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3 years ago

6th grade math both please

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

Answer:

5. 6 baskets

6. 4 inches

Step-by-step explanation:

Both of these questions are about the Lowest Common Multiple <em>(LCM)</em>.

5. The first thing we need to do is make the numbers so that they are split into only the prime multiples.

So,

$30 = 2 * 3 * 5$

and

$42 = 2*3*7$

Now that we've done that, the next step is to see which numbers are common in both of them. This will be the LCM of the two numbers.

so the answer $=2*3 = 6$

This will have 5 sandwiches and 7 cookies in each basket.

6. Similarly here, we need to do the same thing and split them.

So,

$52=2*2*13$

and

$64=2*2*2*2*2*2$ .

The two multiples that are common are $2*2 = 4$ , so they will be 4 inches.

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3 years ago

If EFH = (5x + 1)°, HFG = 62°, and EFG = (18x + 11)°, find EFH

olga55 [171]

Given:

Consider the below figure attached with this question.

∠EFH = (5x + 1)°, ∠HFG = 62°, and ∠EFG = (18x + 11)°

To find:

The measure of ∠EFH.

Solution:

From the figure it is clear that ∠EFG is divide in two parts ∠EFH and ∠HFG. So,

$\angle EFG=\angle EFH+\angle HFG$

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$18x+11=5x+63$

Isolate variable terms.

$18x-5x=63-11$

$13x=52$

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$x=\dfrac{52}{13}$

$x=4$

The value of x is 4.

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8 0

3 years ago

The total cost of producing a type of tractor is given by C(x)=11000−20x+0.02x2, where x is the number of tractors produced. How

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Answer:

Step-by-step explanation:

You need to complete the square.

C(x) = 0.02(x^2 - 1000x ...) + 11000

C(x) = 0.02 (x^2 - 1000x + 500^2) + 11000 - 5000

C(x) = 0.02 (x^2 - 1000x + 500^2) + 6000

C(x) = 0.02(x - 500)^2 + 6000

Now if you look at the answer you will find that the square is completed. That means that number of tractors you could produce is 500 at a cost of 6000

There is a flow to this question that you may have trouble understanding.

First of all the 500^2. That comes from taking 1/2 of 1000 and squaring it. That's what you need to complete the square.

Bur that is not what you have adding into the equation. Remember that there is a 0.02 in front of the brackets.

500^2 = 250000

0.02 * 250000 = 5000

So that number must be subtracted to make the square = 0. When you remove the brackets, you should get 11000 all in all.

So what you have outside the brackets is 11000 - 5000 = 6000

The rest is just standard for completing the square.

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Answer:

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