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3 years ago

Can every even number be written as a sum of two primes?

1 answer:

5 0

The Goldbach Conjecture is a yet unproven conjecture stating that every even integer greater than two is thesum of two prime numbers. The conjecture has been tested up to 400,000,000,000,000. Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics.

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Find the slope between the two points given. Then, use the slope and one of the points to write the equation of the line in Slop

Anika [276]

Answer:

Equation: y=2x-1

Slope: 2

y-intercept: -1

Step-by-step explanation:

Hi there!

We are given the points (-1, -3) and (-2, -5). We need to find the slope, equation of the line, and the y intercept of the line

First, let's find the slope

The formula for the slope (m) calculated from two points is $\frac{y_2-y_1}{x_2-x_1}$ where ( $x_1$ , $y_1$ ) and ( $x_2$ , $y_2$ ) are points

We have everything we need for the formula, but let's label the values of the points to avoid any confusion

x1=-1

y1=-3

x2=-2

y2=-5

Now substitute into the formula (remember: the formula has SUBTRACTION):

m= $\frac{-5--3}{-2--1}$

simplify

m= $\frac{-5+3}{-2+1}$

add

m= $\frac{-2}{-1}$

divide

m=2

So the slope is 2

Now let's find the equation of the line

The question asks for it to be in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We calculated the slope from earlier, so let's substitute that into the equation

y=2x+b

Now we need to find b

The equation will pass through both (-1, -3) and (-2, -5) so we can use either one of them to solve for b (doesn't matter which one)

Let's take (-1, -3) as an example

substitute -1 as x and -3 as y into the equation

-3=2(-1)+b

multiply

-3=-2+b

Add 2 to both sides

-1=b (the value of the y intercept!)

Substitute -1 as b into the equation

y=2x-1

We found everything needed for this problem

Hope this helps!

8 0

3 years ago

Dylan makes 3 submarine sandwiches. He cuts each sandwich into sixths to share. He stacks all the sandwich pieces on a plate. Ho

Oliga [24]

Answer:

Step-by-step explanation:

Each sandwich will be divided into 6 pieces. 1 sandwich equals 6 pieces, 2 sandwiches equals 12 pieces, so 3 sandwiches equals 18 pieces.

8 0

3 years ago

Read 2 more answers

For every 1 litre of water used to make a medicine, 269ml of sucrose and 61ml of saline solution are used. Express the amount of

Burka [1]

Answer:

Step-by-step explanation:

1 litre = 1000 ml

water : Sucrose : Saline = 1000 : 269 : 61

This is simplest form. We cannot reduce this as 61 is a prime number and 1000; 269 will not come in 61th table or

We can say 100 ; 269 ; 61 don't have common term

8 0

3 years ago

Does anyone have the answers for all?

Shkiper50 [21]

Answer and Step-by-step explanation:

1-6

What you can do is plug in 6 and start by doing the first machine first, then the second. If this doesn't work, do the second machine, then the first machine.

The order that works is second machine, then first machine.

Second Machine:

y = $(6)^{2} -6$ = 36 - 6 = 30

Plug into first machine now.

First Machine:

y = $\sqrt{(30) - 5} = \sqrt{25} = 5$

We see that the result is 5.

b. If we were to do the order of second machine, then first machine, we will never get a negative result (or -5 for that matter), due to the fact that you can't algebraically square root a negative number.

However, if we were to do the order of first machine, second machine, we can get a negative number. To get -5, we plug in 6 for x in the first machine, getting an answer of 1. We plug this into the second machine, getting 1^2 - 6, which results in -5.

1-7. The absolute value of a value is the positive version of that value.

a. |54| = 54

b. $-|-7\frac{3}{5}|$ = $-7\frac{3}{5}$

c. |3| - |-1| = 3 - 1 = 2

d. |2.2 - 5.13| = |-2.93| = 2.93

1-8.

| |

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(5 boxes on each side)

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(6 boxes on each side)

b. The amount of squares on each side of the figure increases by 1.

c. There would be 1 square, because we know that the pattern is there is 2 squares added to the next figure, 1 at each end. If we go back a figure, we take away 2 squares.

1-9.

a. -42 - 17 = -59

b. 8 - (-9) = 8 + 9 = 17

c. 8(-9) = -72

d. -42 ÷ (-7) = 6

e. -2(-3)(-4) = 6(-4) = 24

f. -18 - 7 = -25

g. $(-5)^{2}$ = 25