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3 years ago

Teacher: Find the Slope and Y-interce 1) x + 4y = 32 slope = y-intercept =

Mathematics

2 answers:

OverLord2011 [107]3 years ago

8 0

Answer:

Slope = -1/4

y-intercept = 8

Step-by-step explanation:

Given a line equation, x + 4y = 32

To get the slope and y-intercept from this equation, we shall represent it in the slope form of a line equation

The slope form of a line equation is given as

y = mx + c

Where;

m = slope

c = y-intercept

Step 1

x + 4y = 32

Subtract x from both sides of the equation

x + 4y - x = -x + 32

4y = -x + 32

Step 2

Divide both sides by 4 to make y subject

4y/4 = -x/4 + 32/4

y = -x/4 + 8

y = (-1/4)x + 8

This equation corresponds to

y = mx + c

m = -1/4

c = 8

Therefore, the slope, m = -1/4

The y-intercept, c = 8

adoni [48]3 years ago

8 0

Slope m= -1/4
Intercept c=8

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

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Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

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Step-by-step explanation:

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Black_prince [1.1K]

Answer:

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$4v\leq -20$

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3 years ago

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The most appropriate choice for unitary method will be given by-

Length of driveway in the drawing is 3 inch

What is unitary method?

Unitary method is the method in which value of a single unit can be calculated from the value of a multiple unit and value of a multiple unit can be calculated from the value of a single unit.

Sometimes value of single unit is less than value of multiple unit

For example - cost of food and quantity of food

Sometimes value of single unit is more than value of multiple unit

For example- Number of men and time taken by those men to do a work

Here,

Scale used by Maureen is 1 inch = 8ft

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8 ft of room is equal to 1 inch on scale

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24 feet of room is equal to $\frac{1}{8} \times 24$ inch on scale

24 feet of room is equal to 3 inch on scale

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To learn more about unitary method, refer to the link-

brainly.com/question/24587372

#SPJ9

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Answer:

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