Negative 6 and negative 2
Answer:
24) $495
25) 14%
26) 25/X = 83/100
27) 0.7p
28) x + .085x and 1.085x
29) $221.90
30) $24.10
31) $6.13
32) 40%
Step-by-step explanation:
24) 600 - (600 × 0.25) = 450
450 × 1.10 = 495
25) (106 - 93) ÷ 93 = 0.13978
0.13978 × 100 = 13.978 ~ 14
27) 1.0 - 0.3 = 0.7
28) 1.00 + 0.085 = 1.085
29) 100% - 15% = 85%
240 × 0.85 = 204
204 × 1.0875 = 221.85
30) 25.89 × 4 = 103.56
103.56 + 179.99 = 283.55
283.55 × 0.085 = 24.10175
31) 8.75 × 0.70 = 6.125
32) 80 - (80 × 0.40) = 48
Answer:
Step-by-step explanation:
All the sides are complete, hence we can use the information given to find just 1 triangle
Triangles
From the given information, we have that:
m<B = pi/6 = 30 degres
c = 10
b = 5
This shows that we can use the cosine rule to find the third side b of the triangle. Since all the sides are complete, hence we can use the information given to find just 1 triangle
Answer:
![log_3_2(5)=\frac{1}{5} k](https://tex.z-dn.net/?f=log_3_2%285%29%3D%5Cfrac%7B1%7D%7B5%7D%20k)
Step-by-step explanation:
Let's start by using change of base property:
![log_b(x)=\frac{log_a(x)}{log_a(b)}](https://tex.z-dn.net/?f=log_b%28x%29%3D%5Cfrac%7Blog_a%28x%29%7D%7Blog_a%28b%29%7D)
So, for ![log_2(5)](https://tex.z-dn.net/?f=log_2%285%29)
![log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)](https://tex.z-dn.net/?f=log_2%285%29%3Dk%3D%5Cfrac%7Blog%285%29%7D%7Blog%282%29%7D%5Chspace%7B10%7D%281%29)
Now, using change of base for ![log_3_2(5)](https://tex.z-dn.net/?f=log_3_2%285%29)
![log_3_2(5)=\frac{log(5)}{log(32)}](https://tex.z-dn.net/?f=log_3_2%285%29%3D%5Cfrac%7Blog%285%29%7D%7Blog%2832%29%7D)
You can express
as:
![2^5](https://tex.z-dn.net/?f=2%5E5)
Using reduction of power property:
![log_z(x^y)=ylog_z(x)](https://tex.z-dn.net/?f=log_z%28x%5Ey%29%3Dylog_z%28x%29)
![log(32)=log(2^5)=5log(2)](https://tex.z-dn.net/?f=log%2832%29%3Dlog%282%5E5%29%3D5log%282%29)
Therefore:
![log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)](https://tex.z-dn.net/?f=log_3_2%285%29%3D%5Cfrac%7Blog%285%29%7D%7B5%2Alog%282%29%7D%3D%5Cfrac%7B1%7D%7B5%7D%20%5Cfrac%7Blog%285%29%7D%7Blog%282%29%7D%5Chspace%7B10%7D%282%29)
As you can see the only difference between (1) and (2) is the coefficient
:
So:
![\frac{log(5)}{log(2)} =k\\](https://tex.z-dn.net/?f=%5Cfrac%7Blog%285%29%7D%7Blog%282%29%7D%20%3Dk%5C%5C)
![log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k](https://tex.z-dn.net/?f=log_3_2%285%29%3D%5Cfrac%7B1%7D%7B5%7D%20%5Cfrac%7Blog%285%29%7D%7Blog%282%29%7D%20%3D%5Cfrac%7B1%7D%7B5%7D%20k)