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4 years ago

15

The endpoints of PQ are at P (-4,-2) and Q (6,3). What are the coordinates of point S which divides PQ such that PS: SQ is equal

to 3:2?

1 answer:

GrogVix [38]4 years ago

7 0

Answer:

The coordinates are (2,1)

Step-by-step explanation:

We use the internal division formula here;

x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)

Where;

m = 3 and n = 2

x1 = -4 , x2 = 6

y1 = -2 , y2 = 3

Substituting these values;

(x,y) = (2(-4) + 3(6))/(3 + 2) , (2(-2) + 3(3))/(2+3)

= (10/5 , 5/5)

= (2,1)

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WILL RATE BRAINLIEST PLZ HELP<br> MUST EXPLAIN THO

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Answer:

A -- base 3, height 4
B -- base 4, height 4
C -- base 3, height 3
D -- base 3, height 5

Step-by-step explanation:

A sort of straightforward way to approach this is to define base and height variables for each of the figures: ba, ha, bb, hb, bc, hc, bd, hd. Then the statements can be used to make equations in these variables.

0. hc = bc . . . . figure C is a square

1. ba = bd

2. ba = bb -1

3. hc = ba

4. hb = ha = bb

5. hc·bc = 9

6. (1/2)ha·ba +(1/2)hb·bb +hc·bc+hd·bd = 38

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Using equations 0 and 5, we find ...

hc² = 9 ⇒ hc = 3

From equation 3, ...

ba = 3

From equation 2, ...

3 = bb -1 ⇒ bb = 4

From equation 1, ...

bd = 3

From equation 4, ...

ha = hb = 4

Filling in the values we know in equation 6, we get ...

(1/2)(4)(3) +(1/2)(4)(4) +9 +hd(3) = 38

23 +3hd = 38

hd = 15/3 = 5

The dimensions are:

A -- base 3, height 4
B -- base 4, height 4
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3 years ago

4. The quotient of x and 7 is 5 more than three times x.

Lostsunrise [7]

Well,

it says The quatient of x and seven is 5 more than three times x

The quotient = x/7

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1 year ago

Which is the graph of f(x)

padilas [110]

I don’t understand please put it in a form i could possibly understand

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3 years ago

What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brot

Nat2105 [25]

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

$a = 500$ --- starting balance

$m = 10$ --- monthly rate

Her brother

$a = 100$ ---- starting balance

$r = 10\%$ --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

$y = ab^x$

Where $b = 1 + r$

So, we have:

$y = ab^x$

$y = 100 *(1 + 10\%) ^x$

$y = 100 *(1 + 0.10) ^x$

$y = 100 *(1.10) ^x$

Hence:

$g(x) = 100 *(1.10) ^x$

Next, we calculate Molly's function (a linear function)

The monthly function is:

$y = mx + a$

So, we have:

$y = 10x + 500$

Annually, the function will be:

$y = 10x*12 + 500$

$y = 120x + 500$

So, we have:

$f(x) = 120x + 500$

At this point, we have:

$f(x) = 120x + 500$ ---- Molly

$g(x) = 100 *(1.10) ^x$ ---- Her brother

<u>Next, we test each option</u>

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

$y = 120x + 500$

The slope of a linear function with the form: $y = mx + b$ is m

By comparison:

$m = 120$

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

$m = 120$

For his brother:

Rate of change is calculated using:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(40) - g(32)}{40 - 32}$

$m = \frac{g(40) - g(32)}{8}$

Calculate g(40) and g(32)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{40} =4526$

$g(32) = 100 * 1.10^{32} = 2111$

So, we have:

$m = \frac{4526 - 2111}{8}$

$m = \frac{2415}{8}$

$m = 302$

By comparison: $302 > 120$

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(30) - g(24)}{30 - 24}$

$m = \frac{g(30) - g(24)}{6}$

Calculate g(30) and g(24)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{30} =1745$

$g(32) = 100 * 1.10^{24} = 985$

So, we have:

$m = \frac{g(30) - g(24)}{6}$

$m = \frac{1745 - 985}{6}$

$m = \frac{760}{6}$

$m = 127$

By comparison: $127 > 120$

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(4) - g(0)}{4 - 0}$

$m = \frac{g(4) - g(0)}{4}$

Calculate g(4) and g(0)

$g(x) = 100 *(1.10) ^x$

$g(4) = 100 * 1.10^4 =146$

$g(0) = 100 * 1.10^{0} = 100$

So, we have:

$m = \frac{g(4) - g(0)}{4}$

$m = \frac{146 - 100}{4}$

$m = \frac{46}{4}$

$m = 11.5$

By comparison: $120>11.5$

Hence, Molly's account has a faster rate over [0,4]

(c) is false

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3 years ago

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Answer:

Step-by-step explanation:

The first step is to distribute.

2(2x) 2(5)

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then, you add 10 and 6, which will give you 16

4x +16=20

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x=1

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3 years ago

Read 2 more answers