The coordinates of the points A and B, after scaling becomes
A(x, y) → A'(2x, 2y)
B(x₁, y₁) → B'(2x₁, 2y₁)
What is scaling? How is it done?Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. Similarly, if the initial coordinates are (x, y) then after scaling the coordinates would be {Kx, Ky}.Scale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities. In case of length scaling, we can write -{K} = L{final}/L{initial}
Given is that shape is being enlarged using a scale factor of 2 and centre (6, 3).
Assume the coordinates of the point are A(x, y) and B(x₁, y₁). After scaling, the coordinates will become -
A(x, y) → A'(2x, 2y)
B(x₁, y₁) → B'(2x₁, 2y₁)
Therefore, the coordinates of the points A and B, after scaling becomes
A(x, y) → A'(2x, 2y)
B(x₁, y₁) → B'(2x₁, 2y₁)
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the cost in dollars, of a three-day car rental can be determined by the expression 70+0.30m, where mis the number of miles drive. use this expresion to find the cost of a rental car driven150 miles.
Answer:
70+0.30m, where mis the number of miles =
Which function describes a transformation that maps trapezoid FGHI to trapezoid F'G'H'I'?
The function that maps the trapezoid FGHI to trapezoid F'G'H'I' is
B. (x, y) → (1/2 x - 5, 1/2 y)
How to determine the transformation?The change of shape as seen in the two objects was reduction in size and linear movement to the left.
The reduction is size is reduction by half and this is dilation with a scale factor of 1/2. This is represented by the formula
(x, y) → (1/2 x, 1/2 y)
Then linear movement to the left is translation to the left and this id 5 units to the left. The formula to show this as below
(x, y) → (1/2 x - 5, 1/2 y)
This is equivalent to B and hence the correct option
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Write the product (2 + 7i)(2 − 7i) in the form a + bi.
A. 4 − 49i
B. 53
C. 4 − 14i2
D. 53 + 14i
The product of (2 + 7i)(2 − 7i) is (B) 53. It can be written in the form of a + bi as 53 + 0i.
What are Complex Numbers?A complex number is formed by multiplying a real and an imaginary number.
Complex numbers are denoted by the symbol z and have the formula a + ib.
Both a and b are real numbers here.
The real component is denoted by Re(z), while the imaginary component is denoted by Im (z). As a result, 'ib' is an imaginary number.
Here, we have the given expression, (2 + 7i)(2 − 7i) ------(1)
We know that, (a+b)(a-b) = a² - b²
Using the above formula, we get (1) as
(2 + 7i)(2 − 7i) = (2)² - (7i)²
⇒ (2 + 7i)(2 − 7i) = 4 - 49i²
Since, i² = -1, we get
(2 + 7i)(2 − 7i) = 4 - (-49)
Solving, we get
(2 + 7i)(2 − 7i) = 4 + 49
⇒ (2 + 7i)(2 − 7i) = 53
Hence, the product of (2 + 7i)(2 − 7i) in the form a + bi is 53 + 0i.
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a right triangle has a hypotenuse with a length of 10cm. one angle of the three in this triangle is 53.1 degrees. what is the length of the side opposite this angle?
The length of the side opposite this angle of the hypotenuse is 12.51°.
A right triangle consists of the hypotenuse (longest side), the opposite(length of the leg) and the adjacent.
The angle at the corner is 90degrees
In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle.
Given that,
Length of the leg = 10cm
angle opposite the side = 53.1 degrees
To get the hypotenuse,
sin θ = opposite/hypotenuse
sin 53.1 = 10/hypotenuse
hypotenuse = 10/sin53.1°
hypotenuse = 10/0.799
hypotenuse = 12.51
Therefore,
The length of the side opposite this angle of the hypotenuse is 12.51°.
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the diagram shows two joined rectangles the total area of the compound shape ABCDEF is 36cm^2
Note that given the diagram showing joined Rectangles with the total area of the compound shape given as: ABCDEF = 36cm², the value of length AB = 4.5 or 9/2
What is a compound shape?A compound form is created by combining simple shapes. It's also known as a "composite" or "complex" form.
To solve for the value of AB, lets start form the given:
Given that:
The area of the shape ABCDEF is 36 square centimeters.
From the given figure:
In the smaller rectangle, length of sides AB is x and BC is (2-4) cm.
In the larger rectangle, length of the sides DE is (x-2) and EF is 3x cm.
thus the area if the Smaller Rectangle is:
A(Small) = x(x-4)
= x² - 4x
The area of the larger rectangle will be:
A(Large) = 3x(x-2)
= 3x² -6x
The total area of the shape will be:
A(Small) + A(Large) = 36
X²-4x+3x²-6x = 36
⇒ 4x² - 10x - 36 = 0; Divide both sides by 2
⇒2x² - 5x - 18 = 0
solving the above using the factoring method, we have:
⇒2x2-5x-18=0
⇒2x2-9x+4x-18=0
⇒x(2x-9)+2(2x-9)=0
⇒(2x-9)(x+2)=0
⇒(2x-9)=0or(x+2)=0
⇒ 2x = 9or x= -2
Thus, x = 9/2 or -2
Since the value of AB cannot be a negative value, thus the correct answer is: 9/2 or 4.5
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Full Question:
See image attached
A. -4(2t-8)
B. -2(4t+16)
C.-4t(2+8)
D. -4(2t+8)
E.-2(4t-32)
F. -8(t+4)
G. -2(4t-16)
H. -8(t-4)
what’s equivalent to -8t – 32? select all that apply.
Answer:
BCDF
Step-by-step explanation:
B. -2(4t+16)
C.-4t(2+8)
D. -4(2t+8)
F. -8(t+4)
6. (5 pts) consider the following statement: do you agree or disagree , and why ? " if i prove that an algorithm takes o(n2) worst-case time, is it possible that it takes o(n) on some inputs?"
We Disagree with the statement that "" If i prove that an algorithm takes O(n²) worst-case time, is it possible that it takes O(n) on some inputs" because if the algorithm is proven to take O(n²) time in the worst-case, it is likely to take even more time on many inputs.
The "big-O" notation provides an upper bound on the growth rate of a function, and is used to describe the asymptotic behavior of an algorithm as the size of the input grows to infinity.
If an Algorithm is proven to take O(n²) time in the worst-case, it means that the running time grows quadratically as the size of the input increases.
It is not likely that the same algorithm will take O(n) time on some inputs because the big-O notation provides an upper bound, and O(n) represents a much faster growth rate than O(n²).
Therefore , O(n²) represents the "worst-case" scenario, so any scenario where the algorithm runs faster is not considered .
The given question is incomplete , the complete question is
Consider the following statement: do you agree or disagree , and why ?
" If i prove that an algorithm takes o(n²) worst-case time, is it possible that it takes o(n) on some inputs?"
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2. Melissa, a city planner, had two pieces of wire of equal length. She shaped one piece into a
square to represent a new building site and the other into an isosceles triangle to represent a
nearby park. The base of the triangle is 4 cm shorter than a side of the square, and each leg of
the triangle is 9 cm longer than a side of the square. How long was each piece of wire?
Answer:
Step-by-step explanation:
Daniel has a circular piece of paper with a radius of 13 cm. He cuts a circular hole
with a radius of 5 cm in the centre of his piece of paper to make the shape shown
below.
Calculate the area of this shape.
Give your answer in cm² to 1 d.p.
13 cm
5 cm
Not drawn accurately
Answer:
Step-by-step explanation: Area of circle = pi.r²
A= pi. 5²
A= pi. 25
A≈78cm²
Determine the value(s) of the variable for which the expression is undefined.
1)-
5
x-10
A)x= 10, x=-5
12
4)=
2)
Write the rational expression in lowest terms.
8z³
3)
20z6
15
12-4
C)
A).
A)
A) Never undefined-any real number may be substituted for y
B) 15
C) -2, 2
D) 4
+ 5y - 36
1²-16
y + 9
y-4
8
20z³
B)x= -10
5y-36
16
C)x=10
B) 23⁹
2
99-3333
B) cannot simplify
D)
y+9
y+4
D) x=5
D) 2535
1)
3)
4)
Whole page pls
A rational expression seems to be undefined when ever the denominator is zero.
How does an expression becomes undefined?A rational expression seems to be undefined when its denominator becomes zero. Set the denominator to zero and solve the resulting equation to find the values that make a rational expression undefined.An expression in mathematics that has no meaning and thus does not have an interpretation. In the field of real numbers, for example, division by zero is undefined.Here given expression, 5/(x - 10)
The expression becomes undefined when denominator becomes 0.
So here, if x = 10 then the denominator becomes 0.
That is 5/10-10
= 5/0
which is undefined, when x = 10.
Given expression, 15/(y² + 4)
To a expression to be undefined denominator has to be 0.
But here denominator cannot become zero.
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What is the value of x?
X =
X-38°=90°
Answer:
This is the answer you want
X=90°-38°
X=52°
Answer:
128°
Step-by-step explanation:
X-38°=90°
X=90°+38°
X=128°
suppose you take a sample of 50 students from your school and measure their height. which one of the following is a random variable?
If we take a sample of 50 students from your school and measure their height , then (c) The mean of the sample data. will be a Random Variable .
A Random Variable is a defined as a variable whose value depends on the outcome of a random event.
Option (c) : the random event is the selection of 50 students from the school to measure their height. The mean height of this sample of 50 students is a random variable because it can vary depending on the specific students who are selected.
Option (a) : The true mean height of all students from your school is a population parameter and is a fixed value, so it cannot be called as a random variable.
Option (b) : The mean of the sampling distribution of mean heights for samples of size 50 is a population parameter as well, and it represents the average of all possible sample means of size 50 taken from the population. So, it is a fixed value and not a random variable.
Therefore , The mean of the sample data will be a random variable .
The given question is incomplete , the complete question is
Suppose you take a sample of 50 students from your school and measure their height. Which one of the following is a random variable?
(a) The true mean height of all students from your school.
(b) The mean of the sampling distribution of mean heights for samples of size 50.
(c) The mean of the sample data.
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here are the weights (in pounds) of 20 steers on an experimental feed diet: 183 140 136 142 172 153 172 156 70 167 192 166 113 171 159 129 112 135 174 155 where is the center of the distribution of this data set?
The centre of the distribution of weights of the 20 steers is 149.85 pounds.
The centre of a distribution of data can be described as the central tendency or typical value of the data. The most common measure of central tendency is the mean, which is calculated by summing all the values in a data set and dividing by the number of values.
To calculate the mean weight of the 20 steers, we can use the following formula:
mean = (183 + 140 + 136 + 142 + 172 + 153 + 172 + 156 + 70 + 167 + 192 + 166 + 113 + 171 + 159 + 129 + 112 + 135 + 174 + 155) / 20
mean = 2997 / 20
mean = 149.85
Therefore, the centre of the distribution of weights of the 20 steers is 149.85 pounds.
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What is 4=3/5b
Can you send help?
Answer:
b=20/3, or b=6.67
Step-by-step explanation:
4=3/5b
20=3b
b=20/3
Or, b=6.67
Answer:
20/3 = b or 6 2/3
Step-by-step explanation:
4=3/5b
To solve for b, multiply each side by 5
4 * 5=3/5b * 5
20 = 3 b
Divide each side by 3
20/3 = 3b/3
20/3 = b
We can change the improper fraction to a mixed number.
3 goes into 20 6 times with 2 left over.
6 2/3
b = 6 2/3
5. The set V = {(x, y): 0, y ≥ 0}, together with the usual operations in R2, is not a vector space. Of the ten axioms that must hold for a vector space, give specific examples showing that two of them do not hold.
Two of the axioms that do not hold for the set V with the usual operations in R2 are the existence of additive inverses and distributivity of scalar multiplication over addition.
Additive Inverses: For a vector space, every vector has an additive inverse, meaning that there exists a vector in the set such that their sum is equal to the zero vector. However, in the set V, the vector (0, 0) is not an additive inverse of any vector of the form (x, y) where y > 0, since their sum is (x, y) which is not equal to the zero vector (0, 0).Distributivity of Scalar Multiplication over Addition: For a vector space, scalar multiplication must be distributive over addition, meaning that (a + b)v = av + bv for all scalars a, b and all vectors v. However, in the set V, this property does not hold, since if we take a = 1, b = -1, and v = (0, 1), then (a + b)v = (1 + (-1))(0, 1) = (0, 0), which is not equal to av + bv = 1(0, 1) + (-1)(0, 1) = (0, 1) + (0, -1) = (0, 0).To learn more about axioms here:
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a rectangular storage container with an open top is to have a volume of 14 cubic meters. the length of its base is twice the width. material for the base costs 13 dollars per square meter. material for the sides costs 6 dollars per square meter. find the cost of materials for the cheapest such container.
The cost of the side material is $148.91, the cost of the base material is $73.67 and the cheapest cost of material is $222.58 and this can be determined by using the arithmetic operations.
Let the width of the rectangular storage container be 'x' then according to the given data the length is '2x' and let the height of the container be 'h'.
The base area of the rectangular storage container is given by:
Base Area = 2x² -- (1)
The side area of the rectangular storage container is given by:
Side Area = 2(2x)h + 2xh
= 6xh -- (2)
Now, the volume of the rectangular storage container is given by:
Volume = l x b x h
14 = 2x²h
h = 7/x²
Now, the cost is given by:
C(x) = 13(2x²) + 6(6xh)
C(x) = 26x² + 252/x
To minimize C(x), differentiate the C(x) with respect to x.
C'(x) = 52x - 252/x² --3()
52x - 252/x² = 0
x³ = ∛(63/13)
Now, differentiate equation (3) with respect to x.
C''(x) = 52 + 504/x³
C"( ∛(63/13) ) = 156 > 0
Therefore, ∛(63/13) is the point of minima.
Now, the cost of the base material is:
= 13 x 2 (62/13)^(2/3)
= $73.67
Now, the cost of the side material is:
= 252/(∛(63/13))
= $148.91
Therefore, the total cost is given by:
= 73.67 + 148.91
= $222.58
Hence, the cheapest cost of material is $222.58
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solve the separable differential equation for u. dudt=e3u 6t use the following initial condition: u(0)=3
The solution to the separable differential equation with the initial condition u(0)=3 is u = 3e−3t²/2
solve the separable differential equation for u. dudt=e3u 6t use the following initial condition: u(0)=3
The solution to the separable differential equation is found by separating the variables dudt and t.
dudt = e3u6t
We can then rearrange this equation to get t on one side and u on the other.
t = (e3u)⁄6
We can then integrate both sides of the equation to get the solution.
∫tdt = ∫(e3u)⁄6du
t²/2 = e3u/3 + c
We can then use the initial condition to solve for c.
3²/2 = e3(3)/3 + c
c = 0
Therefore the solution to the differential equation is:
t²/2 = e3u/3
u = 3e−3t²/2
This is the solution to the separable differential equation with the initial condition u(0)=3.
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Complete question:
Given a separable differential equation dudt=e3u 6t with the initial condition u(0)=3, find the solution u(t).
Which statement describes the relationship between x and y in these two equations? y = 4x y=x+4 In y = 4x, the value of y is ________ In y=x+4, the value of y is ________ Answer Bank: four more than the value of x four times the value of x
Answer:
In y = 4x, the value of y is four times the value of x. In y=x+4, the value of y is four more than the value of x.
write down the multiplication tables for z/6zand z/7z. list the elements have multi- plicative inverses.
For Z/6Z and Z/7Z, the multiplication tables are 1-5 and 0 and 1-6 and 0 correspondingly. The elements 1, 2, 3, 4, 5 and 1, 3, 5, 6 respectively have multiplicative inverses.
The multiplication table is as follows for the group Z/6Z:
1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4\s5 * 1 = 5\s0 * 1 = 0
1, 2, 3, 4, and 5 are the elements with multiplicative inverses.
The multiplication table is as follows for the group Z/7Z:
1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4
5 * 1 = 5\s6 * 1 = 6\s0 * 1 = 0
1, 3, 5, and 6 are the elements with multiplicative inverses.
The group members in a group Z/NZ are the remainders after dividing the integers by N. For instance, the elements in Z/6Z are 0, 1, 2, 3, 4, and 5. The product of each element is shown in the multiplication table.by itself when multiplied. The multiplication table for Z/6Z is as follows: 0 * 1 = 0; 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 4, 5 * 1 = 5. 1, 2, 3, 4, and 5 are the elements with multiplicative inverses. The multiplication table is also the same for Z/7Z: 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 5, 6 * 1 = 6, 0 * 1 = 0. 1, 3, 5, and 6 are the elements with multiplicative inverses.
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need help fast!!!!!!!!!!!!
The result of operations between two functions is listed below:
(f + g) (x) = x² + 7 · x - 3, Domain: All real numbers. (f - g) (x) = x² - 7 · x + 3, Domain: All real numbers. (f · g) (x) = x² · (7 · x - 3), Domain: All real numbers.How to apply operation between functions
In this question we need to determine the result of three operations between two functions, a quadratic equation and a linear equation, both polynomic functions. According to function theory, the domain of polynomials is equal to the set of all real numbers. There are three operations:
Addition
(f + g) (x) = f(x) + g(x)
Subtraction
(f - g) (x) = f(x) - g(x)
Multiplication
(f · g) (x) = f(x) · g(x)
If we know that f(x) = x² and g(x) = 7 · x - 3, then the result of the operations are:
Addition
(f + g) (x) = x² + 7 · x - 3, Domain: All real numbers.
Subtraction
(f - g) (x) = x² - 7 · x + 3, Domain: All real numbers.
Multiplication
(f · g) (x) = x² · (7 · x - 3), Domain: All real numbers.
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URGENT! WILL MARK BRAINLIEST!!!
A flower kiosk is selling roses and carnations that are either red or white. 3/5 of all the flowers are red, 1/3 of all the flowers are roses, and 9/20 of all the roses are white. What percent of all the flowers are white carnations?
Answer:
25%
Step-by-step explanation:
If 3/5 of the flowers are red, then 2/5 of them are white. Since 9/20 of the roses are white, then 9/20*2/5=3/20 of all of the flowers are white roses. Subtracting the number of white roses from the total amount of white flowers will give us the fraction of how many of the flowers are white carnations. 2/5-3/20=5/20=1/4 of all of the flowers, which is 25% as a percentage.
The percent of all the flowers are white carnations is 255.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
3/5 of the flowers are red.
2/5 of them are white.
and, 9/20 of the roses are white.
fraction of white roses of all flower
= 9/20 x 2/5
=3/20
Fraction of Flowers that are white Carnations
= 2/5 - 3/20
= 5/20
= 1/4.
Then, the percent of all the flowers are white carnations is
= 1/4 x 100
= 25%
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22. Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?
(A) 100
(B) 120
(C) 80
(D) 90
(E)Other
If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?
(A) 282435
(B) 283000
(C) 283283
(D) 282000
(E)Other
What is the product of 4% of 112 and 61% of 375?
(A) 144
(B) 90
(C) 120
(D) 105
(E)Other
. Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?
(A) 4/9
B) 1/3
(C) 5/12
D) 1/2
(E)Other
What is the remainder when the sum of the terms of the arithmetic series 101 108 + 115 + 290 is divided by 28?
(A) 7
(B) 0
(C) 14
(D) 21
(E)Other
Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?
A) 150
(B) 112
(C) 120
(D) 144
(E)Other .
A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f (3) if x is divisible by 3. What is the value of f(2020)?
A) 16
B) 14
C) 12
D) 8
E)Other
Answer:
(A) 22. Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?
Answer: (C) 80
(B) If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?
Answer: (B) 283000
(C) What is the product of 4% of 112 and 61% of 375?
Answer: (B) 90
(D) Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?
Answer: (C) 5/12
(E) What is the remainder when the sum of the terms of the arithmetic series 101 + 108 + 115 + 290 is divided by 28?
Answer: (A) 7
(F) Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?
Answer: (A) 150
(G) A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f(3) if x is divisible by 3. What is the value of f(2020)?
Answer: (A) 16
Hi can someone check my work for me! im unsure of my answers, please tell me if get any wrong! please someone
1. The number of possible outcomes are 12
2. The probability of getting head and rolling a 5 is 1/12.
3. The probability of getting a tail as rolling 1 is 1/12.
4. The probability of getting head and rolling any number on the die is 1/2.
5. The probability of getting tails and rolling an odd number is 1/4.
6. The probability of getting heads and rolling a number greater than 3 is 1/4.
How to calculate the probability?The probability of getting head and rolling a 5 is:
= 1/2 × 1/6
= 1/12.
The probability of getting a tail as rolling 1 is:
= 1/2 × 1/6
= 1/12.
The probability of getting head and rolling any number on the die is:
= 1/2 × 1
= 1/2.
5. The probability of getting tails and rolling an odd number is:
= 1 /2 × 3/6
= 1/4.
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8. Value Hardware sells 3-in. finishing nails for 0.99/lb and 2-in finishing nails sell for $1.39/1b. Toni needs 5 lb of nails. If his bill totals $6.15, how many pounds of each size did he buy?
Answer:
This algebraic problem can be solved by setting up a system of equations. For example, let x be the number of pounds of 3-inch nails that Toni buys, and y be the number of pounds of 2-inch nails that Toni buys. We know that x + y = 5 (since Toni believes a total of 5 pounds of pins) and that 0.99x + 1.39y = 6.15 (since that is the total cost of the nails). We can solve for one of the variables using one equation and then substitute that value into the other equation.
Solving for x in the first equation: x + y = 5
x = 5 - y
Substituting this into the second equation: 0.99(5 - y) + 1.39y = 6.15
4.95 - 0.99y + 1.39y = 6.15
4.95 = 0.4y + 6.15
-1.2 = 0.4y
y = -3
Since the number of pounds of nails cannot be harmful, we know that this solution is not possible. We can check by plugging in y = 3 (possible) into the first equation and seeing that x + 3 = 5, so x = 2.
Hence, Toni bought 2 lb of 3-inch nails and 3 lb of 2-inch nails.
Step-by-step explanation:
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Answer:
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Three tudent that hare a townhoue find that their electric bill for October i le than the September bill. The total of both bill i , and each bill i plit evenly among the roommate. How much did each owe in September?
Three student that hare a townhouse find that their electric bill for October, each owe in September is amount $20.31.
Let amount that September's bill was, be S
Then October's bill was: S - $2.32
Therefore, we get: S + S - 2.32 = 119.56
2S - 2.32 = 119.56
2S = 119.56 + 2.32
2S = 121.88
S, or September's bill was: 121.88/2 or $60.94
Amount each owed for September: 60.94/3 = $20.31
We consume electricity produced for our use by a corporation whenever we switch on a light, plug in a device, or let our refrigerator run. You can purchase this company's electricity by the Kilowatt-hour to power your home. When the firm requests payment for the electricity you consumed, they send a letter outlining the amount of electricity you consumed, the rates they charge, and the amount owed to the company.
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Raj was selling cricket bats. He sold 8 bats with 20% profit. If the net amount of profit he earned was 560 Rs, what was the selling price of one bat?
The price of one bat when Aaryan purchased is ₹500
What was the amount of profit?Revenue less costs equals profit. You deduct a few expenses from your earnings. Subtract all costs to determine net profit. The path to net profits is paved with gross and operating profits. The Profit First formula urges you to take the profit from each sale and use the balance for expenses since it places the emphasis on profit.A profit and loss statement (P&L), also known as an income statement, is a financial document that displays the sales and costs incurred by a firm over a specific time period, typically a fiscal quarter or year. Loss = C P - S P (C P > S P) Where C.P. is the item's or commodity's actual price and S.P. is the price at which the item was purchased by the consumer.Let cost price of 1 bat x
Cost price of 8 bats = 8x
He sold 8 bats with 15% profit. If the net amount of profit he earned was ₹ 600
[tex]$\frac{15}{100} \times 8 x=600$[/tex]
[tex]$8 x=\frac{600 \times 100}{15}$[/tex]
[tex]$8 x=40 \times 100$[/tex]
[tex]$x=\frac{40 \times 100}{8}$[/tex]
[tex]$x=500$[/tex]
[tex]$x=500$[/tex]
The price of one bat when Aaryan purchased is ₹500
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To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this? because the system of equations actually has only one solution because the system of equations actually has no solution because the graphs of the two equations overlap each other because the graph of one of the equations does not exist
The given system of equations have infinitely many solutions.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the system of equations as -
3x - 2y = 4
9x - 6y = 12
We can write the system of equations as -
3x - 2y = 4
9x - 6y = 12
We can write (9x - 6y = 12) as -
3(3x - 2y) = 3(4)
3x - 2y = 4
So both the lines coincide. We can say that the given system of equations have infinitely many solutions.
Therefore, the given system of equations have infinitely many solutions.
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they are One-fifth of an inch apart. What scale could Lyle include on the map? Select three options.
One-fifth inch = Three-fourths mile
Three-fourths inch = One-fifth mile
Four-fifths inch = 3 miles
3 inches = 12 miles
4 inches = 15 miles
The scale that Lyle could include on the map is /5 inch = 3/4 mile, 4/5 inch = 3 miles, and 4 inches = 15 miles. Hence, option A, option C and option E is the correct answer.
What is the distance?Distance is calculated as the sum of a person's movement and time.
Let D be the actual distance in miles between any two points, and let d be the distance shown on the map between any two points, measured in inches.
The distance between the location on the map and the real distance is equal to 1/5 of an inch since the scale on the map is 1/5 inch = 3/4 mile.
d/D = (1/5)/ (3/4)
1/5 inch = 3/4 mile
4/5 inch = 3 miles
4 inches = 15 miles
Hence, the scale that Lyle could include on the map is /5 inch = 3/4 mile, 4/5 inch = 3 miles, and 4 inches = 15 miles. Hence, option A, option C and option E is the correct answer.
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A line segment has endpoints (5, 4) and (-3, -6). What are the coordinates of the midpoint of this line segment?
Answer:
( 1,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2.
( 5+-3) /2 = 2/2 = 1
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2.
(4+-6)/2 = -2/2 = -1
The coordinates of the midpoint are ( 1,-1).
