Explain how System 1 becomes equivalent to System 2.
System 1:
AX + By = C
LX + My=N
System 2:
(A + L)X + (8 + M)y = C+N
AX + By = C
A.The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.
B.The first equation in System 2 is the difference of the equations in System 1. The second equation in System 2 is the first equation in System 1.
C.The first equation in System 1 is the sum of the equations in System 2. The second equation in System 1 is the second equation in System 2.
D.The first equation in System 1 is the difference of the equations in System 2. The second equation in System 1 is the second equation in System 2.
Answer:
[tex]\left\{\begin{array}{ccc}(A+L)x+(B+M)y=C+N\\Ax+By=C\end{array}\right[/tex]
A.The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}Ax+By=C\\Lx+My=N\end{array}\right}\qquad\text{add both sides of the equations}\\(Ax+Lx)+(By+My)=C+N\qquad\text{distributive}\\(A+L)x+(B+M)y=C+N[/tex]
Equivalent expressions are expressions that have the same value.
The true statement is: (a) The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.
The systems of equations are:
System 1
[tex]\mathbf{Ax + By = C}[/tex]
[tex]\mathbf{Lx + My = N}[/tex]
System 2
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
[tex]\mathbf{Ax + By = C}[/tex]
When the equations of system 1 are added, we have:
[tex]\mathbf{Ax + Lx + By + My = C + D}[/tex]
Factor out x and y
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
The above equation is the first equation of system 2.
While [tex]\mathbf{Ax + By = C}[/tex] is the second equation of the system
Hence, the true statement is (a)
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A phere has a diameter of 12 ft. What is the volume if the sphere? Give the exact value in terms of pi
if the diameter of it is 12, its radius is half that or 6.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3} \begin{cases} r=radius\\ \cline{1-1} r=6 \end{cases}\implies V=\cfrac{4\pi (6)^3}{3}\implies V=288\pi[/tex]
Evaluate sin-1(-1/2) for the angles between 0 and 360°
PLEASE HELP!!!!
Check the picture below, notice the angles encircled in purple.
What is the measure of AC?
А. 299
В. 122
с. 58
D. 116°
Answer:
○ D. 116°
Step-by-step explanation:
Think of the Unit Circle. You know that half of 360° is 180°, and that angle has a measure of 58°, so you do this:
-58° + 180° = 122°
Now, that chord of the circle drags it a bit by a few units, so that will be approximately 116°.
*This may not be the best explanation I can give, but I gave one.
I am joyous to assist you anytime.
which of the following is the probability that a Blue Marble will not be selected from a bag containing 9 red marbles 6 blue marbles 7 green Marbles and 11 yellow marbles if one is selected randomly
79%
32%
18%
82%
Answer: 82%
Step-by-step explanation: Count the total number of marbles.
9+6+7+11=33 marbles in total.
We are trying to find the probability of NOT picking a blue marble. There are 6 blue marbles. Subtract the blue marbles from the total.
33-6=27
The probability of not picking a blue marble is 27/33. Divide the fraction.
27/33=0.82
Multiply by 100 to get the percent.
0.82 x 100 = 82%
There is an 82% chance of not picking a blue marble.
Here are the heights in inches of 10 professional basketball players: 66, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these heights is 77.6 inches. Does this set have an outlier and, if so, how does removing it affect the mean?
The set has 66 as an outlier and removing it decreases the mean by about 1.3 inches.
The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
The set has 66 as an outlier and removing it decreases the mean by about 6.6 inches.
The set has no outliers.
Question 5
Here are 10 test scores: 50, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 76. How does removing the outlier 50 affect the mean?
The set has 50 as an outlier and removing it decreases the mean by about 10.
The set has 50 as an outlier and removing it decreases the mean by about 2.
The set has 50 as an outlier and removing it increases the mean by about 3.
The set has 50 as an outlier and removing it decreases the mean by about 6.
Answer:
Question 4: The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
Question 5: The set has 50 as an outlier and removing it increases the mean by about 3.
Step-by-step explanation:
Question 4:
Given heights are:
66, 74, 76, 77, 78, 79, 80, 80, 82, 84
The mean is: 77.6 inches
Removing 66 will make the mean increase to 78.9
So,
The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
Question 5:
50, 74, 76, 77, 78, 79, 80, 80, 82, 84
The mean is 76.
We can clearly see that 50 is an outlier as it is quite less than the given data.
Calculating mean after removing 50 will give us mean equal to 78.9
So the correct answer is:
The set has 50 as an outlier and removing it increases the mean by about 3.
Solve for x.
4x – 4 <8 AND 9x + 5 > 23
Answer:
[tex]\large\boxed{2<x<3\to x\in(2,\ 3)}[/tex]
Step-by-step explanation:
[tex](1)\\4x-4<8\qquad\text{add 4 to both sides}\\4x<12\qquad\text{divide both sides by 4}\\x<3\\\\(2)\\9x+5>23\qquad\text{subtract 5 from both sides}\\9x>18\qquad\text{divide both sides by 9}\\x>2\\\\\text{From (1) and (2) we have}\ 2<x<3[/tex]
Answer:
[tex]2<x<3[/tex]
Step-by-step explanation:
Given : Inequality [tex]4x-4<8[/tex] and [tex]9x+5>23[/tex]
To find : Solve for x?
Solution :
Inequality 1 - [tex]4x-4<8[/tex]
Add 4 both side,
[tex]4x<12[/tex]
Divide by 4 both side,
[tex]x<3[/tex]
Inequality 2 - [tex]9x+5>23[/tex]
Subtract 5 both side,
[tex]9x>18[/tex]
Divide by 9 both side,
[tex]x>2[/tex]
From Inequality 1 and 2,
[tex]x<3[/tex] and [tex]x>2[/tex]
or [tex]2<x<3[/tex]
SOLVE y = 3x – 2 x – y = 4 BY USING SUBSTITUTION!! SHOW ALL WORK! HELPPP!
Answer:
(-1,-5)
Step-by-step explanation:
So we have the system:
y=3x-2
x-y=4.
We are asked to use substitution. Luckily, it is already setup for this because one of the equations has one of the variables solved for, namely the y=3x-2 equation. We are going to insert y=3x-2 into x-y=4 and solve for x.
x-y=4 (with y=(3x-2) ):
x-(3x-2)=4
Distribute:
x-3x+2=4
Combine like terms:
-2x+2=4
Subtract 2 on both sides:
-2x =2
Divide both sides by -2:
x =-1
Now if y=3x-2 and x=-1, then y=3(-1)-2=-3-2=-5.
So the solution is (-1,-5).
10 - 4(2.4 • 3.5)2 + 0.12 10 - 4(8.4)2 + 0.12 10 - 4(70.56) + 0.12
Answer:
- 406.278
Step-by-step explanation:
10 - 4(2.4 • 3.5)2 + 0.12 10 - 4(8.4)2 + 0.12 10 - 4(70.56) + 0.12
Using BODMAS rule, first operation under bracket will be done. Then after Multiplication, addition and subtraction will be solved.
= 10 - 4 (8.4) 2 + 0.1210 - 4(8.4) 2 + 0.1210 - 4 (70.56) + 0.12
= 10 - 67.2 + 0.1210 - 67.2 + 0.1210 - 282.24 + 0.12
= - 406.278
Is BES - GES? If so, identify the similarity postulate or theorem that
applies
Answer:
A
Step-by-step explanation:
∠BES = ∠GES = 40°
∠BSE = ∠GSE = 90°
ΔBES and ΔGES are similar by the AA postulate → A
The given ΔBES and ΔGES are similar triangles according to the AA similarity postulate or theorem. Option A true.
What is the AA similarity postulate or theorem?The AA similarity postulate is that " If any two triangles have a pair of angles with equal measures then they are said to be similar triangles". If two angles are equal then the third one will also be equal in both the triangles.
Checking similarity in both the triangles:The given triangles are ΔBES and ΔGES
The ΔBES has dimensions as ∠BES=40° and ∠ESB=90° and the ΔGES has dimensions as ∠GES=40° and ∠ESG=90°
Thus, both the triangles have pair of angles with equal measures. I.e., ∠BES=∠GES=40° and ∠ESB=∠ESG=90°. So, they satisfy the AA similarity theorem.
Hence, the given triangles are said to be similar according to the AA similarity postulate or theorem. So, option A is true.
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Solve the equation for the indicated variable
A = 8v for v
Answer:
A=8v
8v=A
8v/8=A/8
v=A/8 answer
Which of the following is the radical expression of a^4/9
For this case we must find an expression equivalent to:
[tex]a ^ {\frac {4} {9}}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, rewriting the expression we have:
[tex]\sqrt [9] {a ^ 4}[/tex]
Answer:
Option 4
Answer: OPTION 4.
Step-by-step explanation:
By definition, Radical expressions are those that use a root.
In this case you have this expression:
[tex]a^{\frac{4}{9}[/tex]
In order to find the radical expression of [tex]a^{\frac{4}{9}[/tex], it is important to remember that:
[tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex]
Therefore, once you apply this, you get:
[tex]a^{\frac{4}{9}=\sqrt[9]{a^4}[/tex]
You can observe that it matches with the expression provided in Option 4.
Choose a system of equations with the same solution as the following system: 6x + 2y = −6 3x − 4y = −18
Final answer:
To find a system with the same solution, multiply one of the original equations by a constant and/or add the two original equations together to derive a new equation. An example is the alternative system 6x - 8y = -36 and 9x - 2y = -24, which shares the same solution as the original.
Explanation:
To find a system of equations with the same solution as the given system:
6x + 2y = −6
3x − 4y = −18
We must ensure that the alternative system is equivalent, meaning they share the same solution. A common technique is to multiply both sides of one or both of the equations by a constant to create new equations that have the same solutions. For example, we could multiply the second equation by 2:
3x − 4y = −18 becomes 6x − 8y = −36 after multiplying by 2.
Then, to avoid having the same equation, we could add the original second equation to the first one to get a different second equation:
6x + 2y + (3x − 4y) = −6 + (−18) becomes 9x − 2y = −24.
So, the alternate system that shares the same solution as the original would be:
6x − 8y = −36
9x − 2y = −24
Thirty cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum of these cities, 15 had a professional
sports team 15 had a symphony, 13 had a children's museum, 8 had a professional sports team and a symphony, 7 had a professional sports team and a children's
museum 7 had a symphony and a children's museum, and 3 had all three activities Complete parts a) through e) below
Answer:
the way its set up its kind of confusingStep-by-step explanation:
Answer:
Step-by-step explanation:
cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum. Of these cities, had a professional sports team, had a symphony, had a children's museum, had a professional sports team and a symphony, had a professional sports team and a children's museum, had a symphony and a children's museum, and had all three activities. Complete parts a) through e) below.
PLEASE HELP!!! ASAP!!!!!!
6 units right is the answer, since plugging in values(since it's asking for the translation you can ignore the -3) so your answer is:
The graph is translated 6 units RIGHT
Hope this helps!
plz brainliest
help!! asap!
A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading.
The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.
Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)
Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)
Answer:
A) A(p(t)) = 25πt²
B) 314 square units.
Step-by-step explanation:
Part A)
Flow of paint can be expressed by the function:
p(t) = 5t
Area of the pattern is expressed as:
A(p) = πp²
Since area is given in terms of p, we can use the expression of p to express the area of pattern in terms of time(t). Using the value, we get:
A(p(t)) = π (5t)²
A(p(t)) = 25πt²
Part B)
We have to calculate the area of the pattern after time t. Substituting the value of t in above expression, we get:
A(p(2)) = 25 x 3.14 x 4 = 314 square units.
Therefore, the area of spilled paint after 2 minutes will be 314 square units.
Use the given area to find XY. A. 8 cm B. 12 cm C. 16 cm D. 24 cm
Answer:
A
Step-by-step explanation:
Since the triangles are similar then the ratio of corresponding sides = a : b
and ratio of areas = a² : b²
Here the ratio of areas = 7 : 28 = 1 : 4, hence
ratio of sides = [tex]\sqrt{1}[/tex] : [tex]\sqrt{4}[/tex] = 1 : 2
Hence
XY = 2 × DE = 2 × 4 = 8 cm
The answer is XY=2*DE=2*4=8cm, in summary, eight cenimeters.
Given EG = 16 and FH = 12, what is the length of one side
of the rhombus?
6 units
8 units
10 units
14 units
Answer: 10 units
Step-by-step explanation:
The length of one side of the given rhombus is; C: 10 units
What is the length of the rhombus?
The half diagonals of a rhombus are the legs of a right angle triangle with the hypotenuse being the side of the rhombus.
We see that EG and FH are the diagonals of the rhombus. This means that the half-diagonals measure 8 and 6.
Using Pythagoras theorem, we can find the hypotenuse which is the length of the side of the rhombus.
Thus;
8² + 6² = c²
64 + 36 = c²
100 = c²
c² = 100
c = 10
In conclusion, the length of one side of the rhombus is 10 units
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7 × (–3) × (–2)2 = ?
Answer:
84
Step-by-step explanation:
Order of operations (Parentheses first, exponents next, then multiplication, etc.)
-3 * -2 = 6
Multiply
7 * 6 = 42
42 * 2 = 84
Answer:
84
Step-by-step explanation:
7 x (-3) x (-2) x 2 =
v
-21 x (-2) x 2 =
v
42 x 2 =
84
Two equations are given below:
a − 3b = 16
a = b − 2
What is the solution to the set of equations in the form (a, b)?
(−2, −6)
(−7, −9)
(−11, −9)
(−12, −10)
Answer:
(-11,-9)
Step-by-step explanation:
b-2-3b=16
-2b-2=16
-2b=18
b= -9
a= -9-2
a=-11
If f(x) is a third degree polynomial function how many distinc complex rules are possible ?
Answer:
2
Step-by-step explanation:
According to the fundamental theorem of Algebra
A polynomial of degree 3 has 3 roots
However, complex roots occur in conjugate pairs, hence
There can only be 2 distinct complex roots.
a train traveling at an average speed of 85 miles per hour. At this rate, how far will the train travel in 12 1/4 hours?
Answer:
1041.25 miles
Step-by-step explanation:
You just have to multiply 12.25 (which is equivalent to 12 1/4) by 85 and you'll get the answer 1041.25
Answer:
1041.248 miles
Step-by-step explanation:
Points to remember
Speed = Distance/Time
It is given that,a train traveling at an average speed of 85 miles per hour.
To find the speed of train
Speed = 85 miles/1
= 136.794 km/1 = 136.794 km/hr
To find the distance traveled in 12 1/4 hours
Distance = Speed * time
= 136.794 * 12 1/4
= 136.794 * 49/4
= 1675.7265
= 1041.248 miles
Find the surface area of the right rectangular prisim
Answer:
46 units^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is
SA = 2(lw +lh+wh) where l is length, w is width and h is height
SA = 2 (2.5* 4+ 2.5*2 + 4*2)
= 2 (10+5+8)
= 2( 23)
= 46 units^2
Answer:
46 units^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is
= 2(lw +lh+wh) is the formula
= 2 (2.5* 4+ 2.5*2 + 4*2)
= 2 (10+5+8)
= 2( 23)
= 46
Step-by-step explanation:
Ifa-b=4 and a^2- b^2=3, what is the value of a+b?
Answer:
[tex]\large\boxed{a+b=\dfrac{3}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ a^2-b^2=(a-b)(a+b).\\\\\text{We have}\ a-b=4\ \text{and}\ a^2-b^2=3.\\\\\text{Substitute:}\\\\3=4(a+b)\qquad\text{divide both sides by 4}\\\\\dfrac{3}{4}=(a+b)\to a+b=\dfrac{3}{4}[/tex]
Suppose the odds in favor of me being nice are given as 100:1. What is the probability that the next time we meet I will be nice?
the probabiltity is:
outcome/total possible outcomes
therefore, 100/101
The probability that the next time we meet I will be nice is [tex]\frac{100}{101}[/tex].
Given that,
Suppose the odds in favor of me being nice are given as 100:1.
Based on the above information, the calculation is as follows:
[tex]= 100 \div (100 + 1)\\\\= 100\div 101[/tex]
Therefore we can conclude that The probability that the next time we meet I will be nice is [tex]\frac{100}{101}[/tex].
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What is the solution to the system of equations -x+2y+2z=0, -x-2y-2z=0, x-z=-1
Answer:
x = 0, y = 1, z = -1 ⇒ (0, 1, -1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}-x+2y+2z=0&(1)\\-x-2y-2z=0&(2)\\x-z=1&(3)\end{array}\right\qquad\text{add both sides (1) and (2)}}\\\underline{\left\{\begin{array}{ccc}-x+2y+2z=0\\-x-2y-2z=0\end{array}\right}\\.\qquad-2x=0\qquad\text{divide both sides by (-2)}\\.\qquad x=0\\\\\text{Put it to (3):}\\\\0-z=1\\-z=1\qquad\text{change the signs}\\z=-1\\\\\text{Put the value of x and z to (1):}\\\\-0+2y+2(-1)=0\\2y-2=0\qquad\text{add 2 to both sides}\\2y=2\qquad\text{divide both sides by 2}\\y=1[/tex]
Write a function for (0,4)(1,8)
Firstly, find the slope.
Let m = slope
m = (8 - 4)/(1 - 0)
m = 4/1
m = 4
Now use the point-slope formula.
y - y_1 = m(x - x_1)
Pick one of the given points. I will use the point (0, 4) but you can certainly use (1, 8) if you'd like.
We now plug and chug.
y - 4 = 4(x - 0)
y - 4 = 4x
y = 4x + 4
Replace y with f(x).
f(x) = 4x + 4
Did you follow?
Answer:
f(x) = 4 x (2)^x
Step-by-step explanation:
How many different 5-letter words can be created using the letters M, A, G, I, C without any letter being used more than once?
Answer:
You can spell only one word using the letters (M,A,G,I,C) the only word able to be made would be magic.
Step-by-step explanation:
Hope this helped you! :3
Answer:Meets,Abuzz,Glows,Inner,Creepy
Step-by-step explanation:
100 + 20m when m= 5 1/4
Answer:
205
Step-by-step explanation:
100 + 20m
Let m = 5 1/4
Change this to an improper fraction
5 1/4 = (4*5+1)/4 = 21/4
100 + 20*21/4
100 + 5*21
100 + 105
205
Which of the following is the inverse of f(x)=-2x+3
The inverse of [tex]\( f(x) = -2x + 3 \)[/tex] is [tex]\[ f^{-1}(x) = \frac{x - 3}{-2} \][/tex].
To find the inverse of f(x) = -2x + 3 , you need to interchange x and y and solve for y .
Start with y = -2x + 3 .
Swap x and y to get x = -2y + 3 .
Solve this equation for y .
x = -2y + 3
First, subtract 3 from both sides:
x - 3 = -2y
Then, divide both sides by -2 :
[tex]\[ \frac{x - 3}{-2} = y \][/tex]
Thus, the inverse of [tex]\( f(x) = -2x + 3 \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x - 3}{-2} \][/tex]