solve the following system of equations algebraically please ty
Eliminating y right away is easiest. Add -3(equation 1) to equation 2, and add 3(equation 3) to equation 2:
-3(2x + y + 3z) + (-3x + 3y - 2z) = -3(3) + (-8)
-6x - 3y - 9z - 3x + 3y - 2z = -9 - 8
-9x - 11z = -17
9x + 11z = 17 [equation 1]
3(5x - y + 5z) + (-3x + 3y - 2z) = 3(13) + (-8)
15x - 3y + 15z - 3x + 3y - 2z = 39 - 8
12x + 13z = 31 [equation 2]
Eliminating x next is easier than eliminating z. Add -4(equation 1) to 3(equation 2):
-4(9x + 11z) + 3(12x + 13z) = -4(17) + 3(31)
-36x - 44z + 36x + 39z = -68 + 93
-5z = 25
z = 25/(-5)
z = -5
Plug this into either of the previous equations and solve for x :
9x + 11z = 17
9x + 11(-5) = 17
9x - 55 = 17
9x = 72
x = 72/9
x = 8
Plug x and z into any of the 3 original equations and solve for y :
2x + y + 3z = 3
2(8) + y + 3(-5) = 3
16 + y - 15 = 3
1 + y = 3
y = 2
What is the volume of a
triangular pyramid that is
21 meters tall and has a
base area of 4 square
meters?
cubic meters
Volume of a pyramid: V = {Bh (Where "B" is the area of the pyramid's base.)
Answer:
V = 28 m³
Step-by-step explanation:
V = (1/3)Bh
V = (1/3)(4 m²)(21 m)
V = 28 m³
Evaluate 3 x 6 - 12 + 6.
3 x 6 - 12 / 6
Answer:
16
Step-by-step explanation:
Pemdas is the order of operations
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Answer:
16
Step-by-step explanation:
3 x 6 - 12 / 6.
18 - 2
16
Help with this question please
Answer: Isosceles, acute
Step-by-step explanation:
What number does Point A represent?
Answer:
I think 4.3 is your answer.
I think it will help you.
Answer:
4.3have a good day
............✿................
Which number line shows the solution to 2/3x - 5 > 3
Answer:
Step-by-step explanation:
The binomial (x 5) is a factor of x2 8x 15. what is the other factor? (x 3) (x 7) (x 12) (x 13)
The other factor of the polynomial [tex]\rm x^2+8x+15[/tex] is ( x + 3 )
It is given that the polynomial [tex]\rm x^2+8x+15[/tex] has one factor that is [tex]\rm (x+5)[/tex].
It is required to find another factor of the above polynomial.
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have a polynomial of degree two:
[tex]\rm = x^2+8x+15[/tex]
By using the factorization method we get:
[tex]\rm = x^2+8x+15\\\rm = x^2+3x+5x+15\\\rm = x(x+3)+5(x+3)\\\rm = (x+3)(x+5)\\[/tex]
Thus, the other factor of the polynomial [tex]\rm x^2+8x+15[/tex] is ( x + 3 )
Learn more about Polynomial here:
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Answer: (x + 3) or A!
Step-by-step explanation:
have a nice eday.
correct on edge 2023
Which equation represents a parabola? 4x2 – 2x 3y2 – y 1 = 0 x2 x – 2y2 – 4y 2 = 0 –3x 4y2 – 2y 6 = 0 2x2 y2 – 4y 6 = 0.
The equation which can be represents a parabola in the standard form is given in the option C which is,
[tex]-3x +4y^2 - 2y+ 6 = 0[/tex]
What is equations of the parabolas?The equation of parabola is the way to represent a parabola in a algebraic expression from using its vertex points.
The general form of the of the parabola can be given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) are the vertex.
The equation of the parabola in the quadratic equation form can be given as,
[tex]y=ax^2+bx+c[/tex]
Lets check all the option. Equation given in the first option is,
[tex]4x^2 - 2x+ 3y^2 - y +1 = 0[/tex]
This option can not be converted in the above from of parabola.
Equation given in the second option is,
[tex]x^2+ x - 2y^2 - 4y +2 = 0[/tex]
This option can not be converted in the above from of parabola.
Third option is given as,
[tex]-3x +4y^2 - 2y+ 6 = 0\\-3x=-4y^2+2y-6[/tex]
Change the sign of both side of the equation as,
[tex]3x=4y^2-2y+6[/tex]
Divide by number 3 as,
[tex]x=\dfrac{4}{3}y^2-\dfrac{2}{3}y+2[/tex]
This can be compared with the form of parabola equation.
Hence, the equation which can be represents a parabola in the standard form is given in the option C which is,
[tex]-3x +4y^2 - 2y+ 6 = 0[/tex]
Learn more about the equation of parabola here;
https://brainly.com/question/4148030
Write the equation of a line that is perpendicular to y=5 and that passes through the point (−7,−5)
Answer:
hope this helps!
Step-by-step explanation:
A pound of blueberries costs $3.98 how much will 0.6 pounds of blueberries cost?
[tex]\begin{array}{ccll} lbs&\$\\ \cline{1-2} 1 & 3.98\\ 0.6& x \end{array} \implies \cfrac{1}{0.6}=\cfrac{3.98}{x}\implies x \approx 2.39[/tex]
A rectangle’s perimeter and its area have the same numerical value. The length of the rectangle is 6. What is the width of the rectangle in units?.
Answer:
Step-by-step explanation:
Formula
P = 2*w + 2*L
Area = L*w
Givens
Area = P
L = 6
Create equation and Solve
LW = 2w + 2L
6w = 2w + 2*6
6w = 2w + 12 Subtract 2w from both sides
6w - 2w = 12 Combine
4w = 12 Divide by 4
4w/4 = 12/4
w = 3
Check
Area = 6*3 = 18
Perimeter = 2*3 + 2*6
Perimeter = 6 + 12 Combine
Perimeter = 18
It does check.
Which expression is equivalent to 1/2(16x+2)+5?
Answer:
8x + 6
Step-by-step explanation:
1/2(16x + 2) + 5
(1/2 × 16x + 1/2 × 2) + 5
8x + 1 + 5
8x + 6
That should be the answer.
Can You Solve This?
6 / 2(1+2) =
814x 407
Answer: Well 6 / 2(1+2) = 9
and 814 x 407 = 331,298
Step-by-step explanation:
Use the given property to complete the statement. Division Property of EqualityIf 2(AX) = 4(BY), then AX
Answer:BY is the answer
What is the lenght of the side opposite the 30 degree angle?
Answer: 60 degrees
Step-by-step explanation:
a triangle has a interior sum of 180°
90 + 30 = 120
180 - 120 = 60
What is the period of y = csc(x)?
1. Pi
2. 2pi
3. 3 pi
4. 4pi
Answer:
2pi
Step-by-step explanation:
ANSWER QUICKLY PLZZZZZZ ASAP
READ QUESTIONS CAREFULLY
Answer:
a) 60 %
b) 55%
These are the answers.
Answer: 0.6 or 60%
Step-by-step explanation: Uh calculator
WILL GIVE BRAINLIST HELLLLLLLLLPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
b) Type one to two paragraphs that describe your models and relate them to the law of
conservation of mass. Your document should:
i. identify the names of the reactants and products in the reaction.
ii. identify the number of molecules that make up the reactants and products.
iii. identify the type and number of atoms in each molecule of the reactants and products.
iv. explain what happens during the chemical reaction.
v. explain how mass is conserved during the chemical reaction
Assignment: Type one to two paragraphs that describe your models and relate them to the law of conservation of mass. Your document should:
Identify the names of the reactants and products in the reaction.
Identify the number of molecules that make up the reactants and products.
Identify the type and number of atoms in each molecule of the reactants and products.
Explain what happens during the chemical reaction.
Explain how mass is conserved during the chemical reaction
The name of the reactant in this reaction is called Calcium Carbonate (CaCO3) and the products in this reaction are Calcium Oxide (CaO) and Carbon Dioxide (CO2). There are 5 atoms total in calcium carbonate: one calcium atom, one carbon atom, and 3 oxygen atoms. In calcium oxide there are 2 atoms total: one calcium atom and one oxygen atom. In carbon dioxide there are 3 atoms total: one carbon and two oxygen atoms. So in the reaction the mass of the products stayed the same because according to the law of conservation, “in a closed or isolated system, matter cannot be created or destroyed. It can change forms but is conserved.” This can be seen in the reaction because no matter was made or destroyed, it was all just rearranged. To further explain, the law of mass conservation in chemistry states that, “in a chemical reaction, the mass of the products equals the mass of the reactants,” which further proves that no matter was created or destroyed, just rearranged. In conclusion, in the reaction the products had the same number of atoms as the reactant because no matter was destroyed or created, simply rearranged to create new products!
Somebody plz help me
Answer:
A
Step-by-step explanation:
is the function.
Am % sure
A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 6 hours. The company has only 600 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day. If the company profits for the cord-type model for $36.50 and the cordless model for $109.50, how many of each type should it produce per day to maximize profits?
Answer:
P=$14600The company should produce 100cordless and 100 cord-typeStep-by-step explanation:
This is a linear programming question
let the cordless trimmer be X
and the cord type be Y
the objective function is
maximize
36.50x+109.50y=P
constraints
2X+6Y<=600-----1
X+Y=200-----------2
solve 1 and 2 simultanouesly
mutiply eqn 2 by 2 we have
2x+6y=600-------1
2x+2y=200--------3
subtract the eqns 3 from 1
4y=400
y=100
put y=100 in eqn 2 we have
x+100=200
x=200-100
x=100
36.50x+109.50y=P
36.50(100)+109.50(100)=P
3650+10950=P
P=$14600
The company should produce
100cordless and 100 cord-type
randy read a book in the afternoon. He looked at his watch when he started and finished reading. How long did randy read?
Answer:
Is this a joke?
Step-by-step explanation:
Please tell me this is.
dont mind this one / 14.55 + 20.17
Answer:
34.72
Hope that helps!
Answer:
Your answer is: 34.72
Use long addition to evaluate.
Step-by-step explanation:
Hope this helped : )
PLZ HELP MEEEEE!!!!! IN TEST
Use point-slope form, y - y1 = m(x - x1), to find the linear equation of a line that
passes through the points (3, -1) and (1, 1).
Plug it in.
y = -1, y1 = 1
x = 3, x1 = 1
-1 - 1 = m( 3 - 1)
-2 = 2m
m = -1
The slope is -1
y = -x +b
-1 = -3 +b
b = 2
The equation is y = -x + 2
Hope this helps.
Answer:
y=-1·x+2
Step-by-step explanation:
M is directly proportional to L^3
When L = 2, M= 160
Find the value of M when L = 3
Answer:
2,160
Step-by-step explanation: since M is proportional to L^3 so when L=2 then L^3=8 so M=160 which means if L = 3
When L = 3, the value of M is 540. The relationship between M and L³ holds true.
When two variables, M and L, are directly proportional, it means that their ratio remains constant.
In this case, M is directly proportional to L³, which can be written as M = k × L³, where k is the constant of proportionality.
To find the value of k, we can use the given information when L = 2, and M = 160:
160 = k × 2³
160 = k × 8
k = 160 / 8
k = 20
Now that we have the value of k, we can find the value of M when L = 3:
M = 20 × 3³
M = 20 × 27
M = 540
So, when L = 3, the value of M is 540. The relationship between M and L³ holds true for any value of L when multiplied by the constant of proportionality k, which we found to be 20 in this case.
To learn more about the proportional relationship;
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The observation deck of a building forms a sector with the dimensions shown.
Isafety rail
10 yd
10 yd
Find the length of the safety rail and the area of the deck. Round your answers to the nearest tenth.
The length of the safety rail is about
yards.
The area of the deck is about
square yards.
1. The length of the safety rail = Arc length is: 15.7 yd
2. The area of the deck = area of sector is: 78.5 yd²
What is the Area of a Sector?Area of sector = ∅/360 × πr²
What is the Length of an Arc?Arc length = ∅/360 × 2πr
1. Length of the safety rail = Arc length = ∅/360 × 2πr
= 90/360 × 2π(10)
= 15.7 yd
2. Area of the deck = area of sector = ∅/360 × πr²
= 90/360 × π(10²)
= 78.5 yd²
Learn more about area of sector and length of arc on:
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A pet store had 2,578 fish. 3,384 fish were sold. How many fish does the pet store have now?
Answer:
806
Step-by-step explanation:
add 2,578-3,384 you have to subtract that to get our final answer which is 806 that's how many they have left.
PLEASE HELP, EZ QUESTION Given 2a−b
Answer:
I think your answer is ab.
I think it will help you.
Work out these calculations.
Use the priority of operations.
Use a calculator to check your answers.
Answer:
a) 961 b)37
Step-by-step explanation:
a) (5² + √36)²= (25+6)²= 31²=961
b) 4³ - (5-2)³= 64-3³= 64-27= 37
-(1 – 7d) = 3(8a - 6)
Answer:
-(-71)=3(8a-6)
remove parenthesis
-(-71)=24a-18
71=24a-18
-24a=18-71
-24a=-89
a=89/24.
Question 1 of 6
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction
Solve the following equation for x, and express its value in terms of c.
3(cx – 7) = 9
The value of x in the equation is
Answer:
If c=2 than x=5 because 2x5=10 and 10-7=3 and 3x3=9
Step-by-step explanation: