a) Chloe will run 105 miles in 30 days.
b) the expression total miles he ran in d days is 3.5d.
What's Expression?Mathematical expressions correspond of at least two figures or variables, at least one computation operation, and a statement. It's possible to multiply, divide, add, or abate with this fine operation. An expression's structure is as follows Expression( Math Operator, Number/ Variable, Math Operator)
Given:
Chloe daily route is 3.5 miles long.
So, in 30 days Chloe will run
= 30 x 3.5
= 105 miles.
b) the expression for total distance Chloe has run after d days.
= 3.5 x d
=3.5d
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The question attached here is in other Language whose translation is:
Chloe jogs every morning. His daily route is 3.5 miles long.
a) How far will Chloe have run after 30 days?
b) Write an expression for the total distance Chloe has run after d days.
Tickets to a concert cost $25.00 each, including tax. Austin has $150.00 and
wants to get tickets for himself and some friends. How many friends can he
invite?
10. Sleeping 8 hours a day is the same as sleeping 10 days a month. How many days is this per year?
If there are 10 days of sleeping a month then in a year there are 120 days of sleeping.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Sleeping 8 hours a day is the same as sleeping 10 days a month.
In according to hours the number of hours sleeping in month will be
= 8 x 30
= 240 hours
= 240 / 24
= 10 days
So, in a year the number of days of sleeping is
= 10 x 12
= 120 days
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Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their hcf is 101.
The smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101 are 1010 and 1313.
HCF (Highest Common Factor) of two numbers, which is the largest number that divides both numbers evenly.
Let's call the smaller of the two numbers "x". The larger number would be "x + 303".
The HCF of these two numbers must be 101, which means that 101 must be a factor of both x and x + 303.
To find the smallest possible value of x, we need to find the smallest number that is divisible by 101 and also a 4-digit number.
The smallest multiple of 101 that is a 4-digit number is
=> 101 x 10 = 1010.
Therefore, x = 1010.
The larger number would be
=> x + 303 = 1010 + 303 = 1313.
To check if the HCF of these two numbers is indeed 101, we can use the Euclidean Algorithm or the Prime Factorization method to find the HCF.
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mai poured 2.6 of water into a partially-filled pitcher. the pitcher now contains 10.4.mai wants to know how many liters of water was originally in the pitcher.
Answer:
Step-by-step explanation:
Let's call the original volume of water in the pitcher "V". Then, after Mai added 2.6 liters, the total volume of water in the pitcher became V + 2.6 = 10.4 liters.
To find the original volume of water in the pitcher, we can isolate V by subtracting 2.6 from both sides of the equation:
V + 2.6 = 10.4
V = 10.4 - 2.6
V = 7.8 liters
So the original volume of water in the pitcher was 7.8 liters.
Answer: 7.8
Step-by-step explanation:
really sorry if im wrong
I need help with this please and thank you.
Answer:
(3x -4 ) (x^2 -5x -1) multiply the binomial by trinomial3×^3 -15x^2 -3x -4x^2 +20x +4group like terms , then get your answer as3x^3 -19x^2 +17x +4A fifth-degree polynomial function has a zero at r = -3 with a multiplicity
of 2. It also has a zero at r = 2 with a multiplicity of 3. The value of the
function is negative when I = −4.
Which graph could model this polynomial function?
Answer:
The graph that could model this polynomial function will be a fourth-degree function.Step-by-step explanation:
It will have two roots at r = -3 and r = 2, and it will cross the x-axis twice at both those roots.It will also be negative for all values below -4, which means that it will also cross the x-axis two times above r = -4.if U={1,2,3,4,5,6,7,8,9,10}
A={4,6,8,10} and B={2,3,7}
Find (AUB)¹
Compliment set of set A union set B is {1, 6, 9}.
What is set?Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set.
The given sets are U={1,2,3,4,5,6,7,8,9,10}, A={4,6,8,10} and B={2,3,7}
Here, (A∪B)={4,6,8,10}∪{2,3,7}
= {2,3,4,5,7,8,10}
(A∪B)'=U-(A∪B)
= {1,2,3,4,5,6,7,8,9,10}-{2,3,4,5,7,8,10}
= {1, 6, 9}
Therefore, (A∪B)' is {1, 6, 9}.
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How is Purdue GPA calculated?
The Grade Point Average at Purdue University is determined using a 4.0 scale (GPA).
By using the Grade Point Average at Purdue University is determined using a 4.0 scale (GPA). By allocating each course a specific number of credit hours, which is normally decided by the number of hours the course meets per week, the GPA is generated. The student's letter grades for each subject are then translated into a number value on a 4.0 scale, as seen below:
A = 4.0 A- = 3.67 B = 3.0 B- = 2.67 C = 2.0 C- = 1.67 D = 1.0 F = 0.0
The sum of the products of the credit hours and the numerical values of the letter grades obtained is used to compute the student's GPA after each letter grade has been given a numerical value.
The Grade Point Average at Purdue University is determined using a 4.0 scale (GPA). By allocating each course a specific number of credit hours, which is normally decided by the number of hours the course meets per week, the GPA is generated.
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Find the area of the polygon?
The area of the polygon will be equal to 58.1 square units.
What is an area of a polygon?A polygon's area is the region that it occupies. Polygons can be both regular and irregular in shape. Triangles, squares, rectangles, pentagons, hexagons, and other basic polygons are used in geometry. Each of these polygons has its own area.
A pentagon is a given polygon. The apothem is the perpendicular line drawn from the octagon's midpoint to the base of one of its sides.
The formula for determining the area of a regular polygon is expressed as
Area = a² × n × tan 180/n
Where n represents the number of sides of the polygon.
n = 5
Area = 4² × 5 × tan(180/5)
Area = 80 × tan 36
Area = 58.1 Square units
Hence, the polygon will have an area of 58.1 Square units.
The missing image is attached with the answer below.
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Help please helpppppppppppppppp
15x = 180
divide both by 15, and you get
x = 12
I'm unsure if this is correct
Answer: Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees
Keshawn is 1.45 meters tall. At 12 noon, he measures the length of a tree's shadow to be 15.05 meters. He stands 10.8 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
If Keshawn is 1.45 meters tall. At 12 noon, he measures the length of a tree's shadow to be 15.05 meters. the height of the tree to the nearest hundredth of a meter is 2.02 meters.
How to find the height?To find the height of the tree, we can use the similar triangles method. Let's call the height of the tree "h".
Since Keshawn and the tree are standing in the same spot, the same light source is casting their shadows, so the ratios of their shadow lengths to their heights are equal. This means we can set up the following proportion:
1.45 / h = 15.05 / 10.8
We can solve for "h" by cross-multiplying:
h = 15.05 * 1.45 / 10.8
h = 2.02 meters
Therefore, the height of the tree to the nearest hundredth of a meter is approximately 2.02 meters.
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Answer: 5.13
Step-by-step explanation:
HELP PLEASEEEEEEEEEEEEE
Answer: look at the image for the answers and solutions
Step-by-step explanation:
Question 4 help please
Answer:
for 8x + 9 Y = 0
for xsmall2 + 4x + 13 y = 6x + 13
Step-by-step explanation:
What is the area of the enclosure? Round to the nearest tenth. Explain.
Elevations
Anna 690 ft
Benito 713 ft
Charlie 743 ft
Deon 725 ft
Sight Line Angles
of Depression and
Elevation
Anna to Benito 2° angle of elevation
Anna to Deon 3° angle of elevation
Charlie to Benito 5° angle of depression A trapezoid ABCD named Anna, Benito, Charlie and deon on the four coordinates respectively with angle ABC as 124 degree, BCD as 85 degree and CDA as 96 degree
The area of the enclosure is approximately 128.6 acres
To find the area of the trapezoid ABCD, we first need to find the lengths of its parallel sides. Let's use the fact that the angles of a quadrilateral add up to 360 degrees:
Angle ABC = 124 degrees
Angle BCD = 85 degrees
Angle CDA = 96 degrees
Angle DAB = 360 - 124 - 85 - 96 = 55 degrees
Now we can use the tangent function to find the lengths of the sides:
tan(2 degrees) = (height of AB) / (distance between Anna and Benito)
(height of AB) = (distance between Anna and Benito) × tan(2 degrees)
(distance between Anna and Benito) = (713 - 690) / tan(2 degrees) ≈ 18490.3 ft
(height of AB) ≈ 429.4 ft
Similarly, we can find the height of CD:
tan(3 degrees) = (height of AD) / (distance between Anna and Deon)
(height of AD) = (distance between Anna and Deon) × tan(3 degrees)
(distance between Anna and Deon) = (725 - 690) / tan(3 degrees) ≈ 8639.5 ft
(height of AD) ≈ 459.6 ft
Now we can use the trapezoid area formula:
Area = (height of AB + height of CD) × (sum of the parallel sides) / 2
Area = (429.4 + 459.6) × ((18490.3 + 8639.5) / 2) / 5280 ≈ 128.6 acres
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Solve by substitution
**Pls explain answer
y = -6x + 5
-2x + y = 5
Answer: 0,5
x = 0
y = 5
Answer: (0,5)
Step-by-step explanation:
Since "y" is equal to -6x+5 everywhere you see a "y" you can replace it with -6x+5.
-2x-6x+5=5
Combine like terms
-8x+5=5
Isolate x (subtract 5 from both sides)
-8x=0
Solve for x
x=0
Now that you have the value for "x" you can substitute the value into either equation and solve for y
-2(0)+y =5
y=5
or
y=-6(0)+5
y=5
what are 2 equations for d 2 miles and t 30 minutes
two equations are: v = u + 0.5a and (v)² = (u)² + 4a.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, the distance traveled by an object in t = 30 minutes is 2 miles
Let "v" be the final velocity of an object,
"u" be the initial velocity of an object,
and "a" be the acceleration of an object.
From the standard velocity equation:
final velocity = initial velocity + acceleration * time.....(1)
(final velocity)² = (initial velocity)² + 2*acceleration * distance....(1)
From equation (1)
v = u + a*30 minutes
time in hours,
v = u + 0.5a
From equation (2)
(v)² = (u)² + 2*a* 2
(v)² = (u)² + 4a
therefore, two equations are: v = u + 0.5a and (v)² = (u)² + 4a.
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Solve the system of two linear equations below graphically y= -x + 1 y= -1/3x + 3
(-3, 4) is the solution to the given system of simultaneous equation
Solving system of equation graphically.Given the system of equation
y = -x + 1
y = -1/3x + 3
When solving graphically, the point of intersection of both lines on an xy plane is the solution to the system of equation.
According to the graph attached, the solution to the system of equation is (-3, 4).
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Are the lines with the equation y = -5x + 1 and y = -5x + 8 parallel? (use a graph, might help)
Answer:
Yes, the lines y = -5x + 1 and y = -5x + 8 are parallel. This is because they have the same slope (-5) but different y-intercepts (1 and 8). Parallel lines have the same slope, and different y-intercepts.
Answer:
For y = -5x + 1
x = [tex]\frac{1-y}{5}[/tex].
And
y = 1 - 5x.
Put on a graph: look at picture 1.
The for y = -5x + 8
x = [tex]\frac{8-y}{5}[/tex]
And
y = 8 - 5x.
Put on a graph: look at picture 2.
These two lines are parallel.
45a^3b^4+36a^2b^5 ÷ 9a^2b^4
step by step please
The result is 45a^3b^4+4b
Calculate exponents numberThe given expression is 45a^3b^4+36a^2b^5 ÷ 9a^2b^4 First, we will simplify the term 36a^2b^5 ÷ 9a^2b^4 by dividing the coefficients and subtracting the exponents of the variables.
36 ÷ 9 = 4
a^2 ÷ a^2 = a^(2-2) = a^0 = 1
b^5 ÷ b^4 = b^(5-4) = b^1 = b
So, 36a^2b^5 ÷ 9a^2b^4 = 4b
Now, we can substitute this value back into the original expression:
45a^3b^4+4b
We cannot simplify this expression any further since the terms do not have the same power of the variables.
So, the final answer is: 45a^3b^4+4b
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World War II began in the year 1939.
Let x represent any year. Write an inequality in terms
of x and 1939 that is true only for values of x that
represent years before the start of World War II.
The Inequality to represent year is x < 1939.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Let x represent any year.
If we want years before 1939, then x must be less than 1939.
Then, the Inequality can be
x < 1939.
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For the function y = 3x - 1, what is always a correct conclusion?
A. The variable y is always positive.
B. The variable y is always greater than x.
C. As the value of x increases, the value of y increases.
D. The variable y is always three times x
For the function y = 3x - 1, the correct conclusion is C.As the value of x increases, the value of y increases.
About functionAs the value of x increases, the value of y increases.
In this function, y is dependent on the value of x. The variable x is multiplied by 3 and then subtracted by 1 to find the value of y. As the value of x increases, the value of y will also increase because it is being multiplied by 3.
For example, if x = 1, then y = 3(1) - 1 = 2. If x = 2, then y = 3(2) - 1 = 5. As you can see, as the value of x increases, the value of y also increases.
Therefore, the correct conclusion for this function is C. As the value of x increases, the value of y increases.
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fuel pressure in the fuel tank of the space shuttle is decreasing at a rate of r(t)= 17e^-0.1t psi per second at time t in seconds. at what rate is pressure decreasing at 15 seconds
The pressure is decreasing at a rate of approximately 0.26 psi/s at t = 15 seconds.
What is pressure ?
In physics, pressure is the amount of force applied per unit area. It is a scalar quantity, which means that it has a magnitude but no direction. Pressure is typically denoted by the symbol P, and its units are commonly expressed in pascals (Pa), which is the SI unit of pressure.
Pressure can be defined as the amount of force F applied per unit area A:
P = F / A
For example, if a force of 100 newtons (N) is applied to an area of 2 square meters (m^2), then the pressure would be:
P = 100 N / 2 m^2 = 50 Pa
Pressure is an important concept in many areas of physics, including fluid dynamics, thermodynamics, and atmospheric science. It is commonly used to describe the behavior of gases and liquids under different conditions, such as changes in temperature or volume. Pressure can also be used to calculate other physical properties, such as the flow rate of a fluid or the speed of sound in a gas.
According to given condition :
The rate of change of the fuel pressure in the fuel tank of the space shuttle is given by the derivative of the function [tex]r(t) = 17e^(-0.1t)[/tex]psi per second with respect to time t. Taking the derivative of r(t), we get:
[tex]r'(t) = (-0.1) * 17e^(-0.1t)[/tex]Simplifying this expression, we get:
[tex]r'(t) = -1.7e^(-0.1t)[/tex]
To find the rate at which the pressure is decreasing at t = 15 seconds, we substitute t = 15 into the expression for r'(t):
[tex]r'(15) = -1.7e^(-0.1*15)[/tex]
r'(15) ≈ -0.26 psi/s
Therefore, the pressure is decreasing at a rate of approximately 0.26 psi/s at t = 15 seconds.
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How do I convert 3/4 to a percentage?
The ratio 3:4 into percentage is 75%.
3/4 is expressed as 75% in terms of percentage.
Percentage:
In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.
According to the Question:
The fraction 3/4 to an equivalent fraction with the denominator equal to 100
(3 × 25) / (4 × 25) = 75/100
Now,
75/100 is expressed as 75% in terms of percentage.
Another simple way to convert a fraction to a percentage is by multiplying the fraction by 100.
In this case, 3/4 × 100 = 75%
Thus, 3/4 is expressed as 75% in terms of percentage.
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Find f(4) for f(x) = x3 - 2x2 + 3x - 7
I'm not sure how to find out the x in f(x) in equations like this. Any help understanding this would be appreciated.
Answer:37
Step-by-step explanation:
just write 4 instead of x
f(4)=[tex]4^{3} -2*4^{2} +3*4-7=64-32+5=37[/tex]
the product of permutation matrices is again a permutation matrix. True/False
The statement which is given as , "The product of permutation matrices is again a permutation matrix." is True.
A permutation matrix is a square matrix whose entries are either 0 or 1 and has exactly one "1" in each row and each column. In other words, it is a matrix that represents a permutation of the rows (or columns) of the identity matrix.
When two permutation matrices are multiplied, the result is another square matrix with exactly one "1" in each row and each column. To see why this is true, consider two permutation matrices, A and B. Suppose that A is a m x m matrix and B is a m x m matrix. The product of these two matrices is another m x m matrix, C = AB.
Each entry in the matrix C is given by the dot product of the corresponding row in A and the corresponding column in B. If the row in A has a "1" in the i-th position and the column in B has a "1" in the j-th position, then the i,j-th entry in C will be "1".
Since both A and B are permutation matrices, each row in A and each column in B has exactly one "1". This means that each row in C will have exactly one "1", and each column in C will also have exactly one "1". Hence, C is also a permutation matrix.
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PLEASE HELP ASAP!!!
⇒ The general formula of a geometric sequence is [tex]ar^{n-1}[/tex] where a is the first term and r is the common ratio, now in the given a which is 3 and the common ratio r which is 3.
to get the 10th term we use the same general formula
[tex]a_{n} =ar^{n-1}[/tex]
where [tex]T_{n}[/tex] is the nth term that is then output and n is the place of the nth term in the general sequence.
For the 10th term we substitute 10 in the place of n and simplify to find the value of the output.
[tex]a_{10} =ar^{(10-1)} \\a_{10} =ar^{9} \\[/tex]
Now since we know which formula to use to get the 10th term we can substitute the known values of the variables to get the output .
[tex]a_{10} =(3)(3)^{9} \\a_{10} =59049[/tex]
goodluck
Does someone mind helping me with this? Thank you!
The required equation which intersects the points (12, -2) and (6, -8) in the point-slope form is y+2 = x-12.
What is point-slope form?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
To understand more about it and see some instances, watch this video.
Both the slope-intercept form and the point-slope form can be used to write the equation of a straight line.
The slope and ANY point on the line are highlighted using the point-slope form.
Slope intercept form merely shows the slope and the y-intercept of a line.
So, we have:
m = 1
And points are (12, -2) and (6, -8)
We need to use the points: (12, -2)
Now, form the equation as follows:
y - (-2) = m (x-12)
y + 2 = 1(x-12)
y+2 = x-12
Therefore, the required equation which intersects the points (12, -2) and (6, -8) in the point-slope form is y+2 = x-12.
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The legs of a right triangle have lengths of
2x + 3 and 4x - 1. Which polynomial is equivalent
to c²?
A 6x + 2
B 4x² + 12x + 9
C 20x² + 4x + 10
D 36x² + 24x + 4
A polynomial f (x) has the given zeros of 7, –1, and –3.
Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form. Show all necessary calculations. (3 points)
Part B: Divide the polynomial f (x) by (x2 – x – 2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote. (4 points)
Part C: List all locations and types of discontinuities of the function g(x). Be sure to check for all asymptotes and holes. Show all necessary calculations. (3 point
The answers to all parts are shown below.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
Given:
The polynomial zeros are given as:
x = 7, x = -1 and x = -3
x - 7 = 0, x + 1 = 0 and x + 3 = 0
So, f(x) = (x - 7)(x + 1)(x + 3)
f(x) = (x - 7)(x² + 4x +3)
f(x) = x³ -3x² -25 x -21
Now, Rational function g(x)
g(x) = f(x) / (x² - x + 2)
After Factorizing
g(x) = (x-2) - 25x+ 25 / (x² - x + 2)
The slant asymptote is the quotient i.e. x - 2
Hence, the slant asymptote of the function g(x) is x - 2
So, the discontinuities of g(x)
g(x) = (x³ -3x² -25 x -21) / (x² - x + 2)
Set the denominator to 0
x² - x + 2 = 0
(x - 2)(x + 1) = 0
x= 2 or x= -1.
So, the discontinuities and their types are:
Essential discontinuity at x = 2
Removable discontinuity at x = -1
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Exactly $9 was used to purchase an equal number of each of the three types of tokens
$0.10, $0.15 and $0.20, how many of each type of tokens were purchased?
A)45
B)30
C)25
D)20
E)15
Answer:
The answer is 20, so the answer is (D) 20.
Step-by-step explanation:
Let's say x is the number of tokens purchased for each of the three types. Then, the total amount spent is 0.10x + 0.15x + 0.20x = $9.
Combining like terms, we get 0.45x = $9.
Finally, dividing both sides by 0.45, we get x = 20.
So, 20 tokens were purchased for each of the three types.
The answer is 20, so the answer is (D) 20.