Which of the following ordered pairs are solutions to the system of
inequalities? Check all that apply.
2x < y
y>7
O A. (8,2)
O B. (0,0)
O C. (5,5)
O D. (1,9)
O E. (17,50)
OF. (-1, 10)
Answers
Answer:
Options D, E, F
Step-by-step explanation:
Given the following system of linear inequalities in two variables:
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
We can substitute the given ordered pairs to see whether they satisfy both linear inequalities.
Option A: (8, 2)[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(8) < 2
⇒ 16 < 2 (False statement).
y > 7
⇒ 2 > 7 (False statement).
⇒ (8, 2) is not a solution to the system.
Option B: (0, 0)[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(0) < 2
⇒ 0 < 2 (True statement).
y > 7
⇒ 0 > 7 (False statement).
⇒ (0, 0) is not a solution to the system.
Option C: (5, 5)[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(5) < 5
⇒ 10 < 2 (False statement).
y > 7
⇒ 5 > 7 (False statement).
⇒ (5, 5) is not a solution to the system.
Option D: (1, 9)[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(1) < 9
⇒ 2 < 9 (True statement).
y > 7
⇒ 9 > 7 (True statement).
⇒ (1, 9) is a solution to the system.
Option E: (17, 50)[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(17) < 50
⇒ 34 < 50 (True statement).
y > 7
⇒ 50 > 7 (True statement).
⇒ (17, 50) is also a solution to the system.
Option F: (-1, 10)[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(-1) < 10
⇒ -2 < 10 (True statement).
y > 7
⇒ 10 > 7 (True statement).
⇒ (-1, 10) is also a solution to the system.
Final Answer:Therefore, Options D, E, and F are the solutions to the given system of linear inequalities.
___________________________Keywords:Linear Inequalities in two variables
System of linear inequalities
________________________________
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Related Questions
Identify the equation for the parabola with the focus F(0,-9.5) and directrix y =9.5
Answers
Considering the given focus and directrix, the equation of the parabola is given by:
[tex]y = -2.375x^2[/tex]
What is the equation of a parabola?The equation of a parabola, with a directrix in y, is:
[tex]y - k = a(x - h)^2[/tex]
In which:
The value of a is of 0.25C.The vertex is (h,k).The focus if (h, k+C).The directrix if y = k - C.In this problem, we have that the x-coordinate of the vertex is h = 0.
From the focus and the directrix, we have that:
k+C = -9.5
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Hence k = 0, C = -9.5 = a = 0.25C = -2.375.
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Part B: What are the solutions to this equation? Show your work. (6 points)
Your answer:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
2 (y-value increase as x-value also increase)
Step-by-step explanation:
Lets look at the graph! when x is 7, y is 4. and when x is 9, y is 5 which is proving that they BOTH increase
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Answers
Answer:
x = - 15
Step-by-step explanation:
[tex]\frac{x}{9}[/tex] + [tex]\frac{1}{3}[/tex] = - [tex]\frac{4}{3}[/tex] ( multiply through by 9 to clear the fractions )
x + 3 = - 12 ( subtract 3 from both sides )
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Solve for x by simplifying both sides of the equation, then isolating the variable.
x=−15
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square root of 193 is 13.892
What is the multiplicity of (-4,0)?
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Answer:
A "zero" of a polynomial is a value of x at which the polynomial, when evaluated, is equal to zero. Since (−x)4=(−1)4x4=x4 ( − x ) 4 = ( − 1 ) 4 x 4 = x 4 , the zero 0 has multiplicity 4 .
...
Russ and Vickie are trying to solve this problem: There are 130 students taking buses to the museum. If each bus holds 22 students, how many buses will they need? Vickie says the students need 5 buses. Russ says they need 6 buses. Who is correct? They will need ? buses. So, ? is right.
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Answers
Answer:
Russ is correct
Step-by-step explanation:
Russ is correct because 130/22 will not be quite to 6, but you can't have 9/10 of a bus so you will round up to 6.
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AD = BD
A
D
Given: ADI AC
DBI CB
ACE BC
B
O A. True
B. False
Answers
Answer:
True
Step-by-step explanation:
The triangles are both right triangles, meaning they can be used with pythagorean theorem. If the triangles CAD and CBD share the same "hypotenuse" (CD), and they have a pair of congruent sides, they other pair of sides must be able to fit into the pythagorean theorem/
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Answer:
im sorry I don't know I didn't do stuff like this in school
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Answers
Answer:
slope: 1equation: y = x +3Step-by-step explanation:
The slope of the line between two points can be found using the slope formula:
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Answers
#1
Passes through
(-1,4)y=x² passes through (-1,1)
Stepped 4 times
y=4x²#2
First make a negative as parabola is opening downwards.
y=-x²Passes through (1,-2)
y=-x² passes through (1,-1)
So
final graph
y=-2x²Answer:
a) Stretched parallel to the y-axis by a scale factor of 5
b) Stretched parallel to the y-axis by a scale factor of 5/2 and reflected in the x-axis.
Step-by-step explanation:
Transformation
y = a f(x)
The graph of a f(x) is f(x) stretched parallel to the y-axis (vertically) by a factor of a.If a < 0, the graph is also reflected in the x-axisPart (a)[tex]\textsf{Parent function}:\quad y=x^2[/tex]
[tex]\textsf{Transformed function}:\quad y=5x^2[/tex]
Transformation: Stretched parallel to the y-axis by a scale factor of 5.
Part (b)
[tex]\textsf{Parent function}:\quad y=x^2[/tex]
[tex]\textsf{Transformed function}:\quad y=-\dfrac{5}{2}x^2[/tex]
Stretched parallel to the y-axis by a scale factor of 5/2 and reflected in the x-axis.
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Answer:
Step-by-step explanation:
The question is 10b/(2b + 8)
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Answer: A is the correct reciprocal.
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Enter the correct answer.
Answers
Answer:
-> (x,y) => (1,5)
x = 1y = 5Step-by-step explanation:
Let's solve your system by elimination.
18x−7y=−17;3x−3y=−12
Multiply the second equation by -6, then add the equations together.
(18x−7y=−17)
−6(3x−3y=−12)
Becomes:
18x−7y=−17
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Add these equations to eliminate x:
11y=55
Then solve 11y=55for y:
11y=55
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(Divide both sides by 11)
y=5
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
18x−7y=−17
Substitute5foryin18x−7y=−17:
18x−(7)(5)=−17
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18x−35+35=−17+35(Add 35 to both sides)
18x=18
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a group of 10 people are ordering pizza. each person wants 2 slices and each pizza has 5 slices. how many pizzas should thay order
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Answer:4
Step-by-step explanation:
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What is the value of k? G(x)=f(x+k)
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Answer:
K=6
Step-by-step explanation:
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[tex] {t}^{3} = \frac{64}{27} \\ [/tex]
[tex]t = \sqrt[3]{ \frac{64}{27} } \\ [/tex]
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Next question
In an isosceles triangle, one angle is 81° greater than each of the other two equal angles. Find the measure of all three angles.
The two smaller angles are each
The larger angle is °.
Answers
Explanation:
Isosceles is 2 r the same which means that 81 and 81 minus 180
The measure of all three angles is 81, 49.5 and 49.5 degrees.
What is Angle sum property?According to the angle sum property of a triangle, the sum of all three interior angles of a triangle is 180 degrees. A triangle is a closed figure formed by three line segments, consisting of interior as well as exterior angles.
The angle sum property formula for any polygon is expressed as, S = (n − 2) × 180°, where 'n' represents the number of sides in the polygon. This property of a polygon states that the sum of the interior angles in a polygon can be found with the help of the number of triangles that can be formed inside it.
Given:
The triangle is isosceles which has two sides equal.
Also Two angles equals.
Let the equal angles are x.
third angle= 81 degree
Now, Using Angle Sum property
x+ +x + 81 = 180
2x= 180-81
2x= 99
x= 99/2
x= 49.5 degrees
Hence, the two smaller angles are 49.5 degrees.
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Pls help me
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Answers
Answer:
DWest I think
Step-by-step explanation:
I dont really know if this is right so pls forgive me if this is wrong.
Simplify. Write the answer with positive exponents only.
x3 x5
x3 x5 =
Answers
Answer:
1/x^2
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x5" was replaced by "x^5". 1 more similar replacement(s).
Step 1:
Simplify x^3 / x^5
Dividing exponential expressions :
x^3 divided by x^5 = x ^ (3-5) = x^(-2) = 1/x^2
Gus bought 12 gallons of gas at $2.17
a gallon, a bottle of oil for $2.49 and
two jugs of anti-freeze for $7.98 each.
He paid $1.52 in tax for the oil and
anti-freeze. If he paid with a $50 bill,
how much change did he receive?
bro help lol
Answers
Answer:
$3.99
Step-by-step explanation:
a gallon of gas=2.17$
12 gallons of gas=2.17$×12 =26.04$
2 jugs of anti freeze =7.98$ × 2 = 15.96$
a bottle of oil = 2.49$
tax= 1.52$
total= 46.01$
he paid 50$
so the change could be 50$-46.01$ = 3.99$
the answer is 3.99$
Find the missing measurement
A= 5
B=
C =11
Answers
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + b^2 =11^2
25 + b^2 = 121
b^2 = 121 - 25
b^2 = 96
b =9.8
I don't know if this what you need but I hope this helps
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Answer:
volume of cuboid = lbh = 8.2 ft x 9.4 ft x 10.7 ft
= 824.8 ft^3
A total of 133 million square miles of the Earth's surface are covered in water. The ratio of the area covered in water to the area of land is 7/3. Find the area of land on Earth.
URGENT! Whoever gets first correct answer is brainliest
Answers
Answer:
57 million square milesStep-by-step explanation:
Let the area of water is w and area of land is l.
Their ratio is:
w/l = 7/3or
133 / l = 7/3Find the value of l
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133/x=7/37x=399x=399/7x=57M mi²or 22,4:58:53 AM
Watch help video
Cooper gave out a survey to some students in his school about their favorite color.
tudents could choose between red and blue. 129 of those surveyed said their favorite
color was red. 57% of the students surveyed said their favorite color was blue. How
many students were surveyed in total?
Answers
Answer:
300 students were surveyed.
Step-by-step explanation:
Well, we know that 57% of students like blue, so that leaves 43% who like red. By simply dividing 129 by 43, we get 3, so know we can conclude that 1% is equal to 3 students. Knowing this, we can multiply 3 by 57 to get 171. Adding these up, we get 300, and we can verify this, by simply finding the difference between 57 and 43, which is 14. Now that we also know that 1% is equal to 3 students, we can multiply 14 by 3, to get 42, which is also the difference between 171 and 129.
which number has 5 that is 1/10 the value of the 5 in 522.12?
Answers
Answer:
50,12
Step-by-step explanation:
any number that has 5 in the tensplace is correct
1/10 of 100 is 10
simplify a^9xa^4
how i do this
Answers
Answer:
a13
Step-by-step explanation:
a^9 × a^4 = a(9 + 4)
= a13
give the missing angle
Answers
Answer:
60°, 115°, 65°Step-by-step explanation:
Angles a and 60°, also c and 65° are alternate interior angles and therefore are equal:
a = 60°c = 65°Angles b and 65° form a linear pair, so they sum to 180°
b + 65° = 180°b = 180° - 65°b = 115°Answer:
a = 60°
b = 115°
c = 65°
Step-by-step explanation:
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent (same).
Therefore, a = 60° and c = 65°
Angles on a straight line sum to 180°
⇒ b + 65° = 180°
Subtracting 65° from both sides:
⇒ b + 65° - 65° = 180° - 65°
⇒ b = 115°
A triangle has one angle that measures 56° and one angle that measures 63º.
The measure of the triangle's third angle is degrees.
The solution is
Answers
need this answer ASAP 20 points as reward
Answers
2- 6
see below for methods