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Gennadij [26K]
3 years ago
14

AB=10, AD=24. What is the value of AC+AD?​

Mathematics
1 answer:
Rainbow [258]3 years ago
5 0

Answer:

52

Step-by-step explanation:

Given:

AB = 10, AD =24

Required:

Value of AC + BD

SOLUTION:

AC = BD (both are diagonals of the rectangle)

Use pythagorean theorem to find AC.

Thus:

AB² + AD² = BD²

Plug in the values

10² + 24² = BD²

676 = BD²

√676 = BD

26 = BD

BD = AC = 26

Therefore,

AC + BD = 26 + 26 = 52

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Please help!!!
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Answer:

Step-by-step explanation:

<u>Compound Interest</u>

It's the type of financial calculations that includes the interest of previous periods into the new interests earned by some initial investment or principal P.

If we want to compute the final value FV of a series of n payments R at a fixed compound interest rate i, then

FV=F_m\cdot R

Where

\displaystyle F_m=\frac{(1+i)^n-1}{i}

The question provides us the following data

i=10% compounded twice a year

n=3 1/2 years

FV=15,000

We need to convert the number of periods and the interest rate to a semester base:

\displaystyle i=\frac{10}{100\cdot 2}=0.05

n=3.5\cdot 2= 7\  semesters

Let's calculate Fm

\displaystyle F_m=\frac{(1+0.05)^7-1}{0.05}=8.142

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FV=F_m\cdot R

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3 0
4 years ago
A group of retailers will buy 104 televisions from a wholesaler if the price is $300 and 144 if the price is $250. The wholesale
const2013 [10]

Answer:

(275,122)  

When the price will be $275, the quantity will be 122 televisions.

Step-by-step explanation:

We have been given that a group of retailers will buy 104 televisions from a wholesaler if the price is $300 and 144 if the price is $250.

As the quantity of televisions depends on price of televisions, so our demand curve will pass through points (300,104) and (250,144).

Let us find slope of demand line using slope formula.

m=\frac{y_2-y_1}{x_2-x_1}, where,

m =\text{Slope of line},

y_2-y_1=\text{Difference between two y-coordinates},

x_2-x_1=\text{Difference between same x-coordinates of two y-coordinates}

Upon substituting coordinates of our given points in slope formula we will get,

m=\frac{104-144}{300-250}

m=\frac{-40}{50}

m=-\frac{4}{5}

Let us substitute m=-\frac{4}{5} coordinates of point (250,144) in slope intercept form of equation (y=mx+b).

144=-\frac{4}{5}*250+b

144=-4*50+b

144=-200+b

144+200=-200+200+b

344=b

Upon substituting b=344 and m=-\frac{4}{5} we will get equation of our demand line as:

y=-\frac{4}{5}x+344

Similarly we will find the equation of supply line using points (225,88) and (315,168).  

m=\frac{168-88}{315-225}

m=\frac{80}{90}

m=\frac{8}{9}

Let us substitute m=\frac{8}{9} and coordinates of point (225,88) in slope intercept form of equation (y=mx+b).

88=\frac{8}{9}*225+b

88=8*25+b

88=200+b

88-200=200-200+b

-112=b

Upon substituting b=-112 and m=\frac{8}{9} we will get equation of our supply line as:

y=\frac{8}{9}x-122

Let us equate both lines to find the point where both lines intersect.

-\frac{4}{5}x+344=\frac{8}{9}x-122

-\frac{4}{5}x-\frac{8}{9}x+344=\frac{8}{9}x-\frac{8}{9}x-122

-\frac{4}{5}x-\frac{8}{9}x+344=-122

-\frac{4}{5}x-\frac{8}{9}x+344-344=-122-344

-\frac{4}{5}x-\frac{8}{9}x=-466

Let us have a common denominator.

-\frac{4*9}{5*9}x-\frac{8*5}{9*5}x=-466

-\frac{36}{45}x-\frac{40}{45}x=-466

\frac{-36-40}{45}x=-466

\frac{-76}{45}x=-466

\frac{-76}{45}*\frac{45}{-76}x=-466*\frac{45}{-76}

x=466*\frac{45}{76}

x=6.1315789473684211*45

x=275.9210526315789495\approx 275

Let us substitute x=275 in any of our equation to solve for y.

y=-\frac{4}{5}*275+344

y=-4*55+344

y=-220+344

y=122

Therefore, the equilibrium point for the market will be (275,122).

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