Samantha makes a conjecture that the product of two odd integers is always an odd integer. Which choice is the best proof of her conjecture? CLEAR CHECK Look at these different examples: 7 × 3 = 21, 5 × 9 = 45, 11 × 3 = 33. So the product of two odd numbers must be odd. Every time you multiply two odd numbers, the product is an odd number. Let (2a + 1) be an odd number. Let (2b + 1) be another odd number. The product 2(2ab + a + b) + 1 is a multiple of 2 plus 1, which is an odd number. Let a and b both represent odd numbers, and let a × b be an odd number. Therefore, a × b = b × a, which shows that the product of two odd numbers is odd.

Answer:

[tex]0.10d + 0.25q > 143.88[/tex]

Step-by-step explanation:

Let the total dimes collected be d.

[tex]1\ dime = \$0.10[/tex]

[tex]d\ dimes = \$0.10d[/tex]

Let the total quarters collected be q.

[tex]1\ quarter = \$0.25[/tex]

[tex]q\ quarters = \$0.25q[/tex]

[tex]Last\ Year = \$143.88[/tex]

Required

Represent as an inequality

The total collection, this year, can be represented as:

[tex]Total = 0.10d + 0.25q[/tex]

From the question, we understand that:

This year's collections is expected to be greater than last year's

This can be represented as:

[tex]Total > Last\ Year[/tex]

Substitute in the right values:

[tex]0.10d + 0.25q > 143.88[/tex]

Answer: 1. x= 20 units,   2. x= [tex]5\sqrt{3}[/tex] units    3. x= [tex]4\sqrt{2}[/tex] units.

Step-by-step explanation:

In a right triangle,

[tex]Hypotenuse^2= Perpendicular^2+Base^2[/tex]  (Pythagoras theorem)

1. Hypotenuse = x , Base = 16, Perpendicular = 12

[tex]\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=\sqrt{400}=20[/tex]

2. Hypotenuse = 14 , Base = 11, Perpendicular = x

[tex]\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}[/tex]

3.  Hypotenuse = 9 , Base = x, Perpendicular =7

[tex]\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}=\sqrt{16\times2}\\\\\Rightarrow\ x=4\sqrt{2}[/tex]

Answer:

-8,4 and 4,-5

Step-by-step explanation:

no

the table does not represent a proportional relationship.

Answer:

i was able to get y = 1.3x - 2

Answer:

your picture is not loading for me

Step-by-step explanation:

The answer is 10 percent

Step-by-step explanation:

10% is the answer of this questions

Answer:

1250 people

Step-by-step explanation:

Population density = total population / land area

Population density = 50

total population = x

land area 25

50 = x / 25

x = total population = 50 x 25 = 1250 people

Answer:

Quick

Step-by-step explanation:

Step-by-step explanation:

-6x-2y+8

-6x -6x

÷-2 (-2y=-6x+8)

3x=-4

x= 3x

y= -4

y=-4-3x

Answer:

2

Step-by-step explanation:

Answer:

The 7th term is 0

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are identified because every term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

[tex]a_n=a_1+(n-1)d[/tex]

Where

an = nth term

a1 = first term

d   = common difference

n  = number of the term

We are given the first term a1=-12 and the common difference d=2. Let's find the 7th term (n=7):

[tex]a_7=-12+(7-1)2[/tex]

[tex]a_7=-12+12=0[/tex]

The 7th term is 0

Answer:

90

Step-by-step explanation:

x•y-z²

x=9,y=14,z=6

9 • 14 - 6²

126-36=90

Answer:

x = 98

Step-by-step explanation:

Answer:

[tex]x=26\\[/tex]

Step-by-step explanation:

The sum of the interior angles of a triangle add up to [tex]180^{\circ}[/tex]. Therefore, an equiangular triangle will have each of its angles equal to [tex]60^{\circ}}[/tex]. We can then set up the following equation:

[tex]2x+8=60, \\2x=52, \\x=\fbox{$26$}[/tex].

Answer: x=10

Step-by-step explanation:

Answer:

it depends. If you are driving really fast then hit it. Your life matters more than the animal. But if you are driving slow, then try to stop as long as there isn't anyone behind you.

Step-by-step explanation:

NEVER SWERVE OFF THE ROAD

Answer: Grab a towel or a piece of clothing and wrap it around the animal to protect it from harmful virus’s and diseases we might transmit to them. Then walk 30 feet away from the road and carefully place the animal on flat ground.

Step-by-step explanation: Hope this helps! Btw, I found this from an instructional video I found. So I don’t take any credit. ;)

Answer:

6 x

Step-by-step explanation:

because 1 times 6 then 2 then 3 and so on

Answer:

p=500

Step-by-step explanation:

The value of p is 500 in the equation  100+0.05p=0.25p.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

The equation,

100+0.05p=0.25p

To solve the equation:

Simplify the equation,

100 = 0.25p - 0.05p

0.20p = 100

p = 100/0.20

p = 500

Therefore, 500 is the value of p.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ6

Answer:

The percent of discount is 35%

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

AE = 14.6 I think. If I'm wrong, use whatever number it is.

Sin(x) = 5/14.6

Sin(x) = 0.3425

x = Sin-1 (0.3425)

x =20.03

Now the other larger triangle has an acute angle of 90 -20.03 =  69.97

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

Cos(69.97) = 13.1/DE

DE = 13.1/cos(69.97)

DE = 38.25

Answer:

x = 3

m<PAW = 1

Step-by-step explanation:

☆They are supplementary angles.

☆Supplementary angles equal 180 degrees.

[tex] - 11x + 17 3 - 1x + 43 = 180 \\ - 12x + 216 = 180 \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: - 216 = - 216}{ \frac{ - 12x}{ - 12} = \frac{ - 36}{ - 12} } \\ x = 3[/tex]

☆Plug in for m<AEZ

[tex] - 1(3) + 4 \\ - 3 + 4 \\ 1[/tex]

☆m<PAW is corresponding to m<AEZ

☆Corresponding angles are congruent.

☆m<PAW equals 1.

Answer:

Step-by-step explanation:

1) √36 = 6

2) ^3 √8 = 2

3) ^3 √64 = 4

Answer:

Answer choice A (<A,<B,<C)

Step-by-step explanation:

I have attached a rough drawing of this type of triangle (not to scale)

The longest side of the triangle is always the side opposite of the largest angle. Since side AB is the longest, we know that angle C is the largest angle.

This is also true for the smaller angle. The smallest angle is always opposite the shortest side. The shortest side is side BC. The angle opposite this side is angle A, meaning angle A is the smallest.

Hope this helps :-)

Answer:

292.32

Step-by-step explanation:

i took 9.75 times 30 and then minus 10% minus 6.2% and minus 1.45% and got that answer

Answer:

49π ft²

Step-by-step explanation:

The area for a circle is A=πr² (Area=pi times radius squared)

and d=2r (diameter = 2 times the radius)

So, if we want to find area using the radius, we can get rearrange the equation d=2r to get r= d/2

r=d/2

r=14/2

r=7 ft

Then we can plug that answer into the area equation.

A=π×7²

7 squared is 49 so

A=49π ft²

Answer:

u can use "a squared + b squared = c squared"

in this case the two legs are 10 and 24 because they are near the right angle. the hypotenuse is always across from the right angle, so it's the long side that connects the two legs. Now you can plug in 10 and 24 for the pythagorean theorem and solve for the hypotenuse. that would be 10 squared plus 24 squared equal to c squared.

Answer:

26

Step-by-step explanation:

You would use the Pythagorean theorem to solve for the last side.

Pythagorean theorem- a^2+b^2=c^2

a and b =sides

c=hypotenuse

Since you are finding the hypotenuse(c), you don't have to rearrange the formula

plug in a and b.

10^2+24^2=c^2

solve

100+576=c^2

676=c^2

do the square root of 676 to get rid of the c^2

26=c

Answer:

The maximum possible is 20 intersections.

Step-by-step explanation: