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eduard
3 years ago
14

The sum of the squares of two consecutive integers is 145. Find the two integers.

Mathematics
1 answer:
worty [1.4K]3 years ago
6 0

Answer: The two integers are 8 and 9.

Step-by-step explanation: Let n represent the number.

n^2 + (n + 1)^2 = 145

By foiling, this can be rearranged to:

n^2 + n^2 + 2n + 1 = 145

Subtract 145 from both sides:

2n^2 + 2n - 144 = 0

Divide both sides by 2:

n^2 + n - 72 = 0

Factor the polynomial:

(n + 9)(n - 8) = 0

Solve for n:

n = -9, n = 8

Since they need to be consecutive, make the 9 positive. It will be positive either way because it is being squared.

Now, n = 9 and n = 8.

These are your two integers. Hope this helps!

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a store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for 27.93 and large bags cost 66.98.w
Nonamiya [84]

Answer

Find out the ratio of price to pound for each bag.

To prove

As given

A store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for $27.93 .

7 pound = $27.93

Now find out the cost for the 1 pound.

1\ pound\ cost= \frac{27.93}{7}

1 pound cost = $3.99

As given large bags cost $66.98.

Now find out pounds in the large bags.

Let us assume that the number of pounds in the large bags be x.

Than

3.99 × x = 66.98

x = \frac{66.98}{3.99}

x = 16.8 pounds (approx)

Now find out the ratio of  price to pound for each bag.

As small bags weight = 7 pounds

Cost of the small bags = $27.93

\frac{Price\ of\ small\ bag}{Cost\ of\ the\ small\ bags} = \frac{27.93}{7}

As large bags weight = 16.8 pounds

Cost of the large bags = $66.98

\frac{Price\ of\ large\ bag}{Cost\ of\ the\ large\ bags} = \frac{66.98}{16.8}

Hence proved


7 0
3 years ago
State if the two triangles are similar and the rule that applies.
kobusy [5.1K]

Answer:

The SAS rule states that two triangles are similar if the ratio of their corresponding two sides is equal and also, the angle formed by the two sides is equal. Side-Side-Side (SSS) rule: Two triangles are similar if all the corresponding three sides of the given triangles are in the same proportion.

Step-by-step explanation:

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2 years ago
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To factor a polynomial we need to find 2 numbers that add up to -15 and multiply into -54.
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From the box plot, it can be seen that for grade 7 students,
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</span>Similarly, from the box plot, it can be seen that for grade 8 students,
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6 0
3 years ago
Read 2 more answers
If the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept, name another x-intercept
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