Using the Factor Theorem, it is found that the complete factorization of the polynomial x³ + 8x² + 19x + 12 is given by:
A. (x+4)(x+3)(x+1)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, using a calculator, the roots of the polynomial x³ + 8x² + 19x + 12 are x = -4, x = -3 and x = -1, hence:
f(x) = (x + 4)(x + 3)(x + 1)
Which means that option A is correct.
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Im Ms.Barclay classroom 2/3 of the students play sodoku, 3/8 also play checkers. If there are 24 students in her class, how many play sodoku and checkers?
[tex]\frac{3}{8}(24)=\boxed{9}[/tex]
A total of 6 students play sudoku and checkers both.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given that,
Number of students = 24
Fraction who plays checkers = 2/3
So,
⇒ 2/3 × 24 = 16 students.
Now,
3/8 fraction of students(out of this 16) also play sudoku
So,
3/8 × 16 = 6 students.
Hence "A total of 6 students play sudoku and checkers both".
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The given question is incorrect,the correct question is ;
In Mr. Barclay's classroom, 2/3 of the students play checkers. Of the students who play checkers 3/8, also play sudoku. If there are 24 students in his class, how many play checkers and sudoku? There is/are a student(s) who play both checkers and sudoku
The stem-and-leaf display below gives the fuel efficiencies (in miles per gallon) for a sample of new cars. Use the display to answer the questions that follow.
Fuel efficiency (miles per gallon)
1 3
2 3 9
3 1 1 6 7
4 3 4 5 6
5 1 3 3 8
Key: 1/3 means a fuel efficiency of 13 miles per gallon.
A) What is the lowest fuel efficiency in the 30 0s?
B) What is the lowest fuel efficiency in the sample overall?
C) How many cars in the sample have fuel efficiencies in the 40s?
Answer:31
Step-by-step explanation:
59=64
(a) The lowest fuel efficiency in 30's is 31
(b) The lowest fuel efficiency in the overall sample is 13
(c) There are 4 cars in the sample that have fuel efficiencies in 40's
Given :
Stem and leaf display of data
Fuel efficiency (miles per gallon)
1 3
2 3 9
3 1 1 6 7
4 3 4 5 6
5 1 3 3 8
Explanation :
(A) We need to find the lowest fuel efficiency in 30's
So we look at the data's in third row
It shows the fuel efficiency of 31,31,36,37 miles per gallon
The lowest fuel efficiency in 30's is 31
(B) Lets write the fuel efficiency from the given table
13, 23, 29, 31,31,36, 37, 43, 44, 45, 46, 51, 53, 53, 58
The lowest fuel efficiency in the overall sample is 13
(C) Lets write the fuel efficiency of 40's
43, 44, 45, 46
So, there are 4 cars in the sample that have fuel efficiencies in 40's
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a car can drive 165 miles in 5 hours. how many yards can thee car travel in a hour
Answer:
33
Step-by-step explanation:
because 165 divided by 5 is 33 and if you add 33 5 times it gives you 165
Answer:
58080 Yards
Step-by-step explanation:
165/5 = 33 miles an hour
33 miles an hour ~ 58080 yards an hour
Emmanuel brews a full pot of coffee every morning. The pot makes 12 cups
of coffee in 4 minutes. How many cups of coffee does it make per minute?
O 3 minutes/cup
O 333 cups/minute
О O
3 cups/minute
O .333 minutes/cup
A deck of cards is shuffled and then divided into two halves of 26 cards each. A card is drawn from one of the halves; it turns out to be an ace. The ace is then placed in the second half-deck. The half is then shuffled, and a card is drawn from it. Compute the probability that this drawn card is an ace. Hint: Condition on whether or not the interchanged card is selected.
Answer:
[tex]\frac{3}{52}[/tex]
Step-by-step explanation:
Hope this helps! Ask me anything if you have any questions! I'm free to help you anytime!
4.) What is the better buy?:
$5 for 8 pens
OR
$32.50 for 50
pens?
Show your work.
Answer:
$5 for 8 pens
Step-by-step explanation:
0.625 times 8= 5 dollars
0.625 times 50= 31.25
which is way cheaper
Answer:
5 for 8 pens
Step-by-step explanation:
I did it on a paper.
Lol
Which theorem or postulate proves that △ABC and △DEF are similar?
The two triangles are similar by which postulate or theorem?
SAS Similarity Theorem
SSS Similarity Theorem
AA Similarity Postulate
Answer:
AA Similarty
Step-by-step explanation: We are given that two angles are congruent so we use AA SImilarity. Stating that if two angles are congruent, then the figures are similar.
The postulate that can be used to prove that triangles ABC and DEF are similar triangles is: C. AA Similarity Postulate.
What is the AA Similarity Postulate?The AA similarity postulate states that when two triangles have two pairs of corresponding angles that are congruent to each other, the two triangles are regarded as similar triangles.
Thus, triangles ABC and DEF have:
two pairs of congruent angles - ∠B ≅ ∠E and ∠C ≅ ∠F.
Therefore, the postulate that can be used to prove that triangles ABC and DEF are similar triangles is: C. AA Similarity Postulate.
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a boat travels upstream for 108 miles in 4 hours, and returns in 3 hours traveling downstream in a river. What is the rate of the boat in still water, and what is the rate in the current?
Answer:
Rate in still water = 27 mph
Rate in the current =36 mph
Step-by-step explanation:
The rate is the speed the boat use to travel in the water
The distance travelled upstream = 108 miles
The time taken to travel upstream = 4 hours
The rate in still water /upstream = 108/4 = 27 mph
The rate in the current /downstream = 108/3 =36 mph
Simplify
(5i²+8i+10) - (3i²-10i+3)
Answer:
2i^2+18i+7
Step-by-step explanation:
(5i^2+8i+10)-(3i^2-10i+3)
5i^2+8i+10-3i^2+10i-3
2i^2+18i+7
pls pls pls help i’m so confused
Answer:
x=50
hope it helps........
Answer:
50°
Step-by-step explanation:
Thousands of years ago, a group of people called the Sumerians decided that, since a year is roughly 360 days, 360 was a nice number of parts to split a circle into (that, and it's a very easy number to divide up into smaller parts without dealing with
2. Solve the equation.
x - 5(x - 1) = x - (2x - 3)
Answer:
=2/3
Step-by-step explanation:
Ales read 1/3 of a book Monday. 28 pages Tuesday . still has 1/3 left to read. how many pages in book
Answer:
there are 84 pages in the book.
Step-by-step explanation:
let's call the pages in the book b.
1/3b + 1/3b + 28 = b
2/3b + 28 = b
subtract 2/3b from both sides of the equation
2/3b - 2/3b + 28 = b - 2/3b
28 = b - 2/3b
28 = b/3
multiply both sides of the equation by 3
28 * 3 = b/3 * 3
28 * 3 = b
84 = b
Answer:
The book has 84 pages
Step-by-step explanation:
Equations
Let's make:
x = number of pages of the book
Alex read 1/3x of the book on Monday, 28 pages on Tuesday, and still has 1/3x left to read. The sum of all these portions add up to the number of pages of the book, thus:
[tex]\displaystyle \frac{x}{3}+28+\frac{x}{3}=x[/tex]
Multiplying by 3:
[tex]x+84+x=3x[/tex]
Simplifying:
x = 84
The book has 84 pages
if you can help please do :)
Step-by-step explanation:
A
[tex]180 - 60 - 70 = 50 \\x = 180 - 50 = 130 \\ x = 130[/tex]
HELPPPPPPPPPPPPPPPPPPP
Answer:
simple.
Step-by-step explanation:
If you know the angle of a straight line, its 180. first, subtract 180-135. this wqould be 45. therefore, the interior angle is 45. We know that a triangles area always adds to 180, so it would be 45+x+74=180. this would be x=61. to check, add the same thing, 45+74, but instead of x add 61.
Five units to the right of -6
Answer: -1
Step-by-step explanation:
On Saturday, Ms. Rivera went to the store with $50. She needed to get clothes for the gym. She bought 5 pairs of socks for $3 dollars each, then paid $25 for shorts. Thankfully, Ms. Rivera had a coupon for half off everything! How much money did Ms. Rivera go home with?
Answer:
20
Step-by-step explanation:
She bought 5 pairs of socks which are 3 dollars each
(5 times 3 = 15 )
With the 25 dollar shorts
( 25 + 15 = 40 )
with a coupon of half off
( 40 divided by 2 = 20)
HELP PLEASE ASAP!!!!!!!
PLZ HELP ASAP
A cereal box holds 729 cubic inches if the area of the base measures 40.5 square inches
Answer:
The height = 18 inches
Step-by-step explanation:
The volume = area of the base × height
Area of the base = 40.5 inches²
The volume = 729 inches³
729 = 40.5 × height
Height = 729 ÷ 40.5 = 18 inches
Four of our eight planets are gas giants.
The rest are made of rock. What fraction
of our planets are gas giants?
Answer:
half of them 50% .5 4/8 1/2
Answer:
4/8 or 1/2 or 50%
Step-by-step explanation:
According to your info in the question:
4 planets are gas giants.
8 total planets.
4 / 8 simplified is 1/2
A U.S. Senator from Indiana wanted to know what all her constituents thought about the Clean Air Act that was coming up for a vote in the Senate. She sent a letter to a sample of 257 Indiana voters asking them if they supported the Clean Air Act even if it meant they would have to pay higher prices for gasoline. The results indicated that 39% of the sample supported the Clean Air Act, even if it meant higher gasoline prices. The sample of Indiana voters was intended to represent all Indiana voters; therefore, the value of 39% would be called __________.
Answer:
The value of 39% would be called parameter.
Step-by-step explanation:
When a percentage refers to a sample, it is called a statistic.
When it refers to a population, it is called a parameter.
The sample of Indiana voters was intended to represent all Indiana voters;
This means that the percentage will be used with the following meaning:
"39% of all Indiana voters ..."
That is, referring to the entire population(in this case, all Indiana voters), so would be a parameter.
find the height of the cylinder if the volume is 340, and the length is 3
Answer:
113
Step-by-step explanation:
divide the volume with the length
45°
V7
45°
Х
find the length of side x in simplest radical form with a rational denominator
Answer:
[tex]x = \sqrt{\frac{7}{2} }[/tex]
Step-by-step explanation:
Explanation
From given graph
AC = √7
Given angle ∝ = 45°
[tex]cos\alpha = \frac{adjacentside}{Opposite side}[/tex]
[tex]cos45 = \frac{x}{\sqrt{7} }[/tex]
[tex]\frac{1}{\sqrt{2} } = \frac{x}{\sqrt{7} }[/tex]
[tex]x = \frac{\sqrt{7} }{\sqrt{2} }[/tex]
[tex]x = \sqrt{\frac{7}{2} }[/tex]
x = 1.8708
3 ÷ 1/8 simplified dont use calculator the answer is not 24
Answer:
Step-by-step explanation:
Since we converted 3 1/8 to 25/8, this is actually (25/8)/100. This simplifies to: (25/8)/100 = 25/(8*100) = 1/8 * 25/100 = 1/8 * 1/4 or 1/(4*8) = 1/32. A simplest fraction is a fraction of the form a/b where a and b share no factors other than 1. And 1/32 is the simplest fraction you can get.
Answer: 24/1
Step-by-step explanation:
The answer is 24....maybe just add the 1 under it
The occupancy of the room must be less than 437 people
a) p 437
c) p ≤ 437
d) p ≥ 437
an area of 6 yards is equal to 54 square feet. 9 square yards is equal to how many square feet? explain or show your reasoning
Answer:
81 squared feet
Step-by-step explanation:
20x-3y = 4 and 3x -y = -5
Answer:
Step-by-step explanation:
3x-y=-5
y=3x+5
20x-3(3x+5)=4
20x-9x-15=4
11x=19
x=[tex]\frac{19}{11}[/tex]
y=3([tex]\frac{19}{11}[/tex])+5
y=[tex]\frac{112}{11}[/tex]
1) All birds can fly. (2) Penguins are birds. Therefore, (3) Penguins can fly. Question 1 options: Passes the true premises test and passes the proper form test. Passes the true premises test and fails the proper form test. Fails the true premises test and passes the proper form test. Fails the true premises test and fails the proper form test. None of the above.
Answer:
The correct Answer is - Fails the true premises test and passes the proper form test.
Step-by-step explanation:
Given,
The first premise is - All birds can fly
The second premise is - Penguins are birds
Conclusion - Penguins can fly
As we know that all birds cannot fly , so first premise is not true.
Penguins is a bird , it is true . So second premise is true.
As , to pass the true premise test, both premises has to be true
But here, in this question , one premise is not true
So, it Fails the true premises test.
As the argument is valid
If the premises is true , then the conclusion is valid
So, it passes the proper form test.
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 6 engines and the mean pressure was 5.4 pounds/square inch with a standard deviation of 0.7. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answer:
Do no reject null hypothesis.
Conclusion:
there is no sufficient statistical evidence at 0.025 level of significance to support the claim.
Step-by-step explanation:
Given that;
mean x" = 5.4
standard deviation σ = 0.7
n = 6
Null hypothesis H₀ : μ = 5.0
Alternative hypothesis H₁ : μ > 5.0
∝ = 0.025
now,
t = ( 5.4 - 5.0) / ( 0.7/√6) = 0.4 / 0.2857 = 1.4
degree of freedom df = n-1 = 6 - 1 = 5
T critical = 2.571
Therefore; t < T critical,
Do no reject null hypothesis.
Conclusion:
there is no sufficient statistical evidence at 0.025 level of significance to support the claim.
Can anyone help me pls
‼️‼️‼️‼️‼️‼️‼️‼️HELPPPPPPPP NOWWWW and any other questions on my page recently ill mark you brainliest
Answer:
A) t(x)=948(0.955)^x
Step-by-step explanation:
The key term here is decreases by. This means there's going to be exponential decay. The exponential decay factor, r, in this case, will be r=1-0.045=0.955 and we also know this is exponential decay because r<1. The only possible option that works is A because when x=0 the result should be $948 because only 0 years have passed!