Answer:
Yes, 2² = -2².
Step-by-step explanation:
Given that,
→ prove that 2² equals to -2².
Let's prove the equation,
→ 2² = -2²
→ 4 = 4
→ [ LHS = RHS ]
Hence, it is proved to be equal.
Write each arithmetic series in summation notation. 7+9+11+ . . . . . . +21
The given arithmetic series can be expressed in summation notation as [tex]\sum\limits^8_{n=1} {(2n+5)}[/tex] or in simplified notation [tex]40+2 \sum\limits^8_{n=1} {n}[/tex]
The summation notation is used to express long summation in one expression.
The given arithmetic series is:
7+9+11+ . . . . . . +21
Find the explicit formula for the nth term in the given series.
Recall:
a(n) = a(1) + (n-1) . d
where:
a(1) = the first term
d = common difference = a(2) - a(1) = a(n) - a(n-1)
From the series, we get:
a(1) = 7
d = 9 - 7 = 2
Hence,
a(n) = a(1) + (n-1) . d
a(n) = 7 + (n-1) . 2
a(n) = 2n + 5
Find number of terms in the given series.
From the given series, we know that the last term is 21.
Let the last term be a(n), then,
a(n) = 2n + 5
21 = 2n + 5
2n = 16
n = 8
Write the summation notation with lower limit n = 1 and upper limit n = 8.
[tex]\sum\limits^8_{n=1} {a(n)}= \sum\limits^8_{n=1} {(2n+5)}[/tex]
If necessary, simplify the summation.
[tex]\sum\limits^8_{n=1} {(2n+5)}= \sum\limits^8_{n=1} {2n}+ \sum\limits^8_{n=1} {5}[/tex]
[tex]= \sum\limits^8_{n=1} {2n}+ 8\times5[/tex]
[tex]=40+2 \sum\limits^8_{n=1} {n}[/tex]
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Several friends buy jeans for $20.00 a price. What type of relation exists between the amount of money spent and the number of jeans purchased
The amount of money spent and the number of jeans purchased have a direct relationship.
What do we mean by direct relationship?A direct relationship exists when both variables increase or decrease together. In a direct relationship, Y rises as X rises. A direct relationship always has a positive slope on a graph. A positive relationship is another term for a direct relationship. The relationship between the height from which a ball bounces and the height from which it bounces back is an example of a direct relationship. The higher the ball is bounced (variable x), the higher it will rebound (y).So, in the given situation where several friends buy jeans for $20.00 a price.
The amount of money spent and the number of jeans purchased have a direct relationship.Therefore, a direct relationship exists between the amount of money spent and the number of jeans purchased.
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pls help! 50pts
Which statement best describes why the steady state theory cannot explain the radiation detected in space?
Answer:
D. The theory is based on the idea that an explosion did not occur; therefore, evidence of radiation would not be predicted in the theory.
Step-by-step explanation:
You want to identify the statement that best describes why the steady state theory cannot explain the radiation detected in space.
RadiationThe Big Bang theory explains the cosmic background radiation as remanent thermal energy from the explosion creating the known universe. The Steady State theory presumes there was no explosion. It offers no alternative explanation for the observed cosmic background radiation.
The cosmic background radiation was first observed in 1965 by two radio astronomers who set out to map radio signals from the Milky Way. They found microwave signals that could not be attributed to a specific source, and were of the same intensity in every direction at every time of day or season of the year. The spectrum of this radiation is consistent with a source temperature of about 2.725 K, explained as the cooled remains of the hot plasma that once filled the universe.
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Determine a base and a height for each shape.
Answer:
base :6 units
height:4units
area of a triangle: 1/2 ×b×h
1/2× 6×4=12
12sqaure units should be the area
writ all the factors other than 1 and the number itself
for 5th grade
Answer:
A prime number has exactly two factors, 1 and itself. For example, 13 is a prime number because the only factors of 13 are 1 and 13
if this is what you are looking for..
Pls pls pls help with the math quetion!
Answer:
Answer no. 4
Step-by-step explanation:
1.67 x 10^3 = 1670
16.7 x 10^3 = 16700
those number are clearly the biggest in their categories, so answers 1 and 2 are not worth further consideration. Also note that all the numbers are the same in every answer except 1.67 x 10^3 or 16.7 x 10^3, so the 16.7 might be an error. Fortunately it does not change the answer.
Let's choose between answers 3 and 4. We start with easy numbers:
4^2 = 16
50/3 = 16.6666...
So 50/3 must come after 4^2.
We're left with answer 4.
We can also convert everything to decimal:
[tex]15.75\\\sqrt{250} = 15.8113883...\\4^2 = 16\\50/3 = 16.666666....\\16.7 \cdot 10^3 = 16700\\1.67 \cdot 10^3 = 1670[/tex]
from which we can order conventionally
what is the probability that the customer is either older than 50 or younger than 30 ?
Answer: 0.71
Step-by-step explanation:
Older than 50: 50-60 and >=60
50-60 : 90 customers
>=60 : 52 customers
90+52=142 customers
Younger than 30: <20 and 20-30
<20 : 67 customers
20-30: 100 customers
67+100=167 customers
142+167=309 customers are either older than 50 or younger than 30
Total customers:
67+100+55+72+90+52=
167+127+142=
294+142=434 customers
309/434=0.71
Is the sequence geometric? If it is, what are a₁ and r ?
a. 2,4,8,16, . . . . . . . . .
The given sequence 2, 4, 8, 16,... is geometric, with a₁ = 2 and r = 2.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now,
Given: 2, 4, 8, 16, ...
The sequence can also be written as: 2¹, 2², 2³, 2⁴,...
Thus, it follows the definition of geometric progression, having a₁ = 2 and a constant increment of 2, i.e., r = 2.
Hence, The given sequence 2, 4, 8, 16,... is geometric, with a₁ = 2 and r = 2.
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If X+y=x, show that (a+b)²= a²+2ab+b²
Answer:
a^2+2ab+b^2
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
a(a+b)+b(a+b)
(a^2+ab)+(ab+b^2)
a^2+2ab+b^2
Find the arithmetic mean a n of the given terms. a n₋₁ =100, an ₋₁ =140
The arithmetic mean a n of the given terms a n₋₁ =100, an ₋₁ =140 is
a (n) = 20.
What is arithmetic mean?a n₋₁ =100, an ₋₁ =140
a (n) = (140-100)/2
a (n) = 20
The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.
The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).
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help please and thank you
Step-by-step explanation:
False!
the correct equation should be ( x - 3)² + 2
3 units shifted to the right and 2 units upward.
also you can expand the equation to find the axis of symmetry to be sure. :)
6.8 divided by 34 HELP PLSSSSSS i also need it in step by step because i have to show my work ;) RIGHT ANSWER GETS MARKED BRAINLIST
Answer:
[tex]\mathrm {\dfrac{1}{5} \; or\; 0.2 \; in \; decimal}[/tex]
Step-by-step explanation:
We are asked to find [tex]\dfrac{6.4}{34}[/tex]
Multiply numerator and denominator by 10 to convert them to whole numbers
[tex]\dfrac{6.8}{34} = \dfrac{6.8 \times 10}{34 \times 10} = \dfrac{68}{34 \times 10}\\\\= \dfrac{68}{34} \times \dfrac{1}{10}\\\\= 2 \times \dfrac{1}{10}\\\\= \dfrac{2}{10}\\\\= \dfrac{1}{5}\\\\= 0.2[/tex]
Let f(x) = x²+1 and g(x)=3 x . Evaluate each expression. (g ₀ f) (1/2)
The value of the expression (g ₀ f) (1/2) is 15/4
In this question, we have been given two functions f(x) = x² + 1 and g(x) = 3x.
We need to evaluate an expression. (g ₀ f) (1/2)
We know that the composite function is a function where the output of one function becomes the input of another function.
First we find the composite function (g ₀ f) (x)
(g ₀ f) (x)
= g(f(x))
= 3(f(x))
= 3 (x² + 1 )
= 3x² + 3
So, (g ₀ f) (x) = 3x² + 3
Now, we find the value (g ₀ f) (1/2)
(g ₀ f) (1/2)
= 3(1/2)² + 3
= 3(1/4) + 3
= 3/4 + 3
= 15/4
Therefore, the value of the expression (g ₀ f) (1/2) is 15/4
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D bisects AB. If AD = 2² - x and DB= 2x - 2, find the value(s) of x, AB, DB, and
AD.
The required values are x = 2 , AB = 4 , DB = 2 and AD = 2 .
Since D bisects AB , therefore AD = DB
hence , ( 2 ^ 2 ) - x = 2 x - 2
Solving linear equation ,
4 - x = 2 x - 2
3 x = 6
x = 2
AD = 4 - 2 = 2 .
DB = AD = 2 .
AB = AD + DB = 2 + 2 = 4 .
Hence , x = 2 , AB = 4 , DB = 2 and AD = 2 .
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Please show your work!! Identify the volume of the composite figure. Round to the nearest tenth.
The volume of the composite figure = 860.7 m³
How to Find the Volume of a the Composite Figure?The volume of the composite figure = volume of rectangular prism - Volume of cylinder.
Volume of rectangular prism = (length)(width)(height)
Length = 10 mWidth = 10 mHeight = 12 mVolume of rectangular prism = (10)(10)(12)
Volume of rectangular prism = 1,200 m³
Volume of the cylinder = πr²h
r = 3 m
h = 12 m
Volume of the cylinder = π(3²)(12)
Volume of the cylinder = 339.3 m³
The volume of the composite figure = 1,200 - 339.3
The volume of the composite figure = 860.7 m³
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Rebecca used 3/15 of string on Monday and 5/15 on Tuesday. How much string does she have left?
answer choices
7/15
8/15
6/15
Answer: 7/15
Step-by-step explanation:
Jessica wants to attach ribbon around her wardrobe.
1 3/4 m, 2/3 m
She has 4 metres of ribbon.
How much more does she need?
Give your answer as a fraction.
Based on the fact that Jessica wants to attach ribbons around her wardrobe, the amount more of ribbons that she needs is 5/6 meters of ribbons
How much ribbons does Jessica need?Find out the distance wound Jessica's wardrobe:
= 1¹/₃ + ²/₃ + 1¹/₃ + ²/₃
= 58 / 12
= 4 ⁵/₆ meters
The amount more that Jessica needs is therefore:
= 4 ⁵/₆ - 4
= 5/6 meters of ribbons
In conclusion, Jessica needs 5/6 meters of ribbons
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. If BD 1 AC, m/DBE = (2x - 1)°, and
m/CBE = (5x - 42), find the value of x.
Step-by-step explanation:
well, because the 2 lines are intersecting each other at a right angle (90°), the complete angle CBD is 90°.
that means the sum of the sub-angles must be 90° :
DBE + CBE = 90
2x - 1 + 5x - 42 = 90
7x = 133
x = 19
Choose the vocabulary term that correctly completes each sentence.
There is a constant ________ between consecutive terms in a geometric sequence.
There is a Constant Ratio between consecutive terms in a geometric sequence.
The consecutive terms in a Geometric Progression or Sequence are separated by a Constant Ratio which remains constant for the whole sequence and all of the terms in that sequence are separated by that Ratio. Generally, the Constant Ratio is denoted by 'r'. The next term of the sequence can be determined by using this Ratio.
To determine the next term or [tex]n^{th}[/tex] term, we need to multiply the previous term with the Ratio. There is a specific formula to determine the [tex]n^{th}[/tex] term in a geometric sequence. The formula for determining the next term or [tex]n^{th}[/tex] term is: => [tex]a_{n} = ar^{(n-1)}[/tex]
Here, [tex]n = n^{th}[/tex] term, [tex]a =[/tex] First term, and [tex]r =[/tex] Constant Ratio
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ASAP PLEASE!!!!!!!!!!!!!
An unbiased statistic is one in which the average value of the statistic is ____________ the population parameter.
a. less than
b. greater than
c. either greater than or less than
d. equal to
An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.
Unbiased Statistic/estimator is defined as the accurate statistic that is used in approximation a population parameter.
In the above statement the word "accurate" means that it should be neither greater than nor less than the population parameter.
If the average value is less than the population parameter or greater than the population parameter then the statistic will be termed as "biased".
Therefore , An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.
The correct option is (d) equal to.
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in his garden Tim plants the seed 4 3/4 below the ground. after one month the tomato plant has grown a total of 8 1/2. How many inches is the plant above the ground
Answer: 3 3/4
Step-by-step explanation:
The plant is 4 3/4 below ground, but then it grows 8 1/2.
Use subtraction to find the difference.
8 1/2 - 4 3/4 = 3 3/4
Answer:the answer would be 3 3/4
Step-by-step explanation:
what asserts that a 3-dimensional manifold is the same as the 3-dimensional sphere precisely when a certain algebraic condition is satisfied.
I will sleep with whoever is correct
In topology, the Pointcare conjecture is the one that states a 3-dimensional mainfold is the same as the 3-dimensional sphere.
What does topology studies?Topology is a branch derived from geometry, this branch focuses on studying and analyzing geometrical properties and spatial relationships. One of the focuses of this area is the equivalences of some shapes or spaces.
What is the Pointcare conjecture?This conjecture created by Pointcare in the 19th century proposes a three dimensional mainfold is the same or it is equivalent to a three dimensional sphere.
This conjecture was first proven as valid by Pointcare and other mathematicians/experts in the topic. However, some years later the same Pointcare and other experts showes this conjuction is not always true and therefore it is not valid.
Despide this, to this day this conjecture remains very popular and people around the world are still trying to prove it or dispprove it.
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Solve the system of equations. 4x – y = 4 2x2 – y = 4 (0, 4) and (0, –4) (1, 0) and (1, –6) (2, 4) and (0, –4) (3, 8) and (0, –4)
Answer: Choice C
(2, 4) and (0, -4)
========================================================
Explanation:
Let's solve the first equation for y
4x - y = 4
-y = -4x+4
y = 4x-4
Now plug this into the other equation and solve for x.
2x^2 - y = 4
2x^2 - ( y ) = 4
2x^2 - ( 4x-4 ) = 4
2x^2 - 4x+4 = 4
2x^2 - 4x+4-4 = 0
2x^2 - 4x = 0
2x(x - 2) = 0
2x = 0 or x-2 = 0
x = 0 or x = 2
-----------------
If x = 0, then,
y = 4x-4
y = 4(0)-4
y = -4
This gives one solution as (0, -4)
-----------------
If x = 2, then,
y = 4x-4
y = 4(2)-4
y = 4
The other solution is (2, 4)
-----------------
To check the answers, plug the x and y coordinates into each equation. You should get the same thing on both sides.
Below is verification using a graph. The points of intersection are the solutions.
To steer an airboat, rudders sit behind the fan. When the air
passes through the turned rudders, it turns the boat. Use Newton's third
law to construct an explanation on how the rudders turn the boat.
The fluid is redirected by the rudders, which then produce an opposing force that helps the boat move in the desired direction.
Describe Newton's third law of motion?According to Isaac Newton's law, whenever an object X applies a force on another object Y, object Y must respond by applying a force that is equal in magnitude but directed in the opposite direction.
In the case of the rudder, it causes the fluid to flow in a different direction while still exerting an equivalent force of the same size. Consequently, this causes the boat to move, making it the best option.
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Rotate the figure 90° clockwise. Then rotate the figure 180°
Answer:
this is super easy...
u first rotate it 90° until the BC is downwards.
then rotate it one round until it comes to the way it was..that means once again BC down...hope it is clear...
How am I supposed to do this? I know that the x = 11, but I have no clue on what to do from there
Find m∠CED.
Answer: 140°
Step-by-step explanation:
x = 11
5 x 11 = 55
55 - 15 = 40
The 5x-15 = 40°
tHe 3x+7 is opposite, so it also equals 40°
40 + 40 = 80°
360° - 80° = 280
280 divided by 2 = 140°
find the area of the shaded section ABC
Answer:
The shaded area is 66.40 cm²============================
The shaded section is the difference of sector OAB and triangle OAC.
Area of sectorFind the measure of angle Ocos ∠O = OC/OAcos ∠O = 5/13m∠O = arccos (5/12)m∠O = 65.4° (rounded)Find the area of sector OABA = πr²θ/360A = 3.14*13²*65.4/360A = 96.40 cm²Area of triangleFind the height of triangleUse Pythagorean
OA² = OC² + AC²13² = 5² + AC²AC² = 169 - 25AC² = 144AC = √144AC = 12Find area of triangleA = bh/2A = 5*12/2A = 30 cm²Shaded areaFind shaded areaA = 96.40 - 30A = 66.40 cm²URGENT: DUE TODAY
In the picture, k || p, m 21 = 2x + 24, and mz3 = 10x. Find m<2.
Answer:
C
Step-by-step explanation:
Write a flow proof of the Exterior Angle Theorem.
Given: ΔXYZ
Prove: m ∠ X + m ∠ Z = m ∠ 1
Triangle angle sum property states that the sum of a triangle's interior angles is 180°. parallel to the given triangle's side BC. As a result, the sum of a triangle's interior angles is 180°.
What is meant by angle sum property?
Triangle angle sum property states that the sum of a triangle's interior angles is 180°. parallel to the given triangle's side BC. As a result, the sum of a triangle's interior angles is 180°.
The Triangle Angle-Sum Theorem and the Definition of a Linear Pair serve as the foundation for this proof. Create two equations based on the diagram, one for each of these relationships. When two angles form a linear pair, we know they are supplementary and add up to 180 degrees. At this point in the proof, you can set the two equations equal to each other and simplify to obtain the proof's final conclusion.
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