What is domain restrictions and what causes them?

Answers

Answer 1
Domain restrictions are values of x which are not acceptable in a function.

They may be arbitrary because we simply want to ignore them. eg y = x^2 between 0 and 4

They may make no sense in the context, eg graph a compounding investment over next 20 years.
Negative values for x make sense here.

They may avoid mathematical impossibilities eg y = (x^2 - 4x) / (x - 4) which must avoid dividing by zero, so x cannot = 4.
The graph will look like the line y = x but have a hole where x= 4

Related Questions

Need help with this :(

Answers

Answer:

B.    m = [tex]\frac{3}{2}[/tex], y-int = 3

Step-by-step explanation:

To find the slope of the line, we need to plot two points

(2, 6) (-2, 0)

m = slope

Then use the Slope-Formula to Solve for the slope

m = [tex]\frac{y2-y1}{x2-x1}[/tex]        

m = [tex]\frac{0-6}{-2-2}[/tex]

m = [tex]\frac{-6}{-4}[/tex]

m = [tex]\frac{6}{4}[/tex]

m = [tex]\frac{3}{2}[/tex]

The Slope is [tex]\frac{3}{2}[/tex]

The y-intercept is 3 because the line is going 3 units upwards on y axis!

Equation: y = 3/2x + 3

Slope: 3/2

y-intercept: 3

Answer:

m = 3/2      int- 3

Step-by-step explanation:

The line goes up 3 and goes right 2. The line crosses the y-intercept at 3.

Solve ay+b = cx for y

Answers

Answer:

y=cx-b/a

Step-by-step explanation:

ay+b=cx

ay=cx-b

y=cx-b/a

A(n) ___ expression is an expression that contains a radical symbol.
A.exponential
B.constant
C.polynomial
D.variable
F.radical

Answers

Answer:

radical

Step-by-step explanation:

Can 17, 9, and 11 be the side lengths of a triangle?

Answers

Answer:

No it cant

Step-by-step explanation:

You have to use the Pythagoras theorem which is a^2 + b^2 = c^2. So 9^2 + 11^2= 202. Then 17 is the hypotenuse so 17^2= 289. They are not equal so they are not.

One year, the population of a city was 99,000. Several years later it was 82,170. Find the percent decrease.

Answers

82170/99000=0.83
1-0.83=0.17
answer is 17%

Find the area of the shaded region

Answers

Answer:

Area of the shades region = 244.6 ft²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC

Area of the rectangle = Length × width

                                    = 29.8 × 13

                                    = 387.4 ft²

By applying Pythagoras theorem in the right triangle DEC,

(Hypotenuse)² = (leg 1)² + (leg 2)²

CD² = DE² + EC²

(29.8)² = DE² + (28)²

888.04 = DE² + 784

DE² = 888.04 - 784

DE = 10.2 ft

Area of ΔDEC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                        = [tex]\frac{1}{2}(10.2)(28)[/tex]

                        = 142.8 ft²

Area of the shades region = 387.4 - 142.8

                                             = 244.6 ft²

There are 120 students in class 7. It is known that
2/3
out of them like Maths, out of which 35
are girls. Also, out of total students,
3/5
are boys. (3)
(a) What is the number of girls in the class?
(b) How many students like Maths?
(c) How many boys like Maths?

Answers

Multiply total students by 2/3 to find how many like math:

Like math = 120 x 2/3 = 240/3 = 80 total students like math

Multiply total students by 3/5 to find number of boys:

120 x 3/5 = 360/5 = 72 boys

A) number of girls = total students - boys = 120 -72 = 48 girls

B) from above 80 students like math

C) number of boys that like math = number of students that like math minus girls that like math: 80- 35 = 35 boys like math

72 boys xjtxkttkftkxktx

Help,anyone can help me do quetion​

Answers

Answer:

B2--> the answer is 121 degrees.This is because due to alternate interior angles, the triangle

helppppopoop help help help

Answers

Answer:

160

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

VOLUME...

1) π*r^2*h

π*(2.5)^2 *h

(π)*(2.5)^2* 6

= 117.8

2) π*r^2*h + 1/2 *[(4/3) · π · r3]

(π)*(3)^2* 3 + 1/2 *[(4/3) · π · 3^3]

        84.8+ 56.5 = 141.41

3) (1/3) π*r^2*h

(1/3) π*3^2*h

3^2 + h^2 = 36

h = sqrt(27) = 5.1

(1/3) π*3^2*5.1

= 48.06

which of the following is equivalent to 2cos^2(x) - cos(2x)? A. sin(2x) B. Sin^2(x) C. 1 D. 2

Answers

Answer:

C. 1

Step-by-step explanation:

2cos²(x) - cos(2x) = 1

Answer:

C

Step-by-step explanation:

Using the identity

cos2x = 2cos²x - 1 , then

2cos²x = cos2x + 1

Given

2cos²x - cos2x

= cos2x + 1 - cos2x

= 1 → C

Jameson middle school give bottles of water to teachers and students who are going on a field trio. The school orders 500 bottles of water. They plan to give 35 bottles of water to teacher . They orderd at least 2 bottles of water for each student. How many students could be going on the field trip? Show your work

Answers

Answer: Almost 232 students going on the field trip.

Step-by-step explanation:

Let x be the number of students going on the field trip.

As per given,

[tex]2x+35 \leq500[/tex], where [tex]x\geq2[/tex].

To solve the inequality , subtract 35 from both sides

[tex]2x\leq465\\\\x\leq232.5[/tex] [divide both sides by 2]

i.e Almost 232 students going on the field trip.

What is the volume of this rectangular prism?
5 cm
3 cm
4 cm

A. 12 cm3
B. 94 cm3
C. 120 cm3
D. 60 cm3

Answers

Answer:

The volume of this rectangular prism is D. 60[tex]cm^{3}[/tex].    

Step-by-step explanation:

In order to find the volume of a rectangular prism, we need to multiply the length by the width, and then multiply their product by the height of the prism. We can write what I said above as a formula...

V = l × w × h    

(In the formula above "V" is the volume, "l" is the length, "w" is the width, and "h" is the height).

Now we just substitute the values into the formula and we get...

V = l × w × h    

V = 4cm × 3cm × 5cm

V = 60[tex]cm^{3}[/tex]

Therefore, the volume of this rectangular prism is D. 60[tex]cm^{3}[/tex].    

Substitute the given side lengths into the equation for the Pythagorean Theorem.

Answers

Answer:

15 is the missing side (hypotenuse)h

Step-by-step explanation:

A^2+b^2=c^2

9^2+12^2=c^2

81+144=c^2

225=c^2

15=c

Nine split into four groups is two, with a ___ of one.

Answers

Nine split into four groups is two, with a remainder of one.

A man is now 3 times as old as his son. In 10 years time, the sum of their ages will be 76.
How old was the man when his son was born?​

Answers

Answer:

28

Step-by-step explanation:

A man is now 3 times as old as his son.

m = 3s

In 10 years time, the sum of their ages will be 76

(m + 10) + (s + 10) = 76

Subsitute for m = 3s

(3s + 10) + (s + 10) = 76

4s + 20 = 76

4s = 56

s = 14

m = 3s = 14 * 3

m = 42

------------------------

How old was the man when his son was born?

m - s = 42 - 14

m - s = 28

select all of the following statements that are true

Answers

Answer:

1234 no statement is there

Please help me! I need to get this done but don't know how!

The polynomial x³+5x²-57x-189 expresses the volume, in cubic inches, of a shipping box, and the width is (x+3) in. If the width of the box is 15 in., what are the other two dimensions?

a. height: 19 in.
depth: 5 in.

c. height: 19 in.
depth: 7 in.

b. height: 21 in.
depth: 5 in.

d. height: 21 in.
depth: 7 in.

Answers

Answer:

Step-by-step explanation:

your answer would be b

if a recipe calls for 0.8 cups of water per cup of water per 5/8 cups of milk. What is the unit rate per cup of milk ( with correct labels )

Answers

Answer: 1.28 cups of water per cup of milk

Step-by-step explanation:

0.8 divided by 5/8 equals 1.28

verified by my teacher :)

Mandy gets 6 out of every 8 questions on a test correct. If she gets 27 questions correct, how many questions are on the test?

Answers

Answer:

36

Step-by-step explanation:

She gets 6 question right for every 8 question that means a ratio of 6/8 which is equal to 3/4

so we can say the ratio multiplied by the number of questions equals the correct answers

while x is the number of questions:

solve for x

3/4 * x = 27

x = 27 / (2/3) = 36

Please help with my math! Question number 2

Answers

Answer:

17.804

Step-by-step explanation:

Pythagorean theorem. 14^2 + 11^2 = c^2

Cuanto interes ganara lesli si presta 5000 L a pagar en tres años con un interés simple anual de 5%

Answers

Answer:

Amount of simple interest in three year = 750

Step-by-step explanation:

Given:

Amount invested = 5,000

Number of year = 3 year

Rate of interest = 5% Annually

Find:

Amount of simple interest in three year

Computation:

Simple interest = (P){R)(T)

Amount of simple interest in three year = (5,000)(3)(5%)

Amount of simple interest in three year = (5,000)(3)(0.05)

Amount of simple interest in three year = (5,000)(0.15)

Amount of simple interest in three year = 750

convert the decimal number 356 to a Quinary number

Answers

Answer : Yes the answer to your question is 2411.

Explanation : how I got the answer

To convert decimal number 356.625, we convert its integer and fraction part individually and then add them to get the equivalent quinary number, as below:

To convert integer 356 to quinary, follow these steps:

Divide 356 by 5 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get the equivalent quinary number.

356 / 5 = 71 with remainder 1

71 / 5 = 14 with remainder 1

14 / 5 = 2 with remainder 4

2 / 5 = 0 with remainder 2

Here is the answer to 356 decimal to quinary number:

2411

PLEASE HELP DUE TONIGHT (W/ WORK IF POSSIBLE) THANK YOU

Answers

The answer is c because I did it and got it right

BRAINLY OPPORTUNITY
ANSWER ASAP
If f(x) = -9x – 9 and g(x)= x-9,
what is (fºg)(10)?

Answers

Answer:

-18

Step-by-step explanation:

fog(x) = -9(x-9) -9

=> f o g (10) = -9(10-9)-9 = -9-9 = -18

How many times larger than
(15 + 10) is 8 x (15 + 10)?

Answers

Answer:

8 times larger

Step-by-step explanation:

(15+10) is the singular equation alone. Muiltiply it by 8, and it's 8 times larger then the initial singular expression. Therefore, the answer is 8 times larger.

How do I solve this

Answers

For all real numbers, except zero, a x 1/a = 1

Multiplying any real number by it’s reciprocal will result in 1.
This is why a reciprocal of a number is called it’s multiplicative inverse.

The reciprocal of zero is 1/0 and is undefined because dividing by zero is not valid.

Help plz I dont get it

Answers

Roxanne finished more of her to do list because if you take 5/6 and turn it into a decimal you get 0.83, while Quinn finished least because 7/9 is 0.77

4) Determine the solution. Show your work.
17 + x2 = 42

Answers

Answer:    x = 5 or x = -5

================================================

Work Shown:

17 + x^2 = 42

x^2 = 42-17

x^2 = 25

x = sqrt(25)  or  x = -sqrt(25)

x = 5 or x = -5

What is the domain of the function of y=√x+8 -7

Answers

Answer:

Step-by-step explanation:

Recall that the argument of the square root function y = √x must always be 0 or greater.

If you meant y=√x+8 -7, the domain is therefore [0, infinity).

But if you meant y=√(x+8) -7, the domain is [-8, infinity).

Those parentheses are important!

(x, y) ----> (x + 2, y - 3) please help this is my final ​

Answers

slide right 2 and down 3

OPTION B is the correct answer.

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