Simplify, write without absolute value sign<br><br>

A quadrilateral is graphed on a coordinate plane. If the vertices are A(2, 6), B(6, 0), C(2, –6) and D(–4, 0), which two points

Alik [6]

Check the picture below.

6 0

3 years ago

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Which polynomial can be simplified to a difference of squares

Mrrafil [7]

<h2>Hello!</h2>

The answer is:

The polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}=(4-1)(4+1)$

To solve this problem, we need to look for which of the given quadratic terms given for the different polynomials can be a result of squaring (elevating by two).

So,

Discarding, we have:

The quadratic terms of the given polynomials are:

$First=10a^{2}$

$Second=16a^{2}$

$Third=25a^{2}$

$Fourth=24a^{2}$

We have that the coefficients of the quadratic terms that can be obtained by squaring are:

$16a^{2} =(4a)^{2} \\\\25a^{2} =(5a)^{2}$

The other two coefficients are not perfect squares since they can not be obtained by square rooting whole numbers.

So, the first and the fourth polynomial are discarded and cannot be simplified to a difference of squares at least using whole numbers.

Therefore, we need to work with the second and the third polynomial.

For the second polynomial, we have:

$16a^{2} -4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2} =(4-1)(4+1)$

So, the second polynomial can be simplified to a difference of squares.

For the third polynomial, we have:

$25a^{2} +6a-6a+36=16a^{2}+36=(5a)^{2}+(6)^{2}$

So, the third polynomial cannot be simplified to a difference of squares since it's a sum of squares.

Hence, the polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}$

7 0

3 years ago

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A hot tub that holds 300 gallons of water drains at a rate of 8 gallons write an equation that represents how many gallons of wa

Salsk061 [2.6K]

Answer:the number of gallons of water left in the tub after it has drained for x minutes is 300 - 8x

Step-by-step explanation:

A hot tub that holds 300 gallons of water drains at a rate of 8 gallons.

Let x represent the number of minutes for which the hot tub has drained water.

If the hot tub drains 8 gallons of water per minute, it means that in x minutes, the number of gallons of water that the hot tub would have drained is 8x

Therefore, the number of gallons of water left in the tub after it has drained for x minutes would be

300 - 8x

7 0

3 years ago

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

12 cm long 10 cm wide area square meters

Stels [109]

Answer:

120 sqcm, is the answer

6 0

2 years ago

Simplify, write without absolute value sign | x+3 |, if x > 5