Answer:
M = (3, 3.25)
Step-by-step explanation:
First, using the internal selection formula
Given
m:n = 3:5
(x1,y1) =(0,1)
(x2,y2) =(8,7)
![M={[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}](https://tex.z-dn.net/?f=M%3D%7B%5B%28mx2%2Bnx1%29%2F%28m%2Bn%29%5D%2C%5B%28my2%2Bny1%29%2F%28m%2Bn%29%5D%7D)
M = (3, 3.25)
2.
M is the point on XY that is 3/8 of the way from X to Y.
x-coordinate of M = 0 + (3/8)(8) = 0 + 3 = 3
y-coordinate of M = 1 + (3/8)(6) = 1 + 2.25 = 3.25
So, M = (3, 3.25)
or (3, 3 1/4)
Answer:
g
Step-by-step explanation:
h
Answer:
11 cm
Step-by-step explanation:
1m = 100cm
By examining the graph carefully, we can see that the record in 1985 is 2.4 m. In 1970 it was slightly under 2.3 m. For it to be 15cm it would have to be 2.25m. For it to be 9 cm it would the record would have been above 2.3m.
ANSWERx = 5/4
EXPLANATION ![2^x \cdot 2^{x-2} = \sqrt{2}](https://tex.z-dn.net/?f=2%5Ex%20%5Ccdot%202%5E%7Bx-2%7D%20%3D%20%5Csqrt%7B2%7D)
Note that
![\sqrt{a} = a^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
so
![\sqrt{2} = 2^{\frac{1}{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
Note that on the left-hand side, we can use exponent properties for multiplying two powers of the same base together:
![\begin{aligned} 2^x \cdot 2^{x-2} &= \sqrt{2} \\ 2^{x + (x-2)} &= 2^{\frac{1}{2}} \\ 2^{2x - 2} &= 2^{\frac{1}{2}} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A2%5Ex%20%5Ccdot%202%5E%7Bx-2%7D%20%26%3D%20%5Csqrt%7B2%7D%20%5C%5C%0A2%5E%7Bx%20%2B%20%28x-2%29%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5C%0A2%5E%7B2x%20-%202%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%0A%5Cend%7Baligned%7D)
We can now equate the exponents because both sides of the equation are of the same base with no other terms.
![\begin{aligned} 2^{2x - 2} &= 2^{\frac{1}{2}} \\ 2x - 2 &= \tfrac{1}{2} \\ 2x &= \tfrac{1}{2} + 2 \\ 2x &= \tfrac{5}{2} \\ x &= \tfrac{5}{4} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A2%5E%7B2x%20-%202%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5C%0A2x%20-%202%20%26%3D%20%5Ctfrac%7B1%7D%7B2%7D%20%5C%5C%0A2x%20%26%3D%20%5Ctfrac%7B1%7D%7B2%7D%20%2B%202%20%5C%5C%20%0A2x%20%26%3D%20%5Ctfrac%7B5%7D%7B2%7D%20%5C%5C%0Ax%20%26%3D%20%5Ctfrac%7B5%7D%7B4%7D%0A%5Cend%7Baligned%7D)
The answer is x = 5/4. We can confirm this by using this value in the original equation to get a true statement.
D.
I hope this helped
Please give brainliest :)