Answers
The solution of the given expression is,
x = 1/2.
The given expression is,
[tex]36^{3x} = 216[/tex]
Since we know that,
As the name indicates, exponents are utilized in the exponential function. An exponential function, on the other hand, has a constant as its base and a variable as its exponent, but not the other way around (if a function has a variable as its base and a constant as its exponent, it is a power function, not an exponential function).
Now we can write it as,
⇒ [tex]6^{2^{3x}} = 6^3[/tex]
⇒ [tex]6^{6x}} = 6^3[/tex]
Now equating the exponents we get,
⇒ 6x = 3
⇒ x = 3/6
⇒ x = 1/2
Hence,
Solution is, x = 1/2.
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Related Questions
What additional information is needed to prove the triangles are congruent by the SAS Postulate?
Answers
An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.
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On an exam students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. what is the probability that the
Answers
The probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.
How to solveIf the student randomly orders the events, there is only one correct order out of all possible permutations.
Hence, the likelihood of selecting the accurate sequence is equal to 1 over the total count of potential arrangements.
As there are 5 occurrences, the overall count of conceivable sequences is equivalent to 5 factorial (5!), amounting to 120.
Therefore, the probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.
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On an exam, students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. What is the probability that the student chooses the correct order?
Create TWO equivalent expressions for the following.
14(8−16x)+3x
Answers
Two equivalent expressions for the given expression 14(8 - 16x) + 3x are 112 - 221x and 112 - 221x.
Equivalent expression 1:
Expanding the expression 14(8 - 16x) and combining like terms, we get:
112 - 224x + 3x
Simplifying further, we have:
112 - 221x
Equivalent expression 2:
Distributing the coefficient 14 to both terms inside the parentheses, we have:
112 - 224x + 3x
Combining the terms with the same variable, we get:
112 - 221x
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1. What will the coordinates of Triangle RST be after it is translated 4 units down and 3 units left?
--5-5
R
Da
4
64
5-
4
3-
bo
24
4
10
=arpy 5
-3
--5-
1 2 3 4 5 6 x
O Re(-7,-2), Sc(2, -1), Tc(-1,-9)
ORE(-1,-2), Sc(8,-1), Tc (5,-9)
ORE(-1,6), Sc(8,7), TC(5, -1)
O Re(-7,-2), Sc(8,-1), Tc(-1,-1)
Answers
The coordinates of the Triangle RST after it is translated 4 units down and 3 units to the left is the option;
R¢(-7, -2), S¢(2, -1), T¢(-1, -9)
What is a translation transformation?A translation transformation is one in which the location of the pre-image is transformed from its initial location to the destination location.
The coordinates of the vertices of the triangle RST are; R(-4, 2), S(5, 3), T(2, -5)
The translation transformation that is applied on the triangle RST includes;
A vertical translation 4 units downwards
An horizontal translation 3 units to the left
The translation transformation is therefore; T₍₋₃, ₋₄₎
Therefore, applying each transformation, we get;
R(-4, 2) ⇒ T₍₋₃, ₋₄₎ ⇒ R¢(-4 -3, 2 - 4) = R¢(-7, -2)
S(5, 3) ⇒ T₍₋₃, ₋₄₎ ⇒S¢(5 - 3, 3 - 4) = S¢(2, -1)
T(2, -5) ⇒ T₍₋₃, ₋₄₎ ⇒ T¢(2 - 3, -5 - 4) = T¢(-1, -9)
The correct option is therefore, the first option
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TriangleTriangle WXY with vertices W(8,-8), X(5,-2), and Y(3,-4) is drawn inside a rectangle, What is the area, in square units, of triangle LMN?
Answers
The area of the triangle whose dimensions are given in a vertices form would be = 9
How to calculate the area of a triangle given above?To calculate the area of the triangle, the formula that should be used is the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2
Where; W=A, X= B, Y = C
Ax= 8
By= -2
Cy= -4
BX= 5
Ay = -8
CX= 3
That is:
= 8(-2--4)+5(-4--8)+3(-8--2)/2
= 16+20-18/2
= 18/2
= 9
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Given the following Mayan Number, write the equivalent Base-10 number in the Answer Box. Each
row (place value) is separated with white space.
> Next Question
Your Answer:
:|| :||- €
Answers
The Mayan number || :||- € is equivalent to the base-10 number 1021.
How to find Mayan number?To convert a Mayan number to base-10, use the following steps:
Read the number from bottom to top, starting with the ones place.Assign a value to each digit, based on its position.Multiply each digit by its place value.Add the products together to get the final value.In this case, the values of the digits are as follows:
Ones: 1
Twentys: 0
Four-hundreds: 2
Eight-thousands: 1
The place values are as follows:
Ones: 1
Twentys: 20
Four-hundreds: 400
Eight-thousands: 8000
The final value is calculated as follows:
1 × 1 + 0 × 20 + 2 × 400 + 1 × 8000 = 1021
Therefore, the Mayan number || :||- € is equivalent to the base-10 number 1021.
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find the surface area
Answers
The Surface area of Triangular Prism is 132 cm².
We have have the dimension of prism as
Sides = 3 cm, 4 cm, 5 cm
and, l = 10 cm
and, b= 4 cm
Now, Surface area of Triangular Prism as
= (sum of sides) l + bh
= (3 + 4 + 5)10 + 4 x 3
= 12 x 10 + 12
= 120 + 12
= 132 cm²
Thus, the Surface area of Triangular Prism is 132 cm².
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Graph shows two triangles plotted on a coordinate plane. One triangle is at A (minus 4, 4), B (minus 8, 2), and C (minus 6, minus 6). Another triangle is at A prime (4, minus 2), B prime (2, 2), and C prime (6, 0). A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a followed by a .
Answers
The sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.
To determine the sequence of transformations that maps triangle ABC onto triangle A'B'C', let's analyze the given coordinate points.
Triangle ABC:
A (-4, 4)
B (-8, 2)
C (-6, -6)
Triangle A'B'C':
A' (4, -2)
B' (2, 2)
C' (6, 0)
By comparing the corresponding vertices, we can identify the transformations:
Translation:
To transform A to A', we can observe that A' is obtained by moving 8 units to the right and 6 units downwards from A. Therefore, the first transformation is a translation by (+8, -6).
Reflection:
Next, we notice that B' is the reflection of B across the y-axis. Thus, the second transformation is a reflection about the y-axis.
Therefore, the sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.
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Write the equation of the line, in slope-intercept form, with the
following information:
rate of change: undefined
point: (-3,2)
Answers
y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.
Thus, The most "popular" type of a straight line is one with a slope-intercept. Due of its simplicity, this is helpful to a lot of kids.
The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.
You may learn how to determine the equation of a line from any two points that this line passes through using the slope intercept form calculator.
Continue reading to find out what a linear equation's slope intercept form is, how to calculate a line's equation, and the significance of the slope intercept form equation in practical applications.
Thus, y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.
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3500pounds is placed into a savings account that pays interest at arate of 1.5% compounded annually.
Calculate the total compound amount at the end six years of investment, rounded to 2 decimal places.
Answers
Answer:
$3827.00
Step-by-step explanation:
To calculate the total compound amount at the end of six years with an interest rate of 1.5% compounded annually, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Total compound amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $3500
r = 1.5% = 0.015 (as a decimal)
n = 1 (compounded annually)
t = 6 years
Substituting these values into the formula, we have:
A = 3500 * (1 + 0.015/1)^(1*6)
Calculating this expression, we get:
A ≈ 3500 * (1.015)^6 ≈ 3500 * 1.093717 ≈ 3827.00
Rounding the total compound amount to 2 decimal places, the final value is approximately $3827.00
2x + y ≤ 2
a. change the inequality into slope-intercept form, and then change it into an equation.
b. create a table. Use the x-values indicated
c. Graph the points and draw a line.
d. Shade the solution area.
e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.
Answers
2x + y ≤ 2
y ≤ -2x + 2
To change it into an equation, we remove the inequality symbol and obtain:
y = -2x + 2
b. Using the x-values indicated, we can create a table of corresponding y-values:
|x | y |
|---|---|
|0 | 2 |
|1 | 0 |
|2 |-2 |
c. To graph the points and draw a line, we plot the points (0, 2), (1, 0), and (2, -2) on the coordinate plane and connect them with a straight line.
d. To shade the solution area, we need to determine which side of the line satisfies the inequality. Since the inequality is less than or equal to, we shade the area below the line.
e. To check the solution, we plug in the test point (0, 0) into the original inequality:
2x + y ≤ 2
2(0) + 0 ≤ 2
0 ≤ 2
The inequality holds, so the point (0, 0) is in the shaded area and satisfies the conditions of the original inequality. Therefore, the solution is valid.
9x⁸y² - 6x³y⁴ /3xy simplified is:
a. 3x⁹y³- 2x⁴y⁵
b. 3x⁷y - 2x²y³
c. 3x⁹y³ - 2x⁴y⁵
d. None of these choices are correct.
Answers
Answer: B
Step-by-step explanation:
The coefficients 9 & 6, divided by 3, equal 3 & 2.
For the exponents, if you divide the entire equation by xy, you need to subtract the corresponding exponents of x and y. Subtract the denominator's exponent from the numerator's exponent.
So, for the first part x^8/x^1=x^7
y^2/y^1=y
For the second part: x^3/x=x^2
y^4/y=y^3
So, if you put the coefficients and both parts of the equation together, you get 3x^7y - 2x^2y^3 (answer letter B).
Hope this helped!
A dance team is made up of 9 girls and 3 boys. Two of the girls and 1 of the boys are also on the debate team. What percent of the dance team is also on the debate team? Enter your answer in the box.
Answers
Answer:
25%
Step-by-step explanation:
9+3=12 dance people total
divide 3 by 12 to determine debate members over dance members
=.25 or 25%
33 + 78 + 10 + 98 + 76
Answers
Answer:
The sum of 33, 78, 10, 98, and 76 is 295.
Answer:
295
Step-by-step explanation:
add the numbers by using the addiction sign
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
Step-by-step explanation:
32 60 68
A truck travels from warehouse A at (–4,8) to warehouse B at (–4,–1). If each unit represents 20 miles per hour, how long will it take the truck to travel this distance?
Answers
It will take the truck 9 hours to travel from warehouse A to warehouse B.
To determine the time it takes for the truck to travel from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.
First, let's find the vertical distance between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.
Next, we convert the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.
Now, we can calculate the time it takes to travel this distance. We divide the distance by the speed of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.
Therefore, it will take the truck 9 hours to travel from warehouse A to warehouse B.
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7x 2/9 what the answer
Answers
Answer:
1.55
Step-by-step explanation:
2/9=0.22 x 7 =1.55
i hope this helps!
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
A)19.0
B)10.0
Step-by-step explanation:
Using [tex]\frac{1}{2} * absin(C)[/tex]
This is used when you have an angle between two sides
Kindly check the attached image for the solution
Michelle was fishing in her canoe at point A in the lake depicted
above. After trying to fish there, she decided to paddle due east
at a steady speed of 10 miles per hour. As she paddled, a wind
blowing due south at 5 miles per hour caused a change in her
direction. To the nearest tenth of a mile, what is the velocity,
represented by vector AC, of her canoe?
A 8.6 miles per hour
B 10 miles per hour
11.2 miles per hour
D 17.2 miles per hour
Answers
The velocity represented by vector AC of Michelle's canoe is approximately option C. 11.2 miles per hour.
How did we get the value?To determine the velocity, represented by vector AC, of Michelle's canoe, use the concept of vector addition.
Break down the motion into its components:
1. Paddling due east at 10 miles per hour: This motion can be represented by a vector pointing in the positive x-direction with a magnitude of 10 mph.
2. Wind blowing due south at 5 miles per hour: This motion can be represented by a vector pointing in the negative y-direction with a magnitude of 5 mph.
To find the resultant velocity, add these two vectors. Using the Pythagorean theorem, calculate the magnitude of the resultant velocity:
AC² = AB² + BC²
AB (paddling east) = 10 mph
BC (wind blowing south) = -5 mph (negative sign due to opposite direction)
AC² = (10 mph)² + (-5 mph)²
AC² = 100 mph² + 25 mph²
AC² = 125 mph²
Taking the square root of both sides:
AC ≈ √(125) mph
AC ≈ 11.2 mph (rounded to the nearest tenth)
Therefore, the velocity represented by vector AC of Michelle's canoe is approximately 11.2 miles per hour.
The correct answer is option C: 11.2 miles per hour.
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There are books on a shelf. of these books are new. The rest of them are used. what is the ratio of used books to all books on the shelf?
Answers
Let's denote the total number of books on the shelf as 'total_books', and the number of new books as 'new_books'.
The number of used books can be calculated as the difference between the total number of books and the number of new books:
used_books = total_books - new_books
To find the ratio of used books to all books on the shelf, we divide the number of used books by the total number of books:
Ratio of used books to all books = used_books / total_books
Substituting the expression for used_books, we have:
Ratio of used books to all books = (total_books - new_books) / total_books
Simplifying further:
Ratio of used books to all books = 1 - (new_books / total_books)
Therefore, the ratio of used books to all books on the shelf is equal to 1 minus the ratio of new books to total books.
The volume of a cone with height h and radius r can be found using the formula V= 1/3 π r^2h
Find the volume of a cone with radius 9 feet and height 4 feet. Round your answer to two decimal places.
Answers
Answer:
To find the volume of a cone with radius 9 feet and height 4 feet, we can use the formula:
V = (1/3) * π * r^2 * h
Plugging in the values:
V = (1/3) * π * (9^2) * 4
Calculating:
V = (1/3) * π * 81 * 4
V ≈ 108.19 cubic feet
Therefore, the volume of the cone is approximately 108.19 cubic feet (rounded to two decimal places)
The perimeter of an isosceles triangle is 45 inches. Two sides of the triangle are congruent,
and the third side is twice as long as the sum of the congruent sides. What is the length of the
third side of the triangle in inches?
Answers
Answer:
Length of third side = 30 inches
Step-by-step explanation:
We will need a system of equations to find the length of the third side.
First equation:
Let x represent the length of just one of the congruent sides and let y represent the length of the third side.We know the perimeter of a triangle is simply the sum of its sides.
Thus, since the perimeter is 45, our first equation is x + x + y = 45, which simplifies to 2x + y = 45.
Second equation:
Since we're told that the length of the third side is twice as long as the sum of the congruent sides, our second equation is y = 2(x + x), which simplifies to y = 2(2x) and then finally y = 4x
Method: Substitution.
We can first solve for x (length of one of the congruent sides) by substituting y = 4x for y in 2x + y = 45:
2x + 4x = 45
6x = 45
x = 7.5
Find y:
Now we can find y (length of the third side) by plugging in 7.5 for x in y = 4x:
y = 4(7.5)
y = 30
Thus, the length of the third side is 30 inches.
Optional Step to check validity of answers.
First equation: Check that the sum of 7.5, 7.5, and 30 = 45
7.5 + 7.5 + 30 = 45
15 + 30 = 45
45 = 45
Second equation: Check that 30 is twice the sum of 7.5 + 7.5
30 = 2(7.5 + 7.5)
30 = 2(15)
30 = 30
Thus, our answers are correct and we've correctly determined the length of the third side of the triangle in inches.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer: its D! not 8!!!
Step-by-step explanation:
What is the equation for this line?
Answers
y=2/3x-4 is the equation of the line where 2/3 is the slope.
We have to find the equation of line which is passing through points (0, -4) and (3, -2).
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁.
Slope = -2+4/3-0
=2/3
Now let us find the y intercept.
-4=2/3(0)+b
b=-4
The equation of line is y=2/3x-4.
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a pyramid and a cone are both 10 centimeters tall and have the same volume what statement
Answers
Answer: "The pyramid and the cone have the same volume despite their different shapes."
Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:
"The pyramid and the cone have the same volume despite their different shapes."
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Taylor recorded Weekly grocery expense for the past 16 weeks and determine the mean weekly expense was $83.20 later she discovers that one week expense of $90 was incorrectly recorded at $38. What is the mean
Answers
The mean weekly expense, after correcting the incorrectly recorded week, is $81.25.
How to solveGiven that Taylor recorded the past 16 weeks' expenses, excluding the incorrect recording of $90 as $38, we have 15 correct expense values.
Sum of correct expenses = $83.20 * 15 = $1248
Now we need to include the corrected expense of $90 instead of $38.
New sum of expenses = $1248 - $38 (incorrectly recorded) + $90 (corrected) = $1300
Finally, we calculate the mean by dividing the new sum by the total number of weeks, which is 16.
Mean weekly expense = $1300 / 16 = $81.25
Therefore, the mean weekly expense, after correcting the incorrect recording, is $81.25.
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Eleanor used a ruler to report the length of a
piece of wood as 9.7 inches.
Part A:
What is the range of values in inches for the
actual measurement of the piece of wood?
Part B :
How many significant digits does the measurement have?
Answers
Answer:
Part A: The actual measurement of the piece of wood could be between 9.65 and 9.75 inches.
Part B: The measurement has three significant digits.
Step-by-step explanation:
Significant digits are the digits in a number that carry meaning in terms of the precision or accuracy of the measurement. In this case, the number 9.7 has three significant digits, which means that the measurement is accurate to the tenths place.
What is the meaning of "[tex]dom(R)\subset \cup\cup R[/tex]"?
Answers
"dom(R) ⊂ UU R" means that the domain of relation R is a subset of the universal set associated with relation R
Understanding Set NotationThe notation "dom(R) ⊂ UU R" refers to the domain of a relation R being a subset of the universal set U.
Let me help you to break it down
1. dom(R): This represents the domain of the relation R. The domain of a relation is the set of all elements that appear as the first component in any ordered pair of the relation.
2. ⊂: This symbol indicates a subset relationship, meaning that the set on the left-hand side is a subset of the set on the right-hand side. In this case, "dom(R) ⊂ U" implies that the domain of relation R is a subset of the universal set U.
3. "UU R": The term "UU R" likely represents the universal set associated with relation R. It indicates the set that contains all possible elements that can be related by R.
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PLEASE ANSWER ASAP!!!!!
Answers
Answer:
[tex]\huge\boxed{\sf r = 5}[/tex]
Step-by-step explanation:
Given that,
7(q + 5) = (q + r)7Distribute7q + 35 = 7q + 7r
Subtract 7q from both sides7q - 7q + 35 = 7q - 7q + 7r
35 = 7r
Divide both sides by 735/7 = r
5 = r
OR
r = 5[tex]\rule[225]{225}{2}[/tex]
Answer:
r = 5
Step-by-step explanation:
Given statement,
→ 7(q + 5) is equivalent to (q + r)7.
Forming the equation,
→ 7(q + 5) = 7(q + r)
Now we have to,
→ Find the required value of r.
Then the value of r will be,
→ 7(q + 5) = 7(q + r)
Applying Distributive property:
→ 7(q) + 7(5) = 7(q) + 7(r)
→ 7q + 35 = 7q + 7r
Cancelling 7q from both sides:
→ 35 = 7r
→ 7r = 35
Dividing the RHS with number 7:
→ r = 35/7
→ [ r = 5 ]
Therefore, the value of r is 5.
Find the area of each shape
Answers
The area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.
From the given figure, the dimensions of trapezium are parallel sides a=7 ft, b= 13 ft and height = 5 ft.
Here, area of trapezium = 1/2 (Sum of parallel sides)×Height
= 1/2 ×(7+13)×5
= 1/2 ×20×5
= 50 square feet
Dimensions of triangle are base = 8 ft and height = 6 ft
Area of a triangle = 1/2 ×8×6
= 24 square feet
Therefore, the area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.
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