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jeyben [28]
3 years ago
15

Please help!! More pages after this one

Mathematics
1 answer:
Mademuasel [1]3 years ago
3 0
1) Since x = -4 and x = -6 are zeros, then, by definition, (x + 4) and (x + 6) are factors of the polynomial. Another way in understanding this is that when x = -4, there would be no remainders.

Thus, we can simply write it as: P(x) = (x + 4)(x + 6) = x² + 10x + 24 (ie C)

2) Using the discriminant, we can find whether a quadratic has two, one, or no roots at all. Symbolised as delta (Δ), the discriminant formula goes as follows:

Δ = b² - 4ac
Thus, if we move the 3 to the other side, we get:
Δ = (-5)² - 4(3)(-10) > 0
Since Δ > 0, then there lies two solutions.

To find rationality or irrationality, we need to check whether or not the square root of the discriminant is an integer or not. If the square root of the discriminant is not an integer, we have irrational roots.

Thus, we've worked out that the discriminant is 145. But 145 is not a perfect square, so when we take the square root of it, we get irrational roots.
Hence, we have two irrational roots.

3) Since we have a fraction, we know that the denominator cannot be zero. Thus, to find places where undefined x-values occur, we need to let the denominator equal to zero:

x² - 16 = 0
x² = 16
x = 4 and -4

These are the restricted values for x, since x cannot equal to 4, or -4.
Hence, your answer is x = 4, -4

4) We can expand and move everything to the LHS.
2(x + 2)² - 32 = 0
2(x² + 4x + 4) - 32 = 0
2x² + 8x + 8 - 32 = 0
2x² + 8x - 24 = 0

We can factorise 2 outside.
2(x² + 4x - 12) = 0

x² + 4x - 12 = 0

We can factorise this further.
(x + 6)(x - 2) = 0

x = -6, 2 are our solutions.
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ANSWER ASAP!!!<br> PLS HELP. <br> ANSWER BOTH QUESTIONS FOR ALL POINTS.
iVinArrow [24]

Answer:

128°

Step-by-step explanation:

x + 154° + 78° = 360° {being complete turn}

x + 232° = 360°

x = 360° - 232°

x = 128°

8 0
3 years ago
Read 2 more answers
Theorem: A line parallel to one side of a triangle divides the other two proportionately.
Kisachek [45]

Answer:

Segment BF = 16

Step-by-step explanation:

The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately

The given theorem is the Triangle Proportionality Theorem

According to the theorem, given that segment DE is parallel to segment BC, we have;

\dfrac{AD}{BD} = \dfrac{AE}{EC}

Therefore;

BD = \dfrac{AD}{\left(\dfrac{AE}{EC} \right) }  = AD \times \dfrac{EC}{AE}

Which gives;

BD = 6 \times \dfrac{18}{12}= 9

Similarly, given that EF is parallel to AB, we get;

\dfrac{AE}{EC} = \dfrac{BF}{FC}

Therefore;

BF = FC \times \dfrac{AE}{EC}

Which gives;

BF = 24 \times \dfrac{12}{18} = 16

Therefore, the statement that can be proved using the given theorem is segment BF = 16.

8 0
3 years ago
A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?
Troyanec [42]
X + x+1 + x + 2 = 20
3x + 3 = 20
3x = 17 but can't start with x = 6 because 6+7+8 > 20,
so have start with 5 + 6 + 7 = 18 are the 3 sides.
3 0
2 years ago
i have been trying to solve this compound and double angle question please help me find the answer to these question guys​
natali 33 [55]

Answer:

These type of questions are super tricky b/c you have to remember all the different versions of the identities, and then they put the question in some odd form,  I feel like this should land math professors in jail , for dishonesty , b/c it's really a form of "how tricky can I make a question and still have a way to solve it"   anyway,

Step-by-step explanation:

a)

next the question asks   1-cos 2A   and this is total abuse of notation.   the way this should be written is   1- cos( 2A)  so we know that the A is part of the cosine functions input... btw.. in any computer program,  it would never ever let you get away with that top form of the expression.  :/   anyway... I keep ranting.. huh... sorry  :P

1-cos(2A) is an odd form of the identity  1/2(1-cos(2A) = sin^{2}(A)  the 1/2 is missing but we can add that pretty easy, we just have to remember to take it out too. I usually forget to do that. and my professor marks me off completely,  totally wrong, but I just miss one small thing  :/  anyway....

our 1-cos(2A) needs the 1/2 added to it.  or if we move that 1/2 to the other side it looks like  2*sin^{2}(A)  = 1-cos(2A)  and this is that "odd" from of the identity that I was talking about.  

next let's deal with sin(2A)  it has an identity of  2 sin(A)cos(A) which is really nice for us b/c it will cancel out the 2 in then numerator for us, nice !

now our fraction looks like  [2* sin^{2}(A)] / 2 sin(A)cos(A)

so cancel out one of the sines

2*sin(A) / 2 cos(A)

cancel the 2s

Sin(A) / Cos(A) = Tan(A)

nice  it worked out  :P

b)

by the above that we just worked out, then

Tan(15) = Sin(15) / Cos(15)

I had to look up what sin of 15 is b/c it's not one of those special angles but it does have an exact form of

Sin(15) = (√3 - 1) / 2√2

Cos(A) = (√3 + 1) / 2√2

you can use rule of Cos(A-B) = Cos(A)Cos(B)+Sin(A)Sin(B) to get the above and a similar rule for Sin(A-B)

back to our problem,  the 2√2 will cancel out

then we have

Tan(15) =  (√3 - 1) /(√3 + 1)

in the form that is above that's exact, the roots could be approximated but i'll just leave that in the form that is exact.  Most math professors like that form.  

 

4 0
2 years ago
I need the answer for −n+(−4)−(−4n)+6
antoniya [11.8K]
The answer for <span>−n+(−4)−(−4n)+6 is 2

</span>
5 0
3 years ago
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