Answers
[tex] {36}^{2x + 5} = {216}^{x - 1} [/tex]
[tex] {6}^{2(2x + 5)} = {6}^{3(x - 1)} [/tex]
[tex] {6}^{(4x + 10)} = {6}^{(3x - 3)} [/tex]
Since bases i.e 6 are same exponents are equal
4x+10= 3x-3
4x-3x = -3-10
x= -13
Answer:
x = -13
Step-by-step explanation:
36 = 6^2
216 = 6^3
36^(2x + 5) = 6^(2)^(2x + 5)
When taking an exponent to an exponet: multiply the exponents
36^(2x + 5) = 6^(4x + 10)
216^(x - 1) = 6^(3)^(x - 1)
When taking an exponent to an exponet: multiply the exponents
216^(x - 1) = 6^(3x - 3)
-----------------------------
Therefor
6^(4x + 10) = 6^(3x - 3)
Since the bases are the same the exponents are equal
4x + 10 = 3x - 3
Subtract 3x from both sides
x + 10 = -3
subtract 10 from both sides
x = -13
Related Questions
which statement is true?
Answers
Answer:
A. The slope of Function A is greater than the slope of Function B.
Step-by-step explanation:
The slope of a function can be defined as rise/run. In Function A, the rise/run is 4. The slope in Function B is much easier to see: it is 2. Because 4 is greater than 2, Function A has a greater slope than Function B.
The Hamilton’s are installing a new pool in their backyard .The scale drawing below represents the new pool,where 1 centimeter represents 5 feet.
Answers
6cm X 5 = 40ft
20ft : 40ft pool
20x40 = 800 square ft
900sq ft - 800sq ft
100 square feet
The following set of data represents the ages of the women who won the Academy Award for Best Actress from 1980 - 2003:
31 74 33 49 38 61 21 41 26 80 42 29
33 35 45 49 39 34 26 25 33 35 35 28
Make frequency table using # of classes as per the following criteria:
i) if you are born in Jan, Feb, Mar: No of classes = 5
ii) if you are born in Apr, May, Jun: No of classes = 6
Answers
Answer:
Step-by-step explanation:
Given the data :
Using 6 classes :
Class interval ____ Frequency
21 - 30 _________ 6
31 - 40 _________ 10
41 - 50 _________ 5
51 - 60 _________ 0
61 - 70 _________ 1
71 - 80 _________ 2
F(x) = x3 + x2 -8x - 6
According to the Fundamental Theorem of Algebra, how many solutions/roots will there be?
According to Descartes' Rule of Signs, what are the possible combinations of positive, negative, and/or complex roots will there be?
Using the Rational Root Theorem, list all the possible rational roots.
Use a combination of Synthetic Division, Factoring, and/or the Quadratic Formula to find all the roots. PLEASE SHOW ALL WORK!
This is my 4th time posting this and no ones helping. Please someone who is smart help me out lol
Answers
Answer:
Given function:
f(x) = x³ + x² - 8x - 6This is the third degree polynomial, so it has total 3 roots.
Lets factor it and find the roots:
x³ + x² - 8x - 6 = x³ + 3x² - 2x² - 6x - 2x - 6 = x²(x + 3) - 2x(x + 3) - 2(x + 3) = (x + 3)(x² - 2x - 2) = (x + 3)(x² - 2x + 1 - 3) = (x + 3)((x - 1)² - 3) = (x + 3)(x - 1 + √3)(x - 1 - √3)The roots are:
x = -3x = 1 - √3x = 1 + √3It has highest degree 3 so 3 roots
1 positive and 2 negative rootsLets find
x³+x²-8x-6=0x²(x+3)-2x(x+3)-2(x+3)=0(x+3)(x²-2x-2)=0(x+3)(x-2.732)(x+0.732)=0Roots are
-3,2.732,-0.732I need help please asp !!!!
Answers
identify a transformation of a function f(x)=x^2 by observing the equation of the function g(x)=5(x)^2
Answers
Answer:
Thus the function g is the function f stretched vertically by a factor 5.
Step-by-step explanation:
Multiplication of a function by a constant:
When a function is multiplied by a constant a > 1, the function is stretched vertically by a factor of 5.
In this question:
f(x) = x^2
g(x) = 5x^2
Thus the function g is the function f stretched vertically by a factor 5.
Which absolute value equation represents the graph
Answers
Answer:
the first one
Step-by-step explanation:
Hope this helps!
x^(2)+y^(2)+14x+18y+114=0
i will give u brainliest and my eternal love
Answers
Answer:
(x+7)^2+(y+9)^2=16
Step-by-step explanation:
This is the equation written in standard form, I'm not sure if that's what you wanted.
The formula to find the area of a rectangle is: area = length x width.
Mason put a garden in his yard in the shape of a rectangle.
The garden is 7 feet long and 15 feet wide.
What is the area of the garden?
A. 22 square feet
B. 44 square feet
C. 75 square feet
D. 95 square feet
E. 105 square feet
Answers
Explanation : 7 x 15 = 105
What is the difference between a bar chart and a histogram?
Answers
Answer:
In simple terms, a bar chart is used in summarizing categorical data, where a histogram uses a bar of different heights, it is similar to the bar chart in many terms but the histogram groups the numbers into the ranges while representing the data.
bar chart is a graph in the form of boxes of different heights, with each box representing a different value or category of data, and the heights representing frequencies.
but,
Histogram is graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency.
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.)
Answers
Answer:
0.42ft/mn
Step-by-step explanation:
we have the following information to answer this question
dv/dt = 40 feet
height = 11 ft
volume = 1/3πr²h
= 1/3π(h/2)²h
= 1/3πh³/4
= πh³/12
dv/dt = π3h²/12
= πh²/4
dh/dt = 4/πh²dv/dt
= 4(40)÷22/7(11)²
= 160/380.29
= 0.42 ft/min
The height of the pile is therefore increasing by 0.42ft/min at a height of 11 feets
You're at the aquarium, staring into a large exhibit, when you look to your left and slightly downward and you see a jellyfish. You notice that the jellyfish body looks like a very wide, upside-down parabola. What is a possible equation that models the jellyfish, assuming your eyes are at (0, 0)?
a) -2(x + 3)2 + 4
b) -3(x - 2)2 - 1
c) -25(x + 1)2 - 5 .
d) 3(x-4)2 + 2
e) Answer is not there
Answers
Step-by-step explanation:
c is an upside down parabola but it is not wide, it is very then so maybe e?
PLEASE HELPPP
A perfume bottle is in the shape of a cone. Its diameter is 13 centimeters and its height is 21 centimeters. What is the volume of the perfume bottle? Round to the nearest tenth.
Answers
Answer:
hello hello hello hèllo
Answer:
V = 1/3 pie r2 h
= 1 /3 x 22/7 x 6.5 x 6.5 x 21
= 929.5 cm^3
two thirds of a number is negative six. find the number
Answers
Answer:
-9
Step-by-step explanation:
Two-thirds of a number is negative six. The number is -9. Let the number is x, 2/3x =-6, x=-6x3/2=-9.
Chris was given 1/3 of the 84 cookies in the cookie jar. He ate 3/4 of the cookies that he was given. How many cookies did Chris eat?
Answers
Answer:
21 cookies
Step-by-step explanation:
First we know that Chris was given a third of 84 cookies so we can start working on this problem by figuring out what a third of 84 is. We can do this by multiplying 84 by 1/3 or just dividing by 3, which gives us: 84/3 = 28
So now we know that Chris was given 28 cookies, we can figure out what 3/4 of that is to work out how many cookies he ate. 28 x (3/4) = 21 cookies.
Chris ate 21 cookies.
Hope this helped!
Answer:
21 cookies
Step-by-step explanation:
1/3 × 84 = 28
3/4 × 28 = 21
Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
35 is the value of x
can anyone prove this:
1+1=3
Answers
Answer:
indeed
Step-by-step explanation:
just carry the one when adding
Step-by-step explanation:
1 = 1
41 – 40 = 61 – 60
16 + 25 – 40 = 36 + 25 – 60
4² + 5² – 2 * 4 * 5 = 6² + 5² – 2 * 6 * 5
(4 – 5)² = (6 – 5)²
4 – 5 = 6 – 5
4 = 6
2 = 3
1 + 1 = 3…proved
baby im jealous....
finish it
Answers
A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $20.00 to prepare, and it costs $125.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs
Answers
Answer:
25
Step-by-step explanation:
From the given information;
Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.
= 1000x
Thus, the required number of hours it will take can be computed as:
[tex]\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}[/tex]
cost per hour = 125
If each plate costs $20 to make, then the total number of plate will equal to 40x
∴
The total cost can be computed as:
[tex]C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)[/tex]
[tex]C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)[/tex]
At C'(x) = 0
[tex]\dfrac{12500}{x^2} = 20[/tex]
[tex]\dfrac{12500}{20} = x^2[/tex]
[tex]x^2= 625[/tex]
[tex]x = \sqrt{625}[/tex]
x = 25
[tex]C'' (x) = -12500 \times \dfrac{-2}{x^3} +0[/tex]
[tex]C'' (x) = \dfrac{25000}{x^3}[/tex]
where; x = 25
[tex]C'' (x) = \dfrac{25000}{25^3}[/tex]
C''(x) = 1.6
Thus, at x = 25, C'' > 0
As such, to minimize the cost, the printer needs to make 25 metal plates.
When too many variables are categorized in an analysis, several potential issues may occur. Which of the following is not one of the issues that may occur?
A. model performance suffers.
B. rarely occurring categories may not be captured accurately.
C.difficulty in differentiating among observations.
D. an increase in the number of categories as the data set becomes larger.
Answers
Answer: D. an increase in the number of categories as the data set becomes larger.
Step-by-step explanation:
When too many variables are categorized in an analysis, there are different potential issues may occur, some of these issues include:
• model performance suffers.
• rarely occurring categories may not be captured accurately.
• difficulty in differentiating among observations.
It should be noted that an increase in the number of categories as the data set becomes larger isn't one of the issues. Therefore, the correct option is D.
PLEASE HELP EASY MATH
Tomas needs lumber to make corner braces for a piece of furniture he is building. He cuts 4 feet from a board that is 8 feet long. With the wood he has left, Tomas makes 18 corner braces of equal size.
How many inches of wood does each brace use? - in
Answers
Answer: each brace is 2 & 2/3 inches long
=====================================================
Explanation:
"he cuts 4 feet from a board that's 8 feet long" means that he has 8-4 = 4 feet to work with. This converts to 4*12 = 48 inches.
Next, we cut that into 18 equal pieces
48/18 = 8/3 = 2 & 2/3
This is approximately 2.667 inches
write a rational number between root2 and root3
Answers
Answer:
prational number between root2
Solve the system using substitution.
y = 4x – 8
y = 2x + 10
Answers
Answer:
9,28
Step-by-step explanation:
see image below:)
0=2x-18
By moving x to other side
2x=18
Dividing by 2
X= 9
Putting the value of x in any equation
y=4(9)-8 = 36-8 =28
Y=28
URGENT PLEASE ANSWER
Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio
Cleopatra : Dalila : Ebony =
5 : 7 : 8
A) How many dollars do they have in total?
B) Dalila spends 12$ on a hat, how many dollars does she have left?
Answers
Answer:
A)$60
B)$9
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW
Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio
Cleopatra : Dalila : Ebony =
5 : 7 : 8
Cleopatra has $15.
A) How many dollars do they have in total?
B) Dalila spends 12$ on a hat, how many dollars does she have left?
A)
Total ratio=(5 +7 +8)= 20
Cleopatra has $15.
Let X = total money
Ratio of Cleopatra= 5/20 ×X=15
5X /20 = 15
5X= (15×20)
X= $60
They have $60 in total
B) ratio of Dalila= 7/20 × 60 = $21
But 12$ was spent by Dalila on a hat
Then Dalila will have ($21 - 12$) Left
= $9
Select the correct answer
Consider event A and event 8. What is the probability that event Boccurs, given that event A has already occurred?
OA
PB n A)
PLA). P(8)
Ов,
P(BA)
P(A)
OC. P(BA)
P(8)
OD
PIBUA)
P(B)
Reset
Next
Answers
Answer:
[tex]P(B|A)[/tex]
Step-by-step explanation:
Probability notation:
Suppose that we have two events, event A and event B. The probability of event B occuring, considering that event A has occurred, is given by:
[tex]P(B|A)[/tex], which is the answer to this question.
A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4blue marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
Answers
Answer:
5/12 is already in simplest form
Step-by-step explanation:
12m = 5r + 3y + 4b
red is chosen = 5r / 12 = 5/12
Step-by-step explanation:
the answer is 5/12. It's quite simple
Robin saved money during the months of July and August can some one help me
Answers
Step-by-step explanation:
(340*20)-3
HOPE IT HEPL U
1. p-4= -9+p
2. 4m-4= 4m
Extra Credit, need help
Answers
Answer:
1. No solution
2. No solution
Step-by-step explanation:
1. p-4=-9+p
-4=-9
No solution
2. 4m-4=4m
-4=0
No solution
If this helps please mark as brainliest
find the smallest number by which 2925 should be divided to be a perfect square
Answers
Answer: 13
Step-by-step explanation:
Given
The number is 2925
The prime factorization of 2925 is
[tex]\Rightarrow 2925=3\times 3\times 5\times 5\times 13\\\Rightarrow 2925=3^2\times 5^2\times 13[/tex]
To make 2925 a perfect square, we have to eliminate 13 from it, so divide 2925 by 13 to make it a perfect square
The perfect Sqaure becomes [tex](3\times 5)^2=225[/tex]
translate into algebraic expression " the sum of five times m and n
Answers
"Five times" means
5
(
...
)
,
"the sum of a number, say
x
, and
−
3
", means"{(x+(-3)}=(x-3)#.
Taking all these together, the reqd. Algebraic Expression turns out to be
5
(
x
−
3
)
.
