Question

1. which of the following is true about the expression below(check all that apply)$13x^{3}-5y^{4}+12xy^{3}-10y^{6}+3?$$square$ the coefficient of the first term is 3$square$ the coefficient of the second term is -5$square$ the coefficient of the third term is 6$square$ the coefficient of the fourth term is -10$square$ the are no negative coefficientsevaluate the real world polynomial. (1 point each)charlize wants to measure the depth of an empty well. she drops a ball into the well and measures how long it takes the ball to hit the bottom of the well. she uses a stopwatch, starting when she lets go of the ball and ending when she hears the ball hit the bottom of the well. the polynomial$h=-16t^{2}+6$ represents how far the ball has fallen after t seconds.4. how far has the ball fallen after one second?5. charlizes stopwatch measured a time of 3.2 seconds when the ball hit the bottom of the well. how deep is the well?evaluate the real world polynomial. (2 points)6. the polynomial expression $x(3x^{2}+25)(10x^{2}+4x+6)$, where x is in inches, can be used to model the number of cubic inches of cement that will be needed for a new porch. the cement contractor used 2 for value of x.complete the table to determine the dimensions, in inches, of the cement needed for the porch.|side|dimension|| ---- | ---- ||height (shortest length side)| ||width (medium length side)| ||length (longest length side)| |

Explanation:

Step1: Identify term coefficients

For $13x^3 - 5y^4 + 12xy^3 - 10y^6 + 3$:

• 1st term coefficient: $13$
• 2nd term coefficient: $-5$
• 3rd term coefficient: $12$
• 4th term coefficient: $-10$
• 5th term coefficient: $3$

Step2: Evaluate $h$ at $t=1$

Substitute $t=1$ into $h=-16t^2+6$:
$h=-16(1)^2+6=-16+6$

Step3: Evaluate $h$ at $t=3.2$

Substitute $t=3.2$ into $h=-16t^2+6$:
$h=-16(3.2)^2+6=-16(10.24)+6=-163.84+6$

Step4: Substitute $x=2$ into factors

For $x(3x^2+25)(10x^2+4x+6)$:

• $x=2$
• $3x^2+25=3(2)^2+25=12+25$
• $10x^2+4x+6=10(2)^2+4(2)+6=40+8+6$

Step5: Order calculated dimensions

Compare the three values: $2 < 37 < 54$

Answer:

For Question 3:

• The coefficient of the second term is -5
• The coefficient of the fourth term is -10

For Question 4:

$-10$ units

For Question 5:

$-157.84$ units (the negative sign indicates downward distance, so the well depth is 157.84 units)

For Question 6:

Side	Dimension
Width (medium length side)	37 inches
Length (longest length side)	54 inches

Total cubic inches of cement: $2 \times 37 \times 54 = 3996$ cubic inches