Maths-

SAT

Easy

Question

Ryan has 1,500 yards of yarn. He wants to knit at least 2 scarves and at least 3 hats. Each scarf requires 300 yards of yarn, and each hat requires 120 yards of yarn. If s represents the number of scarves and h represents the number of hats, which of the following systems of inequalities represents this situation?

s + h $\leq$ 1,500 s $\geq$ 2 h $\geq$ 3
2s + 3h $\leq$ 1,500 s $\geq$ 2 h $\geq$ 3
2s + 3h $\leq$ 1,500 s $\geq$ 300 h $\geq$ 120
300s + 120h $\leq$ 1,500 s $\geq$ 2 h $\geq$ 3

The correct answer is: 300s + 120h $less or equal than$ 1,500

s $greater or equal than$ 2

h $greater or equal than$ 3

Given scarfs = s ≥ 2
hats = h ≥ 3
scarf = 3000s
hats = 120h
$therefore$ The inequality equation = 300s + 120h ≤ 1500

A collection of more than one inequality in one or more variables is known as a system of inequalities. Systems of inequalities are helpful when a problem's potential solutions are subject to several constraints, and a variety of potential solutions are required.
¶An infinite number of ordered pair solutions for inequality in the set, each specified by a region in a rectangular coordinate plane. When two inequalities are considered, the collection of simultaneously ordered pair solutions is defined by the intersection of these sets.
¶Systems of inequalities can be solved slightly differently than systems of linear equations because the substitution and elimination methods are not applied. Only the limitations of the inequality signs, ≤, and ≥, are responsible for this.

Seed or nut	Calories	Total fat (grams)	Protein (grams)
Pecan	198	20.2	3.0
Pistachio	80	6.5	3.0
Pumpkin	159	13.9	8.5
Sunflower	166	14.6	5.9
Walnut	185	18.5	4.3

Seed or nut	Calories	Total fat (grams)	Protein (grams)
Pecan	198	20.2	3.0
Pistachio	80	6.5	3.0
Pumpkin	159	13.9	8.5
Sunflower	166	14.6	5.9
Walnut	185	18.5	4.3

Seed or nut	Calories	Total fat (grams)	Protein (grams)
Pecan	198	20.2	3.0
Pistachio	80	6.5	3.0
Pumpkin	159	13.9	8.5
Sunflower	166	14.6	5.9
Walnut	185	18.5	4.3

Seed or nut	Calories	Total fat (grams)	Protein (grams)
Pecan	198	20.2	3.0
Pistachio	80	6.5	3.0
Pumpkin	159	13.9	8.5
Sunflower	166	14.6	5.9
Walnut	185	18.5	4.3

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s + h 1,500 s 2 h 32s + 3h 1,500 s 2 h 32s + 3h 1,500 s 300 h 120300s + 120h 1,500 s 2 h 3

The correct answer is: 300s + 120h 1,500s 2h 3

Given scarfs = s ≥ 2hats = h ≥ 3scarf = 3000shats = 120hThe inequality equation = 300s + 120h ≤ 1500

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s + h $\leq$ 1,500 s $\geq$ 2 h $\geq$ 3
2s + 3h $\leq$ 1,500 s $\geq$ 2 h $\geq$ 3
2s + 3h $\leq$ 1,500 s $\geq$ 300 h $\geq$ 120
300s + 120h $\leq$ 1,500 s $\geq$ 2 h $\geq$ 3

The correct answer is: 300s + 120h $less or equal than$ 1,500

s $greater or equal than$ 2

h $greater or equal than$ 3

Given scarfs = s ≥ 2
hats = h ≥ 3
scarf = 3000s
hats = 120h
$therefore$ The inequality equation = 300s + 120h ≤ 1500

$x space minus space 2 space equals space square root of x plus 10 end root$
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$x space minus space 2 space equals space square root of x plus 10 end root$
Which of the following values of x is a solution to the equation above?

Which expression is equivalent to (2x² − 4) − (−3x² + 2x − 7) ?

Which expression is equivalent to (2x² − 4) − (−3x² + 2x − 7) ?

h(t)=-16t² + 48t +72
If air resistance is ignored, the function h defined above models the height above ground, in feet, of a toy rocket t seconds after it is launched from the roof of building. Based on the model, what is the height above ground, in feet, of the toy rocket 1 second after launch?

h(t)=-16t² + 48t +72
If air resistance is ignored, the function h defined above models the height above ground, in feet, of a toy rocket t seconds after it is launched from the roof of building. Based on the model, what is the height above ground, in feet, of the toy rocket 1 second after launch?

g(x) = 2^x - 2
The function g is defined by the equation above. Which of the following points in the xy-plane is an x-intercept of the graph of the equation y = g(x)?

g(x) = 2^x - 2
The function g is defined by the equation above. Which of the following points in the xy-plane is an x-intercept of the graph of the equation y = g(x)?

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Which of the following is a solution to the equation above?

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Which of the following is a solution to the equation above?

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