Answers
Solve the first equation for [tex]x[/tex].
[tex]x+3y = -2 \implies x = -3y - 2[/tex]
Substitute this into the second equation and solve for [tex]y[/tex].
[tex]-3(-3y-2) + y = 6 \implies 9y + 6 + y = 6 \implies 10y = 0 \implies y=0[/tex]
Now solve for the value of [tex]x[/tex].
[tex]x = -3\cdot0 - 2 = -2[/tex]
So the solution to the system is the point [tex](x,y) = \boxed{(-2,0)}[/tex]
Answer:
[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x+3y=-2\\-3x+y=6 \end{cases}[/tex]
To solve using the method of substitution, solve one equation for one of the variables.
Solving equation 2 for y:
[tex]\implies -3x+y=6[/tex]
[tex]\implies -3x+y+3x=3x+6[/tex]
[tex]\implies y=3x+6[/tex]
Substitute this expression into the other equation and solve for x:
[tex]\implies x+3y=-2[/tex]
[tex]\implies x+3(3x+6)=-2[/tex]
[tex]\implies x+9x+18=-2[/tex]
[tex]\implies 10x+18=-2[/tex]
[tex]\implies 10x+18-18=-2-18[/tex]
[tex]\implies 10x=-20[/tex]
[tex]\implies 10x \div 10=-20 \div 10[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the expression for y, and solve for y:
[tex]\implies y=3x+6[/tex]
[tex]\implies y=3(-2)+6[/tex]
[tex]\implies y=-6+6[/tex]
[tex]\implies y=0[/tex]
Therefore, the solution to the given system of equations is:
[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]
Related Questions
a boy has a metal of density 14000kg/m3 .He intends to use it to make a rectangular pipe with external dimension of 18 cm by 10 cm and internal dimension of 15 cm by 8 cm .The length of the pipe is150 cm .Calculate the mass of the pipe in kg
Answers
Mass of the pipe= 100.8kgs
Mass is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force.
mass= density x volume
given that, the area of cross- section of the pipe is rectangular ring with area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
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Answer:
The pipe weighs 100.8 kg.
Step-by-step explanation:
Mass is essentially a body of matter's resistance to having its speed or position change when a force is applied. The change caused by an applied force is smaller the more mass a body has.
density x volume equals mass.
Considering that the pipe's cross-section is a rectangular ring of area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
The trail mix that you are making requires 4 cups of raisins for every 10 cups total of trail mix. If you use 24 cups of peanuts (the other ingredient), how many total cups will you have?
Answers
Answer:
40 cups
Step-by-step explanation:
4/10 is raisin
6/10 is peanuts
24/40 is peanuts
Enter the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating
decimal.
4/5
Answers
need help please find the height of a cylinder with a volume of 500 cubic meters
Answers
Answer:
height = 20 cm
Step-by-step explanation:
the volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
here r = 5 and V = 500π , then
π × 5² × h = 500π
25πh = 500π ( isolate h by dividing both sides by 25π )
h = [tex]\frac{500\pi }{25\pi }[/tex] = 20 cm
Sergei runs a bakery. He needs at least 175 kilograms of flour in total
to complete the holiday
orders he's received. He only has 34
kilograms of flour, SO he needs to buy more.
The flour he likes comes in bags that each contain 23 kilograms of flour. He wants to buy the
smallest number of bags as possible and get the amount of flour he needs.
Let F represent the number of bags of flour that Sergei buys.
Answers
Answer:
Step-by-step explanation: Using proportions, it is found that Sergei needs to buy 7 bags.
-----------
This question is solved by proportions, using a rule of three.
He has 34 kilograms of flour.
He needs 175 kilograms.
Thus, he needs to buy 175 - 34 = 141 kilograms.
Each bag contains 23 kilograms. How many bags are needed for 141 kilograms?
1 bag - 23 kilograms
x bags - 141 kilograms
Applying cross multiplication:
[tex]23x = 141[/tex]
[tex]x = \frac{141}{23}[/tex]
[tex]x = 6.1[/tex]
Rounding up, he needs to buy 7 bags
find the interest rate if $13400 has a final value of $17829 in 4 years give your answer to 1dp
Answers
Answer: It is $4429 (interest combined) or $1107.25 (interest annually)
Step-by-step explanation:
1. Subtract 13400 from 17829:
17829 - 13400 = 4429
2. Now, we know that 4429 is the accumulated interest in 4 years, now divide 4429 by 4:
4429/4 = 1107.25
3. Now we know that 1107.25 is the interest accumulated every year.
me i don't now this help please
Answers
Frequency is measured in Hertz, which is one per second. If the wave vibrated 10 times in 10 seconds, it would have a frequency of 1Hz According to the graph, the frequency is increasing to 2Hz then 3Hz.
This is further explained below.
What is Frequency?Generally, The number of instances of a recurring event that takes place in a certain amount of time is referred to as its frequency.
In conclusion, Hertz is the unit of measurement for frequency, and one Hertz equals one second. If the wave vibrated once per second for a whole minute, its frequency would be one hertz (Hz).
The graph indicates that the frequency will reach 2Hz, and eventually 3Hz, in the near future.
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Solve each equation. (m-2)-5=8-2(m-4)
Answers
The solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
According to the given question.
We have a linear equation in one variable
(m-2)-5=8-2(m-4)
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable (m-2)-5=8-2(m-4) is given by
(m -2) -5 = 8 -2(m -4)
⇒ m -2 - 5 = 8 -2m + 8 (by distributive rule)
⇒ m -7 = 16 - 2m (adding and subtracting the line terms)
⇒ m + 2m = 16 + 7
⇒ 3m = 23
⇒ m = 23/3
Hence, the solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
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can someone please help me I don’t understand and it’s a really important homework
Answers
Smaller number: 9
Answer: Large number: 36
Smaller number: 9
Step-by-step explanation:
|x+1|+|3x-2|=2
Solve each equation
Answers
Answer:
2
Step-by-step explanation:
x+1 +3x-2=2 group them in like terms
3x-x+2+1=2 then subtract the variable and add the number
2x=3-2 arrange them
2x=1 divide both side by 2
therefore x=2
8=3x+6y. I need help on how to find Y?
Answers
Answer:y =20
Step-by-step explanation:8 = 3x + 6y.
subtract 3x from both sides:
8-3x = 6y,
Divide both sides by 6:
8/6 - 3x/6 = Y,
4/3 - x/2 = Y.
what is the answer to b?
Answers
Answer:35
Step-by-step explanation:because x equals 3y +2 so if x=11 then just mutlipy 11x3 thats 33 then plus 2 is 35
hope that helps :}
x = 14
Because 3(4) + 2 = 14
b)
y = 3
Because 11 = 3y + 2
11-2 = 9
9 divided by 3 = 3
If each student in the class drinks
1 cups of juice during the party
and there are 9 students in the
class, how many cups of juice will
be needed?
Answers
Answer:9
Step-by-step explanation:
2.
lons that are made of more than
one atom are called
A ionic compounds
B crystals
C polyatomic atoms
D ionic bonds
Answers
Answer:
C polyatomic atoms
Step-by-step explanation:
43 43. The area of a circle is 100 cm². Calculate its radius.
Answers
Answer:
About 5.6 cm
Step-by-step explanation:
The formula for the radius of a circle (based on the area) is [tex]\sqrt{\frac{A}{\pi } }[/tex], where [tex]A[/tex] is the area of the circle?
Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 2,1,0.5,0.25, . . . . . .
Answers
It is a geometric sequence. The next two terms are: 0.125, 0.0625
The given sequence is:
2, 1, 0.5, 0.25, . . . .
Let a(n) be the nth term, then in the above sequence
a(1) = 2
a(2) = 1
a(3) = 0.5
a(4) = 0.25
Notice that:
a(2) = a(1) x 0.5
a(3) = a(2) x 0.5
a(4) = a(3) x 0.5
A sequence, of which its next term is obtained by multiplying the previous term by a constant is called a geometric sequence. The constant is called the ratio.
Therefore this is a geometric sequence with r = 0.5
To find the next two terms, continue the multiplication process:
a(5) = a(4) x 0.5 = 0.25 x 0.5 = 0.125
a(6) = a(5) x 0.5 = 0.125 x 0.5 = 0.0625
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PLS HELP I NEED TO FINISH THES IN ORDER TO PASS MY GRADE
Use the graph to answer the question.
graph of triangle ABC with vertices at negative 2 comma negative 2, 3 comma 3, 2 comma negative 5
Determine the coordinates of triangle A′B′C′ if triangle ABC is rotated 270° clockwise.
A′(−2, 2), B′(3, −3), C′(−5, −2)
A′(2, −2), B′(−3, 3), C′(5, 2)
A′(2, 2), B′(−3, −3), C′(5, −2)
A′(2, −2), B′(−3, 3), C′(2, 5)
Answers
Answer:
A′(2, −2), B′(−3, 3), C′(5, 2) (2nd choice)
Step-by-step explanation:
Rotating a point 270° clockwise about the origin is the same as rotating the point counterclockwise by 90°
In either case, the coordinates of any point (x, y) become new coordinates (-y, x)
I will summarize the original and rotated points,.
Original Rotated
Point(x, y) Point(-y, x) Remarks
-------------- -------------- -------------
A(-2, -2) A'(2, -2) eliminates 1st and 3rd choices
B( 3, 3) B'(-3, 3) no luck, both 2nd and 4th choices have this
C(2, -5) C'( 5, -2) only the 2nd choice fits all three
Answer: A′(2, −2), B′(−3, 3), C′(5, 2)
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
The correct answer is (A).
What are coordinates in a graph?The coordinates in a graph indicate the location of a point concerning the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
To rotate a point (x,y) 270° clockwise about the origin,
We can use the formulas:
x' = y and y' = -x.
So, to rotate triangle ABC 270° clockwise, we need to apply these formulas to each vertex:
A' = (-2, 2) rotated 270° = (2, -2)
B' = (3, 3) rotated 270° = (-3, 3)
C' = (2, -5) rotated 270° = (5, 2)
Therefore,
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
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Evaluate each algebraic expression for x=3 and (y=-2).
2x-3y
Answers
The result of the algebraic expression 2x-3y for x=3 and y=-2 is 12
Given,
The algebraic expression = 2x-3y
x= 3
y= -2
Substitute the values in the expression
2x-3y= 2(3)-3(-2)
=6+6
=12
Hence, the result of the algebraic expression 2x-3y for x=3 and y=-2 is 12.
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The path is 8,000 meters. How long
is the path in kilometers?
kilometers
Answers
Explanation:
Convert from meters to km by diving by 1000.
8000/1000 = 8km
Answer:
8 kilometers
Step-by-step explanation:
8000/1000
= 8 kilometers.
Solve the following problem for x. If there is more than one solution include all solutions in your answer.
|3z-6|=9
X=
X=
Answers
Answer:
z = - 1 , z = 5
Step-by-step explanation:
| 3z - 6 | = 9
the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is
3z - 6 = 9 ( add 6 to both sides )
3z = 15 ( divide both sides by 3 )
z = 5
or
- (3z - 6) = 9
- 3z + 6 = 9 ( subtract 6 from both sides )
- 3z = 3 ( divide both sides by - 3 )
z = - 1
As a check
substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 5
| 3(5) - 6 | = | 15 - 6 | = | 9 | = 9 = right side
x = - 1
| 3(- 1) - 6 | = | - 3 - 6 | = | - 9 | = 9 = right side
then solutions are z = - 1 , z = 5
Determine whether the following statement is true or false. If false, give a counterexample. If true, give an argument to support your conclusion.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
Answers
The statement given is true.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
What is acute angle ?The acute angle can be defined as the angle less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle. In the triangle all the angles gives the sum of 180 degree, that means, at least two angles in every triangle are always acute angles.
According to statement given in the question. This statement is absolutely true. If the sum of two acute angle is greater than 90 then the third angle of that polygon i.e. triangle must be less than 90 which makes the whole triangle a acute . Since, all the angles are now acute angles that means less than 90 thus this made the triangle as a acute triangle.
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Suppose you pull a card from a standard 52-card deck. Find the probability of following event. The card is a face card.
Answers
3/13 is the probability of following event. The card is a face card.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Total no.of cards = 52
Let A be the event of taking face card.
No.of face cards = 4×3 = 12
Now n(S)= 52C1 = 52, n(A) = 12C1 = 12
So P(A) = n(A)/n(S) = 12/52 = 3/13
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5
y≥--x-3
2
how do i graph this?
Answers
The given inequality can be graphed by solving the inequation first.
What is an inequality?
Inequality is defined as an equation that lacks an equal sign. Inequality is a phrase that defines the relative magnitude of a statement and may be used to compare these two statements.
The given inequality can be solved as
[tex]5y\geq -x-32[/tex]
[tex]for, x=1, 5y\geq -1-32[/tex]
[tex]or, 5y\geq -33[/tex]
[tex]or, y=\frac{33}{5}[/tex]
Solve for two more values of x and then plot the inequality on the graph
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Which is an equivalent expression for (5^2 • 3^4)^3?
15^18
5^6 • 3^12
5^2 • 3^12
5^5 • 3^7
Answers
Answer:
answer 2
Step-by-step explanation:
3*4=12
Answer:
B. 5^6 x 3^12
Step-by-step explanation:
(5^2 x 3^4)^3 =
5 x 5 x 3 x 3 x 3 x 3 =
25 x 81 =
2025
2025^3 =
8,303,765,625
Option B is correct because,
5^6 x 3^12 =
5 x 5 x 5 x 5 x 5 x 5 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 =
15,625 x 531,441 =
8,303,765,625
Write an equation for the line on the graph below:
Answers
Answer:
y= - 6
Step-by-step explanation:
the coordinate- y of every point on the line will be - 6
A refrigerator that originally costs $ 1,200 it's on sale for 15% off. Tax is 8%. What would be the sale price of this refrigerator be including tax
Answers
The sale price of this refrigerator be including tax $1101.6 .
The value on the label of associate article/product is termed the marked price or asking price. this is often the worth at that product is meant to be sold-out. However, there will be some discount given on this value and therefore the actualof the merchandise could also be but the marked price. it's typically denoted by MP.When Discount is obtainable, M.P. > S.P.When Discount isn't offered, M.P. < S.P.Discount is outlined because the quantity of rebate given on the label value (marked price) of a piece. it's given by merchants/shopkeepers for attracting customers for increasing their sales.Discount = Marked value – priceIt is given that a refrigerator that originally costs $ 1,200 it's on sale for 15% off.
Discount percentage = [(Discount)/(Marked price)]× 100
15 = Discount / 1200 × 100
15 = Discount / 12
Discount = 15 × 12
= $ 180
Selling price = marked price - discount
= 1200 - 180
= $ 1020
The selling tax is given by = 8% 1020
= 8 / 100 ×1020
= $ 81.6
The total amount one has to pay to buy a refrigerator is = 1020 + 81.6
= $ 1101.6
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i need 3.234 minus 3.234 written out
Answers
Kevin needs to order some new supplies for the restraunt where he works. the restraunt needs at least 492 glasses. there are currently 333 glasses. if each set on sale contains 18 glasses
Answers
Answer:
Step-by-step explanation:492 is needed right,and Kevin has 333 glass.So you need 159 glasses,but you need to find out how many sets you need to get 492 glasses.If 18 glasses comes in a set you'll need to divide 159 by 18 and get 8.83333333333. Then simplefiy the number to 8.8
54 x 10 to the power of 4
Answers
Answer: 54*10^4=540000
Step-by-step explanation:
→
List all the 4-digit even numbers
that can be created by
rearranging
these number tiles.
3472
Answers
3472
3742
3724
3274
7342
7324
7234
7432
2374
2734
4732
4372
