Answer:
27 x 9^3x = 3^3 x 9^3x = 3^3 x (3^3)^3x = 3^3 x 3^9x = 3 ^3+9x
3^3+9x = 3k
ln(3^3+9x) = ln(3^k)
3+9x(ln3)=k(ln(3))
k= 3(1+3x)/ln(3)
Step-by-step explanation:
ln(x^n) = n(ln(x))
The perimeter of a rectangular picture frame is 120 inches. The length of the picture frame is 10 inches more than the width. Find the length and width of the picture frame.
Answer:
Length is 35 width is 25
Step-by-step explanation:
How to prove p is a midpoint of AB and Q midpoint of BC
Answer:
Step-by-step explanation:
see the figure below
As O is mid point of rectangle
distance between O to AB and DC is same
also distance between O to AD and BC is same
OP and OQ are perpendiculars so it is straight
and OP divides AB into equal segments as distance between O to AD and BC is same
same goes with OQ
[tex]if \: \sqrt{2} + \sqrt{3} \div 3 \sqrt{2} - 2 \sqrt{3} = x + \sqrt{6y} \: find \: the \: value \: of \: x \: and \: y[/tex]
Given info:- [tex]\textsf{If (√3+√2)/(3√2-2√3) = x+y√6,} [/tex]
[tex]\textsf{then find the value of x and y?}[/tex]
Explanation:-
[tex]\textsf{Consider LHS=}\\[/tex]
[tex] \rm \: \frac{ \sqrt{2 } + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \\ [/tex]
[tex] \rm \: = \frac{ \sqrt{2 } + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \\ [/tex]
[tex] = \rm \: \frac{( \sqrt{2 } + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} )}{(3 \sqrt{2} - 2 \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3}) } \\ [/tex]
[tex] \rm \: = \frac{3 \sqrt{2 \times 2} + 2 \sqrt{3 \times 2} + 3 \sqrt{2 \times 3} + 2 \sqrt{3 \times 3} }{(3 \sqrt{2} {)}^{2} - (2 \sqrt{3} {)}^{2} } \\ [/tex]
[tex] \rm = \frac{3 \times 2 + 2 \sqrt{6} + 3 \sqrt{6} + 2 \times 3}{18 - 12} \\ [/tex]
[tex] \rm \: = \frac{12 + 5 \sqrt{6} }{6} \\ [/tex]
[tex] \rm \: = 2 + \frac{5}{6} \sqrt{6} \\ [/tex]
[tex] \rm \therefore \: 2 + \frac{5}{6} \sqrt{6} = x + y \sqrt{6} \\ [/tex]
[tex]\textsf{On, comparing with RHS we notice that:}\\[/tex]
[tex]\textsf{the value of x = 2 and y = 5/6.}\\[/tex]
[tex]\bf{Read more:}[/tex]
[tex]\textsf{Similar questions}\\[/tex]
[tex] \sqrt{6} + \sqrt{11} \div \sqrt{5} + \sqrt{3} [/tex] A. [tex] \sqrt{30} + 3 \sqrt{2} + \sqrt{55} + \sqrt{33} \div 8[/tex] B. [tex] \sqrt{30} - 3 \sqrt{2} ...
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Model with Two-Step Inequalities: Quiz! (ONLY 4 QUESTIONS PLS DONT PUT LINK :< )
Q1. A hot-air balloon is 1000 feet off the ground and its altitude is slowly changing at a constant rate of −412 feet per second.
How many seconds, s, will it take for the balloon to drop to below 215 feet?
Drag and drop a symbol and value to correctly complete the solution to this inequality.
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QUESTION 2. For an experiment, the temperature of a liquid must stay above 60.4°F. The starting temperature of the liquid is 90.7°F. It is placed in a cooler, which lowers its temperature 3°F each minute.
How many minutes can the liquid can stay in the cooler?
Select from the drop-down menus to correctly complete the statement.
The liquid can stay in the cooler _______ minutes.
Choose..."At most 10.1", "More then 10.1", "At least 10.1" or "Fewer than 10.1"
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QUESTION 3. A gopher lives in an underground burrow. It starts at a certain point, p, underground and digs straight down to triple its distance under the surface. It then climbs straight down another 2 feet. Its final position is deeper than 8 feet under the surface.
What was the gopher's original position, p, relative to the surface?
Enter your answer to complete the inequality.
p__
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Q4. Robbie is going shopping. He has no more than $65.00 to spend. He wants to buy a pair of shoes for $21.95 and some shirts that cost $10.50 each.
Which inequality can Robbie use to determine how many shirts, s, he can buy?
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YAY YOU MADE IT! Thanks if you actually answered correctly...you really made my day! :)) Sending virtual hugs your way! And here is 50 points for completing my quiz you smart and mighty warrior! <3 <3 <3 Bye!
Answer:
For an experiment, the temperature of a liquid must stay above 60.4°F. The starting temperature of the liquid is 90.7°F. It is placed in a cooler, which lowers its temperature 3°F each minute.
How many minutes can the liquid can stay in the cooler?
Select from the drop-down menus to correctly complete the statement.
The liquid can stay in the cooler fewer than 10.1 minutes.
Step-by-step explanation:
two ferries start moving toward each other from opposite riverbanks, a and b. when they pass each other for the first time, the distance to riverbank b is 100 meters. each ferry starts its return trip as soon as it reaches its destination. when the ferries meet for the second time, the distance to riverbank A is 50 meters. what is the distance between riverbanks a and b? Help I will give 40 points
Let 'x' be the distance from THE far bank where 700 is the distance to the NEAR bank
boat one has travelled 700 (rate = 700/unit time) boat two has travelled x rate = x / unit time
boat one then travels x + 400 more and boat two travels 700 + (700+x -400) more when they meet
The time is the same rate x time = distance distance/rate = time equate the distances divided by the respective rates
(700 + x + 400)/700 = ( x + 700 + (700+x-400) )/x
1100x + x^2 = 1400x + 700000
x^2-300x -700000 = 0 quadratic formula yields x = 1000
One boat travels 700 the other 1000 whe they first meet.....width of river = 700+ 1000 = 1700 m
4) Which orde
inequality
3) Which ordered pair is a solution to the linear
inequality below?
2x – 3y < 9
A. (6,-4)
B. (-1,-9)
C. (2,-5)
D. (-3,-3)
Answer:
D)
Step-by-step explanation:
A is incorrect because: 2(6) -3(-4)<9 which is 24<9 which is not true
B is incorrect because: 2(-1) -3(-9)<9 which is 25<9 which is not true
C is incorrect because: 2(2) -3(-5)<9 which is 19<9 which is not true
D is correct because: 2(-3) -3(-3)<9 which is 3<9 which is true
The emotional atmoshere a reader sences in a poem or story is referred toas its
If 24 people fit in 12 RVs,
How many people are in each RV?
Answer:
2 people per RV.
Step-by-step explanation:
24 / 12 = 2
Divide x5+15x4+54x3−25x2−75x−34 by x+8
Step-by-step explanation:
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x+8x5+15x4+54x3-25x2-75x-34
Divide the highest order term in the dividend x5 by the highest order term in divisor x.
x4x+8x5+15x4+54x3-25x2-75x-34
Multiply the new quotient term by the divisor.
x4x+8x5+15x4+54x3-25x2-75x-34+x5+8x4
The expression needs to be subtracted from the dividend, so change all the signs in x5+8x4
x4x+8x5+15x4+54x3-25x2-75x-34-x5-8x4
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x4x+8x5+15x4+54x3-25x2-75x-34-x5-8x4+7x4
Pull the next terms from the original dividend down into the current dividend.
x4x+8x5+15x4+54x3-25x2-75x-34-x5-8x4+7x4+54x3
Divide the highest order term in the dividend 7x4 by the highest order term in divisor x.
On dividing, x⁵+15x⁴+54x³−25x²−75x−34 by x+8, Quotient is x⁴+7x³−2x²−9x−3 and Remainder is -10.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
Dividend is x⁵+15x⁴+54x³−25x²−75x−34
Divisor is x+8
After division, the solution is attached in the image.
Quotient is ( x⁴+7x³−2x²−9x−3)
Remainder is -10
To know more about Expression
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The perimeter of a rectangle is 30 inches. If the length of the rectangle is 10 inches, which equation could be used to find the width of the rectangle "w" in inches
Answer:
30=2(10 x w)
Step-by-step explanation:
P=2(l x w)
Perimeter(P) equals two times length(l) times width(w)
Hope this helps
what is the mass of 18 crayons
Answer:144 grams
Step-by-step explanation:normal crayons usually weigh 9g
On August 19, 2002, the ratio of stocks gaining value on the New York Stock
Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how
many gained?
A)892
B)1953
C)1797
D)1868
Answer:
D: 1868
Step-by-step explanation:
43:20 ratio
43/20 = 2.15
869 * 2.15 = 1,868.35
round down to nearest whole number
1,868
Marian is making accessories for the soccer team. She uses 666.12 inches of fabric on headbands for 36 players and 3 coaches. She also uses 310.68 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
I need help with this
Answer:
answe is about 23. something
Step-by-step explanation:
When an object moves in a circle the __________ of the object is continually changing. What is the missing word in this sentence?
Answer:
velocity
Step-by-step explanation:
The velocity of the object is continually changing. This velocity is the slope of the tangent line to the curve at a given point on the curve.
The corrected sentence is: When an object moves in a circle, the velocity of the object is continually changing.
What is a circular motionCircular motion involves not only changes in the object's orientation or direction but also changes in its velocity.
Velocity includes both the speed of the object's movement and its direction. As an object moves around a circle, even if it maintains a constant speed, its velocity is changing because the direction in which it is moving is always changing.
This change in velocity is what allows the object to maintain its circular path rather than moving in a straight line.
Learn more about Velocity
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find the sum of an arithmetic sequence 9, 15, 21, 27,…,183?
Answer:
It Jumps by six every number, so six would be my guess
how can u calculate 23x4 if the 4 buton is broken?
Answer:
23x2x2
Step-by-step explanation:
Elena is paid a constant rate for each hour she works. The table shows the amounts of money that Elena earned for various amounts of
time that she worked.
Constant rates are used to illustrate linear functions.
The average rate of change is $9.0 per hourThe function that models the table is: [tex]\mathbf{f(x) = 9x }[/tex]The amount earned in 7.5 hours is $67.5(a) The average rate of change
This is calculated using:
[tex]\mathbf{Rate = \frac{y_2 -y_1}{x_2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{Rate = \frac{31.5-22.50}{3.5 - 2.5}}[/tex]
[tex]\mathbf{Rate = \frac{9}{1.0}}[/tex]
[tex]\mathbf{Rate = 9.0}[/tex]
Hence, the average rate of change is $9.0 per hour
(b) A function that models the table of values
Let x represent hours, and y represent the earnings.
So, we have:
[tex]\mathbf{y =m (x - x_1) + y_1}[/tex]
Where:
m =Rate = 9.0
So, we have:
[tex]\mathbf{y = 9(x - 2.5) + 22.5}[/tex]
Expand
[tex]\mathbf{y = 9x - 22.5 + 22.5}[/tex]
[tex]\mathbf{y = 9x }[/tex]
Represent as a function
[tex]\mathbf{f(x) = 9x }[/tex]
Hence, the function that models the table is: [tex]\mathbf{f(x) = 9x }[/tex]
(c) Amount earned for 7.5 hours
This means that x = 7.5
So, we have:
[tex]\mathbf{f(7.5) = 9 \times 7.5 }[/tex]
[tex]\mathbf{f(7.5) = 67.5}[/tex]
Hence, the amount earned in 7.5 hours is $67.5
Read more about constant rates at:
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Work out the shaded area of this shape.
Answer:
73
Step-by-step explanation:
Sales tax rate is 8% if Ayana buys a set of spoons price that 17.88 what will be the total cost including tax
Extra:
Percentage = 1% = 0.01, 10% = 0.1 and 100% = 1
Increase in percentage = 1 + percentage eg. (1 + 0.08 = 1.08)
Decrease in percentage = 1 - percentage eg. (1 - 0.08
Pls answer all 4 questions AND HURRY!!!!
Answer:
5pts
Step-by-step explanation:
Foster is centering a photo that is 9 1/2 inches wide on a scrapbook page that is 10 inches wide. How far from each side of the page should he put the picture? Enter your answer as a mixed number. / pls help quick
Answer:
should be 1/4 inches away from each side
Step-by-step explanation:
all I did was take the 10 inches,subtract 9.5 from that to get 1/2 left.
since it needs to be centered, divide that by two for each side.
and 1/2 ÷ 2 = 1/4
so I got 1/4 inches on each side.
If an airplane in a 1 in : 2 ft scale drawing is 6 inches long, how long is the actual airplane? 12 ft 24 ft 8 ft 3 ft.
Answer:
the answer is 12ft hope that helps
PLS HELP ME
How do you find the radius???
Answer:
r = 15
Step-by-step explanation:
Using Pythagoras' identity in the right triangle OAB
with OM and OB the radii r of the circle
OA² = OB² + AB²
(r + 10)² = r² + 20² ← expand left side using FOIL
r² + 20r + 100 = r² + 400 ( subtract r² from both sides )
20r + 100 = 400 ( subtract 100 from both sides )
20r = 300 ( divide both sides by 20 )
r = 15
Graph the line that has a slope of 4 and includes the point (0,4)
Answer:
Step-by-step explanation:
it goes straight across 4 ( up and down)
Answer:
Step-by-step explanation:
Start with the standard form of an equation for a straight line:
y=mx+b,
where m is the slope and b is the y-intercept (the value of y when x = 0).
We are given the slope (4), so we have:
y = 4x + b
We can calculate b from the given point, (0,4). Just enter the values for x and y and solve for b. But in this case the given point already tells us the value of b since at x = 0, y = 4. So we can enter it directly.
------
For reference, if we went ahead and solved for b, this is what we'd get:
y = 4x + b
4 = 4*(0) + b
b = 4
-----
So the final equation of this line is y = 4x + 4
The graph is attached.
Describe the location of the point having the following coordinates.
nonzero abscissa, negative ordinate
O Quadrant II or Quadrant IV
Quadrant I or Quadrant II
Quadrant III or Quadrant IV
Quadrant I or Quadrant IV
Answer:
The best and most correct answer among the choices provided by your question is the fourth choice or letter D.
Nonzero abscissa, negative ordinate is located in Quadrant III or Quadrant IV.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Step-by-step explanation:
Miko wants to build a toy
box for her sister. It is to be 2 feet high,
and the width is to be 3 feet less than its
length. If it needs to hold a volume of
80 cubic feet, find the length and width
of the box.
Answer:
kk
Step-by-step explanation:
3w-4z=8
2w+3z= -6
What is w and z for these two equations?
If the side lengths are
doubled, then which of
the following
statements about its
perimeter will be true?
The new perimeter will be
times the old
Answer:
It would be 2 times the old perimeter.
Given f(x) = 5x + 2 and g(x) = 5x - x5X What is the value of (f 9)(1)?
Answer:
the answer is 5×9+2=47
Step-by-step explanation:
the answer is 47
solve simultaneously for x and y if: x(x-3)+y(3-x)= 0