Exercise 2.4.4: Showing a statement is true or false by direct proof or counterexample. About Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (a) If and are even integers, then is an even integer. Solution (b) If is an even integer, then and are both even integers. (c) If , then . Solution (d) If x and y are real numbers and , then . Solution (e) If and are positive real numbers and , then . (f) The average of two odd numbers is an odd integer. (g) The average of two even numbers is even. (h) The average of two odd numbers is an integer. Solution

Answer:

x = -5/2

Step-by-step explanation:

y= 0

I dont know but i believe this is it.

Answer:

2x-y=-5

Step-by-step explanation:

y=2x+5

-2x+y=5

-(-2x+y=5)

answer: 2x-y=-5

Answer:

6x + 3h

Step-by-step explanation:

F(X) = 3x^2

F(X+h) = 3(X+h)^2

then F(X+h) - F(X) / h

= 3(X+h)^2 - 3x^2 / h

= 3(x^2 + 2hx + h^2) - 3x^2 / h

= 3x^2 + 6hx +3h^2 - 3x^2 / h

= 6hx + 3h^2 / h

= h (6x +3h) / h

= 6x + 3h

I hope this answer is correct

Answer:

70-14=56     168-56=112

Step-by-step explanation:

The arcs on the Golden Gate Bridge.

I think about the Golden Gate Bridge, which is a suspension bridge.

As in any suspension bridge, a long cable is supported by two large supports.

The cable falls from support, in the form of a curve concave upwards, to a minimum point that is the vertex of the parabola, through which the axis of symmetry passes, and curves again upwards to ascend to the upper end of the other support.

As a unique feature of this parabolic arc, you can tell that the concavity is upward; the parabola opens upward.

Also, you can tell that the parabola is vertical, which means that the axis of symmetry is vertical.

The symmetry is clear because the curve to the left of the vertex is a mirror image of the curve to the right of the vertex. Hope I helped, have a good day!

Answer:

$42.50

Step-by-step explanation:

$42.50 will cover the costs of all people who request full refunds, while still allowing the company to profit.

The average cost the retailer should expect to pay to each customer if It estimates that 60% of customers never make a claim is $4250.

The average is a numeric figure that represents a big amount of data in a single way. The average mark of the class is calculated by averaging the students' grades in a given subject.

It is more important to understand how the class as a whole performed than how each individual student performed.

Given:

It estimates that 60% of customers never make a claim, 25% require a small repair costing an average of $50 and 15% require a full refund costing $200,

Calculate the average cost as shown below,

Assume there are 100 customers, then,

The average cost = 25% of 100 × 50 + 15% of 100 × 200

The average cost = 25 × 50 + 15 × 200

The average cost = 1250 + 3000

The average cost = 4250

Thus, the average cost the retailer should expect to pay to each customer is $4250.

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9514 1404 393

Answer:

  c = 6√2

  d = 12

Step-by-step explanation:

The sides of any isosceles triangle (opposite the congruent angles) are congruent. Hence c = 6√2.

The hypotenuse of an isosceles right triangle is √2 times the side length, so ...

  d = c√2 = (6√2)(√2) = 6·2

  d = 12

__

If you don't believe that, you can always use the Pythagorean theorem to find d:

  d^2 = (6√2)^2 +c^2

  d^2 = 72 +72 . . . . . . . . . since c=6√2

  d = √144

  d = 12

Answer: The text also states, “And her friends told her afterwards that she had spoken in a very loud voice, not shouting, just a very loud voice” (p.2). This proves that Celeste took a risk standing up to the teacher in a firm voice; her actions show that she believed the risk of getting in trouble was worth it to stop the Teacher’s unfair punishment.

Step-by-step explanation:

Answer:

b) no

Step-by-step explanation:

let's put all these options in columns to visualize:

   shirts:                            pants:

    red                               khaki

    white                            black

    black                            white

now i'll list all the combos without matching colors (shirt, pants)

red, khaki;

red, black;

red, white;

white, khaki;

white, black;

white, white;

black, khaki;

black, black;

black, white;

now, we need to get rid of any combos that consist of the same color and combos that consist of black and white paired together.

and we're left with:

red, khaki;

red, black;

red, white;

white, khaki;

black, khaki;

that's only 5 options, so no, she cannot make 8 outfits

Answer:

19.5 my bro!

Step-by-step explanation:

Answer:

19.5 just put it in the calculator

Answer:

both are 79

Step-by-step explanation:

Answer:

20 percent

Step-by-step explanation:

7.5 gallons - 6 gallons = 1.5 gallons

[tex]\frac{1.5}{7.5}[/tex] × 100 = 0.2 × 100 = 20 %

Answer:

20%

Step-by-step explanation:

First, find how much decrease there was: 7.5 - 6 = 1.5

This means the decrease was 1.5/7.5. To convert this to percentage, divide 1.5 by 7.5:

1.5 ÷ 7.5 = 0.20

0.20 = 20% decrease

Answer:

$241,400

Step-by-step explanation:

House costs: $200,000

Percentage increase: 20.7%

This means that the cost of the house increased by that percentage from 2012 to 2013. Therefore the following,

200,000 x 20.7/100 = 41,400

So the value of the house increased by $41,400 in this year.

Now we add to evaluate the total price of the house in 2013.

200,000 + 41,400 = 241,400

House price: $241,400

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

Explanation:

This is because the value -16 is closest to 0, which represents sea level.

I recommend drawing out a vertical number line. Positive numbers are above 0, to indicate elevations above sea level. Negative numbers represent elevations below sea level.

The diagram is shown below. The diagram is not to scale because the red tickmarks shouldn't be equally spaced out; however, the order is correct, and that's all we need to worry about.

Note how -16 is the highest of the four choices, which makes it the closest to sea level. Also note how as you move further down, the negative values get larger in absolute value. It might be helpful to think of a thermometer.

In the given functions, the function f(x) = x+3/7 is a inverse function.

A relation is a function if it has only One y-value for each x-value.

The function should be bijective function ( one-to-one and onto) to be a  inverse function.

f(x)=|x-4|+1

It is absolute function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [1,∞)

So the function  f(x)=|x-4|+1 is not inverse.

f(x) = 25x²+70x+49

It is quadratic function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

So the function f(x) = 25x²+70x+49 is not inverse.

f(x) =x⁴

It is polynomial function with even degree. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

F(x) = x+3/7

It is linear function. one-to-one and onto

Domain: All real (-∞,∞)

Range: All real (-∞,∞)

F(x) = x+3/7 is a inverse function.

Hence, in the given functions, the function f(x) = x+3/7 is a inverse function.

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Answer:

5 and 6: 30

2 and 9: 18

6 and 8: 48

2, 5, and 6: 30

Answer:

A third degree binomial

Step-by-step explanation:

The highest power is 3 hence the 3rd degree

and there are 2 terms hence the bi-nomial

Answer:

yes it does

a. 27

b. -32

Step-by-step explanation:

a. 3 times 3 times 3 = 27

b. -2 times -2 times -2 times -2 times -2= -32

hope this helps!!

Answer:

deed

Step-by-step explanation:

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Step-by-step explanation:

Answer:

10 pieces

Step-by-step explanation:

7 1/2 / 3/4 =

7.5 / .75 =

10 pieces

Hope that helps!

9514 1404 393

Answer:

Step-by-step explanation:

Generally, the single variable on the left side of the equation is the "output" or dependent variable, while any other variables on the right side of the equation are considered to be independent variables, or "input."

So, we assume your first question is asking for the value of t that makes w=176. Put the values in the equation and solve for the unknown.

  w = 112 +8t

  176 = 112 + 8t

  64 = 8t . . . . . . . subtract 112

  8 = t . . . . . . . . . divide by 8

The input for an output of 176 is 8.

__

Ordered pairs are always written as ...

  (input, output)

So, (4, 144) means the output is 144 for an input of 4.

Answer:

8

144

Step-by-step explanation:

Answer:

2009

Step-by-step explanation:

The question can be interpreted as:

[tex]f(x) = -1.330x^2 + 5.149x + 5.517[/tex]

Required

Determine x when f(x) = 10.5

Substitute 10.5 for f(x) in [tex]f(x) = -1.330x^2 + 5.149x + 5.517[/tex]

[tex]10.5 = -1.330x^2 + 5.149x + 5.517[/tex]

Collect Like Terms

[tex]-1.330x^2 + 5.149x + 5.517-10.5=0[/tex]

[tex]-1.330x^2 + 5.149x -4.983=0[/tex]

Using quadratic formula

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

Where

[tex]a = -1.330[/tex]

[tex]b = 5.149[/tex]

[tex]c = -4.983[/tex]

[tex]x = \frac{-5.149 \± \sqrt{5.149^2 - 4*-1.330*-4.983}}{2*-1.330}[/tex]

[tex]x = \frac{-5.149 \± \sqrt{0.002641}}{-2.660}[/tex]

[tex]x = \frac{-5.149 \± 0.0514}{-2.660}[/tex]

Split:

[tex]x = \frac{-5.149 + 0.0514}{-2.660}\ or\ x = \frac{-5.149 - 0.0514}{-2.660}[/tex]

[tex]x = \frac{-5.0976}{-2.660}\ or\ x = \frac{-5.2004}{-2.660}[/tex]

[tex]x = 1.92\ or\ x = 1.96[/tex]

Both values of x approximates to 2.

So:

[tex]x = 2[/tex]

2 years after 2007 is 2009.

Hence, the funding is about $10.5 billion in 2009

pls help him Step-by-step explanation:

Answer:

The coordinates of B are (5,2).

Step-by-step explanation:

Given that,

The midpoint of AB is M (4,-2).

The coordinates of A are (3,-6)

We need to find the coordinates of B. Let the coordinates of B are (x,y).

The mid point is given by :

[tex]M=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\\\\(4,-2)=(\dfrac{3+x}{2},\dfrac{y-6}{2})\\\\\dfrac{3+x}{2}=4\ \text{and}\ \dfrac{y-6}{2}=-2\\\\3+x=8\ \text{and}\ y-6=-4\\\\x=5,y=2[/tex]

So, the coordinates of B are (5,2).

Answer:

I think 200

Step-by-step explanation:

47600/238=200

200*238=47600

Answer:

the answer is actually 20000

Step-by-step explanation:

238%             x  =47,600

2.38x=47,600

47,600/2.38= 20000

Answer:

A

Step-by-step explanation:

A is the answer because its rate of change is 3 while the rest are smaller than that

Answer:

$18.51 tax

$226.51 total cost

Step-by-step explanation:

208 x 0.089 = 18.51 tax

Answer: 2,5

Step-by-step explanation:

In order to find the domain of a function, check the function for two conditions:

a zero in a denominator

a negative under an even root

Exclude the values at which the function satisfies either or both of these conditions from its domain.

G(x) has no root but it does have a denominator. Therefore, check the first condition by setting the denominator equal to zero and excluding those solutions from the domain.

x2 - 7x + 10 = 0

(x - 2)(x - 5) = 0

x = 2, 5

Answer:

3rd power

Step-by-step explanation:

When the radius of the sphere was doubled it doubled 8 times . it raised so much because of the third power.

Glad I could help (Maybe)