To prove that n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3, we can start by factoring the expression:
n^2 - 7n + 12 = (n - 4)(n - 3) . Since n ≥ 3, both factors in the expression are positive. Therefore, the product of the two factors is also positive.
(n - 4)(n - 3) > 0
We can also use a number line to visualize the solution set for the inequality:
n < 3: (n - 4) < 0, (n - 3) < 0, so the product is positive
n = 3: (n - 4) < 0, (n - 3) = 0, so the product is 0
n > 3: (n - 4) > 0, (n - 3) > 0, so the product is positive
Therefore, n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3.
Alternatively, we can complete the square to rewrite the expression in a different form:
n^2 - 7n + 12 = (n - 3.5)^2 - 0.25
Since the square of any real number is nonnegative, we have:
(n - 3.5)^2 ≥ 0
Therefore, adding a negative constant (-0.25) to a nonnegative expression ((n - 3.5)^2) still yields a nonnegative result. This confirms that n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3.
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Factorize the expressions 8a⁶ + 5a³ + 1.
Use a³+b³ +c³ - 3abc
Here a = 2a²
b= -a
And c = 1
Answer:
Step-by-step explanation:
Part A:
What is the solution to the inequality below?
|x + 6| ≥ 5
Part B:
In 3-4 sentences, write a description of solution as it would look on a number line. Be sure to include the words:
-Shaded or Not Shaded
-Open or closed
-Solution
The solution of the inequality, |x + 6| ≥ 5 is given as follows,
(A) x > -1
(B) It follows that x either belongs to the interval (-∞, -11) or to the interval (-1,∞) for the given absolute inequality.
(A) Solving the Given Inequality:
|x + 6| ≥ 5
x+6 ≥ 5 or x+6 ≤ (-5)
x+6-6 ≥ 5-6 or x+6-6 ≤ (-5)-6
x ≥ -1 or x ≤ -11
Hence the solution of the given inequality is given as,
x ∈ (-∞, -11] or x ∈ [-1, ∞)
(B) Description of the Solution
From the given absolute inequality, it can be concluded that x either belongs to the interval (-∞, -11] or to the interval [-1, ∞). Hence, on the number line, the solution of the inequality will be shown as a shaded region from -∞ to -11 and from -1 to ∞. The area between -1 and -11 will remain unshaded.
In the deduced solution, the interval is either open or closed on both sides. Open interval means the extreme value is not includes. On the other hand, closed interval indicates inclusion of the extreme point in the solution of the inequality.
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The equation table below represents Lavaughn's earnings in dollars and
cents, y, for working a hours. Find the rate of change.
The rate of change is also known as the slope. The formula to find the slope of a line is (y2 - y1) / (x2 - x1).
You can use any two points, as long as both are on the line.
Point 1 = (2, 55)
Point 2 = (8, 220)
slope = (220 - 55) / (8 - 2)
slope = 165 / 6
slope = 55 / 2 = 27.5 / 1
Lavaughn earns $27.50 for working one hour.
Hope this helps!
44. The table below lists the tallest waterfalls in the world, in feet.
Name/Location Height (ft.)
Mutarazi - Zimbabwe 24.99 x 102
Gocta Cataracts - Peru 2.532 x 103
Utigord - Norway 2,625 x 100
Angel - Venezuela .3212 x 104
Espelands - Norway 2.307 x 103
Yosemite - California (USA) 2,425
Monge - Norway 25.4 x 102
Tugela - South Africa 3.11 x 103
**Heights are approximations**
[Part 1]
List the waterfalls from tallest to shortest.. Show all of your work and/or explain your reasoning.
[Part 2]
What is the difference between the tallest and shortest heights? Show your work.
The difference between the tallest and shortest heights is 0.787 × 10
StatisticsMutarazi - Zimbabwe 24.99 x 10²Gocta Cataracts - Peru 2.532 x 10³Utigord - Norway 2,625 x 10^0Angel - Venezuela .3212 x 10⁴Espelands - Norway 2.307 x 10⁴Yosemite - California (USA) 2,425Monge - Norway 25.4 x 10²ugela - South Africa 3.11 x 10³From tallest to shortest:
Angel - Venezuela 3.212 x 10⁴Espelands - Norway 2.307 x 10⁴ugela - South Africa 3.11 x 10³Utigord - Norway 2,625 x 10^0Monge - Norway 25.4 x 10²Gocta Cataracts - Peru 2.532 x 10³Mutarazi - Zimbabwe 24.99 x 10²Yosemite - California (USA) 2,425Difference between tallest and shortest heights =
3.212 x 10⁴ - 2,425
= 3.212 x 10⁴ - 2.425 × 10³
= (3.212 - 2.425) × 10^4 - 3
= 0.787 × 10
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In what type of triangle is the orthocenter located outside of the triangle?
Answer:
obtuse angle triangle
Step-by-step explanation:
please make me Brilliant for this correct answer
The floor of a rectangular room measures 5m by 4m and the ceiling is 3m from the floor. An ant is at the top of a corner of the room and crawls to the opposite bottom corner of the room. Find the shortest distance it can travel.
Answer: [tex]5\sqrt{2}[/tex] m
Step-by-step explanation:
Using the pythagorean theorem, we get that the shortest distance it can travel is [tex]\sqrt{3^2+4^2+5^2}[/tex] = [tex]5\sqrt{2}[/tex] m
Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are?
Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are repeated.
This is an exercise related to Game Theory.
What are repeated game?The extended form is typically used to depict repeated games, commonly referred to as supergames, in game theory since they occur repeatedly across time.
The potential of collaborating means that we may choose to compromise in order to continue earning a payout over time, knowing that if we do not fulfill our part of the bargain, our adversary may decide not to either.
As contrast to one-shot games, recurring games provide a new set of incentives.
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A point in quadrant iii is reflected across the y-axis. what is true about the new location? check all that apply.
The new location is in Quadrant IV and The new location has a positive x-coordinate and a negative y-coordinate. Hence, option b and c are correct.
What are Coordinates?The horizontal and vertical addresses of any pixel or addressable point on a computer display screen are, respectively, represented by the x and y coordinates.The pixel (pixel 0) on the far left of the screen serves as the beginning point for the x coordinate, which is a predetermined distance along the horizontal axis of a display.The y coordinate is a specified range of pixels along a display's vertical axis, starting at the top pixel (pixel 0). The x and y coordinates work together to pinpoint any particular pixel location on the screen.As values relative to any beginning point on the screen or any portion of the screen, such as an image, x and y coordinates can also be given.Solution:
If the point were to reflect across the y-axis, it would fall into the fourth quadrant.
Additionally, the coordinates will be positive for the x-axis and negative for the y-axis.
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I hope you are trying to ask the question below:
Question
A point in Quadrant III is reflected across the y-axis. What is true about the new location? Check all that apply.
a. The new location is in Quadrant II.
b. The new location is in Quadrant IV.
c. The new location has a positive x-coordinate and a negative y-coordinate.
d. The new location has a negative x-coordinate and a positive y-coordinate.
e. The new location has negative x- and y-coordinates.
Prove or disprove the following. In any group of two or more people, there are always at least two people who have the same number of friends. Assume that if a person p is a friend of a person q then q is also a friend of p.
Yes we can prove that in the group of more than two people that there are at least two people that have the same number friends given the condition here.
How to go about this proofLet us create a variable P. P is an individual called Joe. Now Joes seems to know all at this party. This tells us that all at this party should at least know him.
We have the set {1,2,...n-1} , given that the minimum number of persons that one person knows is 1.
Let us assume we have Harry. Harry is a party crasher who came to the party. Hence it is possible that someone like Joe that knows all at the party may not even know him. Hence the maximum persons that a person would know is given to be n. The set would then be {0, 1,...,n-2}.
There are n elements in the 2 sets that we have above. Given that n people are at this function, and there are n possibilities for the number that one person can know of the participants, then we can say that at least two people can then know equal number of persons at the party.
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The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10, 798. Find the P-value
The true mean expenditure per student is different from $10,337.
What is hypothesis in math?
A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false.There are basically two types, namely, null hypothesis and alternative hypothesis.Sample size is greater than 30 and the population standard deviation is given. Thus, in order to test
H0: µ =$10,337
H1: µ≠$10,337
The appropriate test is one sample z test.
The formula for one sample z test:
Z= x−μ / σ √ n
x−μ
x=10798
μ=10337
σ=1560
n=150
[tex]Z = \frac{10798 - 10337}{1560 / \sqrt{150} } = 3.62[/tex]
Computation of p-value:
The EXCEL formula to find the p-value for a two-tailed z-test is
“=2*(1-NORM.S.DIST(3.62, TRUE))”
Thus, the p-value obtained is 0.00029
Conclusion using α = 0.05:
Rejection rule using p-value:
If p-value ≤ α, then reject the null hypothesis.
Since, 0.00029 < 0.05, there is sufficient evidence to reject the null hypothesis.
Therefore, the true mean expenditure per student is different from $10,337.
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Determine the explicit formula for the sequence 4, 7, 14, 25
Step-by-step explanation:
You already know that we use tn=an²+bn+c for these kinds of sequences:
4, 7, 14, 25, ...
7–4=314–7=7now
7–3=4
So 2a=4===> a=2
[tex] a_{1} = 4 = = > n = 1 \\ 4 = 2 \times {1}^{2} + b + c = = = = > \\ b + c = 2[/tex]
[tex] a_{2} = 7 = = > n = 2 = = = > \\ 7 = 2 \times {2}^{2} + 2 \times b + c = = = > \\ - 1 = 2b + c[/tex]
b+c=22b+c=–1b=–3, c=5
So the final result is:
[tex] t_{n} = 2 {n}^{2} - 3n + 5[/tex]
A triangle has two sides of lengths 6 and 9
the third side be?
Check all that
What value
apply.
could the length of
Answer:
A, C, E, F
Step-by-step explanation:
since nothing else was said, it is a general triangle. nothing special about it.
so, the only rules are that the sum of any pair of sides must be longer than the 3rd side (otherwise, if the 3rd side is longer, the sides could not connect).
A. 10.
so, we have
6 + 9 > 10 true
6 + 10 > 9 true
9 + 10 > 6 true
therefore this is a possible 3rd side.
B. 2.
so, we have
6 + 9 > 2 true
6 + 2 > 9 false
9 + 2 > 6 true
therefore this is NOT a possible 3rd side.
C. 4.
so, we have
6 + 9 > 4 true
6 + 4 > 9 true
9 + 4 > 6 true
therefore this is a possible 3rd side.
D. 15.
so, we have
6 + 9 > 15 false
6 + 15 > 9 true
9 + 15 > 6 true
therefore this is NOT a possible 3rd side (this triangle is a special case as 6+9 = 15 : it can only exist as a completely flat line and is therefore not a triangle).
E. 12.
so, we have
6 + 9 > 12 true
6 + 12 > 9 true
9 + 12 > 6 true
therefore this is a possible 3rd side.
F. 7.
so, we have
6 + 9 > 7 true
6 + 7 > 9 true
9 + 7 > 6 true
therefore this is a possible 3rd side.
For which mapped relation is the domain ?
Answer:
C.
Step-by-step explanation:
For any of the given functions, all of the first input values (x-values) in the relation are considered the domain values. On the other hand, the output values (y-values) are called the range values of the given equation.
The mapped relation is the domain (1, 2, 3). Since this is domain values (x-values), the correct answer will be the mapped with 1, 2, and 3 on the left side.
The correct answer is C.
Hope this helps!
A steel mill manufactures steel plates. The average number of flaws in the steel is 1.28 flaws per square foot. Find the probability that a randomly selected 1-foot-by-1-foot area of steel plate has 2 flaws or fewer. Use Excel to find the probability. Round your answer to three decimal places.
Using excel, we can determine that the likelihood that a randomly picked steel plate measuring 1 foot by 1 foot contains two or fewer faults is 0.862.
This is further explained below.
What is probability?Generally, the characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.
In conclusion, In this section, we will make the assumption that the number of defects found in a steel plate measuring 1 foot by 1 foot has a Poisson distribution with a mean of 1.28.
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true ir false .
A central angle is equal to half the measure of its intercepted arc.
Answer:
Step-by-step explanation:
Answer
False but close.
The intercept arc and the central angle are equal.
How many more times intense, to two decimal places, was the 2011 earthquake in Japan that measured 9.0 on the Richter scale than the 1905 earthquake in San Francisco that measured 8.1 on the Richter scale?
Using the properties of logarithms, it is found that the earthquake in Japan in 2011 was 12.92 times more severe.
How to find the ratios of the intensity of earthquakes?As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2 > 0, R_1 > R_2[/tex], the ratio of the intensities is given by:
[tex]10^{\frac{R_1}{R_2}}[/tex]
The intensities for this problem are [tex]R_1 = 9, R_2 = 8.1[/tex], hence the ratio is:
[tex]10^{\frac{9}{8.1}} = 12.92[/tex]
The earthquake in Japan in 2011 was 12.92 times more severe.
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What is the area of triangle lmn? 3 square units 4 square units 6 square units 8 square units
The area of the triangle LMN is 4 units squared.
How to find area of a triangle?The area of a triangle can be described as follows:
The area of the triangle by using the base and height of the triangle.
area of a triangle = 1 / 2 bh
where
base of the triangleheight of the triangleTherefore,
base = NL = 4 units
height = PM = 2 units
Therefore,
area of the triangle = 1 / 2 × 4 × 2
area of the triangle = 8 / 2
area of the triangle = 4 units²
Therefore, the area of the triangle LMN is 4 unit squared.
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Answer: B. 4 Square Units
Step-by-step explanation:
PLEASE HELP ME I am stuck for 20 minutes.
Hello,
[tex]( \frac{1}{3} ) {}^{3} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1 {}^{3} }{3 {}^{3} } = \frac{1}{27} [/tex]
Hi! ⋇
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\sf\color{darkblue}{( \frac{1}{3}) ^{3} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1} {27} }[/tex]
Area=
Help me please :(
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Write the equation of the line that is parallel to the line y = -7/4x - 2 through the point (4,-2).
Answer:
y = - [tex]\frac{7}{4}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{7}{4}[/tex] x - 2 ← is in slope- intercept form
with slope m = - [tex]\frac{7}{4}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{7}{4}[/tex] x + c ← is the partial equation
to find c substitute (4, - 2 ) into the partial equation
- 2 = - 7 + c ⇒ c = - 2 + 7 = 5
y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line
Twenty new members are elected to an agency every two years. The agency has 100 members on average overall. How long does a member hold his/her position at the agency
The time that a member hold his/her position at the agency is approximately 0.1 year.
Given that twenty members are elected to an agency every two years and there are 100 members on a average overall.
We have to find the time that a member hold his position at the agency.
To calculate the time we have to use multiplication which means product of two numbers.
In 2 years agency elected 20 members. It shows like under:
2 years=20 members
We require 100 members at one end so we will multiply by 5 both sides.
10 years=100 members
Now take 100 to left side of equal to sign.
10/100=1 member
1 member=1/10
=0.1
Hence a member holds 0.1 year at the agency.
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As a construction estimator you estimate the cost of bathroom remodels for a general contractor one client asks for an estimate for two bathroom remodels. you estimate it will cost $20,000 for both remodels when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $100 less than the budgeted amount what was the difference between the actual cost and estimated cost for the two bathroom remodels
For two bathroom remodel estimate budget is $[tex]20000[/tex] for both remodels. when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $[tex]100[/tex] less than the budgeted .So the actual cost of two bathroom remodel is $ [tex]19800[/tex] and the different of actual and expected budgets is $[tex]200[/tex]
How can we find the actual costing of the bathroom remodel ?
Expected estimate budget of two bathroom's remodel is $[tex]20000[/tex]
So budget of one bathroom remodel is
[tex]20000/2\\=10000[/tex]
All supplies are come except for two vanities which were each $[tex]100[/tex]
So for two bathroom remodels
[tex]=2*100\\=200[/tex]
So the actual cost of remodel of both bathroom is
[tex]=20000-200\\=19800[/tex]
And difference between actual and estimated cost is
[tex]=20000-19800\\=200[/tex]
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Choose the correct simplification of the expression (C^4)^3
A. C^1
B. C^7
C. C^12
D. C^64
Use the rules of exponents to simplify the expression.
[tex]\large\displaystyle\text{$\begin{gathered}\sf (C^{4})^{3} \end{gathered}$}[/tex]
To raise a power to another power, multiply the exponents.
[tex]\large\displaystyle\text{$\begin{gathered}\sf C^{4\times3} \ \to \ Multiply \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf C^{12} \end{gathered}$}}[/tex]
Therefore, the correct option is "C".
HELP swiftly
Im not fully sure but does x measure 100?
x =x=x, equals
^\circ
∘
The value of X is 100 degree.
According to the statement
we have to find the value of x degree which represent the angle.
In this figure
we see that there are two angles which are vertically opposite angles and there is rule that the values of vertically opposite angles are always same.
So, due this reason Here the value of x is 100 degree
because in this figure the given angle which is 100 degree are vertical to the angle which we have to find and that angle which x, so, the value of x is same as the value of vertical angle.
so these angles are vertical angles. that's why x is 100 degree.
So, The value of X is 100 degree.
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what is 8 square root of 6. answered as a square root ?
The value of 8√6 as a square root is √384
Surd expressionSurd are written as the square root of prime numbers. Given the expression below;
8√6
This is can be written as;
8√6 = √(8 * 8 * 6)
8√6 = √64 * 6
8√6 = √384
Therefore the value of 8√6 as a square root is √384
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From a functionalist view point, the U.S. economic system would be seriously strained if we completely eliminated poverty level wages.
It is true that the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."
What is poverty level wages?The poverty level wages stipulates the lowest or minimum possible wages that a person can be paid in a functional economy. The maintenance of the poverty level wages helps the economy to remain functional and afloat.
Thus, it is a true statement that; From a functionalist view point, the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."
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Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.
Step 1: Find the greatest common factor of the given lengths: 7
Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5
Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared
Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct?
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
Yes, any set of lengths with a common factor is a Pythagorean triple.
No, the lengths of Pythagorean triples cannot have any common factors.
No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not
Multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
How to verify if a triangle form Pythagorean triple?Pythagoras's principle follows the rule:
c² = a² + b²
where
a and b are the legsc is the hypotenuse side.Therefore, Pythagorean triples are a² + b² = c² where a, b and c are the three positive integers. The most known and smallest triplets are (3,4,5).
If we reduced the length of the side of the triangle with the greatest common factor, it should give us 3, 4, 5.
Hence,
21, 28 and 35 has greatest common factor as 7
21 / 7 , 28 / 7 and 35 / 7
3, 4, 5
Hence, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
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Tristen is packing lunch boxes for the school trip. Each lunch box consists of 1 sandwich, 1 fruit, and 1 drink. Tristen can choose from 3 types of sandwiches, 4 types of fruit, and 2 types of drinks. How many different lunch boxes can Tristen pack
Answer:
24
Step-by-step explanation:
3x4x2=24
When finding the answer to this problem, you times all of the options by each other.
Can you please solve for X please
Answer: 100
Step-by-step explanation:
The angles with measure 100° and x° are vertical angles, which are two opposite angles made from two intersecting lines. These vertical angles are always the same measure.
Hence, both x and 100 have the same measure.
does anyone want to play tarkov and run customs or something lol? add me on disc destructer11#0001
Answer:
Step-by-step explanation:
Mabye later