Without factoring, determine which of the graphs represents the function g(x)=21x2+37x+12 and which represents the function h(x)=21x2−37x+12. Explain your reasoning. The graph of represents the function g(x)=21x2+37x+12. The graph of represents the function h(x)=21x2−37x+12. Because c is positive, the constant terms in each factor must have signs. Because the function has a positive value for b, the constant terms in each factor will both be which results in Response area roots, and the graph of Response area has two Response area x-intercepts. Because the function has a negative value for b, the constant terms in each factor will both be which results in Response area roots, and the graph of Response area has two Response area x-intercepts.
Answers
Answer:
The graph which represents the function g(x) = 21·x² + 37·x + 12, is described as follows;
Because 'c' is positive, the constant terms in each factor must have the same signs
Because the function has a positive value for 'b', the constant terms in each factor will both be positive which results in negative roots and the graph of the function, g(x) = 21·x² + 37·x + 12, has two negative x-intercepts
The graph which represents the function h(x) = 21·x² - 37·x + 12, we have is described as follows;
Because 'c' is positive, the constant terms in each factor must have the same signs
Because the function has a negative value for 'b', the constant terms in each factor will both be negative which results in positive roots and the graph of the function, g(x) = 21·x² + 37·x + 12, has two positive x-intercepts
Step-by-step explanation:
The given functions are;
g(x) = 21·x² + 37·x + 12
h(x) = 21·x² - 37·x + 12
For the graph which represents the function g(x) = 21·x² + 37·x + 12, we have
Because 'c' is positive, the constant terms in each factor must have the same signs
Because the function has a positive value for 'b', the constant terms in each factor will both be positive which results in negative roots and the graph of the function, g(x) = 21·x² + 37·x + 12, has two negative x-intercepts
For the graph which represents the function h(x) = 21·x² - 37·x + 12, we have
Because 'c' is positive, the constant terms in each factor must have the same signs
Because the function has a negative value for 'b', the constant terms in each factor will both be negative which results in positive roots and the graph of the function, g(x) = 21·x² + 37·x + 12, has two positive x-intercepts
Related Questions
What is the percent of decrease from 500,000 to 200,000?
Answers
Answer:
500,000 to 200,000 is a 60% decrease.
Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain
Answers
Answer:
[tex]Sum = -81[/tex]
Step-by-step explanation:
See the comment for complete question.
Given
[tex]c = 36[/tex] ----- Constant
No coefficient of x^2
Required:
Determine the sum of all distinct positive integers of the coefficient of x
Reading through the complete question, we can see that the question has 3 terms which are:
x^2 ---- with no coefficient
x ---- with an unknown coefficient
36 ---- constant
So, the equation can be represented as:
[tex]x^2 + ax + 36 = 0[/tex]
Where a is the unknown coefficient
From the question, we understand that the equation has two negative integer solution. This can be represented as:
[tex]x = -\alpha[/tex] and [tex]x = -\beta[/tex]
Using the above roots, the equation can be represented as:
[tex](x + \alpha)(x + \beta) = 0[/tex]
Open brackets
[tex]x^2 + (\alpha + \beta)x + \alpha \beta = 0[/tex]
To compare the above equation to [tex]x^2 + ax + 36 = 0[/tex], we have:
[tex]a = \alpha + \beta[/tex]
[tex]\alpha \beta = 36[/tex]
Where: [tex]\alpha, \beta <0[/tex] and [tex]\alpha \ne \beta[/tex]
The values of [tex]\alpha[/tex] and [tex]\beta[/tex] that satisfy [tex]\alpha \beta = 36[/tex] are:
[tex]\alpha = -1[/tex] and [tex]\beta = -36[/tex]
[tex]\alpha = -2[/tex] and [tex]\beta = -18[/tex]
[tex]\alpha = -3[/tex] and [tex]\beta = -12[/tex]
[tex]\alpha = -4[/tex] and [tex]\beta = -9[/tex]
So, the possible values of a are:
[tex]a = \alpha + \beta[/tex]
When [tex]\alpha = -1[/tex] and [tex]\beta = -36[/tex]
[tex]a = -1 - 36 = -37[/tex]
When [tex]\alpha = -2[/tex] and [tex]\beta = -18[/tex]
[tex]a = -2 - 18 = -20[/tex]
When [tex]\alpha = -3[/tex] and [tex]\beta = -12[/tex]
[tex]a = -3 - 12 = -15[/tex]
When [tex]\alpha = -4[/tex] and [tex]\beta = -9[/tex]
[tex]a = -4 - 9 = -13[/tex]
At this point, we have established that the possible values of a are: -37, -20, -15 and -9.
The required sum is:
[tex]Sum = -37 -20 -15 - 9[/tex]
[tex]Sum = -81[/tex]
write the number that is 6 less then 8000
Answers
Answer:
8000-6=7994 is the required number
17 is a prime number. What can you conclude from this?
Answers
Answer:
17 can't be divided into 2 and it's a odd number.
Answer:
17 is a prime number because it is only divisible by 1 and 17 ..
Victoria opens a saving account with $200. She earns 1.6% interest. How much will she have after 4 years?
Answers
Answer:
i think it is 212.8
Step-by-step explanation:
Answer: it’s 212.8
Step-by-step explanation:
g The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people. Assume that this trend is linear and the population has been growing like this since 2000. a. Write a function for the population, P, in terms of the number of years since 2000, ????. (6 points) b. What is the slope of the function and what does it represent in the context of the problem. Include units. (5 points) c. What is the vertical intercept of the function and what does it represent? Include units (5 points) d. What do you believe the population was in 2015?
Answers
Answer:
a) [tex]P(t) = 11500 + 425t[/tex]
b) The slope is of 425 people, which is by how much the population increases each year.
c) The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d) 17,875 people.
Step-by-step explanation:
A linear function that measures population after t years has the following format:
[tex]P(t) = P(0) + at[/tex]
In which P(0) is the vertical intercept, which represents the initial population, and a is the slope, which represents the yearly population.
a. Write a function for the population, P, in terms of the number of years since 2000.
The first step is finding the slope.
Finding the slope:
The slope is the change in the output divided by the change in the input, during a period of time.
The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people.
This means that in 2009 - 2005 = 4 years, the population increased by 15325 - 13625 = 1700.
So the slope is
[tex]a = \frac{1700}{4} = 425[/tex]
So
[tex]P(t) = P(0) + 425t[/tex]
Finding the initial population:
We want to find P(0), which is the population in 2000. The population of Little Townville in 2005 was 13,625 people, which means that [tex]P(5) = 13625[/tex]. So
[tex]P(t) = P(0) + 425t[/tex]
[tex]13625 = P(0) + 425*5[/tex]
[tex]P(0) = 13625 - 425*5[/tex]
[tex]P(0) = 11500[/tex]
So
[tex]P(t) = 11500 + 425t[/tex]
b. What is the slope of the function and what does it represent in the context of the problem. Include units.
The slope is of 425 people, which is by how much the population increases each year.
c. What is the vertical intercept of the function and what does it represent? Include units
The vertical intercept is of 11500 people, and it represents the population of Little Townville in the year 2000.
d. What do you believe the population was in 2015?
2015 is 2015 - 2000 = 15 years after 2000, so this is P(15).
[tex]P(15) = 11500 + 425*15 = 17875[/tex]
17,875 people.
Write the recurring decimal 0.5 as a fraction in its simplest form
Answers
Answer:
Step-by-step explanation:
0.555... = 5/9
The flag football league eventually had 72 kids sign up for the spring season after putting six teams together from the original amount of sign ups they took took it off of everything to make the final rosters how many kids were on the original rosters before removing some players
draw a tape diagram and write an equation to match the situation then solve the equation and put your answer in the context of the situation
Answers
Answer:
each team has 12
Step-by-step explanation:
find the geometric mean between 12 and 20 find the answer in radical form or round to the nearest tenth if necessary
Answers
Geometric mean of two numbers is squre root of thir product.
Given numbers are 12,20
Geometric mean = √(12*20)
= √240
= 15.49
= 15.5
Mark as brainlist
pleaseee somebody tell me the answer.
Answers
Answer:
aprx. 50.24 inches
Step-by-step explanation:
I hope this helps! :)
☁️☁️☁️☁️☁️☁️☁️
Find dy/dx by implicit differentiation.
cot(y) = 9x – 7y
dy/dx = ?
Answers
Answer:
Step-by-step explanation:
Solve for a.
√7a-10 - √2a+5=0
What is the root? If there is no root, choose none.
-1
1
3
none
Answers
Answer:
3
Step-by-step explanation:
√7a-10 - √2a+5=0
√7a-10 = √2a+5
7a-10 = 2a+5
5a = 15
a = 3
Subtract. (12+8i)−(7+4i) Enter your answer in the box.
Answers
Answer:
5+12i
Step-by-step explanation:
So 12-7 = 5 and 8i+4i=12i and that equals 5+12i
(12 - 7) + (8i - 4i)
5 + 4i
Factor completely.
- 3x² + 14x- 8
Answers
Answer =
= - 3x² + 14x - 8
= - 3x² + 12x + 2x - 8
= - 3x(x - 4) + 2(x - 4)
= (x - 4)(-3x + 2)
A tailor used 6 2/3 yards of fabric to make hats. The amount of fabric needed to make each hat is 5/6 yard. How many complete hats did the tailor make?
Answers
Answer: The tailor made 8 complete hats
Step-by-step explanation:
Amount of fabrics available to make hat = 6 2/3 yards
1 hat requires = 5/6 yards
Number of hat to obtain from the available fabric = Amount of fabrics available to make hat / requirement of 1 hat
=(6 2/3) / (5/6)
(20/3) / (5/6)
20/3 x 6/5 = cancelling out, we are left with
4x2= 8 hats
or
(20/3) / (5/6)
6.6666 /0.83333
= 8.00002= 8 hats
Use least common multiple or greatest common divisor to solve the problem.
Three clocks chime every 15 minutes, 39 minutes, and 65 minutes,
respectively. If the three clocks chime together, how much time must pass
before they will chime together again?
Answers
Answer:
Step-by-step explanation:
3) 15,39,65
_________
5 )5,13,65
--------------
13 )1,13,13
----------------
| 1,1,1
L.C.M.=3×5×13=195
They will chime together after 195 minutes.
The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 2.3 times every four hours. The shopping center is open from 10 a.m. to 9 p.m. (11 hours). Let r be the number of shoplifting incident caught by security in an 11 -hour period during which the center is open.
Answers
Answer:
9 hours
Step-by-step explanation:
Which answer choice contains only equations?
Answers
Answer:
A
Step-by-step explanation:
because an equation has to have a = in it and A is the only one with two answers with =
help what is 3²×3⁴×3³=?
Answers
Answer:
19 683
Step-by-step explanation:
To be able to do this, just remember that for example 3 square which is the number "3^" is 3 x 3 and it is the same for others, like 3^^ is 3 x 3 x 3 x 3.
A calculator is helpful for this question, but still doable without calculator.
Jenny earns $30 a day working part time at a supermarket. Write an expression to represent the amount of money she will earn in d days.
Answers
Answer: d($30)
Explanation: $30 times d which d is the number of days.
Decrease 1428g by 38.5%
Answers
Answer:
1428 (1-0.385) = 878.22
Step-by-step explanation:
(giving brainiest)
A bottle holds 2 pints. A carton holds 3 cups. What is the total the two containers hold in fluid ounces?
A. 6 fluid ounces
B. 32 fluid ounces
C. 56 fluid ounces
D. 66 fluid ounces
Answers
Answer:
C
Step-by-step explanation:
One Pint is 16 fluid ounces, and since their are 2 that would be 32 fluid ounces. Then 1 cup is 8 fluid ounces, and since their are 3 that would be 24 fluid ounces. When added thogether the result would be 56 fluid ounces.
The total that the two containers hold in fluid ounces is 56 fluid ounces.
What are Measurements?Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is essential to determine the quantity of any object
Given that,
Capacity of a bottle = 2 pints
Capacity of a carton = 3 cups
We have to convert both of this in to fluid ounces.
1 pint = 16 fluid ounces
Capacity of a bottle = 2 pints = 2 × 16 fluid ounces = 32 fluid ounces
1 cup = 8 fluid ounces
Capacity of a carton = 3 cups = 3 × 8 fluid ounces = 24 fluid ounces
Total capacity of two containers = 32 fluid ounces + 24 fluid ounces
= 56 fluid ounces
Hence the capacity of both containers is 56 fluid ounces.
To learn more about Unit Conversion, click :
https://brainly.com/question/11543684
#SPJ2
Find angle picture below.
Answers
Answer:
Angle M = 63
Angle N = 96
Step-by-step explanation:
By exterior angle of triangle:
Angle M + Angle N = 159
(4y+3)+(6y+6)=159
y = 15
Angle M = 4y + 3 = 4(15) + 3 = 63
Angle N = 6y + 6 = 6(15) + 6 = 96
(giving brainiest)
A pool is filled with 2,980 quarts of water. How many gallons of water are in the pool?
A. 4 gallons
B. 745 gallons
C. 2,980 gallons
D. 11,920 gallons
Answers
Answer:
b.
Step-by-step explanation:
what is 1 x 5555 + -6779 . 55555
Answers
Answer:
−376601790
Step-by-step explanation:
1
⋅
5
5
5
5
−
6
7
7
9
⋅
5
5
5
5
5
5
5
5
5
−
6
7
7
9
⋅
5
5
5
5
5
Answer:
it's -1,224.55555
Step-by-step explanation:
1 x 55,555 = 55,555
55,555 + -6779.55555 = -1224.55555
hope this helps...
Solve the system of equations.
5x - 4y = -10
- 4x + 5y = 8
y =
Answers
Answer:
x= -2
y= 0
Step-by-step explanation:
check answer
5(-2)-4(0)= -10
-10-0= -10 (TRUE)
-4(-2)+5(0)= 8
8+0= 8 (TRUE)
Answer: 5x−4y=−10;−4x+5y=8
Step-by-step explanation:
A bag contains 5 yellow, 6 red, and 4 green marbles. Two marbles are drawn. The first is replaced before the second is drawn. A random variable assigns the number of green marbles to each outcome. Calculate the expected value of the random variable.
a.0.76 c.0.27 b. 1.07 d. 0.53
Answers
Answer:
53
Step-by-step explanation:
I want the answer, Due now.
Answers
Answer: 60
Step-by-step explanation:
180 degrees because of the line so 180-120 = 60
Answer:
Its 60⁰ I'm positive....
The frequency table shows the scores from rolling a dice.
Score
Frequency
Answers
Answer:
The median is 3.5
Step-by-step explanation:
We want to find the median of the set of values.
First, we need to write the set in ascending order.
We get:
1 five times
2 three times
3 five times
4 two times
5 seven times
6 four times
The median will be the midle value (for example in a set of 5 elements, the middle element is the third one) of this set, then the first part is to write the set, we get:
{1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6}
In this set we have
5 + 3 + 5+ 2 +7 + 4= 26 values
So we will not have a middle value, we need to take the mean of the two middle values (the 13th value and the 14th value)
We can see in the set above that these values are:
3 and 4.
Then we want to take the mean between 3 and 4.
We get:
M = (3 + 4)/2 = 3.5
The median of this set is 3.5
HELP PLZ I HAVE LIKE 20-30 MINUTES PLZ I BEG ILL MARK YOU BRAINLIEST
Answers
Answer:
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Step-by-step explanation:
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