The expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.
Equivalent expressionIt follows from the task content that the equivalent expression as in the task content can be determined by the laws of Indices as follows;
3^(2x -3)
= 3^(2x) × 3-³
= (3²)^x × 1/3³
= 9^(x) × 1/27
= 9^(x)/27.
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The expression that is equivalent to 3^(2x - 3) is; Option A: the quantity 9 to the power of x end quantity over 27.
How to use Law of Indices?Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base.
Now, we are given the expression as 3^(2x - 3). This can be broken down into; 3^(2x) × 3⁻³
Now, according to laws of indices;
3^(2x) = (3²)ˣ
Thus, we now have;
= ((3²)ˣ)/3³
= 9ˣ/3³
= 9ˣ/27
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Find a vector function that represents the curve of intersection of the two surfaces. the paraboloid z = 8x 2 y 2 and the parabolic cylinder y = 3x 2 r(t) = t i j
The vector function, r(t) that represents the curve of intersection of the two surfaces, the paraboloid and the parabolic cylinder is given by < t, 3t2, 8t2 + 9t4 >. It is attained by applying the concept of vectors to the assigned problem.
What is a vector?
A vector is any quantity that contains both magnitudes as well as direction. Geometrically, one can imagine a vector as a directed line segment, whose length denotes the magnitude of the vector and the direction is shown by the arrow, which is generally taken from its tail to its head. Using an arrow with a line specifies that it is not only scalar but also has some direction.
Calculation of the vector function representing the curve of intersection of the paraboloid and parabolic cylinder
A vector function r(t) is represented as: r(t) = < x, y, z >
Given: y = 3x2 – 1
z = 8x2 + y2 – 2
Let,
x = t
Using x = t in equations 1 and 2
y = 3t2
z = 8t2 + y2
Putting the value of y in z, we get,
z = 8t2 + (3t2)2
z = 8t2 + 9t4
Substitute these values of x, y, and z in vector representation to obtain the result, i.e. < t, 3t2, 8t2 + 9t4 >
Hence, the value of vector function r(t) is: < t, 3t2, 8t2 + 9t4 >
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estimate the square root to the nearest tenth the square root of 11, and the square root of 62
The square root of 11 and 62 to the nearest tenth is 7.9 and 3.3 .
Given, the numbers are 11 and 62.
we are asked to determine the square root of the given numbers to the nearest tenth.
a. 11
Since the given number is not an even number, hence we can't get a whole number as the square root of 11.
we need to find the number whose square root is nearest to the number 11.
3 × 3= 9
9 is nearer to 11 whereas 4 × 4 = 16 gets greater than 11.
then dividing the number 11 by 3.we get:
√11 = 3.31662479 × 3.316622479
√11 = 3.31662479
√11 = 3.4 (rounding off to the nearest tenth)
b. 62
since we can't get the square root as a whole number so ,
we need to find the number whose square root is nearest to the number 62.
8 × 8 = 64
which gets greater than 62, hence we take 7 × 7 = 49
therefore, √62 = 7.874007874 × 7.874007874
√62 = 7.874007874
√62 = 7.9 (rounding off to the nearest tenth)
hence we get the square root of 11 and 62 as 3.3 and 7.9 respectively.
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HELP ME WITH QUESTION B PLEASE!!!
Cavitation reduces a tree's ability to conduct water due to the formation of air bubbles in water, thereby reducing the hydraulic conductance of the tree.
How does cavitation affects a tree's ability to conduct water?Cavitation, also known as embolism, is said to occur when the tracheid or vessels of the xylem is being filled with bubbles of air. Cavitation is what is said to occur when air bubbles form in water during transpiration.
The effect of cavitation is the prevention of the upward pull of water, leading to a degradation of hydraulic conductance, such that the xylem water potential is reduced.
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9 is subtracted from the product of 9 and a number.
The numerical form of the statement the product of 9 and a number is
9n - 9.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given statement is 9 is subtracted from the product of 9 and a number.
Let the number be 'n'.
Therefore, The statement 9 is subtracted from the product of 9 and a number can be numerically written as,
9n - 9.
We can also take 9 as a common factor,
9(n - 1).
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Choose the system
for the graph
a)
(3x + 4y ≤ 12
(2x - 5y ≤ 10
(3x + 4y ≤ 12
2x - 5y ≥ 10
b)
:
(3x + 4y ≥ 12
c) (2x - 5y ≥ 10
(3x + 4y ≥ 12
d) (2x - 5y ≤ 10
Therefore, option (c) is the correct system for the graph based on the given options.
Based on the given options, the correct system for the graph would be option (c):
(2x - 5y ≥ 10
(3x + 4y ≥ 12
In option (c), both inequalities have the same orientation (greater than or equal to) and the same signs (+ and -) in front of the variables (x and y) as the original problem statement. This ensures that the inequalities maintain the same relationship.
Option (a) has one inequality with the opposite orientation (≤) compared to the original problem statement, which would result in an incorrect solution.
Option (b) has both inequalities with the opposite orientation (≥), which is also not consistent with the original problem statement.
Option (d) has one inequality with the opposite orientation (≤), which does not match the original problem statement.
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Cual es el radio de 35 cm
Answer: 17.5
Step-by-step explanation:
Si un circulo tiene un diametro de 35 centimetros entonces para encontrar el radio se divide en 2. 35 /2 = 17.5
HELPPP 15 pointssssss mathhh
the lengths of plate glass parts are measured to the nearest tenth of a millimeter. the lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.9. determine the mean and variance of the lengths. (a) mean round your answer to two decimal places (e.g. 98.76). (b) variance round your answer to three decimal places (e.g. 98.765)
The mean is 590.45 and the variance is 0.053.
What is arithmetic mean and variance?
A mean refers to a representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.The expectation of a random variable's squared divergence from its population mean or sample mean is known as its variance.Now,
Adding together all the numbers and dividing by the total number of data points yields the mean:=> Sum of all the values = 590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6
=> Since 8 data values are present,
=> Mean = 4723.6/8 = 590.45
We deduct each data value from the mean in order to calculate the variance. Next, we square this discrepancy to determine the average square:=> 590.1 - 590.45 = -0.35;
=> (-0.35)² = 0.1225
=> 590.2 - 590.45 = -0.25;
=> (-0.25)² = 0.0625
=> 590.3-590.45 = -0.15;
=> (-0.15)² = 0.0225
=> 590.4-590.45 = -0.05;
=> (-0.05)² = 0.0025
=> 590.5-590.45 = 0.05;
=> (0.05)² = 0.0025
=> 590.6-590.45 = 0.15;
=> (0.15)² = 0.0225
=> 590.7-590.45 = 0.25;
=> (0.25)² = 0.0625
=> 590.8-590.45 = 0.35;
=> (0.35)² = 0.1225
Thus, variance = [tex]\frac{(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)}{8}[/tex] = 0.42/8 = 0.0525 ≈ 0.053
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A small treasure chest is in the shape of a rectangular prism.
The length of the chest is y feet, the width ½ y feet, and the height
2y feet. The chest holds 8 cubic feet of treasure. What are the
dimensions of the treasure chest?
Answer:
length = 2ft
width = 1 ft
height = 4 ft
Step-by-step explanation:
V = LWH
V = (1/2)y × y × 2y
V = y³ = 8 ft³
y = 2
length = 2ft
width = (1/2)(2 ft) = 1 ft
height = 2(2 ft) = 4 ft
show that 268 can be written as the sum of a power of 3 and a squared number
We have shown that 268 can be written as the sum of a power of 3 and a squared number.
We are given a number:
268
We need to show that it can be written as the sum of a power of 3 and a squared number.
We can write 268 as:
268 = 243 + 25
Now, factors of:
243 = 3 × 3 × 3 × 3 × 3
25 = 5 × 5
So, this can be rewritten as:
268 = 3 ⁵ + 5²
which is he sum of a power of 3 and a squared number
Therefore, we have shown that 268 can be written as the sum of a power of 3 and a squared number.
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Hi! Can someone solve and tell me all the steps so I could understand how to do this?
Answer:
x = 12
AB = 39
AC = 24
Step-by-step explanation:
The sum of AB and BC is equal to the length of AC.
We can write the following equation based on this information :
AB + BC = AB rewrite the equation using given values
4x - 9 + 3x - 12 = 63 add like terms
7x - 21 = 63 add 21 to both sides
7x = 84 divide both sides by 7
x = 12 replace x with 12 in each expression to find the lengths
AB = 4x-9
AB = 4•12 - 9 and
AB = 39
BC = 3x -12
BC = 3•12-12 and
BC = 24
WILL MARK BRAINLIST WILL GIVE 5 STAR REVIEW
Answer: software, hardware, input device, operating system
Step-by-step explanation:
Answer:
windows-software
mouse-input device
microsoft word-operating system
motherboard-hardware
Step-by-step explanation:
22. Pamela is making the legs for a three-legged stool from two pieces of scrap wood. The lengths of the two pieces of wood are 36 inches and 21 inches. Each leg is 16 inches long. a. Pamela cuts one leg from each piece of wood. Write and evaluate two expressions to show how much of each piece of wood is left over. b. Will Pamela have enough wood for a third leg? Explain.
Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.
We are given that:
Pamela wants to make a three legged stool.
She has two pieces of wood: 36 inches and 21 inches.
Length of each leg = 16 inches.
Now, she cut 1 leg from each piece of the wood.
Length of wood pieces left will be given by the expression:
36 inches - 16 inches = 20 inches
and
21 inches - 16 inches = 5 inches.
Yes, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.
Therefore, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.
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I really need some help
Answer:
a
Step-by-step explanation:
The commutative property is related to both addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.
Since the question specifically asked for multiplication, the answer is a.
Find the distance between -2 3/5 and -1 on a number line. Write your answer as a mixed number.
The distance between -2 3/5 and -1 on a number line is -1 3/5.
What is the distance?A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is -2 3/5.
In order to determine the distance, -1 would be subtracted from -2 3/5
[tex]-2\frac{3}{5} - (-1)[/tex]
[tex]-2\frac{3}{5} + 1[/tex]
[tex]-\frac{13}{5} + \frac{5}{5}[/tex]
[tex]\frac{5 - 13}{5}[/tex]
-8/5 = -1 3/5
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over which interval is the graph of f(x)=-(x+8)^2-1 decreasing
The interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).
We are given the function:
f ( x ) = - ( x + 8 )² - 1
We will first simplify the expression:
f ( x ) = - x² - 64 - 16 x - 1
f ( x ) = - x² - 16 x - 65
Now, we will plot the function on a graph.
Now, we can see that, the function is decreasing at [-8, ∞) from the graph of the function.
Therefore, the interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).
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Select the correct answer. ethel is arranging rides so that 27 members of her club can go bowling. some people can ride in a van that belongs to the center where they meet. the rest must ride in cars. if 12 can go in the van, and 5 can go in each car, how many cars will they need? a. 3 cars b. 5 cars c. 7 cars d. 9 cars
There are 3 cars to be needed for the remaining 15 persons in Ethel club.
Unitary method:
Unitary method used to find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Given,
27 people will travel for bowling.
As there is only one van.
and in that one van only 12 people can go.
so remaining people will go by car
no. of people that they will go by car
=> 27 - 12 = 15
in one car 5 people can go
no. of cars needed to take people=no. of people/no. of cars
=> 15 / 5 = 3
Therefore 3 cars will be needed.
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Given the following informat
1
3. slope = y-intercept = -1
TT
The equation of straight line in the cartesian plane with slope and y-intercept of -1 is y+x+1=0
A straight line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.
The x-axis, a horizontal line, and the y-axis, a vertical line, are two perpendicular lines that split the number plane, also known as the Cartesian plane, into four quadrants. The origin is the location where these axes converge.The general equation of a line in the cartesian plane is given by the equation y = mx + c , where m is the slope and c is the y-intercept.The slope of a straight line is calculated by taking tan θ where θ is the angle made by the line with positive direction of x- axis.Given the slope = y-intercept= -1
Therefore m = -1 and c = -1 .
Substituting the values of m and c in the general equation of a straight line we get :
y = -x - 1
or, y + x+ 1 = 0
Therefore the equation of the straight line is y + x+ 1 = 0.
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given h (x)=2x+4 find h(-1)
The required simplified value of the given expression h(-1) = 2.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As given that,
h (x)=2x+4
Put x = -1
h(-1) = 2(-1) +4
h(-1) = 2
Thus, the required simplified value of the given expression h(-1) = 2.
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the answers for 22, 24,and 25?
Answer:
22) -3jk+12k^2---------24)-3xy^4-7xy^3
Step-by-step explanation:
Please explain what the answers are for questions 2, 3, 4, 5, and 6 and how or just help me with the questions you know the answers to, thanks!
Which model shows 4 × 5? 25 or 20 or 9 or 16 witch one? pls help marking brainly pritty pleaseeeeee
Answer:
20.
Step-by-step explanation:
Well, Multiplication is simple. 4*5 is 20, because you're basically writing and solving 5+5+5+5. 5 added to itself 4 times.
Hope this helps!
Side Note
If you have trouble with Division, the way to do it with this equation is:
You know our answer is 20 now, so what is 20/5? (20 divided by 5) This would be 4. This is the Inverse Property of Multiplication.
can anyone help me find the answer to the attatched question
Answer:
Angle BOC = 120°
Angle DOC = 60°
Angle ODC = 90°
Step-by-step explanation:
Triangle ABC is an equilateral triangle, therefore Angle BAC = 60°.
Now that we know Angle BAC, we can find Angle BOC: 2 × 60 = 120°
Angle DOC = ½ Angle BOC ( Radius drawn from centre to midpoint of chord, bisect the angle)
So Angle DOC = ½ (120) = 60°
Angle = 90° because D is the midpoint of chord BD and OD is a radius.
Solve for u.
u +4=7
U =
in the above question we have to do addition and subtraction method. Therefore, u is equal to 3.
What is addition?Addition in math is a process of combining the two or more numbers. Addends are the numbers added, and the result or final answer we get after the process is called the sum. It is one of essential mathematical functions we use in our everyday activities. There are many situations in which we use to add the numbers. One of the most common everyday uses for adding the numbers is when we work with time or money—for example, adding up the bills and receipts.
An addition sentence is a mathematical expression that shows the two or more values added together and their sum. The two or more values that are added are called the addends. The parts of an addition sentence are the two or more addends, plus symbol(s), equal sign, and the sum.
From above question, it is given that:
u+4=7
so, u= 7-4= 3
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(URGENT)Trinity walked to town at a rate of 4 mph. She rode the bus back at 40 mph. The town is 2 miles away. How long did it take Trinity to travel to town and back?
Based on the fact that town is 2 miles away, the time it took Trinity to travel to town and back was 33 minutes
How long did Trinity travel?The time taken can be found as:
= Distance / Speed
Trinity's trip to town took:
= 2 / 4
= 0.5 hours
Trinity's trip back took:
= 2 / 40
= 0.05 hours
The total time it took Trinity to travel to and from town was:
= (0.5 + 0.05) x 60 minutes per hour
= 0.55 hours x 60
= 33 minutes
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Solve the system of equations 2x+y=-2 and -9x-3y=18 by combining the equations.
Answer:
2x+y=-2
-9x-3y=18
So what you would do is see which one you would like to get rid of (either x, or y in this situation get rid of y)
multiply y by postive 3
3(2x+y=-2)
6x+3y=-6
-9x-3y=18 (both y's cross out since 3y+-3y is equal to zero)
-----------------
-3x=-24 (divide both sides by -3)
--- ---
-3 -3
x= 8 (neg/neg=positive)
Then figure out the x so use either the first or second equation
so in this case I will use the first equation (plug in the x for 8)
2(8)+y=-2
16+y=-2
-16 -16
---------------
y=-18
Check:
2x+y=-2
2(8)+y(-18)=-2
16+-18=-2
-2=-2 (therfore you know that you are right)
Ansers:
y=-18
x=8
Hope this helps!
Ratios Equivalent to 15:6 (not 6:15)
Pls tell me what ratios they are
Answer:
30/32
Step-by-step explanation:
15×2=30
16×2=32
30/32
Answer:
5:2 , 30:12 , 60:24 , etc.
Step-by-step explanation:
To identify ratios equivalent to 15:6, all you need to do is multiply or divide both numbers in the ratio by the same amount to find an equivalent ratio.
So, for example:
1:2 --> 1*2 : 2*2 = 2:4 Both one half, so equal.
Now for 15:6...
Let's divide by the least common denominator ( 3 )
15 / 3 and 6 / 3 = 5 and 2
So 15:6 = 5:2
And we can also multiply the ratio by any constant as well...
For example 15 * 2 and 6 * 2
So 30:12 = 15:6
Hope this helped!
A ball is dropped from rest and takes 1.3 s to hit the ground. from what height was it dropped?
Initial velocity=0
Height=45m
G=10m/s^2
By the 2 nd equation of motion …(Under free fall)-
H = ut + 1/2 g t^2
45 = 0 + {1/2 * 10 * (t^2)} •: [0*t=0]
45 = 5 t^2
45/5 = t^2
9 = t^2
√9=t
3=t
Answer-: The time taken would be 1.3 seconds to reach the ground.
To three decimal places, what is the volume of a cube (cm3) with an edge length of 0.843 cm?
The volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.
According to the given question.
Length of the edge of the cube = 0.843 cm.
As we know that, a cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
And the volume of cube is calcualted by the formula
V = a^3
Where,
V is the volume of cube
And, a is the length of the edge of cube
Therefore,
The volume of the cube whose edge length is 0.843 cm
= (0.843cm)^3
= 0.599 cubic centimeters
Hence, the volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.
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two cities are 65 miles apart
a. if their distance on the map is 3 1/4 inches, find the scale of the map
b. on another map, the same cities are 6.5 inches apart. What is the new scale?
c. If the scale was 2 inches: 11 miles, how far apart would the same cities be on the map? Round to the nearest inch.
The scale is 1 inch represent 20 miles.
The new scale is 1 inch represents 10 miles
The distance on the map would be 11.8 inches.
What is the scale of the map?A scale drawing is a reduced form in terms of dimensions of an original image / building / object. A map is a scale drawing of a city.
The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image.
Scale of the drawing = original dimensions / dimensions of the scale drawing
Initial scale = 65 ÷ 3 1/4
65 X 4/13 = 20
1 inch ; 20 miles
New scale = 65 / 6.5 = 1 10
1 inch : 10 miles
Length of the map = (2 x 65) / 11 = 11,8 inches
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