The function which is created by shifting the graph of function f up 5 units is [tex]f(x)=4^x-1[/tex]
So, Option A is correct.
Step-by-step explanation:
We are given function: [tex]f(x)=4^x-6[/tex]
We need to determine the function which is created by shifting the graph of function f up 5 units.
The translation is vertical
If g(x)=f(x)+h then the graph is shifted up h units.
So, Applying translation:
[tex]f(x)=4^x-6[/tex]
[tex]g(x)=(4^x-6)+5[/tex]
Simplifying:
[tex]f(x)=4^x-6+5[/tex]
[tex]f(x)=4^x-1[/tex]
The function which is created by shifting the graph of function f up 5 units is [tex]f(x)=4^x-1[/tex]
So, Option A is correct.
Keywords: Transformation
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Claim: Most adults would ease all of their personal information online if they could. A software firm survey of 609 randomly selected adults showed that 55% of
would erase all of their personal information online if they could find the value of the test statistic
The value of the test statisticis
(Round to two decimal places as needed.)
Answer:
2.480 is test statistic
Step-by-step explanation:
Given that the claim is most adults would ease all of their personal information online if they could.
[tex]H_0: p = 0.50\\H_a: p >0.50[/tex]
(right tailed test)
p difference = 0.05
Std error=
[tex]\sqrt{pq/n} =\sqrt{0.5*0.5/609}[/tex]
0.0202
p difference / std error
Test statistic = p difference / std error
= [tex]\frac{0.05}{0.0202} \\=2.480[/tex]
Use natural logarithms to solve the equation. Round to the nearest thousandth.
3e^2x+2=28
A. 1.0797
B. 0.4689
C. 0.9261
D. 2.1595
Answer:
A. 1.0797
Step-by-step explanation:
Given the equation,
3e^2x+2=28
To solve for x, first we move 2 to the other side of the equation.
3e^2x = 28-2
3e^2x = 26
Dividing both sides by 3
e^2x = 26/3
e^2x = 8.67
Taking the natural logarithm if both sides
ln(e^2x) = ln8.67
2x = ln8.667
2x = 2.1595
x = 2.1595/2
x = 1.0797
y-5, y=2x^2-16x+29, use substitution to solve the system of equations
Answer:
2x^2-16x+34
Step-by-step explanation:
Since Y is equal to -5
And you substitute -5 in the equation.
You now have -5=2x^2-16x+29
Add 5 to both sides
5-5=2x^-16x+29+5
The solution of the system of equations will be given as x = 4 ± i.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
y = – 5 ....1
y = 2x² – 16x + 29 ....2
From equation 1 and 2, we have
2x² – 16x + 29 = –5
2x² – 16x + 34 = 0
x² – 8x + 17 = 0
Then the value of x will be
[tex]\rm x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4 * 1 * 17}}{2*1}\\\\x = \dfrac{8\pm \sqrt{-4}}{2}\\\\x = \dfrac{8 \pm 2\iota}{2}\\\\x = 4 \pm \iota[/tex]
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The similarity ratio of two similar polygons is 2:3. Compare
the smaller polygon to the larger polygon. Find the ratio
of their areas.
Answer:
The ratio of their areas is 4:9
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area of the smaller polygon
y ---> the area of the larger polygon
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]z=\frac{2}{3}[/tex] ---> the scale factor is given
substitute
[tex](\frac{2}{3})^2=\frac{x}{y}[/tex]
[tex]\frac{4}{9}=\frac{x}{y}[/tex]
Rewrite
[tex]\frac{x}{y}=\frac{4}{9}[/tex]
therefore
The ratio of their areas is 4:9
PLEASE help me I really need this done by today
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The axis of symmetry for a quadratic equation can be found using the formula x =
where a and b are coefficients in the
quadratic equation and x represents the values along a vertical line on the coordinate plane.
What is the equation when solved for a?
Answer:
The denominator of the fraction is 2x and the answer is a= -[tex]\frac{b}{2x}[/tex]
Step-by-step explanation:
Suppose we have a quadratic equation of the form:
ax²+bx+c
The axis of symmetry of the parabola is given by:
[tex]x= \frac{-b}{2a}[/tex]
From here, we must clear the value of a.
For this, we follow the following steps:
1) Pass 2a multiplying to the other side of the equation:
2ax=-b
2) Clear the value of a by passing 2x to divide:
[tex]a= \frac{-b}{2x}[/tex]
Answer:
B.
a= -b/2x
Step-by-step explanation:
Oceanside bike rental charges 11 dollars plus 8 hours for renting. Tom paid 51 dollars to rent a bike . How many hrs did he pay to have the bike checked out
Answer:
Tom paid $51 renting the bike for 5 hours
Step-by-step explanation:
Given:
Oceanside bike rental charges $11 plus $8 per hour for renting.
Tom paid $51 to rent a bike.
To find the number of hours Tom rented the bike for.
Solution:
Let Tom rent the bike for =[tex]x[/tex] hours.
Hourly rate of renting = $8 per hour
Using unitary method find cost of renting for [tex]x[/tex] hours.
If renting for 1 hour costs = $8
Then for [tex]x[/tex] hours, the cost in dollars will be = [tex]8x[/tex]
Fixed charges = $11
∴ Total cost of renting a bike in dollars for [tex]x[/tex] hours will be given as:
[tex]8x+11[/tex]
Tom paid a total charge of = $51.
So, we have:
[tex]8x+11=51[/tex]
Subtracting both sides by 11.
[tex]8x+11-11=51-11[/tex]
[tex]8x=40[/tex]
Dividing both sides by 8.
[tex]\frac{8x}{8}=\frac{40}{8}[/tex]
∴ [tex]x=5[/tex]
Thus, Tom rents the bike for 5 hours.
Johnny sold crafts at a show. His prices included .07 sales tax. Johnny grossed $1236.00. What was johnny's taxable amount?
The taxable amount was $80.86
Step-by-step explanation:
Given,
Sales tax = .07
Total grossed = $1236.00
Let,
x be the price before sales tax, therefore,
Amount of sales tax = 0.07x
Price before sales tax + Sales tax = Total amount grossed
x+0.07x = 1236
1.07x=1236
Dividing both sides by 1.07
[tex]\frac{1.07x}{1.07}=\frac{1236}{1.07}\\x=1155.14[/tex]
Taxable amount = Total amount grossed - Price before tax
Taxable amount = 1236 - 1155.14 = $80.86
The taxable amount was $80.86
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Answer:
$80.86 was taxed
Step-by-step explanation:
x+ 1/8 =1.375 what is the anser
Answer:
1.25
Step-by-step explanation:
x+1/8=1.375
x=1.375-0.125
x=1.25
Answer: 1.25
Move all terms not containing x to the right side of the equation.
Exact Form:
x = 54
Decimal Form:
x = 1.25
Mixed Number Form:
x = 1 1/4
Hope this helps
the temperature is -4 it increases to 8 how many degrees did the temperature increase
Answer:
12 degrees.
Step-by-step explanation:
8 - (-4) = 12. So, the temperature increased by 12 degrees.
The temperature increased by 12 degrees from -4 to 8.
Explanation:The question is asking for the temperature change from -4 to 8 degrees. To find the increase in temperature, you subtract the initial temperature from the final temperature. In this case, 8 (final temperature) minus (-4) (initial temperature), equals 12°C. Hence, the temperature increased by 12 degrees.
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Help Asap will give brainliest if you start answering by 21 minutes
A function is shown: f(x) = 4x2 − 1.
Choose the equivalent function that best shows the x-intercepts on the graph.
f(x) = (4x + 1)(4x − 1)
f(x) = (2x + 1)(2x − 1)
f(x) = 4(x2 + 1)
f(x) = 2(x2 − 1)
Answer:
f(x) = (2x + 1)(2x − 1)
Explanation:
As we can see from the above function f(x) = 4[tex]x^{2}[/tex] − 1, we need to find x-intercept, i.e., the value of x where this function's value is zero.
So let us Equate the function with zero
4[tex]x^{2}[/tex] - 1 = 0 => 4[tex]x^{2}[/tex] = 1 => [tex]x^{2}[/tex] = 1/4 => x = [tex]\sqrt{1/4}[/tex]
Hence we get 2 values of x, i.e., +1/2, and -1/2.
So now we need to check out the functions which are zero at this values of x, so let us substitute values of x in each and every option and see the values of functions.
Option A - f(x) = (4x + 1)(4x − 1) = 3, -3
Option B - f(x) = (2x + 1)(2x − 1) = 0
Option C - f(x) = 4(x2 + 1) = 5
Option D - f(x) = 2(x2 − 1) = -3/2
Hence answer is Option B
What is the first step to solve this equation 11 minus 3x equals 44
Answer:
x=-11
Step-by-step explanation:
11-3x=44
3x=11-44
3x=-33
x=-33/3
x=-11
Thomas is starting a new company. He has two quotes from a computer company for the cost of computers and printers. If he buys three computers and one printer, the cost is $825. if he buys 4 computers and 2 printers, the cost is $1200. How much does each computer and printer cost?
Each computer costs $225 and each printer costs $150
Step-by-step explanation:
Thomas is starting a new company. He has two quotes from a computer company for the cost of computers and printers
If he buys three computers and one printer, the cost is $825If he buys 4 computers and 2 printers, the cost is $1200We need to find how much each computer and printer costs
Assume that the cost of each computer is $x and the cost of each printer is $y
∵ The cost of each computer is $x
∵ The cost of each printer is $y
∵ The cost of 3 computers and one printer is $825
- Multiply x by 3 and add the product to y, equate the sum by 825
∴ 3x + y = 825 ⇒ (1)
∵ The cost of 4 computers and 2 printers is $1200
- Add the product of 4, x and the product of 2 , y and equate the
sum by 1200
∴ 4x + 2y = 1200 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -2 to eliminate y
∵ -6x - 2y = -1650 ⇒ (3)
- Add equations (2) and (3)
∴ -2x = -450
- Divide both sides by -2
∴ x = 225
Substitute the value of x in equation (1) to find y
∵ 3(225) + y = 825
∴ 675 + y = 825
- Subtract 675 from both sides
∴ y = 150
Each computer costs $225 and each printer costs $150
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By setting up a system of equations from the scenarios provided, we can determine that each computer costs $225 and each printer costs $150.
To determine the cost of each computer and printer, we can set up a system of equations based on the information provided. Let C represent the cost of one computer and P represent the cost of one printer. Using the first scenario where three computers and one printer cost $825, we can write the first equation as:
3C + P = $825 ... (1)
For the second scenario where four computers and two printers cost $1200, we can write the second equation as:
4C + 2P = $1200 ... (2)
Next, we'll solve this system of equations using either substitution or elimination method. To use elimination, we can multiply equation (1) by 2 to eliminate the printers:
6C + 2P = $1650 ... (3)
Now, we subtract equation (2) from equation (3) to find C:
6C + 2P - (4C + 2P) = $1650 - $1200
2C = $450
C = $225
We now know each computer costs $225. To find the cost of a printer, we can replace C in either equation (1) or (2). Let's use equation (1):
3(225) + P = $825
675 + P = $825
P = $825 - 675
P = $150
Thus, each computer costs $225 and each printer costs $150.
has a y-intercept of 21 and slope of -5.
Answer:
Step-by-step explanation:
Intercept c = 21 and slope m = -5
y = mx + c
y = -5x + 21
is (2,4), (-5,2), (7,1), (-6,2) a relation or function
Answer: Function
Step-by-step explanation: A function is a special type of relation and for a relation to be a function, each x-term must correspond with exactly 1 y-term.
The easiest way to determine whether a relation is a function is to look at the x-coordinate of each ordered pair. If any of our ordered pairs have the same x-coordinate with a different y-coordinate, then our relation is no a function.
Since none of our x-terms repeat with different y-terms, this is a function.
Find the X COORDINATE OF THE intersection of 9x - 6y = 12 and 3x + 2y =8
Answer: [tex]x=2[/tex]
Step-by-step explanation:
Given a System of linear equations, the solution of the system is the point [tex](x,y)[/tex] in which the lines intersect, where "x" is the x-coordinate and "y" is the y-coordinate.
Having the following System of equations:
[tex]\left \{ {{9x - 6y = 12} \atop {3x + 2y =8}} \right.[/tex]
You can use the Elimination method to find the value of "x":
-Multiply the second equation by 3.
- Add the equations.
- Solve for "x".
Then, you get:
[tex]\left \{ {{9x - 6y = 12} \atop {9x +6y =24}} \right.\\.......................\\18x=36\\\\x=\frac{36}{18}\\\\x=2[/tex]
5(x+2)+3x = 4(2x+2)+2
Use a matrix to solve the system.
8.
2x + 6y = 38
(5x - y = 15
Answer:
x=4 and y=5
Step-by-step explanation:
The given system of equations are
[tex]2x+6y=38[/tex]
[tex]5x-y=15[/tex]
The matrix form is
[tex]\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
Let as assume
[tex]A=\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}[/tex]
[tex]X=\begin{bmatrix}x\\ \:y\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
then,
[tex]AX=B[/tex]
[tex]X=A^{-1}B[/tex]
We know that,
[tex]\begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}^{-1}=\frac{1}{\det \begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}}\begin{bmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{\det \begin{bmatrix}2&6\\ 5&-1\end{bmatrix}}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}\left(-1\right)\cdot \:38+\left(-6\right)\cdot \:15\\ \left(-5\right)\cdot \:38+2\cdot \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-128\\ -160\end{bmatrix}[/tex]
[tex]\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}4\\ 5\end{bmatrix}[/tex]
Therefore, the value of x is 4 and value of y is 5.
x^2 -9x+12=(x-p)^2-q
Find the value of p and the value of q
Good evening ,
Answer:
x²-9x+12 = (x - (9/2))²- (33/4)
Step-by-step explanation:
Look at the photo below for the details.
:)
In order to find the variables p and q in the equation x^2 - 9x + 12 = (x-p)^2 - q, we first complete the square on the left-hand side which leads us to determine that p=4.5 and q=32.25.
Explanation:The original equation given is x^2 - 9x + 12 = (x-p)^2 - q. To find the values of p and q, we need to rewrite the left-hand side of the equation in the format of (x-p)^2. This can be done through a process known as completing the square. Looking at the equation x^2 - 9x + 12, we have a perfect square x^2 - 9x + (9/2)^2 = (x-4.5)^2. However, remember, we added (9/2)^2 to both sides, so we have (x-4.5)^2 = x^2 - 9x + 12 + 20.25. Simplifying, (x-4.5)^2 = x^2 - 9x + 32.25, which is our original equation format. Thus, p=4.5 and q=32.25.
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You have a cake that is 10 inches in diameter. You expect 12 people to share it, so you cut it into 12
equal slices. What is the area of each slice of cake? (Hint: the entire cake is 360°)
Answer:
The area of each slice of cake is [tex]\frac{25}{12}\pi\ in^2[/tex]
Step-by-step explanation:
step 1
Find the area of the complete cake
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (5)^{2}[/tex]
[tex]A=25\pi\ in^2[/tex]
step 2
Find the area of each slice of cake
Remember that the area of complete circle subtends a central angle of 360 degrees
If you cut the cake into 12 equal slices
then
the central angle of each slice is equal to [tex]\frac{360^o}{12}=30^o[/tex]
so
Using proportion
Find out the area of each slice for a central angle of 30 degrees
[tex]\frac{25\pi}{360^o}=\frac{x}{30^o} \\\\x= \frac{25\pi}{360^o}(30^o)\\\\x=\frac{25}{12}\pi\ in^2[/tex]
Note This problem could be solved by directly dividing the area of the circle by 12, however, proportions and concepts of central angle were applied for didactic purposes
Each slice of the 10-inch diameter cake, cut into 12 equal slices, has an area of approximately 6.54 square inches.
To find the area of each slice of the cake, we need to calculate the area of the entire cake first and then divide it by 12 since the cake is divided into 12 equal slices.
The formula for the area of a circle is: Area = πr².
Given the diameter of the cake is 10 inches, we first need to find the radius: radius = diameter / 2 = 10 / 2 = 5 inches.
Now, calculate the area of the entire cake:
Area of the full cake = π × (5 inches)² = 25π square inches.
Since the cake is cut into 12 equal slices, the area of each slice is:
Area of each slice = (25π) / 12 = 25π / 12 ≈ 6.54 square inches.
Therefore, each slice of cake has an area of approximately 6.54 square inches.
Melinda creates jewelry. After purchasing supplies, she had $150 left in her account. She sells five bracelets and a necklace making her new account total $235. If the necklace sold for $22.50, which equation can be used to determine the sales price of the bracelets?
Answer:
b
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equation can be used to find the cost of the bracelets.
5x + 22.50 + 150 = 235
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of bracelets sold = 5
The number of necklaces sold = 1
Cost of the necklace = $22.50
Cost of the bracelets = x
The amount left = $150
The total amount in the account after selling them = $235
Now,
The equation can be used to find the cost of the bracelets.
5x + 22.50 + 150 = 235
Thus,
The equation can be used to find the cost of the bracelets.
5x + 22.50 + 150 = 235
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is it possible for one body to be at rest and moving at the same time? Why is that?
Answer:
yes
Step-by-step explanation:
it is possible that a body can be moving and at rest at the Same time. this is relative motion. an object that seem to be in motion for one subject can be stationary for another.
For example, A passenger in a bus. he/she is moving for a person walking on the pathway. but for the passenger next to him/her, they are at rest.
Answer:
Yes
Step-by-step explanation:
It is possible if you take into account different points of reference.
If you are in a car, sitting on a seat, while the car is moving, you are not moving with respect with the car. Since the car is moving with respect to the ground, you are moving with respect to the ground.
If you think bigger, you are always in motion. You may be standing in a position not moving at all with respect to the ground, but since the Earth is moving around the sun, you are moving with respect to the sun.
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Alisa buys a watermelon every year. The first time she bought a watermelon, in Year 0, it cost $2.50. She notices the price is getting more expensive, at a rate of 3% per year.
Alisa sketches a graph of the situation.
Which statements are true?
Select each correct answer.
The graph increases from left to right.
The point (0, 2.50) is on the graph.
The graph has an x-intercept and a y-intercept.
The graph has a y-intercept but no x-intercept.
The point (2.50, 0) is on the graph.
The graph decreases from left to right
Answer:
Okay, so the first one is" The point (0, 2.50) is on the graph" second one is "The graph has a y-intercept but no x-intercept" And the third one would be "The graph increases from left to right"
An experiment was conducted to compare the mean reaction times to two types of
traffic signs: No Left Turn and Left Turn Only. Ten drivers were included in the
experiment. Each driver was presented with 40 traffic signs - 20 No Left Turn and 20
Left Turn Only - in random order. The mean reaction time to each type of sign was
recorded for each driver. So, for example, individual #1 reacted, on average, within
824 milliseconds to the No Left Turn and within 702 milliseconds to the Left Turn
Only sign. The design of this experiment most closely resembles a:
Matched pairs before and after design?
The design of this experiment is a Within-Subjects Design, where each participant is exposed to both types of signs and their reaction times are compared.
Explanation:The design of this experiment most closely resembles a Within-Subjects Design. In this design, each participant is exposed to both conditions, in this case, the No Left Turn and the Left Turn Only signs. The participants' reaction times to each sign are measured and compared within the same group of participants, allowing for a direct comparison between the two types of signs.
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If every 3 hours John walked 8 miles. How many miles did John walk in 1 hour
8 ÷ 3 = 2 2/3 miles
yeeeeeeeee
Answer:
2.66 miles every hour
Step-by-step explanation:
8/3
Rudolph ate 30 pounds of reindeer food in 3 hours. How many pounds did he eat each hour?
Answer:
Step-by-step explanation:
30 lbs in 3 hrs....
30/3 = 10 lbs per hr <==
Answer:
10 pounds
Step-by-step explanation:
if you divide 30 by 3 you will get 10 and becuase there are three hours you will have the answer as 10
30÷3=10
10×3=30
all uses the expression 4.2 * 12.3 * 14.6 to determine the cost of tile in the Floor of a room that measures 12.3 ft by 14.6 feet each square foot of tile cost 4.20 dollars how many decimal places will be in Polish final answer
one
three
five
eight
Answer:
There are three decimal places in the final answer.
Step-by-step explanation:
We have to calculate the expression 4.2 × 12.3 × 14.6, in which the floor dimensions are 12.3 ft by 14.6 ft. which I have to cover with tiles and each square foot of tile costs $4.20.
So, the area of the floor is (12.3 × 14.6) sq. ft. = 179.58 square feet.
Now, the cost of covering the floor with tiles will be = $(179.58 × 4.2) = $754.236.
Therefore, there are three decimal places in the final answer. (Answer)
Round 8923 to the thousands
Answer:
9000
Step-by-step explanation:
When you are rounding to the thousands, if the hundreds place is 500 or greater you have to round up in the thousands place.
That would mean 8923 rounded to the thousands place would equal 9000
Hope This Helps!
Answer:
9000
Step-by-step explanation:
To round a number to the nearest thousand, you look at the number in the hundreds place.
If the number in the hundreds place is
greater than 5, you add 1 to the number in the thousands place less than 5, you keep the number in the thousands place exactly 5 with only zeros following it, you round the number in the thousands place to the nearest even numberHere's how to round 8923 to the nearest thousand.
The digit in the thousands place is the 8. The number in the hundreds place (8) is greater than 5. Add 1 to the digit in the thousands place.The rounded number is 9000.
What is the Square root of -1
Answer:
the square root of -1 is i
Step-by-step explanation:
Answer:
[tex]\large\boxed{\sqrt{-1}=i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\\\\i-\text{immaginary unit}\ \left(i^2=-1\right)\\\\\text{It's a complex number.}[/tex]
if logx=-5 what is x
Answer :The value of x when log(x) = -5 is 0.00001.
Step-by-step explanation: