Answer:
Choice b.
.
Step-by-step explanation:
The highest power of the variable 
in this polynomial is 
. In other words, this polynomial is quadratic.
It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to 
.)
After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.
Apply the quadratic formula to find the two roots that would set this quadratic polynomial to . The discriminant of this polynomial is 
.
.
Similarly:
.
By the Factor Theorem, if 
is a root of a polynomial, then 
would be a factor of that polynomial. Note the minus sign between and 
.
- The root
corresponds to the factor 
, which simplifies to 
. - The root
corresponds to the factor 
, which simplifies to 
.
Verify that 
indeed expands to the original polynomial:
.
Answer:
Hi there!
The correct answer to this question is: x=3
Step-by-step explanation:
because these two triangles are similar, that means the hypotenuse are similar. which means you can set the sides equal to each other like this:
13 = 4x + 1 minus one on both sides and you should get 4x = 12 and then divide 4 on both sides and you should finally get x = 3
The question is incomplete. Here is the complete question.
As a part of city building refurbishment project, architects have constructed a scale model of several city builidings to present to the city commission for approval. The scale of the model is 1 inch = 9 feet.
The model includes a new park in the center of the city. If the dimensions of the park in the model are 9 inches by 17 inches, what are the actual dimensions of the park?
Answer: 81 feet by 153 feet
Step-by-step explanation: <u>Unit</u> <u>Scale</u> is a ratio comparing actual dimensions of an object to the dimensions of model representing the actual object.
In the refurbishment project, the unit scale is given by
1 inch = 9 feet
So, the dimensions of the new park in actual dimensions would be
1 inch = 9 feet
9 inches = x
x = 9.9
x = 81 feet
1 inch = 9 feet
17 inches = y
y = 17.9
y = 153 feet
The actual dimensions of the new park are 81 feet by 153 feet.
Answer:
y = -x + 9
Step-by-step explanation:
The line that passes through the points (-2,4) and (0,6) has a slope of 1, and a y intercept of 6. The equation to the first line is y = x + 6. and perpendicular lines always have the opposite, reciprocal slope of the other line. So the slope for the second line would be -1. A line with the slope of -1 and a point of (5,4) would contain the points (5,4) , (4,5) , (3,6) , (2,7) , (1,8) , and (0,9) , which is the y intercept for the second line. So the equation for the second line would be y = -x + 9
3m + 7y + 5 + -1m + -6y = 0
Reorder the terms:5 + 3m + -1m + 7y + -6y = 0
Combine like terms: 3m + -1m = 2m5 + 2m + 7y + -6y = 0
Combine like terms: 7y + -6y = 1y5 + 2m + 1y = 0
Solving5 + 2m + 1y = 0
Solving for variable m'.
Move all terms containing m to the left, all other terms to the right.
Add '-5' to each side of the equation.5 + 2m + -5 + 1y = 0 + -5
Reorder the terms:5 + -5 + 2m + 1y = 0 + -5
Combine like terms: 5 + -5 = 00 + 2m + 1y = 0 + -52m + 1y = 0 + -5
Combine like terms: 0 + -5 = -52m + 1y = -5
Add '-1y' to each side of the equation.2m + 1y + -1y = -5 + -1y
Combine like terms: 1y + -1y = 02m + 0 = -5 + -1y2m = -5 + -1y
Divide each side by '2'.m = -2.5 + -0.5y
Roots m=-2.5 + -0.5y
Simplify the following:3 m + 7 y + 5 - m - 6 y
Grouping like terms, 3 m + 7 y + 5 - m - 6 y = (7 y - 6 y) + (3 m - m) + 5:(7 y - 6 y) + (3 m - m) + 5
7 y - 6 y = y:y + (3 m - m) + 5
3 m - m = 2 m:Answer: y + 2 m + 5
Not sure what you need so I gave you Simplification and Roots.
