-5x + 12 = 20
-5x = 20 - 12
-5x = 8
x = -8/5
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]?
The ratio of male to female bats under the Congress Avenue Bridge in Austin, Texas is 5/4. If you were to see 486 bats fly out from under the bridge, how many would you expect to be female?
Answer:
216 bats will be female
Step-by-step explanation:
First, you set it up for a cross multiply
9 = 486
4 x
We use nine because the ratio of male to female is 5/4 so the ratio of total to female is 9/4. Cross multiply.
9x = 1944
x= 216
So 216 bats will be female
If you liked this, please give me brainliest.
Thankyou
5
Find the arc length of the semicircle.
Elther enter an exact answer in terms of or use 3.14 for and enter your answer as a decimal,
units
Answer:
area is 39.27
Step-by-step explanation:
Evaluate the expression x=7.x+8
Answer:
15
Step-by-step explanation:
For each time I see x, I replaced it with 7 because I know that x is equal to 7.
I only see one x so I am only replacing that one x so instead of x + 8, I get 7 + 8 and you could split 8 into 5 + 3 and split 7 into 5 + 2.
5 plus 5 is 10. If you are having trouble adding the numbers you could put up 5 fingers first and then add one finger up one by one to still the number 10. Now that just leaves you with 3 + 2.
You could first put up 3 fingers and then add two more to get a total of 5 fingers.
At last, you could just add 10 + 5 to get 15 in total.
Hope this works you!!!
For what value of x is line m parallel to line n?
x=?
pleaseeee, helppp, mee ill give brainiest if correct
Answer: Reflection
Step-by-step explanation: reflection: when a figure flips over a line
Write down an equation of the line that is perpendicular to y=2x+5
I will mark as brainliest
Answer:
y = -1/2x +5
Step-by-step explanation:
The perpendicular slope will be the negative reciprocal of the original slope
the reciprocal of 2 is 1/2, and the negative of that is -1/2
solve pls brainliest
Answer:
3421
Step-by-step explanation:
3421 the order the tiles are in
What is the solution to the inequality -6_5>-29
Answer:
If it's true or false than it's true.
help i really need it :(
Answer:
The correct equation is [tex]2\frac{2}{3}+r = 3[/tex].
Why?
To find the correct answer we have to isolate r from the other numbers. To isolate r from this equation, we have to subtract [tex]2\frac{2}{3}[/tex] from both sides of the equation. Remember that you can do whatever you need to one side of the equation, but you must do the exact same thing to the other side, so the equation remains the same value. By subtracting [tex]2\frac{2}{3}[/tex] from the equation, we get [tex]2\frac{2}{3}-2\frac{2}{3}+r=3-2\frac{2}{3}[/tex]. Simplify: [tex]r=\frac{1}{3}[/tex]. Therefore, answer D is the solution.
Good luck!
Find the quotient. 1,329 ÷ 4
Answer:
Quotient is basically division.
Step-by-step explanation:
1329/4 is basically
332.25 is the answer
does anyone know this i need it fast
Please help me with this MATH question.
Answer: first and third choice
Step-by-step explanation:
it would be the first and third choices. the first choice employs the distributive property— it distributes b to x and c.
the third choice performs opposite operations. so instead of multiplying b by (x+c) it does the opposite and divides it by both sides
Please explain.
No bit links.
Answer:
Top right
Step-by-step explanation:
The equation is saying that x is greater than or equal to the number two. That mean our line will be bold and not dotted and the the shaded area will be everywhere past the 2 line
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
Solve the inequality:
-h + 4 ≤ 6
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
( h ≥ -2 ).
Answer:
Refer to the attachment
Find the measure of the angle marked with a question mark using inverse trig
functions. Round your answer to the nearest degree. Enter the number only.
I need the answer quick
Applying the tangent ratio, the value of x in the right triangle is approximately: 5.
What is the Tangent Ratio?Tangent ratio that can be applied to solve a right triangle is expressed as: tan ∅ = opp/adj.
Given the following:
∅ = 63°Opp = 10 Adj. = xtan 63 = 10/x
x = 10/tan 63
x ≈ 5
Learn more about the tangent ratio on:
https://brainly.com/question/4326804
#SPJ1
Solve for b
Is it square root 39?
Or
Square root 89?
Answer:39
Step-by-step explanation:
Answer:
[tex]\sqrt{39}[/tex]
Step-by-step explanation:
By the Pythagorean Theorem:
[tex]b^2+5^2=8^2[/tex]
We can rearrange this equation to find b:
[tex]b^2=8^2-5^2\\\\b^2=64-25=39\\\\\sqrt{b^2}=\sqrt{39}\\\\b=\sqrt{39}[/tex]
The system of equations below form a line and a parabola. Select all possible solutions to this system from the answer choices below.
2 + y = 5
2? + y = 11
A(-2,7)
B(7,2)
C(3,2)
D(2,3)
ח
F(5,0)
Answer:
B dude also also watch out the jews are coming
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box
Quick please!!!! 50 points!!
Answer:
2,1
Step-by-step explanation:
can someone please tell me what is 12 x 8 +5?
Use BODMAS
first solving 12×8
which is = 12×8=96
than add +5
so, 96+5= 101
Hope This HelpsAnswer: 12x8=26+5= 31
Step-by-step explanation:
A rope is stretched tight between the tops
of two flag poles. One pole is 16 m tall, the
other is 8 m tall and they stand on level
ground 6 m apart. Find the rope's length.
m
Answer:
10 m.
Step-by-step explanation:
We have a triangle with hypotenuse h m (the rope's length) and one leg 16 - 8 = 8 m and the other 6 m.
So h^2 = 8*2 + 6^2 = 100
h = 10 m.
Jeffrey purchased a car for $180 that gives him 20 visits to a new gym and includes a one time fee for unlimited use of the sauna. After five visits, Jeff has $123.75 left on the card, and after 11 visits, he has $74.25 left on the card. Write an equation in point slope form, then determine the cost of each visit in the fee for the sauna use.
What is the slope of the line that passes through the ordered pairs(1,14)and(−5,−34)?
Answer:
The answer is 8!
Step-by-step explanation:
I took the quiz. Have a great day, hope this helps!
In ΔNOP, p = 7.5 inches, ∠O=8° and ∠P=25°. Find the length of n, to the nearest 10th of an inch.
Answer: 10.17898 so
About 10.2
Answer: 10.6
Step-by-step explanation:
3.5x^3-2.3x^2+1.4x+15.6-1.2x^3+4.5x^2-0.3x-3.2
Answer: 12.4 + 1.1x + 2.2x^2 + 2.3x^3
Step-by-step explanation:
add the like variables
solve pls brainliest
Answer:
0.28 repeating- yes, this is a repeating decimal
0.74...- yes, this is a repeating decimal
0.3162..- no, this is a decimal that neither terminates nor repeats
0.816..- yes, this is a terminating decimal
Step-by-step explanation:
Terminating decimals:
a decimal that comes to an end, has a finite number of decimal placescan be expressed/written as a fraction Example: 0.25Repeating decimals:
a decimal that has has digit/digits that repeat over and over (go to infinity)can be expressed/written as a fractionexample: 0.333333333...Non-terminating, Non-repeating decimals:
a decimal number that continues on forever with no group of digits being repeated (the digits are basically randomized)cannot be expressed/written as a fractionexample: π9,000,000 times 30 divided by 2 plus three minus 36 time 1 divided 93
135000002.613! At least I think!
The value of x varies directly with y, and when x=1/3,y=5
Answer: y = 36x
Step-by-step explanation: Given that x and y vary directly then the equation relating the is
y = kx ← k is the constant of variation
To find k use the condition x = , y = 12, then
k = = = 12 × 3 = 36
y = 36x ← equation of variation
could someone please help me on one of these and explian to me too? plz show work
Answer:
3) rate of change = -5/4
4) rate of change = 3
5) rate of change = 1
6) steepest slope = #4
7) Please see the attached graph and explanation below
8) Please see the attached graph and explanation below
Step-by-step explanation:
Note:I will do questions 3, 4, 6, 7, and 8, and will let you work on question 5 (since it involves the same process of solving for the rate of change as questions 3 and 4). However, the rate of change for question 5 is 1.
3) Calculate the Rate of Change from the Graph:The rate of change is essentially the same as the slope of a linear equation, where it represents the ratio of a change in y to a corresponding change in x.
In order to solve for the rate of change, choose two points from the given graph.
Let (x₁, y₁) = (0, 200)
(x₂, y₂) = (80, 100)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (100 - 200)/(80 - 0)
m = -100/80
Reduce to lowest terms by dividing the numerator and the denominator by 20/20:
m = -5/4
Therefore, the rate of change is -5/4.
4) Calculate the Rate of Change from the Table:Similar to what we did in question 3, choose two ordered pairs from the given table:
Let (x₁, y₁) = (0, -1)
(x₂, y₂) = (3, 8)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
[tex]m = \frac{8 - (-1)}{3 - 0}[/tex]
[tex]m = \frac{8 + 1 }{3}[/tex]
[tex]m = \frac{9}{3}[/tex]
m = 3
Therefore, the rate of change from the given table is 3.
6) Which linear function has the steepest slope?The positive-sloped lines whose rate of change has the highest value will have the steepest slope. For lines with negative slopes (downward-tilting lines), the highest absolute value for its rate of change will have the steepest negative slope.
Hence, the linear function with the steepest slope is #4 because the value of y changes by 3 units for every unit of change in x values.
7) Graph the equation: y = -6x - 4:The linear equation, y = -6x - 4, where the slope, m = -6, and the y-intercept is (0, -4).
To graph this equation, start by plotting the y-intercept. Then, use the slope, m = -6/1 (down 6 units, run 1 unit to the right) to plot other points on the graph. In doing so, your next graph should occur at point, (1, -10). Connect the two points to create a line that will represent the given equation, y = -6x - 4.Technically, two points are sufficient enough to connect and create a line with. Please see the attached screenshot of the graph for y = -6x - 4.
8) Graph the following equation: 3x - 4y = 12The given linear equation is in its standard form, Ax + By = C. It is easier to graph when the equation is in its slope-intercept form, y = mx + b.
In order to transform the given standard equation to slope-intercept form, start by subtracting 3x from both sides:
3x - 4y = 12
3x -3x - 4y = -3x + 12
-4y = -3x + 12
Divide both sides by -4 to isolate y:
[tex]\frac{-4y}{-4} = \frac{-3x + 12}{-4}[/tex]
y = ¾x - 3 ⇒ This is the slope-intercept form where the slope, m = ¾, and the y-intercept is (0, -3).
Graph:Similar to how we graphed the equation from question 7, start by plotting the y-intercept (0, -3) on the graph. Then, use the slope, m = ¾ (3 units up, 4 units run), to plot other points on the graph. Your next point occurs at the x-intercept, (4, 0). The x-intercept is the point on the graph where it crosses the x-axis. Connect the two points to create a line that will represent the given equation, 3x - 4y = 12.
Please see the attached screenshot of the graph for 3x - 4y = 12.