First, raise the denominator (27) to the power of 1:
3^-(x-2) = 1/27^1
Next, use the negative exponent rule that is represented by the equation of 1/b^n = b^-n and then move 27 to the numerator:
3^-(x-2) = 27^-1
Rearrange the term so that both equations have the same base:
3^-(x-2) = 3^-3
Now when noticing how this has been completed, it is noticed that since both of these equations have the same bases, the only thing left to do is have the exponents equal one another. For now, ignore the bases and focus only on the two sets of exponents -(x - 2) and (-3). Lets make a new equation with only the exponents:
-(x - 2) = -3
Next, add the distributive property on the left side of the equation to remove the - sign outside (Note: Double negatives equal positive)
-x + 2 = -3
Subtract 2 from both sides:
-x = -5
Finally, it is asking for positive x not negative, so divide both sides by -1:
x = 5
So, the answer is A which is 5.
If 3-(x - 2) = 1/27 then the value of x is a) 5.
To solve for x, we'll follow these steps:
1. Distribute:
Distribute the negative sign into the parentheses:
3 - (x - 2) = 1/27
3 - x + 2 = 1/27
Simplify:
5 - x = 1/27
2. Isolate x:
To solve for x, we need to get it alone on one side of the equation. Subtract 5 from both sides:
5 - x - 5 = 1/27 - 5
-x = -134/27
3. Multiply by -1:
To solve for x, multiply both sides by -1 to isolate x:
-1 * -x = -1 * -134/27
x = 134/27
4. Simplify:
[tex]x = \approx 4.9629[/tex]
Since none of the given options exactly match the calculated value, we can see that option a) 5 is the closest answer.
However, the precise solution is a fraction between 4 and 5, so none of the provided options is an exact match.
In summary, while none of the given options is an exact solution, the closest answer is a) 5.
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Complete Question
Choose the correct answer from the given options:
If 3-(x - 2) = 1/27, what is the value of x?
a) 5
b) 3
c) -1
d) -5
The magnitude of an earthquake measured on the Richter scale is given by:
R(L) = log (l/l0), where l = amplitude.
Find the Richter scale rating of an earthquake with amplitude 1. 80 X 10 l0.
HELP ME PLEASEEEEEEEEEEE
Answer:
1.26
Step-by-step explanation:
R(L)=log((1.8 ×10)=log(18)=1.26
What is the answer for -6 + x/4 = -5?
Answer:
4
Step-by-step explanation:
-6 + x/4 = -5 --> add 6 to both sides
x/4 = 1 --> times 4 on each side
x = 4
Which of the following represents a function?
Answer:
B) Graph of an Absolute Value Function
Step-by-step explanation:
A function is a relation in which no two ordered pairs have the same input and different outputs. Whenever you're trying to determine whether a given relation is a function, observe whether each input correspond with exactly one output.
The given table in Option A) is not a function because there are two corresponding y-values for x = 3.
Option C is also not a function because the input value of x = -1 has two output (y-values): -11 and 5.
Option D is also not a function because the input value of 3 has two output values: -5 and 0.
Option B represents a function because each input value has exactly one corresponding output value. A useful technique to use in determining whether a given graph represents a function is the Vertical Line Test. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
Attached is an edited screenshot of Option B, where it shows that each blue vertical line has its own corresponding point. This means that the each line crosses the graph at most once. Therefore, the correct answer is Option B.
Answer:
The graph
Step-by-step explanation:
I got it right on plato
f(x) = 2.5e-0.04x and g(x) = 1.2 + 0.2x.
f(x) - g(x)
2.5e - 0.04x - 1.2 + 0.2
0.16x + 5.59570457
Carly withdraws $18 from her bank account. Which number line represents this amount?
-20 -15 -10 -5 0 5 10 15 20,
10 15 20 -20 -15 -10 -5 0 5
10 15 20 -20 -15 -10 -5 0 5,
-20 -15 -10 -5 05 10 15 20.
pls answer quick!!! i'll give brainliest if right!
Answer:
Step-by-step explanation:
$0.11
per ounce
1.32/12=0.11!!
Answer: 1.21
Since we know that $1.32 is 12 ounces all we need to do is figure out how much is in each ounce which is "0.11", so this means for each unit equals to "0.11" so
0.11 x 11=1.21 ounces Good luck!
10 pls pls pls help meeee!
Answer:
SAS
I THINK CORRECT ME IF IM WRONG
what is 2x(7+66) i need help
7+66 is 73,so that means 73 x 2
73 x 2 is 146.
So it is 146
Hope you have a great day.
Good luck
Answer:
146x
Step-by-step explanation:
hope it helps
mark me brainliest
i work on this on last friday
Please help me! It’s for geometry
The answer to this is 2 67.5
HELP ASAP PLEASE I BEG TOU
Answer:
(0,-2)
(2,-1)
(4,0)
Step-by-step explanation:
The points are the above ones.
x intercept: (4, 0)
y intercept: (0, -2)
Can somebody solve this for me?
Answer:
Area of rectangle = L x W
Step-by-step explanation:
A = L x W
L = 18
W = 10 + 5
so,
A = 18 x (10+5)
A = 18 x 15
A = 270
PLS HELP ME, I REALLY NEED THIS RIGHT NOW, 100 POINTS, IF YOU ANSWER WITH NO EXPLANATION, OR ANSWER FOR THE POINTS YOU WILL BE REPORTED
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 4(1.08)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent? (4 points)
9514 1404 393
Answer:
0 ≤ m ≤ 70.4541 cm/month; average rate of growth over last 4 months of studyStep-by-step explanation:
Part A:
The study was concluded after 7 months. The fish cannot be expected to maintain exponential growth for any significant period beyond the observation period. A reasonable domain is ...
0 ≤ m ≤ 7
__
Part B:
The y-intercept is the value when m=0. It is the length of the fish at the start of the study.
__
Part C:
The average rate of change on the interval [3, 7] is given by ...
(f(7) -f(3))/(7 -3) = (4(1.08^7) -4(1.08^3))/4 = 1.08^3·(1.08^4 -1)
≈ 0.4541 cm/month
This is the average growth rate of the fish in cm per month over the period from 3 months to 7 months.
over the last 4 years michael has earned $240 interest on an initial investment of $2,000. what simple annual interest rate is the bank paying on this account
Answer:
.03 or 3%.
Step-by-step explanation:
Important:
I = interest
P = principal (investment)
R = simple interest rate
T = years
Formula: I = PRT
Given:
I = $240
P = 2000
T = 4 years
R = ?
Plug into formula:
240 = 2000(R)4
Multiply right side 2000*4
240 = 8000R
Divide both sides by 8000.
R = 240/8000
R = .03
The simple annual interest rate was .03 or 3%.
Therefore it .03 or 3%
please help fast ^^
Using the discriminant, determine the number of real solutions,
-2x^2+x-28= 0
Ono real solutions
O one real solution
O two real solutions
The number of real solutions is 0, the correct answer is A.
How to use discriminant to find the property of solutions of given quadratic equation?Let the quadratic equation given be of the form ax^2 + bx + c = 0, then
The quantity b^2 - 4ac is called its discriminant.
The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:
Real and distinct if the discriminant is positive
Real and equal if the discriminant is 0
Non-real and distinct roots if the discriminant is negative
There are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.
We are given that;
The equation -2x^2+x-28= 0
Now,
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by b^2 - 4ac. The discriminant can be used to determine the number of real solutions of the equation as follows:
If the discriminant is positive, there are two distinct real solutions.
If the discriminant is zero, there is one repeated real solution.
If the discriminant is negative, there are no real solutions.
In this case, the quadratic equation is -2x^2 + x - 28 = 0. Comparing it with the standard form, we can identify that a = -2, b = 1, and c = -28. Therefore, the discriminant is:
b^2 - 4ac
= 1^2 - 4(-2)(-28)
= 1 - 224
= -223
Since, the discriminant is negative, there are no real solutions for this equation.
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In the triangle below, suppose that mZL=(x+3)°, mZ M=(5x-7)°, and m N= (2x).
Find the degree measure of each angle in the triangle.
N
(2x)
mL =
日。
х
M
(5x - 7).
m M =
•
•
mZN =
(x + 3)°
Answer:
GivenTriangle ABC is right angled at A.
[tex]m\angle B=(5x+7)^∠B=(5x+7)∘[/tex]
[tex]m\angleC=(4x+29)^∠C=(4x+29) [/tex]
To find:
The degree measure of each angle in the triangle.
Solution:According to the given information,
[tex]m\angleA=90^\circm∠A=90[/tex]
[tex]m\angleB=(5x+7)^\circm∠B=(5x+7) [/tex]
[tex]m\angleC=(4x+29)^\circm∠C=(4x+29) ∘[/tex]
Now,
[tex]m\angleA+m\angleB+m\angleC=180^\circm∠A+m∠B+m∠C=180 ∘[/tex]
(Angle sum property)
[tex]90^\circ+(5x+7)^\circ+(4x+29)^\circ=180^\circ90∘+(5x+7)∘+(4x+29) ∘ =180[/tex]∘
[tex](9x+126)^\circ=180^\circ(9x+126)∘ =180∘[/tex]
9x+126=1809x+126=180
9x=180-1269x=180−126
9x=549x=54
Divide both sides by 9.
[tex] \sf{x=\dfrac{54}{9}x=954}[/tex]
x=6x=6
Now,
[tex]m\angle A=90^\circm∠A=90
∘[/tex]
[tex]m\angleB=(5(6)+7)^\circm∠B=(5(6)+7) [/tex]
∘
[tex]m\angle B=37^\circm∠B=37[/tex]
∘
[tex]m\angleC=(4(6)+29)^\circm∠C=(4(6)+29)[/tex]
∘
[tex]m\angle C=53^\circum \: ∠C=53[/tex]
Therefore,
The measures of ∠A, ∠B, ∠C are 90°, 37°, 53° respectively.
Answer:
26°, 108°, 46°Step-by-step explanation:
Assumed the given is:
ΔLMN with angle measures of (x + 3), (5x - 7) and 2x.We need to find the angle measures in degrees.
We know the sum of interior angles is 180:
x + 3 + 5x - 7 + 2x = 1808x - 4 = 1808x = 184x = 184/8x = 23Find the angle measures:
m∠L = x + 3 = 23 + 3 = 26m∠M = 5x - 7 = 5*23 - 7 = 108m∠N = 2x = 2*23 = 46HELP ASAP PLS 10 POINTS
Answer:
try a or b hope this helps
Answer:
top right
Step-by-step explanation:
SOMEONE HELP ITS DUE TONIGHT
Answer:
n=27 degrees
m=36 degrees
Step-by-step explanation:
So the inside triangle has two equal sides. To find these angles you would do the degrees of a triangle (180) minus the known value and then divided by two.
so it is: 180-126/2 which gives you 27 degrees.
this means the n value is 27.
to find m, you have to take away 90 degrees and the n value from 180.
so it is: 180-90-27 which gives you 63 degrees.
now you must take the smaller angle from 63 degrees to find m.
so it is: 63-27 which gives you 36
therefore...
n=27 degrees
m=36 degrees
Evaluate the expression when x=-4. X^2+5x+7
Answer:
-29
= -16 + 5(-4) + 7
=16 - 20 + 7
=-29
Help stuck on question number 9
Answer:
y=4x-4
Step-by-step explanation:
You know that a line perpendicular to the equation (y= -1/4x-14) would have an opposite reciprocal slope.
The slope from the given equation is -1/4x. Take the opposite reciprocal and you get 4/1x or 4x as your slope.
Now use the point-slope formula to find your b value.
(y-y1)=m(x-x1)
m= 4
Plug in (3,8) for x and y, and solve.
(y-8)= 4(x-3)
y-8= 4x -12
y=4x-4
WHAT ARE CONGRUENCE LINES
Answer:
Line segments are congruent if they have the same length. However, they need not be parallel. They can be at any angle or orientation on the plane. ... Rays and lines cannot be congruent because they do not have both end points defined, and so have no definite length.
explain how you got the answer because I somehow got x > -5 as my answer, please and thanks.
Answer: x>-5
Step-by-step explanation:
-5(x+7)<-10
Distribute the -5.
-5x-35<-10
Add 35 to both sides.
-5x<25
Divide both sides by -5.
x>-5
Answer:
x > - 5
Step-by-step explanation:
-5(x+7)< -10
-5x - 35 < - 10
- 5x < - 10 + 35
x > 25/-5
Use the graph below to find the x- and y - intercepts .
x-intercept : - 6; y - in ; intercept : 9
x-intercept: 1.5 ; y-intercept: 9
x-intercept : 9; y-intercept : - 6
x-intercept: -6; y-intercept: 3
May I please receive help?
Answer:
m<1=47 and m<2=29
Step-by-step explanation:
PLEASE HELP ME I NEED TO ANSWER THIS
Answer:
the correct answer is 37°
Step-by-step explanation:
just simple geometry haha
Answer:
37
Step-by-step explanation:
( x + 71 ) and 108 are vertically opposite angles.
Vertically opposite angles are equal.
x + 71 = 108
x = 108 - 71
x = 37
Can someone tell me the answer to this please???
Answer:
36
Step-by-step explanation:
Answer:
It's 36 ya know
Step-by-step explanation:
60 and 60 so 36 and 36
:)
Please help :(((((((((
Answer:
Yes it is a linear function
Step-by-step explanation:
What is the equation of the line shown in this graph
Answer:
y=1
Step-by-step explanation:
The line is hoizonatal so the slope would be undefined and the y intercept would be 1
Chau rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 97 cents for each mile driven. Chau had to pay $306.13 when he returned the truck. For how many miles did he drive the truck?
Answer:
Chau drove 13.96 miles while he was using the truck
Step-by-step explanation:
Answer:
294 miles!!!!!!
Step-by-step explanation:
SHOW WORK FOR CREDIT.
4. −10(x − 3)
A) −15x + 30
B) −10x + 30
C) −15x + 35
D) −15x + 37
Answer:
B) -10x + 30
Step-by-step explanation:
You have to multiply -10*x and -10*-3. -10*x equals -10x and -10*-3 is +30.
Answer:
[tex]\sf -10x+30[/tex]
Step-by-step explanation:
[tex]\sf -10(x - 3)\\-10x-\left(-10\right)\times \:3\\-10x+30[/tex]
If Sarah sold 20 bags of dog treats for $3.25 each, how much money did she earn? You must show your work to earn full credit.
Answer:
$65
Step-by-step explanation:
20 bags of dog treats multiplied by 3.25 = $65.00
Sarah made 65 dollars.
Answer:
Sarah earned $65.
Step-by-step explanation:
Create an equation.
20 representing the bags she has sold, 3.25 representing the value of each bag. If Sarah sold 20 bags of dog treats, with each of them being worth 3.25, then 20(3.25) = 65, meaning Sarah earned $65.