Answer:
option A) Agree, because the solutions are the same is correct.
Step-by-step explanation:
FIRST SYSTEM
[tex]6x + y= 2[/tex]
[tex]-x-y=-3[/tex]
solving the system
[tex]\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18[/tex]
[tex]\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}[/tex]
adding the equation
[tex]-6x-6y=-18[/tex]
[tex]+[/tex]
[tex]\underline{6x+y=2}[/tex]
[tex]-5y=-16[/tex]
so the system becomes
[tex]\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}[/tex]
solve -5y for y
[tex]-5y=-16[/tex]
Divide both sides by -5
[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]
simplify
[tex]y=\frac{16}{5}[/tex]
[tex]\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]
[tex]6x+\frac{16}{5}=2[/tex]
subtract 16/5 from both sides
[tex]6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}[/tex]
[tex]6x=-\frac{6}{5}[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{-\frac{6}{5}}{6}[/tex]
[tex]x=-\frac{1}{5}[/tex]
Therefore, the solution to the FIRST SYSTEM is:
[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]
SECOND SYSTEM
[tex]2x-3y = -10[/tex]
[tex]-x-y=-3[/tex]
solving the system
[tex]\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6[/tex]
[tex]\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}[/tex]
[tex]-2x-2y=-6[/tex]
[tex]+[/tex]
[tex]\underline{2x-3y=-10}[/tex]
[tex]-5y=-16[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}[/tex]
solve -5y for y
[tex]-5y=-16[/tex]
Divide both sides by -5
[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]
Simplify
[tex]y=\frac{16}{5}[/tex]
[tex]\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]
[tex]2x-3\cdot \frac{16}{5}=-10[/tex]
[tex]2x=-\frac{2}{5}[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{-\frac{2}{5}}{2}[/tex]
Simplify
[tex]x=-\frac{1}{5}[/tex]
Therefore, the solution to the SECOND SYSTEM is:
[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]
Conclusion:
As both systems of equations have the same solution.
Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.
Hence, option A) Agree, because the solutions are the same is correct.
PLEASE HELP WILL MARK BRAINLIST
A company is designing a new cylindrical water bottle. The volume of the bottle will be 167 cm. The height of the water bottle is 7.1 cm. What is the radius of the water bottle? Use 3.14 for pi.
Answer:
23
Step-by-step explanation: i took it
Solve the system using substitution.
y + 8x = 10
2y - 4x = 40
(-1, [?])
Solve for
y
in the first equation.
Tap for more steps...
y
=
−
20
+
4
x
−
2
x
−
2
y
=
10
Replace all occurrences of
y
in
−
2
x
−
2
y
=
10
with
−
20
+
4
x
.
y
=
−
20
+
4
x
−
2
x
−
2
(
−
20
+
4
x
)
=
10
Simplify
−
2
x
−
2
(
−
20
+
4
x
)
.
Tap for more steps...
y
=
−
20
+
4
x
−
10
x
+
40
=
10
Solve for
x
in the second equation.
Tap for more steps...
y
=
−
20
+
4
x
x
=
3
Replace all occurrences of
x
in
y
=
−
20
+
4
x
with
3
.
y
=
−
20
+
4
(
3
)
x
=
3
Simplify
−
20
+
4
(
3
)
.
Tap for more steps...
y
=
−
8
x
=
3
The solution to the system of equations can be represented as a point.
(
3
,
−
8
)
The result can be shown in multiple forms.
Point Form:
(
3
,
−
8
)
Equation Form:
x
=
3
,
y
=
−
8
The solution of the given system of linear equations using substitution method is [tex]x = -1, y = 18[/tex].
What is substitution method?The substitution method can be defined as a way to solve a linear system algebraically. The substitution method works by substituting one y-value with the other. To solve it easily, the method involves finding the value of the x-variable in terms of the y-variable. After that, we then end up substituting the value of x-variable in the second equation. This helps us to directly find the value of the y-variable. We can now put the value of y in any of the given equations to find x.
The given system of equations are:
[tex]y + 8x = 10[/tex]..... (1)
[tex]2y - 4x = 40[/tex]..... (2)
The given value of [tex]x = - 1[/tex]. Therefore, the given value of 'x' satisfies for both the equations given.
Now using substitution method, substituting the value of 'x' in the equation(1), we will get the value of 'y'.
Therefore:
[tex]y + 8(-1) = 10[/tex]
⇒ [tex]y = 10 + 8[/tex]
⇒ [tex]y = 18[/tex]
Again, we can verify the value of 'y' by substituting the value of 'x' in equation (2).
Therefore,
[tex]2y - 4(-1) = 40[/tex]
⇒ [tex]2y = 40 - 4[/tex]
⇒ [tex]y = \frac{36}{2}[/tex]
⇒ [tex]y = 18[/tex]
Hence,
The solution of the given system of linear equations using substitution method is [tex]x = -1, y = 18[/tex].
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If 3/5 of a cup of water fills 3/4 of a plastic container, how much water, in cups, is needed to fill one whole container?
Step-by-step explanation:
3/4 of plastic container = 3/5 cups
4/4 of plastic container = 3/5 * (4/3) = 4/5 cups.
4/5 cups of water is needed to fill 1 whole container.
PLEASE HELP ITS DUE TODAY!!
the mean of 67004, 67004, 67005, 67005, 67005, 67005, 67006, 67006
Answer:
the answer is 59467
hope it will help you.....for every 1 book harry reads, Emily reads 3. the table shows the ratio 1:3 and two equivalent ratios. which graph shows the correct way to plot ratios of harry's books to Emily's books as ordered pairs?
Answer:
(1,3) (2,6) (3,9) (4,12)
Step-by-step explanation:
Meanwhile the x value increases by 1, the y value increases by 3.
I need help please aspa
Answer:
139⁰
Step-by-step explanation:
90+49+41=180
180-41=139⁰
ANSERR GIVE ME ANSWERS PLS
Answer:
Concept: Mathematics
When you multiply a number by something to the 10 power of something then you move whatever place of the exponential to the right if its positive and left if it's negative.
1.365 × 10^1 You see its positive 1 hence we move one space to the right Our answer is now 13.65You keep doing the same thing
1.365 × 10^2 136.5Lastly
1.365 ×10^3 1365Rate positively and give 5 stars
y greater than or equal to |x| + 3
which of the following is NOT a solution of the inequality
Answer:
We conclude that the point (-3, 0) does NOT satisfy the inequality.
Step-by-step explanation:
Given the expression
[tex]y\ge \:\left|x\right|+3\:\:\:\:[/tex]
putting x = -3 and y = 6
[tex]6\ge \left|-3\right|+3\:\:\:[/tex]
Apply absolute rule: |-a| = a
[tex]6\ge \:6[/tex]
TRUE
Thus, the point (-3, 6) satisfies the inequality.
Given the expression
[tex]y\ge \:\left|x\right|+3\:\:\:\:[/tex]
putting x = 0 and y = 4
[tex]4\ge \left|0\right|+3[/tex]
Apply absolute rule: |a| = a, a≥0
[tex]4\ge \:3[/tex]
TRUE
Thus, the point (0, 4) satisfies the inequality.
Given the expression
[tex]y\ge \:\left|x\right|+3\:\:\:\:[/tex]
putting x = -3 and y = 0
[tex]0\ge \left|-3\right|+3\:\:\:[/tex]
Apply absolute rule: |-a| = a
[tex]0\ge \:6[/tex]
FALSE
Thus, the point (-3, 0) does NOT satisfy the inequality.
Therefore, we conclude that the point (-3, 0) does NOT satisfy the inequality.
Compare properties of squares and rhombi to properties of other quadrilaterals by answering each question.
(a) Describe a property of squares that is also a property of rectangles.
(b) Describe a property of squares that is NOT necessarily a property of all rectangles.
(c) Describe a property of rhombi that is also a property of squares.
(d) Describe a property of rhombi that is NOT necessarily a property of all parallelograms.
(e) Describe a property that applies to ALL parallelograms.
Answer:
(a) Describe a property of squares that is also a property of rectangles.
All the angles of a rectangle are 90° Diagonals of a rectangle bisect each other(b) Describe a property of squares that is NOT necessarily a property of all rectangles.
All sides of a square are equal and parallel to each other(c) Describe a property of rhombi that is also a property of squares.
Diagonals bisect each other perpendicularly(d) Describe a property of rhombi that is NOT necessarily a property of all parallelograms.
All sides are equalDiagonals bisect each other perpendicularly(e) Describe a property that applies to ALL parallelograms.
Opposite angles are equal Opposite sides are equal and parallel Diagonals bisect each other Sum of any two adjacent angles is 180°Plz help! Will give Brainliest!!!
Does coordinate mmm or coordinate nnn represent a greater number?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
mmm
(Choice B)
B
nnn
Answer:
choice A m
Step-by-step explanation:
n= 1
m= 7
dgcjbknohhfg
helpppp! how do I solve this!
Answer:
maybe similiar, check again
Step-by-step explanation:
Answer:
it is similar
Step-by-step explanation:
Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a
congruence statement.
If no, justify your answer.
Please help !!!
[tex]\boxed{\boxed{\pink{\bf\leadsto No }}}[/tex]
Step-by-step explanation:No , theres not enough information provided to Prove that both the triangles are congruent. Here in the figure we can see that there are two triangles ∆ BDA and ∆ BDC. And its given that
AB = BC BD = BD ( common side )The congruence conditions for two ∆s are :-
1) SAS ( Side Angle Side )
→ Two triangles are said to be congruent by SAS if two respective sides of the two triangles and the included angle between two sides are equal.
2) AAS ( Angle Angle Side )
→ Two triangles are said to be congruent by AAS if two angles and one side of triangle is congruent to other two angles and one side of the triangle .
3) SSS ( Side Side Side )
→ Two triangles are said to be congruent by SAS if all the three sides of one triangle is equal to three sides of the other triangle.
4) RHS ( Right Hypotenuse Side )
→ In two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.
And the given data doesn't satisfies any of the conditions.
Hence there is not enough information provided to Prove that two triangles are congruent .No, there are not enough information provided to Prove that both the triangles are congruent.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
In the figure we can see that there are two triangles ∆ BDA and ∆ BDC. And its given that
AB = BC
BD = BD ( common side )
The congruence conditions for two ∆s are :-
1) SAS ( Side Angle Side )
Two triangles are said to be congruent by SAS Postulate if two respective sides of the two triangles and the included angle between two sides are equal.
2) AAS ( Angle Angle Side )
Two triangles are said to be congruent by AAS Postulate if two angles and one side of triangle is congruent to other two angles and one side of the triangle .
3) SSS ( Side Side Side )
Two triangles are said to be congruent by SAS Postulate if all the three sides of one triangle is equal to three sides of the other triangle.
4) RHS ( Right Hypotenuse Side )
In two right angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.
The given data doesn't satisfies any of the conditions.
Hence, there is not enough information provided to Prove that two triangles are congruent .
Learn more about congruent triangles;
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please answer if you think you are kind and beautiful of world
Answer:
y = 0
Step-by-step explanation:
Given (-5, 0) and (0, 0),
Find the slope (m):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 0}{0 - (-5)} = \frac{0}{5} = 0 [/tex]
Slope (m) = 0.
Find the y-intercept (b):
y-intercept (b) = 0. This is the value of y, when x = 0.
To write the equation of the line, substitute m = 0, and b = 0 into y = mx + b
y = (0)(x) + 0
y = 0 + 0
y = 0
-6+6y^2
factorize the expression
Answer:
6(-1+y∧2)
Step-by-step explanation:
The number of the students the bus holds, s, is less than 40
Answer:
yes
Step-by-step explanation:
The required expression represents the number of students on the bus would be S < 40.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
According to the question,
The number of students the bus holds, s which is less than 40,
So
S is less than 40
S < 40
[in math we have inequality represent the less than relation or greater than the relation with symbols "<" and ">"]
Learn more about inequality here:
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rebecca is cleaning her house. She cleans 1/3 of the house in 5/6 hour. what is her rate per hour
Answer:
5/6:1/3
=5/2
Step-by-step explanation:
hope it helps
am i right
need help with my geometry question please
Answer:
The correct answer is C 62°
Answer:
C. 62
Step-by-step explanation:
Vertically opposite angles are congruent.
Angle RSQ = 62, therefore Angle TSU must also equal 62 degrees.
A spinner divided into six equal parts. It has three green parts, two purple parts, and one white part. What is the probability of spinning green twice in 2 spins
Answer:
1/4
Step-by-step explanation:
Given that :
Number of green = 3
Number of purple = 2
Number of white = 1
Probability of spinning green twice in 2 spins :
Probability = required outcome / Total possible outcomes
P(green on first spin) = 3 / 6 = 1/2
P(green on second spin) = 3/6 = 1/2
Hence, Probability of spinning green twice in 2 spins will be :
1/2 * 1/2 = 1/4
Determine if the following relations are functions, and justify why.
a) **{(1, −2), (−2, 0), (−1, 2), (1, 3)}
Function?: ____________
Justification: ____________________________________________________________________________
If u steal point i report
Answer:
The correct answer is option A.
Step-by-step explanation:
please help! i don’t understand this
Answer:
[tex]No\ Solutions[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\-x+2y=7\\x-2y=7\\By\ simply\ adding\ the\ system\ of\ equations,\\(-x+x)+(2y-2y)=(7+7)\\0+0=14\\Hence,\\0=14\\As\ the\ equation\ above\ doesnt\ make\ sense\ as\ 0\ doesn't\ equal\ to\ 14,\\There\ are\ no\ solutions\ that\ satisfy\ the\ equation.[/tex]
What will be the result of substituting 2 for x in both expressions below?
One-half x + 4
x + 6 minus one-half x minus 2
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
Answer:
A
Step-by-step explanation:
These triangles are proportional.
What is the value of x?
Pls help ASAP first one to answer will be marked brainliest ty
Answer:
x= 70°
y= 60°
Step-by-step explanation:
y= 180-120= 60°
REASON: angles in a straight line add up to 180°
x= 180-(50+60)= 70°
REASON: angles in a traingle add up to 180°
hope it helps! please mark me brainliest...
Happy new year have a great day ahead!
Answer:
y = 60°
x = 70°
Step-by-step explanation:
→ To work out y, remember the fact that angles on a straight line add up to 180° ∴ 180° - 120° = 60°
→ To work out x, remember the fact that angles in a triangle add up to 180° ∴ 180° - (50° + 60°) = 70°
what is effect of interest charged on capital on accounting system
Answer:
The amount of interest charged on capital is an indirect expense of the business and on the other hand, it is an income of the owner. Interest on Capital has the following two effects on final accounts: It is an expense of the business, therefore; it will be recorded on the debit side of Profit and Loss Account.
A car travels 350 miles in 5 hours at a constant rate. At this rate, how far will the car travel in 8 hours?
Answer:
560 is the answer
Step-by-step explanation:
if you divide by you get 70 so times 70 by 8 to get 560
Answer: 560 miles
Step-by-step explanation: the car travels at a speed of 70 miles per hour. Therefore, multiply 70 by 8 and you get 560
What is the value of x in the figure shown below?
650
35°
Respond in the space provided.
Answer:
[tex]x=100[/tex]
Step-by-step explanation:
[tex]From\ the\ triangle\ given,\\Angles\ measuring\ 65\ and\ 35\ are\ interior\ opposite\ to\ x.\\Hence,\\As\ we\ know\ that\ the\ sum\ of\ two\ interior\ opposite\ angles\ will\ be\\ equal\ to\ the\ exterior\ angle.\\Here,\\35+65=x\\x=100[/tex]
Simplify (5^-2)^4
Please explain i keep getting a weird answer.
Answer:
[tex] \dfrac{1}{5^8} = \dfrac{1}{390625} [/tex]
Step-by-step explanation:
[tex](5^{-2})^4 = 5^{-2 \times 4} = 5^{-8} = \dfrac{1}{5^8} = \dfrac{1}{390625}[/tex]
Pretend this is the answer in da comments
Find the smallest perimeter and the dimensions for a rectangle with an area of 36 in squared.
Answer:
Therefore the smallest parameters is (6,6) and a dimension of 24 inches
Step-by-step explanation:
From the question we are told that
area of dimension is [tex]A=36[/tex]
Generally the perimeter of rectangle is given as
[tex]x,y=36[/tex]
Given by
[tex](x,y)=2x+2y[/tex]
Mathematical solving for perimeter of rectangle
[tex]x=\frac{36}{y}[/tex]
[tex]f(y)= 2\frac{36}{2} +2y\\f(y)= \frac{72}{y} +2y[/tex]
Generally in finding minimum perimeter
[tex]f'(y)=\frac{-72}{y^2} +2=0\\[/tex]
[tex]y=6[/tex]
[tex]f(6,6)=2(6)+2(6) \\f(6,6)=24 inches[/tex]
Therefore the smallest parameters is (6,6) and a dimension of 24 inches