-x^2 + 4 = 2x + 1
-x^2 - 2x + 4 - 1 = 0
-x^2 - 2x + 3 = 0
(x + 3)(-x + 1)= 0
x + 3 = 0 -x + 1 = 0
x = -3 -x = -1
x = 1
so x = -3 and x = 1
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
Table B could represent Relationship B
Time (weeks) 3 4 6 9
Plant growth (in.) 0.9 1.2 1.8 2.7
The correct answer between all
the choices given is the second choice or letter B. I am hoping that this
answer has satisfied your query and it will be able to help you in your
endeavor, and if you would like, feel free to ask another question.
Answer: Bob has 62 cards.
All has 124 cards.
Jane has 186 cards
Step-by-step explanation:
Let x represent the number of cards that Bob has.
Al has twice as many cards as Bob. It means that the number of cards that All has is 2x.
Jane has three times as many cards as Bob. It means that the number of cards that Jane has is 3x.
Together, they have 372 cards. It means that
x + 2x + 3x = 372
6x = 372
x = 372/6
x = 62
The number of cards that Al has is
2 × 62 = 124
The number of cards that Jane has is
3 × 62 = 186
