Step-by-step explanation:
This is most easily solved by writing the factored form:
[tex]f(x) = (x + 9)(x + 1)[/tex]
Notice how, if we were to substitute -9 for x, the left part would be -9 + 9 = 0. Since (x + 1) × 0 = 0, this makes the function 0. The same logic applies for the right part.
Final answer:
A quadratic function with zeros at -9 and -1 can be written as f(x) = (x + 9)(x + 1) or f(x) = x^2 + 10x + 9 when expanded.
Explanation:
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical phrase or statement. Expressions can consist of variables, constants, arithmetic operations (such as addition, subtraction, multiplication, and division), exponents, and functions.
To write a quadratic function f with zeros at -9 and -1, we use the fact that a quadratic function f(x) can be represented in the form f(x) = a(x - r1)(x - r2), where r1 and r2 are the zeros of the function and a is a nonzero coefficient. In this case, our zeros are -9 and -1, giving us f(x) = a(x + 9)(x + 1). To keep the function in simplest form, we can choose a = 1, which gives us the quadratic function f(x) = (x + 9)(x + 1) or f(x) = x2 + 10x + 9 after expanding the expression.
Final answer:
A quadratic function with zeros at -9 and -1 can be written as f(x) = (x + 9)(x + 1) or f(x) = x^2 + 10x + 9 when expanded.
Explanation:
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical phrase or statement. Expressions can consist of variables, constants, arithmetic operations (such as addition, subtraction, multiplication, and division), exponents, and functions.
To write a quadratic function f with zeros at -9 and -1, we use the fact that a quadratic function f(x) can be represented in the form f(x) = a(x - r1)(x - r2), where r1 and r2 are the zeros of the function and a is a nonzero coefficient. In this case, our zeros are -9 and -1, giving us f(x) = a(x + 9)(x + 1). To keep the function in simplest form, we can choose a = 1, which gives us the quadratic function f(x) = (x + 9)(x + 1) or f(x) = x2 + 10x + 9 after expanding the expression.
What are the possible values of 6
Answer:
The possible values of v are 6 and -6
Step-by-step explanation:
The opposite operation of an absolute value is to add a ± to the other side, so when we solve for v we get
|v|=6
v=±6
Which is the same as
v=-6 and 6
Answer:
C
Step-by-step explanation:
|6| and |-6| have the same meaning. Both are equal to 6
The answer is C
A pizza delivery person earns AED 30 per house plus AED 10.50 for each delivery made, the expression 30h+10.50d can be used to find the earnings for him how much money will he earn after working for 15 hours and making 8 deliveries
Money earned after working for 15 hours and making 8 deliveries is $ 534
Solution:
Given that pizza delivery person earns 30 per hour plus 10.50 for each delivery made
The expression used to find the earnings for him is given as:
30h + 10.50d
Where "h" is the number of hours and "d" is the number of deliveries
We have to find the money earned by him after working for 15 hours and making 8 deliveries
Therefore we get, h = 15 and d = 8
Substitute h = 15 and d = 8 in given expression
Money earned = 30(15) + 10.50(8)
Money earned = 450 + 84 = 534
Thus money earned after working for 15 hours and making 8 deliveries is $ 534
Ronnie surveyed the senior class for a math project. Below are the results of his survey.
What type of graph is best for Ronnie to display his data?
A. Double Bar Graph
B. Histogram
C. Double Line Graph
D. Circle Graph
Answer:
i think C
Step-by-step explanation:
what is the average height of a person
Answer:
well it would kinda depend on their age,and size,but the average height of an ADULT male is : 5.6 ft
ADULT female:5.2ft
(remember it would depend on their age,but some people might even have medical reasons to be shorter or taller than their original height too. At a age children don't HAVE to be that exact height,but atleast close enough to that height.)
(changes may occur depending on medical reasons,or age too!)
solve for r 4/r = 5/7
Work is provided in the image attached.
A group of 9 workers was assigned to paint the walls in a house, which could be completed in 48 hours. However, after working 8 hours, some of the workers left the group and the remaining workers could complete the job in 72 hours. How many workers left the team?
Answer:
4 workers
Step-by-step explanation:
A group of 9 workers was assigned to paint the walls in a house, which could be completed in 48 hours. Then 1 worker will complete the whole job in [tex]48\times 9=432[/tex] hours.
If 1 worker completes the whole work in 432 hours, then he completes [tex]\dfrac{1}{432}[/tex] of the work per hour.
9 workers complete [tex]9\times\dfrac{1}{432}=\dfrac{1}{48}[/tex] of work per hour and complete [tex]\dfrac{1}{48}\times 8=\dfrac{1}{6}[/tex] of work in 8 hours.
[tex]1-\dfrac{1}{6}=\dfrac{5}{6}[/tex] of work left.
This could be completed by n workers in 72 hours, so
[tex]\dfrac{n}{432} \times 72=\dfrac{5}{6}\\ \\\dfrac{n}{6}=\dfrac{5}{6}\\ \\n=5[/tex]
9 - 5 = 4 workers left the team.
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 30 books and each large box can hold 40 books. There were twice as many large boxes sent as small boxes, which altogether can hold 330 books. Determine the number of small boxes sent and the number of large boxes sent.
3 small boxes and 6 large boxes were sent to the retailer.
Step-by-step explanation:
Number of books held by small boxes = 30
Number of books held by large boxes = 40
Total books held by boxes = 330
Let,
x represent the number of small boxes
y represent the number of large boxes
According to given statement;
y = 2x Eqn 1
30x+40y=330 Eqn 2
Putting value of y from Eqn 1 in Eqn 2
[tex]30x+40(2x)=330\\30x+80x=330\\110x=330[/tex]
Dividing both sides by 110
[tex]\frac{110x}{110}=\frac{330}{110}\\x=3[/tex]
Putting x=3 in Eqn 1
[tex]y=2(3)\\y=6[/tex]
3 small boxes and 6 large boxes were sent to the retailer.
Keywords: linear equation, substitution method
Learn more about substitution method at:
brainly.com/question/10387593brainly.com/question/10402163#LearnwithBrainly
If the standard deviation of a set of data is zero, what can you conclude about the set of values?
Answer:
Step-by-step explanation:
I think it means every data value should be equal to the "mean" to make the standard variation of this set to be zero. Or all data value of the set are equal.
Use the graphs of f and g
Find the following values
Answer:
(i) 5
(ii) - 1
(iii) - 1
(iv) 0
(v) 1
(vi) 1
Step-by-step explanation:
See the graph attached to this question.
The blue graph shows y = f(x) and the red graph shows y = g(x).
(i) (f + g)(- 3) = f(-3) + g(-3) = 4 + 1 = 5
(ii) (g - f)(- 2) = g(- 2) - f(- 2) = 2 - 3 = - 1
(iii) (fg)(2) = f(2) × g(2) = (- 1) × (1) = - 1
(iv) [tex](\frac{g}{f})(3) = \frac{g(3)}{f(3)} = \frac{0}{- 3} = 0[/tex]
(v) (fog)(1) = f[g(1)] = f(1) = 1
(vi) (gog)(- 1) = g[g(-1)] = g(2) = 1 (Answer)
After using the graph with the values of f and g we find the values as follows:
(i) (f+g)(-3) = 5
(ii) (g-f)(-2) = -1
(iii) (fg) (2) = -1
(iv) (g/f) (3) = 0
(v) (f o g) (1) = 1
(vi) (g o g)(-1) = 1
i) ( f +g ) (-3)
= ( f (-3) + g(-3) )
Values we got from the graph are:
f(-3) = 4
g(-3) = 1
After substituting these values in the given equation we get
( f + g) (-3) = 5
ii) ( g - f ) (-2)
= ( g(-2) - f(-2) )
Values we got from the graph are:
g(-2) = 2
f(-2) = 3
After substituting these values in the given equation we get
( g - f ) (-2) = - 1
iii) ( fg) (2)
= ( f(2) g(2))
Values we got from the graph are:
f(2) = -1
g(2) = 1
After substituting these values in the given equation we get
( fg)(2) = -1
iv) (g/f) (3)
( g(3) / f(3) )
Values we got from the graph are:
g(3) = 0
f(3) = - 3
After substituting these values in the given equation we get
( g / f ) (3) = 0
v) ( f o g ) (1)
= ( f(1) o g(1) )
Values we got from the graph are:
g(1) = 1
f(1) = 1
After substituting these values in the given equation we get
( f o g ) (1) = 1
vi) ( g o g ) (-1)
= ( g(-1) o g(-1) )
Values we got from the graph are:
g(-1) = 2
g(2) = 1
After substituting these values in the given equation we get
( g o g ) (-1) = 1
Convert 2000 ft./min. to miles per hour round to the nearest 10th
Answer:
The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour .
Step-by-step explanation:
Given as :
The speed = s = 2000 ft per min
Now, ∵ 5280 feet = 1 miles
so, 1 feet = [tex]\dfrac{1}{5280}[/tex] miles
∴ 2000 feet = [tex]\dfrac{1}{5280}[/tex] × 2000 miles
i.e 2000 feet = 0.378 miles
Again
∵ 1 minute = [tex]\dfrac{1}{60}[/tex] hour
So, The speed in miles per hour
s = [tex]\dfrac{distance}{time}[/tex]
∴ s = [tex]\frac{0.378}{\frac{1}{60}}[/tex]
i.e s = 2.268 miles per hour
Hence, The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour . answer
To convert 2000 ft./min. to miles per hour, multiply by appropriate conversion factors, and round the result, yielding 22.7 miles per hour.
To convert 2000 ft./min. to miles per hour, follow these steps:
Convert feet to miles: 2000 ft/min x (1 mile/5280 ft) = 0.3788 miles/min
Convert minutes to hours: 0.3788 miles/min x 60 min/hr = 22.73 miles/hr
Rounded to the nearest tenth, 2000 ft/min is 22.7 miles per hour.
a pair of shoes originally cost $250. the price was decreased by 20%. a week later it was marked down again, this time 25%. what is the final price of the shoes?
Answer:
$150.
Step-by-step explanation:
$250 - 0.20 *250 = $200.
Final price = 200 - 0.25*200
= $150.
The scale on a map is 4cm = 25 mi what is the actual distance in miles represented by a line that is 20 cm on map
Answer:
Step-by-step explanation:
4 cm to 25 miles = 20 cm to x miles
4 / 25 = 20 / x
cross multiply
4x = (25)(20)
4x = 500
x = 500/4
x = 125 miles <=====
Answer:
The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Scale on a map: 4 cm = 25 miles
2. What is the actual distance in miles represented by a line that is 20 cm on map ?
For calculating the distance in miles represented, we will use the following equation:
Actual distance in miles represented = Miles in the scale/Centimeters in the scale * 20
Replacing with the real values:
Actual distance in miles represented = 25/4 * 20 = 25 * 5 = 125
The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.
What is 10*10? Please help! :)
Answer:
100
Step-by-step explanation:
It will help in the future to memorize your time tables
10*10 is basically 10 plus 10, 10 times but in a easier form
10+10+10+10+10+10+10+10+10+10=100
10+10=20
20+10=30
30+10=40
40+10=50
50+10=60
60+10=70
70+10=80
80+10=90
90+10=100
22,432.49 divided by 61.4
Answer:
365.35
Step-by-step explanation:
USE A CALCULATOR!!!!
Write an equation of the line that passes through (-2,0) and is perpendicular to the line y=-1/3x+3
Answer:
y=3x+6
Step-by-step explanation:
Perpendicular means negative reciprocal of the slope.
y-y1=m(x-x1)
y-0=3(x-(-2))
y-0=3(x+2)
y=3x+6+0
y=3x+6
-3x = 2x + 19 solve
Answer:
x=-19/5
Step-by-step explanation:
-3x=2x+19
-3x-2x=19
-5x=19
x=19/-5
Answer:
get x to one side by subtracting 2x from 2x+19
new equation:
-3x-2x=19
-5x=19
divide both sides by -5
x=-19/5
or x=-3 4/5
A number y is no more than −8.
help me
Answer:
y <= -8
Step-by-step explanation:
This algebraic expression would read as:
Y is Less than or equal to -8
Answer:
No more than means less than or equal to
y <= -8
Ten subtracted from the qoutient of a number 5 is 18
Question:
Ten subtracted from the quotient of a number and 5 is 18. What is the number?
Answer:
140 is the number.
Step-by-step explanation:
Let consider the number as ‘X’
Quotient of a number and 5 can be written as
[tex]X \div 5[/tex]
Ten subtracted from the quotient of a number and 5 can be written as
[tex](X \div 5) - 10[/tex]
Ten subtracted from the quotient of a number and 5 is 18 can be written as
[tex](X \div 5) - 10 = 18[/tex]
By solving the above equation, find ‘X’
[tex](X \div 5) = 18 + 10[/tex]
[tex]\frac{X}{5} = 28[/tex]
[tex]X = 28 \times 5 = 140[/tex]
Which of the following numbers could be the sides of a right triangle. A)8,15,17. B)6,8,12 C)9,11,21 D)4,13,16
Answer:
A) 8, 15, 17.
Step-by-step explanation:
Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option (the hypotenuse) that means that those numbers could be the sides of a right triangle.
The Pythagorean theorem states that: [tex]a^2+b^2=c^2[/tex]
Thus:
[tex]\sqrt{a^2+b^2}=c[/tex]
Option A:
[tex]\sqrt{8^2+15^2}=17[/tex] → 17 = 17 OK!
Option B:
[tex]\sqrt{6^2+8^2} = 10[/tex] → 10 ≠ 12 NO
Option C:
[tex]\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex][/tex] → [tex]\sqrt{202}[/tex] ≠ 21 NO
Option D:
[tex]\sqrt{4^2+13^2} = \sqrt{185}[/tex] → [tex]\sqrt{185}[/tex] ≠ 16 NO
Write an equation in point-slope form for the line that is perpendicular to the given line and passes through the given point.
Y - 3 = 4 (x + 2) through the point (- 2,6)
Answer: 4y + x - 22 = 0
Step-by-step explanation:
Recall that for two lines to be perpendicular m1m2 = -1 ie, the product of their gradients must = -1
from the equation given, y - 3 = 4(x + 2), we need to rearrange it in the form
y = mx + c in order for us to ascertain the gradient.
y -3 = 4x + 8
y = 4x + 8 + 3
y = 4x + 11
Therefore, m1 = 4 while m2 = -1/4
The coordinate of the line = (-2, 6) . We now use this to find the value of c.
6 = -1/4 x -2 + c
6 = 1/2 + c
multiply by 2
12 = 1 + 2c
12 - 1 = 2c
11 = 2c
c = 11/2
now to find the equation of the second line
y = -x/4 + 11/2
now multiply through by 4
4y = -x + 22
4y + x - 22 = 0 is the required equation
Mia's mother gives her $10 per week for allowance Mia gets an additional $3 for every hour she spends watching
Ther. Mia wants to make at least $25 this week to spend shopping with her friends. Use this
information to answer the questions below.
10 Write an inequality, using variables to represent the number of times that Mia has to watch her brother in order to
get at least $25.
Answer:
5 times
Step-by-step explanation:
$25 - $10 (fixed rate) = $15
$15 / $3 = 5 times.
Mia must watch her brother 5 times within the week to make the desired amount. Hope this helps :)
Which system of equations has one solution? –5x – 10y = 24 5x + 10y = 16 3x + 4y = –7 –3x – 4y = 7 –12x + 8y = 16 12x – 8y = 16 –2x + 7y = –5 2x + 7y = –9
Answer:
The last system is that one with exactly one solution:
–2x + 7y = –5
2x + 7y = –9
Step-by-step explanation:
We can easily check the number of solutions that each system has in this problem, since the equations contain most of them combinations of terms in y and in x that can be easily cancelled out via simple term by term addition.
Going through them system by system, and adding term by term the equations which are in standard form we get:
(1) –5x – 10y = 24
5x + 10y = 16
---------------------------
0x + 0y = 40 which sates a mathematical absurd: "0 = 40", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)
(2) 3x + 4y = –7
–3x – 4y = 7
--------------------
0x + 0y = 0 which gives that zero equals zero, which any pair (x, y) belonging to any of the two equations can verify, so an infinite number of solutions (the lines in the system overlap)
(3) –12x + 8y = 16
12x – 8y = 16
-------------------
0x + 0y = 32 which sates a mathematical absurd: "0 = 2", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)
(4) –2x + 7y = –5
2x + 7y = –9
---------------------
0x + 14y = -14
This is the only system that shows solution. It allows us first to solve for "y" in the resultant equation: 14 y = -14 giving us the value y = -14/14 = -1
and then using it the unique value for x can be determined:
2x + 7y = –9
2x + 7 (-1) = -9
2x -7 = -9
2x = -9 + 7
2x = -2
x = -2/2 = -1
Therefore, the pair (-1, -1) is the unique solution to the system
Answer:
The answer is D.Step-by-step explanation:
Trust me guys. The guy above me has a full explanation, but if you are just looking for a simple answer, then I gotchu
a circle is centered at the point 0,0 and has a radius of the square root of 53. Where does the point -3,-7 lie? I will give the brainiest Help Please
Answer:
The point lie outside the circle
Step-by-step explanation:
step 1
Find the distance between the center of the circle and the given point
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
(0,0) and (-3,-7)
substitute the values
[tex]d=\sqrt{(-7-0)^{2}+(-3-0)^{2}}[/tex]
[tex]d=\sqrt{58}\ units[/tex]
step 2
Compare the distance with the radius
If d=r ----> the point lie on the circle
If d > r -----> the point lie outside the circle
If d < r -----> the point lie inside the circle
we have
[tex]d=\sqrt{58}\ units[/tex]
[tex]r=\sqrt{53}\ units[/tex]
so
[tex]\sqrt{58}\ units > \sqrt{53}\ units[/tex]
[tex]d > r[/tex]
therefore
The point lie outside the circle
Answer:
C outside the circle
Step-by-step explanation:
khan
A stack of 250 cards are placed next to a ruler, and the height of the stack is measured to be 5/8 inches. How thick is one card?
Answer:
The thickness of 1 card = 0.0025 inches
Step-by-step explanation:
Here, the total number of cards in the stack = 250 cards
The total height of the stack = 5/8 inch = 0.625 in.
[tex]\textrm{Thickness of one card} = \frac{\textrm{The total thickness of the stack}}{\textrm{The total cards in the stack}}[/tex]
[tex]\implies \textrm{Thickness of one card} =\frac{0.625}{250} = 0.0025[/tex]
Hence, the thickness of 1 card = 0.0025 inches
Let $x=(0.\overline{6})(0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?
Answer:
[tex]32\text{ for }x=0.\overline{40}[/tex]
Step-by-step explanation:
It looks like you want the sum of digits of the product ...
[tex]x = (0.\overline{6})(0.\overline{60})=\dfrac{2}{3}\cdot\dfrac{20}{33}=\dfrac{40}{99}=0.\overline{40}[/tex]
Since the decimal fraction starts off with 4 and has an even number of repeating digits, there will be 8 4's and 7 0's in the sum of the first 15 decimal digits:
sum = 8×4 +7×0 = 32
The sum of the first 15 digits after the decimal point is 32.
21. Brian wants to purchase a piece of fabric
that is between 49 and 53 inches long.
He can choose between three pieces of
fabric. Choice A is 4 3/4 feet long. Choice
B is 4 1/2 feet long. Choice C is 4 1/3 feet
long. Which piece of fabric should Brian
purchase?
(Show WORK!!)
Brian should purchase Choice C of fabric
Solution:
Given that Brian wants to purchase a piece of fabric that is between 49 and 53 inches long
So piece of fabric should be between: 49 and 53 inches
Choice A is [tex]4\frac{3}{4}[/tex] feet longLet us convert feet to inches
[tex]4\frac{3}{4} feet = \frac{4 \times 4 + 3}{4} = \frac{19}{4} feet[/tex]
Now convert to inches
We know that,
1 feet = 12 inches
[tex]\frac{19}{4} feet = \frac{19}{4} \times 12 = 57 inches[/tex]
But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches
So this is not correct
Choice B is [tex]4\frac{1}{2}[/tex] feet long[tex]4\frac{1}{2} feet = \frac{2 \times 4 + 1}{2} = \frac{9}{2} feet[/tex]
Now convert to inches
[tex]\frac{9}{2} feet = \frac{9}{2} \times 12 inches = 54 inches[/tex]
But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches
So this is not correct
Choice C is [tex]4\frac{1}{3}[/tex] feet long[tex]4\frac{1}{3} feet = \frac{3 \times 4 + 1}{3} = \frac{13}{3} feet[/tex]
Now convert to inches
[tex]\frac{13}{3} feet = \frac{13}{3} \times 12 inches = 52 inches[/tex]
So this 52 inches lies between 49 and 53 inches
So Brian should purchase Choice C of fabric
Is (-1,8),(0,15),(1,-4),(2,0) a function
Answer:
?
Step-by-step explanation:
It could be
Answer:
Yes
Step-by-step explanation:
Yes because it is a one-to-one relation. Every x-value maps to a unique value of y.
The school board administered a math test to all students in grade 6 at High Achievers Charter School and determined that 15%, percent of them were below grade level in math.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
A
15%, percent of students in the sample are below grade level in math, but we cannot conclude anything about the students in grade 6 at HACS.
B
15%, percent of all students in grade 6 at HACS are below grade level in math.
C
15%, percent of all students at HACS are below grade level in math.
The valid conclusion based on the provided data is that 15% of students in the sample are below grade level in math, but this does not necessarily indicate the same for all students in grade 6 at HACS.
Explanation:The question pertains to drawing a valid conclusion from given statistical data about the math proficiency level of students in a specific school.
When it states that 15% of students are below grade level in math, the conclusion can only pertain to the group specified in the data set.
Therefore, the most valid conclusion from the given choices is that 15% of students in the sample are below grade level in math, and we cannot infer the same for the entire grade 6 at High Achievers Charter School (HACS) without further context.
In light of the provided information, one cannot come to any conclusions regarding the math proficiency of students in other grades, nor can one generalize to all students in grade 6 at HACS from a mere sample unless the sample is clearly stated to be the entirety of the grade.
The correct conclusion is B. 15% of all students in grade 6 at HACS are below grade level in math.
To understand why this conclusion is valid, let's analyze the given information and the options provided:
- The school board determined that 15% of the students who took the test were below grade level in math. Since the test was administered to all grade 6 students at HACS, this percentage applies to the entire population of grade 6 students at the school, not just a sample.
Now, let's evaluate the conclusions:
A) 15% of students in the sample are below grade level in math, but we cannot conclude anything about the students in grade 6 at HACS.
- This conclusion is incorrect because the sample includes all grade 6 students at HACS. Therefore, we can generalize the results to the entire population of grade 6 students at the school.
B) 15% of all students in grade 6 at HACS are below grade level in math.
- This conclusion is correct because the test was given to all students in grade 6 at HACS, making the sample representative of the entire population of grade 6 students. Thus, the 15% figure accurately reflects the proportion of grade 6 students at HACS who are below grade level in math.
C) 15% of all students at HACS are below grade level in math.
- This conclusion is incorrect because the test was only administered to grade 6 students. We do not have data on students in other grades at HACS, so we cannot extend the 15% figure to the entire student body of the school.
Identify the interval(s) on which the function y = x + 12x + 27 is positive.
Answer:
So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.
Step-by-step explanation:
We are given a function and we have to find the intervals in which the function has positive value.
y = [tex]x^{2} +12x+27[/tex]
y =(x + 3)(x + 9)
For the function to be positive , y ≥ 0
(x + 3)(x + 9) ≥ 0
Here there are two cases , either both should be positive or both should be negative.
If both are positive,
(x + 3)≥0 and (x + 9)≥0
So, x ≥ -3
If both are negative,
(x + 3)≤0 and (x + 9)≤0
So, x ≤ -9
So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.
The intervals on which the function y = x² + 12x + 27 is positive are
x > -3 and x > -9
For the function given to be positive, it has to be greater than zero.
Since the expression is greater then zero, hence;
x² + 12x + 27 > 0
Factorize the resulting expression
x² + 3x + 9x + 27 > 0
x(x+3) + 9(x+3) > 0
(x+3) (x+9) > 0
x+3 > 0 and x + 9 > 0
x > -3 and x > -9
Hence the intervals on which the function y = x² + 12x + 27 is positive are
x > -3 and x > -9
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Gwen Mows 1/4 acre 3/4 hour. How many acres will Gwen mow in one hour
Answer:
0.33...acre
Step-by-step explanation:
1/4=0.25
3/4=0.75
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0.25/0.75=x/1
cross product
0.75*x=0.25*1
0.75x=0.25
x=0.25/0.75
x=0.3