Which graph represents the solution set of the system of inequalities?
−2x+y≤4
{
y>x+2
Answers
For equation -2x + y = 4,
Solutions are (0, 4), (-2, 0)
For equation y = x + 2,
Solutions are (-2, 0), (0, 2)
Graph second & Third obey this solution,
Take a point (5, 0) and put into the equations,
It does not obey both the equations,
So, Graph second is the correct answer.
Answer:
Graph 2
Step-by-step explanation:
Given system of inequalities,
−2x + y ≤ 4,
y > x + 2
∵ Related equation of −2x + y ≤ 4 is,
-2x + y = 4 ⇒ y = 4 + 2x ----(1)
While, the related equation of y > x + 2 is,
y = x + 2
From equation (1),
4 + 2x = x + 2 ⇒ 4 + 2x - x = 2 ⇒ 4 + x = 2 ⇒ x = 2 - 4 ⇒ x = -2
Again by equation (1),
y = 4 + 2(-2) = 4 - 4 = 0
Hence, the intersection point of the related equation is (-2,0),
∴ Graph 1 and graph 3 can not be the graph of the given system.
Now, −2(0) + (0) ≤ 4 ( true )
That is, −2x+y ≤ 4 would contain the origin,
Also, 0 > 0 + 2 ( False )
That is, y > x + 2 does not contain the origin.
Therefore, by the above explanation it is clear that,
Grap 2 represents the solution set of the system of inequalities.
Related Questions
how many times longer is the baby alligator 3/4 ft than the baby 2/15ft
Answers
2. Multiply the numerator by how much the denominator goes into the common denominator so 3 x 15 and 2 x 4
3.You get left with 45/60 - 8/60
4. Subtract the numerators to get 37/60
5. You can't simplify it so the final answer is 37/60
We need to find how much longer is the baby alligator compared to a baby.
The baby alligator is [tex]\dfrac{45}{8}[/tex] times longer than the baby.
The baby alligator is 3/4 ft long.
The baby is 2/15 ft long.
According to the question
[tex]\dfrac{3}{4}=\dfrac{2}{15}x[/tex]
The value of x will give us how many times is the baby alligator longer by
[tex]x=\dfrac{\dfrac{3}{4}}{\dfrac{2}{15}}\\\Rightarrow x=\dfrac{3\times 15}{4\times 2}\\\Rightarrow x=\dfrac{45}{8}[/tex]
So, the baby alligator is [tex]\dfrac{45}{8}[/tex] times longer than the baby.
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This square has the hypotenuse of a right triangle as one of its sides.
The estimated value of the length of the hypotenuse is units. The estimated value of the area of the square is square units.
(Hint: The hypotenuse is the side opposite the right angle. To find the hypotenuse of a right triangle, use the Pythagorean Theorem, c2= a2 + b2.)
Answers
The question is about using the Pythagorean Theorem to calculate the length of the hypotenuse of a right triangle. It also asks how to calculate the area of a square when the hypotenuse of the right triangle is one of its sides. The hypotenuse's length would be useful to determine the square's area, as the square's area is calculated as the square of the length of one side.
Explanation:The subject of this question is Mathematics, and it is appropriate for a High School level student. The question is discussing a scenario where a square has the hypotenuse of a right triangle as one of its sides, and the student is asked to estimate the value of the length of the hypotenuse and calculate the area of the square.
To solve this problem, we will use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (let's call it 'c') is equal to the sum of the squares of the lengths of the other two sides (let's call them 'a' and 'b'). In other words, c² = a² + b². The length of the hypotenuse is the square root of this sum, √(a² + b²).
Since we aren't given specific lengths for the sides of the triangle, I cannot provide exact values. However, let's say that the length of the hypotenuse is 'd', then the area of the square, which is calculated as the length of one side squared (d²) would be equal to the given value.
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How do you write 53.9 in expanded form?
Answers
The "expanding" is adding the number, I believe... It's is the same way of the regular method!
So, your [tex]Answer: 50 + 3 + 0.9 [/tex]
Good luck on your assignment and enjoy your day!
~[tex]MeIsKaitlyn:)[/tex]
Muthu reads 20 pages of a book in a day. After 6 days, 2/5 of the book is still unread. How many pages are there in this book?
Answers
At 1 pm, there were 16 seagulls on the beach. At 3 pm, there were 40 seagulls. What is the constant rate of change?
Answers
The cost of 16 oranges is $1. What is the cost of 4 dozen oranges?
Answers
=.25
$.25
Hfhfjsjnwbebt
48 /16 = 3
$3
Word problem
Really need help with this, and by end of day today would be best
The total imports of petroleum ( in millions of barrels per day) in a given year is approximated by the polynomial 40x^3 -526x^2+2089x+6056, where x represents the number of years since 1975. The corresponding total of exports of petroleum is -x^3 +13x^2 +29x+189. Write a polynomial that represents how many more barrels per day were imported than exported in a given year.
Answers
40x^3 -526x^2+2089x+6056 - (-x^3 +13x^2 +29x+189)=
40x^3 -526x^2+2089x+6056 + x^3 -13x^2 - 29x -189=
41x^3 -539x^2+2060x+5867
Dave has $13 to spend on a $4 book and two birthday cards (c) for his friends. How much can he spend on each card if he buys the same card for each friend?
Answers
what is -4/5 + 3/20 in simplest form
Answers
then, -16 + 3 is -13, so the solution is -13/20
To subtract 2 fractions, they both need to have the same denominator.
Since 5 is one of the divisors of 20, we can just multiply the numerator and denominator of 4/5 by 4.
4/5 = (4*4) / (5*4) = 16/20
P.S. when the denominators of both fractions don't have any relation, you multiply the numerator and denominator of the first fraction by the denominator of the second, and the numerator and denominator of the second by the denominator of the first.
3/20 - 4/5 = 3/20 - 16/20
Now you just subtract the numerators:
3/20 - 16/20 = (3-16)/20 = -13/20
So -4/5 + 3/20 = -13/20
Hope this helps! :)
Find two integers whoes sum is -7 and whose product is 12. Explain how you found the numbers.
Answers
- 3 and -4 because when you add both of them you end up with the sum of -7 and when they both are multiplied together they give the product 12 as the answer
What is the GCF of 28,56,and 84.
Also what is the GCF of 30,45, and 75.
Answers
2.) 15 (30/2, 45/3, and 75/5)
The gcf for the numbers 28, 56 and 84 is 28
Since
28: 1, 2, 4, 7, 14, 28
56: 1, 2, 4, 7, 8, 14, 28, 56
84: 1,2,3,4,6,7,12,14,21,28,42,84
Since the biggest number they all have is 14 so the gcf is 14.
The gcf for the numbers 30, 45, and 75 is 15
30: 1,2,3,5,6,10,15,30
45: 1,3,5,9,15,45
75: 1,3,5,15,25,75
Since the biggest number they all have is 15 so the gcf is 15.
Hope this helped
in Mr. Rodgersd' Social Studies class the stuents took a test. The scores on the test were: 95, 85, 75, 90, 70, 95, 85, 80, 75, 95, 70, 80, 65. What was the MEDIAN score for the class? A)80 B)81.6 C)85 D)95
Answers
Order the numbers from least to greatest.
95, 85, 75, 90, 70, 95, 85, 80, 75, 95, 70, 80, 65 becomes
65, 70, 70, 75, 75, 80, 80, 85, 85, 90, 95, 95, 95
The Median is the number in the middle:
80 is your answer
hope this helps
Ronny read for 2.75 hours yesterday. His older brother read for 1.18 hours and his younger brother read for 0.43 hours. How much longer did Ronny read than his two brothers combined?
Answers
Fiona and her friends went to a smoothie shop. They ordered three strawberry smoothies and two protein shakes for a total of $24.00. Last week they ordered one strawberry smoothie and four protein shakes for a total of $25.50. The system that represents their purchases is below. x + 4y = 25.50 3x + 2y = 24.00 What is the price of a protein shake? $3.75 $4.50 $4.95 $5.25
Answers
Answer: Fourth option is correct.
Step-by-step explanation:
Since we have given that
[tex]x+4y=25.50------------------(1)\\\\3x+2y=24.00-----------------------(2)[/tex]
Here, x is the number of strawberry smoothies.
and y is the number of protein shakes.
So, using elimination method, we get that,
Multiplying 2 by eq(2), we get that
6x+4y=48---------------(3)
From eq(1) and (3), we have
[tex]x+4y=25.50\\\\6x+4y=48\\\\-----------------------------------\\\\-5x=-22.5\\\\x=\dfrac{22.5}{5}\\\\x=4.5[/tex]
Put the value of x in eq(1), we get that
[tex]4.50+4y=25.50\\\\4y=25.50-4.50\\\\4y=21\\\\y=\dfrac{21}{4}\\\\y=5.25[/tex]
Hence, the price of protein shake is $5.25.
Thus, Fourth option is correct.
Answer:
D. $5.25.........................
Which number sentence correctly solves this problem?
Jimmy gave $550 to his favorite charity. He had already given $492 to this charity. How much money did Jimmy give to this charity?
A.
550 + 492 = 942
B.
550 + 492 = 1,042
C.
550 - 492 = 58
D.
550 - 492 = 168
Answers
How would you convert 3x- 2y = -6 into a y= mx+ b equation.
Answers
-2y = -3x - 6
Divide -2 from both sides:
[tex]y = \frac{3}{2} x + 3[/tex]
what is the value of the expression
3.2(2.3)-4.8
Answers
Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x) George reads 200 pages in 40 minutes. x g(x) 4 −8 4 10 4 28
Answers
Therefore, since the slope of f(x) is defined and g(x) has an undefined slope, the correct option is: d) The function f(x) has a larger slope.
To determine the slopes of the functions f(x) and g(x), we need to calculate the rate of change or the slope of each function.
The slope of a function represents how much the output (y-value) changes for a given change in the input (x-value).
For function f(x), the rate of change can be calculated as follows:
[tex]\[ \text{Slope of } f(x) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{200 \text{ pages}}{40 \text{ minutes}} = 5 \text{ pages/minute} \][/tex]
Now, let's calculate the slope for function g(x) using the given data points:
[tex]\[ \text{Slope of } g(x) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{28 - (-8)}{4 - 4} = \frac{36}{0} \][/tex]
As the denominator is zero, the slope for g(x) is undefined.
A store allows customers to fill their own bags of candy. Terri decides she only wants jelly beans and chocolate drops. Jelly beans sell for $0.90 per pound, and chocolate drops sell for $0.70 per pound. Terri’s bag weighs 5 pounds and it costs $4.10. How many pounds of jelly beans and chocolate drops did Terri buy?
A. 3 pounds of jelly beans; 2 pounds of chocolate drops
B. 2 pounds of jelly beans; 3 pounds of chocolate drops
C. 4 pounds of jelly beans; 1 pound of chocolate drops
D. 1 pound of jelly beans; 4 pounds of chocolate drops
I think it might be c
Answers
PLEASE HELP I WILL GIVE 99 POINTS Aida applied the distributive property to write the equivalent expressions below. 15 + 21 = 3(4 + 8) What is Aida’s error? Aida used 3 as the factor, which is not common to 15 and 21. Aida did not correctly divide by the common factor to get (4 + 8). Aida did not apply the correct operations to the expressions. Aida wrote two expressions that are not equivalent.
Answers
She should have written: (5 + 7)
It would look like this: 15 + 21 = 3(5 + 7)
This make both sides equivalent: 15 + 21 = 15 + 21 Yay!
Hope this helps!
and May the Force Be With You
-Jabba
I need help with the second one!!
Answers
[tex]1 \frac{1}{2} * \frac{5}{8} = \frac{3}{2} * \frac{5}{8}= \frac{15}{16} [/tex]
So, they will need 15/16 cups of coca for the new recipe.
Y-b=m(x-a) solve for a
Answers
y-b-mx=am
(y-b-mx)/m=a
Laura family is going on vaction.they will drive 4,180 miles over the next two weeks.about how many miles will they drive on average each week?
Answers
What are the expanded forms of the two factors in the equation?
76 × 18 = n
Choose exactly two answers that are correct.
A.
10 + 8
B.
71 + 5
C.
70 + 6
D.
10 × 8
Answers
what does this expression represent 12f+24
Answers
Hope this helps!! :)
Answer:
This is an algebraic expression which means that 12 multiplied by the value of a variable "f", plus 24 would give an integer.
Step-by-step explanation:
This expression can be solved when the value of f is known. Thus its solution is dependent on the known value of "f".
So, assuming the value of f is 2, then the answer would have been 48.
Sea level is considered to be 0 feet. A probe released at sea level dropped at a constant rate for 3.25 minutes, reaching an elevation of −35.75 feet relative to sea level.
What was the probe's elevation relative to sea level after the first minute?
Explanation too, please!
Answers
What Is the answer I am really struggling with fractions
Answers
3/1 x 3/5 =
3x3/1x5=
9/5 or 1 4/5
a grandmother is making clothes for her three granddaughters. She'll make a jacket and one other item for each granddaughter. The three other items will be exactly the same. A jacket takes 1 5/8 yards of fabric. She had 10 yards of material of. She's trying to figure out how much fabric she has for each of the three extra items. Write a number sentence to represent the situation of the total fabric use.
Answers
The total amount of fabric use is 7 1/2
The required number to represent the situation is 67/24.
What is the ratio of two numbers?The ratio of two numbers a and b can be written as a : b = a/b.
The ratio of two quantities is the unit rate of one quantity with respect to the other.
Given that,
The cloth required for jacket is 1(⁵/₈) = 13/8 yards.
Then the remaining cloth for the three other items = 10 - 13/8 = 67/8 yards.
Now, the cloth for each of the items is calculated by taking the ratio as,
(67/8)/3
= 67/24
Hence, the yards of cloth available for each of the item is given as 67/24 yards.
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A line has a slope of -2 and passes through the point (3, 1). What is the equation of this line in slope-intercept form?
Question 7 options:
y = -2x + 7
y = -2x + 5
y = 3x + 1
Write the equation of the line that passes through the points (1,4) and (5,8) in standard form. (Ax + By = C)
Question 8 options:
x + 4y = 1
5x + 8y = 4
-2x + y = 5
-x + y = 3
Answers
Answer:
b
Step-by-step explanation:
just did it
What number is the opposite of the opposite of 5?
Answers
Answer:
The opposite of 5 is negtive -5. Then you can simplify that to
what is the opposite of -5 and then you could get 5 again