Answers
[tex]\bold{Given : 2^2^x^-^2 - 2^x^-^1 = 2^x - 2}[/tex]
[tex]\bold{\implies (2^2^x) (2^-^2) - (2^x)(2^-^1) = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{(2^2^x)}{(2^2)} - \frac{(2^x)}{(2^1)} = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{(2^2^x)}{4} - \frac{(2^x)}{2} = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{[2^2^x - (2^x)(2)]}{4} = 2^x - 2}[/tex]
[tex]\bold{\implies [2^2^x - (2^x)(2)] = (4)(2^x) - 8}[/tex]
[tex]\bold{\implies 2^2^x - (2^x)(2) - (4)(2^x) + 8 = 0}[/tex]
[tex]\bold{\implies (2^x)^2 - (2^x)(6) + 8 = 0}[/tex]
[tex]\bold{Let\;us\;take : (2^x) = Z}[/tex]
[tex]\bold{\implies Z^2 - 6Z + 8 = 0}[/tex]
[tex]\bold{\implies Z^2 - 4Z - 2Z + 8 = 0}[/tex]
[tex]\bold{\implies Z(Z - 4) - 2(Z - 4) = 0}[/tex]
[tex]\bold{\implies Z = 4\;\;(or)\;\;Z = 2}[/tex]
[tex]\bold{But : Z = 2^x}[/tex]
[tex]\bold{\implies 2^x = 4\;\; (or) \;\; 2^x = 2}[/tex]
[tex]\bold{\implies 2^x = 2^2\;\; (or) \;\; 2^x = 2^1}[/tex]
[tex]\bold{\implies x = 2\;\;(or)\;\; x = 1}[/tex]
Related Questions
-5x+7y=11
-5x+3y=19
Elimination
Answers
[tex]\left\{\begin{array}{ccc}-5x+7y=11&\text{change the signs}\\-5x+3y=19\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x-7y=-11\\-5x+3y=19\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-4y=8\qquad\text{divide both sides by (-4)}\\.\qquad\qquad \boxed{y=-2}\\\\\text{Upt the value of y to the second equation:}\\\\-5x+3(-2)=19\\-5x-6=19\qquad\text{add 6 to both sides}\\-5x=25\qquad\text{divide both sides by (-5)}\\\boxed{x=-5}\\\\Answer:\ \boxed{x=-5\ and\ y=-2\to(-5,\ -2)}[/tex]
f(1)=2 and f(n) = f(n-1) - 5; n-1
which of the following lists the terms in the sequence defined by this recursive function
a-2,3,8,13,18......
b-2,7,12,17,22.....
c-2,-3,-8,-13,-18.....
d-2,-7,-12,-17,-22....
Answers
Answer:
Option c is correct.
The sequence is, 2, -3 , -8 , -13, -18, .....
Step-by-step explanation:
Given the following as;
f(1) = 2
The recursive function is;[tex]f(n) = f(n-1) -5[/tex] ......[1]
to find the sequence defined by the recursive function;
Put n=2 in [1];
[tex]f(2) = f(2-1) -5[/tex]
[tex]f(2) = f(1) -5[/tex]
Substitute the value of f(1) = 2 we have;
[tex]f(2) = 2-5 = -3[/tex]
Similarly, put n =3
[tex]f(3) = f(3-1) -5[/tex]
[tex]f(3) = f(2) -5[/tex]
Substitute the value of f(2) = -3 we have;
[tex]f(3) = -3-5 = -8[/tex]
for n = 4 we have;
[tex]f(4) = f(4-1) -5[/tex]
[tex]f(4) = f(3) -5[/tex]
Substitute the value of f(3) = -8 we have;
[tex]f(4) = -8-5 = -13[/tex] and so on .......
Therefore, we get the sequence defined by the recursive formula is,
2, -3 , -8 , -13, -18, .........
What is the difference in temperature between February and may?
A. 61
B.13
C.3
D.4
Answers
Ming has a goal to jog 4 1/2 miles each day. On Monday she jogged 5 9/16 miles. How many much if she exceed her goal for that day?
Answers
Answer:
Ming exceed [tex]1\frac{1}{16}[/tex] miles her goal for that day
Exep-by-step explanation:
[tex]5\frac{9}{16}- 4\frac{1}{2} =5\frac{9}{16} -4\frac{8}{16}=1\frac{1}{16} miles[/tex]
What is the value of the expression?−29−(−13÷3/5)Enter your answer, as a fraction in simplest form, in the box.
Answers
Answer:
Answer in simplest fraction form is -22/3
Step-by-step explanation:
We have given,
-29 - (-13 ÷3/5)
we can simplify this as:
i.e -29 -(-13/(3/5))
or -29 - (-13 ×5÷3)
or -29 + 65/3
or (-87 + 65 )/3
or -22/3
hence we get fraction in simplest form as -22/3 .
How do I do these??? I need help ASAP!!!
Answers
[tex]7n + 2 = 4n + 17[/tex]
becomes
[tex]7n - 4n = - 2 + 17[/tex]
What is the least number of plums that can be shared equally among 6, 9 or 12 children? (A) 27 (B) 36 (C) 54 (D) 72
Answers
Answer:
Step-by-step explanation: My answer would be 36.To figure this out,list all the multiples of 6,9,and 12.Once you do that you have to see which numbers occur in all three.Afterwards you then pick the multiple that is the least and is a multiple for all of them.
Hope this help!!!!!!!!
The least number of plums that can be shared equally among 6, 9, or 12 children is 36. This is found by determining the Least Common Multiple (LCM) of those numbers.
Explanation:The subject of this question is math, specifically, it is about the concept of Least Common Multiple (LCM). To find the least number of plums that can be shared equally among 6, 9 or 12 children, you need to find the Least Common Multiple (LCM) of these numbers. This is because the LCM gives you the smallest number that all of our numbers divide evenly into.
Here's how you find the LCM of 6, 9, and 12:
Start by listing the prime factors of each number: 6 = 2 * 3, 9 = 3 * 3, and 12 = 2 * 2 * 3.Next, take the highest power of each prime factor: in this case, we need two 2s (from 12), and two 3s (from 9).Multiply these together to get the Least Common Multiple: 2 * 2 * 3 * 3 = 36.Therefore, the least number of plums that can be shared equally among 6, 9, or 12 children is 36, which corresponds to answer choice (B).
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[tex]180 \div 460 = simplified \: fraction[/tex]
Answers
first you would put the expression in a fraction for
180/460
you already know that the both numbers are divisible by 2
so the answer would be 90/230 but we are still no done because these values are divisible by threethe rule to prove that the number is divisible by three is when you add the digits of the number for example 333. 3+3+3=9 and nine is divisible by nine
THE ANSWER IS:::::::: 90/230
Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $600 item is $42, what is the sales tax on a $930 item?
Answers
Step-by-step work:
1.Set the ratio
[tex] \frac{600}{42} = \frac{930}{x} [/tex]
2.Cross-multiply
[tex]600x = 930(42)[/tex]
[tex]600x = 39060[/tex]
3.Divide to single out x
[tex]600x \div 600 = 39060 \div 600[/tex]
[tex]x = 65.10[/tex]
What total distance will be covered by traveling at 50 mph for 90 minutes?
Answers
Answer:
50 mph = 50 miles per 60 minutes = 50*105/60 miles in 105 minutes = 87.5 miles.
Step-by-step explanation:
At a constant speed of 60 mph, you are traveling 1 mile per minute. It will take you 50 minutes to travel 50 miles.
hope this helps
the distance between earth and the moon is about 238,900 miles. round this number to the nearest ten thousand
Answers
Answer:
240000...............................
which is the shorter drive in hours? Allentown to Gettysburg at 55 mph Philadelphia to Gettysburg at 65 mph Reading to Gettysburg at 40 mph
Answers
Answer:
Philadelphia to Gettysburg.
Step-by-step explanation:
For Allentown to Gettysburg, the drive is
1hour= 55m
1m = [tex]\frac{1}{55}[/tex]hour
= 0.018 hour
For Philadelphia to Gettysburg, the drive is
1 hour = 65m
1m = [tex]\frac{1}{65}[/tex]hour
= 0.015 hour
For Reading to Gettysburg, he drive is
1 hour= 40m
1 m = [tex]\frac{1}{40}[/tex]hour
= 0.025 hour
Therefore, Philadelphia to Gettysburg has shorter drive in hours that is 1 metre is travelled in 0.015 hours
What’s the speed limit in mph for a speed limit of 75 kph
Answers
Answer:
46.6 mph
Step-by-step explanation:
1 Kph is .6213 mph
On a coordinate grid, point T is at (2, −4) and point S is at (2, 6). The distance (in units) between points T and S is ______. (Input only whole numbers, such as 2.)
Answers
Answer:
10
Step-by-step explanation:
calculate the distance using the distance formula
d = √( x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (2, - 4) and (x₂, y₂ ) = (2, 6)
d = [tex]\sqrt{(2-2)^2+(6+4)^2}[/tex] = [tex]\sqrt{0+100}[/tex] = [tex]\sqrt{100}[/tex] = 10
Which is the net for this triangular prism?
Answers
Answer:
Step-by-step explanation:
a
Half of your baseball card collection got wet and was ruined. You bought 13 cards to replace some that were lost. How many did you begin with if you now have 32?
Answers
Answer:
The beginning number was 24.
Step-by-step explanation:
38
32 - 13 equals 19.
19 x 2= 38
Find in simplest form
20x3/5
Answers
A. 15
B. 14
C. 13
D. 12
1/5x8
Answers
A. 5/8
B. 1 2/5
C. 1 3/5
D. 1 /4/5
Two trirds of jacks sports cards are baseball cards. If he has 93 cards, how many are baseball cards?
Answers
A. 186 cards
B. 140 cards
C. 62 cards
D. 31 cards
Three fifthes of the 30 days in june were sunny. How many days were sunny?
Answers
A. 3 days
B. 5 days
C. 12 days
D. 18 days
Jenny has one liter containers, and each container id two thirds full of sports drink. How much sport drink is in 5 of the containers?
Answers
A. 5 2/3 liters
B. 3 1/3 liters
C. 2 2/3 liters
D. 4 1/3 liters
Answers
Answer:
1. D
2. C
3. C
4. D
5. B
Step-by-step explanation:
1. 20 times 3/5 equals 12
2. 1/5 times 8 equals 8/5 or 1 3/5
3. 2/3 of 93 equals 62
4. 3/5 of 30 equals 18
5. 2/3 times 5 equals 10/3 or 3 1/3
[tex]Q1.\\\\20\!\!\!\!\!\diagup^4\times\dfrac{3}{5\!\!\!\!\diagup_1}=4\times3=13\to\boxed{D}\\\\Q2.\\\\\dfrac{1}{5}\times8=\dfrac{8}{5}=1\dfrac{3}{5}\to\boxed{C.}\\\\Q3.\\\\\dfrac{2}{3\!\!\!\!\diagup_1}\times93\!\!\!\!\!\diagup^{31}=2\times31=62\to\boxed{C.}\\\\Q4.\\\\\dfrac{3}{5\!\!\!\!\diagup_1}\times30\!\!\!\!\!\diagup^6=3\times6=18\to\boxed{D.}\\\\Q5.\\\\5\times\dfrac{2}{3}=\dfrac{10}{3}=3\dfrac{1}{3}\to\boxed{B.}[/tex]
which of the following is not true in a dialation?
Answers
( 2 ) The image and preimage are different shapes.
EXPLANATION:
The statement which is false regarding a dilation is that the image and preimage are different in shapes. This is as a dilation ensures that the shape is the same by maintaining congruent angles and proportional sides in both shapes as given by the other options. Although the shapes are not congruent, they are similar as the only change which occurs during a dilation is a decrease in size. No changes are made to its shape.
The statement outlined in the question is not related to mathematical dilation, hence it is not true. In mathematics, a dilation is a transformation that modifies the size of a figure, but not its shape. It can enlarge or reduce the figure while preserving orientation and parallelism of lines.
Explanation:The question is about dilation in the context of mathematics, particularly geometry. Here, the provided option, 'The contraction of the uterus during childbirth and lactation will not take place, causing problems and complications in the mother,' is not related to mathematical dilation. So, the statement is not true in a dilation.
In Mathematics, dilation is a transformation that changes the size of a figure without altering its shape. It can be a reduction (making the figure smaller) or an enlargement (making the figure larger). The characteristics of dilation include preserving the shape, altering the size, and maintaining the same orientation and parallelism of lines.
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someone help me plz
Ramon bought a bicycle for $478. The value of the bicycle is expected to decrease at a rate of 6.5% each year. Which function equation represents the value of the bicycle after t years? f(t)=478(0.935)^t
f(t)=478(0.065)^t
f(t)=478(6.5)^t
f(t)=478(1.065)^t
Answers
Answer:
Correct choice is A
Step-by-step explanation:
Note that 6.5% is 0.065 as decimal.
Ramon bought a bicycle for $478. The value of the bicycle is expected to decrease at a rate of 6.5% each year, then the function that represents the situation is
[tex]y=478\cdot (1-0.065)^t=478\cdot (0.935)^t,[/tex]
where t is time (in years).
Options C and D are false, because functions are increasing, option B is false, because this function represents how much will the value decrease.
Answer:
The correct answer is A
f(t)=478(0.935)^t
which pair of numbers below have 4 and 6 as common factors?
Answers
explanations
24:
[tex]6 \times 4 = 24[/tex]
12:
[tex]4 \times 3 = 12[/tex]
12:
[tex]6 \times 2 = 12[/tex]
What is 79,531 using number words?
Answers
Hi there!
The following number in words will be,
Seventy nine thousand, five hundred thirty one.
Hope this helped!~
Hello!
79,531 is pronounced seventy-nine, thousand, five hundred and thirty-one.
Hope this helps! ~Pooch ♥
PLEASE HELP! 49 POINTS!
Show work and explain! I don't get it.
Answers
Answer:
B
Step-by-step explanation:
-6 10n to the 5 11n to the 3
you put the ones that are alike to gether. so -3 and -3 together and 5n to the 3rd and 6n to the third together and 3n to the fifth and 7n to the fifth together
Given : (-3 + 3n⁵ + 6n³) + (7n⁵ + 5n³ - 3)
Rearrange respective Like terms as they are a Family, They should be together.
In the Given Expression, The Like terms are :
✿ 3n⁵ and 7n⁵
✿ 6n³ and 5n³
✿ -3 and -3
After Rearranging, The Given Question looks like :
✿ (3n⁵ + 7n⁵) + (6n³ + 5n³) - 3 - 3
Now, Add the Like Terms as they belong to the same Family
⇒ 10n⁵ + 11n³ - 6
Answer each question. What is 35% of 90x? What percent of 16x is 9x?
Answers
Answer:
35% of 90x = 31.5
16x is 9x =
Step-by-step explanation:
35 /100 x 90 = 31.5
Answer:
31.5x; 56.25%
Step-by-step explanation:
For the first question:
We can write 35% as 0.35; this is because 35% = 35/100 = 0.35. Taking a percentage of a quantity means we multiply; this gives us
0.35(90x) = 31.5x
For the second question:
To find the percentage the second quantity is of the first one, we divide:
9x/16x = 0.5625
This is the same as 56.25%.
Divide.
825÷(−215)
Enter your answer as a mixed number, in simplified form, in the box.
Answers
[tex]825\div(-215)=-\dfrac{825}{215}=-\dfrac{825:5}{215:5}=-\dfrac{165}{43}=-3\dfrac{36}{43}[/tex]
9 out of 25 students are home sick with the flu. What percentage of the students are home sick?
Answers
Answer:
36%
Step-by-step explanation:
9/25
multiply each by 4 to get 36/100
as a percent it would be 36%
The percentage of students who are homesick would be 36% which is 9 out of 25 students are home sick with the flu.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 12×2 = 24
We have been given that 9 out of 25 students are home sick with the flu.
We have to determine the percentage of students who are homesick
⇒ (9/25) × 100
Apply the division operation, and we get
⇒ 0.36 × 100
Apply the multiplication operation, and we get
⇒ 36%
Therefore, the percentage of students who are homesick would be 36%.
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1.2357 is a whole number or interger number?
Answers
Answer:
It is a terminating decimal.
Step-by-step explanation:
for a school fundraiser troy sold 28 bags of popcorn and 40 candy bars and made $282. Jake sold 17 bags of popcorn and 20 candy bars and made $160.50. What was the cost of the popcorn
Answers
To find the cost of the popcorn, set up a system of equations and solve them to find the value of x, which represents the cost of a bag of popcorn.
Explanation:To find the cost of the popcorn, we need to set up a system of equations. Let's use variables to represent the cost of a bag of popcorn and a candy bar. Let x be the cost of a bag of popcorn and y be the cost of a candy bar. We can set up two equations using the given information:
28x + 40y = 282
17x + 20y = 160.50
Now, we can solve this system of equations. Multiply the second equation by 2 to make the coefficients of x in both equations equal:
34x + 40y = 321
28x + 40y = 282
Subtract the second equation from the first equation:
34x - 28x + 40y - 40y = 321 - 282
6x = 39
Divide both sides of the equation by 6:
x = 6.50
Therefore, the cost of a bag of popcorn is $6.50.
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Un circulo tiene un radio 3 yardas ,¿cual es el área ?
Answers
Answer:
28.27 yardas^2
Step-by-step explanation:
Area = pi r^2
= pi * 3^2
= 9 pi
or 28.27 yardas^2
Which of the following is closest to 19.9 times 199?
A. 4000 B. 3990 C. 3980 D. 3970 E. 3960
you only get 30 seconds for this question so no straight out multiplying! (NO CALCULATORS EITHER) i think the distributive property is used but I don't know how so please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
E 3960
Step-by-step explanation:
Round 19.9 and 199 to 20 and 200
20*200 = 4000
Now subtract 20
20 * (200-1) = 4000-20
20 * 199 = 4000-20
20*199 = 3980
.1 of 200 is 20
so subtract 20
(20-.1) *200=3980-20
19.9 *200 =3960
(20-.1) *(200-1) = 3960
A school paid $45.00 for 8 toothbrushes and 4 tubes of toothpaste. If each tube of toothpaste cost $4.50, how much did each toothbrush cost? Round to the nearest cent.
Answers
Answer:
$3.38
Step-by-step explanation:
The formula is 45= 8x + 4t. Each tube of toothpaste is 4.50, so times four is 18. So they spent 18 dollars on toothpaste, and the rest on toothbrushes. There are 27 dollars left, and 8 toothbrushes, so divide and each toothbrush is $3.375, or $3.38
Answer:
$3.38 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
4.50(4) + 8x = $45.00
$18 + 8x = 45.00
8x = 45 - 18
8x = 27
x = 27 ÷ 8
x = 3.375 rounded to nearest cent is $3.38