Answer:
14 dollars off the original price
Step-by-step explanation:
A right rectangular prism whose surface area and volume are numerically equal has edge lengths $\log_2 x$, $\log_3 x$, and $\log_4 x$. What is $x
The value of [tex]x[/tex] is 29.
The formulae for the surface area ([tex]A_{s}[/tex]) and volume ([tex]V[/tex]) are, respectively:
[tex]A_{s} = 2\cdot (h\cdot l + w\cdot l + h\cdot w)[/tex] (1)
[tex]V = w\cdot h \cdot l[/tex] (2)
Where:
[tex]w[/tex] - Width.[tex]h[/tex] - Height.[tex]l[/tex] - Length.According to the statement, we must equalize (1) and (2) and substitute the remaining variables:
[tex]2\cdot (h\cdot l + w\cdot l + h\cdot w) = w\cdot h\cdot l[/tex]
[tex]2\cdot h\cdot l + 2\cdot w \cdot l + 2\cdot h\cdot w = w \cdot h \cdot l[/tex]
[tex]2\cdot \log_{2}x\cdot \log_{4}x+2\cdot \log_{3}x\cdot \log_{4}x+2\cdot \log_{2}x\cdot \log_{3}x = \log_{2}x\cdot \log_{3}x\cdot \log_{4}x[/tex]
By applying logarithm properties, we simplify the expression:
[tex]2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right) = \log_{2}x \cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right)[/tex]
[tex]2\cdot \left[\frac{1}{\log_{2}4}+\frac{1}{\log_{2}3\cdot \log_{2}4}+\frac{1}{\log_{2}3}\right] = \left(\frac{1}{\log_{2}3\cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]
[tex]2\cdot \left(\frac{\log_{2}3+\log_{2}4+1}{\log_{2}3\cdot \log_{2}4} \right) = \left(\frac{1}{\log_{2}3 \cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]
[tex]\log_{2}x = 2\cdot (\log_{2}3 + \log_{2}4+1)[/tex]
[tex]\log_{2}x = \log_{2}9 + \log_{2}16 +2[/tex]
[tex]x = 9 + 16 + 4[/tex]
[tex]x = 29[/tex]
The value of [tex]x[/tex] is 29.
We kindly invite to check this question on logarithms: https://brainly.com/question/20838017
Nota - The statement of this question presents typing mistakes and is also incomplete, the corrected form is presented below:
A right rectangular prism whose surface area and volume are numerically equal has edge lengths [tex]\log_{2} x[/tex] (height), [tex]\log_{3}x[/tex] (width) and [tex]\log_{4}x[/tex] (length). What is [tex]x[/tex]?
Suppose you have a coin collection of dimes and quarters containing 46 coins. If you have $6.70, how many of each type of coin do you have?
answer:
32 dimes and 14 quarters
step by step:
32 x 10 = 320
14 x 25 = 350
320 + 350 = 670
670¢ = 6.70$
What is an equation of the following line?
Answer:
y = 5
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through all points with a y- coordinate of 5 , then
y = 5 ← equation of line
i need help: solve (4x^(6))^((3)/(2))
Answer:
(4x^{(6)})^{(\frac{(3)}{(2)})}
(4x(6))((2)(3))
Step-by-step explanation:
I think that's the answer
What is the solution (pls help ASAP )
Answer:
c the factor of the inequality is correct - took this test already
Step-by-step explanation:
sandra babysat for the millers for 4.5 hours. the millers gave her 40$. write and solve an equation to calculate how much sandra earned per hour. round to the nearest hundrefth.
What is the are of a circle if pi is 22/7
Answer:
In-sufficient data
Step-by-step explanation:
The formula for area is pi*radius*radius
[tex]\frac{4x}{5}+\frac{5x}{6}[/tex]
To solve this issue, first we have to match the denominators, for this we have to take the LCM from the denominators 5.6, Then just solve the fraction normally, See:
[tex]\sf \dfrac{4x}{5}+\dfrac{5x}{6}\to LMC~(5,6)=30\\\\\\\sf =\dfrac{24x}{30}+\dfrac{25x}{30}\\\\\\\sf =\dfrac{24x+25x}{30}\\\\\\\boxed{\sf \frac{49x}{30}}[/tex]
Okay?!The nth term of a sequence is n^2 + 5.
Find the first three terms and show that 261 is a term in this sequence.
Answer:
first 3 terms: 6, 9, 14
16^2+5=261
Step-by-step explanation:
1^2+5= 6
2^2+5= 9
3^2+5= 14
For the problem 12(-3)(-2), will the answer be positive or negative?
Answer:
the answer is positive.
Step-by-step explanation:
12(-3)(-2)
the 2 negatives cancel out, so you get a positive 6
12(6)
72
positive 72
hope this helped!
mark me brainliest :D
9x^2-(3x+1)(4x-5)+1+6x=0
Answer:
x = -1/3 or x = 6
Step-by-step explanation:
For this equation, you should use the FOIL method or the BOX method. Break it apart to solve it easier. Sites like mathpapa or symbolab can help break these down for you.
A family buys a studio apartment for 120,000. They pay down payment of 18,000.
A. Their down payment is what percent of the purchase price?
B. What percent of the purchase price would a 48,000 down payment be?
Answer:
EZ
Step-by-step explanation:
A. 15 Percent
B. 40 Percent
Answer:
A) 15% B) 40%
Step-by-step explanation:
Select all of the given points in the coordinate plane that lie on the graph of the linear equation $$.
5 16/17 as an improper fraction
Answer:
5 16/ 17
17 x 5 + 16
85+16
101/17
Step-by-step explanation:
goodluck
Answer:
answer is 101/17
82837848+8383830.84-73327.00.73 =?
Answer:
91148351.8327
Step-by-step explanation:
Calculator
6(4x-3)-9x distributive property
Answer:
15x-18
Step-by-step explanation:
use pemdas
do parenthesis first
6(4x-3)-9x
24x -18 -9x
15x-18
The simplified expression after applying the distributive rule for the expression 6(4x - 3) - 9x becomes 15x - 18
The given expression is:
6(4x-3)-9x
Expanding the expression using the distributive rule
24x - 18 - 9x
Collect like terms
24x - 9x - 18 (since 24x and 9x are similar)
The resulting expression becomes:
15x - 18
The simplified expression after applying the distributive rule for the expression 6(4x - 3) - 9x becomes 15x - 18
Learn more on distributive property here:
https://brainly.com/question/4077386
graph the line with slope -3 passing through the point (4, -3)
Answer:
my suggestion to you is that you use a ruler and a piece of paper to draw out the graph then plot the point down and draw the line.
(I hope this helps you!)
Dan earns £300 over the course of a five-day week. How much is that per day?
Answer:
£60 per day
Step-by-step explanation:
1 week = 5 days
Dan earned = £300
therefore 1 day = 300 ÷ 5 = £60 per day
90/9 as a whole number
Answer:
10
Step-by-step explanation:
If you can get poland spring water, 3 for $11.00 how much would be 2 cases of water?
explain
3 cases /3= $11 /3
1 case x 2= 11/3 x2
2 case = 22/3 = (round to the hundreth) $7.33
Which numbers are irrational
Answer:
A & B
Step-by-step explanation:
A rational number is a number that can be written as a fraction or a terminating or repeating decimal. An irrational number is one that cannot be written as a fraction, or one that goes on forever without terminating or repeating in any way. Let's check all of our options and find the ones that are irrational.
Our first option (A) looks irrational! The "..." shows us that it goes on forever, and it doesn't look like it repeats. So this option is irrational.
Our next option is B, the square root of 24. What is the square root of 24? Well, if we look it up on a calculator, we get 4.89897948557..., and it looks like this one doesn't terminate or repeat either. So option B is also irrational.
Option C is the square root of 121. The square root of 121 is 11, which can be written as a fraction (11/1) and is a terminating decimal. So it's rational.
Our last option is D, and it is written already as a fraction, so we know for sure that it's rational. If we divide it out, we get 0.44444... with the 4 going on forever. It's a repeating decimal, and repeating decimals are rational.
So our final answers for which are irrational are A & B.
i need a lot of help and please help i need it
1. write a mathematical expression that explains the following sentence:
The sum of 4 and d, then multiply the result by 2
Answer:
(4 + d) × 2
Step-by-step explanation:
Write the equation of the line in slope-intercept form.
The equation of the line in slope-intercept form is
i need help please no bots
Answer:
>
Step-by-step explanation:
Squares eventually get bigger then when you multiply
Analyze the diagram below and complete the instructions that follow.
so we know m<3=70
m<2=90
m<2+m<1=m<4
try 50?
let me know if it is wrong
will give brainliest no files will report.
Help pleasee giving brainliest!!
Answer:
x=21
<1=120
Step-by-step explanation:
So to find x set up an equation like this:
(5x+15)+(3x-3)=180
since the bottom and top lines are congruent they are 'interior angles on the same side of a transversal' which are always supplementary, so that's where 180 comes from.
calculate the equation and you'll get x=21 :D
next to find 1 just put 21 in place of x: 3(21)-3=60
since it's supplementary to angle 1 you take 180-60=120
angle <1=120!
Math 8 Question! :)
Four different positive integers have a mean (average) of 100. If the positive difference between the smallest and largest of these integers is as large as possible, determine the average of the other two integers.
Answer:
2.5
Step-by-step explanation:
"Four different positive integers have a mean (average) of 100"
The total of the 4 numbers is then 4* 100 = 400
"the positive difference between the smallest and largest of these integers is as large as possible"
to get the greatest difference the first 3 numbers must be
1, 2 and 3 which totals 6
the 4th number is then 400 - 6 = 394
the four numbers are 1, 2, 3 and 394
The greatest difference is between 1 and 394
"the average of the other two integers"
(2 + 3)/2 = 2.5
The average of the other two integers is 1.5.
What is the average of the two numbers?
An integer is an whole number. An example of an integer is 20.
If the mean of the four integers is 100. It means that the sum of the integers must be 400. If the integers are 0,1,2, 397. The largest number is 397 and the smallest number is 0. The average of the other two integers is (1 + 2 ) / 2 = 1.5
To learn more about mean, please check: https://brainly.com/question/25842202
The measures of angles x and y in the above figure is:
Step-by-step explanation:
sum of 2 angles on a straight line = 180°
therefore,
y + 120 = 180
y = 180 - 120 = 60
y = 60°
now apply angle sum property of triangle
now,
50 + x + y = 180
50 + x + 60 = 180
110 + x = 180
x = 180 - 110
x = 70
therefore, x = 70 & y = 60
hope this answer helps you dear! take care
Answer:
x = 70°
y = 60°
Step-by-step explanation:
hope it helps u
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