Answer:
[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]
Step-by-step explanation:
Going through all answer choice to find the solution:
[A] [tex]\begin{bmatrix}x+y=0\\ y-z=-2\\ x+y-z=-4\end{bmatrix}[/tex]
[tex]\mathrm{Isolate\;x\;for\;x+y=0;x=-y}[/tex]
[tex]\mathrm{Substitute\:}x=-y[/tex]
[tex]\begin{bmatrix}y-z=-2\\ -y+y-z=-4\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}y-z=-2\\ -z=-4\end{bmatrix}[/tex]
[tex]\mathrm{Isolate\;z\;for\;-z=-4;z=4}[/tex]
[tex]\mathrm{Substitute\:}z=4[/tex]
[tex]\begin{bmatrix}y-4=-2\end{bmatrix}[/tex]
[tex]\mathrm{Isolate\;y\;for\;y-4=-2;y=2}[/tex]
[tex]\mathrm{For\:}x=-y[/tex]
[tex]\mathrm{Substitute\:}z=4,\:y=2[/tex]
[tex]x=-2[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=-2,\:z=4,\:y=2[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]
[tex]\begin{bmatrix}y+2z=-6\\ z-y-z=2\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}y=-2[/tex]
[tex]\begin{bmatrix}-2+2z=-6\end{bmatrix}[/tex]
[tex]\mathrm{For\:}x=-6-2y[/tex]
[tex]\mathrm{Substitute\:}z=-2,\:y=-2[/tex]
[tex]x=-6-2\left(-2\right)[/tex]
[tex]x=-2[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=-2,\:z=-2,\:y=-2[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[C] [tex]\begin{bmatrix}3x-y=-8\\ y-3z=-8\\ x+y+z=-8\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}x=\frac{-8+y}{3}[/tex]
[tex]\begin{bmatrix}y-3z=-8\\ \frac{-8+y}{3}+y+z=-8\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}y-3z=-8\\ z+\frac{-8+4y}{3}=-8\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}y=-8+3z[/tex]
[tex]\begin{bmatrix}z+\frac{-8+4\left(-8+3z\right)}{3}=-8\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}\frac{15z-40}{3}=-8\end{bmatrix}[/tex]
[tex]\mathrm{For\:}y=-8+3z[/tex]
[tex]\mathrm{Substitute\:}z=\frac{16}{15}[/tex]
[tex]y=-8+3\cdot \frac{16}{15}[/tex]
[tex]y=-\frac{24}{5}[/tex]
[tex]\mathrm{For\:}x=\frac{-8+y}{3}[/tex]
[tex]\mathrm{Substitute\:}z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]
[tex]x=\frac{-8-\frac{24}{5}}{3}=x=-\frac{64}{15}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=-\frac{64}{15},\:z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]
[tex]x=-\frac{64}{15}=-4.26666666667, z=\frac{16}{15}=1.06666666667,y=-\frac{24}{5}=-4.8[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[D] [tex]\begin{bmatrix}x-2y+z=0\\ 2y+9z=-20\\ x-y+z=0\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}y=\frac{-20-9z}{2}[/tex]
[tex]\begin{bmatrix}x-2\cdot \frac{-20-9z}{2}+z=0\\ x-\frac{-20-9z}{2}+z=0\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}x+20+10z=0\\ x+\frac{20+11z}{2}=0\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}x=-10z-20[/tex]
[tex]\begin{bmatrix}-10z-20+\frac{20+11z}{2}=0\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}\frac{20-9z}{2}-20=0\end{bmatrix}[/tex]
[tex]\mathrm{For\:}x=-10z-20[/tex]
[tex]\mathrm{Substitute\:}z=-\frac{20}{9}[/tex]
[tex]x=-10\left(-\frac{20}{9}\right)-20[/tex]
[tex]x=\frac{20}{9}[/tex]
[tex]\mathrm{For\:}y=\frac{-20-9z}{2}[/tex]
[tex]\mathrm{Substitute\:}x=\frac{20}{9},\:z=-\frac{20}{9}[/tex]
[tex]y=\frac{-20-9\left(-\frac{20}{9}\right)}{2}=0[/tex]
[tex]y=0[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=\frac{20}{9},\:z=-\frac{20}{9},\:y=0[/tex]
[tex]x=\frac{20}{9}=2.22222222222,\:z=-\frac{20}{9}-2.22222222222,\:y=0[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Kavinsky
Which expression shows 48 + 36 written as a product of two factors
Answer:
12(4+3)
Step-by-step explanation:
You need a 55% alcohol solution. On hand, you have a 50 mL of a 25% alcohol mixture. You also have 60% alcohol mixture. How much of the 60% mixture will you need to add to obtain the desired solution?
Answer:
300 mL
Step-by-step explanation:
There is a simple diagrammatic way to solve mixture problems, illustrated in the attachment. In the left column are the available solution percentages. In the center is the percentage of the desired mix. In the column to the right of that are the diagonal differences between the desired value and the constituent values. Those differences represent the proportions of the constituents on the same horizontal line.
__
Here, that means 30 parts of 60% solution are needed for 5 parts of 25% solution. Since we have 50 mL of 25% solution, we can multiply these ratio values by 10 mL to find the quantities needed. That has been done here in the right-most column.
300 mL of 60% solution are needed to obtain the desired mixture.
__
Additional comment
If you want to write an equation, you can let x represent the quantity of high-concentration solution needed. Then the amount of alcohol in the mix is ...
0.60x +0.25(50) = 0.55(x +50)
0.05x = 0.30(50) . . . . . . . subtract 0.55x+0.25(50)
x = 300 . . . . . . . . . . . . mL of 60% solution needed
Find the distance between the points (7,14) and (18,5).
Answer:
Exact distance = [tex]\sqrt{202}[/tex]
Approximate distance = 14.2127
==========================================================
Work Shown:
[tex](x_1,y_1) = (7,14) \text{ and } (x_2, y_2) = (18,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(7-18)^2 + (14-5)^2}\\\\d = \sqrt{(-11)^2 + (9)^2}\\\\d = \sqrt{121 + 81}\\\\d = \sqrt{202}\\\\d \approx 14.2127\\\\[/tex]
Note: I used the distance formula. Though you could plot the points, form a right triangle, and use the pythagorean theorem as an alternative route. The distance formula is effectively a modified version of the pythagorean theorem.
PLEASE HELP!!!!!
Abigail is studying for the school spelling bee. She already knows 204 words from the vocabulary list. Each day, she learns
24 additional words from the vocabulary list.
Which equation can be used to determine the total
number of words Abigail knows from the vocabulary list, y, over x days?
• A. y=24-204
•b y=24+204
• y=24(x+204)
Answer:
I think that it is y=24(x+204)
Skylar wanted to show the proportional relationship between the dollar value of the original investment, x, and its value after a 10% decrease, y. He creates the table of values shown. Does it model the relationship? Explain. Then, provide a correct equation for the relationship Skylar wants to model.
After checking the information of the table, it is to notice that the table fulfills the behavior of a direct relationship described by the linear equation y = 0.9 · x. #SPJ1
How to analyze a relationship between the two variablesLet be x and y the original investment and the value after applying the change, both in monetary units. A direct relationship is observed by following this model:
y = (1 + r/100) · x (1)
Where r is change rate, in percentual units.
After checking the information of the table, it is to notice that the table fulfills the behavior of a direct relationship described by the linear equation y = 0.9 · x. #SPJ1
RemarkThe table of the change in investment with respect to initial investment is missing and is now introduced below:
(x₁, y₁) = (75, 7.5), (x₂, y₂) = (100, 10), (x₃, y₃) = (200, 20), (x₄, y₄) = (300, 30), (x₅, y₅) = (400, 40)
To learn more on direct relationships, we kindly invite to check this: https://brainly.com/question/14293770 #SPJ1
a food server at harpers restaurant earns 5 dollars plus a 15% tip on the money made on each table he serves. Sam worked as a food server for six hours last friday and his tables earned $600. How much money did Sam make that day?
Answer:
The answer is given in the picture
Step-by-step explanation:
Do you remember me calista
I am alvena
Answer:
$70
Step-by-step explanation:
$5 x 6 hours = $30
$600 ÷ 15% = $40
$30 + $40 = $70
Do these for me pls
Answer:
1) C or B
2) J
3) C
4) J
Step-by-step explanation:
1) I am not sure but I think you start with the x so that is -5 then y which is 7 so y= 5/7x - 5 or y= 7/5x - 5
2) The graph always starts at the origin (0.0) that where the line should be put
3) 39 in + 78 in = 117 in
4)
2/3.5 = 0.57
4/7 = 0.57
6/9 = 0.57
7/12 = 0.57
Two consecutive numbers have a sum of 107. What is the larger of the two numbers?
Answer:
54
Step-by-step explanation:
54 + 53 = 107
54
[tex] \: \: \: \: \: \: \: \: \: \: \: \bold{54 + 53 = 107}[/tex]
Note : To solve a problem like this, all we have to do is find a number that matches the result, in this case it is [tex]\bold{54}[/tex] and [tex]\bold{53}[/tex]
[tex]\therefore[/tex] it gives us a result of [tex]\bold{107.}[/tex]
The radius of a circle is 7 m. Find its circumference in terms of \piπ
Answer:
I think its 43.98 or 44 I think its one of those
Step-by-step explanation:
C=2πr=2·π·7≈43.9823
=2π(7)=2⋅722⋅7=2⋅22=44 cm.
Please use cofunction or even odd identities to solve this problem!
50 points !
Answer:
cot(θ) = -1.45
Step-by-step explanation:
The identity applicable to this problem is ...
tan(π/2 -θ) = cot(θ)
__
Substituting for tan(π/2 -θ), you have the desired cotangent value:
cot(θ) = -1.45
Using the recurrence relation s(1) = 2 and s(2)=3, s(k) =s(k-1)+2s(k-2)+6, find the fourth term
Recurrence functions are used to preedict the subsequent value in a sequence. The fourth term of the sequence based on the recurrence relation is 25
How to find the recurrence relation of a function?Given the recurrence relations according to the question
s(1) = 2 and
s(2)=3
s(k) =s(k-1)+2s(k-2)+6
If s(1) = 2, hence;
s(3) =s(3-1)+2s(3-2)+6
s(3) = s2 + 2s1 + 6
s(3) = 3 + 2(2) + 6
s(3) = 13
Determine the fourth term:
s(4) =s(4-1)+2s(4-2)+6
s(4) = s3 + 2s2 + 6
s(4) = 13 + 2(3) + 6
s(4) = 25
Hence the fourth term of the sequence based on the recurrence relation is 25
Learn more on recurrence relation here: https://brainly.com/question/10636530
What is the surface area of this triangular pyramid? 3 m 3 m 3 m 3 m 2.6 m
[tex]\stackrel{\textit{3 standing triangles}}{3\left[\cfrac{1}{2}(\stackrel{b}{3})(\stackrel{h}{3}) \right]}~~ + ~~\stackrel{\textit{triangular base}}{\cfrac{1}{2}(3)(2.6)}\implies 13.5~~ + ~~3.9\implies 23.4~m^2[/tex]
Which graph represents the function f(x) = 1/3|x|?
Answer:
The answer is D.
Step-by-step explanation:
You pick a card at random.
1 2 3 4
567
What is P(not even)?
Write your answer as a fraction or whole number.
Answer:
p7
Step-by-step explanation:
If it includes 4 then 0.8, if not then 0.6.
Find the area of the shaded region
Answer:
Area of square - area of circle
Step-by-step explanation:
ALEKS Knowlege Check:
Evaluate the expressions.
Answer:
1, -1
Step-by-step explanation:
(-2/3)⁰
Anything that is raised to the power of 0 automatically becomes the value 1. Knowing this, apply the exponent.
(-2/3)⁰ = 1
-(7)⁰
Now using what we know, apply the exponent to the 7.
-(7)⁰ = -1
Notice that the negative is NOT inside the parenthesis and therefore does NOT get affected by the power.
13 yd
10 yd
8 yd
What is the area in square yards
Answer:520 yd
Step-by-step explanation:
multiply 13 x 10 x 8 then divide by 2
I think
QUICK HELP PLEASEEEE SOMEBODY PLEASE HELP
Answer:
Infinite answers is the correct answer
Step-by-step explanation:
A number is chosen at random from 1 to 50. Find the probability of selecting numbers with a last digit of 9.
Answer:
10%
Step-by-step explanation: There are 5 numbers between 5 and 50 that end in 9. 5 is 10 percent of 50. Pls give brainliest.
5 aplicaciones de notación científica en la vida cotidiana
Answer:
In scientific notation:
The first number in the mathematical equation is called the "coefficient." The coefficient must be greater than or equal to one and less than 10. For example to create the scientific notation for the number 256, the coefficient would be 2.56.
The second number in the equation is a power of 10, written as 10 with an exponent, like 102 which stands for 10 x 10.
Combining these two numbers would create this scientific notation equation for 256 - 2.56 x 102.
A negative exponent shows the decimal is moved that many places to the left and a positive exponent shows the decimal is moved that many places to the right.
Scientific Notation Examples
Here are examples of scientific notation:
1 = 100
10 = 1 x 10¹
100 = 1 x 10²
1000 = 1 x 10³
10000 = 1 x 104
100000 = 1 x 105
42,000,000 = 4.2 x 107
676,000,000,000 = 6.76 x 1011
0.1 = 1 x 10-1
0.01 = 1 x 10-2
0.001 = 1 x 10-3
0.0001 = 1 x 10-4
0.00001 = 1 x 10-5
0.00000078 = 7.8 x 10-7
0.000000000000000 = 3.56 x 10-13
Real Life Examples of Scientific Notation
Explore how scientific notation is used to express large numbers.
7 x 109 = Population of the world is around 7 billion written out as 7,000,000,000
1.08 x 109 = Approximate speed of light is 1080 million km per hour or 1,080,000,000 km per hour
2.4 x 105 = Distance from the Earth to the moon is 240 thousand miles or 240,000 miles
9.3 x 107 = Distance from the Earth to the sun is 93 million miles or 93,000,000 miles
3.99 x 1013 = Distance from the sun to the nearest star (Proxima Centauri) is 39,900,000,000,000 km
9.4605284 × 1015 = Distance light travels in a year is less than 9.5 trillion kilometers, or exactly 9,460,528,400,000,000 km
1.4 x 108 = Amount of water surface area on the Earth is 140 million square miles or 140,000,000 square miles
1.0 x 1014 = Approximate number of cells in the human body is 100 trillion or 100,000,000,000,000
1.332 x 10-3 = Density of oxygen is 1332 millionths g per cc or .001332 g per cc
2.4 x 10-3 = Diameter of a grain of sand is 24 ten-thousandths inch or .0024 inch
7.53 x 10-10 = Mass of a dust particle is 0.000000000753 kg
9.1093822 × 10-31 = Mass of an electron is 0.00000000000000000000000000000091093822 kg
4.0 x 10-7 = Length of the shortest wavelength of visible light (violet) is 0.0000004 meter
!!!!PLEASE HELP HAS TO BE DONE TODAY!!!!
What is the LCD of
45
015
03
05
8
15
-
ن
and 2/3/?
The answer would be B: 15.
NO LINKS!!
Determine if each statement is always, sometimes, or never true
Answer:
sometimessometimesalwaysStep-by-step explanation:
These questions can be answered by reference to the formulas for the volume of a cone, cylinder, and sphere.
__
ConeV = 1/3πr²h . . . volume depends on height as well as radius
Cones with the same radius will sometimes have the same volume. (When they have the same height.)
__
CylinderV = πr²h . . . volume depends on height as well as radius
Cylinders with the same radius will sometimes have the same volume. (When they have the same height.)
__
SphereV = 4/3πr³ . . . volume depends only on radius
Spheres with the same radius will always have the same volume.
Lets note the formulas first to make clear.
For cone
V=1/3πr²hFor cylinder
V=πr²hFor sphere
V=4/3πr³We can see
for first two
the volume depends upon the height hence if they have same radius then their volume may or may not be sameFor sphere
volume depends upon radius so if radius is same the volume is sameNine of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are to be put in two groups so that the sum of the numbers in each group is a multiple of four.
What is the largest number that could be left out?
Answer:
13,62,75,48,1092
Step-by-step explanation:
1+3=4, 6+2=8, 7+5=12, 4+8=12& 1+0+9+2=12.
Determine the equation for a circle in standard form with a radius of 18, and center (18,-18).
Answer:
(x-18)²+(y+18)²=18².
Step-by-step explanation:
1) the formula is: (x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates of the centre, r - the length of the radius;
2) according to the formula above:
(x-18)²+(y+18)²=18².
Find the area of the figure.
(50 POINTS On Last post)
Answer:
173,056,00
Step-by-step explanation:
f(x) = 2x + 3 and g(x) = 24 – X.
Solve the equation f(x) = g(14).
Answer:
x = 3.5
Step-by-step explanation:
f(x) = 2x + 3
g(x) = 24 – x
-> g(14) = 24 - 14
-> g(14) = 10
f(x) = g(14) (Given)
-> 2x + 3 = 10
-> 2x = 10 - 3
-> 2x = 7
-> x = 7/2
-> x = 3.5
Pls help me in this khan academy exercise
Answer:
x= 180° - (103°+33°)
x= 180° - 136°
x= 44°
help me pwesssssssssss
Answer:
858 Remainder 4
Step-by-step explanation:
A triangle has an angle that measures 44.3 and another that measures 52.4" What is the measure of the third angle
The measure of the third angle, if the other angles measure 44.3 and 52.4, is 83. 3 degrees.
How to determine the angle?To determine the angle, we need to know the following;
The sum of the interior angles of a triangle is 180 degreesAlternating angles are equalCorresponding angles are equalSupplementary angles sum up to 180 degreesComplementary angles sum up to 90 degreesThen, from the information given, we have that;
A triangle has an angle that measures 44.3 and another that measures 52.4"
Then, we get; x + 52.4 + 44.3 = 180
collect the like terms'
x = 180 - 96.7
x = 83. 3 degrees
Learn about angles at: https://brainly.com/question/25716982
#SPJ2
The ceiling of Stacy's living room is a square that is 22 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 22 ft, but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your work. (Hint: the answers should be the same!)
Answer:
I don't understand trig very well but I do get pythagorean theorem, which I can help with. Your final answer will end up being 31.
Step-by-step explanation:
First off the formula for pythagorean theorem is a^2 + b^2 = c^2
We know that C stands for the hypotenuse so we want to know what C is.
A and B are both 22 so our equation turns into 22^2 + 22^2 = c^2
22 squared is 484 which leads to 484 + 484 = c^2
484 + 484 = 968
968 is our C^2 but we still need to find the square root
The square root of 968 is 31.11269837... and a whole lot of other numbers
You round that out to 31 and get the length of your diagonal