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3 years ago

Write the natural numbers from 1 to 30. What fraction of them are prime numbers?

Mathematics

2 answers:

kobusy [5.1K]3 years ago

7 0

Prime Numbers can only divide by themselves and 1.

Prime Numbers From 1 to 30: 2,3,5,7,11,13,17,19,23,29.... ( 10 )

kicyunya [14]3 years ago

3 0

Answer:

The natural numbers from 1 to 30:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

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Which graph shows a line with the same y intercept as the graph of 10x - 16y = 40

Amanda [17]

Answer:

The graph option where the y-axis is intercepted at y = -2.5 by the line of the graph.

Step-by-step explanation:

The answer choices for the possible graphs that have the same y-intercept as the graph of 10x - 16y = 40 is missing here.

However, the answer can still be explained here.

We can figure out how the graph would look like.

First, understand that the y-intercept of a graph is the value of y, of the point where the line intercepts the y-axis.

Let's figure out what the y-intercept is given a graph represented by the equation, 10x - 16y = 40.

Rewrite the equation in slope-intercept form.

10x - 16y = 40

-16y = -10x + 40

y = -10x/-16 + 40/-16

y = ⅝x - ⁵/2

Therefore, the y-intercept of the graph of 10x - 16y = 40 is -⁵/2 or -2.5.

✅The graph shows a line with the same y-intercept as the graph of 10x - 16y = 40, would have it's y-axis intercepted at y = -2.5.

4 0

3 years ago

Ava wants to draw a parallelogram on the coordinate plane. She

wolverine [178]

Answer:

$k =(2,1)$

$JK = 2$

Step-by-step explanation:

Given

$J = (0,1)$ ---- $(x_1,y_1)$

$H = (1,-2)$ --- $(x_2,y_2)$

$I = (3,-2)$ --- $(x_3,y_3)$

See attachment for grid

Solving (a): The coordinates of K

The parallelogram has the following diagonals: IJ and HK

Diagonals bisect one another. So:

Midpoint of IJ = Midpoint of HK

This gives:

$\frac{1}{2}(I + J) = \frac{1}{2}(H+K)$

$\frac{1}{2}(x_3+x_1,y_3+y_1) = \frac{1}{2}(x_2+x,y_2+y)$

$\frac{1}{2}(3+0,-2+1) = \frac{1}{2}(1+x,-2+y)$

$\frac{1}{2}(3,-1) = \frac{1}{2}(1+x,-2+y)$

Multiply through by 2

$(3,-1) = (1+x,-2+y)$

By comparison:

$1 + x = 3$

$-2 + y = -1$

Solve for x and y

$x = 3 - 1 =2$

$y = -1 +2 = 1$

So, the coordinates of k is:

$k =(2,1)$

The length of JK is calculated using distance (d) formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

$J = (0,1)$ ---- $(x_1,y_1)$

$k =(2,1)$ ---- $(x_2,y_2)$

So:

$d = \sqrt{(0 - 2)^2 + (1 - 1)^2$

$d = \sqrt{(- 2)^2 + (0)^2$

$d = \sqrt{4 + 0$

$d = \sqrt{4$

$d = 2$

Hence:

$JK = 2$

8 0

3 years ago

There were 820 orange buttons in a container. The number of orange buttons was 160 fewer than the number of yellow buttons and 2

denis-greek [22]

Answer: There are 3615 buttons

Step-by-step explanation:

From this situation we can write a system of equations if we tag the orange buttons with $o$ , the yellow buttons with $y$ , the green buttons with $g$ and the blue buttons with $b$ :

There were 820 orange buttons:

$o=820$ (1) Number of orange buttons

The number of orange buttons was 160 fewer than the number of yellow buttons:

$o=y-160$ (2)

The number of orange buttons was 210 more than the number of green buttons:

$o=g+210$ (3)

1/3 of the total number of buttons in the container were blue buttons:

If the total is the sum of the buttons of each color, we have:

$\frac{1}{3}(o+y+g+b)=b$ (4)

At this point we have our system with 4 equations and 4 unknowns.

Let's begin by substituting (1) in (2):

$820=y-160$ (5)

Isolating $y$ :

$y=980$ (6) Number of yellow buttons

Subsituting (1) in (3):

$820=g+210$ (7)

Isolating $g$ :

$g=610$ (8) Number of green buttons

Substituting (1), (6) and (8) in (4):

$\frac{1}{3}(820+980+610+b)=b$ (9)

Isolating $b$ :

$b=1205$ (10) Number of blue buttons

Now we can find the total number of buttons:

$o+y+g+b=820+980+610+1205=3615$ (11) This is the total number of buttons

4 0

3 years ago

Solve the system of linear equations by graphing. y−2x = 5 6x−3y = −15

kykrilka [37]

Yes c_€\€]]^ Times the longest string

3 0

3 years ago

I will mark Brainliest and I WILL REPORT LINKS!!!

Stells [14]

Answer:

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

y = -3(x-1)

y = -3x+3

-3x y = 3

x y = -1

x(0) y = -1

y = -1

Step-by-step explanation:

6 0

3 years ago

Write the natural numbers from 1 to 30. What fraction of them are prime numbers?​

Write the natural numbers from 1 to 30. What fraction of them are prime numbers?