I am not sure but I think I know ok
Answer:
x = 2.81 and 2.096
Step-by-step explanation:
Given the expression
10(2^x) + 7(3^x) = 6^x + 70
This can also be expressed as;
10(2^x) + 7(3^x) = (2*3)^x + 70
10(2^x) + 7(3^x) = 2^x*3^x + 70
Let a = 2^x and b = 3^x
10a + 7b = ab + 70
10a + 7b - ab = 70
10a-ab + 7b - 70 = 0
a(10-b)+7(b-10) = 0
a(10-b)-7(10-b) = 0
a-7 = 0 and 10-b = 0
a = 7 and b = 10
Since a = 2^x
7 = 2^x
log 7 = log2^x
log7 = xlog2
x = log7/log2
x = 2.81
Similarly
10 = 3^x
log 10 = log 3^x
log 10 = xlog3
x = log 10/log 3
x = 1/0.4771
x = 2.096
Hence the values of x that satisfies the equation are 2.81 and 2.096
Given:
Total number of students at Colfax Middle School = 270
Ratio of boys to girls is 5:4.
Total number of students at Winthrop Middle School = 180
Ratio of boys to girls is 4:5.
The two schools hold a dance and all students from both schools attend.
To find:
The fraction of the students at the dance are girls
Solution:
There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.
Number of boys
Number of girls
There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.
Number of boys
Number of girls
Now,
Total number of students in both schools
Total number of girls in both schools
The fraction of the students at the dance are girls is
Therefore, the required fraction is .
The answers are:
Thea reads 180 words per minute...
Eleanor reads 450 words every 2 minutes...
After 1 hour of reading, Elanor reads more words than Thea
Answer:
It is a right triangle.
Step-by-step explanation:
A right triangle is a triangle with at least one angle with 90 degrees.
We know that every triangle has 180 degrees. The other unknown angle is 180 - (30+60) = 180 - 90 = 90. That means that the other angle is 90 degrees. Therefore, it is a right triangle
We also know that in this triangle, that the square of one side plus the square of another is side is equal to the square of the hypotenuse of the triangle. (According to Pythagorean theorem)