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Readme [11.4K]
3 years ago
8

How many distinct pairs of perfect squares differ by 35? (the pair $a, b$ is the same as the pair $b, a$.)?

Mathematics
1 answer:
Phantasy [73]3 years ago
5 0
35 has 4 divisors, hence two factor pairs: 1*35 and 5*7. Each corresponds to a set of perfect squares that differ by 35

One pair is ((35±1)/2)^2 = {17^2, 18^2} = {289, 324}
The other is ((7±5)/2)^2 = {1^2, 6^2} = {1, 36}
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Please help me with these questions FAST it's formal and I can't faillllllll!!!!!!,
GaryK [48]
A. I think it would be -40/297
3 0
3 years ago
You roll a 6-sided number cube (dice) 75 times. You rolled a one 13 times, a two
max2010maxim [7]

Answer:

1/6 im not sure how to explain it but u have 5/6 chance of not rolling it

8 0
3 years ago
A new Community Center is being built in Oak Valley. The perimeter of the rectangular playing field is 382 yards. The length of
vesna_86 [32]

Answer:

The width is 50 yards and the length is 141 yards.

Step-by-step explanation:

Let's call: L the length of the field and W the width of the field.

From the sentence, the perimeter of the rectangular playing field is 382 yards we can formulate the following equation:

2L + 2W = 382

Because the perimeter of a rectangle is the sum of two times the length with two times the width.

Then, from the sentence, the length of the field is 9 yards less than triple the width, we can formulate the following equation:

L = 3W - 9

So, replacing this last equation on the first one and solving for W, we get:

2L + 2W = 382

2(3W - 9) + 2W = 382

6W -18 +2W = 382

8W - 18 = 382

8W = 382 + 18

8W = 400

W = 400/8

W = 50

Replacing W by 50 on the following equation, we get:

L = 3W - 9

L = 3(50) - 9

L = 141

So, the width of the rectangular field is 50 yards and the length is 141 yards.

3 0
3 years ago
The number y of deer in a county after x years can be modeled by y=0.75x^2 + 10.5x + 1300. When were there about 2000 deer? Roun
Lemur [1.5K]

Answer:

24 years

Step-by-step explanation:

We are told that the model of number of deers is;

y = 0.75x² + 10.5x + 1300

Where;

y represents number of deers

x represents number of years

Now, we want to find how many years it will take to get to 2000 deers.

Thus;

2000 = 0.75x² + 10.5x + 1300

0.75x² + 10.5x + 1300 - 2000 = 0

0.75x² + 10.5x - 700 = 0

Using quadratic formula, we have;

x = [-b ± √(b² - 4ac)]/2a

x = [-10.5 ± √(10.5²- (4*0.75*-700)]/(2*0.75)

x = [-10.5 ± √(110.25 + 2100)]/(1.5)

x = [-10.5 ± √2210.25]/(1.5)

x ≈ -38 or 24

Number of years can't be negative, so we will take the positive value.

So, x = 24 years

3 0
3 years ago
Other ways to write 50897
NARA [144]
Written form: fifty thousand eight hundred ninety-seven.

expanded form: 50000+800+90+7
3 0
3 years ago
Read 2 more answers
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