Answer:
[tex]\log _3\left(x^9\right)=9\log _3\left(x\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]\log _3\:x^9[/tex]
now rewriting the expression
[tex]\log _3\:x^9[/tex]
[tex]\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0[/tex]
[tex]=9\log _3\left(x\right)[/tex]
Therefore,
[tex]\log _3\left(x^9\right)=9\log _3\left(x\right)[/tex]
Answer:
B
Step-by-step explanation:
edge
Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(6, 0) and line x = −6.
The equation of the graph is [tex]x = \frac 1{24}y^2[/tex]
How to determine the equation?Generally, a point is represented as:
(x,y)
The line x = -6 means that:
(-6, y)
So, we calculate the distance between (x,y) and (-6, y) as follows:
[tex]d = \sqrt{(x + 6)^2 + (y - y)^2}[/tex]
This gives
[tex]d = \sqrt{(x + 6)^2 }[/tex]
Next, we calculate the distance between (6,0) and (x, y) as follows:
[tex]d = \sqrt{(x - 6)^2 + (y - 0)^2}[/tex]
This gives
[tex]d = \sqrt{(x - 6)^2 + y^2}[/tex]
Equate both distance expressions
[tex]\sqrt{(x + 6)^2} = \sqrt{(x - 6)^2 + y^2}[/tex]
Square both sides
[tex](x + 6)^2 = (x - 6)^2 + y^2[/tex]
Expand
[tex]x^2 + 12x + 36 = x^2 - 12x + 36 + y^2[/tex]
Evaluate the like terms
[tex]12x = - 12x + y^2[/tex]
Add 12x to both sides
[tex]y^2 = 24x[/tex]
Make x the subject.
[tex]x = \frac 1{24}y^2[/tex]
Hence, the equation of the graph is [tex]x = \frac 1{24}y^2[/tex]
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An apple tree can grow about 400 apples. Jake says that 13 apple trees can grow about 6,000 apples. Do you agree? Explain.
Answer: No. Since 13×400=5,200, 13 apple trees can grow about 5,200 apples. Jake's estimate of 6,000 is much higher than 5,200.
Answer:
you answered it
Step-by-step explanation:
you put no blah blah blah
Geometry: Express the area of each figure as a monomial. I need help with this, anyone?
Answer:
answer 28ab³ I think maybe
The area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].
Here,
The formula to calculate the area of a right-angled triangle is:
Area = (1/2) * base * height
In this case, the right-angled triangle has a height of [tex]6ab^3[/tex] and a base of [tex]4a^2b[/tex].
Now, let's substitute these values into the formula:
Area = [tex](1/2) * 4a^2b * 6ab^3[/tex]
Now, simplify the expression:
Area = [tex]2 * a^2b * 6ab^3[/tex]
To find the monomial representation, multiply the coefficients and add the exponents of like terms:
Area = [tex]12a^{(2+1)}b^{(1+3)[/tex]
Finally, simplify the exponents:
Area = [tex]12a^3b^4[/tex]
So, the area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].
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The measure of the angle is 44 times greater than its supplement.
What is the measure of the supplement?
Answer: The measure of it's supplement is 4°
Step-by-step explanation:
If an angle is 44 times is supplement, then we can represent it by the equation x = 44y where x is the angle and y is it's supplement.
Supplementary angles add up to 180 degrees, meaning that x + y = 180.
x = 44y
x + y = 180
Using both equations substitute the value for x in the first equation, into the second equation and solve for y.
44y + y = 180 Combine like terms on the left side
45y = 180 Divide both sides 45
y = 4
This means the measure of it's supplement is 4 degrees.
Now input 4 into one of the equations for y and solve for x to find the main angle.
x = 44(4)
x = 176
This also means that the angle itself is 176 degrees.
The measure of the supplementary angle is 4°.
It is given that the measure of the angle is 44 times greater than its supplement.
We have to find out the measure of the supplement.
What are supplementary angles ?
Two angles are said to be supplementary angles if the sum of two angles is 180°.
As per the question ;
The measure of the angle is 44 times greater than its supplement.
Let's assume the supplementary angle is x .
So,
The other angle will be 44 × x .
We know that sum of two angles if they are supplementary is 180°.
⇒ x + 44 x = 180 °
⇒ 45 x = 180°
⇒ x = 180 ÷ 45
⇒ x = 4°
And the other angle will be ;
= 44 × 4
= 176°
Thus , the measure of the supplementary angle is 4°.
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Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% confidence. Assume that s = 15 based on earlier studies.
Answer:
67
Step-by-step explanation:
You have to use fractions to show your work and I'm not going to do that but just know that it is the answer.
(Ill give brainliest if u help!)
Which equation has a value less than 54,811?
A) 54,811 x 2 = ________
B) 54,811 x one and two fourths = ________
C) 54,811 x 1 = ________
D) 54,811 x two fourths = ________
Answer:
Answer is D
Step-by-step explanation:
Answer:
The answer would be D.
Step-by-step explanation:
Consider a limousine that gets m(v)= (120 - 2v) / 5 miles per gallon at speed v , whose chauffeur is paid $15/hour, and gas costs $3.5/gallon.
a. Write the function that finds the cost per mile at speed v
b. What speed results in the most inexpensive driving speed?
Answer:
(17.5 / 120 - 2v) + (15 / v)
Step-by-step explanation:
Given : m(v)= (120 - 2v) / 5 miles per gallon at speed v ,
chauffeur is paid $15/hour
gas cost = $3.5/gallon.
Gasoline cost per mile :
Cost per gallon = $3.5
Cost per gallon * 1/(m(v))
$3.5 * 1 / (120 - 2v) / 5
$3.5 * 5 / 120 - 2 v
= 17.5 / 120 - 2v
Time = distance / speed
Chauffeur cost = 15 per hour / v
Hence ;
Total cost :
Cost of gasoline + Cost of chauffeur
(17.5 / 120 - 2v) + (15 / v)
Answer would be - (17.5 / 120 - 2v) + (15 / v)
First Given : m(v)= (120 - 2v) / 5 miles per gallon at speed v , The chauffeur is paid $15/hour. Then gas cost = $3.5/gallon. Gasoline cost per mile : Cost per gallon = $3.5 Cost per gallon * 1/(m(v)) When, $3.5 * 1 / (120 - 2v) / 5 $3.5 * 5 / 120 - 2 vThen result will be = 17.5 / 120 - 2v
Time = distance / speed Chauffeur cost = 15 per hour / v
Hence ;
The total cost will be : Cost of gasoline + Cost of chauffeur
(17.5 / 120 - 2v) + (15 / v)
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f(x) = 72-12x what is the domain and range
Answer:
The domain is x and the range is f(x)
Step-by-step explanation:
Sam wrote his bike 2/5 of a mile and walked another 3/4 of a mile how far did he travel?
Answer:
1.15 miles
Step-by-step explanation:
Answer:
24/20
Step-by-step explanation:
Changed denominator to 20 since 4 and 5 both go into 20. Got 8/20 and 15/20. Added and got 24/20. As a mixed number it is 1 1/5/ Hope this helps!
What is the slope and the y- intercept of the line on the graph
Answer:
its c for sure, its obvious
what is the solution to this equation: 5x to the 2 power - 36x - 81 = ?
Answer:
5x² - 36x - 81
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Combining Like TermsStandard Form: ax² + bx + c = 0Step-by-step explanation:
Step 1: Define expression
5x² - 36x - 81
Step 2: Simplify
We cannot simplify the expression down further.
What is the x-coordinate of point B? Write a decimal coordinate.
(brainliest ) Edge 2020
If Paul’s savings are 25% more than Janet’s savings,
What percentage of Paul
savings are Janet’s savings
(A) 25 %
(B). 50%
(C) 75%
(D) 80%
helllppp meee please
Answer:
2, 3, 6, 7
Step-by-step explanation:
The subset of the sample space probability experiment
Step-by-step explanation:
The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1. The probabilities of all the outcomes add up to 1.
Which direction am I going if I drive from Washington DC to Dallas texas
Answer:
north
Step-by-step explanation:
The selling price of a watch is rs 220. If 10% profit has been included in the marked price of the watch, what is the marked price??
Answer:
22 is 10 of 220
Step-by-step explanation:
hope it help
Michael buys pants from a clothing company for $70 dollars. He then sells each pair of pants in his clothing shop at a 40% markup. How much is the markup on the pants?
Answer:
$98
Step-by-step explanation:
70 is the original price, but the mark up is 40%. So, 40% of 70 is 28
$70 + $28 = $98
Who is the most powerful undertale character
Answer:
Asriel Dreemurr
Step-by-step explanation:
Answer:
clearly the gay robot
hes my favorite <3
FINANCE
2. Which of the following statements is FALSE?
A. Common stockholders have an upper limit on their dividends
B. Preferred stockholders are more protected from risk than common stockholders.
C. Common stockholders own the firm and are among the last to be paid in the event of bankruptcy.
D. Preferred stockholders are
Answer: I think its C
Step-by-step explanation:
what is the correct evaluation of 3x-x+2,when x is equal to -4?
14
-6
6
-14
Answer:
The answer is -6.
Step-by-step explanation:
You have to substitute x = -4 into the expressions :
3x - x + 2
= 3(-4) - (-4) + 2
= -12 + 4 + 2
= -6
8y-2x=-72 in slope form
Answer:
y=1/4x-9
Step-by-step explanation:
Slope-intercept form is y=mx+b.
8y-2x=-72
Add 2x to both sides
8y=2x-72
Divide both sides by 8.
y=1/4x-9
HTH :)
A car and a truck leave the same intersection, the truck heading north at 60 mph and the car heading west at 55 mph. At what rate is the distance between the car and the truck changing when the car and the truck are 30 miles and 40 miles from the intersection, respectively?
Answer: -81
Step-by-step explanation:
Let x = the car moving towards west = 30
Let y = truck moving towards north = 40
dx/dt = -55
dy/dt = -60
We the use Pythagoras theorem to solve further where,
s² = x² + y²
s² = 30² + 40²
s² = 900 + 1600
s² = 2500
s =✓2500
s = 50
We then differentiate with respect to t, then we will have:
s² = x² + y²
2s ds/dt = 2x ds/dt + 2y dy/dt
50 ds/dt = (30 × -55) + (40 × -60)
50 ds/dt = -1650 - 2400
50 ds/dt = - 4050
ds/dt = -4050/50
ds/dt = -81
For a hypothesis test of the claim that the mean amount of sleep for adults is less than 6 hours, technology output shows that the hypothesis test has power of 0.4013 of supporting the claim that 6 hours of sloep when the actual population
mean is 4.5 hours of sleep. Interpret this value of the power, then identify the value of B and interpret that value
Interpret this value of the powers
Answer:
b
Step-by-step explanation:
Please help I need these quickly. Please answer sensibly! I will give brainliest to the correct answer.
Answer:
n+n= 2n
[tex](3n) ^{2} = 9n ^{2} [/tex]
5(n+2)=5n+10
2(n+1)=2n+1
[tex]n \div 4 = \frac{n}{4} [/tex]
[tex]n(n - 2 = n{2} - 2n[/tex]
The number of passengers in the bus double every minute. The bus was full of
passengers at 7.45am. When was it one quarter full?
Answer:
7:43 am.
Step-by-step explanation:
it was 1/2 full one minute ago then another 1/2 = 1/4 full 2 minutes ago.
Knowing how the bus fills, we want to find the time where the bus is one-quarter full.
The bus is one-quarter full at 7:43 am.
We know that at 7:45 am the bus is full. Let's say that the full bus has N people inside.
Each minute the population doubles, so if we go backwards, each minute the population is divided by 2.
One minute before, the bus must have half of the above population, meaning that at 7:44 am, the bus has N/2 people.
Another minuter before the people inside is halved again, then at 7:43 am we will have (N/2)/2 = N/4 people.
And if N is the people in a full bus, then N/4 represents the buss a quarter full.
Then we can answer the question as:
The bus is one-quarter full at 7:43 am.
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why was mom now saying that Augie did not have to go to school
Answer:
Is there suppose to be a picture?
Step-by-step explanation:
Answer:
Because she liked Augle more than the other child
Step-by-step explanation:
She didn't want him to go to school so that she could spend the day with her favorite child
What is the measure of angle G? Type only the number:
Answer: 48
Step-by-step explanation:
total of all the degrees of the angles of the triangle is ALWAYS 180
let the measure of angle G be x
180 = 102+30+x
180 = 132+x
x = 48
I need help again please help me with this question
Answer:
The size of a sundae and the amount of calories it contains.
Step-by-step explanation:
The answer choice is the only one with a positive correlation, because it is the only one that isn't depleting or going down in size. No matter if you eat the sundae or what size it becomes, the calories it contains will still be the same for the whole amount.
When a car travels, gas is used and it depletes. As a snowball does when it melts. And "the temperature on Tuesday" has no correlation involved at all
84 y is directly proportional to x. Given that y = 144 and x = 12. Find the value of y when x = 7.