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jeka57 [31]
3 years ago
10

What is x2 – 6 = 16x + 30 rewritten in standard form, then factored?

Mathematics
1 answer:
kaheart [24]3 years ago
5 0

Answer:

Step-by-step explanation:

x^2-6=16x+30\\\mathrm{Subtract\:}30\mathrm{\:from\:both\:sides}\\x^2-6-30=16x+30-30\\Simplify\\x^2-36=16x\\\mathrm{Subtract\:}16x\mathrm{\:from\:both\:sides}\\x^2-36-16x=16x-16x\\\Simplify\\x^2-16x-36=0

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In this number tree, the integers greater than or equal to 0 are written out in increasing order, with the top row containing on
lozanna [386]

Answer:

The fifth integer in row 10 using the number tree pattern is 515.

Step-by-step explanation:

The attached picture is instrumental to understanding the solution to this. There are different methods to approach this problem. But we will use observations to solve the problem.

Looking at the tree diagram, we see that the first row has 1 integer, the second has 2, the third has 4 and the fourth has 8. From here, we can see that a row has 2^n numbers where n = 0, 1, 2, 3, 4, . . .

Row 1 = 2^0 = 1 number

Row 2 = 2^1 = 2 numbers

Row 3 = 2^2 = 4 numbers

Row 4 = 2^3 = 8 numbers. And so on.

Also we notice that the last number in row 4 is 14. This can be gotten by adding the total number of numbers from row 1 to row 4 which is

1 + 2 + 4 + 8 = 15 but the first number on the chart is 0 which means we have to take out the first integer to get the last integer on row 4. Doing this, we have 14.

Since our aim is to know the fifth number in row 10, then we need to know the last number in row 9 then count from the first number in row 10 to the fifth. Using 2^n to get the number of numbers in each row like we've done above we can add the number of numbers to know the total numbers we have from row 1 to row 9 as follows:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 = 511

As we've said previously, 0 is the first integer in the tree and should be removed to know the last number in row 9. This would be 510.

If 510 is the last number in row 9 is 510, then the first number in row 10 would be 511. Counting to the fifth number we get to 515. Thus the fifth number in row 10 using the number tree pattern is 515.

8 0
3 years ago
Suppose that Y takes on the values {0, 1, 2, 3}, each with probability 1/4. Take a random sample of 5 numbers from this distribu
arsen [322]

Answer:

The total number of samples that give this outcome is 5.

Step-by-step explanation:

Since Y takes values in {0,1,2,3}, For us to have that Y_1+Y_2+Y_3+Y_4+Y_5=1 implies that all of them are zero but one. The one that is non-zero necessarily is equal to 1. To calculate the number of samples that give this outcome is equivalent to counting the total number of ways in which we can pick the i-index such that Y_i=1. Note that in this case we can either choose Y1 to be 1, Y2 to be 1 and so on. So, the total number of samples that give this outcome is 5.

8 0
3 years ago
What is the volume of the square pyramid? Round to the nearest tenth.
goldfiish [28.3K]

Answer:

V=718.7\ cm^{3}

Step-by-step explanation:

we know that

The volume of the square pyramid is equal to

V=\frac{1}{3}b^{2}h

we have

b=14\ cm ----> the length of the base of the square pyramid

h=11\ cm ---> the height of the pyramid

substitute the values in the formula

V=\frac{1}{3}(14)^{2}(11)

V=718.7\ cm^{3}

4 0
3 years ago
270 is ninety percent of what number ?
harina [27]
The correct answer is 300.
6 0
3 years ago
Evaluate the expression when m=6 and n=39
IRINA_888 [86]

Answer: 639

Step-by-step explanation:

7 0
3 years ago
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