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shepuryov [24]
2 years ago
14

2,036,017 expanded form exponents

Mathematics
2 answers:
Tresset [83]2 years ago
5 0
2,000,000 + 30,000 + 6,000 + 10 + 7
liq [111]2 years ago
3 0
2 × 10^{6}
+ 0 × 10^{5}
+ 3 × 10^{4}
+ 6 × 10^{3}
+ 0 × 10^{2}
+ 1 × 10x^{1}
+ 7 × 10^{0}
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Emma has 18 yellow flowers and 30 white flowers. She wants to split them into vases in equal groups. What is the largest number
8090 [49]
6 groups,3 yellow and 5 white in each group
3 0
3 years ago
Read 2 more answers
−2x=x^2−6
Iteru [2.4K]

Step-by-step explanation:

Example 1

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution

f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2

f(2) = 23 − 3×22 – 2×2 + 4 = −4

f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

f(4) = 43 − 3×42 – 2×4 + 4 = 12

f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.

Now we can factorise our expression as follows:

x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0

It now remains for us to solve the quadratic equation.

x2 − 2x − 4 = 0

We use the formula for quadratics with a = 1, b = −2 and c = −4.

We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:

x = 1

x = 1 + Ö5

x = 1 − Ö5

Example 2

We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.

First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.

f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution

f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4

f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4

f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.

The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.

First divide by x + 2

Now divide the resulting cubic factor by x − 1.

We have now factorised

f(x) = x4 − x3 − 5x2 + 3x + 2 into

f(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation

x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1.

Now we have found a total of four solutions. They are:

x = 1

x = −2

x = 1 +

x = 1 −

Sometimes we can solve a third degree equation by bracketing the terms two by two and finding a factor that they have in common.

6 0
3 years ago
Read 2 more answers
A random sample of 84 students at a university showed an average age of 22 years and a sample standard deviation of 3 years. Fin
Debora [2.8K]

Answer:

The margin of error for the 94% confidence interval is 0.6154.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population mean is:

CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

The margin of error of this interval is:

MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

The critical value of <em>z</em> for 94% confidence level is, <em>z</em> = 1.88.

Compute the margin of error for the 94% confidence interval as follows:

MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

          =1.88\times\frac{3}{\sqrt{84}}\\\\=0.6154

Thus, the margin of error for the 94% confidence interval is 0.6154.

7 0
2 years ago
Marge and Kimo equally Shared 1/4 of a pie that was left over. What fraction of the original pie did each friend get? Use the pi
luda_lava [24]

Answer:

1/8

Step-by-step explanation:

1/4 divided by 2

8 0
2 years ago
Solve x2 – 10x + 25 = 35 for x
ira [324]

Answer:

  x = 5 ± √35

Step-by-step explanation:

Rewrite the left side as a square, then take the square root. Finally, add 5.

  (x -5)² = 35

  x -5 = ±√35

  x = 5 ±√35

4 0
2 years ago
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