 0

<u>When the quadratic equation has equal roots its discriminant is zero</u>

D = 0
b² - 4ac = 0
(k + 4)² - 4*5 = 0
(k + 4)² = 20
k + 4 = ± √20
k = - 4 ± √20
or
k = -4 ± 2√5

5 0

2 years ago

Please solve the following sum or difference identity.

xxTIMURxx [149]

Answer:

$sin(A - B) = \frac{4}{5}$

Step-by-step explanation:

Given:

$sin(A) = \frac{24}{25}$

$sin(B) = -\frac{4}{5}$

Need:

$sin(A - B)$

First, let's look at the identities:

sum: $sin(A + B) = sinAcosB + cosAsinB$

difference: $sin(A - B) = sinAcosB - cosAsinB$

The question asks to find sin(A - B); therefore, we need to use the difference identity.

Based on the given information (value and quadrant), we can draw reference triangles to find the simplified values of A and B.

sin(A) = $\frac{24}{25}$

cos(A) = $\frac{7}{25}$

sin(B) = $-\frac{4}{5}$

cos(B) = $\frac{3}{5}$

Plug these values into the difference identity formula.

$sin(A - B) = sinAcosB - cosAsinB$

$sin(A - B) = (\frac{24}{25})(\frac{3}{5}) - (-\frac{4}{5})(\frac{7}{25})$

Multiply.

$sin(A - B) = (\frac{72}{125}) + (\frac{28}{125})$

Add.

$sin(A - B) = \frac{4}{5}$

This is your answer.

Hope this helps!

6 0

2 years ago

Read 2 more answers

Simplify the expression: <br> r -3 -r

Ymorist [56]

Answer:

$-3$

Step-by-step explanation:

Combine the opposite terms in r − 3 − r .

8 0

2 years ago

Which inequality describes this graph?

ZanzabumX [31]

The inequality that describes this graph of the number line is x ≥ 4

<h3>How to determine the inequality that describes this graph?</h3>

From the question, we have the following properties:

The graph is a number line
The number line extends at both ends
The number line starts from less than -5 and ends at greater than 5
There is a heavy arrow that extends from a circle over positive 4 to the right.

The property 3 above implies that the domain of the number line is the set of all real numbers.

The property 4 above implies that the inequality of the number line is a greater than or equal to inequality, and the value starts from 4

This is represented by the following inequality

x ≥ 4

Hence, the inequality that describes this graph of the number line is x ≥ 4