A paper factory makes cardboard sheets like the one shown below. If the area of each sheet is given by the expression 6x ^ 2 + 7x + 2, what are the dimensions of each sheet of cardboard?
Answers
Answer:
(3x+2) by (2x+1)
Step-by-step explanation:
A cardboard is a rectangle, and has two dimensions. Given a quadratic equation, you should find a way to split it in two.
The easiest way to do so is through factoring. (There are many ways to do this, take a look at the plethora of sources offered on the internet.)
When the expression 6x^2 + 7x + 2 is factored, it is (3x+2)(2x+1). Hence, these are your dimensions.
Related Questions
find csc theta and sin theta if tan theta = 7/4 and sin theta less than 0
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9514 1404 393
Answer:
sin(θ) = (-7√65)/65
csc(θ) = (-√65)/7
Step-by-step explanation:
The angle will have the given characteristics if its terminal ray passes through the 3rd-quadrant point (-4, -7). The distance from the origin to that point is ...
d = √((-4)² +(-7)²) = √65
The sine of the angle is the ratio of the y-coordinate to this value:
sin(θ) = -7/√65
sin(θ) = (-7√65)/65
The cosecant is the inverse of the sine
csc(θ) = (-√65)/7
Solve the following system of equations by using the inverse of a matrix.
Give your answer as an ordered triple (x , y , z)
Answers
Answer:
(x, y, z) = (-8,4,-2)
Step-by-step explanation:
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porfavor se los agradeceria mucho y de corazon :D
Answers
Answer:
1=2p+3
2=
Step-by-step explanation:
please help me i need the answers help me please
Answers
Answer:
scientists
Step-by-step explanation:
Which proportion correctly shows the equivalence of two fractions?
A)
19∕95 = 57∕76
B)
32∕116 = 9∕29
C)
18∕36 = 72∕144
D)
18∕36 = 144∕72
Answers
Answer:
32/166=9/29 if two ratio are equivalent to other
Which statement is true about the parts of this expression?
StartFraction 5 over 6 EndFraction + one-fourth x minus y
The constant is StartFraction 5 over 6 EndFraction.
The only coefficient is One-fourth.
The only variable is y.
The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
Answers
Answer:
The constant is StartFraction 5 over 6 EndFraction
Step-by-step explanation:
StartFraction 5 over 6 EndFraction + one-fourth x minus y
5/6 + 1/4x - y
A. The constant is StartFraction 5 over 6 EndFraction.
True
B. The only coefficient is One-fourth.
False
There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1
C. The only variable is y
False
There are 2 variables: variable x and variable y
D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
False
5/6 and 1/4x are not like terms
The only true statement is: The constant is StartFraction 5 over 6 EndFraction
Answer:
It's A if you don't want to read. A). The constant is 5/6
Step-by-step explanation:
Find the missing side length, and enter your answer in the box below. If
necessary, round your answer to 2 decimal places.
6
8
Answers
6^2+8^2=c^2
36+64=c^2
100=c^2
square root 100 = square root c^2
10=c
answer is 10
The missing side length is 10 unit.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
We have,
Perpendicular = 6
Base = 8
Using Pythagoras theorem
c² = P² + B²
c² = 6² + 8²
c²= 36 + 64
c² = 100
c= 10 unit.
Thus, the missing length is 10 unit.
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A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 9 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that at least 7 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
The probability that at least 7 employees were over 50 is 0.0073%.
Step-by-step explanation:
Given that a town recently dismissed 8 employees in order to meet their new budget reductions, and the town had 9 employees over 50 years of age and 16 under 50, if the dismissed employees were selected at random, to determine what is the probability that at least 7 employees were over 50, the following calculation must be performed:
9/25 x 8/24 x 7/23 x 6/22 x 5/21 x 4/20 x 3/19 = X
0.36 x 0.33 x 0.304 x 0.272 x 0.238 x 0.2 x 0.157 = X
0.000073 = X
100X = 0.0073
Therefore, the probability that at least 7 employees were over 50 is 0.0073%.
Find the total surface area of this square based pyramid. 10ft 10ft (in the image)
Answers
300ft^2
Step-by-step explanation:
Surface Area = 2bs + b^2 where s = height of each triangular surface and b = base
Surface Area = 2(10)(10) + 10^2
Surface Area = 2(100) + 100
Surface Area = 200 + 100
Surface Area = 300ft^2
If one root of the quadratic equation is 2x2 +kx -6= 0 is 2
find the value of k
Answers
This is ur answer plz mark brainliest
Translate To An Algebraic Expression:
S% of 1/r
Answers
Answer:
S/100r
Step-by-step explanation:
S% of 1/r = (1/r x S) : 100
(1/r x S) : 100
S/r : 100
S/100r
Have a great day! Stay safe. Hope it helped
What system of equations is shown on the graph below
Answers
Answer:
A.
Step-by-step explanation:
x-2y=4 has a x-intercept of 4, a slope of 1/2, and a y-intercept of -2. 2x+y=4 has a x-intercept of -2, a slope of 2, and a y-intercept of -4.
Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?
Answers
Answer: -3/8
Step-by-step explanation:
Expanding z we get
z = 4x^2 - 4xy + y^2 - 2y^2 - 3y
= -y^2 - (4x + 3) y + 4x^2.
After Archimedes chooses x, Brahmagupta will choose
y=-(4x+3/2) in order to maximize z
Then
z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2
z=8x^2+6x+9/4
To minimize this expression, Archimedes should choose x=-3/8
Please helpppp me I really confused
Answers
Answer:
The answer would be D
Step-by-step explanation:
This is a piecewise function, meaning that it is split into two parts. The right side is an exponential and that part is greater than one, the left side is a line less than or equal to one. The only equation that matches the criteria for that is D.
Choose the correct solution for the given equation x^2-6x=40
Answers
Answer:
10,-4
Step-by-step explanation:
not sure where the options are but if you were to solve this equation first bring everything to one side.
x^2 - 6x - 40 = 0
factor it
(x-10)(x+4) = 0
set each part to 0
x-10 = 0 and x+4 = 0
solutions are 10 and -4
Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 22.8 minutes. How many employees must be included in a sample to create a 99 percent confidence interval for the average commute time with a confidence interval width of no more than 12 minutes
Answers
Answer:
96 employees
Step-by-step explanation:
Given that the standard deviation = 22.8
The width in the question = 12
We solve for the margin of error E.
E = width / 2
= 12/2 = 6
At 99%
Alpha = 1-0.99
= 0.01
Alpha/2 = 0.01/2 = 0.005
Z0.005 = 2.576
Sample size n
= ((2.576x22.8)/2)²
= 95.8
= 96
The number of employees is 96
Thank you!
Nick nas cup of syrup. He uses cup of syrup to make a bont of granota
PartA: How many bow's or granola can Nick make with cup of syrup? (4 points)
Part 8: on your own paper, draw a fraction model that shows the total number of bouts of granola that Nick can make with cup of syrup. Make sure to label the model seks
explain your model in detail to descnbe how this model visually shows the solution for Part A. (6 points). I’ll make u brainless if u help
Answers
Answer:
Step-by-step explanation:
its easyk
Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?
Answers
Answer:
15
Step-by-step explanation:
3/8 = 9
9÷3= 3
the remainder of 3/8 is 5/8 so
5x3=15
one month is what percentage of a year given that there are 7 days in a week, and 12 months in a year
Answers
Answer:
it should be 8.333333%
Step-by-step explanation:
!!!HELPPP PLEASEEE!!! For this problem I thought it meant to subtract 0.1492 - 0.1515 = -0.0023 however my answer was incorrect. How do I solve this problem then? Help Please!
Answers
Answer:
0.1492-0.1515= -0.0023
factor 9-x^2 completely
Answers
Answer:
-(x + 3)(x - 3)
Step-by-step explanation:
Using the difference of squares we can factor this expression.
[tex](9 - x^2)\\= (3^2 - x^2)\\= (3 + x)(3 - x)\\= -(3 + x)(-3 + x)\\= -(x + 3)(x - 3)[/tex]
You are dividing a rectangular garden into 2 equal sections by
placing a wooden plank diagonally across it, from one corner to
the opposite comer. The garden measures 4 feet by 6 feet. What
length diagonal plank should you buy, and why?
Diagonal planks are available in 1-foot increments (you can
buy a 1-foot board, or a 2-foot board, or a 3-foot board, and
so on...)
• You can cut the plank down from the size you buy to the
exact size, but you want to waste as little wood as possible.
Answers
Answer:
You can cut the plank down from the size you buy to the
exact size, but you want to waste as little wood as possible.
(2/3)^x-1=27/8, find x. Please add a step-by-step explanation.
[tex]( \frac{2}{3} ) {x - 1 = \frac{27}{8} }^{?} [/tex]
Answers
so basically after doing all the algebra, you will have to use the log function to solve. rearranging things and you will get the log expression that I obtained, then solve it using the change of base formula.
Based on a poll, among adults who regret getting tattoos, 24% say that they were too young when they got their tattoos. Assume that six adults who regret getting tattoos are randomly selected, and find the indicated probability.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
Answers
Answer:
a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
24% say that they were too young when they got their tattoos.
This means that [tex]p = 0.24[/tex]
Six adults
This means that [tex]n = 6[/tex]
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]
0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
This is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]
0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
This is:
[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]
0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
While planning a hiking trip, you examine a map of the trail you are going on hike. The scale on the map shows that 2 inches represents 5 miles.
If the trail measures 12 inches on the map, how long is the trail?
Answers
Answer:
30 miles
Step-by-step explanation:
Given that :
Scale = 2 inches represents 5 miles
This means that 2 inches in the map equals to 5 miles on ground ;
Hence, if the trail measures 12 inches on the map, the length on ground will be ; x
2 inches = 5 miles
12 inches = x miles
Cross multiply :
2x = (12 * 5)
2x = 60
x = 60 / 2
x = 30 miles
Scores on the SAT are approximately normally distributed. One year, the average score on the Math SAT was 500 and the standard deviation was 120. What was the score of a person who did better than 85% of all the test-takers
Answers
Answer:
The score of a person who did better than 85% of all the test-takers was of 624.44.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
One year, the average score on the Math SAT was 500 and the standard deviation was 120.
This means that [tex]\mu = 500, \sigma = 120[/tex]
What was the score of a person who did better than 85% of all the test-takers?
The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 500}{120}[/tex]
[tex]X - 500 = 1.037*120[/tex]
[tex]X = 624.44[/tex]
The score of a person who did better than 85% of all the test-takers was of 624.44.
C = ſa²+b² Please describe the Mathematical order of Operation
Answers
Step-by-step explanation:
C + ſa6+b5 bescribe the Mathematical order of Operation
How many gallons each of 15% alcohol and 10% alcohol should be mixed to obtain 5 gal of 13% alcohol?
Answers
9514 1404 393
Answer:
3 gallons 15%2 gallons 10%Step-by-step explanation:
Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...
0.15x +0.10(5-x) = 0.13(5)
0.05x +0.5 = 0.65 . . . . . . . simplify
0.05x = 0.15 . . . . . . . . . subtract 0.5
x = 3 . . . . . . . . . . . . . divide by 0.05
3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.
find x
thank you thank you thank you!!
Answers
Answer:
Step-by-step explanation:
x=120°
Find the number of distinguishable arrangements of the letters of the word SEPTILLION
Answers
Answer:
10!
Step-by-step explanation:
Septillion-10 letters
1-s-10 places to be in
2-e-9
3-p-8
4-t-7
5-i-6
6-l-5
7-l-4
8-i-3
9-o-2
10-n-1
So, then
10×9×8×7×6×5×4×3×2×1=10!
or 3628800
The arrangement of the number will be equal to 3628800.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a way to choose items or numbers from a collection or group of items without worrying about the items' chronological order.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
The given word is SEPTILLION. The word has 10 characters. The different ways of the arrangement will be calculated as,
Arrangement = 10!
Arrangement = 10×9×8×7×6×5×4×3×2×1
Arrangement = 3628800
Therefore, the arrangement of the number will be equal to 3628800.
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