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DiKsa [7]
3 years ago
15

What is the equation of the line that contains point(3, -2) and has a slope of 5?

Mathematics
2 answers:
Olenka [21]3 years ago
5 0

Answer:

y = 5x - 17

Step-by-step explanation:

y = mx + c

m = the gradient/slope = 5

y = 5x + c

Substitute (3, -2) into the equation above to find c.

-2 = 5(3) + c

-2 = 15 + c

-2 - 15 = c

-17 = c

y = 5x - 17

tino4ka555 [31]3 years ago
5 0

Answer:

Step-by-step explanation:

point(3, -2) and has a slope of 5

Slope m = 5

y1 = -2 and x1 = 3

The equation is

y - y1 = m(x - x1)

y + 2 = 5(x - 3)

y + 2 = 5x - 15

y = 5x - 15 - 2

y = 5x - 17

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Divide ( - 3 z 2 – 15z )÷<br> (<br> z<br> +<br> 5<br> )
blondinia [14]
Factor the numerator to get:

(-3z(z+5))/(z+5)  now you notice that (x+5) cancel out leaving:

-3z
4 0
3 years ago
Suppose that in one metropolitan area, 25% of all home- owners are insured against earthquake damage. Four home-owners are to be
emmasim [6.3K]

Answer:

Step-by-step explanation:

Given that,

25% home owners are insecure of earthquake problem

If we select 4 home owners at random

let X denote the number among the four who have earthquake insurance

Let find the probability distribution of X

Let S- denotes a home owner who has insurance

Let F denotes a home owner who does not have insurance.

Then, P(S) =25% = 0.25

P(F) = 1 — P(S) = 1 —0.25

P(F) = 0.75

The possible outcomes of X is

X(0) = If no person has insurance

X(1) = If only 1 person has insurance

X(2) = If only 2 persons has insurance

X(3) = If only 3 persons has insurance

X(4) = If only 4 persons has insurance.

The cardinality of the sample space is n(C) = 2ⁿ = 2⁴ => 16

So, the sample space is given as

{FFFF, FFFS, FFSF, FFSS, FSFF, FSFS, FSSF, FSSS, SFFF, SFFS, SFSF, SFSS, SSFF, SSFS, SSSF, SSSS}

For X=0, the possible is {FFFF} i.e. no insurance, the one without insurance.

P(X) = 0.25×0.25×0.25×0.25

P(X) = 0.25⁴

P(X) = 0.00390625

For X=1, the possible outcome are

FFFS, FFSF, FSFF, SFFF

P(X=1) = 0.25³•0.75 + 0.25³•0.75 + 0.25³•0.75 + 0.25³•0.75

P(X=1) = 0.046875

For X=2 the possible outcomes are

FFSS, FSFS, FSSF, SFFS, SFSF, SSFF,

P(X=2)=0.25²•0.75²+0.25²•0.75²+ 0.25²•0.75²+ 0.25²•0.75²+ 0.25²•0.75²+ 0.25²•0.75²

P(X=2) = 0.2109375

For X=3 the possible outcomes are

FSSS, SFSS, SSFS, SSSF

P(X=3) = 0.25•0.75³+0.25•0.75³+ 0.25•0.75³+0.25•0.75³

P(X=3) = 0.421875

X=4 the possible outcomes are

SSSS

P(X=4) = 0.75×0.75×0.75×0.75

P(X=4) = 0.31640625.

Or

Using normal distribution

P(X=k) = ⁿCk • 0.25^k • 0.75^(4-k)

So,

P(X=0) = 4C0 • 0.25^0 • 0.75^4

P(X=0) = 0.31640625

P(X=1) = 4C1 • 0.25^1 • 0.75^3

P(X=1) = 0.421875

P(X=2) = 4C2 • 0.25^2 • 0.75^2

P(X=2) = 0.2109375

P(X=3) = 4C3 • 0.25^3 • 0.75^1

P(X=3) = 0.046875

P(X=4) = 4C4 • 0.25^4 • 0.75^0

P(X=4) = 0.00390625.

6 0
3 years ago
Describe how you would convince a friend that sin(x + y) does not equal sin x + sin y.
Citrus2011 [14]

Answer:

Step-by-step explanation:

PEMDAS

anything done in the parentheses comes first

so you have to add first then multiply

this is not the distributive property unless the two numbers in parentheses are not like terms

4 0
2 years ago
When a deposit of $1000 is made into an account paying 2% interest, compounded annually, the balance, $B, in the account after t
labwork [276]

Answer:

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

Step-by-step explanation:

Given a function y, the average rate of change S of y=f(x) in an interval (x_{s}, x_{f}) will be given by the following equation:

S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}

In this problem, we have that:

B(t) = 1000(1.02)^{t}

Find the average rate of change in the balance over the interval t = 0 to t = 5.

B(0) = 1000(1.02)^{0} = 1000

B(5) = 1000(1.02)^{5} = 1104.08

Then

S = \frac{1104.08 - 1000}{5-0} = 20.82

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

8 0
3 years ago
If 5 miles is 8km . Convert 33.7 km into miles
LenKa [72]

Answer:

20.94021

Step-by-step explanation:

mark me brainlist

7 0
2 years ago
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