Round 8,500,976 three ways: nearest thousand, hundred thousand, and million.
1 answer:
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The Alyssa will spend $14.915 for wrap a ribbon around the gift, if a ribbon costs $0.50 per inch.
Step-by-step explanation:
The given is,
A circular gift has a 4.75 inch radius
Ribbon that costs $0.50 per inch
Step:1
Formula to calculate the perimeter of circle,
......................(1)
Where, r - Radius of circle
From the given,
r = 4.75 inches
Equation (1) becomes,
(∵
= 3.14)
Perimeter, P = 29.83 inches
Step:2
Cost for wrap the ribbon to around the circular gift,
= Perimeter of circular gift × ribbon cost per inch
= (29.83 × 0.50)
= $14.915
Cost for wrap the ribbon to around the circular gift = $14.915
Result:
The Alyssa will spend $14.915 for wrap a ribbon around the gift, if a ribbon costs $0.50 per inch.
Answer: ok bet
Step-by-step explanation: theres a picture below and to graph it you simply start with the y coordinate, which is 7. you put 7 on the graph then go down 3 because 3 is negative, then go right one because 1 is postitive. (you get 1 from making the slope into a fraction, -3/1) also remember the formula for this is y=mx+b. its tricky but i hope this helped
Answer:
# The solution x = -5
# The solution is x = 1
# The solution is x = 6.4
# The solution is x = 4
# The solution is 1.7427
# The solution is 0.190757
Step-by-step explanation:
* Lets revise some rules of the exponents and the logarithmic equation
# Exponent rules:
1- b^m × b^n = b^(m + n) ⇒ in multiplication if they have same base
we add the power
2- b^m ÷ b^n = b^(m – n) ⇒ in division if they have same base we
subtract the power
3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply
them
4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same
power then we multiply them ad put over the answer the power
5- b^(-m) = 1/(b^m) (for all nonzero real numbers b) ⇒ If we have
negative power we reciprocal the base to get positive power
6- If a^m = a^n , then m = n ⇒ equal bases get equal powers
7- If a^m = b^m , then a = b or m = 0
# Logarithmic rules:
1-
2-
3-
4-
5-
* Now lets solve the problems
#
- Change the base 9 to 3²
∴
∴
- Same bases have equal powers
∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides
∴ 1 - 6 = 2x - x
∴ -5 = x
* The solution x = -5
# ㏒(9x - 2) = ㏒(4x + 3)
- If ㏒(a) = ㏒(b), then a = b
∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides
∴ 5x = 5 ⇒ divide both sides by 5
∴ x = 1
* The solution is x = 1
#
- Use the 1st rule in the logarithmic equation
∴ 6² = 5x + 4
∴ 36 = 5x + 4 ⇒ subtract 4 from both sides
∴ 32 = 5x ⇒ divide both sides by 5
∴ 6.4 = x
* The solution is x = 6.4
#
- Use the rule 3 in the logarithmic equation
∴
- Use the 1st rule in the logarithmic equation
∴ 2² = x(x - 3) ⇒ simplify
∴ 4 = x² - 3x ⇒ subtract 4 from both sides
∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets
∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0
∴ x - 4 = 0 ⇒ add 4 to both sides
∴ x = 4
OR
∵ x + 1 = 0 ⇒ subtract 1 from both sides
∴ x = -1
- We will reject this answer because when we substitute the value
of x in the given equation we will find and this
value is undefined, there is no logarithm for negative number
* The solution is x = 4
#
- You can use the calculator directly to find x
∴ x = 1.7427
* The solution is 1.7427
# ⇒ divide the both sides by 2
∴
- Insert ln for both sides
∴
- Use the rule ⇒ ln(e) = 1
∴ 8x = ln(4.6) ⇒ divide both sides by 8
∴ x = ln(4.6)/8 = 0.190757
* The solution is 0.190757
Answer:
(1) y=C,
(2) x=C
(1) y=0
Step-by-step explanation:
For the linear equation, the power on the solitary variable must be 1.
When the graph of a function crosses/ touches the x-axis than the equation has solution/solutions otherwise it does not has a solution.
When it touches/cresses the x-axis for infinite times then it will have an infinite number of solutions.
(1) The linear equation y-C=0, where y is a variable and C is a non-zero constant, , has the graph parallel to the x-axis. It has no solution as the graph will never cross/touch the x-axis.
Algebraically, in linear equation y-C=0, is independent of x, so there is no value of x for the solution to be exist.
(2) The linear equation x-C=0, where x is a variable and C is a constant, has one solution.
The solution for the equation is
x-C=0
, where
.
(3) The linear equation y=0, where y is a variable, has the graph coinciding with the x-axis. So, it has infinitely many solutions.
Algebraically, in linear equation y=0, is independent of x, so for all value of x, the given equation is zero. Hence, there are infinitely many solutions.