We call m the slope or gradient of the line. It represents the change in y-value per unit change in x-value. For example, consider the line given by the equation y = 2x + 1. Here are some points on the line. ~hope that helps

4 0

3 years ago

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Nathan has 80 us stamps,64 Canadian stamps,and 32 Mexican stamps. He wants to put the same number of stamps on each page. Each p

Feliz [49]

Answer:

The greatest number of stamps that Nathan can put on each page = 16.

Step-by-step explanation:

Given:

Nathan has:

80 US stamps

64 Canadian stamps

32 Mexican stamps

The stamps need to put on a page such that each page has same number of same country stamps on each page.

To find the greatest number of stamps he can put on each page.

Solution:

In order to find the greatest number of stamps Nathan can put on each page, we will find the G.C.F. of the three numbers.

The numbers are:

$80,64,32$

We will list down the prime factors of each number.

$80=2\times 2\times 2\times 2\times 5$

$64=2\times 2\times 2\times 2\times 2\times 2$

$32=2\times 2\times2\times 2\times 2$

The G.C.F can be given as = $2\times 2\times 2\times 2$ = 16

Thus, the greatest number of stamps that Nathan can put on each page = 16.

6 0

3 years ago

What is the exact perimeter of kite ? Show your work.

Afina-wow [57]

Answer:

The perimeter of the kite is 29 units.

Step-by-step explanation:

1. Let's use the Pythagorean Theorem to find the perimeter of the kite:

With the information given, we have four right triangles with a new point A, intersecting UW and VX. Those triangles are:

Δ UVA

Δ VWA

Δ UXA

Δ XWA

As we can see in the figure, length of UV and VW is the same and the length of UX and WX is also the same.

2. Let's find the value of UV and VW

UV is the hypotenuse of Δ UVA and it sides are 3 and 4 units length. So, we can calculate the length of UV this way:

Length of UV ² = UA ² + VA ²

Replacing with the real values:

Length of UV ² = 3 ² + 4 ²

Length of UV ² = 9 + 16

Length of UV ² = 25

√Length of UV ² = √25

Length of UV = 5 units ⇒ Length of VW = 5 units

3. Let's find the value of UX and WX

UX is the hypotenuse of Δ UXA and it sides are 3 and 9 units length. So, we can calculate the length of UX this way:

Length of UX ² = UA ² + XA ²

Replacing with the real values:

Length of UX ² = 3 ² + 9 ²

Length of UX ² = 9 + 81

Length of UV ² = 90

√Length of UV ² = √90

Length of UV = 9.5 units (rounding to the nearest tenth) ⇒ Length of WX= 9.5 units

4. Let's calculate the perimeter of the kite:

Perimeter of the kite = UV + VW + WX + UX

Perimeter of the kite = 5 + 5 + 9.5 + 9.5

Perimeter of the kite = 29 units

7 0

3 years ago

A tiny but horrible alien is standing at the top of the Empire State Building (which is

Leto [7]

Answer:

87.7 degrees.

Step-by-step explanation:

In triangle ABC, attached.

The height of the building |AB|=443 meters

The distance of the agent across the street , |BC|=18 meters

We want to determine the angle at C.

Now,

$Tan C=\dfrac{|AB|}{|BC|} \\C=arctan (\dfrac{|AB|}{|BC|} )\\=arctan (\dfrac{443}{18} )\\=87.67^\circ\\\approx 87.7^\circ $(correct to the nearest tenth)$

The agent should sfoot his laser gun at an angle of 87.7 degrees.

7 0

3 years ago