Given,
[tex]\longrightarrow\rm{64^x=\dfrac{1}{256^y}}[/tex]
We have to find out the value of 3x + 4y.
Multiplying both sides by [tex]\rm{256^y}[/tex] we get,
[tex]\longrightarrow\rm{64^x\cdot256^y=1}[/tex]
Then we will write 64 and 256 as powers of 4 as,
[tex]\rm{64=4^3}[/tex]
[tex]256=4^4[/tex]
Then,
[tex]\longrightarrow\rm{(4^3)^x\cdot(4^4)^y=1}[/tex]
[tex]\longrightarrow\rm{4^{3x}\cdot4^{4y}=1\quad\quad[\because(a^m)^n=a^{mn}]}[/tex]
[tex]\longrightarrow\rm{4^{3x+4y}=1\quad\quad[\because a^m\cdot a^n=a^{m+n}]}[/tex]
Now we will take log to the base 4.
[tex]\longrightarrow\rm{\log_4(4^{3x+4y})=\log_4(1)}[/tex]
[tex]\small\text{$\longrightarrow\rm{(3x+4y)\log_4(4)=\log_4(1)\quad\quad[\because\log_b(a^m)=m\cdot\log_b(a)]}$}[/tex]
We have,
[tex]\rm{\log_4(4)=1}[/tex]
[tex]\log_4(1)=0[/tex]
Then,
[tex]\longrightarrow\rm{(3x+4y)(1)=0}[/tex]
[tex]\longrightarrow\rm{\underline{\underline{3x+4y=0}}}[/tex]
Hence 0 is the answer.
if there are 24 boys and 6 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answer:
4:1, 6:2, 12:3, 24:6
Step-by-step explanation:
24 boy
6 girls
possible ratio
24 ÷ 6 = 4
6÷ 6 = 1
4 : 1
24 ÷ 3 = 6
6 ÷ 3 = 2
6 : 2
24 ÷ 2 = 12
6 ÷ 2 = 3
12 : 3
24 ÷ 1 = 24
6 ÷ 1 = 6
24 :6
Find the Are of the Shaded Region
Answer:
≈ 84.8 cm²
Step-by-step explanation:
The area of the shaded region is calculated as
area of circle - area of unshaded sector
area of circle = πr² = π × 6² = 36π
unshaded area = area of circle × fraction of circle
= 36π × [tex]\frac{90}{360}[/tex] = 36π × [tex]\frac{1}{4}[/tex] = 9π
area of shaded region = 36π - 9π = 27π ≈ 84.8 cm² ( nearest tenth )
A muffin recipe calls for 1 cup of flour, 1/2 cup of sugar and 3/4 cup of milk and makes 20 muffins. How much of each ingredient would you need to make 120 muffins?
Answer:
well you multiple 20 by 6 to get 120, so that means multiple everything by 6
SO, 6 cups of flour, 3 cups of sugar, and 4 1/2 cups of milk
The price of BZG CO's stock is tracked over several days, as displayed in the table below. Based on the data given, what linear equation can be used to predict the price of this stock in the future? Round the variables to 3 decimal places.
Answer:
Y= 1.165x18.703
And the equation from the previous problem to predict the price BZG stock on day 30 is y=1.165(30) + 18.703 -$53.65
Jackson will buy the items listed below. He has $422.76 in his checking account. He had a stored-valued card worth $75. He withdrew cash to cover the remaining cost of the items. His bank automatically deducts a fee of $2.50 from the account for the withdrawal. After purchasing the items, how much money is left in Jackson's account?
Items. Cost($)
video game. 44.99
video game console. 299.49
a
$150.78
b
$269.48
c
$344.48
d
$497.76
Answer:
A
Step-by-step explanation:
44.99+299.49 = $344.38
$344.38 - store card ($75) = $269.48
422.76 - 269.48 - 2.5 = $150.78
Therefore answer is A
The dot plot below shows the drawing scores of some students: A number line is shown from 1 to 5 in increments of 1. The horizontal axis label is Score. There is 1 dot above 1, 2 dots above 2, 3 dots above 3, 4 dots above 4, and 5 dots above 5. The title of the line plot is Dance Scores. Which statement best describes the shape of the data? It is not symmetric and has a peak at 1. It is not symmetric and has a peak at 5. It is symmetric and has a peak at 1. It is symmetric and has a peak at 5.
Answer:
10 maybe
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Which expression is equivalent to (r^-7)^6?
A: r^42
B: 1/r^42
C: -7r^6
D: 1/r
Answer:
B
Step-by-step explanation:
(r^-7)^6 = r^-42 = 1/r^42
Plz help fill in the blanks the options are
108 sq ft
21 sq fr
22 sq ft
Answer:
12
9
21
Step-by-step explanation:
The top rectangle is L*W
L = 6
W = 2
Area = 6 * 2 square Feet
Area = 12 sq ft.
The Bottom figure is a square
Area = s * s
s = 3 feet
Area = 3 * 3 = 9 square feet
Total
12 + 9 = 21 square feet.
Help im sister needs help and i can't help her im doing my school work !
Given the sequence {-2,5,12,19...} ,find a34
Answer:
the answer is in the attachment
The 34th term of the arithmetic value progression is a₃₄ = 229
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the sequence be represented as A
Now , the value of A is
A = {-2,5,12,19...}
And , to find the 34th term of the sequence {-2, 5, 12, 19, ...}, we first need to find the common difference between consecutive terms:
The common difference = 5 - (-2) = 7
So, to get the 34th term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values we have:
a₃₄ = -2 + (34-1)7
a₃₄ = -2 + 231
a₃₄ = 229
Hence , the 34th term of the sequence is 229
To learn more about arithmetic progression click :
https://brainly.com/question/1522572
#SPJ3
Solve for x. With explanation
Answer:
129
Step-by-step explanation:
the sum of the interior angles of a quadrilateral is 360, so you add 71+112+48 and subtract it from 360 to get x
PLEASE HELP ME ON THIS QUESTION ASAP!!!! NO LINKS
Answer:
4π in.
Step-by-step explanation:
formula circumference= 2πr
r = half of diameter
Solve for all values of x by factoring.
x^2+10x+12=2x+5
Answer:
x = -1, -7
Step-by-step explanation:
=> x² + 8x + 7 = 0
=> (x + 1) (x + 7) = 0
=> x = -1, -7
you throw a basketball from a height of 4 feet with an upward velocity of 15 feet per second the function h=-16t^2+15t+4 gives the height of the basketball after t seconds when does the basket ball hit the floor round your answer to the nearest tenth
Answer:
After 1.2 seconds
Plzzz help me!!! ASAP
Ruth buys 19 identical tickets for £280.25.
Estimate the cost of one ticket.
Answer:
The cost of one ticket is $14.75
Step-by-step explanation:
To find the cost of one ticket we need to divide 280.25 by 19
=$14.75
plz mark me as brainliest
Answer:
The cost of one ticket is $14.75
Step-by-step explanation:
The cost of one ticket is $14.75
To find the cost of one ticket we need to divide 280.25 by 19
=$14.75
please mark as brainliest
Jed wants to earn 25% annual net income on his $50,000 cash investment in property his annual expense of owning the property are $9600 what monthly rent must jed charge
Answer: $1,842
Step-by-step explanation:
John wants to earn 25% of his investment of $50,000 which is:
= 25% * 50,000
= $12,500
He has expenses of $9,600 yearly so the rent he should charge per year in order to make his 25% requirement as income is:
= Expenses + Return
= 9,600 + 12,500
= $22,100
Rent per month is:
= 22,100 / 12
= $1,842
Help please not sure what it can be!
Answer:
y=40x-30
Step-by-step explanation:
Find the distance between the pair of points (-6.-17) and (-8.-19) The distance is (Round to the nearest thousandth as needed.)
Answer:
2.83
Step-by-step explanation:
d= Square root of (x2 - x1 )^2 +( y2- y1)^2
from the point given you
x1= -6
y1 = -17
x2 = -8
y2 = -19
by applying the formula
Square root of ( -8 - (-6))^2 + ( -19 - (-17))^2
Square root of (-8+6) + (-19+17)^2
Please don’t not provide links I just need steps to understand
What is measure of egd
Answer:
I got you fam.
the answer is 180
Step-by-step explanation:
so if you look at how HE is 115 then you take 180 and -115 to get 65 so your answer is 65.
Hoped that helped! :)
How many tiles will figure 13 have ??
FREE POINTS!
Answer:
more tiles than i laid in ur momms
Step-by-step explanation:
Figure 13 has 11 tiles
Help me please m, it due soon
Answer and explanation
Answer:
200in
Step-by-step explanation:
theres two squares in this face, so find the area of them
A = 10x10
A = 100in
A = 10x10
A = 100in
100 + 100 = 200in
Write a numerical expression Add 8 and 7 and then multiply by 2 ? Guys i need help ASAP please write a numerical expression HELP ME brainlest
Answer:
30
Explanation
Add 8 and 7. 8 + 7 = 15. 15 x 2 is 30
Answer:
the answer will be 30
Step-by-step explanation:
Add 8 and 7. 8 + 7 = 15. 15 x 2 is 30
PLEASE HELP ASAP HELPPPPP PLEASEEE!!!! find the value of x. round to the nearest tenth
x
12
4
x =?
Answer:
70.5
Step-by-step explanation:
cos x = [tex]\frac{4}{12}[/tex]
x = [tex]cos^{-1}\frac{1}{3}[/tex]
x = 70.53
Fill in the blank. The solution to 2 x - 2 + 5 = 13 is ______
Which equations are correct? Select each correct answer.
6a5(6a5)=36a25
6b4(−3b4)=−18b8
5x4(4x2)=20x6
3z7(4z2)=12z9
Answer:
2, 3, 4,
Step-by-step explanation:
I took the k12 quiz and i remeber putting these as my answer.
Hope this helps!
Find the value of x.
(3x+20) º
12°
Answer:
x=32°
Step-by-step explanation:
2x+3x+20=180 co interior angle
5x=180-20
x=160/5=32°
Answer:
12°
Step-by-step explanation:
a straight line adds up to 180°
(3x+20)+2x=180
3x+2x+20=180
5x+20=180
5x=180-20
5x=60
5x/5=60/5
x=12
x=12°
Please I’m struggling
Answer:
120 cm³
Step-by-step explanation:
multiply all the numbers together
4*6*5
120
Can someone help me please?