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FrozenT [24]
2 years ago
5

Find all positive and negative integers b such that x2 +bx+6 factors

Mathematics
1 answer:
kumpel [21]2 years ago
4 0

Answer:

b = - 5 , - 7 , 5 , 7

Step-by-step explanation:

Standard quadratic equation is of the form :

ax² + b x + c , where b = p + q and c = pq

Where p and q are factors of c.

Therefore , we will consider the factors of 6.

Factors of 6 = ( -1 , -6 ) , ( -2 , -3 ) , ( 1, 6 ) , ( 2 , 3)

x² + bx + 6

b = p + q

So, b = - 7 , -5, 7 , 5

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Plot the vertex, focus, and directrix for the parabola represented by this equation. X=-1/12(y-2)^2+1
alukav5142 [94]

The vertex of the parabola is (1, 2), focus of the parabola is  (-2, 2), and directrix x = 4.

<h3>What is a parabola?</h3>

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have a parabola equation:

\rm x = -\dfrac{1}{12}(y-2)^2+1

The standard form of the parabola:

\rm x = \dfrac{1}{4(f-h)}(y-k)^2+h

(h, k) is the vertex of the parabola and (f, k) is the focus.

\rm x = \dfrac{1}{4(-2-1)}(y-2)^2+1

h = 1, k =2, and f = -2

The directrix is x = 4

Thus, the vertex of the parabola is (1, 2), focus (-2, 2), and directrix x = 4.

Learn more about the parabola here:

brainly.com/question/8708520

#SPJ1

5 0
2 years ago
Graph f(x)=−0.5x+3. Use the line tool and select two points to graph the line.
NikAS [45]

Answer: These are some points of the grahp:

(-2,4)

(0, 3)

(2, 2)


Explanation:


1) f(x) =  -0.5x + 3, is the equation of the form y = mx + b


2) y = mx + b is slope-intercept  equation of a line where the slope is m and the y-intercept is b, so, f(x) = - 0.5x + b has slope m = -0.5 and y-intercept b = 3.


3) To graph f(x) = -0.5x + 3, follow these steps:

  • draw two perpedicular axis: vertical axis, labeled y, and horizontal axis, labeled x.
  • draw marks on each axis, each mark equivalent to one unit.
  • the intersection point of the vertical and horizontal axis is the origin, i.e. point (0,0).
  • you can make a table with two or more points:

        x       f(x) = - 0.5x + 3

        -2         4

        0          3

        2          2

        4           1

        6          0


4) You can see the graph in the figure attached, and select any of the points on the line either by using the table or by using the equation f(x) = -0.5x + 3.

8 0
3 years ago
Read 2 more answers
Omealio received a grade of 80 on Exam 1. If his grade in Exam 2 was 15% higher, what was his grade in Exam 2? Please help
ExtremeBDS [4]

Answer:

well if the max grade he could get was 100 then you need to find 15% of 100 which is 15, after that add 15 to 80 and you get 95.

his grade for exam 2 was 95

Step-by-step explanation:

15% of 100 = 15

80 + 15 = 95

7 0
3 years ago
Read 2 more answers
Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression.
vitfil [10]

Answer:

(A) e^2

(b) e^{-3}

(c) e^2

(d) e^3

Step-by-step explanation:

We have given expression and we have to simplify the expression using exponent property

(A) (\frac{1}{e})^{-2}

So (\frac{1}{e})^{-2}=\frac{1}{e^{-2}}=e^2

(b) (\frac{e^5}{e^2})^{-1}

So (\frac{e^5}{e^2})^{-1}=(e^{3})^{-1}=e^{-3}

(c) \frac{e^5}{e^3}

So \frac{e^5}{e^3}=e^2

(d) \frac{1}{e^{-3}}=e^3

7 0
2 years ago
Rewrite the decimal fraction as a decimal number.
Sergio039 [100]

Answer:

8.025

Step-by-step explanation:

If you count the zeros in 1000, it's three. Count three starting from the back of 25. Add 0 in front of 25 to make it a three digit number. You then put the decimal point with the whole number.

7 0
3 years ago
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