Me answer and explain step by step for
#10 and
#11

10. C, Quadratic trinomial

11. D, (6d - 1) (2d + 1)

Step-by-step explanation:

10. 7x² - 5x + 9 is a quadratic trinomial as there are 3 terms in the expression (trinomial)

11. to factor 12d² + 4d - 1 we can use the quadratic formula, factoring, or completing the square. when the first term is not equal to 1, it may be easier to use the quadratic formula or factoring by grouping. in this example, i will use factoring by grouping which is another way to factor. I will write the middle term (4d) as a subtraction using 2 numbers that when multiplied together give us 12. these 2 numbers are 6 and 2, as 6 x 2 = 12 and 6 - 2= 4

we have the following:

12d² + 6d - 2d - 1 < group 2 factors together

(12d² + 6d) (-2d - 1) < solve for each factor by factoring

to factor 12d² + 6d, we need to find a common factor between the 2 numbers. both have the number 6 in common and the letter d, so we can factor out 6d from the expression

6d(2d + 1)

now we will factor (-2d - 1). we want to get 2d + 1 as a result of the factorization we do, so we need to find a number that gives us that. both -2d and -1 have a -1 in common, so we can factor out a -1 from the expression

-1(2d + 1)

we now have the following:

6d(2d + 1) - 1(2d + 1) < since we have 2 (2d + 1), we only need to write one. we can combine 6d and -1 into one factor

(6d - 1) (2d + 1) is our answer. the answer choice would be D

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!