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2 years ago

Given that the line is x/3 + y/2 =1 i ) make y the subject ii ) gradient of line

Mathematics

1 answer:

miss Akunina [59]2 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

(i)

$\frac{x}{3}$ + $\frac{y}{2}$ = 1 ( multiply through by 6 to clear the fractions )

2x + 3y = 6 ( subtract 2x from both sides )

3y = - 2x + 6 ( divide through by 3 )

y = - $\frac{2}{3}$ x + 2

(ii)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient ) and c the y- intercept )

y = - $\frac{2}{3}$ x + 2 ← is in slope- intercept form ( that is part (i)

with gradient m = - $\frac{2}{3}$

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100 Point need help ASAP

antiseptic1488 [7]

Answer:

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Step-by-step explanation:

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3 years ago

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Brielle and Joshua are running a half marathon race, which is 13.1 miles long. It takes Brielle 10 minutes to run 1.25 miles and

CaHeK987 [17]

Answer: Brielle will run the marathon faster.

Brielle = 104.8 minutes

Joshua = 157.2 minutes

Step-by-step explanation:

Speed rate = distance /time

Brielle = 1.25 /10 = 0.125 miles per minute

Joshua = 1.5/18 = 0.083333 =1/12 miles per minute

Since 0.125 (Brielle) > 1/12 (Joshua)

Brielle will run the marathon faster.

To calculate the time that takes each one to run the entire race (13.1 miles)

Time= distance / speed

Brielle = 13.1 /0.125 = 104.8 minutes
Joshua = 13.1 / (1/12)= 157.2 minutes

Feel free to ask for more if needed or if you did not understand something.

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3 years ago

Area and estimate helpp

Vikki [24]

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2 years ago

Six different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic re

Yanka [14]

Answer:

$Range=14$

$\sigma^2 =32.4$

$\sigma = 5 .7$

The standard deviation will remain unchanged.

Step-by-step explanation:

Given

$Data: 136, 129, 141, 139, 138, 127$

Solving (a): The range

This is calculated as:

$Range = Highest - Least$

Where:

$Highest = 141; Least = 127$

So:

$Range=141-127$

$Range=14$

Solving (b): The variance

First, we calculate the mean

$\bar x = \frac{1}{n} \sum x$

$\bar x = \frac{1}{6} (136+ 129+ 141+ 139+ 138+ 127)$

$\bar x = \frac{1}{6} *810$

$\bar x = 135$

The variance is calculated as:

$\sigma^2 =\frac{1}{n-1}\sum(x - \bar x)^2$

So, we have:

$\sigma^2 =\frac{1}{6-1}*[(136 - 135)^2 +(129 - 135)^2 +(141 - 135)^2 +(139 - 135)^2 +(138 - 135)^2 +(127 - 135)^2]$

$\sigma^2 =\frac{1}{5}*[162]$

$\sigma^2 =32.4$

Solving (c): The standard deviation

This is calculated as:

$\sigma = \sqrt {\sigma^2 }$

$\sigma = \sqrt {32.4}$

$\sigma = 5 .7$ --- approximately

Solving (d): With the stated condition, the standard deviation will remain unchanged.

5 0

2 years ago

If a sequence is defined recursively by (0)=3 and (n+1)=-f(n)+5 for n≥0, Then f(2) is equal to

lana66690 [7]

Answer:

f(2) = 3

Step-by-step explanation:

We are given:

f(0) = 3

and

f(n+1) = -f(n) + 5

We have to find the value of f(2). In order to find f(2) we first have to find f(1)

f(n + 1) = - f(n) + 5

Using n = 0, we get:

f(0 + 1) = - f(0) + 5

f(1) = -f(0) + 5 Using the value of f(0), we get

f(1) = -3 + 5 = 2

Now using n = 1 in the function, we get:

f(1 + 1) = - f(1) + 5 Using the value of f(1), we get

f(2) = -2+ 5

f(2) = 3

Thus the value of f(2) will be 3

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3 years ago