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rosijanka [135]
3 years ago
10

Find the domain of the function. (Enter your answer using interval notation.) f(x) = 7 − 1 2 x if x ≤ 2 8x − 4 if x > 2 g

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
4 0

Answer\left ( -\infty,2\right ]

Step-by-step explanation:

Given

(i)

F(x)=7-12x

and x\leq 2

Domain is \left ( -\infty,2\right ]

(ii)F(x)=8x-4

x>2

Domain is (2,\infty)

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Round to nearest thousandth!! (3 decimal places) photo attached
aliina [53]

Answer:

<em>Probability point lies on shaded region: ( About ) 0.294</em>

Step-by-step explanation:

<em>~ If we are to find the probability, we must find the area of the shaded figure, over that of the total area of this trapezoid ( whole figure ) ~</em>

Let us get the general dimensions. Firstly, the base of the trapezoid is composed of parts 5, 12, and 5. This is an isoceles trapezoid, meaning that the triangles ( shaded region )  are congruent to one another, including the altitudes. That would mean the non - shaded region is a parallelogram, provided altitudes are congruent and by definition of a trapezoid the bases are congruent.

1. Given the information above, the smaller base is congruent to the opposite side of the parallelogram created, so it is 12 units in length, the larger base being 12 + 5 + 5 ⇒ 22 units

2. By Pythagorean Theorem, if x ⇒ altitude of one of the triangles ( shaded region), 5^2 + x^2 = 13^2 ⇒ 25 + x^2 = 169 ⇒ x^2 = 144 ⇒ altitude = 12 units

3. Now we can find the area of this trapezoid by:  ( base + base/2 ) * altitude ⇒ ( 12 + 22 / 2 ) * 12 ⇒ ( 34 / 2 ) * 12 ⇒ ( 17 ) * 12 ⇒ 204 units^2

5. The shaded region is composed of two triangles, and knowing the triangles are ≅, let us solve for the area of one triangle and multiply that by 2 to find the total area of the shaded region. Area of triangle: 1/2 * base * altitude ⇒ 1/2 * 5 * 12 ⇒ 30 units^2. Area of shaded region: 30 * 2 = 60 units^2

<em>Probability point lies on shaded region: 60/204 ⇒ ( About ) 0.294</em>

8 0
3 years ago
Find the radius, and the approximate circumference and area of the circle below. (Use 3 for \pi)
Marina CMI [18]

Answer:

Circ=37.704, Area= 112.112

Step-by-step explanation:

Circumference= pi *Diameter

Taking pi=3.142, Diameter=12

Circ=3.142*12=37.704

Area= pi * r^2

Area= 3.142*6*6=112.112

4 0
2 years ago
Mikis ice cream parlor sold 345 scoops of ice cream on Saturday and 21 scoops on Sunday how many more were sold on Saturday then
svp [43]
345-21 is 324 so 324 more scoops
5 0
2 years ago
The angle bisectors of AXYZ are XG, YG, and ZG. They meet at a single point G.
Harrizon [31]

Answer:

m∠FXD = 36°

EG = 10

m∠FZG = 24°

Step-by-step explanation:

In triangle XYZ, G is the incenter of the triangle.

Since, m∠FXG = 18°

And m∠FXD = 2(m∠FXG)

                     = 2 × 18°

                     = 36°

Since, point G is equidistant from all sides (Property of incenter of a triangle)

Therefore, DG = EG = GF = 10

Since, m∠X + m∠Y + m∠Z = 180°

2(m∠FXG) + m∠DYE + 2(m∠FZG) = 180°

2(18)° + 96° + 2(m∠FZG) = 180°

2(m∠FZG) = 180° - 132°

m∠FZG = 24°

3 0
3 years ago
Please help me :( I’m not that good with math
d1i1m1o1n [39]

Answer:

Step-by-step explanation:

5 0
2 years ago
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