The zeros of
y = x(x + 2)(x + 5)y=x(x+2)(x+5)
are
x=0,x=-2,x=-5x=0,x=−2,x=−5
EXPLANATION
The given function is
y = x(x + 2)(x + 5)y=x(x+2)(x+5)
To find the zeros of the above function, we just have to equate the function to zero and solve for x.
x(x + 2)(x + 5) = 0x(x+2)(x+5)=0
This implies that,
x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0x=0orx+2=0orx+5=0
x = 0 \: \: or \: x = - 2\:or \: x = - 5x=0orx=−2orx=−5
To graph the above function, we need to consider the multiplicity.
We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.
We also need to consider the position of the graph on the following intervals,
x < - 5x<−5
When
x = - 10x=−10
y = - 10( - 8)( - 5) \: < \: 0y=−10(−8)(−5)<0
The graph is below the x-axis.
- 5 \: < \: x \: < \: - 2−5<x<−2
When
x = - 3x=−3
y = - 3(2)( - 1) \: > 0y=−3(2)(−1)>0
The graph is above the x-axis.
- 2 \: < \: x < \: 0−2<x<0
when
x = - 1x=−1
y = -1(1)(4) \: < \: 0y=−1(1)(4)<0
The graph is below the x-axis.
Finally the interval,
x \: > \: 0x>0
when
x = 1x=1
y = 1(3)(6) \: > \: 0y=1(3)(6)>0
The graph is above the x-axis.
We can now use the above information to sketch graph as shown in the diagram above
Write an equation in slope-intercept form of the line that passes through the points.
Answer:
y=-2x
Step-by-step explanation:
M= y2-y1/x2-x1
= 6-0/-3-0
= 6/-3
= -2
when X is 0 Y is also so C is 0
A bag holding 7 1/5 pounds of mixed nuts will be divided equally among 9 people.
How many pounds of nuts will each person get?
Answer:
4/5
Step-by-step explanation:
So sorry if im wrong <3
Answer:
Each person will get 4/5, or 0.8 pounds of nuts.
Step-by-step explanation:
First, we need to convert 7 1/5 into an improper fraction, by multiplying
7 x 5 = 35
and adding
35 + 1 = 36
Our improper fraction is 36/5
Now, we can divide
36 / 9
5 / 1
To do so, we need to switch 9/1 to its reciprocal, 1/9, and then multiply
36 x 1 = 36
5 x 9 = 45
Our answer is 36/45
We can simplify our answer by dividing by 9
36 / 9 = 4
45 / 9 = 5
Our final answer is 4/5, or 0.8 pounds of nuts
During a sale, a store offered a 25% discount on a tablet computer that originally sold
for $320. After the sale, the discounted price of the tablet computer was marked up
by 25%. What was the price of the tablet computer after the markup? Round to the
nearest cent.
Answer:
304
Step-by-step explanation:
x/760 40/100=
760x40=30,400
30,400 divided by 100=304
Answer: she/he is wrong.
Step-by-step explanation:
no offence.
PLEASE HELP ME!!!
Will give Brainlest
Answer: C. (1, 0.80) represents the unit rate
Step-by-step explanation:
Please attach all answer options.
If it is given that log2 a= 5 , write the value of a as a power of 2
In other words, write it in exponential form.
To write a as a power of 2, your log form should be written this way: log_2 (5) = a.
We can then then write it in exponential form showing a as a power of 2.
Here it is:
2^(a) = 5
2. A group of 40 subjects was divided into two groups with one group given an energy drink and one group
given water. The subjects were then given a spelling test and
the mean number of words correctly spelled was
recorded for each member of the two groups. This experiment was designed this way to quantify which of the
following types of variability?
(1) natural
(3) induced
(2) sampling
(4) measurement
The design of the experiment was done to quantify induced variability.
What is induced variability?
Induced variability is when a variable that is not naturally present in the experiment is introduced into the experiment in order to test the response of respondents to the variable introduced. The artificial variable that was introduced into the experiment was energy drinks.
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You have an account that starts at $2500 with an interest rate of 3.25% compound yearly. How much is in the account after 10 years? Round your answer to the nearest hundredth.
Answer:3,312.50
Step-by-step explanation:1. We assume, that the number 2500 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 2500 is 100%, so we can write it down as 2500=100%.
4. We know, that x is 3.25% of the output value, so we can write it down as x=3.25%.
5. Now we have two simple equations:
1) 2500=100%
2) x=3.25%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
2500/x=100%/3.25%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
Which integer in the set has the smallest value (-17, -7, -12, 2)? A. 2 B. -7 C. -12 D. -17
The smallest integer from the given set {-17, -7, -12, 2} is -17, making option D the right choice.
An integer is a whole number that can be positive, negative, or zero and is not a fraction.
The integer values are in the following order: negative, zero, then positive.
The real value of a negative integer decrease as the number increases.
For positive integers, the real value increases as the number increases.
In the question, we have been asked for the integer with the smallest value in the set {-17, -7, -12, 2}.
As discussed above, we know the order for negative and positive integers.
Thus, arranging the set in ascending order, we get:
-17 < -12 < -7 < 2.
Thus, the smallest integer from the given set {-17, -7, -12, 2} is -17. Hence, option D is the right choice.
Learn more about integers at
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8.517
In word form, please
and expanded, please help
Answer:
eight point five one seven.
Step-by-step explanation:
I NEED HELP PLEASE!!!!!!!!!!!!!!!
Answer:
$2580
Step-by-step explanation:
$1500 dollars increased by 9%. In 8 years how much money he will have.
Ok, he has 1500 bucks in there
percents are an amount out of 100 so 9%=9/100
which, 9/100 in decimal form is .09
1500*.09 which is 135
135 dollars every year added
in 8 years, he will have earned 1080 bucks due to interest
1500+1080 which is 2580 dollars
he will have 2580
Answer:
1,616.60
Step-by-step explanation:
we know that
The compound interest formula is equal to
A=P(1+\frac{r}{n})^{nt}A=P(1+
n
r
)
nt
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
\begin{gathered}t=5\ years\\ P=\$1,500\\ r=1.5\%=1.5/100=0.015\\n=4\end{gathered}
t=5 years
P=$1,500
r=1.5%=1.5/100=0.015
n=4
substitute in the formula above
A=1,500(1+\frac{0.015}{4})^{4*5}A=1,500(1+
4
0.015
)
4∗5
A=1,500(1.00375)^{20}A=1,500(1.00375)
20
A=\$1,616.60A=$1,616.60
Can you help me with this question please!!
Answer:
Can you help me with this question please!! (D)
A student earns $8 per hour plus a $15 bonus each weekend day worked. Last week, the student worked 1 weekend day and earned a total of $115 for h hours of work.
Answer:
12.5 hours
Step-by-step explanation:
[tex]115 - 15 = 100 \\ \frac{100}{8} = 12.5[/tex]
The student worked for 12.5 hours.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A student earns $8 per hour plus a $15 bonus each weekend day worked.
Now, let the student works for h hours.
So, the earning would be= 15+ 8h
As, he earned $115
So, 15+ 8h= 115
8h = 100
h = 12.5 hours
Hence, the student worked for 12.5 hours.
Learn more about Algebra here:
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Hello! so is this correct? is 16.093 x 10 = 5,000? or278,300? please help me if you see this. Thanks.
Answer:
160.93
Step-by-step explanation:
I'm not that great at math so forgive me if I'm wrong, but from my knowledge the answer would be 160.93 since you're multiplying 16.093 to 10.
hope this helped! :)
Guys, Take a look at the screenshot below, do you understand this problem? If you do so, please tell me the answer!
Answer:
there is no screenshot or I just can't see it
add the quotient of 9 and 7 to d
Answer:
9 ÷ 7 + d.
Step-by-step explanation:
f(x)= 2/(x+3) find domain
Answer:
x < -3 or x > -3
NEED HELP ASAP 50 POINTS PLEASE DO ALL OF THEM !!!!!in the item Bank are key terms and expressions, each of which is associated with one of the columns. Some terms may display additional information when you click on them. Drag and drop each item into the correct column. Order does not matter. 1 2 4 3 5/6 7 8 ITEM BANK Move to Bottom 1&8 267 3 &5 3 & 6 3 & 8 4 & 5 4 & 6 4&7 Alternate Interior Zs Corresponding Ls Alternate Exterior Zs Consecutive Interiors 1 & 5 2 & 6
Answer:
the top two on the right hand corner go in coressponding the one by the middle of the top row gos in alternative int and the far left gos in alt in bottom two go in cosecutive the middle far right go alt int middle row far left consecutive interior left gos alt ext and middle row right gos alt
Step-by-step explanation:
Sorry if this is late lol. Hope this helps other people too though.
Alternative interior
4 & 6
3 & 5
Corresponding
1 & 5
4 & 7
2 & 6
3 & 8
Alternative
1 & 8
2 & 7
Consecutive
4 & 5
3 & 6
please i beg on my knees i will give brainlist!!!!!!!!!!!
Answer:
i think it's letter c. f (n) = 4n-1
Step-by-step explanation:
1x4= 4, 2x4= 8, 3x4= 16, and so on
hope this helps!! :))
Can anyone help me on this one??
Find the slope and the y-intercept of the equation below:
1. 4x-3y=12
2. 2y=6x-12
if you can put the step please do so. Tysm.
Answer + Explanation:
1. you want to rearrange the equation ( don't change the actual value ) to put it in the form y = mx + b. in this form, m represents the slope and b represents the y-intercept.
this is how you would do that:
4x - 3y = 12
subtract 4x from both sides
-3y = -4x + 12
divide both sides by -3
y = 4/3x - 4
this means the slope is 4/3 and the y-intercept is -4
2. do the same thing, rearranging into y = mx + b form
2y = 6x - 12
divide both sides by 2
y = 3x - 6
this means the slope is 3 and the y-intercept is -6
nineteen students named lacrosse as there favorite sport. explain how to use the circle graph for the total number of students? 20% chosr swimming 42% chose volleyball and 38% chose laccrosse
The total number of students is 50
The number of students that named lacrosse as their favorite sport is given as:
[tex]Lacrosse = 19[/tex]
From the circle graph, 38% chose lacrosse.
So, the proportion of students that represent lacrosse is:
[tex]Lacrosse = 38\% \times Students[/tex]
Substitute 19 for lacrosse
[tex]19= 38\% \times Students[/tex]
Multiply both sides by 100
[tex]1900 = 38 \times Students[/tex]
Divide both sides by 38
[tex]50 = Students[/tex]
Rewrite as:
[tex]Students = 50[/tex]
Hence, the total number of students is 50
Read more about circle graphs at:
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A cone has a height of 15 millimeters and a radius of 15 millimeters. What is its volume?
Use a 3.14 and round your answer to the nearest hundredth,
Answer:
10,597.50 cubic mm
Step-by-step explanation:
V(cone) = [3.14(h)(r²)] ÷ 3
= 3.14(15)(15²) ÷ 3
= 10,597.5
What is the solution of the system of equations shown below?
y = –x + 3
y = 4x – 2
Answer:
b
Step-by-step explanation:
[tex]y=-x+3~~.....(i)\\\\y = 4x-2~~....(ii)\\\\\text{Substitute}~ y = -x+3~ \text{in equation (ii):}\\\\\\-x+3 = 4x-2\\\\\implies 4x +x = 3+2\\\\\implies 5x = 5\\\\\implies x = \dfrac 55 =1\\\\\\\text{Substitute x= 1 in equation (i):}\\\\y= -1 +3 = 2\\\\\text{Hence}~ (x,y)=(1,2)[/tex]
can someone help me do this
Answer:
a) S gets tends to infinity
b) S tends to zero
Step-by-step explanation:
As you know, dividing by larger numbers makes a quotient smaller. The converse is also true: dividing by smaller numbers makes the quotient larger.
__
a) The area of the label will get larger as r gets closer to zero. It will tend toward infinity.
__
b) The area of the label will get smaller as r gets larger. It will tend toward zero.
Bones or no bones day?
Answer:
I'm gonna say no bones day, but I have no idea what you are talking about, so I will change my answer once you explain...
Step-by-step explanation:
Answer:Bones Day
Step-by-step explanation:
A balanced scale has 3 marbles, 2 pennies, and 4 quarters on one side and 4 marbles, 2
quarters, and 1 penny on the other side. If pennies weigh one gram and quarters weigh
3 grams, find the weight of a marble. Explain or show your reasoning.
Answer:
See image
Step-by-step explanation:
An equation is really like a scale with two equal things on both sides. You could use the idea of a scale and lift off the same amount from both sides to keep it balanced. But I will show you the algebra version. When we subtract the same thing from both sides that's how we work back to our answer while keeping the scale balanced.
Let m = weight of a marble
p = weight of a penny = 1 gram
q = weight of a quarter= 3 grams
The problem says how many of each marble, penny, quarter, then set them equal to each other. See image
The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick
Which property explains why these two expressions are equal?
5 (g + h) = 5g + 5h
A associative
B commutative
C distributive
D inverse
Find the solution to each system using elimination.x - 2y = 7x−2y=7 and 2x + 5y = -42x+5y=−4
Answer: dont even know tbh
Step-by-step explanation:?
NEED ANSWERS PLEASEEE! PROGRESS REPORTS GO IN SOON.
Answer:
1. they both are the same length and diameter, the difference is thw diameter is a different direction.
2. 4 cm
3. EB and 8 cm
Step-by-step explanation:
Diameter is the length of the circle aross, hope this helps!
Find the solutions to x2 = 24.
=
O A. x = +4,16
=
O B.
X =
< = +2.1/6
O C. X= = +62
O D. x= 1514
=
Answer:
[tex]x\approx\pm4.8989[/tex]
Step-by-step explanation:
[tex]x^2=24[/tex]
[tex]\sqrt{x^2}=\sqrt{24}[/tex]
[tex]x=\pm\sqrt{24}[/tex]
[tex]x\approx\pm4.8989[/tex]