Answers
Step-by-step explanation:
We are going to use the following properties of logarithms to solve this problem:
[tex]\log{\dfrac{a}{b}} = \log{a} - \log{b}[/tex]
and
[tex]\log{ab} = \log{a} + \log{b}[/tex]
So we can rewrite the given equation as
[tex]\log{2x^3} - \log{x} = \log{\left(\dfrac{2x^3}{x}\right)} = \log{2x^2}[/tex]
Also,
[tex]\log{16} + \log{x} = \log{(16x)}[/tex]
So we can write
[tex]\log{2x^2} = \log{(16x)}[/tex]
or eliminating the log symbols, we get
[tex]2x^2 = 16x[/tex]
The solutions for the equation above are
[tex]x = 8\:\text{and}\: 0[/tex]
Related Questions
A number to be a rational number that is not an integer but a while number
Answers
Answer:
So coming back to the question; No, there is no rational number that is not an integer but is a whole number. The number is called as a rational number if it can be expressed as p/q where p & q are integers & q is not 0. All negative integers are rational numbers but those are not whole numbers.Jan 1, 2020
Step-by-step explanation:
Going to sleep goodbye
Answers
A motorboat travels 448 kilometers in 8 hours going upstream and 440 kilometers in 5 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answers
9514 1404 393
Answer:
boat: 72 km/hcurrent: 16 km/hStep-by-step explanation:
The speed difference between boat and current is the upstream rate:
(448 km)/(8 h) = 56 km/h
The sum of speeds of boat and current is the downstream rate:
(440 km)/(5 h) = 88 km/h
The rate of the boat is half the sum of these:
(56 +88)/2 = 72 . . . km/h
The rate of the current is half their difference:
(88 -56)/2 = 16 . . . km/h
The rate of the boat is 72 km/h; the rate of the current is 16 km/h.
3=g/-4-5 ((for 25 points))
Answers
Answer:
3=g/-4 -5
3+5=g/-4
8= g/-4
8x(-4)=g
g=-32
Step-by-step explanation:
what is - 7/10 + (- 5/6) =
Answers
-7/10 + (-5/6) = -(7/10 + 5/6) =
= -(21/30 + 25/30) = -46/30 =
= -1 16/30 = -1 8/15 ← the end
A store in Iowa advertises that during their Labor Day sale, everything is 25% off, plus they will pay the sales tax. Mike buys shoes for $80 and socks for $5. Since there will be no tax added, what is the final price for Mike’s purchase?
Answers
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Answer:
$63.75
Step-by-step explanation:
Mike's final price will be 1-25% = 75% of the marked price.
($80 +5)(0.75) = $63.75
The final price for Mike's purchase is $63.75.
What is the point on the graph of f(x+5)
Answers
Answer:
=fx+5f
Step-by-step explanation:
=fx+5f
If I have 500 and have a 6% annual interest how long will it take to get 2000
Answers
Answer:
23.8 years
Step-by-step explanation:
Assuming this is compound interest, we'll use the compound interest formula
A = P(1 + r)ⁿ
A = Final amount (2000)
P = Initial amount (500)
r = Annual interest rate (.06)
n = ?
Our equation will look like this
2000 = 500(1.06)ⁿ
First, divide both sides by 500
2000/500 = (500(1.06)ⁿ)/500
(1.06)ⁿ = 4
Then we have to take the log₁.₀₆ out of both sides
n = log₁.₀₆(4)
n = 23.79132
In December yanni’s chocolate shop received 180 telephone orders. In January they received only 72 telephone orders. By what percent did the number of telephone orders decrease from December to January
Answers
Answer:
Step-by-step explanation:
At the 2010 Olympics in Vancouver, Yu-Na Kim scored 226.56 points in woman's figure skating. Akiko Suzuki scored 181.44 points in the event. About how many more points did Yu-Na Kim score than Akiko Suzuki?
Answers
Answer:
5 more matches was won by yu-na kim
What is 8(9h - 6) simplifyed
Answers
72h - 48
Step-by-step explanation:
Use distributive property
8(9h - 6)
Multiply 8 out of 9h - 6
72h - 48
Convert 8 2/3% into a decimal.
Answers
Answer:
the answer is = 0.08666666666
The decimal value of 8 2/3% is 866.677.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
8 2/3% into decimal.
So, 8 2/3%
= 26/3 %
= 26 /3 x 100
= 8.6666667 x 100
=866.6777
Learn more about Percentage here:
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Her jump rope Ella can make 17 jumps in 15 second.at this rate how make jumps can she make in20 minute?
Answers
Answer:
1360
Step-by-step explanation:
there are 1200 seconds in 20 minutes. if Ella can do 17 jumps in 15 seconds, you would divide 1200 by 15 (which equals 80) because that would be the number of 15 seconds in 20 minutes. then you would divide 80 by 17, which gives you your final answer of 1360 jumps in 20 minutes.
235Px=235P(x-1)*(3x)
Answers
Answer:
2456
Step-by-step explanation:
g(x)=
Write a relationship for a function whose g(x) values are 2 more than five times the principal square root of x.
Answers
Lets do
2 more than five times the square root of x[tex]\\ \sf\longmapsto g(x)=5\sqrt{x}+2[/tex]
Lets take an example
[tex]\\ \sf\longmapsto g(4)=5\sqrt{4}+2[/tex]
[tex]\\ \sf\longmapsto 5(2)+2[/tex]
[tex]\\ \sf\longmapsto 10+2[/tex]
[tex]\\ \sf\longmapsto 12[/tex]
“5 times” means “multiply by 5”.
The principal square root just means the regular square root.
Putting that together, you have
g(x) = 5 * sqrt(x) + 2
Which of the equations below could be the equation of this parabola?
Vertex
(0, 0)
0
10
ОА
A. x = - 1 2 3 4
B. y = - 1/2 x ²
C. x = 1 / 4²
Do y = x
Answers
Answer:
the answer is "B"
the "a" (as in ax^2) is negative thus the parabola "goes downward"
Step-by-step explanation:
The equation of parabola is,
y = - 1/2x²
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
We have to given that;
In a parabola,
Vertex = (0, 0)
Since, We know that;
Standard form of equation of parabola is,
y = a (x - h)² + k
Where, (h, k) = (0, 0) = vertex
Hence, We get;
y = a (x - 0)² + 0
y = ax²
Here, A point on parabola is, (2, - 2)
- 2 = a (2)²
a = - 2 / 4
a = - 1/2
Hence, The equation of parabola is,
y = - 1/2x²
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How do you get 2.5 out of 20/8
Answers
9514 1404 393
Explanation:
If you can't operate a calculator, perhaps you can do long division. The attachment shows the work for that.
__
[tex]\dfrac{20}{8}=\dfrac{5\cdot4}{2\cdot4}=\dfrac{5}{2}\\\\=\dfrac{5\cdot5}{2\cdot5}=\dfrac{25}{10}=2.5[/tex]
We assume that you know dividing by 10 moves the decimal point one place left.
Which of the following equations has exactly one solution?
2x + 3 – 6x=-4x – 3
3x + 12 – 9x = -11x + 12 + 5x
6x +9 - 8x = 2x + 9
7x + 3 – 8= 13x + 5 – 6x
Answers
Answer:
I belive I might be c not completely sure but pretty positive
Give the slope of a line perpendicular to AB
Answers
Answer:
m = -1
Step-by-step explanation:
Find the equation in slope intercept form [ y = mx + b ] for line AB. Find the slope using the formula [ y2-y1/x2-x1 ].
8-5/7-4
3/3
1
Find the y-intercept.
5 = 1(4) + b
5 = 4 + b
1 = b
So the equation of the line AB is y = x + 1.
The slope of a perpendicular line is the opposite reciprocal of the original line.
1 -> -1/1 -> -1
Best of Luck!
How do I write three fourths of a number is 12 as an equation?
Answers
Answer:
[tex] \frac{3}{4} n = 12[/tex]
Step-by-step explanation:
let the number be n :
[tex] \frac{3}{4} \: of \: n = 12 \\ \\ \frac{3}{4} n = 12[/tex]
further more:
[tex]3n = 12 \times 4 \\ n = \frac{12 \times 4}{3} \\ \\ n = 4 \times 4 \\ n = 16[/tex]
Answer:
3x4=12
Step-by-step explanation:
Emily gets paid $40 just for showing up to watch her sister’s dog. Her sister then pays her $25 per everyday she watches the dog.
Answers
Answer:
Step-by-step explanation:
2.
Match the graph of the function with the function rule.
A. [tex]y=\frac{1}{4}[/tex]·4^x
B. y = 1 • 4x
C. [tex]y=\frac{1}{2}[/tex]·4^x
D. y = 2 • 4x
Answers
Answer:
C) [tex]y = \frac{1}{2}[/tex] × [tex]4^x[/tex]
Answer:
C. y= 1/2*4^x
Step-by-step explanation:
Solve the equation.
6(x + 7) = 5(x - 7) + x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is
(Simplify your answer.)
OB. The solution is all real numbers.
O C. There is no solution.
(Answer quickly)
Answers
Answer:C
Step-by-step explanation:
6(x+7)=5(x-7)+x
⇔6x+42=5x-35+x
⇔6x-5x-x=-35-42
⇔0x=-77
Question 5
1 pts
Write the equation of a line through (5,1), parallel to y=-*+1
o
Answers
Answer:
3rd, y=-1/5x
Step-by-step explanation:
What is the value of p?
A.60°
B. 40°
C. 90°
D. 50°
Answers
Answer:
D . p = 50
Step-by-step explanation:
To find the value of p we first need to find the values of inner angles
180 - 140 (linear pair)
= 40
180 -90 (linear pair)
= 90
now use angle sum property of triangle
40 + 90 + p = 180
130 + p = 180
p = 180 - 130
p = 50
Find an ordered pair (x, y) that is a solution to the equation. 4x-y=4 (x, y) = 00 X Х ?
Answers
,
−
4
)
,
(
1
,
0
)
,
(
2
,
4
)
Is the awnser
help with this math question plz
Answers
Answer: The length of LK is 40.
Step-by-step explanation:
LK = 6x+10
KM = 2x+8
LM = 58
so
LM = LK + KM
or, 58 = 6x+10+2x+8
or, 58 = 8x + 18
or, 58-18 = 8x
or, 8x = 40
so, x = 5
now
LK = 6x + 10
= 6*5+10
= 30 +10
= 40
Find the average of the list of numbers.
- 13, – 25, – 24, – 14
Answers
Answer:
-19
Step-by-step explanation:
-13-25-24-14
= -76/4
= -19
2x2 − 2z4 + y2 − x2 + z4 if x = −4, y = 3, and z = 2.
Answers
answer: 9
Step-by-step explanation:
x = - 4; y = 3; z = 2;2 x² - 2 z^4 + y² - x² + z^4 = = 2 * (-4)² - 2 * 2^4 + 3² - ( -4)² + 2^4 == 2 * 16 - 2 * 16 + 9 - 16 + 16 = = 32 - 32 + 9 - 16 + 16 = 9
Answer and explanation please?
Answers
Answer:
c= 13
Step-by-step explanation:
The complementary angles add up to 90° so we use some basic algebra to solve this question. like in the step by step explaination I have provided on paper
