Jim bought two packages of candy at the store for $1.20 each. How much change did he receive from $3.00?

Answer:

suppose 2^2 + b^2 = c^2 with 2 < b < c (it should be clear that this assumption is fine, 12 + 22 = 5 and sqrt(5) is not an integer; 22 + 22 = 8 and sqrt(8) is not an integer). Then c^2 - 4 = b^2 so (c+2)(c-2) = b^2. As b is prime, this means c-2=b or c-2=1 (since c+2 > 1). So either c=b+2 or c=3. The c=3 case can't happen since that would make b^2 = 5 so we are left with c=b+2. Then we have 4 + b^2 = (b+2)2 = b2 + 4b + 4 meaning that b=0. So there are no triples involving 2.

Step-by-step explanation:

A Pythagorean triple of this form cannot contain integer 2 if we add extra 2x²y² because it will increase the value of the coefficient of xy to 4.

The given function:

[tex](x^2-y^2) + (2xy)^2 = (x^2 + y^2)^2[/tex]

This function is expanded as follows;

[tex](x^2-y^2)^2 + (2xy)^2 = (x^2 + y^2)^2\\\\x^4 + y^4 -2x^2y^2 + 4x^2y^2 = x^4 +y^4 + 2x^2y^2\\\\add \ \ (+2x^2y^2) \ to \ both \ sides \\\\x^4 +y^4 +4x^2y^2 = x^4 +y^4 +4x^2y^2[/tex]

In this expanded form of the given function, it is clear that non of the coefficients of x and y contains integer 2 and the supposed coefficient value of xy increase to 4 because of the extra 2x²y² added to the function.

Thus, we can conclude that a Pythagorean triple of this form cannot contain integer 2 if we add extra 2x²y² because it will increase the value of the coefficient of xy to 4.

Learn more here: https://brainly.com/question/11279692

Answer:

see below

Step-by-step explanation:

We want to solve each equation for y, so y must be alone on one side of the equation.

a) 10x + 5y = 20

Subtract 10x from both sides.

5y = 20 - 10x

Place the x term in front to follow  y = mx + b form.

5y = -10x + 20

We want to isolate y completely, so divide both sides by 5. On the right side, be sure to divide each component by 5.

5y/5 = -10/5x + 20/5

y = -2x + 4

This equation is in slope-intercept form.

b) 3x - 2y = 10 + 4x

We can see that y is negative in this original equation. Let's add 2y to both sides to make y positive.

3x = 10 + 4x + 2y

Now we want to isolate y, so subtract 4x from both sides.

3x - 4x = 10 + 2y

Simplify.

-x = 10 + 2y

Isolate y further by subtracting 10 from both sides.

-x - 10 = 2y

Again, we want to isolate y completely, so divide both sides by 2. On the left side, be sure to divide each component by 2.

-x/2 - 10/2 = 2y/2

-1/2x - 5 = y

This looks backwards (although it is in slope-intercept form), so let's rearrange it just to make it more clear.

y = -1/2x - 5

This equation is in slope-intercept form.

Hope this helps!

Answer:

5+4x=21

Step-by-step explanation:

Let's say the "number" is x.

"more than" indicates addition, and "times" indicates multiplication.

5+4x=21

Answer:

Hey, hope your good and you got a great friend here <3

Step-by-step explanation:

Answer:87

Step-by-step explanation:added all numbers and divided by 3

Answer:

(-5, 7)

Step-by-step explanation:

Translate A left 6, and up 4

Answer:

Ava drove 56 miles per hour (mph) Oscar drove 58 mph, Oscar drove 2 mph faster than Ava.

Step-by-step explanation:

Answer:

Given vertices:

These have same x-coordinate, so when connected form a vertical segment.

The length of the segment is:

The area of the rectangle is 72 square units, so the horizontal segment has the length of:

Possible location of the remaining vertices (to the left from the given):

and

Similarly to previous exercise:

The distance between the given vertices:

The other side length is:

Possible location of the other vertices (to the right from the given):

and

Answer:

H²=a²+b²

H²=4²+7²

H= 8.06

Answer:

x = 70

Step-by-step explanation:

Answer:

Step-by-step explanation:

b/c we know that the inside angles of a triangle add to 180

180 = 38 + x + x + 2

180 = 40 + 2x

140 = 2x

70 = x

Answer:

1 4/6 tons.

Step-by-step explanation:

5/6+5/6

Add the numerator first to get 10.

Then convert the fraction from an improper fraction to a mixed number.

I need to know how many days buttttt

1 day = 1 2/3

2 days = 3 1/3

3 days = 5

4 days = 6 2/3

5 days = 8 1/3

6 days = 10

7 days = 11 2/3

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

that's what I got, I apologize if it's incorrect

Answer:

The median value would be 105.

Step-by-step explanation:

I would say the answer is 105. I hope that's right.

Answer:

Aaron will have enough water for 3 hours. he should have 380 milliliters left.

The first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For this case, we want the expression that could be used to predict the number of winners of a game.

Thus, event = event of winning the game, and its probability is evaluated as:

[tex]P(event) = \dfrac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}} \\\\P(\text{Winning the game})= \dfrac{\text{Number of winners}}{\text{Number of contestants}}[/tex]

Thus, the first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

Learn more about probability here:

brainly.com/question/1210781

Answer: 0

Step-by-step explanation: The answer is 0

Answer:

y=0

Step-by-step explanation:

Answer:

1. We would hear better at Dunkin's since its distance from the radio station is the shortest.

2. McDonald's is out of range of the radio station since its distance is greater than the range of the radio station.

Step-by-step explanation:

1) Will we hear it better at Zaxby's (2,-4), McDonalds (4, -4), or Dunkin' (-3,3). Show work to support your decision and explain your reasoning.

We need to find the distance of each point from the tower.

The shorter the distance from the radio station the better the signal.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

Since Dunkin's distance, d₃ = 4.24 is the least distance from the radio station and is within range of 5 miles, we would hear better at Dunkin's.

2) Are any of these location outside the range of the radio station? If so, which one(s). Defend your decision mathematically.

The radio station is outside of range if its distance is greater than 5 miles. That is, d > 5 miles.

So, we calculate the distance of each point from the radio station.

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

So, for each of the distances calculated above, only McDonald's distance, d₂ = 5.66 miles > 5 miles.

So, McDonald's is out of range of the radio station.

12 (tell me if im wrong sorry if i am)

Step-by-step explanation:

Answer:

D. (-3/8) (-5/7) (-1/4)

Step-by-step explanation:

Hints:

- * - * + = +

+ * - * - = +

+ * + * + = +

- * - * - = -

A. (-3/8)(-5/7)(1/4)

= (-3*-5*1) / (8*7*4)

= 15/224

B. (3/8)(-5/7)(-1/4)

= (3*-5*-1) / (8*7*4)

= 15/224

C. (3/8)(5/7)(1/4)

= (3*5*1) / (8*7*4)

= 15/224

D. (-3/8) (-5/7) (-1/4)

= (- 3*-5*-1) / (8*7*4)

= (-15)/(224)

= -15/224

The correct option is

D. (-3/8) (-5/7) (-1/4)

Answer: she made $8.40

Step-by-step explanation: divide 42 by 5 to get your answer

Answer:

A - $8.40

Step-by-step explanation:

You would have to do 45÷5

Answer:

Step-by-step explanation:

[tex] - 1 \times ( - w) = - 8 \times 7[/tex]

[tex]1 \times w = - 8 \times 7[/tex]

[tex]w = - 8 \times 7[/tex]

[tex]w = - 56[/tex]

Answer:

C

Step-by-step explanation:

Answer:

here

Step-by-step explanation:

B. 39, 45. C. 162, 972. D. 33, 39. 2. Based on the pattern, what are the next two ... If two angles are complementary, then the sum of their measures is 90°. ... D. alternate exterior angles. 56. 7. 8. 11. Find m2. The diagram is not to scale. 180 ... perpendicular to one of two parallel lines, then it is also perpendicular to the other.

Answer:

3546

Step-by-step explanation:

1460+405+996+85+120+390+90= 3546

Answer:G i think sorry if wrong

Step-by-step explanation:

Answer:G

Step-by-step explanation:

Answer:

[tex] \sqrt{ {( - 1 - 4)}^{2} + {(2 - ( - 3))}^{2} } = \sqrt{ {5}^{2} + {5}^{2} } = 5 \sqrt{2} [/tex]

Answer:

62.1=3 sig fig

185.3=4 sig fig

1,760= 3 sig fig

0.06= 1 sig fig

I don't know if that's all the questions you have or you didn't get the last one In the pic

Answer:

Step-by-step explanation:

standard form is:

Ax+By=C

for problem 2:

y= 1/2 x-8

y- 1/2 x - 8= 0

rearrange:

- 1/2x + y +8 = 0

2 (- 1/2x + y + 8) = 0

-x + 2y + 16= 0

-x + 2y = -16

leading coefficient can't be negative

so multiply everything by -1

x -2y = 16

Answer:

1 yes   no

Step-by-step explanation:

1 this is in standard form as it is  a linear form and the intercepts can be found  

2 This is not  in standard form as it is a linear equation and both the x and y intercepts cant  be found  so must be written in the form AX+BY=C

so

-x + 2y = -6

and leading coefficient cant be - so multiply by -1

so

x-2y=6

Answer:

Solution given:

length[a]=3cm

base(b)=7cm

hypotenuse [c]=?

we have

by using Pythagoras law

a²+b²=c²

3²+7²=c²

c=√58=7.61m

the length of the hypotenuse is 7.61m.

Answer:

4

Step-by-step explanation:

half gallon is 64 oz. 256 ÷ 64 is 4

Answer

4

Step-by-step explanation:

1 gallon = 128 fluid ounces

1/2 gallon = 64 fluid ounces

Use gallons to convert 256 fl oz then multiply result by 2

256 / 128 = 2

2 x 2 = 4

4 half gallon containers

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K