Answers
Part (a)
Plug in y = 0 and solve for x. Use the zero product property
y = x(x+3)(x-2)
0 = x(x+3)(x-2)
x(x+3)(x-2) = 0
x = 0 or x+3 = 0 or x-2 = 0 .... zero product property
x = 0 or x = -3 or x = 2
The three roots or zeros are x = 0 or x = -3 or x = 2
================================================
Part (b)
The roots of the graph are: x = -2, x = 1, x = 3. Each root is where the graph crosses or touches the horizontal x axis.
Note how x = 0 is found in part (a), but not found here. This is one example where the graphs don't match. Another would be x = -3 is in part (a), but not here.
So that's why the graph does not match with the function in part (a)
Related Questions
Which expression is equivalent to 100+20? 5(20+3)5(20+3) 4(25+6)4(25+6) 10(10+2)10(10+2) 5(20+20)5(20+20)
Answers
Answer:
Step-by-step explanation:
10 (10+2)
What is the value of x? Round to the nearest tenths place....
Answers
Answer:
x = 12.64911064
Step-by-step explanation:
a^2 + b^2 = c^2
8^2 + b^2 = 14^2
36 + b^2 = 196
PLEASE HELP!!! 30 POINTS
Solve the inequality for x. Show each step of the solution.
12 + 7 > 9(2 − 3)− 8
Answers
Answer:
True
12+7>9(2-3)-8
19> (-9)-8
19>-17
Step-by-step explanation:
Answer:
12+7=19 and 9(2-3)-8=-17
Step-by-step explanation:
1. Amy Lynn's Kitchen offers a breakfast
special. Customers have a choice of fried,
poached, scrambled, or soft-boiled eggs;
bacon or sausage; hash browns or grits; and
cornbread or biscuits. How many breakfast
combinations does Amy Lynn serve?
F. 8
G. 10
H. 16
J. 32
Answers
Answer: F
Step-by-step explanation: Amy lynn's kitchen offers a variety of breakfast specials, there are four choices for customers to choose from, but each choice has a combination. Which makes it 8 combinations Amy Lynn' serves
Rewrite in simplest terms: -10(-3m-10)-3(-8m+3) i don't usually ask questions that often but I actually need help this time. so if you know answer please :D
Answers
Answer:
The simplest form is 6m+91.
Step-by-step explanation:
Consider the given information.
[tex]-10(-3m-10)-3(-8m+3)[/tex]
First, remove the parenthesis by multiplying -10 and -3 inside the parenthesis.
[tex]30m+100-24m-9[/tex]
Now, rearrange the like terms.
[tex]30m-24m+100-9[/tex]
Combine the like terms.
[tex]6m+91[/tex]
Hence, the simplest form is 6m+91.
Hay sorry I forgot the picture last time but can some one help
Answers
Answer:
Marina's design uses more cardboard.
in Kristen's design, it uses:
3*4/2*2+10*5+3*10+4*10=132 sq inches.
in Marina's design, it uses:
6*3*2+3*7*2+7*6*2=162 sq inches.
132<162
Therefore Marina's design uses more cardboard.
The difference between 2 designs are:
162-132
=30 sq inches
2〖sen〗^2 x+3 senx+1=0
2cotxsecx+ 2secx+cotx+1=0
senx〖cos〗^2 x=senx
2〖cos〗^2 x+2senx-12=0
2〖csc〗^2 x+〖cot〗^2 x-3=0
Answers
2 sin²(x) + 3 sin(x) + 1 = 0
(2 sin(x) + 1) (sin(x) + 1) = 0
2 sin(x) + 1 = 0 OR sin(x) + 1 = 0
sin(x) = -1/2 OR sin(x) = -1
The first equation gives two solution sets,
x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ
x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ
(where n is any integer), while the second equation gives
x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ
2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0
2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0
(2 sec(x) + 1) (cot(x) + 1) = 0
2 sec(x) + 1 = 0 OR cot(x) + 1 = 0
sec(x) = -1/2 OR cot(x) = -1
cos(x) = -2 OR tan(x) = -1
The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives
x = tan⁻¹(-1) + nπ = -π/4 + nπ
sin(x) cos²(x) = sin(x)
sin(x) cos²(x) - sin(x) = 0
sin(x) (cos²(x) - 1) = 0
sin(x) (-sin²(x)) = 0
sin³(x) = 0
sin(x) = 0
x = sin⁻¹(0) + 2nπ = 2nπ
2 cos²(x) + 2 sin(x) - 12 = 0
2 (1 - sin²(x)) + 2 sin(x) - 12 = 0
-2 sin²(x) + 2 sin(x) - 10 = 0
sin²(x) - sin(x) + 5 = 0
Using the quadratic formula, we get
sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2
but the square root contains a negative number, which means there is no real solution.
2 csc²(x) + cot²(x) - 3 = 0
2 (cot²(x) + 1) + cot²(x) - 3 = 0
3 cot²(x) - 1 = 0
cot²(x) = 1/3
tan²(x) = 3
tan(x) = ± √3
x = tan⁻¹(√3) + nπ OR x = tan⁻¹(-√3) + nπ
x = π/3 + nπ OR x = -π/3 + nπ
how do you solve for x
-3x-6y=0
Answers
Answer:
x = 2y
Step-by-step explanation:
Simplifying
3x + -6y = 0
Solving
3x + -6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6y' to each side of the equation.
3x + -6y + 6y = 0 + 6y
Combine like terms: -6y + 6y = 0
3x + 0 = 0 + 6y
3x = 0 + 6y
Remove the zero:
3x = 6y
Divide each side by '3'.
x = 2y
Simplifying
x = 2y
translate the sentence into an equation
The sum of 6 times a number and 2 is equal to 3
Answers
Answer:
6x + 2 = 3
Step-by-step explanation:
x would represent the unknown number
The sum refers to addition
6 times a number would be 6x (you can use any variable, but for this example I'm using x)
When you put it all together, it is 6x + 2 = 3
The required equation is 6x + 2 = 3.
It is required to find the equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers
Given:
The sum of 6 times a number and 2 equals 3.
According to given question we have,
Let the number be x.
6 times a number would be
6x
The sum of 6 times a number and 2 equals 3.
6x + 2 = 3.
Therefore, the required equation is 6x + 2 = 3.
Learn more about equation here:
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An SEO account manager is concerned website developers are using too many keywords per web page. The SEO account manager would like to carry out a hypothesis test and test the claim that a web page has, on average, more than 10 keywords. Why is this hypothesis test right-tailed
Answers
Answer:
The hypothesis test is right tailed because of claim made by SEO account manager that a web page on average has more than 10 keywords.
Step-by-step explanation:
The given hypothesis test is right tailed due to the claim made by SEO account manager. The tail of hypothesis test decided by looking at alternative hypothesis. The claim stated as " a web on average has more than 10 keywords" and this leads to alternative hypothesis as
Ha:μ>10.
The alternative hypothesis shows the greater than area or also known as right tailed area. Thus, given hypothesis test is right tailed.
what is the slope of the line thru passes thru (1,1) and (9,6)
Answers
Answer: 0.6
Step-by-step explanation:
x1=1
x2= 9
y1=1
y2=6
SLOPE OF THE LINE
= y2-y1/x2-x1
= 6-1/9-1
=5/8
=0.6
Need help like ASAP
Answers
1. In 1995, the average level of mercury uptake in wading birds in the Everglades was 15 parts per million. If we assume that the distribution of mercury uptake has a standard deviation of 1 part per million, and a current sample of 25 wading birds has an average of 14.6 parts per million. Which null and alternative hypotheses would be used to test that the level of mercury uptake in the Everglades has decreased since 1995?
Answers
Answer:
We reject H₀, we find that the current level of mercury uptake in the Everglades has decrease
Step-by-step explanation:
We need to test the current wading bird average 14,6 vs the 1995 average. As sample mean is 14,6 and population mean is 15 we are going to check test is of one tail (left tail test)
Test Hypothesis:
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ < μ₀
Sample size 25 then n < 30 we will use t-student table
Population mean : μ₀ = 15 ppm
sample mean : μ = 14,6 ppm
sample standard deviation: s = 1 ppm
Sample size n : 25
degrees of freedom df = n - 1 df = 24
We will develop the test for CI 90% then α = 10% α = 0,1 α/2 = 0,05
For that values in t student table we find:
t(c) = 1,711 by symmetry t(c) = - 1,711
To compute ts
t(s) = ( μ - μ₀ ) / s/√n
t(s) = 14,6 - 15 / 1 /√25
t(s) = - 0,4*5 / 1
t(s) = - 2
Comparing t(c)and t(s)
|t(s)| > |t(c) | and t(s) < t(c) -2 < -1,711
Therefore t(s) in in the rejection region, we reject H₀
PLS HELP!! What is the value of X
Answers
A chemist is performing an experiment by observing the effects when she combines two solutions. She monitors the temperature of the combined solution over the course of eight hours and records it in this table below.
The chemist can model the temperature with a polynomial function. During these eight hours, over what interval is the temperature decreasing?
A. From hour 0 to hour 8
B. From hour 5 to hour 8
C. From hour 0 to hour 5
D. From hour 2 to hour 6
Answers
Answer:
A. From hour 0 to hour 5
Step-by-step explanation:
For all Plato users
Interval of the temperature decreasing is from hour 0 to hour 5.
What is interval?
an interval is defined as a group of numbers which includes all numbers between the beginning and the end.
According to given data is showing that the temperature decreasing zero hour to 1 hour , then 1 to 2 hour, then 2 to 3 hour, then 3 to 4 hour, then 4 to 5 hour.
So the interval of the temperature decreasing is from hour 0 to hour 5.
Learn more about interval
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Explain answer??????????????????
Answers
Answer:
the answer is a
Step-by-step explanation:
he:
os and Proportions
This table shows the relationship between the
number of cups of popcorn, p, a popcorn
machine pops and the time in minutes, 1, the
popcorn machine operates.
Answers
Answer:
can you give a chart or something?
what is 35% as a fraction
Answers
Answer:
7/20
Step-by-step explanation:
Select the correct answer.
Each side of a square is
(st
5) units. Which expression can be used to represent the area of the square?
22 - 50 - 10
I2 – 50 + 10
2 – 100 - 25
22 - 10x + 25
Answers
Answer:
D.) x²-10x+25 sq. units
Step-by-step explanation:
The question is not properly written. The question should have been:
If each side of a square is (x-5) units, which expression can be used to represent the area of the square.
Area of a square = L² where:
L is the length of the square
Given
L = x-5
Required
Area of the square
Substitute the given function into the formula to get the required as shown:
Area of the square = (x-5)²
Expand
A(x) = (x-5)(x-5)
A(x) = x(x)-5x-5x-5(-5)
A(x) = x²-10x-25
Hence the area of the square is (x²-10x+25)sq. units. Option D is correct.
If 5% more than a is b, and b is 15% less than, what is the ratio of a to c? Please answer quickly.
Answers
Two large containers A and B of the same size are filled with different fluids. The fluids in containers A and B are maintained at 0° C and 100° C, respectively. A small metal bar, whose initial temperature is 100° C, is lowered into container A. After 1 minute the temperature of the bar is 90° C. After 2 minutes (since being lowered into container A) the bar is removed and instantly transferred into the other container. After 1 minute in container B the temperature of the bar rises 10°. How long, measured from the start of the entire process, will it take the bar to reach 99.7° C? (Round your answer to two decimal places. Assume the final temperature being asked for is reached while the bar is container B.) t = min
Answers
Answer:
What I think, Is that it... It might be, It can take 3 seconds
-74.25
That the right answer
Answers
Answer:
Okay...
Step-by-step explanation:
Pieces of Mail. The number of pieces of mail
handled by the U.S. Postal Service decreased from
212 billion in 2007 to 168 billion in 2011. What is the
percent decrease?
Answers
Answer:
20.8%
Step-by-step explanation:
The number of the pieces of mail handled by the U.S postal service decreased from 212,000,000,000 to 168,000,000
Therefore the percentage decrease can be calculated as follows
= 212,000,000,000-168,000,000,000
= 44,000,000,000/212,000,000,000 × 100
= 0.2075 × 100
= 20.8 %
Hence the percentage decrease is 20.8%
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
Answers
Answer:
Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.
Step-by-step explanation:
this is correct...
trust me :)
The sign is positive because it represents a quantity of something, in this case, months.
Callie has 4 months to pay off the bill.
The rational number is +4.
What is the rational number?
A number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
The sign is positive because it represents a quantity of something, in this case, months.
To learn more about the rational number visit:
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For a school project, the school bought 36 hamsters for $5.90 each and 40 cages for $30.25 each.
How much did the school spend in all?
Answers
13-22 super easy help please wee thank you!
Answers
the answer to the equation is -9
multiply 0.87 x 0.4
I'm writing this for 20 characters
Answers
Answer:
0.348
Step-by-step explanation:
Answer:
.348
Step-by-step explanation:
Hope this helped
One way of solving systems of linear equations is by adding a multiple of one equation to the other. The multiplier for the first equation is chosen so that one of the two variables will cancel out in the sum. What should you multiply the equation y=0 y=0 by so that when added to x+y=40 x+y=40 the variable y yy will cancel out?
Answers
Answer:
Multiply y = 0 by -1
Step-by-step explanation:
Given
y = 0 (1)
x + y = 40 (2)
What should you multiply the equation y=0 by so that when added to x + y = 40, the variable y will cancel out ?
Multiply (1) by -1
y = 0 × -1
-y = 0 (1b)
Add (1b) and (2)
-y = 0
x + y = 40
(0 + x) + (-y + y) = 0 + 40
x + (0) = 40
x = 40
You should multiply the equation y = 0 by -1 so that when added to x + y = 40 the variable y will cancel out
RADIO A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original
price to the nearest nickel?
Answers
Answer:
10% of $50.00 is $5.00 SO ORGINAL PRICE IS $55.00
Step-by-step explanation:
50÷10=5
5 00+50.00= $55.00
At a bargain store, Spongebob bought 3 items that each cost the same amount. Patrick bought 5 items that each cost the same amount, but each was $1.50 less than the items that Spongebob bought. Both Spongebob and Patrick paid the same amount of money. What was the individual cost of each person's items?
Write an equation. Let x represent the cost of one of Spongebob's items.
Solve the equation. Show your work.
Check your solution. Show your work.
State the solution in complete sentences.
Answers
Answer:
Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]
Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]
Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]
Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]
Step-by-step explanation:
Let [tex]x[/tex] denotes cost of each item bought by Spongebob.
Number of items bought by Spongebob = 3
So,
Cost of items bought by Spongebob = [tex]3x[/tex]
Cost of each item bought by Patrick = [tex]x-1.50[/tex]
Number of items bought by Patrick = 5
Cost of items bought by Patrick = [tex]5(x-1.50)[/tex]
Both Spongebob and Patrick paid the same amount of money.
So,
[tex]3x=5(x-1.50)\\3x=5x-7.5\\5x-3x=7.5\\2x=7.5\\x=\frac{7.5}{2} \\x=3.75[/tex]
So,
Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]
Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]
Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]
Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]