(04.06 MC) In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area
where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. One line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded above the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded in below the line. The graph represents which system of inequalities? y ≤ −3x − 1 y ≤ −x − 4 y ≥ −3x + 1 y ≤ −x − 4 y ≤ 3x − 1 y ≤ −x + 4 y ≤ 3x − 1 y ≥ −x + 4
1 answer:
Answer:
(D)y ≤ 3x − 1 y ≥ −x + 4
Step-by-step explanation:
The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded above the line.
The line that satisfies the point (0,4) and (4,0) is y=-x+4
Since it is shaded above the line, we have the inequality sign ≥.
Therefore, one of the lines is y≥-x+4
In the equation of the line y=3x-1
When x=0, y=3(0)-1=-1
When x=2, y=3(2)-1=5
Since it is shaded below the line, we have the inequality sign ≤ .
Therefore, the other line is y≤3x-1.
The correct option is D.
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Answer:
In order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.
Step-by-step explanation:
As the recipe is missing in this question, the recipe is found online which given following information
- Abel needs 5 cups of flour to make brownies.
- If Abel uses 4 cups of sugar.
- he will need to use 2 cups of cocoa powder.
- The recipe will make brownies if Abel uses only 1 egg.
Abel has to make 45 brownies for the sale, this is also missing in this question, however is given in the reference question linked here.
This recipe is to make 9 brownies. Now for 45 brownies the multiplier is found as 45/9=5. So by multiplying quantity of all the ingredients by 5, Abel will be able to make 45 brownies.
Now in order to make 45 brownies
- Abel needs 5*5 =25 cups of flour to make brownies.
- If Abel uses 5*4=20 cups of sugar.
- he will need to use 5*2=10 cups of cocoa powder.
- The recipe will make brownies if Abel uses only 5*1=5 egg.
So in order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.
In this question , we have a graph given, and we have to find the x coordinate of the intersection point .
From the graph , the input value is approximately 3.3 .
In the graph,
And for g(x), we need the slope and y intercept .
Slope is the ratio of rise and run .
Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .
So the equation of g(x) is
We need to do
Substituting the values of the two functions, we will get
Adding 2 to both sides
Cross multiplication
So the input value is 3.3 approx