What is the vertex of the absolute value function defined by f(x) = (x + 2) + 4?

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

8 0

Answer:

Step-by-step explanation:

maximum point should be 4

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We know the following about the numbers a, b and c:

labwork [276]

Step-by-step explanation:

(a + b)² = 9

(b + c)² = 25

(a + c)² = 81

Taking the square root:

a + b = ±3

b + c = ±5

a + c = ±9

By adding these three equations together and dividing both sides by 2, we get the value of a + b + c.

Possible combinations for a + b + c such that the sum is greater than or equal to 1 are:

a + b + c = (-3 + 5 + 9)/2 = 11/2

a + b + c = (3 − 5 + 9)/2 = 7/2

a + b + c = (3 + 5 + 9)/2 = 17/2

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3 years ago

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Mazyrski [523]

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2 years ago

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by: