Find a counterexample to show that the given conjecture is false:

The sum of two positive even integers is always an odd integer.

Answer:

x=1 1/4 (1.25), y=1/4

Step-by-step explanation:

Since the equation "y=x-1" seems simple enough, we're going to plug that in for our other equation, "-4x+3=-2".

1. Rearrange y=x-1 to fit our other equation, -4x+3=-2.

y=x-1 (add 1 to both sides)

y+1=x x=y+1

2. Plug our newly rearranged equation into -4x+3=-2.

-4(y+1)+3=-2

-4y-4+3=-2 (distributive property)

3. Add/subtract like terms.

-4y-1=-2

4. Get y to be by itself.

-4y=-1 (add 1 to both sides)

y=1/4

1. Now for y=x-1. Plug 1/4 into y.

1/4=x-1

1 1/4=x

[tex]\bf \colorbox{black} {\bf {\textcolor{blue}{topic = }{ \bf { \textcolor{orange}{mathematics = }{ \bf{ \textcolor{cyan}{answer = }}}}}}}[/tex]

M.C.M=

[tex] \bf \textcolor{red}{ \huge{48}}[/tex]

3-16-2|2

3-8-1 |2

3-4-1 |2

3-2-1 |2

3-1-1 |3

1-1-1

2⁴•3

M.C.M=

2•2=4

2•2=4

4•4=16

16•3=48

[tex] \bf \textcolor{green}{ \underbrace{48}}[/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{18}=\sqrt{2*3*3}=3\sqrt{2}[/tex]

[tex]\sqrt{12}=\sqrt{2*2*3}=2\sqrt{3}[/tex]

[tex]A=\sqrt{2}+\sqrt{18}\\\\=\sqrt{2}+3\sqrt{2}\\\\=(1+3)\sqrt{2}\\\\=4\sqrt{2}[/tex]

[tex]B=\sqrt{3}+\sqrt{12}=\sqrt{3}+2\sqrt{3}\\\\ = (1+2)\sqrt{3}\\\\ = 3\sqrt{3}[/tex]

[tex]\sqrt{B^{2}+A^{2}-2*B*A}=\sqrt{(B-A)^{2}}\\\\=B-A\\\\=3\sqrt{3}-4\sqrt{2}[/tex]

= 3* 1.732 - 4 *1.4142

= 5.196 - 5.6568

= -0.4608

Exact Answer:   [tex]4\sqrt{2} - 3\sqrt{3}[/tex]

Approximate Answer:  0.46070182678574

Round the approximate value however you need to.

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

Work Shown:

[tex]C = \sqrt{ B^2 + A^2 - 2BA}\\\\C = \sqrt{ B^2 - 2BA + A^2}\\\\C = \sqrt{ (B-A)^2 }\\\\C = -(B-A) \ \ \text{ see note below}\\\\C = -B+A\\\\C = A-B\\\\C = (A) - (B)\\\\[/tex]

[tex]C = (\sqrt{2}+\sqrt{18}) - (\sqrt{3}+\sqrt{12})\\\\C = \sqrt{2}+\sqrt{18} - \sqrt{3}-\sqrt{12}\\\\C = \sqrt{2}+\sqrt{9*2} - \sqrt{3}-\sqrt{4*3}\\\\C = \sqrt{2}+\sqrt{9}*\sqrt{2} - \sqrt{3}-\sqrt{4}*\sqrt{3}\\\\C = \sqrt{2}+3\sqrt{2} - \sqrt{3}-2\sqrt{3}\\\\C = 4\sqrt{2} - 3\sqrt{3} \ \ \text{ ..... exact value}\\\\C \approx 0.46070182678574 \ \ \text{ ..... approximate value}[/tex]

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

Note: The rule used here is

If x is positive then [tex]\sqrt{x^2} = x[/tex]

Or if x is negative, then [tex]\sqrt{x^2} = -x[/tex]

Since B-A = -0.4607 approximately, we will use the second version of the rule above.

Answer:

Y=-2/5x

Step-by-step explanation:

Y-int: (0,0)

x-int:(-2,5)

Answer:

nothing in the first blank -3 in the second blank and +2 in the last blank or just 2.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Use the Vertical Line Test

Vertical Line Test: If a vertical line intersects a graph more than once, then the graph is not a function.

So if you draw a vertical line through that graph, it is only intersected once. Therefore, it is a function.

Answer:

The first bank with the four letter code has the grater probability of me guessing the code.

Step-by-step explanation:

To break the code for the first bank which uses four letters, since there are 26 letters in the alphabet, and require a four letter code, the first letter can be any of the 26 letters. Since one letter has been taken, we are left with 25 letters for the second position, 24 for the third position and 24 for the fourth position.

So, the total number of ways of selecting the 4 letter code without repetition is ²⁶P₄ = 26 × 25 × 24 × 23 = 358800

Since we have only 1 correct code, this is our required outcome. So,  the probability of breaking the code is P = required outcome/total outcome = 1/358800 = 2.787 × 10⁻⁶

To break the code for the second bank which uses 6 digits with repetition, since there are 10 digits, and we require a 6 digit code, each digit can be filled with 10 digits each. Since there is repetition, the total number of ways we can select the 6 digits is (¹⁰P₁)⁶ = 10 × 10 × 10 × 10 × 10 × 10 = 10⁶.

Since there is going to be only 1 correct code, the number of ways of selecting the correct code is 1.

The probability P' of cracking the second bank code is P' = required outcome/total outcome = 1/10⁶ = 1 × 10⁻⁶

Since P = 2.787 × 10⁻⁶ > P' =  1 × 10⁻⁶, the first bank with the four letter code has the grater probability of me guessing the code.

Answer:

2x⁴ + x³ - 3x² - 4x + 2

4

Step-by-step explanation:

Given functions:

     f(x) = 2x⁴ - 3x² - 2x + 5

     g(x)  = x³ - 2x - 3

Unknown:

Sum of the polynomials = ?

Order of the sum  = ?

Solution:

The sum of the polynomial is expressed as;

    f(x) + g(x) = 2x⁴ - 3x² - 2x + 5 +  x³ - 2x - 3

                   = 2x⁴ + x³ - 3x² - 2x - 2x + 5 -3

                   = 2x⁴ + x³ - 3x² - 4x + 2

The order of the sum is the highest power which 4.

This polynomial is of the 4th order.

Answer:

x^5 is the missing

Answer:

It is A

Step-by-step explanation:

Answer:

okay well all i can explain is the image on the far left, the answer would be x=112 and then for the one on the far right (im not sure ) i think its 17

explanation: so a straight line had 180 degress and the outside angle is 126 meaning that if you do 180-126 you can find the amount of the inside angle on the bottom right. When you do this you get 54 degress. Then remember that a triangle has a total of 180 degrees all added up so the final angle inside the triagle is 80 minus the sum of the other two angles. 58+54=112 and 180-112=68. remember that 68 is the angle on the INSIDE and x is clearly on the outside meaning that you would need to do 180-68. your final answer would be 112. (and im really sorry i couldn't answer the other ones they're too blurry  :(

Answer:

y < -11/20

Step-by-step explanation:

4y+8 < -16y -3

Add 16y to each side

4y+16y+8 < -16y+16y -3

20y +8< -3

Subtract 8 from each side

20y+8-8 < -3-8

20y < -11

Divide each side by 20

20y/20 < -11/20

y < -11/20

Answer:

B

Step-by-step explanation:\

The answer must be a negative to transform the answer in parenthesis to a positive (negative times negative = positive) and for B anything less than -11/20 works such as -1, or -4

Answer: y=1/5x -8

Step-by-step explanation:

Answer:

Wouldn’t y be 4 and x be 1?

Answer:

Y = -1X + 5

Step-by-step explanation:

I just solved it, it was a long problem, I don't wanna talk you through it. I think I'm correct.

Hope this helps! Let me know!

Answer:

120 +10w = 75 + 15w, w=weeks, found by adding savings to rate times and unknown variable of weeks and setting equal to each other. 9 wks, $210

Step-by-step explanation:

120 +10w = 75 + 15w

120-75= - 10w+15w

45=5w

45/5=9

9 weeks

120 + 90 = 75 + 135

210= 210

Answer:

25.5 and 1.5

Step-by-step explanation:

AC = 12 cm

BC = 13.5 cm

12 + 13.5 = 25.5 cm

13.5 - 12 = 1.5 cm

The possible length of segment AC is 25.5 cm and 1.5 cm.

A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. Figures such as a triangle, polygon, hexagon, square are made of different numbers of line segments.

For the given situation,

The points A, B, and C lie on a line.

Length AB = 12 cm

BC = 13.5 cm

The possible length of segment AC can be found by adding and subtracting the lengths of AB and BC.

a) Length of AC = [tex]13.5+12[/tex]

⇒ [tex]25.5[/tex] cm

b)  Length of AC = [tex]13.5-12[/tex]

⇒ [tex]1.5[/tex] cm

Hence we can conclude that the possible length of segment AC is 25.5 cm and 1.5 cm.

Learn more about line segment here

https://brainly.com/question/25727583

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Answer:

I hope this is what you were needing the answer to!

Answer:55

Step-by-step explanation:

(1). Toyota Prius: The total distance the car can travel in miles (M) given any gallons of gas (g) is M = 35g *How much gas is used per mile?

(2)Toyota Sienna: Used 2.5 gallons to travel 55 miles *How much gas is used per mile?

The area of rectangle ABCD with the given vertices is: 8 units².

Area of rectangle = (length)(width).

Given the following vertices:

Area = (length)(width) = (AB)(BC)

AB = |-2 - 6| = 8 units

BC = |2 - 3} = 1 unit

Area of rectangle = (8)(1) = 8 units².

Learn more about area of rectangle on:

https://brainly.com/question/25292087

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Answer: 8

Step-by-step explanation:

Answer:

the correct answer is 2

Step-by-step explanation:

Answer: x=2

Step-by-step explanation:

Answer:

Hey!

Your answer is $118.75!

Step-by-step explanation: How did I get this?

STEP 1: So we know that for a ton of rock costs us $47.50...

To get 2 tons all we have to do is to MULTIPLY $47.50 by 2...

(47.50 x 2 = 95)

STEP 2: So for $95, you will get 2 tons of rock!

Now to get the .5 tons of rock in price form, we have to get the price of the whole 2.5 tons and DIVIDE BY 2

(47.50 ÷ 2 = 23.75)

STEP 3: So now we have the costs for 2 tons and the price for HALF a ton.

What we do now is easy...we ADD THE VALUES TOGTHER!

(95 + 23.75 = $118.75)

The result of $118.75 after adding them together is the PRICE OF 2 TONS!

I HOPE THIS HELPED YOU!

Answer:

$118.75

Step-by-step explanation:

Okay, we know a rock per ton is $47.50.

What we need to know is how much 2.5 tons cost.

So if we take our 2.5 tons and we multiply it with our $47.50, this is what it will look like:

($47.50 * 2.5) = $118.75

So 2.5 tons of rock costs $118.75

Have a great day! :)

Answer:

h=8

Step-by-step explanation:

open the brackets

then, 5h - 15= 25

h=(25+15)/5

h=8

Answer:

h = 8

Step-by-step explanation:

Hi there !

5(h - 3) = 25

5h - 15 = 25

5h = 25 + 15

5h = 40

h = 40 : 5

h = 8

Good luck !

Answer:

Second from top

  f(x) = 25(5)ˣ

Step-by-step explanation:

Spot check:

x = 2, f(x) = 625

 f(x) = 25(5)ˣ

 f(x) = 25(5)² = 25(25) = 625

x = -1, f(x) = 5

 f(x) = 25(5)ˣ

 f(x) = 25(5)⁻¹ = 25(0.2) = 5

Answer:

1)2⋅3⋅5=30 2 ⋅ 3 ⋅ 5 = 30 . 2)1, 2, 3, 4, 6, 12

Step-by-step explanation:

to find the rate first we divide the number of students by the number if classes as follows 207 ÷ 9 = 23 student in each class Then we multiply this rate by the number of classes to get 23 students × 6 classes = 138 students in 6 classes

Answer:

measure of whaaaaaaaaaaaaaaaaaaaa tttttt?

Answer:

x≥13

Step-by-step explanation:

add 9 to both sides

2x≥26

divide both sides by 2

x≥13