(1/36)^n = 216
Rewrite 36 as 6^2
(1/6^2) ^n = 216
Since 36 is in the denominator, the exponent is negative
(6^-2) ^n = 216
Rewrite 216 as 6^3
(6^-2)^n = 6^3
We know that a^b^c = a^(b*c) so
6^(-2n) = 6^3
Since the bases are the same, the exponents are the same
-2n = 3
Solving for n
n =-3/2
n = -1.5
Final answer:
The value of n for which [tex](1/36)^n[/tex] equals 216 is -3/2. This is found by expressing both sides of the equation with the common base of 6 and equating the exponents, then solving for n.
Explanation:
To find the value of n for which [tex](1/36)^n[/tex]= 216, first we express 216 as a power of 6, since 36 is a power of 6 (36 = [tex]6^2[/tex]): 216 = [tex]6^3[/tex]. We can then rewrite the equation using this equivalent expression of 216 and the knowledge that 1/36 is [tex]6^-2[/tex]:
[tex](6^-2)^n = 6^3[/tex]
Using the power of a power rule, this simplifies to:
[tex]6^(-2n) = 6^3[/tex]
Since the bases are the same, the exponents must be equal:
-2n = 3
Dividing both sides by -2 to solve for n, we get:
n = -3/2
Someone help please please someone
(1-52/2+5)=(1-26+5)=(-25+5)=-20
continuing:
-20*2*6*6= -40*6*6=-240*6=-1440
result: -1440
math help please help... ive been stuck on this, thank you so much !!!!!
Answer: (-3,4) and (9,20)
I think these two points will make the answer you have been looking for.
A building in a downtown business area casts a shadow that measures 88 meters along the ground. The straight-line distance from the top of the building to the end of the shadow it creates is at a 32° angle with the ground. What is the approximate height of the building? Round your answer to the nearest meter.
Answer: 55 meters
Step-by-step explanation:
Let the height of the building be 'h'.
Since building is standing vertical to the ground making right angle.
Then , the triangle formed is a right triangle .
The given angle of elevation : [tex]32^{\circ}[/tex]
Using trigonometry , we have
[tex]\tan\theta=\dfrac{\text{Perpendicular}}{\text{Base}}\\\\\tan(32^{\circ})=\dfrac{h}{88}\\\\\Rightarrow\ 0.6248693519=\dfrac{h}{88}\\\\\Rightarrow\ h=0.6248693519\times88=54.988502967\approx55\text{ meters}[/tex]
Hence, the approximate height of the building = 55 meters
Simplify.
x + (7 + 14 x )
[tex]x+7+14x[/tex] Take off the parenthesis
[tex]15x+7[/tex] Combine Terms
*(Answer)*= [tex]15+7[/tex]
Hope this helps
BangtanBoyScouts
Write and solve an inequality that models the situation.
Suppose you can get a higher interest rate on your savings if you maintain a balance of at least $1000 in your savings account. The balance in your savings account is now $1053. You deposit $44.50 into your account. What is the greatest amount that you can withdraw and still get the higher interest rate?
Answer:
$99.50
Step-by-step explanation:
Given that only if a minimum balance of 1000 dollars is maintained it will attract high interest.
To enjoy the privilege of high interest, it should be ensured that the balance does not go below 1000 dollars at any point of time.
Keeping the above in mind, we see that
Balance as of now .. 1053 dollars
Deposit .. 44.50 dollars
Balance after deposit .. 1097.50 dollars
Minimum balance .. 1000 dollars
Maximum amount
that can be withdrawn .. 1097.50 -1000 = 97.50 dollars.
which numbers round to 3,100 when rounded to the nearest hundred
one number that could round to 3 100 when rounded is 3 120
for every 13 baskets mr mcdoagh made ,ms klien made 2 baskets.if mr mcdonagh made 22 more baskets than ms klien did, how many baskets did they each make.
Using a system of equations based on the ratio of baskets made by Mr. McDonagh to Ms. Klein (13 to 2) and the information that Mr. McDonagh made 22 more baskets than Ms. Klein, we determine that Ms. Klein made 4 baskets and Mr. McDonagh made 26 baskets.
To solve how many baskets each person made, we will set up a ratio and use algebra to find the number of baskets made by Mr. McDonagh and Ms. Klein. We are given that for every 13 baskets Mr. McDonagh made, Ms. Klein made 2. Let's denote the number of baskets Mr. McDonagh made as M and the number of baskets Ms. Klein made as K.
According to the ratio, we can write [tex]\frac{M }{ K} = \frac{13 }{ 2}[/tex]. We also know that Mr. McDonagh made 22 more baskets than Ms. Klein, which can be written as M = K + 22. Now we have a system of equations:
[tex]\frac{M }{ K} = \frac{13 }{ 2}[/tex]
M = K + 22
Substitute M in the first equation with (K + 22):
[tex]\frac{K+22 }{ K} = \frac{13 }{ 2}[/tex]
2(K + 22) = 13K
2K + 44 = 13K
44 = 11K
Divide both sides by 11:
K = 4
Ms. Klein made 4 baskets. Now we can find how many baskets Mr. McDonagh made by substituting K back into one of our original equations:
M = 4 + 22
M = 26
Mr. McDonagh made 26 baskets.
simplify radical √m^4 n^7
answers
-mn^2 √n
-m^2n^2 √n
-m^2n^3 √n
[tex]\sqrt{m^{4} n^{7} }[/tex]
= [tex]\sqrt{m*m*m*m*m*N*N*N*N*N*N*N}[/tex]
Look for groups of 2 (a group of two on the inside, makes one on the outside)
= [tex]m*m*N*N*N\sqrt{N}[/tex]
= [tex]m^{2} n^{3} \sqrt{n}[/tex]
Answer: C
What is the reason for the fourth and eighth steps in the proof
Answer:
its D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
which of the following doesNOT represent a rational number
HURRY PLEASE
A) 0
B)2 1/2
C)square root of 3
D) -1/10
C. The square root of 3 is an irrational number. I hope that this helps!
What is the simplified product of (2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)
(2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)
Simplifying
(2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)
Remove parenthesis around (2x)
2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)
Multiply x * x2
2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)
Remove parenthesis around (2x)
2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)
Multiply x * x
2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)
Remove parenthesis around (2x)
2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)
Reorder the terms for easier multiplication:
2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)
Multiply 2 * -2
2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)
Multiply 3 * -2
2x3 + 2x2 + -4x + 3x2 + 3x + -6
Reorder the terms:
-6 + -4x + 3x + 2x2 + 3x2 + 2x3
Combine like terms: -4x + 3x = -1x
-6 + -1x + 2x2 + 3x2 + 2x3
Combine like terms: 2x2 + 3x2 = 5x2
-6 + -1x + 5x2 + 2x3
Answer:
The product is,[tex]-6 + -1x + 5x2 + 2x3[/tex]
explanation:
Simplifying
[tex](2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Remove the parentheses (2x)
[tex]2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Multiply [tex]x * x2[/tex]
[tex]2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Remove the closing parentheses (2x)
[tex]2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Multiply [tex]x * x[/tex]
[tex]2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Remove all parentheses (2x)
[tex]2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Rearrange the terms to make multiplication easier:
[tex]2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Multiply [tex]2 * -2[/tex]
[tex]2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)[/tex]
Multiply [tex]3 * -2[/tex]
[tex]2x3 + 2x2 + -4x + 3x2 + 3x + -6[/tex]
Reorder the terms:
[tex]-6 + -4x + 3x + 2x2 + 3x2 + 2x3[/tex]
Combine like terms: -4x + 3x = -1x
[tex]-6 + -1x + 2x2 + 3x2 + 2x3[/tex]
Combine like terms: 2x2 + 3x2 = 5x2
[tex]-6 + -1x + 5x2 + 2x3[/tex]
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Order the correlation coefficients from weakest to strongest negative correlation -0.59 , -0.18 , -0.82 , -0.37
The correlation coefficients from weakest to strongest negative correlation can be arranged as -0.18, -0.37, -0.52, and -0.82.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.Given the correlation coefficients as -0.59 , -0.18 , -0.82 , -0.37. Now, as we know that the number closest to 1 is stronger, while the number closest to 0 is weakest. Therefore, the correlation coefficients from weakest to strongest negative correlation can be arranged as,
-0.18 < -0.37 < -0.59 < -0.82
Hence, the correlation coefficients from weakest to strongest negative correlation can be arranged as -0.18, -0.37, -0.52, and -0.82.
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will give brainliest
Answer:
12
Step-by-step explanation:
2 times 2 is 4
4 divided by 2 is 2
2 times 2 is 4
2 times 6 is 12
12 divided by 2 is 6
4 plus 2 plus 6 is 12
he minute hand of a clock moves from 12 to 10 o'clock, or five sixths of a complete revolution. Through how many degrees does it move? Through how many radians does it move?
The degree of a complete rotation is 360 degrees.
5/6th of a rotation = 5/6 X 360
that is 300 degrees.
Thus the minute hand moves 300 degrees.
(Sorry, I'm not sure about the radians ;-) )
If the minute hand of a clock moves from 12 to 10 o'clock, or five-sixths of a complete revolution, by 300 degrees it will move.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called an "Angle."
It is given that, the minute hand of a clock moves from 12 to 10 o'clock, or five-sixths of a complete revolution.
The degree of a complete rotation is 360 degrees.
5/6th of a rotation it covers,
= 5/6 × 360
=300 degree
Any given angle must be multiplied by π/180 to be converted from the degree scale to the radian scale.
=300 × π/180
=5.235 radians
As a result 5.235 radians, will move.
Thus, if the minute hand of a clock moves from 12 to 10 o'clock, or five-sixths of a complete revolution, by 300 degrees it will move.
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Geometry PLEASE HELP ASAP! Randy wants to attach a 14 foot string of lights to the top of the 12 foot mast of his sailboat. How far from the base of the mast should he attach the end of the light string? Round your answer two decimal places.
The answer is 7.21.
Randy should attach the end of the light string approximately 7.21 feet from the base of the mast using the Pythagorean theorem, as the distance from the base to the end of the string forms the leg of a right-angled triangle with the mast and the string itself.
Explanation:To solve Randy's problem, we need to use the Pythagorean theorem, which is applicable because we are dealing with a right triangle formed by the mast, the ground, and the string of lights. The mast is one leg of the triangle, and the string of lights is the hypotenuse. We are trying to find the length of the other leg, which is the distance from the base of the mast to the point where the end of the light string will be attached.
The formula for the Pythagorean theorem is:
a² + b² = c²
Where:
a is one leg of the triangleb is the other leg of the trianglec is the hypotenuse (the side opposite the right angle)In this scenario, a is the mast with a known length of 12 feet, c is the string of lights with a known length of 14 feet, and b is the distance from the base of the mast we need to calculate.
By substituting the known values into the theorem, we have:
12² + b² = 14²
Which simplifies to:
144 + b² = 196
Subtracting 144 from both sides:
b² = 196 - 144
b² = 52
Then, take the square root of both sides:
b = √52
After calculating, we find that:
b ≈ 7.21 feet
So Randy should attach the end of the light string approximately 7.21 feet from the base of the mast to reach the top.
Are angles 1 and 4 linear pair, vertical angles or neither? Thank you! :)
Answer:
it is a linear one i think
The classification of angles 1 and 4 as either linear pairs, vertical angles or neither is impossible without more context or a diagram. Linear pairs are adjacent angles that form a straight line and total 180 degrees, while vertical angles are directly opposite each other from an intersection of two lines and are equal.
Explanation:Without a proper diagram or more context, it's challenging to determine whether angles 1 and 4 are linear pairs, vertical angles, or neither. However, I can explain what these terms mean. Linear pairs are adjacent angles whose non-common sides form a straight line, adding up to 180 degrees. Vertical angles are angles opposite each other when two lines intersect. They are equal in measure. Unfortunately, without a specific diagram indicating the positions of angles 1 and 4, I can't definitively answer your question.
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GameStop has the Xbox one advertised for 15% off the original price of $350 plus 6% sale tax online Xbox one is advertised at Best Buy for $310.00 plus 9% sales tax which is the better buy
GameStop's total will be 371.00
Best Buy's total will be 337.90
Best Buy will be the better buy
Your answer is Best Buy
Answer:
The best option for buying the Xbox One is GameStop, as the final price would be of $315.35.
Step-by-step explanation:
GameStop: To obtain the price in GameStop, we must first obtain the 15% discount on the price of 350, and subtract it from the initial price. Then, we must calculate the amount of the tax and add it to the price to obtain the final price.
(350 - (350 x 0.15)) x 1.06 = $315.35
Best Buy: Instead, at Best Buy we simply add the sales price tax.
310 x 1.09 = $337.90
What is 7.2 times 10 to the 7th power times 14.6 x 10 to the 5th power?
7 x [tex]10^{7}[/tex] times 14.6 x[tex]10^{5}[/tex]
Multiply 7 and 14.6 and add exponents
Final Answer 102.2 and [tex]10^{5}[/tex]
hope that helps :)
7.2 x 10 x 5 x 14.6 x 10 x 5
7.2 x 100000 x 14.6 x 100000
720000 x 1460000 = 1.0512 x 10 x 12
A map of a town has no scale. You know that the distance between the bus stop and the park is 6 miles. On the map it is 3 inches. Also, on the map you know the distance from the park to the house is 8 inches. What is the actual distance in miles between the park and the house?
Answer:
The answer is 16
Plz help best answer gets brainly
Arrange the number in decreasing order: 8.508 8.58 7.5 7.058
8.58 , 8.508 , 7.5 , 7.058 :]
Answer: 8.58, 8.508, 7.5, 7.058
Determine how much the bill will be if there are 50 text messages
Answer:
about 105
Step-by-step explanation:
Squaring a number and subtracting 6 gives the same result as doubling the number and adding 9.
The answer is 5.
5^2 = 25 25 - 6 = 19
5 x 2 = 10 10 + 9 = 19
Antonio graphs these equations and finds that the lines intersect at a single point, (–5, 0.25). Equation A: Equation B: 4y – 3x = 16 –x – 8y = 3 Which statement is true about the values x = –5 and y = 0.25?
Given equations : Equation A: 4y -3x =16 and
Equation B: -x-8y =3.
We are given a point (-5,0.25) plugging it in first equation
4(0.25) -3(-5) =16
1+15 =16.
16 =16 : Satisfies first equation.
Plugging (-5,0.25) it in second equation.
-(-5)-8(0.25) =3.
5 - 2 = 3.
3=3 : Satisfies first equation.
Therefore, they are the only values that make both equations true.A rectangle is placed inside a circle whose diameter is 13 with all of its corners on the circle. The area of the rectangle is 60. What are the dimensions of the rectangle? Hint: Draw a picture and use the Pythagorean Theorem.
Given
A rectangle is placed inside a circle whose diameter is 13unit all corners of it on the circle.
area of the rectangle = 60 square unit
Find the dimensions of the rectangle.
To proof
As given in the question
rectangle is placed inside a circle whose diameter is 13unit .
now by using the diagram given below
the diagonal of the rectangle is equal to the diameter of the circle.
Thus DB = 13 unit
FORMULA
Area of the rectangle = Length × Breadth
area of the rectangle = 60 square unit
let the value of the length be ( Say AB ) = x
put the value in the above equation
we get
60 = x × Breadth
[tex]Breadth( say AD)= \frac{60}{x}[/tex]
now in ABD
Using the pythagorus theorem
we get
BD²= AB² + AD²
[tex]13^{2} = x^{2}+ (\frac{60}{x}) ^{2}[/tex]
solving the above equation
we get
[tex]169x^{2}= x^{4} + 3600[/tex]
[tex]x^{4} - 169x^{2}+3600 =0[/tex]
[tex]x^{4} - 144x^{2} -25x^{2} + 3600 =0[/tex]
[tex]x^{2} (x^{2} - 144) - 25 (x^{2} - 144) =0[/tex]
(x² - 25) (x² -144) =0
The roots are
x = -12 ,-5, 5, 12
-12 and -5 are neglected because of negative terms .
( Length and breadth of recangle cannot be negative )
thus x = 12 and 5
Two case arise
First case
when
Length of rectangle= 12unit
[tex]Breadth = \frac{60}{12}[/tex]
Breadth of rectangle = 5 unit
Second case
Length of rectangle= 5unit
[tex]Breadth = \frac{60}{5}[/tex]
Breadth of rectangle = 12 unit
Hence proved
Final answer:
To find the dimensions of a rectangle inside a circle with a diameter of 13, we use the Pythagorean Theorem and the area of the rectangle. After substituting values and solving, we find the dimensions are 5 units by 12 units.
Explanation:
To find the dimensions of the rectangle that fits inside a circle with a diameter of 13, one must first recognize that the rectangle forms the sides of a right-angled triangle where the diagonal of the rectangle serves as the hypotenuse of the triangle. This hypotenuse, thus, equals the diameter of the circle, which is 13 units.
Since the area of the rectangle is 60 square units, we let the sides of the rectangle be denoted as length (l) and width (w), with the area equation being l×w = 60.
Using the Pythagorean Theorem, we have: l2 + w2 = 132. We also know that lw = 60, which allows us to solve for one variable in terms of the other. Let's solve for w: w = 60/l. Substituting this into the Pythagorean equation gives l2 + (60/l)2 = 169. Solving this quadratic equation will give us the dimensions of the rectangle that can fit within the circle.
After solving, one finds that the dimensions that satisfy both the area and the Pythagorean Theorem are 5 and 12.
Therefore, the dimensions of the rectangle are 5 units by 12 units.
the temperature in Indianapolis was-4°F at 7:00 am. the temperature rose 3°F by noon. What was the temperature at noon? use a number line to find the answer
What is the product of 3a + 5 and 2a +4a - 2
The product of the expressions 3a + 5 and 6a - 2 is 18a² + 24a - 10. The distributive property is used to multiply each term in the first expression by each term in the second.
The product of the two expressions 3a + 5 and 2a + 4a - 2 can be found using the distributive property. First, combine like terms in the second expression to simplify it to 6a - 2. Now, to find the product, multiply each term in the first expression by each term in the simplified second expression:
Multiply 3a by 6a to get 18a².
Multiply 3a by -2 to get -6a.
Multiply 5 by 6a to get 30a.
Multiply 5 by -2 to get -10.
Combining these products gives you the final answer: 18a² + 24a - 10.
WITH ANSWER
What is the exact value of x in the exponential equation 2(10)^3x=26 in log
*****x=log13/3
[tex]2\cdot 10^{3x}=26\\10^{3x}=13\\\log 10^{3x}= \log 13\\3x\log 10= \log 13\\3x= \log 13\\\\[/tex]
[tex]x=\frac{\log 13}{3}[/tex]
lmk if you have questions
To find the exact value of x in the exponential equation 2(10)^3x=26, divide both sides by 2, apply the common logarithm, use the power rule of logarithms, and simplify to find that x equals log(13)/3.
To solve the exponential equation 2(10)³ˣ=26 for the exact value of x using logarithms, follow these steps:
Divide both sides of the equation by 2 to isolate the exponential term:Thus, the exact value of x is log(13)/3.
A __________ is NOT rigid motion transformation.
rotation
dilation
translation
reflection
*(The Answer)*= C. Dilation
*(Explanation)*= If you search than you will find that translation, rotation, and refection or the one that are ridged, however, dilation is.
Answer:
The correct option is 2. A dilation is NOT rigid motion transformation.
Step-by-step explanation:
Rigid motion transformation : A transformation is called a rigid motion transformation if a point or object is moved, but the size and shape remain the same.
In rotation, the point of figure is rotated about the center of rotation but the size and shape remain the same.
Therefore rotation is a rigid transformation and option 1 is incorrect.
In dilation, the figure is stretched of compressed by the scale factor k along the center of dilation, so the size of figure is either increase of decrease.
Therefore dilation is not a rigid transformation and option 2 is correct.
In translated, the point of figure is shifted but the size and shape remain the same.
Therefore translation is a rigid transformation and option 3 is incorrect.
In reflection, the point of figure is reflected about the line of reflection but the size and shape remain the same.
Therefore reflection is a rigid transformation and option 4 is incorrect.
Violin strings are parallel. Viewed from above, a violin bow in two different positions forms two transversals to the violin strings. Find x and y in the diagram.
ANSWER
[tex]x=10[/tex]
and
[tex]y=20[/tex]
EXPLANATION
Since corresponding angles are equal,
[tex]4x+y=60---(1)[/tex]
Alternate angles are also equal, therefore,
[tex]8x+y=100---(2)[/tex]
Equation (2) minus equation (1) gives,
[tex]\Rightarrow 4x=40[/tex]
[tex]\Rightarrow x=10[/tex]
We put [tex]x=10[/tex] in to equation (1)
[tex]4(10)+y=60[/tex]
[tex]y=60-40[/tex]
[tex]y=20[/tex]
To find x and y in the violin string diagram, use the properties of angles formed by transversals and parallel lines. Corresponding angles and interior angles are key relationships. In the example, x = 15° and y = 90°.
The problem involves understanding the relationships between angles formed by transversals and parallel lines. When a violin bow is placed across parallel violin strings, it forms transversals that create various angles.
Given that the violin strings are parallel, the interior angles formed on the same side of the transversal are supplementary. Let's consider the setup of the diagram:
Identify corresponding angles, alternate interior angles, and alternate exterior angles.Use the properties of parallel lines and transversals to set up equations.Solve for the unknowns (x and y).Example: Suppose the violin strings and the bow are positioned in such a way that we can see the angles formed. Assume the given angles are as follows:
Angle 1 = 30° (corresponding angle)Angle 2 = (2x)° (alternate interior angle)Angle 3 = y°Step 1: Since Angle 1 and Angle 2 are corresponding angles and lie between parallel lines:
30° = 2x → 2x = 30° → x = 15°
Step 2: To find y, use the fact that the sum of angles around a point is 360°. Suppose y is opposite to the sum of Angle 1 and another given angle on the same side:
If the other angle on the same side is 60°:
y = 180° - (Angle 1 + 60°) → y = 180° - (30° + 60°) → y = 90°
Thus, the values of x and y are determined to be 15° and 90°, respectively.