Step-by-step explanation:
First, this is how I read it.
[tex]\log(x^{125})=-3[/tex]
Next, this is how logarithms work:
[tex]b^y=x\implies \log_b(x)=y[/tex]
In your equation, we have all 3 numbers:
b = 10 (implied)x = [tex]x^{125}[/tex]y = -3With that information, you can convert the logarithm into "normal" form:
[tex]10^{-3}=x^{123}[/tex]
The negative power rule [tex]x^{-a}=\frac{1}{x^a}[/tex] is also useful here.
Now, just solve for x:
[tex]x^{125}=\frac{1}{10^3}\\x^{125}=\frac{1}{1000}\\x=\sqrt[125]{\frac{1}{1000}}\\x=\frac{1}{\sqrt[125]{1000} }[/tex]
That's about as simplified as it gets, unless you want this:
[tex]x=\frac{1}{10^{\frac{3}{125}}}[/tex]
Thats 10^(3/125), numbers got very small.
I'm still not confident I understood the problem correctly, so let me know if I need to fix anything.
The average bedroom is an apartment is approximately 16x10
Answer:
Bro what to find with this
Answer:
which would mean it would have the area of 160 square feet
Step-by-step explanation:
What is the standard form of this expression?
(1 + 71i)(3 - i)
the standard form of this expression is
(72+3)(-i)
write a equation of the line that goes through the points (-2,-4) (0,6)
Answer:
323563
Step-by-step explanation:
Hello there!
To find the slope, we use the following formula:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{6-(-4)}{0-2} \\\frac{6+4}{-2} \\\frac{10}{-2} \\-5[/tex]
So the slope is -5.
Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]SilentNature[/tex]
(5.4*10^2)-(1.3*10^4)
answer in a*b form
Answer:
-1.24*10^4
Step-by-step explanation:
Firstly observe the Digit term of the given operation under scientific notation. and now we are left with the 10th exponents which involves the basics of 10^a - 10^b = 10^a/b and so according to this rule...we have 10^2/10^4 which results in 10^-2
and thus we have −12460 = -1.24*10^4
What is the opposite of 3√ ?
13√
−3√
−32
3²
Answer:
D or B
Step-by-step explanation:
Write an equation of the line that passes through the pair of points.
(-5,-4), (5,-3)
Step-by-step explanation:
the most common form of line equation is
y = ax + b
a is the slope of the line. it is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
b is the y-intercept (the y value when x = 0).
once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.
for the slope a :
x changes by +10 (from -5 to 5)
y changes by +1 (from -4 to -3)
the slope is +1/+10 = 1/10
the equation looks now like
y = (1/10)x + b
let's use the first point.
-4 = (1/10)×-5 + b = -1/2 + b
-3 1/2 = -7/2 = b
the equation is
y = (1/10)x - 7/2
so, the second answer option is correct.
The number of ways to choose three different pizza toppings from a group of six is called a ?
Answer:
Uh, 16.
Step-by-step explanation:
We need to choose three different toppings. So here we need to find the number of ways in which we can choose three different toppings out off. 16. So a number of ways are takes three at a time, from a total of 16. That is civilians combination. Here are formula for combination is 16 factorial over three factorial into 16 minus three. Factorial this candidate and a 16 factorial over three factorial into 16 minus trees. 13. Authority in factorial, now 16. Factory converted on a 16 in 2 15 into 14 into 13. Factorial over three factorial into 30. In fact, a real as we can see that 13 factorial is common toward denominator and numerator so we can get through this. Now I remaining times are 16 into 15 into 14. Over three in Toto into one has three factories, three in tow, one So calculating this ticket. Find 60 Soviet 56 TVs to select three different topics. Talked to select three different toppings out off 16 on a bizarre
Work out the size of angle x
Answer:
Opposite angles are equal
Corresponding angles are equal
Angles on straight lines adds to 180
Angles in triangle adds to 180
180-98=82
82+85=167
180-167=13
Answer is 13
Pls help Ive been here since nine this morning...
f(x)=4.5x^2-3x+2
fine the horizontal tangent line
Answer:
x = 13
Step-by-step explanation:
Given: f ( x ) = 4.5 x 2 − 3 x + 2 To determine the critical points, we must first calculate the first derivative of the function.
Differentiate the given function with respect to x using the power rule of differentiation, d d x x n = n x n − 1.
f ′ (x) = d (4.5 x 2 − 3 x + 2)
______
d x
Apply sum rule: d d x (f(x)) + g (x) = d d x f (x) + d d x g (x) } f ′ ( x) = d d x (4.5 x^2) + d d x (−3 x) + d d x (x) f ′ (x) = 9 x − 3
To determine the critical points, set f ′ (x) = 0 . 9 x − 3 = 0 9 x = 3 {∴ x = 13}
Therefore, the tangent line to f(x) is horizontal at the point x = 13
Hope this helps, have a nice day/night! :D
A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 1.5 m above the floor (the peg is) and pushes it downward. The peg reaches a min height of 0.25 m and a max height of 2.75 m above the floor. Sketch two cycles of the graph representing the height above the ground as a function of the total distance moved. Then determine the equation of the sine function
The spin of the wheel by the contestant is an illustration of a sine function whose equation is [tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
The wheel is 1.5 m above the floor, and the peg reaches a maximum height of 2.75 m.
So, the amplitude is:
[tex]\mathbf{A = 1.5 - 2.75}[/tex]
[tex]\mathbf{A = -1.25}[/tex]
The vertical shift is the minimum height of the peg.
So, we have:
[tex]\mathbf{D = 0.25}[/tex]
The period (T) equals one circumference.
So, we have:
[tex]\mathbf{T = (max-min)\pi}[/tex]
This gives
[tex]\mathbf{T = (2.75-0.25)\pi}[/tex]
[tex]\mathbf{T = 2.5\pi}[/tex]
The frequency (B) is then calculated as:
[tex]\mathbf{B = \frac{2\pi}{T}}[/tex]
This gives
[tex]\mathbf{B = \frac{2\pi}{2.5\pi}}[/tex]
Divide
[tex]\mathbf{B = 0.8}[/tex]
A sine function is represented as:
[tex]\mathbf{y =A sin(B(x + C)) + D}[/tex]
Substitute the calculated values
[tex]\mathbf{y =-1.25 sin(0.8(x + C)) + 0.25}[/tex]
The horizontal shift (C) is 0.
So, the function becomes
[tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
See attachment for the graph of the equation
Read more sine function at:
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Find the value of x so that the ratios are equivalent.
x to 0.25 and 6 to 1.5
What does x =
The value of x from the proportion relation is x = 1
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides
Given data ,
Let the proportion equation be represented as A
Now , the equation will be
Substituting the values in the equation , we get
x / 0.25 = 6 / 1.5
On simplifying the equation , we get
Multiply by 0.25 on both sides of the equation , we get
x = ( 6 x 0.25 ) / 1.5
On further simplification , we get
x = 6/6
x = 1
Therefore , the value of x = 1
Hence , the equation is x = 1
To learn more about proportion click :
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PLEASE HELP!! PLEASE AND THANK YOU!
Answer:
50.05 feet
Step-by-step explanation:
The tower have 32.57 feet, and you can find it using the same method than I used in your other question
Now you find the length of the guy wire using the Pythagorean theorem:
38²+32.57² = guy wire²
2504.8 = guy wire²
guy wire = √2504.8
guy wire = 50.05 feet
easy one - giving brainly if correct - show work.
Answer:
47. 1 5/8
48. 1 1/12
Step-by-step explanation:
47.
First, convert the denominators to be the same.
8 1/2 minutes, Ruby's mile time, can be converted to 8 4/8.
Then subtract.
8 4/8 - 6 7/8 = 1 5/8
48.
Make sure the denominators are the same. Both denominators can be multiplied by 3 or 4 to become 12.
1 1/4 can be multiplied by 3 to get 1 3/12. And 1 1/3 can be multiplied by 4 to get 2 4/12.
Then subtract.
2 4/12 - 1 1/3 = 1 1/12
place the decimal point in the product
1. 6.17×8.2=50594
2. 24.01×8.51=2043251
3. 8.94×5.27=471138
Answer:
Step-by-step explanation:
50.594
204.3251
47.1138
What is the final amount if 2024 is increased by 17% followed by a 15% decrease? Give your answer rounded to 2 DP.
Answer:
2059.20
Step-by-step explanation:
2024 increased by 17% is
2024 * 1.17 = 2368.08
2368.08 reduced by 15% is
2368.08 ÷ 1.15 = 2059.20
PLZ HELP ITS TIMED AND IM STUCK
3. option d
2. option a
5. option f
James is following this recipe to make flapjacks.
James uses 330 mL of syrup.
How many flapjacks is James making?
Recipe: Makes 8 flapjacks
100 g sugar
110 mL syrup
220 g oats
165 g margarine
30 g sultanas
Answer:
24 flapjacks
Step-by-step explanation:
330 / 110 = 3
8 *3 = 24
Heyy , help me do this please and thank you?:
Answer: 18 fliers
Step-by-step explanation:
1/3 of 63 is 21. Thus, the remaining fliers are 42.
4/7 of 42 is 24. Thus, the remaining fliers are now 18.
Hope it helps :)
Find the area of the shaded portion.
6
120
Answer:
A = 36√3 - 12π
Step-by-step explanation:
Make 2 identical 30-60-90 triangles out of the "wedge"
For each 30-60-90 triangle:
Since the short leg is 6 the long leg is 6√3
short leg is the base and long leg is the height
a = (1/2)bh
a = (1/2)(6)(6√3)
a = 3(6√3)
a = 18√3
Since there are 2 triangles
a = 36√3
--------------------------------
Then subtract off the area of the 120º sector
a = (120/360)πr^2
a = (1/3)π(6^2)
a = (1/3)π(36)
a = 12π
Shaded area
a = 36√3 - 12π
Step-by-step explanation:
we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).
since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.
basically, the area of a triangle is
1/2 × b×c × sin(A)
A being the angle between the 2 sides b and c. for any 2 sides of the triangle.
one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.
we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.
remember, the sum of all angles in a triangle is 180 degrees.
so, via the law of sines we can then calculate all sides :
a/sin(A) = b/sin(B) = c/sin(C)
with the angles being opposite of the sides.
6/sin(30) = baseline/sin(90)
6/0.5 = baseline/1
12 = baseline
top side² + 6² = 12²
top side² = 12² - 6² = 144 - 36 = 108
top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)
we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.
the area of the 2 triangles is then
6×sqrt(3)×6×sin(90) = 36×sqrt(3)
and the circle segment to be deducted is
pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12
so, the complete answer is
A = 36×sqrt(3) - 12×pi
Write an expression.
1 a. 49 divided by the difference of x and 2
Answer:
x + 2
--------
49
Step-by-step explanation:
that's the answer
can anyone help me with math
Answer:
d = 6
Step-by-step explanation:
diameter is the whole thing while the radius is always half of the diameter.
12 / 2
= 6
Answer:
6
the diameter is always the half of a radius
Tim Worker wants to purchase an automobile warranty costing $6,659.
If he chooses to make 48 equal payments, then in dollars and cents the average payment will be $_____
From the given information, the amount that will be paid averagely each month will be $138.73.
From the information given, Tim Worker wants to purchase an automobile warranty costing $6,659 and he chooses to make 48 equal payments.
Therefore, the amount that will be paid each month will be calculated thus:
= $6,659 / 48
= $138.73
The amount will be $138.73.
Read related link on:
https://brainly.com/question/24429956
y(a -b) =c(y+ a); y
Answer:
y = ac / (a - b - c)
Step-by-step explanation:
y(a - b) = c(y + a)
Distribute
ay - by = cy + ac
Subtract cy from both sides
ay - by - cy = ac
Factor out y
y(a - b - c) = ac
Divide both sides by (a - b - c)
y = ac / (a - b - c)
1.) What three ratios are equivalent to 3/9? *
O 1/3, 2/3, 3/3
1/3, 12/36, 15/45
6/9, 12/15, 18/21
05/12, 9/12, 3/12
Answer:
B
Step-by-step explanation:
3/9 is the same as 1/3.
It can't be D since 5/12 isn't 1/3.
It can't be A since 2/3 and 3/3 don't equal 1/3.
It can't be C since everything listed is equal to 2/3.
4√3⋅10√12⋅√6⋅√2?
plz help!!! for algebra.
Answer:
480[tex]\sqrt{3}[/tex]
Step-by-step explanation:
4[tex]\sqrt{3}[/tex] · 10[tex]\sqrt{4}[/tex][tex]\sqrt{3}[/tex] · [tex]\sqrt{3}[/tex][tex]\sqrt{2}[/tex] · [tex]\sqrt{2}[/tex] = 4 · 10[tex]\sqrt{4}[/tex][tex]\sqrt{3}[/tex][tex]\sqrt{3}[/tex][tex]\sqrt{3}[/tex][tex]\sqrt{2}[/tex][tex]\sqrt{2}[/tex]
= 40 · 2 · 3 · 2 · [tex]\sqrt{3}[/tex]
= 480[tex]\sqrt{3}[/tex]
How would the number of solutions for an equation with two variables differ from the number of solutions for an equation with only one?
Answer: An equation with one variable can have no solutions, one solution, or infinitely many solutions. An equation with two variables can have no solutions, one solution, or infinitely many solutions
Step-by-step explanation:
brainliest me
someone help me please :D ill give brainliest and 32 points :))
Answer:
Could you please show me the question?
Step-by-step explanation:
Which of the following are cube numbers. select all that apply
8/9
27
30
8/27
1/27
27/64
64
1/9
Answer:
Step-by-step explanation:
8/9 8 is a cube but 9 is not. 8/9 is not a cube
27 27 = 3^3, a perfect cube
30 Not a cube
8/27 Both 8 and 27 are perfect cubes, and so 8/27 is one also.
1/27 This is equivalent to 1^3 / 3^3 and is a perfect cube.
27/64 Both 27 and 64 are perfect cubes, so 27/64 is one also
64 64 = 4^3, a perfect cube
1/9 9 is not a cube, so 1/9 is not one either.
Can anyone tell me the answer to this please?
Answer:
-4x + 2
Step-by-step explanation:
The outputs are decreasing by 4, so -4 is the slope, the coefficient for x.
The y- intercept is 2 because when x is zero, y is 2. You can find the y-intercept by adding 4 to -2, the output for when x is 1.
Answer:
y = -4x + 2
Step-by-step explanation:
First find the slope using this equation ....
y2 - y1/x2 - x2 =
plug in two ordered pairs (doesn't matter which one) ....
-2 - (-6)/1 - 2 =
-2 + 6/-1 =
4/-1 = -4
The slope is -4. The next blank is the y-intercept (0,y) ....
y = -4x + b
plug in any ordered pair ....
-2 = -4(1) + b
-2 = -4 + b
+4 +4
2 = b
Put it all together ....
y = -4x + 2
Can somebody help me with this question? (Calculus)
Answer:
y -5 = 4(x -2)
Step-by-step explanation:
The derivative of the function tells you the slope of the line at the point of tangency.
f'(x) = 2x
f'(2) = 4
Then the point-slope equation of the tangent is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -5 = 4(x -2) . . . . . tangent line with slope 4 through tangent point (2, 5)