find the value of x (3/5)^x(5/3)^2x=125/27
Given:
The equation is
[tex]\left(\dfrac{3}{5}\right)^x\left(\dfrac{5}{3}\right)^{2x}=\dfrac{125}{27}[/tex]
To find:
The value of x.
Solution:
We have,
[tex]\left(\dfrac{3}{5}\right)^x\left(\dfrac{5}{3}\right)^{2x}=\dfrac{125}{27}[/tex]
[tex]\left(\dfrac{5}{3}\right)^{-x}\left(\dfrac{5}{3}\right)^{2x}=\dfrac{5\times 5\times 5}{3\times 3\times 3}[/tex] [tex][\because \left(\dfrac{a}{b}\right)^{-m}=\left(\dfrac{b}{a}\right)^{m}][/tex]
[tex]\left(\dfrac{5}{3}\right)^{-x+2x}=\dfrac{5^3}{3^3}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]\left(\dfrac{5}{3}\right)^{x}=\left(\dfrac{5}{3}\right)^{3}[/tex]
On comparing the exponents, we get
[tex]x=3[/tex]
Therefore, the value of x is 3.
It costs $20 to enter an amusement park and $0.50 to go on each ride. You have $24. How many rides are you able to go on?
Answer:
8 rides
Step-by-step explanation:
20 + .50x = 24
-20 -20
.50x = 4
/.50 /.50
x = 8
Answer:
8
Step-by-step explanation:
If you have $24 and you buy a $20 ticket to get in, you are left with four dollars.
Since each ride is $0.50 and that is half a dollar, you can multiply four times two. This gives you eight.
Therefore, you can ride 8 rides :)
What is the missing length?
11.9 in
area = 220.15 in?
Answer:
18.5 is your answer.
Step-by-step explanation:
Divide the area by 11.9 and you get 18.5
PLEASE HURRY!!!!!!!
Clay can run one lap around the track in 1/4 of an hour. how many hours will it take him to run 5 1/3 laps around the track.
Answer: 5.33
Step-by-step explanation: 5 laps in 5/4 of an hour to find the final 1/3 divide 1/4 by 1/3 to find how long it will take him to run that which is 1/12 so just add to the 5/4 time he has already ran to get 16/3 or 5.33333
Which statement is true about the graphed function?
3
O F(x) < 0 over the interval (-0, -4)
O F(x) < 0 over the interval (-0, -3)
O F(x) > 0 over the interval (-00, -3)
O F(x) > 0 over the interval (-00, -4)
2
х
-9
-12
Answer:
F(x)>0 over the interval [tex](-\infty,-4)[/tex]
Step-by-step explanation:
If you pay close attention to the intervals given in the options, you can see that they are talking about the region to the left of either x=-3 or x=-4. The only statements that makes sense is that:
F(x)>0 over the interval [tex](-\infty,-4)[/tex]
When they say F(x)>0, they mean that the graph is above the x-axis and that will only happen when the x-values that are to the left of x=-4, therefore the answer would be:
F(x)>0 over the interval [tex](-\infty,-4)[/tex]
Web Gamer sells texture packs for video games. They charge an initial $5.50 software set-up fee and $15 for each texture pack purchased through their website. Which equation represents the situation?
Answer:
y=15x+5.50
Step-by-step explanation:
the y intercept or initial fee is 5.50 as written in the problem and the slope is 15 and a key word for that is each. meaning that y=15x+5.50
In this picture B and Fare
midpoints.
A
B
5x - 4
23
F
E
x=[ ? ]
Answer:
10
Step-by-step explanation:
In triangle ACE, B and F are mid points of sides CA and CE respectively.
Therefore, BF is the mid segment of triangle ACE.
By Mid-segment formula:
AE =2BF
5x - 4 =2*23
5x - 4 = 46
5x = 46+4
5x = 50
x = 50/5
x = 10
Triangle GHI with vertices G(4, 1), H(5, -4), and I(2, -8) REFLECTED over the line y = x.
Answer:
[tex]G' = (1,4)[/tex]
[tex]H' = (-4,5)[/tex]
[tex]I = (-8,2)[/tex]
Step-by-step explanation:
Given
[tex]G = (4,1)[/tex]
[tex]H = (5,-4)[/tex]
[tex]I = (2,-8)[/tex]
Reflection: [tex]y = x[/tex]
Required
Determine the coordinates of G'H'I'
The following applies when a line A is reflected over [tex]y = x[/tex]
[tex]A = (x,y)[/tex]
[tex]A' = (y,x)[/tex]
i.e, we simply swap the positions of x and y
So, for:
[tex]G = (4,1)[/tex]
[tex]H = (5,-4)[/tex]
[tex]I = (2,-8)[/tex]
The reflections are:
[tex]G' = (1,4)[/tex]
[tex]H' = (-4,5)[/tex]
[tex]I = (-8,2)[/tex]
See attachment
Please help ASAP!! WILL GIVE BRAINLIEST!!!!! This will get my grade up to passing, please. Who ever helps tysm. :)
Answer:
J=18.5
K= 16
L= 17
M= 18
W= 625
X=645
Y= 729
Z= 1000
HEYYYY GUYYYSSS HELPP MEEE, ILL MARK YOU BRAINIEST. PLEEEAAASEEEE thankkyouu
Answer:
Step-by-step explanation:
A dependent variable in an expression is one whose value can be determined only when the value of other variable (i.e independent) is known.
A. The cost at the fitness center depends on the number of months (x).
The cost is the dependent variable, and number of months (x) is the independent variable.
f(x) = 100 + 40x
Example, the cost paid for 12 months can be determined as;
f(12) = 100 + 40(12)
= 100 + 480
= 580
Thus, $580 would be paid for 12 months at the fitness center.
B. The lettuce is sold at $1.69 per pound. The cost depends on the number of pounds of lettuce bought.
The cost is the dependent variable, while the number of pounds of lettuce (x) bought is the independent variable.
So that;
f(x) = 1.69x
The cost of 10 pounds of lettuce can be determined as;
f(x) = 1.69(10)
= 16.9
Thus, the cost of 10 lb of lettuce is $16.90.
help---------------
Answer:
C. (f - g)(x) = 3ˣ - 2x + 14
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Function NotationCombining Like TermsStep-by-step explanation:
Step 1: Define
f(x) = 3ˣ + 10
g(x) = 2x - 4
(f - g)(x) is f(x) - g(x)
Step 2: Find (f - g)(x)
Substitute: (f - g)(x) = 3ˣ + 10 - (2x - 4)Distribute -1: (f - g)(x) = 3ˣ + 10 - 2x + 4Combine like terms: (f - g)(x) = 3ˣ - 2x + 14a firefighter must cut a 2,700 foot rope into 75 equal pieces how long will each be?
Answer:
36
Step-by-step explanation:
75/2700=36
what is 6 9/32 as a decimal
n – 3 = -1 please solve this!!
Answer:
N = 2
Step-by-step explanation:
n - 3 = -1 Original
n ( -3 + 3 ) = ( -1 + 3 ) Add 3 on both sides
n = 2 Simplify
Check:
2 - 3 = -1 Replace
- 1 = -1 Solve
Correct!
Help I have problems to resolve that
5+(−3)(6x−5) using distributive property
Answer:
x= -1.8
Step-by-step explanation:
5+(-3)(6x-5)
the -3 goes into the 6x and -5
5+(-18x)+15
switch so like terms are together
5+(-5) these cancel out leaving you with
-18x+15-5
combine like terms
-18x+10
divide both sides by -18
x=-1.8
which is greater -4/18 or -6 / 27
Answer:
the first one is correct
Step-by-step explanation:
brainliest plzzzz
Answer:
They are equal.
Step-by-step explanation:
If you simplify, you'll get -0.22222... for both fractions
the sum of an even whole number and an odd whole number is always odd.
Answer:
wow, it is.
1+2=3
2+3=5
3+4=7
4+5= 9
5+6= 11
6+7= 13
and so on.
Step-by-step explanation:
Which value of p makes this equation true?
120 + 60p = 150 + 10p
6
1
3/5
5/3
Answer:
3/5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
I need help with this
Answer:
the second one.
top right graph.
Step-by-step explanation:
An angle is 58º less than its supplement. What is the measure of the angle?
Answer:
i think it is 122 degrees, as the solution would be to subtract 58 from 180
Step-by-step explanation:
180-58=122
angle1 = x
angle2 = x - 58
given,
these are supplementary angles
Therefore,
(x) + (x - 58) = 180
x + x - 58 = 180
2x - 58 = 180
2x = 180 + 58
2x = 238
x = 238/2
x = 119
angle1 = 119
angle1 = 119angle2 = 61
Diego pours 6.8 ounces of water from a full bottle. He estimates that he poured out 20% of the water in the bottle. About how much water was in the full bottle? Diego pours out 25% of the remaining water. About how many ounces did he pour the second time? Explain your reasoning.
Answer:
34 ounces were in the full bottle , The second time he poured about 7.48 ounces
Step-by-step explanation:
20 times 5 = 100 so,
6.8 times 5 = 34
PART 2
Diego poured out 20% wich is equal to 6.8 and if you subtract both pour's that he did you get 20.4. The you subtract that amount that he had already poured from the total wich gives you 13.6 and 5% of 13.6 is 0.68. Add 0.68 and 6.8 to get 7.48
I don't understand this?
Answer:
THE ANSWER IS B. If someone owes something the number is negative, and if someone has money the number is positive, MARK ME BRAINLIEST!!!!!!
Step-by-step explanation:
helppppppppppppppppppppp
Answer:
C: 108 Feet
Step-by-step explanation:
You just plug 3 in for t.
h(t) = -18(3)^2 + 18(3) + 216 = 0
-18(9) + 54 + 216 = 0
-162 + 54 + 216 = 0
-108 + 216 = 0
-108 + 216 = 108
So I believe I am correct.
I need that r d d d d d. D d d d d d d. D
Answer:
D is not a function.
Step-by-step explanation:
The first option is a function because it makes up a straight line. The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function. The third option is also a function because there is no more than one point for each x value. The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.
Answer:
D is not a function.
Step-by-step explanation:
The first option is a function because it makes up a straight line. The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function. The third option is also a function because there is no more than one point for each x value. The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.
dows any know what here goes ?
Media aritmetica ponderata a numerelor 1,5 si 6 cu ponderile 4,6 si 3 este egala cu...
Answer: b
Step-by-step explanation:
B because 10+1 is 11
2. Mrs. Ellison brought 30 cookies to the school picnic last year. This year she brought 45
cookies. What was the percent of change?
Answer:
15%
Step-by-step explanation:
45 - 30 = 15
Answer - 15%
Write a positive or negative integer that represents the situation.
A hiker climbs 900 feet up a mountain.
The integer___ represents the situation.
Answer:
X hope it helps
Which of the following relations is a function?
OA. (0,4), (-3,2), (8, 1), (-7, 2)
OB. (0,0), (-3, 3), (8, 1), (-3,5)
OC. (0,4), (-3, 6), (0, 3), (-7, 2)
OD. (8, 1), (-3, 4), (0, 1), (8, 2)