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Mashutka [201]
2 years ago
5

Which statements are true?

Mathematics
1 answer:
ludmilkaskok [199]2 years ago
3 0

Answer:

30x^4−12x^3=6x^3(5x−2) = True

4x^2+10x=2x(2x+5) = True

100x^3+5=5x^3(20x+1) = False

8x^3−6x=2x^3(4−3x3) = False

Step-by-step explanation:

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Solve equation by using the quadratic formula.
Sati [7]

Answer: 1:  x=3, x=1

2:  x= -5

3:  There are 2 real solutions.

4:  There are 2 real solutions.

5:  There are no real solutions.

6.  There is 1 real solution.

7.  

8.  x= -6, x = -2

9.  x = -1/6, x=1

10.  

Explanation:

1.  The quadratic formula is

Substituting our known information we have:

2.  Rewriting the quadratic in standard form we have x²+10x-25=0. Substituting this into the quadratic formula gives us:

3.  The discriminant is b²-4ac.  For this problem, that is 20²-4(-4)(25)=400--400=800.  Since this is greater than 0, there are 2 real solutions.

4.  The discriminant in this problem is 7²-4(2)(-15)=49--120=49+120=169.  This is greater than 0, so there are 2 real solutions.

5.  The discriminant in this problem is 1²-4(-2)(-28)=1-224=-223.  Since this is less than 0, there are no real solutions.

6.  If the discriminant of a quadratic is 0, then by definition there is 1 real solution.

7.  Rewriting the quadratic we have 3x²-4x-2=0.  Using the quadratic formula we have:

8.  Factoring this trinomial we want factors of 12 that sum to 8.  6*2 = 12 and 6+2=8, so those are our factors.  This gives us:

(x+6)(x+2)=0

Using the zero product property we know that either x+6=0 or x+2=0.  Solving these equations we get x= -6 or x= -2.

9.  Factoring this trinomial we want factors of 6(-1)=-6 that sum to -5.  (-6)(1)=-6 and -6+1=-5, so this is how we "split up" the x term:

6x²-6x+1x-1=0

We group together the first two and the last two terms:

(6x²-6x)+(1x-1)=0

Factor the GCF out of each group.  In the first group, that is 6x:

6x(x-1)+(1x-1)=0

In the second group, the GCF is 1:

6x(x-1)+1(x-1)=0

Both terms have a factor of (x-1), so we can factor it out:

(x-1)(6x+1)=0

Using the zero product property, we know either x-1=0 or 6x+1=0.  Solving these equations we get x=1 or x=-1/6.

10.  Substituting our information into the quadratic formula we get:

Step-by-step explanation:

5 0
2 years ago
A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the
Ira Lisetskai [31]

Answer:00-99

Step-by-step explanation:

7 0
3 years ago
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Solve and show work: <br> f(300) = 90 + 0.11x
Vinil7 [7]
300-90= 90-90 +0.11x                                                                                              210=0.11x                                                                                                               210/.11     0.11x/0.11
   1909 = x I think but Idk
6 0
3 years ago
What is the value of 324 + 435 + 546 when written in base 7?
Arada [10]
<span>The sum of 324, 435, and 546 is 1305. If this number were to be expressed by the base of 7, we would need to figure out what value of exponent would satisfy the requirement. This can be done by setting up an equation where 7 to the power of x must equal 1305. Using logarithms, one can solve for x and find it to be 3.6866853. Thus the sum of the aforementioned numbers, expressed in by the base of 7, is 7^3.6866853.</span>
6 0
3 years ago
On factorising 14pq + 35pqr. we get?
Anna71 [15]

Answer:

7pq( 2 + 5r)

Step-by-step explanation:

4 0
2 years ago
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