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3 years ago

What is an expression for “72 less than 12 times a number”?

Mathematics

1 answer:

Burka [1]3 years ago

3 0

Answer:y>6

Step-by-step explanation:

Let the unknown number b y

72<12y

Divide through by 12

y>6

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I've work this one out but I keep getting answers that aren't one of the choices

shtirl [24]

Answer:

2.0

Step-by-step explanation:

Tangent is calculated as the length of the opposite side of an angle divided by the adjacent side of that angle.

The opposite of theta is 4, while its adjacent side is 2

tan theta = 4/2 = 2

5 0

4 years ago

How many subsets of {1, 2, 3, 4, 6, 8, 10, 15} are there for which the sum of the elements is 15?

stepladder [879]

Answer:

512

Step-by-step explanation:

Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7

For instance, if I divide the set into parts {1,2,4}

and {3,5}, the first part adds up to 7, and its complement adds up to 8

Once one makes that observation, the rest of the proof is straightforward. There are 25=32

different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.

8 0

4 years ago

What are the solutions to the quadratic equation x^2-16=0

FinnZ [79.3K]

I hope this helps you

3 0

4 years ago

The sum of two numbers is 51 and the difference is 11. what are the numbers?

stiv31 [10]

(51 - 11) : 2 = 20

20 + 11 = 31

20 and 31

6 0

4 years ago

Divide:(10x²-3x+4)÷(2x-5)

Helen [10]

Answer:

$\frac{10x^2-3x+4}{2x-5}=5x+11+\frac{59}{2x-5}$

Quotient: 5x+11

Remainder: 59

Step-by-step explanation:

I'm going to do long division.

The bottom goes on the outside and the top goes in the inside.

Setup:

---------------------------------

2x-5 | 10x^2 -3x +4

Starting the problem from the setup:

5x +11 (I put 5x on top because 5x(2x)=10x^2)

--------------------------------- (We are going to distribute 5x to the divisor)

2x-5 | 10x^2 -3x +4

-(10x^2 -25x) (We are now going to subtract to see what's left.)

-----------------------------------

22x +4 (I know 2x goes into 22x, 11 times.)

( I have put +11 on top as a result.)

-(22x -55) (I distribute 11 to the divisor.)

-----------------------

59 (We are done since the divisor is higher degree.)

The quotient is 5x+11.

The remainder is 59.

The result of the division is equal to:

$5x+11+\frac{59}{2x-5}$ .

We can actually use synthetic division as well since the denominator is linear.

Let's solve 2x-5=0 to find what to put on the outside of the synthetic division setup:

2x-5=0

Add 5 on both:

2x=5

Divide both sides by 2:

x=5/2

Or realize that 2x-5 is the same as 2(x-(5/2)) which you will have to do anyways if you choose this route:

So 5/2 will go on the outside:

5/2 | 10 -3 4

| 25 55

------------------------------

10 22 59

So we have:

$\frac{10x^2-3x+4}{2x-5}$

$=\frac{10x^2-3x+4}{2(x-\frac{5}{2})}=\frac{1}{2} \cdot \frac{10x^2-3x+4}{x-\frac{5}{2}}=\frac{1}{2}(10x+22+\frac{59}{x-\frac{5}{2}})$

Distribute the 1/2 back:

$\frac{10x^2-3x+4}{2x-5}=\frac{10x+22}{2}+\frac{59}{2(x-\frac{5}{2})}$

$\frac{10x^2-3x+4}{2x-5}=5x+11+\frac{59}{2x-5}$

3 0

4 years ago