Consider the inequality -5(x+7)<-10. Write and inequality representing the solution for x
1 answer:
Let's solve your inequality step-by-step.<span><span>−<span>5<span>(<span>x+7</span>)</span></span></span><<span>−10</span></span>Step 1: Simplify both sides of the inequality.<span><span><span>−<span>5x</span></span>−35</span><<span>−10</span></span>Step 2: Add 35 to both sides.<span><span><span><span>−<span>5x</span></span>−35</span>+35</span><<span><span>−10</span>+35</span></span><span><span>−<span>5x</span></span><25</span>Step 3: Divide both sides by -5.<span><span><span>−<span>5x</span></span><span>−5</span></span><<span>25<span>−5</span></span></span><span>x><span>−5
</span></span>Answer:<span>x><span>−5
Good luck mate :P</span></span><span>
</span>
</span></span>Answer:<span>x><span>−5
Good luck mate :P</span></span><span>
</span>
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9514 1404 393
Answer:
3. no; does not have the correct ratio to other sides
4. (1; right), (2; obtuse), (3; right)
Step-by-step explanation:
3. There are a couple of ways you can go at this.
a) the ratio of sides of a 30°-60°-90° right triangle (half an equilateral triangle) is 1 : √3 : 2. Here, the ratio of sides is ...
(√30/2) : √15 : √30 = 1 : √2 : 2 . . . . MQ is <em>not</em> the height
b) the height is perpendicular to the base, so if MQ were the height, the sides of the triangle would satisfy the Pythagorean theorem:
LQ² +MQ² = LM²
(√30/2)² +(√15)² = (√30)²
30/4 +15 = 30
22.5 = 30 . . . . NOT TRUE
The length MQ cannot be the height of ∆LMN. (It is too short.)
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4. To see if these lengths form a right triangle, you can test them in the Pythagorean theorem relation. In the attached we have reformulated the equation so it gives a value of 0 if the triangle is a right triangle:
c² = a² +b² . . . . . Pythagorean theorem
c² -a² -b² = 0 . . . . rewritten
If the value of c² -a² -b² is not zero, then the side lengths do not form a right triangle. The attached shows this math performed by a graphing calculator. The results are ...
- right triangle
- not a right triangle — long side is too long, so the triangle is obtuse
- right triangle
_____
<em>Additional comment</em>
The attached table demonstrates an artifact of computer arithmetic. Not all numbers can be represented exactly in a computer, so a difference that is expected to be zero using exact arithmetic may be slightly different from zero when computed by a computer or calculator. Here, we see a difference of about 6×10^-14 when zero is expected. On most calculators (with 10, or 12 displayed digits), this would be displayed as 0.
The same calculation done "by hand" gives ...
(√425)² -5² -20² = 425 -25 -400 = 0 . . . Triangle 1 is a <em>right triangle</em>
Answer:
Step-by-step explanation:
step 1
Convert mixed number to an improper fraction
step 2
Using proportion
step 3
Convert to mixed number