MATHEMATICS HIGH SCHOOL

Find the domain of the following function:

\[ y=\sqrt{x} \]
\[y= \sqrt{x+3} \]

Answers

Answer 1
Answer:

Firstly we have to determine the domain of the function y=√(x)

The domain of the function is the set of values for which the function is real and defined.

In the function y=√(x) we can clearly observe that for the negative values of x , the value of y will not be real.

So, the domain for this function is [0,\infty ) or x\geq 0.

The second function is y=√((x+3))

In this function we can clearly observe that for the values of x less than -3, the function is not real.

So, the domain for this function is [-3,\infty ) or x\geq -3
Answer 2
Answer:

y=√(x)

As we know, the square root of negative numbers.

Hence, the x must be a positive value and greater than 0.

So, x:x∈[0,∞)

y=√(x+3)

x+3\geq 0

subtracting 3 from both sides

x\geq -3

x:x∈[-3,∞)

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Answers

Answer:

1

Step-by-step explanation:
Answer: 1

Explanation: 0v0

The product of 16 and 4 less than a number is 208. Find the number.

Answers

This is a word problem signifying an algebraic expression.

Translating this to mathematics:

16x - 4 = 208

add 4 to both sides.

16x = 212 

divide 16 to both sides. 

x = (212)/(16) 

this is:

x = 13.25 

Rolex worked 40 hours last week. He had 74 deducted from his earnings for taxes. If he had 286 left after the deduction how much does Rolex earn per hour?

Answers

Answer:

Rolex earns $9 per hour.

Step-by-step explanation:

Let the number of dollars he earns each hour be x.

To create our equation we need to find the total number of dollars he earned before his deduction which is 40x.

Then we know that he got 74 dollars deducted from his total earnings leaving him with 286 which gives us an equation. 40x + 74 = 286

40x - 74 = 286          (Equation)

40x = 360                  (Add 74 from both sides)

x = 9                           (Divide both sides by 40)

Write a linear equation to represent the line shown on the graph

Answers

The linear equation representing the line passing through the points (0, 4) and (2, -2) is y=−3x+4.

Here, we have to write a linear equation that represents the line passing through the points (0, 4) and (2, -2), we can use the point-slope form of a linear equation:

y - y_1 = m(x- x_1)

where:

m is the slope of the line,

(x_1,y_1)is one of the given points on the line.

Given the points (0, 4) and (2, -2),

let's calculate the slope m:

m= −2−4/ 2−0

 = −6/2

 =−3.

Now, use the point-slope form with the point (0, 4):

y−4=−3(x−0).

Simplify the equation:

y−4=−3x.

Add 4 to both sides:

y=−3x+4.

So, the linear equation representing the line passing through the points (0, 4) and (2, -2) is y=−3x+4.

To learn more on equation click:

brainly.com/question/14468218

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Answer:

y=-3x+4

Step-by-step explanation:

it's negative bc the slope is going from left to right. you just have to do rise over run to find the slope.

A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like algebra or geometry. What are the correct values of a, b, c, d, and e?


a = 16, b = 29, c = 22, d = 30, e = 24

a = 29, b = 16, c = 30, d = 22, e = 24

a = 16, b = 29, c = 24, d = 22, e = 30

a = 29, b = 16, c = 24, d = 30, e = 22

Answers

Let x be the number of students that like both algebra and geometry. Then:

1. 45-x is the number of students that like only algebra;

2. 53-x is the number of students that like only geometry.

You know that 6 students do not like any subject at all and there are 75 students in total. If you add the number of students that like both subjects, the number of students that like only one subject and the number of students that do not like any subject, you get 75. Therefore,

x+45-x+53-x+6=75.

Solve this equation:

104-x=75,

x=104-75,

x=29.

You get that:

  1. 29 students like both subjects;
  2. 45-29=16 students like only algebra;
  3. 53-29=24 students like only geometry;
  4. 24+6=30 students do not like algebra;
  5. 16+6=22 students do not like geometry.

The correct choice is D.

It is very easy to find the values for a, b, c, d and e. All you have to do is use the Algebra vs. Geometry table to use the given values to find the rest. Please see attachment to see the table. For example if we want to find e we simply subtract 53 from 75. This way e = 22, then use this to find the next value which will be b.



The answer is:

a = 29, b = 16, c = 24, d = 30 and e = 22


I hope this helps, Regards.

Find the value of the expression
2r x s
for r = 2 and s = 4.

Answers

Answer:

16

Step-by-step explanation:

2rs

Let r=2 and s=4

2*2*4

4*4

16
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