Answer:
The derivative of the function is:
dy/dx = 9x(3x^2 + 5x + 1)^(1/2) + (15/2)(3x^2 + 5x + 1)^(1/2)
Step-by-step explanation:
To find the derivative of the function, we can use the chain rule and the power rule:
Let y = (3x^2 + 5x + 1)^(3/2)
Then, we have:
dy/dx = (3/2)(3x^2 + 5x + 1)^(1/2) (6x + 5)
Simplifying this expression, we get:
dy/dx = 9x(3x^2 + 5x + 1)^(1/2) + (15/2)(3x^2 + 5x + 1)^(1/2)
Therefore, the derivative of the function is:
dy/dx = 9x(3x^2 + 5x + 1)^(1/2) + (15/2)(3x^2 + 5x + 1)^(1/2)
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Determine which of the lines,if any are parallel. Explain
I really need help on this!
Problem 4
I recommend to draw a number line. Place the baseball park at 0 on the number line.
Then place Luke's house at -3. The distance from -3 to 0 is 3 units, to represent the 3 miles.
Place Logan's house at 2 on the number line.
To go from -3 to 2, move 5 units to the right. This is the longest distance possible because each person's house is on opposite sides of the baseball park.
To get the shortest distance possible, we'll place each person's house to the right of 0. This time each person's house is on the same side.
We'll move Luke from -3 to +3. Keep Logan at 2. The distance from 2 to 3 is 1 unit. This is the shortest distance possible.
Answers:
Shortest distance = 1 mile
Longest distance = 5 miles
===============================================
Problem 5
d = distance between Luke's house and Logan's house
Refer to the result of problem 4, where we found d = 1 the smallest possible value of d. And also d = 5 the largest possible value.
In other words: d is between 1 and 5, including each endpoint.
The compound inequality to set up is [tex]1 \le d \le 5[/tex]
The graph involves closed filled in circles at 1 and 5 on the number line. Shade the region between these endpoints. Closed endpoints visually tell the reader "include this endpoint".
Answers:
Inequality: [tex]\boldsymbol{1 \le d \le 5}[/tex]
Graph: Closed filled in circles at 1 and 5; shading in between
===============================================
Problem 6
The largest distance we previously found was 5 miles.
Luke traveled 0.5 miles so far, meaning he has at most 5-0.5 = 4.5 miles left to go.
Answer:
4.5 miles
Answer:
Q4
Shortest distance = 1 mile
Longest distance = 5 miles
Q5
1 ≤ d ≤ 5
Q6
4.5 miles
Step-by-step explanation:
A diagram does help for these questions
Q4
If both Luke and Logan's houses are on the same straight line in the same direction then the difference between their individual distances from the field will be the shortest distance.
See the first diagram
Shortest distance = 3 - 2 = 1 mile
However, if they lived in exactly opposite directions on a straight line then the distance would be the longest and would be 2 + 3 = 5 miles
--------------------------------------------------------------------------------
Q5
The compound inequality would be 1 ≤ d ≤ 5 where d represents all possible distances from the two homes.
(We can also write this as [1, 5] which is called interval notation)
See second figure for how this would be represented on a number line
------------------------------------------------------------------------------
Q6
Since we have determined the greatest distance between the two houses as 5 miles, and Luke has already biked 0.5 mile he has 5 - 0.5 = 4.5 miles left to bike
Eight friends went on a hiking trip they took 40 bottles of water and iced tea each friend carried the same number of bottles they each carried 2 bottles of iced tea how many water bottles did each friend carry
Answer: they each carried 5 water bottles.
Step-by-step explanation: 8x5 equals 40
Answer: 5
Step-by-step explanation:
40 divided by 8
Can you please answer the question o in this image ?
Answer:
-4 x^3 y^2 thus: # 4
Step-by-step explanation:
Simplify the following:
(24 x^6 y^3)/(-6 x^3 y)
The gcd of 24 and -6 is 6, so (24 x^6 y^3)/(-6 x^3 y) = ((6×4) x^6 y^3)/((6 (-1)) x^3 y) = 6/6×(4 x^6 y^3)/(-x^3 y) = (4 x^6 y^3)/(-x^3 y):
(4 x^6 y^3)/(-1 x^3 y)
Combine powers. (4 x^6 y^3)/(-x^3 y) = (4 x^(6 - 3) y^(3 - 1))/(1 (-1)):
(4 x^(6 - 3) y^(3 - 1))/(-1)
6 - 3 = 3:
(4 x^3 y^(3 - 1))/(-1)
3 - 1 = 2:
(4 x^3 y^2)/(-1)
Multiply numerator and denominator of (4 x^3 y^2)/(-1) by -1:
Answer: -4 x^3 y^2
Answer: #4
Step-by-step explanation:
You would divide 24 by -6, leaving u with -4 then u would subtract the powers x to the power of 6 from x to the power of 3 leaving you with x to the power of 3 and then you would subtract y to the power of 3 by y leaving you with y squared.
-4x to the power of 3 y to the power of 2.
PLEASE HELP GEOMETRY FINAL
What is the sequence of transformations that maps A ABC to
A A'B'C'?
Select from the drop-down menus to correctly identify each step.
Step 1: Choose…
rotate 90° clockwise about the origin.
reflect across the line y = x
reflect across the Y axis.
rotate 180° about the origin.
Step 2: Choose..
translate 1 unit right.
Translate 2 units right.
Translate 4 Units down.
Reflect across the x-axis.
Answer:
I believe… ( it might be wrong… )
Reflect across the line y = x.
translate 1 unit right.
Step-by-step explanation:
i took the same test before but i believe i had a question just like this and got it right soooo….. ye
HELP?
A. Acute
B. Obtuse
C. Right
D. Not a triangle
HELP ASAPPPP 20 POINTS WILL MARK BRAINLIEST IF CORRECT
Answer:
first one is 1.-.5
Step-by-step explanation:
What is the y-intercept of 10?
Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .
Step-by-step explanation:
Can someone help me with these pls
Answer:
9) 17 miles/hr
10) 7.14 miles
Step-by-step explanation:
See the attached worksheet. Note the use of conversion factors. In question 9 we want to convert minutes to hours. We know there are 60 minutes/hr. So we can set up a conversion factor in one of 2 ways: (60 minutes/1 hr) or (1 hr/60 minutes). Both are valid, and both are = 1, since the numerator and denominator are both equivalent. This means we can invert a conversion factor and it is still = 1. Since conversion facots are equal to 1, we can multiply them times anything, and the result is numerically the same (anything times 1 = anything) and only the units have changed. For question 9, we want to convert miles/min to miles/hr. I'll choose the conversion factor (60 min/1 hr), mostly because I like multiplication over division. Note how the units cancel in the attachment, resulting in 17 miles/hr. One may also use the factor (1hr/60min), but then a division is required. Perfectly fine, but not my preferred route.
The same approach is used to answer question 10. Again, note how he units cancel, leaving a number wth just the units desired,
A bag and a ign pen cot 153. 75 peo. The bag cot 28. 85 peo more than the ign pen. How much doe each cot?
As per the unitary method, the cost of bag is $93.3 and the cost of pen is $64.45
The term unitary method in math is known as the process of solving the the value of a single unit, and based on this value we can find the value of the required number of units.
Here we have given that the cost of pen and bag is $153.75.
Here we also know that the bag cost $28.85 more than the pen.
Let us consider that x be the cost of pen and here we know that the cost of bag is $28.85 more than the pen then it can be written as,
=> x + 28.85
Therefore, the equation is written as,
=> x + (x + 28.85) = 153.75
Now, we simplify the equation, then we get,
=> 2x + 28.85 = 153.75
Here we need to find the value of x, so, we have to move the other terms on the other side, then we get
=> 2x = 153.75 - 28.85
=> 2x = 124.9
Therefore, the value of x is 64.45.
Therefore, the cost of bag is calculated as,
=> x + 28.85
=> 64.45 + 28.85
=> 93.3
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The expression 4 square root of 3 times 3 square root of 3^5 is equivalent to
The given expression is equivalent to 486√3
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, √4 of 3√3 of 3⁵
√4 of 3√3 of 3⁵ = 2×3√3×243
= 486√3
Hence, the given expression is equivalent to 486√3
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Given the equations `9x + (3)/(4)y = 6` and `2x + (1)/(2)y = 9`, by what factor would you multiply the second equation to eliminate y and solve the system through linear combinations?.
We multiply by -3/2 to get rid of y and figure out the system of equations.
What are equations?A mathematical assertion that has an "equal to" symbol between two expressions with equivalent values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including straight, quadratic, cubic, and others.
So, we have:
9x+3/4y=6 and 2x+1/2y=9
By removing y, we must solve a system of equations.
Therefore, we will first make the y-coefficient equal but with the opposite sign.
In the first equation, the y-coefficient is 3/4
The coefficient of y in equation two is half.
LCM: 3/4 and 1/2 = 3/2
To maintain the same coefficient of y, multiply the second equation by -3/2.
-3/2*2x-3/2*1/2y = -3/2*9
-3x-3/4y = -27/2
9x+3/4y = 6
Combine the two equations and get rid of the y variable.
-3x+9x = -27/2+6
6x = -15/2
x = -5/4
Therefore, we multiply by -3/2 to get rid of y and figure out the system of equations.
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Complete question:
Given the equations 9x+3/4y=6 and 2x+1/2y=9, by what factor the equation to eliminate y and solve the system through linea would you multiply the second equation to eliminate y and solve the system through linear combinations?
Options;
A.) -4/3
B.) -3/4
C.) -3/2
D.) -7/2
How do you use a table to solve a function?
So on solving the provided question we can say that - the function is f(x) = x= +2, -2
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
the function is -
f(x) = x^2 - 2
f(x) = x= +2, -2
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How do you find the value of N example?
N! also called N factorial is the product of all positive non-integers equal to or less than N or simply is the product of the Nth integer and all integers below it.
N! is represented as 1x2x3x4.......x n which is also equivalent to n x (n-1_x(n-2w)x(n-3)......x1. Therefore the formula for N factorial is N! = n × (n - 1)!. For whole numbers, the factorial is a product of natural numbers till 1 of the values is equal to or less than whole numbers.
N is also used to represent the set of natural numbers up to infinity. Natural numbers include the values from till infinity, they can be represented like N=[1,2,3,4,5,6........].
Examples of N! are:-
4!= 4x3x2x1=24 here we take the product of values equal to or less than 4 upto 112= 12x11x10x9x...... x2x1=479001600 here we calculate the product of 12 and lesser natural numbers(N+3)!= (N-3)X(N+2)X(N+1)X......X1To know more about factorials visit:
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The scale on map indicates that 3/4 of an inch represents 3
miles. If the distance between two points on its map is 2
inches, how far apart are two locations?
A map uses scaled drawings. The distance between the two considered cities on that specified map is 6.25 inches
How are scale drawings formed?
For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
1ft : s/k in.
All feet measurements will then we multiplied by s/k to get the drawing's corresponding lengths.
For this case, it is specified that the map uses scaling such that:
3/4 of an inch on map = 3 miles in reality.
Dividing both the quantities by 3, we get:
1 mile in reality = 3/4 / 3 inches on map = 1/4 inches on map
Multiplying both the quantities by 25, we get:
25 miles in reality = 25/4 = 6.25 in map
Since 25 miles is the distance between those two considered cities.
Therefore, the distance between those two cities on map would be of 6.25 inches.
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24 tiny homes are being built from 15 pallets of wood. How many pallets will each home use
Answer: 1 3/5
Step-by-step explanation:15 x 1 3/5 = 24
Which quadrilateral makes this statement true?
Quadrilateral ABCD =
A 114
125
D
Quadrilateral ABCD
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
How is a quadrilateral calculated?The area of the quadrilateral is computed as follows if the diagonal and the length of the perpendiculars from the vertices are known: Area of quadrilateral = (12) diagonal length + sum of the length of the perpendiculars drawn from the remaining two vertices.
What is a quadrilateral's shape?A quadrilateral is a two-dimensional shape with four sides. Quadrilaterals include the following 2D shapes: square, rectangle, rhombus, trapezium, parallelogram, and kite.
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What is the domain of the function f/x )= 4 x?
The domain of the function f/x = 4x is all real numbers.
The domain of a function is the et of all values that can be plugged into the equation and produce a valid output. Since any real number, positive, negative, or zero, can be plugged into the equation and produce a valid output, the domain of the function f/x = 4x is all real numbers.
The domain of a function is the set of values that can be plugged into the equation and produce a valid output. In the case of the function f/x = 4x, the domain is all real numbers; that is, any value, positive or negative, can be plugged into the equation and produce a valid output. This means that the domain of the function f/x = 4x includes all real numbers, from the smallest negative number to the largest positive number, as well as zero.
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what is 3.3 as an exponent
Answer: 3^2
Step-by-step explanation: i would say that is my answer because , there are 2 threes and in exponential form i think it would be unless its a decimal in between the two threes and not a times
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
According to number line, x > 5 is correct,
What is number line?A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when plotting a point.
Here,
Given :
∵ The inequality is -3(2x - 5) < 5(2 - x)
At first simplify each side
∵ -3(2x - 5) = -3(2x) + -3(-5)
Remember (-)(-) = (+)
∴ -3(2x - 5) = - 6x + 15
∵ 5(2 - x) = 5(2) + 5(-x)
Remember (+)(-) = (-)
∴ 5(2 - x) = 10 - 5x
∴ - 6x + 15 < 10 - 5x
Subtract 15 from both sides
∴ - 6x < -5 - 5x
Add 5x to both sides
∴ - x < - 5
∵ The coefficient of x is -1
∴ Divide both sides by -1
∴ x > 5
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In what quadrant-14 -5i located on the complex plane
Third quadrant the complex plane is where the number -14 - 5i is situated.
-14-5i is located in which quadrant?Based on the common knowledge, the complex number's real and imaginary components are considered as the x- and y- coordinates of an ordered pair in a 2-D plane.
first quadrant a+bi =(a,b)
second quadrant -a+bi= (-a,b)
third quadrant -a-bi=(-a,-b)
fourth quadrant a,-b=(a,-b)
According to the question,-14-5i is located in third quadrant(-14,-5)
As a result, the complex plane's third quadrant is where the number -14 - 5i is situated.
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Are reflected triangles congruent?
Answer:
Step-by-step explanation:
Which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3*(2*8)+7 ?
3*(28) + 7 can be rewritten as 316 + 7, which can be further simplified by using the associative property of multiplication and the commutative property of addition as (3*16) + 7 = 48 + 7 = 55
What is the commutative property of addition and the associative property of multiplication?The commutative property of addition states that the order of the numbers being added does not matter, for example, a+b = b+a.
The associative property of multiplication states that the grouping of the numbers being multiplied does not matter, for example, (ab)c = a(bc).
Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3*(2*8)+7 is (3*16) + 7 = 48 + 7 = 55.
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A baseball player gets 15 hits in 45 at bats. Distinguish what the experimental probability is of the player getting a hit.
Show all of your work.
Answer:
Below
Step-by-step explanation:
This IS basically an experiment with 15 hits out of 45 at-bats
15/45 = .333 or 33.3 % experimental probability
Answer:
The experimental probability is of the player getting a hit is 1/3 or 33.33%--------------------------------------
Given:
Number of attempts = 45,Number of hits = 15.Find the experimental probability.
Probability of getting a hit is:
P(hit) = hits / attempts,P(hit) = 15/45 = 1/3 ≈ 33.33%.HELP
How do you solve percentages?
Order the fractions from least to greatest.
3
−
4
, 3
−
8
, 1
−
2
, 1
−
4
The ordering of the fraction from least to greatest will be 1/4, 3/8, 1/2, and 3/4.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
The value of 3/4 will be:
= 3/4 × 100
= 75%
The value of 3/8 will be:
= 3/8 × 100
= 37.5%
The value of 1/2 will be:
= 1/2 × 100
= 50%
The value of 1/4 will be:
= 1/4 × 100
= 25%
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13) AMNP-ARST
a) Find the value of x if MN = 5x + 10, MP-5, RT-4, RS= 6x-8, and ST-42.
b) What is the length of MN, RS, and NP?
MN =
RS=
= 80
x=
NP =
what is number 13
When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
as AMNP-ARST
the x = 80
so MN = 5 * 80 + 10
= 410
RS = 6* 80 - 8
= 400
When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .
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Let z = 19 i and w = 4 10i. what is the first step in determining zw? replace i2 with –1. multiply z by the conjugate of w. apply the distributive property or foil. combine the corresponding real and imaginary parts.
The correct option: 3. Apply the distributive property or FOIL; to determine the value of zw.
What exactly is a complex number?Complex numbers are defined as a combination of real and fictitious numbers. Z = a + ib, where a and bi are real and imaginary numbers, is how a complex number is expressed.Let z = 19 + i and w = 4 + 10i.
Making a decision is the first step.
The steps to find the product of complex numbers z and w are as follows.
z. w = ( 19 + i )( 4 + 10i ).
applying distributive law,z. w = 19 * (4 10i) i * (4 10i).
removing the parenthesis,z. w = 19 * 4 + 19*10i + i * 4 + i * 10i.
Similar to that, further actions are.z. w = 76 + 190i + 4i + 10i².
because i² = -1.
z. w = 76 + 194i - 10.
z. w = 66 + 194i.
Thus, in order to find zw in the first step, use the distributive property or FOIL.
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The correct question is-
Let z = 19 + i and w = 4 + 10i.
What is the first step in determining zw?
Replace i2 with –1.Multiply z by the conjugate of w.Apply the distributive property or FOIL.Combine the corresponding real and imaginary parts.Brooklyn had math and reading homework tonight. Brooklyn can solve each math
problem in 2 minutes and she can read each page in 3 minutes. The number of math
problems Brooklyn solved is twice the number of pages she read and it took her 70
minutes to complete all of her homework. Write a system of equations that could be
used to determine the number of math problems Brooklyn solved and the number of
pages
she read. Define the variables that you use to write the system.
Let
Let
System of Equations:
Brooklyn could calculate how many arithmetic problems she completed and how many pages she read using the equations x = 2y and 2x + 3y = 70.
What is meant by mathematical equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.let
number of math problems Brooklyn solved = x
number of pages she read = y
Time to solve each math = 2 minutes
Time to read each page = 3 minutes
Brooklyn read twice as many pages as there were arithmetic problems to be done.
x = 2y
2x + 3y = 70
Substitute x = 2y into
2x + 3y = 70
2(2y) + 3y = 70
4y + 3y = 70
7y = 70
divide both sides by 7
y = 70/7
y = 10
Recall,
x = 2y
x = 2(10)
x = 20
Therefore, Brooklyn completed 20 math problems and read 10 pages, which equals 20 math problems and 10 pages, respectively.
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What is 2 with an exponent of 7?
2 with an exponent of 7 is 128. It means 2 multiplied by itself 7 times.
When a number is raised to a certain power, it means that the number is multiplied by itself that many times. For example, 2 with an exponent of 7 means 2 multiplied by itself 7 times.
2^7 = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128So, 2 with an exponent of 7 is 128.
It's important to note that the exponent is also known as the power, so 2^7 is also read as 2 to the power of 7.
Exponents are a way of shorthand for repeated multiplication. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.
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