Y = mx + c
If y = 4, and x = 0, then:
4 = -1 (0) + c
c = 4
If c = 4:
y = -1 (2) + 4
y = -2 +4
y = 2
If you plug in the different values of x in each equation, the answer should be:
2,0,-2
Answer:
The scaled surface area of a square pyramid to the original surface area.
The scaled area of a triangle to the original area.
Step-by-step explanation:
Suppose that we have a cube with sidelength M.
if we rescale this measure with a scale factor 8, we get 8*M
Now, if previously the area of one side was of order M^2, with the rescaled measure the area will be something like (8*M)^2 = 64*M^2
This means that the ratio of the surfaces/areas will be 64.
(and will be the same for a pyramid, a rectangle, etc)
Then the correct options will be the ones related to surfaces, that are:
The scaled surface area of a square pyramid to the original surface area.
The scaled area of a triangle to the original area.
Answer:
The circumference of Earth's equator is 40,080 km.
Step-by-step explanation:
Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:
24 x 1,670 = X
40,080 = X
Therefore, the circumference of Earth's equator is 40,080 km.
The equation to find the amount of money spent is 27 + 0.05m. This equation, in this case, needs to be larger or equal to 90.70. So our inequality would be:
27 + 0.05m >= 90.70
Now we can solve this equation for m.
27 + 0.05m >= 90.70
0.05m >= 63.70
m >= 1274
Given:
![$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%5Cright%29%7D)
To find:
The simplified fraction.
Solution:
Step 1: Simplify the numerator
![$\frac{(4 r)^{3}}{15 t^{4}}=\frac{4^3 r^{3}}{15 t^{4}}=\frac{64 r^{3}}{15 t^{4}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%3D%5Cfrac%7B4%5E3%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%3D%5Cfrac%7B64%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D)
Step 2: Simplify the denominator
![$\frac{16 r}{(3 t)^{2}}=\frac{16 r}{3^2 t^{2}}= \frac{16 r}{9 t^{2}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%3D%5Cfrac%7B16%20r%7D%7B3%5E2%20t%5E%7B2%7D%7D%3D%20%5Cfrac%7B16%20r%7D%7B9%20t%5E%7B2%7D%7D)
Step 3: Using step 1 and step 2
![$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%5Cright%29%7D%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B64%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B9%20t%5E%7B2%7D%7D%20%5Cright%29%7D)
Step 4: Using fraction rule:
![$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%7B%5Cfrac%7Bc%7D%7Bd%7D%7D%3D%5Cfrac%7Ba%20%5Ccdot%20d%7D%7Bb%20%5Ccdot%20c%7D)
![$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B64%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B9%20t%5E%7B2%7D%7D%5Cright%29%7D%3D%5Cfrac%7B64r%5E3%20%5Ccdot%209t%5E2%7D%7B16%20r%20%5Ccdot%2015%20t%5E4%7D)
Cancel the common factor r and t², we get
![$=\frac{64 r^{2} \cdot 9 }{16 \cdot 15 t^2 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B64%20r%5E%7B2%7D%20%5Ccdot%209%20%7D%7B16%20%20%5Ccdot%2015%20t%5E2%20%7D)
Cancel the common factors 16 and 3 on both numerator and denominator.
![$=\frac{4 r^{2} \cdot 3 }{ 5 t^2 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B4%20r%5E%7B2%7D%20%5Ccdot%203%20%7D%7B%20%205%20t%5E2%20%7D)
![$=\frac{12 r^{2} }{ 5 t^2 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B12%20r%5E%7B2%7D%20%20%7D%7B%20%205%20t%5E2%20%7D)
![$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{12 r^{2} }{ 5 t^2 }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%5Cright%29%7D%3D%5Cfrac%7B12%20r%5E%7B2%7D%20%20%7D%7B%20%205%20t%5E2%20%7D)
The simplified fraction is
.