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saw5 [17]
3 years ago
7

Find the domain of the function. g(x) = 1 - 2x^2

Mathematics
1 answer:
madam [21]3 years ago
7 0

Domain: ( − ∞ , ∞ ) , { x | x  ∈  R }

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625 ÷ 62.5 × 30 ÷ 10
Naddik [55]

Answer:

30

Step-by-step explanation:

Follow the correct order of operations.

There are only multiplications and divisions, so do them in the order they appear from left to right.

625 ÷ 62.5 × 30 ÷ 10 =

= 10 × 30 ÷ 10

= 300 ÷ 10

= 30

7 0
2 years ago
Pls help 15. Find the exact area of the shaded region of the circle shown in the diagram.
konstantin123 [22]

Answer:

  • The shaded region is 9.83 cm²

Step-by-step explanation:

<em>Refer to attached diagram with added details.</em>

<h2>Given </h2>

Circle O with:

  • OA = OB = OD - radius
  • OC = OD = 2 cm

<h2>To find</h2>

  • The area of segment ADB.

<h2>Solution</h2>

Since r = OC + CD, the radius is 4 cm.

Consider right triangles OAC or OBC:

  • They have one leg of 2 cm and hypotenuse of 4 cm, so the hypotenuse is twice the short leg.

Recall the property of 30°x60°x90° triangle:

  • a : b : c = 1 : √3 : 2, where a- short leg, b- long leg, c- hypotenuse.

It means OC: OA = 1 : 2, so angles AOC and BOC are both 60° as adjacent to short legs.

In order to find the shaded area we need to find the area of sector OADB and subtract the area of triangle OAB.

Area of <u>sector:</u>

  • A = π(θ/360)r², where θ- central angle,
  • A = π*((mAOC + mBOC)/360)*r²,
  • A = π*((60 + 60)/360))(4²) =  16.76 cm².

Area of<u> triangle AO</u>B:

  • A = (1/2)*OC*(AC + BC),  AC = BC = OC√3 according to the property of 30x60x90 triangle.
  • A = (1/2)(2*2√3)*2 = 4√3 = 6.93 cm²

The shaded area is:

  • A = 16.76 - 6.93 = 9.83 cm²

8 0
1 year ago
A hotel has a pool in the shape of a rectangle. The pool is 8 m long, 3 m wide, and 2,000 cm deep. What is the volume of the poo
Maslowich
Ok, first you need to change the 2,000 cm into meters and then you just multiply all the sides.
4 0
3 years ago
The perimeter of a trapezoid is 39a – 7. Three sides have the following lengths: 9a, 5a + 1, and 17a – 6. What is the length of
Airida [17]
We know the perimeter is the total sum of all sides of the shape, we can use this to form an equation: the perimeter=1st side + 2nd side + 3rd side + 4th side 39a-7=9a+(5a+1)+(17a-6)+4th side.
Collect like terms to get 39a-7=31a-5+4th side
If we move everything but the 4th side over to the left we can solve 
C. 8a-2=4th side is the correct answer
3 0
3 years ago
Read 2 more answers
PLEASE HELP I NEED THIS ASAP<br> Find the vertex of y=x^2-7x+4
Goshia [24]

Answer:

\mathrm{Minimum}\space\left(\frac{7}{2},\:-\frac{33}{4}\right)

Step-by-step explanation:

y=x^2-7x+4\\\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}\\\mathrm{The\:parabola\:params\:are:}\\a=1,\:b=-7,\:c=4\\x_v=-\frac{b}{2a}\\x_v=-\frac{\left(-7\right)}{2\cdot \:1}\\\mathrm{Simplify}\\x_v=\frac{7}{2}\\\mathrm{Plug\:in}\:\:x_v=\frac{7}{2}\:\mathrm{to\:find\:the}\:y_v\:\mathrm{value}\\y_v=\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4\\

\mathrm{Simplify\:}\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4:\quad -\frac{33}{4}\\y_v=-\frac{33}{4}\\Therefore\:the\:parabola\:vertex\:is\\\left(\frac{7}{2},\:-\frac{33}{4}\right)\\\mathrm{If}\:a0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}\\a=1\\\mathrm{Minimum}\space\left(\frac{7}{2},\:-\frac{33}{4}\right)

6 0
3 years ago
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