The solution to the given system of equation has exactly one solution at (0,2).
Which property is used in elimination method?The addition property of equality is used in the elimination technique to solve systems of linear equations.
What is elimination formula?To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Given pair of equations is
18x - 2y = -4 ....(i)
4x - y = -2 .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-) (+) (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
So there is exactly one solution (0,2).
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The solution to the given system of equation has exactly one solution at (0,2).
Which property is used in elimination method?
The addition property of equality is used in the elimination technique to solve systems of linear equations.
What is elimination formula?
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Given pair of equations is
18x - 2y = -4 ....(i)
4x - y = -2 .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-) (+) (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
So there is exactly one solution (0,2).
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hello could someone explain the law of sines to me?
Answer:The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
Step-by-step explanation:
Every hour, the population of a colony of bacteria increases by 4% of what the population was at the beginning of the hour. If the population is 2488 at 12 o'clock, what was the population 2 hours before that
The population 2 hours before that is 2691 if the population of a colony of bacteria increases by 4% of what the population was at the beginning of the hour.
What is meant by population?A population is a distinct group of individuals that can be distinguished for the purposes of data collection and analysis by at least one feature. Populations are used in statistics and other branches of mathematics. Data is typically collected from a sample while learning about a large population.
Between sample size and population, the population will always be larger in number. The entire group of individuals under study is referred to as the population. 250 persons make up the population in the illustration, which is the same size as the high school under consideration.
We have P₀=2488
Rate of increase=R=4%
Time=2 hours
Bacteria count =P
P=P₀[tex](1+(R/100)^{T}[/tex]
=2488×(1+(4/100))²
=2488×1.0816
=2691.0208≈2691
Therefore, the population 2 hours before that is 2691.
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A, B, C and D lie on a circle.
AC and BD intersect at X.
The angles BAX and CDX are equal and the length of CX is 8.2 cm.
What are angles?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Given that, the points A, B, C, D lie on a circle and AC and BD intersect at X.
The angles BAX and CDX, they are subtended by the same arc AD, hence, according to the property of angles subtended by the same arc, they are equal.
Thus ∠BAX = ∠CDX
Since, corresponding sides opposite to the equal angles are proportional.
CX/BX = CD/AB
⇒ CX/3.84 = 9.40/4.40
⇒ CX = (9.40*3.84)/4.40
⇒ CX = 8.2
Thus, length of CX is 8.2cm
The angles BAX and CDX are equal and the length of CX is 8.2 cm
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Select the correct answer from each drop-down menu. The Rileys are buying a home that costs $250,000. They are paying 3% in closing costs and 12% for a down payment. Complete the statement. The Rileys will pay a total of BLANK in BLANK costs for the closing costs and down payment on their mortgage
The Rileys will pay a total of $37500 in $250000 cost for the closing costs and down payment on their mortgage.
Given that,
The Rileys are spending $250,000 on a house. They are making a down payment of 12% and paying 3% in closing expenses.
We have to fill the blanks.
We know that,
$250000 Rileys are spending on a house.
The down payment for 12% and closing cost for 3%
So,
$250000×(12+3)%
$250000×15%
$37500
Therefore, The Rileys will pay a total of $37500 in $250000 cost for the closing costs and down payment on their mortgage.
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At a grocery store, a customer pays a total of $11.10 for 1.6 pounds of chicken
and 2 pounds of fish. Another customer pays a total of $12.15 for 2.4 pounds of
chicken and 1.8 pounds of fish. How much does each cost per pound?
Each pound of fish and chicken will cost $3.75 and $2.25 respectively
How to determine how much each cost per pound?
A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Given that:
1. A customer pays a total of $11.10 for 1.6 pounds of chicken
and 2 pounds of fish.
2. Another customer pays a total of $12.15 for 2.4 pounds of
chicken and 1.8 pounds of fish
Let C and F represent the cost of one pound of chicken and fish respectively
Statement 1:
1.6C + 2F = 11.10 ---- (1)
Statement 2:
2.4C + 1.8F = 12.15 ---- (2)
we have simultaneous equations now, let's solve using the elimination method:
1.6C + 2F = 11.10 ---- (1)
2.4C + 1.8F = 12.15 ---- (2)
2.4 × (1.6C + 2F = 11.10) = 3.84C + 4.8F = 26.64
1.6 × (2.4C + 1.8F = 12.15) = 3.84C + 2.88F = 19.44
..........................................
1.92F = 7.2
Thus, 1.92F = 7.2
F = 7.2/1.92 = $3.75
Put F = $3.75 into (1):
1.6C + 2F = 11.10
1.6C + 2(3.75) = 11.10
1.6C + 7.5 = 11.10
1.6C = 11.10 - 7.5
1.6C = 3.6
C = 3.6/1.6 = $2.25
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Solve the system by sSolve the system by substitution. 3x+14
y=x
Step-by-step explanation:
Steps for Solving Linear Equation
3x+14y=x
Subtract x from both sides.
3x+14y−x=0
Combine 3x and −x to get 2x.
2x+14y=0
Subtract 14y from both sides. Anything subtracted from zero gives its negation.
2x=−14y
Divide both sides by 2.
2x/2=-14y/2
Dividing by 2 undoes the multiplication by 2.
x=-14y/2
Divide −14y by 2.
x=−7y
Consider the following points on the graphs of y = cos(x) and y = cos(x/2), with the added vertical dashed lines:
what are c and d in that order?
From the given graphs the values of 'c' and 'd' are c = -0.84,
d = 0.84.
What is sinusoidal wave?
A mathematical curve defined in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.
Let the graphs of y = cos(x) and y = cos(x/2) are given.
From this graphs we have to find the value of c and d.
First from y = cos(x) to find the value of 'a'.
Consider, the point [tex](a, \frac{1}{8})[/tex]
⇒
[tex]cos(a) = \frac{1}{8} \\a = cos^-^1(\frac{1}{8})\\ a = 82.82[/tex]
Now to find the value of 'c'.
Plug a = 82.82 in y = cos(x/2).
[tex]cos(\frac{82.82}{2}) = c \\c = -0.84[/tex]
Hence, the value of 'c' is 'c = -0.84'.
Now to find the value of 'd'.
Consider, the point [tex](b, \frac{1}{8})[/tex]
⇒
[tex]cosb = \frac{1}{8} \\b = cos^-^1(\frac{1}{8})\\b = 82.82[/tex]
Now, plug b = 82.82 in y = cos(x/2)
[tex]cos(\frac{82.82}{2}) = d\\ d = 0.84[/tex]
Hence, from the given graphs the values of 'c' and 'd' are c = -0.84,
d = 0.84.
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the quotient of -9and y
show work
Answer: -9/y
Step-by-step explanation: quotient is a fancy word for divide
-9/y
One person calls 3 people. The next day, those people each call
3 people. The third day, those people each call 3 people. Write
an expression using exponents for the number of calls made on
the third day.
Answer:
3³
Step-by-step explanation:
You want an expression using an exponent to represent the number 3·3·3.
Repeated multiplicationAs you know, a coefficient is used to represent repeated addition:
a + a + a = 3a
The coefficient 3 in the above expression signifies that 'a' appears in the sum 3 times.
Likewise, repeated multiplication can be represented using a specific notation. An exponent signifies the number of times a factor appears in a product:
a · a · a = a³ . . . . . 'a' is a factor 3 times
ApplicationYou have a sequence of numbers of telephone calls:
3 the first day
3·3 the second day
3·3·3 the third day
The calls on the third day can be represented using an exponent:
3³
__
Additional comment
When superscript formatting is not available for the exponent, it is signified by a caret (^). The same number is 3^3 when written in plain text.
As you might expect, a plain text exponent must be enclosed in parentheses if it is other than a single letter or number.
Write an equation of the line in point-slope form that passes through (7,5) and has a slope of m=4
Answer:
y = 4x – 23
Step-by-step explanation:
(7,5) and m= 4
x1 = 7, y1 = 5
using the one point form formula
y – y1 = m(x – x1)
y – 5 = 4(x – 7)
y – 5 = 4x – 28
y = 4x – 28 + 5
y = 4x – 23
i hope this helps
pls rate as brainliest answer
Hello Everyone
Which one has higher density and lower density
cooking oil
water
I need it like like you know like High density and lower density for the materials i used because
I'm doing density Tower project
Send ASAP
The classifications of the densities of these objects are given as follows:
Lower density: Cooking oil.Higher density: Water.What is the density of an object?The density of an object is calculated as the division of the object's mass by the object's volume, according to the equation presented as follows:
Density = mass/volume.
The standard unit of the mass of an object is in grams per cubic centimeters, that is, g/cm³.
Most of the known substances on earth also have known densities, and two examples are cooking oil and water, for which the densities are given as follows:
Cooking oil: 0.6 g/cm³.Water: 1 g/cm³.1 > 0.6, hence we have that:
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PLEASE HELP HURRY!!!!
Answer:
1) y=-2/3x+5
Step-by-step explanation:
Now I know that I didn't actually do the math for this one. I did see though that it needs to have the point (3,3) on the graph. So then I went to desmos graphing calculator, and I put all of them on the graph. The only one with a (3,3) point was number 1. I put it in the image below so you could see. I know that the rest aren't on there, that's because I removed them because they were in the way.
I hope this helps!!!
Circle which of the following ordered pairs that are solutions to the given system of linear
inequalities.
(1,2) (3, -4) (-3, -2) (0, 0) (-4,5) (0, 4)
Answer:
(1,2) - function
(3, -4) - function
(-3, -2) - function
(0, 0) - function
(-4,5) - function
(0, 4) - not a function
there are 75 fifth graders and 125 fourth graders. They are going to be grouped in teams for field day with the same number of with the same number of teams if there must also be the same number of fifth graders on each team how many teams can there be at most?
Please Help
The 25 teams can there be at most.
What is the LCM?
Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers.
We have,
75 fifth graders
125 fourth graders.
They are going to be grouped in teams for a field day with the same number of students on each team.
the same number of teams if there must also be the same number of fifth graders on each team.
take the LCM of the 75 & 125 Which is the 25.
3 fifth graders each
5 fourth graders each
Hence, the 25 teams can there be at most.
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A group of friends were working on a student film that had budget of $400. They used 23% of their budget on equipment. How much money did they spend on equipment?
Answer: they must have used up around 40% of the money if I’m wrong I’m so sorry
Step-by-step explanation: Good luck!
A company bought a van that had a value of £12 000
Each year the value of the van depreciates by 25%.
Work out the value of the van at the end of three years.
Answer:
The value of the car at the end of 3 years will be £5,062.50.
Last month, Paulina earned $520.60. This month, she works overtime and earns $601.30. What is the percent of increase in Paulina’s earnings? Round to the nearest tenth if necessary.
The percent of the increase in Paulina’s earnings is 15.55%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Last month, she earned $520.60. This month, she works overtime and earns $601.30.
The percent of increase = ($601.30 - $520.60)/520.60 x 100%
The percent of increase = (80.7)/520.60 x 100%
The percent of increase = 0.15501 x 100%
Apply the multiplication operation,
The percent of increase = 15.55 %
Thus, the percentage of the increase in Paulina’s earnings is 15.55%.
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6. (3x + 1)(x - 2) =
7. (x − 3)(2x - 1) =
8. (x-3y) (2x - y) =
9. (2x - y)(x-2y) =
Hello is there a tutor who can help
Answer:
6 (3x + 1)(x - 2) = 3x^2 - 2x + x - 2 = 3x^2 - x - 2
7 (x − 3)(2x - 1) = 2x^2 - x - 3x + 3 = 2x^2 - 4x + 3
8 (x-3y) (2x - y) = 2x^2 - yx - 3xy + 3y^2 = 2x^2 - 4xy + 3y^2
9 (2x - y)(x-2y) = x^2 - 3xy + 2y^2 = x^2 - 3xy + 2y^2
Jen wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Jen can pay $52 per month, plus $3 for each group class she attends. Alternately, she can get the second membership plan and pay $31 per month plus $4 per class. If Jen attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that? What is that total amount?
ITS DUE TODAY HELP PLEASE
The number of classes per month that had same total amount paid was 21
The total amount is $115
How to find the total amountlet the number of group class be represented by x
first membership plan, Jen can pay $52 per month, plus $3 for each group class she attends
= $52 + $3x
second membership plan, Jen can pay $31 per month plus $4 per class
= $31 + $4x
when the total amount are equal
$52 + $3x = $31 + $4x
52 - 31 = 4x - 3x
21 = x
The total amount
= $52 + $3 * 21
= $115
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The value of a company's equipment is $33,000 and decreases at a rate of 12% each year. Write an exponential decay function for the value of the equipment after t years.
Answer:
Below
Step-by-step explanation:
Value = 33000 ( .88)^t each year, t , the value is only 88% ( or in decimal: .88) of the prior year ( 12 % decrease leaves 88% )
Please help me with this question. And also are they congruent
From the calculations triangle DEF ≠ triangle PQR
The side lengths of each triangle are
B DE = √13, PQ = √13, EF = √5, QR = √26, DF = √29, PR = √13How to find the side lengths of each of the triangleThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
Triangle DEF
D(-7,-3), E(- 4, - 1)
DE = √{(-7 - -4)² + (-3 - -1)²} = √13D(-7,-3), F(- 2, - 5)
DF =√{(-7 - -2)² + (-3 - -2)²} = √26E(- 4, - 1)), F(- 2, - 5)
EF =√{(-4 - -2)² + (-1 - -2)²} = √5Triangle PQR
P(2,- 2) Q(5, - 4)
PQ = √{(2 - 5)² + (-2 - -4)²} = √13P(2,- 2) R(0, - 5)
PR = √{(2 - 0)² + (-2 - -5)²} = √13Q(5, - 4) R(0, - 5)
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5x+10=35 solve for x
Answer: x=5
Step-by-step explanation:
5
x
+
10
=
35
Subtract
10
from both sides.
5
x
=
35
−
10
Simplify.
5
x
=
25
Divide both sides by
5
.
x
=
25
5
Simplify.
x
=
5
Answer:
X=5
Step-by-step explanation:
Write an equation of the line that passes through (2,-5) and is parallel to the line 2y=3x+10 .
Answer: [tex]y+5=\frac{3}{2}(x-2)[/tex]
Step-by-step explanation:
[tex]2y=3x+10 \implies y=\frac{3}{2}x+5[/tex]
Parallel lines have the same slope, so the slope of the line we need to find is 3/2.
Substituting into point-slope form, the equation is [tex]y+5=\frac{3}{2}(x-2)[/tex].
Which inequality is represented in the following graph?
43 Beacuse mee smart Beacuse mee smart
please help me!!!! i need it done right
The solution of the system of equations is y = 5 and x = 3, and the difference x - y gives:
x - y = -2
How to solve the system of equations?Here we have the system of equations:
5x + 3y = 30
-5x - 2y = -25
If we add the two equations we will get:
(5x + 3y) + (-5x - 2y) = 30 + (-25)
y = 5
So just by doing that we found the value of the variable y.
To find the value of x, we can replace the known value of y on one of the equations, doing that we will get:
5x + 3y = 30
5x + 3*5 = 30
5x + 15 = 30
5x = 30 - 15 = 15
x = 15/5 = 3
x = 3
Then the difference x - y gives:
x - y = 3 - 5 = -2
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A solid has a volume of 128 cubic units and a surface area of 160 square units. The solid is dilated, and the image has a volume of 54 cubic units.
What is the surface area of the image?
Answer:
90 units²
Step-by-step explanation:
The scale factor of the lengths of the sides of a solid must be squared to to find the ratio of the areas and cubed to find the ratio of the volumes.
For example, if you are given two solids with a scale factor of the lengths of the sides of 2, meaning that the sides of the second solid are twice the length of the sides of the first solid, then the surface area of the second solid is 2² (= 4) times the surface area of the original solid, and the volume of the second solid is 2² (= 8) times the volume of the original solid.
Let's say you have a cube with edge of 1 cm. The volume is (1 cm)³ = 1 cm³.
The surface area is the sum of the areas of the 6 faces which are squares 1 cm by 1 cm. 6 × (1 cm)² = 6 × 1 cm² = 6 cm².
The original cube with edge of 1 cm has a volume of 1 cm³ and total surface area of 6 cm².
Now double the size of the edge of the cube. The new cube has an edge of 2 cm. The volume is (2 cm)³ = 8 cm³. Each face of the cube is a square 2 cm by 2 cm. The total surface area of the new cube is 6 × (2 cm)² = 24 cm².
The new cube has volume 8 cm³ and total surface area 26 cm².
Compare the edges, surface areas and volumes of the two cubes:
Original Cube Dilated Cube Ratio new/dilated
Edge 1 cm 2 cm 1:2
Surface area 6 cm² 24 cm² 1:4
Volume 1 cm³ 8 cm³ 1:8
Now here is your problem.
We start with the ratio of the volumes.
Original solid: 128 u³
Dilated solid: 54 u³
ratio of volumes: 54/128 = 27/64 = 3³/4³
The ratio of volumes is the cube of the ratio of the lengths.
ratio of lengths: 3/4
ratio of area: 3²/4² = 9/16
Surface area of original solid: 160 u² × 9/16 = 90 u²
Answer: 90 units²
9(2x + 3y - 5z) expanded form
Answer:
[tex]18x+27y-45z[/tex]
Step-by-step explanation:
[tex]9(2x+3y-5z)[/tex]
[tex]= 9(2x)+9(3y)+9(-5z)[/tex]
[tex]=18x+27y-45z[/tex]
I would appreciate it if you mark my answer as brainliest.
Answer: 18x + 27y -45z
Step-by-step explanation:
9(2x + 3y - 5z)
= 18x + 27y -45z
Isaac has $89,535 in a savings account that earns 8% annually. The interest is not
compounded. To the nearest dollar, how much will he have in total in 4 years?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years..
Round your answer to the nearest dollar.
Answer:
Step-by-step explanation:
Please help me with inequalitys
Answer:
n = -104
Step-by-step explanation:
You want to identify a solution to the inequality -5 +n/13 < -12.
SolutionAdding 5 we get ...
n/13 < -7
Multiplying by 13 gives ...
n < -91
Of the choices available, only -104 is less than -91.
n = -104
<95141404393>
Could you solve and show the step by step please?
Answer:
x1 =1.317
x2=-5.317
Step-by-step explanation: