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lara31 [8.8K]
3 years ago
6

A line passes through the points (0, -2) and (0, 5). Is it possible to write an equation of the line in slope-intercept form? ju

stify your answer
Mathematics
1 answer:
Feliz [49]3 years ago
7 0
Consider what the slope of this line would be. Slope is rise/run; this line rises 7 (5 - (-2)) and runs 0 (0 - 0). This means that the slope would be 7/0. Dividing by zero is not possible, therefore, it cannot be written in slope-intercept form. 
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Let y in the form of a + ib, where a and b are real numbers, be the cubic roots of a complex number z 20, where z =2 4+i3. Find
GalinKa [24]

The possible values of a + b are 0.89, 3.01 and -3.9

<h3>How to determine the value of a + b?</h3>

The given parameters are:

y = a + ib

z = 24 + i3

Where:

y = ∛z

Take the cube of both sides

y³ = z

Substitute the values for y and z

(a + ib)³ = 24 + i3

Expand

a³ + 3a²(ib) + 3a(ib)² + (ib)³ = 24 + i3

Further, expand

a³ + i3a²b + i²3ab² + i³b³ = 24 + i3

In complex numbers;

i² = -1 and i³= -i

So, we have:

a³ + i3a²b + (-1)3ab² -ib³ = 24 + i3

Further expand

a³ + i3a²b - 3ab² - ib³ = 24 + i3

By comparing both sides of the equation, we have:

a³ - 3ab² = 24

i3a²b - ib³ = i3

Divide through by i

3a²b - b³ = 3

So, we have:

a³ - 3ab² = 24

3a²b - b³ = 3

Using a graphing tool, we have:

(a,b) = (-1.55, 2.44), (2.89,0.12) and (-1.34,-2.56)

Add these values

a + b = 0.89, 3.01 and -3.9

Hence, the possible values of a + b are 0.89, 3.01 and -3.9

Read more about complex numbers at:

brainly.com/question/10662770

#SPJ1

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Step-by-step explanation:

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Find the tenth term of the expansion (x+ y)¹³
Anon25 [30]

Answer:

715x^4y^9

Step-by-step explanation:

Given

(x + y)^{13

Required

Determine the 10th term

Using binomial expansion, we have:

(a + b)^n = ^nC_0a^nb^0 + ^nC_1a^{n-1}b^1 + ^nC_2a^{n-2}b^2 +.....+^nC_na^{0}b^n

For, the 10th term. n = 9

So, we have:

(a + b)^n = ^nC_{9}a^{n-9}b^{9

(x + y)^{13} = ^{13}C_{9}x^{13-9}y^9

(x + y)^{13} = ^{13}C_{9}x^4y^9

Apply combination formula

(x + y)^{13} = \frac{13!}{(13-9)!9!}x^4y^9

(x + y)^{13} = \frac{13!}{4!9!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10*9!}{4!9!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10}{4!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10}{4*3*2*1}x^4y^9

(x + y)^{13} = \frac{17160}{24}x^4y^9

(x + y)^{13} = 715x^4y^9

Hence, the 10th term is 715x^4y^9

3 0
2 years ago
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