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3 years ago

Solve the quadratic equation by using a graphic approach. Round your answer to the hundredths place,

Mathematics

1 answer:

NeX [460]3 years ago

7 0

Answer:

Step-by-step explanation:

Well, I really don’t like graphic approaches in math, so hear ya go a formula:

Although there are easier ways that work for some quadratics, but this formula works for them all. (It is atached, have a look)

So,

( -(-2)+- square root of ((-2)^2-4(1)(-40)) ) / 2(1)

Note that for a hear I use one, since there is nothing in front of x.

( 2 + (12.8) ) / 2 < with plus

( 2 -(12.8) ) / 2 < with minus

X = 7.4

X = -5.4

(Quad equations have 2 answers)

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Can you help me with some steps to approach this proof .

Elis [28]

To prove two sets are equal, you have to show they are both subsets of one another.

• X ∩ (⋃ ) = ⋃ {X ∩ S | S ∈ }

Let x ∈ X ∩ (⋃ ). Then x ∈ X and x ∈ ⋃ . The latter means that x ∈ S for an arbitrary set S ∈ . So x ∈ X and x ∈ S, meaning x ∈ X ∩ S. That is enough to say that x ∈ ⋃ {X ∩ S | S ∈ }. So X ∩ (⋃ ) ⊆ ⋃ {X ∩ S | S ∈ }.

For the other direction, the proof is essentially the reverse. Let x ∈ ⋃ {X ∩ S | S ∈ }. Then x ∈ X ∩ S for some S ∈ , so that x ∈ X and x ∈ S. Because x ∈ S and S ∈ , we have that x ∈ ⋃ , and so x ∈ X ∩ (⋃ ). So ⋃ {X ∩ S | S ∈ } ⊆ X ∩ (⋃ ).

QED

• X ∪ (⋂ ) = ⋂ {X ∪ S | S ∈ }

Let x ∈ X ∪ (⋂ ). Then x ∈ X or x ∈ ⋂ . If x ∈ X, we're done because that would guarantee x ∈ X ∪ S for any set S, and hence x would belong to the intersection. If x ∈ ⋂ , then x ∈ S for all S ∈ , so that x ∈ X ∪ S for all S, and hence x is in the intersection. Therefore X ∪ (⋂ ) ⊆ ⋂ {X ∪ S | S ∈ }.

For the opposite direction, let x ∈ ⋂ {X ∪ S | S ∈ }. Then x ∈ X ∪ S for all S ∈ . So x ∈ X or x ∈ S for all S. If x ∈ X, we're done. If x ∈ S for all S ∈ , then x ∈ ⋂ , and we're done. So ⋂ {X ∪ S | S ∈ } ⊆ X ∪ (⋂ ).

QED

8 0

3 years ago

Find the perimeter of the figure to the nearest hundredth

Ostrovityanka [42]

Answer:

Step-by-step explanation:

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3 years ago

Change 11/22 to a ratio

mart [117]

The answers would be 1:2

4 0

4 years ago

Read 2 more answers

write an equation in slope-intercept form of the line that passes through (2,-2) and is parallel y=-x-2

Mekhanik [1.2K]

The y-intercept would be (0,0) so your equation would be y=(-x)+0, or y=(-x)

4 0

3 years ago

If a pair of regular dice are tossed once, use the expectation formula to determine the expected sum of the numbers on the upwar

Darya [45]

Answer:

The expected sum of the numbers on the upward faces of the two dice is 7.

Step-by-step explanation:

Consider the provided information.

If two pair of dice tossed the possible out comes are:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6,6)

Now we need to find the expected sum of the numbers on the upward faces of the two dice.

The expected sums can be:

Sum: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Prob: 1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36

As we know that the expectation of experiment can be calculated as:

$P(S_1)\cdot S_1+P(S_2)\cdot S_2+........+P(S_n)\cdot S_n$

Here S represents the numerical outcomes and P(S) is the respective probability.

Substitute the respective values in the above formula.

$=2\times\frac{1}{36}+3\times\frac{2}{36}+4\times\frac{3}{36}+5\times\frac{4}{36}+6\times\frac{5}{36}+7\times\frac{6}{36}+8\times\frac{5}{36}+9\times\frac{4}{36}+10\times\frac{3}{36}+11\times\frac{2}{36}+12\times\frac{1}{36}\\=\frac{252}{36}\\=7$

Hence, the expected sum of the numbers on the upward faces of the two dice is 7.

8 0

4 years ago