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The area of triangle PQR is 50*sqrt(5).

The possible values of k are 2 and -7.

The perimeter of P is 37.

This is all I can think of (though the result is rather ugly!):

Thanks Alan.  :)

Given ad > bc, and we also know all the variables are positive (so when dividing/multiplying you don't have to switch the inequality), you can use the division property and divide both sides by d that still makes the inequality true: a > bc/d.

Then by the same property, you can keep the inequality true by dividing both sides by b, and you obtain a/b > c/d.

Same way to think of it as the example 5/19 > 6/23, because multiplying 23 to both sides won't change the fact that 5 * 23 / 19 > 6, logically speaking, if you fairly multiply each side by the same number, then it's obvious that the bigger side will be even bigger now. After you fiddle around with the division property, you can obtain a/b > c/d.

6 packs of 15 tickets each has the key word "of". Of means multiply, so 2 packs of 2 pokemon cards each is 2 x 2 = 4.

6 packs of 15 tickets each means 15 + 15 + 15 + 15 + 15 + 15 = 15 x 6 = 90 tickets in total. If she has used 38 already, use subtraction.

90 - 38 = 52. Amy has 52 tickets left.

Let the blank be a variable x.

13(5*13*x*3) = 13(17)

Divide both sides by 13. 5*13*3*x = 17              =>          195x = 17

x = 17/195, so the blank is 17/195.

The inradius of triangle ABC is 66/5.  The circumradius is 5*sqrt(17).

The area of triangle ABC is 5*sqrt(7)

CM = 8*sqrt(5)

a + d is larger.

The largest possible number of matches is 60.

Are you the same person that posted the same question here?  https://web2.0calc.com/questions/algebra_79619

Look under the above question!

There are NO real solutions for a and b. There are several "complex" solutions, however.

See under your first post!

Let the number of matches before weekend==M
Number of matches she had won before weekend==1/2M

[1/2M + 3] / [M + 4] ==0.503, solve for M

M==~330 matches she had played before the weekend

330 / 2 ==~165 matches that she would have won before the weekend.

Check: After the weekend, she would have won:
[165 +3] ==168 matches

168 / [330 + 4] ==~0.503

Use this formula to find the FV:

P=300;   R=0.04/12;  N=3*12;    FV=P*((1 + R)^N - 1)/ R

FV = $ 11,454.47 - FV of the account after 3 years.

Note: I took 4% APR as compounded monthly.

180 x 0.20 ==36 mL of acid and 144 mL of water
180 x 0.30 ==54 mL of acid and 126 mL of water.
S==Solution

[36 - S] / [144 - S] ==54 / 126, solve for S
S ==-45 mL

180 - 45 ==135 mL of solution left

A ==Acid
[0.20 * 135] + A ==0.30 * [ 135 + A], solve for A

Acid ==19+2/7 mL of Acid to give a solution of 30% Acid.

Check:[0.20 * 135 + 19 2/7]==46+2/7 mL of Acid

            135 solution + 19 2/7==154 + 2/7 mL of solution

            [46 2/7] / [154 2/7] ==30%

Do you know what the right answer is from your book? Because it has been "solved" 3 times with 3 different answers !.

What percent of the 180 mL solution is acid? Is it 20% and you want to raise to 30%? Clarify your question.

The probability is 5/8 * 4/7 = 20/56 = 10/28 = 5/14.

I uh think that the answer to (a) is \(2^{10}\)

The other solutions are 4, 24, 48, 65, and 96.