MATHEMATICS COLLEGE

A linear function and a quadratic function both have a domain of all real numbers.True
False
?

Answers

Answer 1
Answer:

Answer: True

Explanation: The domain of a quadratic function in standard format is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

Linear function is almost always going to be all real numbers. The range of a non-horizontal linear function is all real numbers no matter how flat the slope might look.

Answer 2
Answer: true....
the range of the function shows all real values

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What is 1 whole and 5/8 as a decimal

Answers

Answer:

1 whole and 5/8 as a decimal is 1.625
Answer: 1.265
Steps: Convert 1 5/8 to a improper fraction-> 13/5 and dived the numerator by the denominator. 13/5= 1.265

Pls help 5[9+3(3.2-3)]

Answers

Answer:

48

Step-by-step explanation:

3.2 - 3 = .2

3(.2) = .6

9 + .6 = 9.6

5 * 9.6 = 48
This is the working for the answer that is 48

5 ( 9 + 3 ( 3 - 3.2 ) )
5 ( 9 + 3 * 0.2 )
5 ( 9 + 0.6 )

5 * 9.6 = 48

Two guy wires from the top of a 200-foot radio antenna are anchored to the ground by two large concrete posts. The antenna is perpendicular to the ground and between the two posts. If the angles of depression from the top of the antenna to each of the posts is 46o and 48o respectively, then the distance between the two posts is:_______

Answers

Answer: 373.22 feet

Step-by-step explanation:

The attached photo contains the diagram illustrating the scenario. 2 right angle triangles ACD and BCD are formed.

The distance between the two posts is AD + BD

To determine AD, we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side

Tan 46 = 200/AD

AD = 200/Tan 46 = 200/1.0355

AD = 193.14

To determine BD, we would also apply the tangent trigonometric ratio. Therefore

Tan 48 = 200/BD

BD = 200/Tan 48 = 200/1.1106

BD = 180.08

Therefore, the distance between the two posts is

193.14 + 180.08 = 373.22 feet

I need help with this problem

Answers

9514 1404 393

Answer:

  (a)  4 in²

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the height of the prism.

We can find the area of the base by solving for B.

  B = V/h

  B = (12 in³)/(3 in)

  B = 4 in² . . . . . . . . . . matches the first choice

QuestionGiven that tan(0) =5/12
and 0 is in Quadrant III. what is cos(0)? Write your answer in exact form. Do not round.
Provide your answer below:

Answers

Answer:

cosΘ = - (12)/(13)

Step-by-step explanation:

Given that Θ is in the third quadrant then cosΘ < 0

Given

tanΘ = (5)/(12) = (opposite)/(adjacent)

Then 5 and 12 are the legs of a right triangle (5- 12- 13 ) with hypotenuse = 13

Thus

cosΘ = - (adjacent)/(hypotenuse) = - (12)/(13)

In the figure, side AB is given by the expression (5x + 5)/(x + 3), and side BC is (3x + 9)/(2x - 4).The simplified expression for the area of rectangle ABCD is _______, and the restriction on x is ____.

Answers

Answer:

The simplified expression for the area of rectangle ABCD is ( 15(x + 1))/(2(x - 2)), and the restriction on x is x≠2 .

Step-by-step explanation:

Side AB = Width of rectangle = (5x + 5)/(x + 3)

Side BC = Length of rectangle =  (3x + 9)/(2x - 4)

Area of Rectangle = Length * Width

Putting values:

Area\,\,of\,\,rectangle =( (3x + 9))/((2x - 4)) * ((5x + 5))/((x + 3))

Solving,

Area\,\,of\,\,rectangle =( 3(x + 3))/((2x - 4)) * (5x + 5)/((x + 3)) \nArea\,\,of\,\,rectangle =( 3)/(2(x - 2)) * 5x + 5\nArea\,\,of\,\,rectangle =( 3(5x + 5))/(2x - 4)\nArea\,\,of\,\,rectangle =( 15x + 15)/(2x - 4)\nArea\,\,of\,\,rectangle =( 15(x + 1))/(2(x - 2))

The restriction on x is that x ≠ 2, because if x =2 then denominator will be zero.

So, the answer is:

The simplified expression for the area of rectangle ABCD is ( 15(x + 1))/(2(x - 2)), and the restriction on x is x≠2 .
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