Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. 4log x + 2log y
The simplified expression is log (x⁴y²).
What is a logarithm?Inverse to exponentiation is the logarithm.
The given expression is 4log x + 2log y.
Simplify the expression as follows:
4log x + 2log y
= log x⁴ + log y²
= log (x⁴y²)
Hence, the simplified expression is log (x⁴y²).
Learn more about logarithms:
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Is 9760-5,220 more or less then 4,000
Answer:
9760-5220 is more than 4000.
Step-by-step explanation:
Consider the provided numbers.
We need to find 9760-5220 is more or less than 4000.
Subtract the numbers as shown.
9760
-5220
4540
Now compare the number 4540 and 4000
By comparing it can be concluded that the number 4540 is greater than 4000.
Hence, 9760-5220 is more than 4000.
Simplify the expression: Sqrt(16 − x^2)
as much as possible after substituting "4 sin x" for x.
Final answer:
Simplify the expression √(16 − x²) by substituting x with '4 sin x' to get 4|cos x|. Use trigonometric identities to arrive at the simplified expression.
Explanation:
The expression to simplify is: √(16 − x²) after substituting '4 sin x' for x.
Step-by-step solution:
Replace x with 4 sin x in the expression: √(16 − (4 sin x)²)
Simplify: √(16 − 16 sin² x)
Apply trigonometric identity: √(16 cos² x) = 4|cos x|
an insurance company sells a policy that pays $50,000.00 in case of accidental death. According to company figures, the rate of accidental death is 47 per 100,000 each year. What annual premium should the company charge for this coverage?
If mary ellen invest x dollars at 5%, write an equation that describes the total interest
For a one-year investment, the equation is I = x imes 0.05 imes 1.
If Mary Ellen invests x dollars at an interest rate of 5%, we can write an equation that describes the total interest earned on that investment using the simple interest formula. The formula for calculating simple interest is Interest = Principal imes Rate imes Time. Assuming the investment is for 1 year, the equation for the total interest (I) Mary earns would be:
I = x imes 0.05 imes 1
This equation states that the interest Mary earns is equal to the amount of money she invested (x dollars) multiplied by the interest rate (5% or 0.05 as a decimal) and the time the money is invested (1 year).
If Mary Ellen invests $100, the total interest she would earn in one year at a 5% interest rate would be calculated as follows:
I = $100 imes 0.05 imes 1 = $5
greatest common factor for 8x and 40
Ben measures the height of two bottles. One is 12 centimeters, and the other is 15 centimeters. In millimeters, what is the difference of the two heights?
Answer:
30 millimeters
Step-by-step explanation:
Algebra 2 Slope questions
Calculate the rf value for the reactant b spot. estimate the ruler to the nearest tenth, report the answer using two significant figures.
weight A weighs 50 pounds. weight B weighs 100 pounds. if A is placed 6 feet from the pivot, how far must B be placed from the pivot in order for the bar to achieve balance?
To achieve balance, the momentum on both sides must be equal so that it cancels out. Momentum is simply the product of mass and distance, therefore:
50 pounds * 6 ft = 100 pounds * X
X = 3 ft
Hence B must be placed 3 ft from the pivot.
Josh and Eva are packing first-aid supplies. It takes Josh 12 minutes to fill a box with Bandages. It takes Eva 8 minutes to fill a box with antibiotics. If they start packing boxes at the same time, how long will it be before they start filling a new box at the same time.
Which angle pairs are supplementary? Check all that apply
The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles. Therefore, from the given diagram angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles. So, the correct options are: B), C), and E).
Given :
[tex]\angle 3 = 90^\circ[/tex]
The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles.
From the diagram given in the question it can be clearly observe that if [tex]\angle 3 = 90^\circ[/tex] than [tex]\rm \angle 4,\;\angle 5,\;and\;\angle 6[/tex] are also equal to [tex]90^\circ[/tex].
Than according to the definition of supplementary angles:
[tex]\angle 3 +\angle6 = 180^\circ[/tex]
[tex]\angle 3 +\angle4 = 180^\circ[/tex]
[tex]\angle 4 +\angle5 = 180^\circ[/tex]
[tex]\angle 5 +\angle6 = 180^\circ[/tex]
[tex]\angle 7 +\angle8 = 180^\circ[/tex]
Therefore, angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles.
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A restaurant advertises 256 types of nachos. how many topping ingredients must be available
You want to get out of the sun and look for some shade. There are some trees by the side of the lake. You know you are just below 2 metres in height.
Estimate the height of the tree in metres.
A washer and a dryer cost $917 combined. The washer costs $67 more than the dryer. What is the cost of the dryer?
To find the cost of the dryer, set up equations based on the given information and solve for the dryer's cost, which results in the dryer being priced at $425.
Explanation:To solve for the cost of the dryer in the given problem, we can create two equations based on the information provided. Let's denote the cost of the dryer as D and the cost of the washer as W. According to the problem, W = D + $67, and the combined cost of the washer and dryer is $917, so W + D = $917.
Substituting the first equation into the second, we have (D + $67) + D = $917. Simplifying this, we get 2D + $67 = $917. Subtracting $67 from both sides of the equation gives us 2D = $850. Finally, dividing both sides by 2, we find that D = $425.
Therefore, the cost of the dryer is $425.
use rounding or compatible numbers to estimate the sum 171+ 727
Your car is a real gas guzzler getting 15 miles to the gallon on the highway using regular gas which at this time costs $ 4.35/gallon. You have a 25 gallon tank in the car and want to drive to visit a trade show in Memphis, Tennessee which is 1780 miles from Los Angeles. You drive on average 70 miles per hour and spend 2 days and nights at the convention during which time you do not drive your car, You do however check into a hotel room which costs $95.00 per night plus a 12% room tax. Your meals cost a total of $35.00 per day for the 2 days that you are in town. You also decide to leave a tip for the waiter of 20% of your meal bill. On the last day of the trip, you decide to purchase an Apple iPod as a gift for your child and an iPad Tablet for yourself which costs $ 589.00. The iPad costs $589.95 and the iPod costs $ 265.95 plus sales tax of 9.25%. What is the total amount yo will spend for the trip? What are the key elements of the problem and what is the answer?
What is the solution to the inequality |x-4|<3
Answer:
The solution of the given inequality [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]
Step-by-step explanation:
Given inequality [tex]|x-4|<\:3\:[/tex]
We have to find the solution of the given inequality [tex]|x-4|<\:3\:[/tex]
Using absolute rule, [tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex], we have,
[tex]-3<x-4<3[/tex]
Rewrite as [tex]x-4<-3\quad \mathrm{and}\quad \:x-4<3[/tex]
Consider , [tex]x-4>-3[/tex]
Adding 4 both side, we have,
[tex]x-4+4>-3+4[/tex]
Simplify, we have,
[tex]x>1[/tex]
Consider , [tex]x-4<3[/tex]
Adding 4 both side, we have,
[tex]x-4+4<3+4[/tex]
Simplify, we have,
[tex]x<7[/tex]
Combining, we have,
[tex]1<x<7[/tex]
Thus, The solution of the given inequality [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]
The statement 3+3=6 serves as a/an _ to the conjecture that the sum of two odd numbers is an odd number .
A car travels at 65 miles per hours. Going through construction it travels at 3/5 this speed. Write this fraction as a decimal and find the speed.
A projectile is shot from a cannon. The fixed parameters are the acceleration of gravity, g=9.8 m/sec2, and the muzzle velocity, v0=500 m/sec, at which the projectile leaves the cannon. The angle θ, in degrees, between the muzzle of the cannon and the ground can vary. The range of the projectile is
f(θ)=vo^2/g sin πθ/90=25510 sin πθ/90 meters.
The range at θ = 10⁰ is 155.4 meters.
What is a projectile?
A projectile is an object thrown or projected into the air, subject to gravity, following a curved trajectory.
Given that
v₀ = 500m/s
g = 9.8 m/s²
θ = 10⁰
Substitute into the function
f(θ)=v₀²/g sin πθ/90=25510 sin πθ/90 meters.
f(θ)= 25510sin πθ/90
= 25510sin10π/90
= 25510sinπ/9
= 25510sin(3.142/9)
= 25510sin(0.349)
= 25510 * 0.00609
= 155.4 m
The range at θ = 10⁰ is 155.4 meters.
Complete question
The greater the initial velocity of a projectile, the greater the range, with the maximum range achieved at a 45° angle in the absence of air resistance.
Explanation:The initial velocity of a projectile has a significant impact on its range. Specifically, the greater the initial speed, ℓ0, the greater the range. The formula for range R on level ground, neglecting air resistance, is given by R = (v0²/g) sin(2θ), where θ is the launch angle, v0 is the initial velocity, and g is the acceleration due to gravity. The maximum range is reached when the launch angle is 45°. With air resistance, the optimal angle decreases to roughly 38°. Additionally, for every angle other than the optimal, there are two different angles that yield the same range, and their sum totals 90°.
Emelina wrote the equation of a line in point-slope form as shown below. (y+4)=3(x+2) What is Emelina’s equation in slope-intercept form?
Answer:
[tex]y=3x+2[/tex]
Step-by-step explanation:
We are given equation as
[tex](y+4)=3(x+2)[/tex]
Since, we have to write equation in slope-intercept form
so, we can use slope-intercept formula
[tex]y=mx+b[/tex]
where m is a slope
b is y-intercept
so, we can write our equation in this form
[tex](y+4)=3(x+2)[/tex]
Distribute 3
[tex]y+4=3\times x+3\times 2[/tex]
[tex]y+4=3x+6[/tex]
Subtract both sides by 4
[tex]y+4-4=3x+6-4[/tex]
[tex]y+4-4=3x+6-4[/tex]
[tex]y=3x+2[/tex]
So, slope-intercept form of equation is
[tex]y=3x+2[/tex]
Can anyone gimme the answer ASAP please
it is 7 kilometers from Kerry's house to the mall. About what is that distance in miles
What is the square root of 360 rounded to the nearest thousandth
A restaurant used 9.5 ounces of cheese to make 5 slices of pizza. If each slice had the same amount of cheese, how much cheese was on each slice?
What is the sum of the first five terms of the geometric series 2 − 8 + 32 − . . . ?
What is the recursive formula for this geometric sequence?
Answer: B.
[tex]a_1=2\\a_n=a_n\times(-5)[/tex]
Step-by-step explanation:
The given geometric sequence : 2, -10, 50, -250
The first term of the sequence : [tex]a_1=2[/tex]
The common ratio between the terms :[tex]r=\dfrac{-10}{2}=-5[/tex]
We know that the recursive formula for geometric progression is given by :-
[tex]a_n=a_{n-1}r[/tex]
Then , the recursive formula for the given geometric progression will be :-
[tex]a_n=a_n\times(-5)[/tex]
25 POINTS I NEED HELP
what are 2 fractions between 3/5 and 4/5?