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MAXImum [283]
3 years ago
9

If the roots of a quadratic equation are 1±√5, then the product of the roots is

Mathematics
2 answers:
Drupady [299]3 years ago
5 0
The plus-minus sign represents that there are two possible outcomes.

In this case, we have 1 \pm \sqrt{5}. When we branch out the possibilities we got 2 values: 1 + \sqrt{5} and 1 - \sqrt{5}

Those are the roots of this equation. When they ask their product, they want you to multiply both numbers.

When we multiply them: (1 + \sqrt{5}) \times( 1 - \sqrt{5})

When we FOIL the we get: 1 \times 1 - 1 \times \sqrt{5} + 1 \times \sqrt{5} - \sqrt{5} \times \sqrt{5}

Simplify:
1 - \sqrt{5} + \sqrt{5} - 5
1 - 5 = 6

So the product of the two roots of this equation is 6.
Komok [63]3 years ago
4 0
The two roots would be 6
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Complete the proof for the following conjecture.
Ray Of Light [21]

Answer:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD         Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                         Given

BD+CD=AB+BD                            Substitution Property

CD=AB                                         Subtraction Property

AB=CD                                         Symmetric Property

Step-by-step explanation:

By segment addition postulate, we can say the following two equations:

AC+CD=AD and AB+BD=AD.

By either substitution/transitive property, you can say AC+CD=AB+BD.

You are given AC=BD, so we use substitution and write AC+CD=AB+AC.

After using subtraction property (subtracting both sides by AC), you obtain CD=AB.

By symmetric property, you may say AB=CD.

So let's write it into the 2 column-proof you have there:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD        Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                          Given

BD+CD=AB+BD                             Substitution Property

CD=AB                                          Subtraction Property

AB=CD                                          Symmetric Property

Properties/Postulates used:

Transitive property which says:

If a=b and b=c, then a=c.

Substitution property which says:

If a=b, then b can be substituted(replaced with) for a.

Subtraction property which says:

a=b implies a-c=b-c.

Segment Addition Postulate says:

If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.

3 0
3 years ago
What is the measure of the corresponding central angle for XY in radians?
beks73 [17]

Answer:

4 radians

Step-by-step explanation:

Arc Length (Radians) = rθ

Given Arc Length XY  = 40cm and radius, r = 10cm,

we will substitute these 2 values into the formula to find θ.

(10)θ  = 40

θ = 40 / 10

= 4 radians

5 0
2 years ago
Read 2 more answers
You are making a new type of deodorant from two different mixtures the first mixture is 30% smell proof and the second mixture i
Readme [11.4K]

Answer:

600 L of 30% proof and 400 L of 80% proof is needed

Step-by-step explanation:

Let the amount of 30% smell proof be x while that of 80% smell proof is y

Then;

x + y = 1000 •••••(i)

Also;

30% of x + 80% of y = 50% of 1000

0.3x + 0.8y = 500 •••••(ii)

From i, x = 1000 - y

Put this into ii

0.3(1000-y) + 0.8y = 500

300 - 0.3y + 0.8y = 500

0.5y = 500-300

0.5y = 200

y = 200/0.5

y = 400 L

But x = 1000 - y

x = 1000 - 400 = 600 L

3 0
3 years ago
What is the value of n where 131 is the nth term of the sequence -2, 5, 12…..?
Inessa [10]
D means common difference which is the last term minus second last term .
and u can use this formula only if there is a common difference.

6 0
3 years ago
There are 8 2/3 pounds of walnuts in a container which will be divided equally into containers that hold 1 1/5 pounds this would
aev [14]

we'll do the same as before, turning the mixed fractions to improper and do the division, keeping in mind that is simply asking how many times 1⅕ goes into 8⅔.


\bf \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}\\\\\\\stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\cfrac{26}{3}\div \cfrac{6}{5}\implies \cfrac{26}{3}\cdot \cfrac{5}{6}\implies \cfrac{130}{18}\implies \cfrac{126+4}{18}\implies \cfrac{126}{18}+\cfrac{4}{18}\\\\\\\boxed{7+\cfrac{4}{18}}\implies 7\frac{4}{18}

7 0
3 years ago
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