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3 years ago

Write an equation for a line through (9, -11) that is parallel to the line y = - 23 x + 4

Mathematics

1 answer:

lora16 [44]3 years ago

4 0

Answer:

y = -23x + 196

Step-by-step explanation:

Let equation of the line be y = mx + c

since it is parallel to line y = -23x + 4,

their slope/gradient will be the same (aka m = -23)

sub (9, -11):

-11 = -23(9) + c

c = 196

therefore, equation of the line is y = -23x + 196

This is a question on coordinate geometry. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

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If the length of room is four times the height and breadth is twice of its height and the volume of the room is 512 m^2 find its

lisov135 [29]

$Let \: x \: (x>0) \: be \: the \: height \Rightarrow the \: width, length: 2x,4x \\ Volume:V=hwl = 512 \\ \Leftrightarrow x2x4x = 512 \\ \Leftrightarrow 8{x }^{3} = 512 \\\Leftrightarrow {x}^{3} = 64 \\ \Leftrightarrow x = 4 \\ \Rightarrow The \: height \: is \: 4 \: m, the \: width \: is \: 8 \: m$

8 0

3 years ago

in 2012, the population of a city was 63,000. by 2017, the population was reduced to approximately 54,100. identify any equation

Akimi4 [234]

Answer:

$f(x) = 63000(0.97)^x$

Step-by-step explanation:

Given

$f(0) = 63000$ ---x = 0, in 2012

$f(5) = 54100$ -- x = 5, in 2017

Required

Select all possible equations

Because there is a reduction in the population, as time increases; the rate must be less than 1.

An exponential function is represented as:

$f(x) = ab^x$

Where

$b = rate$

rate > 1 in options (a) and (b) i.e. 1.03

This implies that (a) and (b) cannot be true

For option (c), we have:

$f(x) = 63000(0.97)^x$

Set x = 0

$f(0) = 63000(0.97)^0 = 63000*1=63000\\$

Set x = 5

$f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100$

This is true because the calculated values of f(0) and f(5) correspond to the given values

For option (d), we have:

$f(x) = 52477(0.97)^x$

Set x = 0

$f(0) = 52477(0.97)^0 - 52477* 1 = 52477$

This is false because the calculated value of f(0) does not correspond to the given value

For option (e), we have:

$f(x) = 63000(0.97)^\frac{1}{5x}$

Set x = 0

$f(0) = 63000(0.97)^\frac{1}{5*0} = 63000(0.97)^\frac{1}{0} =$ undefined

This is false because the f(x) is not undefined at x = 0

For option (f), we have:

$f(x) = 52477(0.97)^{5x$

Set x = 0

$f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477$

This is false because the calculated value of f(0) does not correspond to the given value

From the computations above, only (c) $f(x) = 63000(0.97)^x$ is true

4 0

3 years ago

Six cakes cost £2.40 how much do ten cakes cost

crimeas [40]

There are a few ways to find out the correct answer. One of them is to divide 2.40 by 6 to get a price of one cake and then multiply it by 10:

2.40 ÷ 6 = 0.40
0.40 * 10 = 4.00

Answer: Ten cakes would cost 4 pounds.

4 0

3 years ago

Which expression shows 36 as a product of prime factors?

Lapatulllka [165]

Answer:

This is ur answer

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