Answer:
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Step-by-step explanation:
Sure! I can help you with that. To graph the inequality y ≤ -2 or y > 1, we will need to create two separate graphs and then combine them.
First, let's graph the inequality y ≤ -2. This represents all the values of y that are less than or equal to -2. We can represent this on a number line or a coordinate plane.
To graph y ≤ -2, we draw a horizontal solid line at y = -2 and shade everything below the line. This includes all the points on the line as well. It would look like this:
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X------------ (y = -2)
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Next, let's graph the inequality y > 1. This represents all the values of y that are greater than 1.
To graph y > 1, we draw a horizontal dashed line at y = 1 and shade everything above the line. This does not include any points on the line itself. It would look like this:
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X------------ (y = -2)
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Now, to combine the two graphs, we shade the area that satisfies both inequalities. In this case, that would be everything above the line y = -2 and everything above the line y = 1. The shaded area would be above y = 1 because it satisfies the condition y > 1.
The final graph would look like this:
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This graph represents the solution to the inequality y ≤ -2 or y > 1.
Answer:
Step-by-step explanation:
3(3)^2 + 5(3) + 25
3*3 = 9, 5*3 = 15
3(9) + 15 + 25
27 + 15 + 25 = 67
b.Find the amount of milk in 3 mugs
Answer:
a) 1/9 quarts
b) 1/3 quarts
Step-by-step explanation:
Gordon pours 4/9 quarts of milk from a pitcher equally into 4 mugs.
a. Find the amount of milk in each mug.
To solve the first part of this question, we can simply use the idea of proportion;
Let x be the amount of milk in 1 mug
4/9 quarts = 4 mugs
x = 1 mugs
We will cross multiply
4x = 4/9
To get the value of x, we will divide both-side of the equation by 4
4x/ 4 = 4/9 ÷ 4
(on the left hand- side of the equation, 4 will divide 4 leaving us with x)
x = 4/9 ÷ 4
( This ÷4 can be change to become × 1/4)
x = 4/9 × 1/4
(The 4 at the numerator will cancel out the 4 at the denominator leaving us with 1/9)
x = 1/9
Therefore the amount of milk in each mug is 1/9 quart
b.Find the amount of milk in 3 mugs
For this second part of the question, we can also use proportion to solve;
Let x be the amount of milk in 3 mugs
4/9 quarts = 4 mugs
x = 3 mugs
Cross multiply
4x = 3 × 4/9
(At the right-hand side of this equation 3 can divide 9 which will give us 3 )
4x = 1 × 4 /3
4x = 4/3
We can now divide both-side of the equation by 4 to get the value of x
4x/4 = 4/3 ÷ 4
(On the left hand side of the equation, 4 will cancel out 4 leaving us with just x and on the right-hand side of the equation ÷ 4 can be changed to ×1/4)
x = 4/3 × 1/4
(4 will cancel 4 leaving us with 1/3)
x = 1/3
Therefore the amount of milk in 3 mugs is 1/3 quarts
2x4 + 5x when x = 6?
By a length of 10.05 meters - 0.5 meters = 9.55 meters, 0.5 meters is less than 10.05 meters.
In mathematics, subtraction involves taking something away from a group or number of items. When you eliminate, what remains in the group grows smaller. The following is an example of a subtraction problem: 7 - 3 = 4.
To determine the difference between the two lengths, we subtract the smaller length from the larger length. In this case, we subtract 0.5 meters, which is the smaller length, from 10.05 meters, which is the larger length. This gives us a difference of 9.55 meters.
Hence, 0.5 meters is less than 10.05 meters by a length of 10.05 meters - 0.5 meters = 9.55 meters.
Learn more about Subtraction operations here:
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can use the Distributive Property to find the number of
books about animals in the bookstore.
The bookstore has 180 animal books in total, as determined by using the Distributive Property of multiplication to multiply the number of shelves (6) by the number of books on each shelf (30).
The question is asking us to use the Distributive Property to determine the total number of animal books in the bookstore. We know that there are 6 shelves and each shelf contains 30 animal books. By the Distributive Property, we can multiply the number of shelves by the number of books on each shelf to determine the total number of books.
Therefore, the calculation is 6 (shelves) * 30 (books on each shelf). This equals 180.
So, the bookstore has 180 animal books in total. This method is a simple application of the Distributive Property where we distribute the multiplication across the items in the question (shelves and books).
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