Factor the expression 28r+42s-35
1 answer:
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Let us assume uniform width = x cm wide.
Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.
Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.
And width of rectangle made by frame = 70+x+x = (2x+70) cm.
We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.
Total area of the rectangle made by frame would be = (2x+50) * (2x+70)
We know,
Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.
We also given "the area of the frame is the same as the area of the portrait."
We can setup an equation now,
3500 = (2x+50) * (2x+70) - 3500.
Subtracting 3500 from both sides, we get
3500-3500 = (2x+50) * (2x+70) - 3500-3500.
0 = (2x+50) * (2x+70) -7000.
FOIL (2x+50) * (2x+70), we get
0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.
0 = 4x^2 +140x +100x +3500 -7000.
4x^2 +240x -3500 = 0.
Dividing whole equation by 4, we get
x^2 +60x - 875 =0
Applying quadratic formula , we get
We cant take negative value.
So,
We could take approximately 12 cm.
<u>Answer:</u>
Both accounts of Nick and Allie will have same amount of $864 in time period of 4 weeks.
<u>Solution: </u>
Given, Yesterday two friends went into a bank to open savings accounts.
Allie started by putting $783 in her account, and she will deposit an additional $27 each week.
Nick made no initial deposit, but he will add $288 more each week.
In a few weeks, the friends will have the same account balance.
Here, account balance of Allie for every week forms an A.P as
783, 810, 837, ……. With common difference 27
And, account balance of nick for every week will be
0, 288, 576, …….. with common difference 288
Let, after n weeks the balance in both accounts be equal.
Then, nth term of both series will be equal, we know that, nth term tn of A.P is a + (n – 1)d
Where, a is first term, d is common difference and n is number of terms.
Now, nth term of allie series = nth term of nick series.
783 + (n – 1) x 27 = 0 + (n – 1) x 288
Here, we used same n for both sides because n represents number of weeks and it is common to both
783 + 27n – 27 = 288n – 288
756 + 288 = 288n – 27n
261n = 1044
n = 4.
So, it will take 4 weeks to have same balance and now, substitute n value in nth term of nick series.
Hence, both accounts will have same amount of $864 in time period of 4 weeks