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.
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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)
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Answer:
3600
Step-by-step explanation:
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Answer:
I smile back :D
Step-by-step explanation:
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
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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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
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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
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.
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
pi = 3.14
r = 3
3.14 x 3x^2
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The answer :
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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(think about where the values go in the chart)
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Answer:
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Step-by-step explanation:
Answer:
it 14 inch because 1 foot is 12 inches, and 14 inches is greater
Step-by-step explanation:
Simplify the following:
a) 49 x 43
b) 69 x 62
c) 88 = 8
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Which of the following quadrilaterals meet all the criteria for parallelograms? Select all that apply.
Square
Rectangle
Trapezoid
Rhombus
Kite
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have a nice day :)
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
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Answers
Answer:
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Step-by-step explanation:
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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)
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2 9
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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
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Answers
Answer:
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Step-by-step explanation:
If the area is 144 that means each side of the square is 12 in. 12x4=48
Solve the following system
y=1.6x
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Answers
Answer:
The answer is (16.538461(repeated), 26.461538(repeated))
Answer:
x=16.538462 and y=26.461538
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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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