Answers
Write both sides as powers of 16:
[tex]\log_4(2-x)=\log_{16}(13-4x) \implies 16^{\log_4(2-x)}=16^{\log_{16}(13-4x)}[/tex]
Since 16 = 4², we can rearrange the left side to get
[tex]16^{\log_4(2-x)}=(4^2)^{\log_4(2-x)}=4^{2\log_4(2-x)}=4^{\log_4(2-x)^2}[/tex]
Then, recalling that [tex]b^{\log_ba}=a[/tex], we have
[tex]4^{\log_4(2-x)^2}=16^{\log_{16}(13-4x)}\implies(2-x)^2=13-4x[/tex]
Now solve for x :
[tex](2-x)^2=13-4x[/tex]
[tex]4-4x+x^2=13-4x[/tex]
[tex]x^2-9=0[/tex]
[tex](x+3)(x-3)=0[/tex]
[tex]\implies x=-3\text{ or }x=3[/tex]
Notice that if x = 3, then log₄(2 - x) = log₄(-1) is undefined, so we throw out this solution. We don't run into this problem with x = -3, so that's the only (real) solution.
Related Questions
Jack swam 8 taps. He swam 6 fewer laps than Lea.
How many laps did Lea swim?
pls quick
Answers
Answer:
Lea swam 14 laps.
Step-by-step explanation:
8+6=14
Jon mixes 1/2 cup of milk and 1 cup of flour to make pancake batter .he uses 1/6 of the batter to make each pancake .how many pancakes can he make
Answers
Answer:
Jon can make 9 pancakes.
Step-by-step explanation:
first add the milk and flour volumes and gives you 1 1/2. After that divide that by 1/6 which gives you 9 so Jon can make 9 pancakes.
The table represents a proportional relationship.
x y
11 2
22 4
33 6
The graph represents another proportional relationship.
(Picture)
Which equation represents the lower unit rate of these two relationships?
A. y=2/9x
B. y=1/4x
C. y=1/5x
D. y=2/11
Answers
Answer:
the answer is d y=2
_ x
11
Step-by-step explanation:
I got it right on the test
2/11 is lower than 2/9, therefore the equation that will represent a lower unit rate (k) of both relationships given is: D. y=2/11
A proportional relationship between variable y and x can be expressed as:
y = kx
Where,k is the unit rate/constant of proportionality.
Therefore,k = y/x
Thus, find the equation for the table and the graph respectively in order to determine which equation represents the lower unit rate.
Equation for the table using a pair of coordinates, say (11, 2):
Find, unit rate (k) by substituting x = 11, and y = 2 into k = y/x
Thus:k = 2/11
Plug in the value of k = 2/11 into y = kx
The equation for the table is:
y = 2/11x
Equation for the graph using a point on the line, say (9, 2):
Find, unit rate (k) by substituting x = 9, and y = 2 into k = y/x
Thus:k = 2/9
Plug in the value of k = 2/9 into y = kx
The equation for the table is:y = 2/9x
In conclusion, 2/11 is lower than 2/9, therefore the equation that will represent a lower unit rate (k) of both relationships given is: D. y=2/11
Learn more here:
https://brainly.com/question/2548051
PLEASEE HELPP!! WILL MARK BRAINLIST!! What is the geometric mean of 2 and 50?
Answers
_______
X=V (2) (50)
_____
-> x = V 100
X= 10
The pizza shop is running a special: 2 medium pizzas
for $6.99 each. How much would it cost to by 12
pizzas?
Answers
Answer:
41.94
Step-by-step explanation:
12 divided by 2 is 6 and six times 6.99 gets you your answer of 41.94
Answer:
$72.00
Step-by-step explanation:
Lets round $6.99 to $7.00. Now we have an easier number to work with.
To find the total price of 12 , we need to multiply $7.00 by 12.
⇒ $7.00 x 12 = $84.00
Since we added 1 cent to $6.99 and multiplied by 12, we need to sutract 1 times 12.
1 x 12 = 12
$84 - $12 = $72.00
4 ( 11 + 7 ) = ? + 28
Answers
Let the missing number be x .
Then :-
[tex]4(11 + 7) = x + 28[/tex]
[tex]4 \times 18 = x + 28[/tex]
[tex]72 = x + 28[/tex]
[tex]x + 28 = 72[/tex]
[tex]x = 72 - 28[/tex]
[tex]x = 44[/tex]
Therefore , 4 ( 11 + 7 ) = 44 + 28 .
No 2 please.Quick. HELP ASAP
Answers
Part A
We have 20 cards, 4 of which are kings (one of each suit). The probability of getting a king on the first draw is 4/20 = 1/5.
Answer: 1/5===========================================================
Part B
We have 20-4 = 16 cards that aren't a king out of 20 total.
The probability of getting a non-king card is 16/20 = 4/5
After selecting the first card and not putting it back, we have 20-1 = 19 cards left. Four of which are a king, so 4/19 represents the probability of getting a king on this draw.
So (4/5)*(4/19) = 16/95 is the probability of getting a king on the second draw where the first draw is not a king.
Answer: 16/95===========================================================
Part C
16/20 is the probability of getting no kings on the first draw
15/19 is the probability of getting no kings on the second draw (notice I stepped the values down by 1)
14/18 is the probability of getting no kings on the third draw
Multiplying out the fractions gives
(16/20)*(15/19)*(14/18) = 28/57
I skipped a few steps when multiplying the fractions but you get the idea.
The probability of drawing 3 cards, none of which are a king, is 28/57
Subtract this from 1 to get the complementary probability
1-(28/57) = 57/57 - 28/57 = (57-28)/57 = 29/57
This works because we have two choices: either we get no kings, or we get at least one king. So that's why the two events are complementary and their probabilities add to 1.
Answer: 29/57A student pushes a the same cart with the same 50N of Force over the same distance of 10m, but on this occasion was timed in 5s by their parents who were in a hurry to get home. What was their power? *
Answers
Answer:
100W
Step-by-step explanation:
Power = Work done / time
Work done = force × distance
given,
force = 50Ndistance = 10mtime = 5sWork = 50 × 10
Work = 500J
Power = 500 / 5
Power = 100W
What are the slope and y- intercept of the linear equation
4x-6y=24
Answers
Answer: 7 = 2/3 + (-24/6)
(4k – 2) (k + 4)
O 44² + 14k - 8
O 4K² - 8
O 5k + 2
0 42² + 16k - 8
Answers
Answer:
4k^2 + 14k - 8
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)
A bookstore packs 6 books in a box. The total weight of the books 14 1/4 pounds. If each book has the same weight, what is the weight of one book?
Answers
Answer:
2.375 or 2 3/8
Step-by-step explanation:
You want to do total weight over total number of items.
14 1/4 / 6 books = 2.375
Answer:
14.25 / 6 = 2.375 or 2 3/8
Y = -(X +5) + X +4 if X = -4. Y = ?
Answers
Answer:
y=-1
Step-by-step explanation:
how do you estimate
Answers
Answer:
The general rule for estimating is to look at the digit to the right of the digit you want to estimate. Estimating or rounding to the nearest whole number means looking at the digit to the right of the decimal. If you see a digit greater than 5, round up, and if it's less than 5, round down.
Step-by-step explanation:
Expand and simplify: 2(x-4^2)+7
Answers
2x-25
Explanation:
2(x-4^2)+7
1) Find the exponent
=2(x-16)+7
2) Use the distributive property on the parentheses
=2x-32+7
3) Subtract 32 and 7
=2x-(32-7)
=2x-25
I hope this helps! Please comment if you have any questions.
what is 5x+19-2(x-7)=5 (2x+5)+22
Answers
HELPP PLZZ ASAP I DON'T UNDERSTAND AND I SUCK AT MATH HELPP ASAP GIVING POINTS AND BRAINLIEST!!!!
Answer the following questions. When you are finished, submit this test to your teacher for full credit.
1. The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
(c) Explain your answer to Part 1b.
Answer:
2. A line goes through the points, and .
(a) What is the slope of the line? Show your work.
(b) Write the equation of the line in point-slope form. Show your work.
(c) Write the equation of the line in slope-intercept form. Show your work.
Answer:
3. Line A is represented by the equation, .
(a) Write in slope-intercept form the equation of a line that is parallel to Line A and passes through the point, . Show your work.
(b) Write in slope-intercept form the equation of a line that is perpendicular to Line A and passes through the point, . Show your work.
Answer:
Answers
Answer:B
Step-by-step explanation:
I HAVE GOT YOU!
What is HCF of 5a and 15a
Please help me I don’t understand
Answers
Answer:
5a.
Step-by-step explanation:
The HCF is short for Highest Common Factor.
Write the 2 expressions in factor form:
5a = 5 * a
15a = 5 * 3 + a
Note that 5 and a are common to both sets of factors, so the HCF = 5a.
SENDDD HELPPP PLZZZ ASAP
Answers
Answer:
the answer is C
Step-by-step explanation:
hope this helps
Hey several brings five breadsticks to the table to people they share them equally how many do they get
Answers
what is the slope of (2, 3) and (4,6)
Answers
Answer:
Slope equals 1 1/2
Answer:
3/2 i think
Step-by-step explanation:
Christa has a rectangular rug in her living room that is 6 feet wide and 8 feet long. She decides that the rug is too small for the room, so she orders a new one that covers twice as much area. If the new rug is 1.5 times as wide as the original rug, how long, in feet, is the new rug?
Answers
Given:
A rectangular rug in her living room that is 6 feet wide and 8 feet long.
She orders a new one that covers twice as much area.
New rug is 1.5 times as wide as the original rug.
To find:
The length of new rug.
Solution:
We have,
Length of rug = 8 feet
Width of rug = 6 feet
Area of rug is
[tex]Area=length \times width[/tex]
[tex]A_1=8 \times 6[/tex]
[tex]A_1=48\text{ sq. feet}[/tex]
Area of new rug is twice of area of original rug.
[tex]A_2=2\times A_1[/tex]
[tex]A_2=2\times 48[/tex]
[tex]A_2=96\text{ sq. feet}[/tex]
New rug is 1.5 times as wide as the original rug.
Width of new rug = 1.5 × 6 = 9 feet
Let the length of new rug be x feets. So, area of new rug is
[tex]A_2=x\times 9[/tex]
[tex]96=x\times 9[/tex]
Divide both sides by 9.
[tex]\dfrac{96}{9}=x[/tex]
[tex]\dfrac{32}{3}=x[/tex]
[tex]x=\approx 10.67\text{ feet}[/tex]
Therefore, the length of new rug is about 10.67 feet.
help! SOS! due by tonight midnight
Answers
Answer:
A. x=35
B. C= 59 degrees
Step-by-step explanation:
Since both angles have the same measurement you set them equal to each other as so & solve for x
3x+16=5x-54
16=2x-54
70=2x
x=35
Now we plug 35 into one of the equations
3(35) + 16
105+ 16 = 121 degrees
Since angle C is a supplementary angles you do 180-121= 59 degrees
please help me with this question!! thank you if you do:))
Answers
Answer:
C
Step-by-step explanation:
What is cos(3π)?
1
0
-1
-2
Answers
Answer:
cos(3π) is 0.986 which rounds to 1
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
edge 2020
Find the 11th term of the geometric sequence 6, -18, 54
AYUDEN CHUCHA
Answers
Step-by-step explanation:
T1=a
T2=ar
r=T2÷T1
r=--18÷6
r=-3
T11=ar^10
T11=6×-3^10
T11=-354294
Answer:
354294
Step-by-step explanation:
a11=6*(-3)10=354294
Interpret the meaning of y-intercept in this context
Answers
Answer:
Its 8
Step-by-step explanation:
This is the highest peak
A dairy calf raiser orders 25 bags of calf milk replacer for $1,050. How much did each bag cost?
Answers
Answer:
$1,054
Step-by-step explanation:
i dont have explination pls dont remind me
Help pleaseeee!!!?thanks
Answers
Answer:it’s c
Step-by-step explanation:
Because it’s 146%
Factor the expression.
2x^2 + 3x - 9
Answers
Answer:
(2x-3)(x+3)
Step-by-step explanation:
The factors of the expression are (2x-3) and (x+3).
The following angle measures could form a triangle
(a)
90° , 37°, 53°
A True
B False
(b)
Explain why the angle measures form a triangle or do not form a triangle.
Answers
B) adding the angles makes 180°, which is the correct number for a triangle
