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3 years ago

Which quadratic inequality does the graph represent

Mathematics

2 answers:

Black_prince [1.1K]3 years ago

7 0

Answer:

Option (1)

Step-by-step explanation:

Equation of a quadratic function,

y = a(x - h)² + k

Here (h, k) is the vertex

From the picture attached,

Vertex of the parabola is (2, -5)

So the equation of the function will be,

y = a(x - 2)² - 5

Since, the graph passes through a point (0, 3)

3 = a(0 - 2)² - 5

3 = 4a - 5

4a = 8

a = 2

Equation will be,

y = 2(x - 2)² - 5

y = 2(x² - 4x + 4) - 5

y = 2x² - 8x + 8 - 5

y = 2x² - 8x + 3

But the shaded area is outside the graph so the quadratic inequality will be,

y ≤ 2x² - 8x + 3

Option (1) will be the answer.

soldi70 [24.7K]3 years ago

7 0

Answer: A

Step-by-step explanation:

Equation of a quadratic function,

y = a(x - h)² + k

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3 years ago

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Rom4ik [11]

(1) See below for a diagram. Basically, the distance on the ground from the person to the building (34 ft) is adjacent to the angle of elevation (74 degrees) and the height of the building (labeled h in the diagram) is the side opposite the angle. Since we are dealing with opposite and adjacent we use the tangent of the angle and tan = opp/adj

Specifically, $tan74= \frac{h}{34}$
$h=(34)(tan74)$ <span class="_wysihtml5-temp-placeholder"></span>
$h=118.6$ feet.

Please be sure your calculator is set to degrees (not radians) when you do this problem.

(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.

sin = opp/hyp. As the sin Q = 9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.

cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.

You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.

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White raven [17]

Answer:

Step-by-step explanation:

5,500 is 50 percent of 11,000 :)

Hope This Helps.

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