$5+m > 4\ or\ 7m < -35\\\\\#1\\5+m > 4\ \ \ \ |subtract\ 5\ from\ both\ sides\\\\m > -1\\\\\#2\\7m < -35\ \ \ \ \ |divide\ both\ sides\ by\ 7\\\\m < -5\\\\Answer:m\in(-\infty;-5)\ \cup\ (-1;\ \infty)$

8 0

3 years ago

What is the equation, in standard form, of a parabola that models the values in the table? x~ -1 0 2

Inessa05 [86]

<h2>Steps</h2>

Standard Form Equation: f(x) = ax² + bx + c

So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):

$5=a*0^2+b*0+c\\5=c$

Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):

$12=a*(-1)^2+b*(-1)+5\\12=a-b+5\\7=a-b$

Next, plug (2,15) into the standard form equation and simplify:

$15=a*2^2+b*2+5\\15=4a+2b+5\\10=4a+2b\\5=2a+b$

Now, with our last two simplified equations we will create a system of equations:

$7=a-b\\5=2a+b$

Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:

$12=3a$

From here, we can solve for the a variable. With it, just divide both sides by 3:

$4=a$

Now that we know the value of a, plug it into either equation to solve for the b variable:

$7=4-b\\3=-b\\-3=b\\\\5=2(4)+b\\5=8+b\\-3=b$

<h2>Answer</h2>

Putting all of our obtained values together, your final answer is:

$f(x)=4x^2-3x+5$

8 0

2 years ago

Please help me solve this

Tpy6a [65]

Answer:

x = 49

top angle = 45

bottom angle = 108

far right angle = 27 degrees

angle 1 = 88 degrees

angle 2 = 57 degrees

angle 3 = 35 degrees

angle 4 = 145 degrees

Step-by-step explanation:

you can find the far right angle by taking 153 and subtracting it from 180:

⇒ 180 - 153 = 27 degrees

you can find x by the following equation ⇒ x - 4 + 2x + 10 + 27 = 180

combine like terms ⇒ 3x + 33 = 180

subtract 33 from each side ⇒ 3x + 33 - 33 = 180 - 33 ⇒ 3x = 147

divide 3 on each side: ⇒ $\frac{3x}{3} = \frac{147}{3}$

x = 49

to find the top and bottom angles, substitute 49 for x:

top angle : x - 4

49 - 4 = 45 degrees

bottom angle: 2x + 10

2 x 49 + 10 = 108 degrees

angle 1:

⇒ 180 - 92 = 88 degrees

angle 2:

⇒ 180 - 123 = 57 degrees

angle 3:

⇒ 180 - (88 + 57) = 35 degrees

angle 4:

⇒ 180 - 35 = 145 dgerees

4 0

2 years ago