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2 years ago

What are the coordinates of the point on the directed line segment from (1,-5) to

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

6 0

Answer:

Q (2.5, -4)

Step-by-step explanation:

Let A (1, -5), C = (10, 1), find Q (x, y), so that AQ:QC = 1:5

AQ = (x - 1, y + 5)

QC = (10 - x, 1 - y)

AQ:QC = 1:5

so 5*AQ = QC

5(x - 1) = (10 - x)

5(y + 5) = 1 - y

Solve them:

5x - 5 = 10 - x

6x = 15

x = 15/6 = 2.5

5y + 25 = 1 - y

6y = -24

y = -24/6 = -4

Then answer is Q (2.5, -4)

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Andrej [43]

Answer:

70 cubic cenimeters

Step-by-step explanation:

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7 0

3 years ago

The average American spent $8,508 on health care in 2011. The cost of health care is projected to rise about 5.8% per year for t

klio [65]

<h3>The projected amount the average American spent on health care in 2014 is $ 10075.91</h3>

Solution:

Given that,

The average American spent $8,508 on health care in 2011

The cost of health care is projected to rise about 5.8% per year for the years 2012-2022

The increasing function is given as:

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate in decimal

t is number of years

From given,

a = 8508

$r = 5.8 \% = \frac{5.8}{100} = 0.058$

t = 2011 to 2014 = 3 years

Substituting the values, we get,

$y = 8508(1 + 0.058)^3\\\\y = 8508(1.058)^3\\\\y = 8508 \times 1.1842\\\\y = 10075.914 \approx 10075.91$

Thus the projected amount the average American spent on health care in 2014 is $ 10075.91

4 0

4 years ago

Evaluate this loglog 10^100

Sloan [31]

Step-by-step explanation:

log(log 10¹⁰⁰)

= log 100

= log 10²

= 2

Note :

log 10ⁿ = n

8 0

3 years ago

Read 2 more answers

PLEASE HELP!!!!!

Katena32 [7]

Answer:6018

Step-by-step explanation:

Given Sequence

$-282-266-250-234.....$

It represent an A.P. with

first term $a=-282$

common difference $d=16$

So sum of 51 term

$S_n=\frac{n}{2}[2a+(n-1)d]$

$S_{51}=\frac{51}{2}\times [2\times (-282)+(51-1)16]$

$S_{51}=\frac{51}{2}\times [-564+800]$

$S_{51}=\frac{51}{2}\times [236]$

$S_{51}=51\times 118$

$S_{51}=6018$

7 0

3 years ago

A rectangular picture frame has outside dimensions of 8 inches wide and 10 inches tall. If the glass on the picture frame has an

Leto [7]

Answer:

1 inch

Step-by-step explanation:

If we call the thickness of the frame x, then the dimensions of the glass are:

w = 8 − 2x

h = 10 − 2x

The area of the glass is width times height:

48 = (8 − 2x) (10 − 2x)

Distribute and simplify:

48 = 80 − 16x − 20x + 4x²

0 = 4x² − 36x + 32

0 = x² − 9x + 8

Factor and solve:

0 = (x − 1) (x − 8)

x = 1 or x = 8

x can't be more than 4 (half the width of the frame), so x = 1 inch.

7 0

3 years ago