Answer:
Step-by-step explanation:
#22
<h3>Given </h3>
- Equation x² -4x + 1 = k(x - 4) with equal roots
<h3>To find</h3>
<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
Answer:

Step-by-step explanation:
Given:


Need:

First, let's look at the identities:
sum: 
difference: 
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) = 
cos(A) = 
sin(B) = 
cos(B) = 
Plug these values into the difference identity formula.


Multiply.

Add.

This is your answer.
Hope this helps!
Answer:

Step-by-step explanation:
Combine the opposite terms in r − 3 − r
.
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
Read more about number line at
brainly.com/question/24644930
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Y = -4x
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