Over which interval(s) is g(x) = x2 + x - 12 positive?
A. -4 < x < 3
B. X <-4 and x > 3
C. X <-3 and x > 4
D. 3 < x < 4
Answers
Answer:
B. x < -4 and x > 3
Step-by-step explanation:
Factor and set = to 0
[tex]x^{2} + x - 12\\( x + 4)(x - 3)[/tex] = 0
x = - 4 or x = 3 I call these critical values
The two numbers would divide a number line into 3 intervals. Pick a value in one of the intervals and put it in the original expression. If it makes the function positive, then all the values in that interval make the function positive. If the value you picked makes the function negative, then the values in the other intervals will make the function negative. Let's pick the value of 0 and substitute it into the function
We get [tex]0^{2}[/tex] + 0 - 12 = -12 which is not positive. Therefore, all the values between -4 and 3 will make the function negative. So, the values less than -4 or greater than 3 will make the function positive. Therefore, B is the correct answer.
Another way to do this problem is to graph the function and see where the graph is above the x-axis. But, sometimes it is not easy to graph the function.
Related Questions
A rectangle with a width of w and a length of ? has a perimeter greater than 100.
Here is a graph that represents this situation.
Write an inequality that represents this situation.
Answers
Answer:
Let L = length
Let w = width
Perimeter = 2L + 2w
L = 100
Perimeter > 400
2(100) + 2w > 400
200 + 2w > 400 is the inequality
Subtract 200 on both sides of inequality.
2w > 200
w > 100
The width is at least 100 centimeters
The inequality that describes the perimeter of a rectangle is greater than 100 is 2(l + w) > 100.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
Given, A rectangle with a width of w and a length of l has a perimeter greater than 100.
We know the perimeter of a rectangle is 2(l + w).
∴ The perimeter of this rectangle is 2(l + w) > 100.
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Find the difference of 58.2–27.674.
a. 30.652
b. 30.526
c. 35.026
d. 35.620
Answers
Answer:
B
Step-by-step explanation:
You just subtract
33 points | dont guess please | no links
Answers
Answer:
Joe mama
Step-by-step explanation:
I need this quick!!What is the surface area of the square pyramid?
square units
Answers
Answer:
Im pretty sure its 16.64
Step-by-step explanation:
please answer fast everyone. Find the perimeter of a square that has a area of 144in
Answers
Answer:
48 in
Step-by-step explanation:
If the area is 144 that means each side of the square is 12 in. 12x4=48
what is 11/4-3/8= what is it or get me the right answer
Answers
Answer:
2 3/8 is the answer
Step-by-step explanation:
11/4 - 3/8
We will find the LCM of 4 and 8, which is 8.
We will do 11/4*8, which 8/4 = 2 and 2*11 = 22
Then we will do 3/8*8 = 8/8 = 1 = 3*1 = 3
So the answer will be 22-3 = 19
8 = 8
Mixed Fraction = 2 3/8
Identify 3 characteristics of the parabola = −2^2 − 3 + 5.
Answers
Answer:
−2
Step-by-step explanation:
−22−3+5
=−4−3+5
=−7+5
=−2
PLS BRAINLIEST
The two lines represent the distance traveled, over time, by two trains. Which train is traveling more quickly?
Answers
Answer:
A
Step-by-step explanation:
if the line is steeper it means that it increases quickly
Simplify the following:
a) 49 x 43
b) 69 x 62
c) 88 = 8
d) 78 - 76
I’ll give brainliest
Answers
Answer:
a) 2107
b) 4278
c)false equation but gessing its a + IT IS 96 or a - =80
d) 2
Step-by-step explanation:
a) 2107 b) 4278 c) i dont think anything can be done with this d)2 hope this helps,
Choose the longer measurement
14 inches 1 foot
Answers
Answer:
tue
Step-by-step explanation:
Answer:
it 14 inch because 1 foot is 12 inches, and 14 inches is greater
Step-by-step explanation:
35/k = 7/3 what does k equal
Answers
(6x10²)+(3x10³). in standard form
Answers
Answer:
3600
Step-by-step explanation:
What is the median?
A(18
B(27
C(33.2
D(34.5
Answers
Answer: 34.5
Step-by-step explanation:
First, write out all of the numbers from least to greatest.
which is (18,20,26,34,34,35,38,40,42,45)
Second, choose the number in the middle of the set of numbers you wrote out from least to greatest. (There are TWO numbers in this case, which are 34 and 35)
Lastly, since there are two numbers you add them both together and then divide by 2. (34+35=69 , 69 divided by 2 = 34.5)
i need help with this question please hurry it is almost due!
Answers
Answer:
I see nothing tho
Step-by-step explanation:
I need help thank you
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Answer:
30 - 60 - 90
Step-by-step explanation:
Please Help!! I will give 50 points and brainliest..
The question is attached below
Answers
Answer:
okey i will help you what is that
When Javier is 2, Arianna is 5. When Javier is 3, Arianna is 6.
When Javier is 8, Arianna will be 11. When Javier is 20, Arianna is 23.
Complete the table. Circle the letter of the equation that relates the age
of Arianna, y, to the age of Javier, x.
Answers
Answer:
Step-by-step explanation:
Arianna will always be 3 years older than Javier no matter how old he gets.
The table is given below.
The equation that relates the age of Arianna y to the age of Javier x is
y = x + 3
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
We can use the given information to complete the table as follows:
Javier(x) Arianna (y)
2 5
3 6
8 11
20 23
Now,
The equation that relates the age of Arianna, y, to the age of Javier, x.
We have,
y = mx + b, where m is the slope and b is the y-intercept.
We can use the first two points (2, 5) and (3, 6) to find the slope.
m = (6 - 5)/(3 - 2)
m = 1
Now,
The y-intercept,
(2, 5) = (x, y)
y = mx + b
5 = 1(2) + b
b = 3
Therefore,
The equation that relates the age of Arianna y to the age of Javier x is
y = x + 3
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marissa invested $800 at 6% per year compound interest for 3 years
Answers
Answer:
Her total would be: $944
Step-by-step explanation:
Given the polynomial function: f(x)=t(x+2)^2(x-5)(x+3), what is the degree of f(x)?
Answers
Answer:
3
Step-by-step explanation:
Every month, Mr. Jones pays his school loans through automatic payments (withdrawals) from his savings account. He pays the same amount on his school loan each month. At the end of the year, his savings account balance changed by -$3,183 from payments made on his school loan. What is the change in Mr. Jones savings account balance each month due to his school payment?
Answers
Answer:
i think the answer is 265.25
Step-by-step explanation:
because there are 12 months in a year so 3,183 ÷ 12 = 265.25
Which of the following quadrilaterals meet all the criteria for parallelograms? Select all that apply.
Square
Rectangle
Trapezoid
Rhombus
Kite
Answers
have a nice day :)
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Answers
Answer:
D
Step-by-step explanation:
pi = 3.14
r = 3
3.14 x 3x^2
= 28.26x^2
The answer :
the last one
Step-by-step explanation:
diameter = 6x so radius = 3x
3.14 * 3x * 3x = 28.26 x
Solve the following system
y=1.6x
2x + 2y = 86
Answers
Answer:
The answer is (16.538461(repeated), 26.461538(repeated))
Answer:
x=16.538462 and y=26.461538
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Answer:
good luck with maths! i know it can be tricky
Step-by-step explanation:
Answer:
0.056, 0.060, 0.560, 0.600, 6.00
Step-by-step explanation:
Place Value Chart
Tens ---- Ones --- Tenths ---- Hundredths ---- Thousandths
(think about where the values go in the chart)
Anybody wanna have a zaam? ID:945 739 7763/Passcode: BRAINLY
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Answer:
Step-by-step explanation:
sure ig (:
Answer:
She told me put my heart in the bag (In the bag)
And nobody gets hurt (Nobody)
Now I'm running from her love, I'm not fast (Fast)
So I'm making it worse (Making it worse)
Now I'm digging up a grave, from my past
I'm a whole different person (A whole different person)
It's a gift and a curse (A gift and a curse)
But I cannot reverse it
Step-by-step explanation:
I will mark brainliest
The snack that smiles back ____
Answers
Answer:
I smile back :D
Step-by-step explanation:
(20 POINTS) Will Give Brainliest If You Explain Your Answer:
The table represents the linear function f(x), and the equation represents the linear function g(x).
Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
x f(x)
0 1
2 9
4 17
g(x) = 3x + 1
A. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
B. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
C. The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
D. The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
Answers
Ruby and her children went into a bakery and she bought $18 worth of donuts and
cookies. Each donut costs $1 and each cookie costs $1.50. She bought a total of 15
donuts and cookies altogether. Graphically solve a system of equations in order to
determine the number of donuts, , and the number of cookies, y, that Ruby bought
Answers
4 cookies and 5 donuts
Answer:
1x + 1.5y = 18
x + y = 15
She bought 9 donuts and 6 cookies.
Please help me solve this
Answers
Answer:
1st pic:
x = 60
y = 50
2nd pic:
y = 8
∠W = 28
∠Y = 128 degrees
∠X = 24
Step-by-step explanation:
first pic:
to find x, subtract 120 from 180 ⇒ 180 - 120 = 60
to find y, add 60 & 70 & subtract the sum from 180 ⇒ 180 - (60 + 70) = 50
2nd pic:
to find ∠Y, subtract 52 from 180:
180 - 52 = 128
to find y, use the following equation:
3y + 4y - 4 + 128 = 180
combine like terms:
7y + 124 = 180
subtract 124 from each side:
7y + 124 - 124 = 180 - 124
7y = 56
divide 7 on both sides:
[tex]\frac{7y}{7} = \frac{56}{7}[/tex]
y = 8
now we can find angles W and X
∠W = 4y - 4
we know that y = 8 so just substitute 8 for y
∠W = 4 x 8 - 4
∠W = 28
∠X = 3y
likewise, subtitute 8 for y
∠X = 3 x 8
∠W = 24
to check, add all angles and if they add up to 180, then its right:
24 + 28 + 128 = 180
180 = 180
Step-by-step explanation:
here's your solution
=> for first figure , (x + 120° ) = 180° [ linear pair]
=> x = 180° - 120°
=> x = 60°
=> now , we know sum of all angles of traingle = 180°
= >so, 60° + 70° + y = 180°
=> y= 180° - 130°
=> y = 50
now in figure second
=> 4y - 4 + 3y = 52° [ exterior angle equal to sum of two opposite interior
=> 7y - 4 = 52°
=> 7y = 52° + 4°
=> 7y = 56°
=> y = 56°/7
=> 8°
hope it helps
What color is a carrot
Answers
Answer:
uh i think its a carrot uh
Step-by-step explanation:
uhh
Answer:
joe biden
Step-by-step explanation: