Answers
y=log3(x)
The logarithmic functions are the inverse of the exponential functions and they have the following form:
y=logb(x)
Therefore, as you can see, the function that has the form of a logarithmic function, is the first option.
Related Questions
Part 1: Solve the system by graphing. Draw the graphs on paper and indicate their intersection point. Type the ordered pair solution here as your answer to Part 1.
Part 2: Solve the system using the substitution method. Show all work here and indicate the solution for the system as an ordered pair.
Part 3: Solve the system using the addition method. Show all work here and indicate the solution for the system as an ordered pair.
2x+3y=6
x-2y=10
Answers
The graph is shown in the attached image.
As we can note from the graph, the solution of the system of equations is indicated by the point of intersection between the two lines which is (6,-2)
Part (2):
The equations given are as follows:
2x + 3y = 6 ...........> equation I
x - 2y = 10
which can be rewritten as:
x = 2y + 10 ...........> equation II
Substitute with equation II in equation I and solve for y as follows:
2x + 3y = 6
2(2y+10) + 3y = 6
4y + 20 + 3y = 6
7y = 6 - 20
7y = -14
y = -2
Substitute with y in equation II to get x as follows:
x = 10 + 2y
x = 10 + 2(-2)
x = 10 - 4
x = 6
The solution is (6,-2)
Part (3):
The equations given are:
2x + 3y = 6 .............> equation I
x - 2y = 10 ...........> equation II
Multiply equation II by -2, this will give:
-2x + 4y = -20 ............> equation III
Add equation I and equation III as follows:
2x + 3y = 6
+ -2x + 4y = -20
.........................................
0x + 7y = -14
7y = -14
y = -2
Substitute with y in equation II to get x as follows:
x - 2y = 10
x - 2(-2) = 10
x + 4 = 10
x = 10 - 4
x = 6
The solution is (6,-2)
Hope this helps :)
watts,volts and amps are used to measure electricity. there is a formula that shows the relationship between watts,volts and amps. volts times amps = watts . if the volts are 120 and the amps are 5 how many watts are there?
Answers
120(5)=W
600=W
600 Watts
The number of watts for a circuit with 120 volts and 5 amps is 600 watts.
Explanation:The formula for calculating the power in an electrical circuit is: Power (P) = Voltage (V) × Current (I).
To calculate the number of watts, we can substitute the given values into the formula:
Volts (V) = 120
Amps (I) = 5
Therefore, the number of watts (P) = 120 V × 5 A = 600 W.
In 1980 the population in Detroit, Michigan was approximately 1, 200, 000. If the population decreased at an annual rate of 14.6% over the next decade What was the population of Detroit in 1990, 10 years later
Answers
1,200,000-175,200=1,024,800
I need help ASAP
The figure of a rocket launched for space exploration is shown below.
Find the volume of the rocket to the nearest hundredth.
A) 90.36 cubic meters
B) 98.91 cubic meters
C) 80.07 cubic meters
Answers
can somebody help me please this is my last question i need to submit this!! help!!
Answers
Which of the following sequences is not arithmetic?
a.1, 2, 3, 4, ...
b.2, 4, 6, 8, ...
c.0, -2, -4, -6, ...
d.1, 4, 9, 16, ...
Answers
===========================
A is arithmetic since we add 1 each time. The common difference is d = 1
B is arithmetic because the common difference is d = 2
C is arithmetic because d = -2 is the common difference
D is not arithmetic. The jump from 1 to 4 is +3 while the jump from 4 to 9 is +5
Answer:
1, 4, 9, 16, ...
Step-by-step explanation:
the initial number of bacteria in a culture is 12,000. the xulture doubles each day write an exponential functin to model the population Y of bacteria after X days
Answers
This equation is of the form y=a*bˣ, where a is the initial population and b is the rate that it increases by. In this problem, a = 12000 and b=2, since it doubles each time.
Answer:
[tex]Y = 12,000 \cdot (2)^X[/tex]
Step-by-step explanation:
The exponential function is given by:
[tex]y =a \cdot b^x[/tex]
where,
a is the initial values and b is the growth factor.
As per the statement:
The initial number of bacteria in a culture is 12,000.
⇒Number of bacteria initially(a) = 12,000
It is also given that the culture doubles each day.
⇒ growth factor [tex]b= 2[/tex]
We have to find the exponential function to model the population Y of bacteria after X days.
By definition of exponential function:
[tex]Y = 12,000 \cdot (2)^X[/tex]
where, x represents the days and Y is the population after X days.
Therefore, an exponential function to model the population is,
[tex]Y = 12,000 \cdot (2)^X[/tex]
which values are outliers ?
5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9
select all correct answers
Answers
Hope this Helped!
;D
:D
:)
;)
XD
:'D
Answer:
0.8 and 1.1 are outliers of the given data set.
Step-by-step explanation:
The given data set is
5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9
Arrange the data set in ascending order
0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9
Divide the data in four equal parts.
(0.8, 1.1), 4.9,( 5.2, 5.8), 5.9,( 6.1, 6.1), 7.4, (10.2, 10.9)
From the above division we get,
[tex]Q_1=4.9[/tex]
[tex]Median=5.9[/tex]
[tex]Q_3=7.4[/tex]
The interquartile range of the data is
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=7.4-4.9=2.5[/tex]
If all the data elements lies in the interval [Q₁-1.5(IQR),Q_3+1.5(IQR)], then the data set has no outliers.
[tex][Q_1-1.5(IQR),Q_3-1.5(IQR)]=[4.9-1.5(2.5),7.4-1.5(2.5)]=[1.15,11.15][/tex]
Since all the elements lie in the interval [1.15,11.15] except 0.8 and 1.1, therefore 0.8 and 1.1 are outliers.
What is the solution of x+8/5x-1>0 ?
Answers
First combine like-terms (x + [tex] \frac{8}{5} [/tex]x).
2.6x - 1 > 0
Add 1 to both sides.
2.6x > 1
Divide both sides by 2.6 to isolate x.
x > 0.38
Answer:
Step-by-step explanation:
what's the answer to this?
Answers
The measure of the side length of the right triangle is 20.
What is the measure of the missing side length?A tangent makes an angle of 90 degrees with the radius of a circle.
Therefore, the triangle formed is a right triangle.
From the diagram:
Leg 1 = 12
Leg 2 = 16
Hypotenuse =?
To find the hypotenuse, we use the Pythagoras theorem:
(Hypotenuse)² = ( Leg 1 )² + ( Leg 2 )²
(Hypotenuse)² = ( 12 )² + ( 16 )²
(Hypotenuse)² = 144 + 256
(Hypotenuse)² = 400
Take the square roots of both sides:
Hypotenuse = √400
Hypotenuse = 20
Therefore, the side length measures 20 units.
Option C) 20 is the correct answer.
The complete question is:
Find the missing line segment in the diagram.
Learn more about Pythagorean theorem here: brainly.com/question/343682
#SPJ1
What is the coefficient of y in the expression 3 ⋅ 6 + 4y?
Answers
Hope this helps:)
Answer:
Sorry I'm late, but I think the answer is D.
Step-by-step explanation:
Which characteristics best describe an obtuse isosceles triangle? I. One angle is greater than 90°. II. All side lengths are equal. III. Two sides meet at a 90° angle. IV. Two sides are equal in length. A. I and IV B. II and III C. I and II D. III and IV
Answers
An obtuse isosceles triangle is defined as a three-sides triangle shape that has one angle (out of three angles) more than 90 degrees and whose two sides are always congruent that includes obtuse angle in between. So it will follow :-
⇒ Obtuse means "one angle is greater than 90 degrees".
⇒ Isosceles means "Two sides are equal in length".
So, option A is correct, i.e. statements I and IV.
The area of this rectangle is 5x2. What does the coefficient 5 mean in terms of the problem?
Answers
Answer: The length is 5 times the width
Step-by-step explanation:
Given: The area of rectangle = [tex]5x^2=(5x)(x)[/tex]
Here x must be a positive real number since it can not be negative.
Also for area of rectangle =[tex]length \times width[/tex]
And length is always greater than width of rectangle, therefore in the given expression 'x' must be width and '5x' must be length of rectangle .
[∵ for every positive x , 5x>x]
Hence, the coefficient 5 means the length is 5 times the width.
helppppppppppppppppppppppppp
Answers
7x + 3 = 9x
Simplify, isolate the x, subtract 7x from both sides
7x (-7x) + 3 = 9x (-7x)
3 = 2x
Set the equation = 0, subtract 3 from both sides
3 (-3) = 2x (-3)
0 = 2x - 3
2x - 3, or D, should be your answer
hope this helps
I need help on these problems
Answers
What is the output value for the following function if the input value is 3.2?
y = 2x - 1
1
2
4.2
5.4
Answers
The given function is y = 2x -1 which is of the form of a straight line with the form y = mx + c
now, we have been given that the value of x is 3.2 as it says input value is 3.2
we plug in x =3.2 in the equation
y = 2x -1
y = 2*3.2 -1
y = 6.4 -1
y = 5.4
So the value of y we get is 5.4
Answer = 5.4 (option D)
a store sign reads take 90% off the original price when you take an additional 15% off the sale price which is 75% of the original price. Is the store sign correct
Answers
Hope This Helps!
~Cupkake
Suppose you have $16,000 to invest in three stocks, A, B, and C. Stock A is a low-risk stock that has expected returns of 4%. Stock B is a medium-risk stock that has expected returns of 5%. Stock C is a high-risk stock that has expected returns of 6%. You want to invest at least $1,000 in each stock. To balance the risks, you decide to invest no more than $7,000 in stock C and to limit the amount invested in C to less than 4 times the amount invested in stock A. You also decide to invest less than twice as much in stock B as in stock A. How much should you invest in each stock to maximize your expected profit? Complete the constraints.
Answers
Answer:
Stock A: 1
Stock B: 1 and y=2
Stock C: 1, 7, 4
To maximize expected profit, you need to determine the amount to invest in stocks A, B, and C while considering the given constraints.
Explanation:To invest in each stock to maximize expected profit, we need to determine the amount to invest in stocks A, B, and C while considering the given constraints.
Let's denote the amount invested in stock A as x, in stock B as y, and in stock C as z.
The constraints are as follows:
At least $1,000 should be invested in each stock: x > $1,000, y > $1,000, z > $1,000No more than $7,000 should be invested in stock C: z < $7,000The amount invested in C should be less than 4 times the amount invested in A: z < 4xThe amount invested in B should be less than twice the amount invested in A: y < 2xTo maximize expected profit, we need to maximize the sum of the expected returns from each stock:
Expected profit = 0.04x + 0.05y + 0.06z
By solving the constraints and optimizing the expected profit function, we can find the optimal values for x, y, and z.
Help with question 12 please
Answers
Teri's Train: 2:35 - 20 min = 2:15
Time between 1:57 and 2:15 is 13 minutes
Cindy's job is to check computer printers for defects. Out of 420 printers she has to check, only 3 of the first 84 have been defective. What is the best prediction of the total numbers of printers in this group that will be defective?
Answers
PLEASE HELP AND FAST, 15 POINTS! In the coordinate plane shown, how far apart are points B and D? Explain how you can use the Pythagorean theorem to determine this.
Answers
9 to the power of 2 = 81
25 + 81 = 106
Square root of 106 = 10.29563
If you round it to the nearest hundredth, it will become 10.30
If you round it to the nearest tenth, it will become 10.3
Eli, Freda and Geoff were given £800 to share in the ratio of their ages.
Eli is 9 years old,Feda is 13 years old and Geoff is 18 years old.
How much should they each get?
Eli-
Freda-
Geoff-
Answers
[tex]9+13+18=40[/tex]
The combined age of Eli, Freda, and Geoff is 40, so the denominator of each ratio will be 40.
Next, we are going to multiply the ratio between the age of the person and their combined age by £800:
For Eli: [tex] \frac{9}{40} *800=180[/tex]
For Freda: [tex] \frac{13}{40} *800=260[/tex]
For Geoff: [tex]\frac{18}{40} *800=360[/tex]
We can conclude that Eli will get £180, Freda will get £260, and Geoff will get £360.
Final answer:
Calculate how £800 should be divided among Eli, Freda, and Geoff based on their ages.
Explanation:
Ratio of ages: 9:13:18 = 9/40 : 13/40 : 18/40
Total amount: £800
Eli: £200
Freda: £290
Geoff: £410
according to the graph what is the value of the constant in the equation below rewritten in
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Answer:
The answer to this is B. 80
the following scatter plot demonstrates that there is a positive correlation between the two quantities.
Answers
four times the sum of a number and 2/3 is 16/3. find the number. express your answer as a fraction in simplest form
Answers
sum= addition
is= equal sign
x= a number
4 times x plus 2/3 equals 16/3.
4x + 2/3= 16/3
subtract 2/3 from both sides
4x= 14/3
divide both sides by 4
x= 14/3 ÷ 4
to divide fractions, multiply by reciprocal/inverse of 4
x= 14/3 * 1/4
multiply numerators (top); multiply denominators (bottom)
x= (14*1)/(3*4)
x= 14/12
simplify by 2
x= 7/6
ANSWER: The number in simplest form is 7/6.
Hope this helps! :)
Find the difference. express your answer in simplest form. (2s/s^2-4s+4) - (4/s^2-4s+4)
Answers
[tex] \frac{2s}{s^2-4s+4} -( \frac{4}{s^2-4s+4} )[/tex]
[tex]\frac{2s}{s^2-4s+4} -\frac{4}{s^2-4s+4}= \frac{2s-4}{s^2-4s+4} [/tex]
Now we can factor both numerator and denominator and simplify:
[tex]\frac{2s-4}{s^2-4s+4} = \frac{2(s-2)}{(s-2)^2} = \frac{2}{s-2} [/tex]
We can conclude that the difference in simplest form is: [tex] \frac{2}{s-2} [/tex]
2s 4 2(s+2)
------ - ------- = ------------
s^2 s^2 s^2
what equation results from completing the square and then factoring.
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Solve the Systems of equations algebraically
4x+5y=15
-4x+6y+7
Answers
A- (5/4, 2)
B- (2, 5/4)
C- (4/5,2)
D (2, 4/5)
Answers
4x + 5y= 15
-4x + 6y= 7
add the two above equations; the x term cancels out; solve for y
11y= 22
divide both sides by 11
y= 2
STEP 2:
substitute the y value in step 1 into either original equation
4x + 5y= 15
4x + 5(2)= 15
4x + 10= 15
subtract 10 from both sides
4x= 5
divide both sides by 4
x= 5/4
ANSWER: (A) x= 5/4, y= 2 or (5/4, 2)
Hope this helps! :)
help me? Answers por favor ?
Answers
4x+50=90.
90-50=4x
40=4x
x=10
7. theyre suplementary, they add to 180 degress, a straight line.
42+6x=180
6x=180-42
6x=138
x=23
8-10, Do i state them all or just some. (Im going to name just 1 or 2)
8. angle AKB and BKG, angle CGD and CGJ
9.CGK and KGJ
10. DGE and KGJ
I need help with the first three please!!!