- Algebra 1~ solving inequality word problems-

Mathematics

1 answer:

pishuonlain [190]3 years ago

5 0

I'm not that sure about the second one. Would recommend asking another source.

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Examine the diagram at right. The smaller triangle (inside of the larger triangle) is similar to larger triangle. How can you so

olchik [2.2K]

As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.

In order to solve for x we can set up the proportion between the horizontal and vertical sides:

$28\div 11.2 = 27+x \div x$

Solving this proportion for x implies $x=18$

Now you can solve for m and p using the pythagorean theorem, because both triangles are right:

$m = \sqrt{18^2+11.2^2} =21.2$

Then, we know that the hypothenuse of the big triangle is m+p, so we have

$m+p=\sqrt{(18+27)^2+28^2} = 53$

which implies

$p = 53-p = 53-21.2=31.8$

6 0

2 years ago

Find S10 for -1 + -7 + -13 + -19

Alex777 [14]

First we find the common difference...to do this we subtract the first term from the second term. -7 - (-1) = -7 + 1 = -6

now we are going to find the 10th term
an = a1 + (n-1)*d <== formula for finding any term in arithmetic series
a1 = 1st term, d = common difference, n = term we want to find
now we sub
a10 = -1 + (10 -1) * -6
a10 = -1 + (9 * -6)
a10 = -1 - 54
a10 = - 55

now we will find the sum
Sn = (n (a1+ an)) / 2 <== formula for finding the sum
S10 = (10(-1 - 55))/2
S10 = (10(-56) / 2
S10 = -560/2
S10 = - 280

so the sum of the first 10 numbers is -280

4 0

3 years ago

10% of what number is 78?

Zepler [3.9K]

Answer: x = 780

Step-by-step explanation: Well percent means over 100 so we can set up an equation for this problem by reading it from left to right.

So we know that 10% means 10/100, of means times, what number means x, is means equals, and 12 means 12.

Notice that 10/100 can be reduced to 1/10.

So rewriting our problem we have X/10 = 78.

To get rid of the fraction, we multiply both sides of the equation by 10 and we have x = 780. So, 10% of 780 is 78.

Now let's check our answer back in the original problem to see if it makes sense.

We have 10% of 780 is 78. Well we know that 100% of of 780 would be 780 so 10% of 780 should be alot less than 780 so 78 seems to make sense.