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shtirl [24]
3 years ago
8

Find the area of a parallelogram with base (b) and height (h)

Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0
Answer is C) 1,095.2 cm2
Formula for area for parallelogram is = b.h
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Mrs Tan bought 4 times as many pens as notebooks and each notebook cost $8.20 more than each pen. She spent $26 more on the book
lilavasa [31]
Let x be the cost of 1 pen
then cost of 1 notebook = x + 8.20

Let y be the number of pens Tan buys
then number of notebooks Tan buys = y/4

She spent $26 more on books than on pens which means

Cost of notebooks - Cost of pens = 26
(x + 8.20) * y/4 - xy = 26

Sinplifying it

(xy + 8.20y)/4 - xy = 26
(xy + 8.20y - 4xy)/4 = 26
8.20y - 3xy = 104

She spent $394 which means

Cost of notebooks + Cost of pens = 394
(x + 8.20) * y/4 + xy = 394

Simplifying it

(xy + 8.20y)/4 + xy = 394
(xy + 8.20y + 4xy)/4 = 394
8.20y + 5xy = 1576

Now, we have two equations,

(1) 8.20y - 3xy = 104
(2) 8.20y + 5xy = 1576

Now we need to find a third equation with either x or y as the subject of any of both the previous equations.

Let's make y the subject of (2) equation

8.20y + 5xy = 1576
y(8.20 + 5X) = 1576
(3) y = 1576/(8.20 + 5x)

Let's substitute the new value of y from (3) into (1) because we rearranged (2) to from (3)

8.20y - 3xy = 104
y(8.20 - 3x) = 104
y = 104/(8.20 - 3x)
1576/(8.20 + 5x) = 104/(8.20 - 3x)
1576 * (8.20 - 3x) = 104 * (8.20 + 5x)
12923.2 - 4728x = 852.8 + 520x
12923.2 - 852.8 = 4728x + 520x
12070.4 = 5248x
12070.4/5248 = x
x = 2.3

Now find the value of y by substituting the value of x in either equation, preferably (3)

y = 1576/(8.20 + 5x)
y = 1576/(8.20 + 5 * (2.3))
y = 80

Therefore cost of 1 notebook = x + 8.20 = 2.3 + 8.20 = $10.50

8 0
3 years ago
What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?
yarga [219]
The vertex is exactly half way between directrix and focus. In this case the vertex is (8,-7)
               (h,k)

P is the distance between the vertex and either the directrix or focus,  in this case p = 1. 

a = 1/(4p)  or 1/(4*1) or 1/4

write the equation in vertex form

y = a(x-h)^2 + k

y = 1/4(x-8)^2 -7
4 0
3 years ago
What is the vertex of the graph of the function below y=x^2+10x+24
swat32
The vertex is (-5,-1)
7 0
3 years ago
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Cynthia ran 4 laps in 40 min.<br><br><br><br><br> What is the rate of number of laps to minutes?
Ulleksa [173]
The answer is:1 lap per minute
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3 years ago
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Which expression has a value of 15 when n = 7? <br><br> 43 - 5n<br> 3n - 5<br> 6n - 28<br> 19 - 28/n
cupoosta [38]
19 - 28/n
n=7
19 - 28/7
19 - 4
=15
8 0
3 years ago
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