Answer:
56
Step-by-step explanation:
There are two ways the answer to this question can be determined
Method 1 : the fast method
We know that 8 is twice 4
4 x 2 = 8
The ratio of diet soda = 8
the ratio of regular sodas = 4
Diet sodas = 112
the number of regular sodas = 112 / 2 = 56
Method 2 : The long method
I would first determine the total number of diet and regular sodas. Let the total number be represented by d
from the question, the following equation can be derived :
(8/12) x d = 112
divide both sides of the equation by 12/8 to determine the value of d
d = 112 x (12/8) = 168
We can now derive a value for the number of regular soda
regular sodas = ( ratio of regular sodas / total soda) x total number of sodas
(4/12) x 168 = 56
How much exterior paint do I need for a 2000 square foot house?
Overall, you required 12 to 14 gallons, or 45 to 53 liters, of paint to paint the exterior of your 2000 square foot home.
It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home. When calculating how much paint you will need, there are many factors to take into account. Every paint has a varied coverage, which determines how many square feet may be painted with each gallon of paint.
According to a rule of thumb and general recommendations, you will require 10 to 12 gallons, or 38 to 45 litres, of exterior paint for a G+0/1 storey house with a 2000 square foot area, as well as 2 gallons of paint for exterior trim for approximately two coats, which includes painting for sliding, overhangs, and soffits, as well as exterior trim for painting the gutters, fascia, and window trims. Overall, you required 12 to 14 gallons, or 45 to 53 liters, of paint to paint the exterior of your 2000 square foot home.
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How do you find the repeating and the missing number in an array?
The basic approach to solve this problem is to first sort array and then traverse through all the the elements and check for missing value and repeating value.
Approach:
Sort the input array.Traverse the array and check for missing and repeating.c++ implementation
#include <bits/stdc++.h>
using namespace std;
void printTwoElements(int arr[], int size)
{
int i;
cout << "The repeating element is ";
for (i = 0; i < size; i++) {
if (arr[abs(arr[i]) - 1] > 0)
arr[abs(arr[i]) - 1] = -arr[abs(arr[i]) - 1];
else
cout << abs(arr[i]) << "\n";
}
cout << "and the missing element is ";
for (i = 0; i < size; i++) {
if (arr[i] > 0)
cout << (i + 1);
}
}
int main()
{
int arr[] = { 8, 3, 4, 5, 5, 6, 1 };
int n = sizeof(arr) / sizeof(arr[0]);
printTwoElements(arr, n);
}
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What is the end behavior of the graph of f x )= x5 8x4 16x3?
The graph of f(x) = [tex]x^{5}-8x^{4}-16x^{3}[/tex] has the following end behavior : as x decreases, x5 increases; as x increases, x5 decreases; and the graph crosses the x-axis at x = 0 instead of at x = 4.
Given, f(x) = [tex]x^{5}-8x^{4}-16x^{3}[/tex]
[tex]x^{5}[/tex] will also approach -∞ as x approaches -∞. This is so because a negative number remains negative when raised to the power of an odd number.[tex]x^{5}[/tex] will go closer to +∞ as x approaches +∞. This is so because the outcome is still positive when we raise a positive number to the power of an odd number.the given function's roots,f(x) = [tex]x^{5}-8x^{4}-16x^{3}[/tex]
= [tex]x^{3}[/tex](x - 4)(x - 4) = 0
[tex]x^{3}[/tex] = 0
x = 0
x - 4 = 0
x = 4
Thus, x = 0 and x = 4 are the roots.
As a result, the graph will touch the x-axis but not the repeated root of x = 4, indicating that the graph has a repeated root.
The graph will cross at x = 0 because 0 is a root and does not cross at x = 4.Correct question :
What is the end behavior of the graph of f(x)= [tex]x^{5}-8x^{4}-16x^{3}[/tex] ?
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4-> Perpetua has 1,800/= to buy pencils. There are 2 types which prices differ by 40/=. If she boys the cheaper type sho will get 15 more pencils than if she buys the expensive type. What are the prices of the pencils?
The price of the two pencils is Rs.100 (expensive) and Rs.60 (cheaper).
Let the price of the expensive pencil be = x
And the price of the cheaper one be = y.
According to the question:
The difference between the price of 2 = 40
Therefore,
x- y =40
Total amount = 1800.
The number of Expensive pencils that can be bought = 1800/x.
The number of Expensive pencils that can be bought = 1800/y.
According to the question,
1800/y -1800/x = 15 (the number of extra pencils)
= (1800x -1800y)/xy = 15
= 1800x -1800y =15xy
= 1800 (x-y) =15xy
Substituting x-y as 40
1800 x 40 =15xy
xy = 4800.
We know that x-y =40
Therefore, x = y+ 40
xy = 4800
(y+40) y = 4800
[tex]y^{2}[/tex] + 40 y = 4800
Using the quadratic equation formula,
y = 52.111 or y = -92.111
Thus, the cost of the cheaper pencil (y)= Rs. 52.111
The cost of the expensive pencil (x) = 52.111 + 40 = Rs 92.111
Therefore the cost of two pencils is = Rs. 52.111 and Rs 92.111.
During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time t, in hours. At time t=0 hours, the population is 300. At time t=24 hours, the population is 1000. At what time t is the population 500 ?.
The time t at which the population is 500 is 45 hours.
The equation gives the rate of change of the population at time t:
dP/dt = kP
where P is the population at time t and k is the constant of proportionality.
We can use this equation to find the value of k by substituting the known values of P and t at time t=24 hours:
dP/dt = kP
1000 = k*300
k = 1000/300
k = 10/3
Now that we know the value of k, we can use the equation to find the time t at which the population is 500:
dP/dt = kP
500 = (10/3)P
P = 500*3/10
P = 150
Since the population at time t=0 hours is 300, the population has decreased by 150 over the 24 hours, so t = -150/(-10/3) = 45 hours.
Therefore, the time t at which the population is 500 is 45 hours.
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dP/dt = kP
We can use this equation to find the value of k by substituting the known values of P and t at time t=24 hours:
dP/dt = kP
1000 = k*300
k = 1000/300
k = 10/3
dP/dt = kP
500 = (10/3)P
P = 500*3/10
P = 150
Since the population at time t=0 hours is 300, the population has decreased by 150 over the 24 hours, so t = -150/(-10/3) = 45 hours.
Therefore, the time t at which the population is 500 is 45 hours.
Which graph represents the function f(x) = 2?
Answer:
The graph of given function is shown below.
Step-by-step explanation:
The absolute parent function is g(x)=|x|. The graph of parent function is a V-shape d and vertex of the function is origin.
The given function is
.... (1)
The vertex from of an absolute function is
.... (2)
where, a is a constant and (h,k) is vertex of the function.
From (1) and (2) we get
The value of a is -1. The value of a is negative it means the graph of parent function reflect across x-axis.
The vertex of the function is (0,-2). It means the graph of parent function shifts 2 units down.
If f(x) has a y-intercept at 3 and x-intercepts at 2 and −4, and if
g(x) = 2f(2x + 3), which intercepts of g(x) can you identify for certain, and what are they?
Answer:
Step-by-step explanation:
The y-intercept of g(x) is 3 * 2 = 6.
To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = 2f(2x + 3), this means we need to find the values of x that make f(2x + 3) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(2x + 3) = 0 for x.
Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(2x + 3) = 0, we get:
f(2(2) + 3) = 0
f(4 + 3) = 0
f(7) = 0
and
f(2(-4) + 3) = 0
f(-8 + 3) = 0
f(-5) = 0
Therefore, the x-intercepts of g(x) are at x = 7/2 and x = -5/2. These are the only intercepts of g(x) that we can determine for certain.
Can 4 year olds count?
Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.
What do you mean by counting?Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.
Here,
Children develop and learn on an individual basis, however many
4 year old are able to learn their numbers between 1 and 100 and can count over 10.
They could be prepared to practice counting by fives or other skip counting techniques (5, 10, 15, 20, and so on).
Start working on number recognition with your kid as soon as you can.
Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.
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Find the nth term of the following sequences. Also find the 9th and 6th terms .
Answer: an=2(-2)ⁿ⁻¹ a₉=512 a₆=-64
Step-by-step explanation:
Since we have an alternating minus sign in this sequence, therefore the first multiplier of the following sequence will be (-1)ⁿ.
And since the first term of the following sequence is positive, the first multiplier of the following sequence is (-1)ⁿ⁻¹.
The second multiplier of the following sequence is 2ⁿ because the sequence has the form: 2, 4, 8, 16, ..., 2ⁿ .
[tex]Thus,\ a_n=(-1)^{n-1}(2^n)\\\\ a_n=2(-2)^{n-1}\ \ \ (1)[/tex]
Find the 9th and 6th terms of the sequence by formula (1):
a₉=2(-2)⁹⁻¹
а₉=2(-2)⁸
a₉=2(256)
a₉=512
a₆=2(-2)⁶⁻¹
а₆=2(-2)⁵
a₆=2(-32)
a₆=-64
Two-Column proof for my geometry class
The two-column proof is given below:
What is meant by geometry?Mathematics' earliest branch is geometry, along with arithmetic. The distance, size, shape, and relative position of objects in relation to one another are all aspects of space that are addressed. The term "geometer" refers to a mathematician who specializes in geometry.
Before the 19th century, Euclidean geometry which incorporates the concepts of point, line, plane, distance, angle, surface, and curve as fundamental concepts—was nearly entirely the focus of geometry.
Geometry's use was greatly expanded during the 19th century by a number of discoveries. One of the first of these discoveries is Gauss Theorema Egregium, which roughly states that the Gaussian curvature of a surface is independent of any particular embedding in a Euclidean space.
Statements Reasons
4.7(2f-0.5)=-6(1.6f-8.3f) Given
4.7(2f-0.5)=-6(-6.7f) Combine like terms
9.4f-2.35= -40.2f Get all the terms to the one
side of an equation
49.6f=23.5 Addition property
f=47/992 Division property
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You roll a 6-sided die.
What is P(odd)?
Write your answer as a fraction or whole number.
Answer: 3/6 or 1/2
Step-by-step explanation:
In a 6-sided die, there are 3 odd numbers 1,3 and 5. So. P(odd) is 3/6 or 1/2.
3. Indrani and Jagad share some money in the ratio Indrani: Jagad = 7:9. Calculate the percentage of the money that Indrani receives.
The percentage of money Indrani receives is 43.75%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Indrani and Jagad share some money in the ratio,
Indrani : Jagad = 7 : 9.
We know the percentage of money for both a and b in the form of a : b can be obtained as, [a/(a + b)]×100.
Therefore, the percentage of money Indrani gets is,
= [7/(7 + 9)]×100.
= (7/16)×100.
= 43.75%.
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Please mark as Brainliest!!
Answer:
43.75%
Step-by-step explanation:
Which statement is true about the function on the interval -7 ≤ x < -4?
(A)
The function is negative and decreasing on the interval.
B The function is negative and increasing on the interval.
C
The function is positive and decreasing on the interval.
The function is positive and increasing on the interval.
The true statement about the interval is that:
B The function is negative and increasing on the interval.How to analyze the intervalThe given interval is -7 ≤ x < -4, the numbers in the interval are
-7, -6, -5,
The numbers are all negative and the number starts from -7 but did not get to -4
since the interval starts from -7 which is a lesser number than -6 and a lesser when compared with -5 we say the interval is increasing
In negative numbers, the larger the number the lesser it has value and and lesser the number the closer it is to zero and the higher the number
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PLEASE HELP!! I’LL MARK THE BRANNIEST!
Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
What is graph?
A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.
f(x)=log(2x)
g(x)=log1/10(x-3) the base of log is 1/10
Domain is x>3
Range is all real numbers
g(x) is decrease on the interval x>3
asymtote is x=3
x intercept is x=4
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What is the equation of the asymptote?
The equations of the asymptotes are y = 2 and x = -1, respectively
How to determine the equations of the asymptotesThe equation of the function is given as
f(x) = 2x² + 7x - 4/x² + 5x + 4
Introduce bracket, to differentiate the numerator and the denominator
So, we have
f(x) = (2x² + 7x - 4)/(x² + 5x + 4)
Next, we plot the graph of the function (see attachment)
The asymptotes are the points on the graph is a line that acts as the limit of another line or curve
From the graph, we have the asymptotes to be
x = -1 and y = 2
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Complete question
What is the equation of the asymptote?
f(x) = 2x² + 7x - 4/x² + 5x + 4
What is an example of a inverse sentence?
"It's pouring if the grass is wet." Our inverse sentence would be, "If it is NOT raining, then it is NOT wet on the grass."
Given,
Inverse Sentence;
Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."
Example of inverse sentence;
Now, we can construct the three other statements using the concepts we established before. If anything, we would say the opposite: "If the grass is wet, it's pouring." "If it is NOT raining, then the grass is NOT wet," would be our inverse claim.
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M3 is the sum of all money in the economy.
Which of the following correctly shows how to
calculate for the entire money supply?
A. M1+ M2 + M3
B. M1+ M2-M3
C. M1x M2 x M3
Answer:
A. M1+ M2 + M3
Step-by-step explanation:
M1 is the money supply that makes it easy to convert assets/items into currency.
M2 is the deposits and money market funds.
Add M1, M2, and M3 to calculate the entire money supply of all the money in the economy.
Answer:
A. M1+ M2 + M3
M3 consists of all currency notes held by the public, all demand deposits with the bank, deposits of all the banks with the RBI and the net Time Deposits of all the banks in the country. So M3 = M1 + time deposits of banks.
Step-by-step explanation:
(04.02 MC)
The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer 28 62 90
Mobile device 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who use a mobile device in a traditional class?
23%
37%
46%
72%
The joint relative frequency of students using mobile devices in traditional classes, is
How to find the joint relative frequency ?The joint relative frequency of students that use mobile devices in the setting of a traditional class is :
= Number of students using mobile devices in traditional class / Number of total students accessing courses
Number of students using mobile devices in traditional class = 46 students
Number of total students accessing courses = 200
The joint relative frequency of students using mobile devices in traditional classes :
= 46 / 200
= 23 %
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What are the 5 Steps to Finding the mean absolute deviation?
The mean absolute deviation of a set of data is the mean distance (or the average distance) between each data element and the mean of the data elements.
The steps for Finding the Mean Absolute Deviation of a Data Set are as follows:
Step 1: Find the mean of the data set.
Step 2: Find the sum of the data values, and divide the sum by the number of data values.
Step 3: Find the absolute value of the difference between each data value and the mean: |data value – mean|.
Step 4: Find the sum of the absolute values of the differences.
Step 5: Divide the sum of the absolute values of the differences by the number of data values.
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What are the factors of 2x² 7x 15 *?
The factors of [tex]2x^2 + 7x + 15[/tex] are [tex](2x + 3)[/tex] and [tex](x + 5)[/tex].
To find the factors of [tex]2x^2 + 7x + 15[/tex] , we can use the factoring method called "splitting the middle term." Here's how it works:
Write the expression as the product of two binomials: [tex](2x^2 + 7x + 15) = (2x^2 + ax + b)(cx + d)[/tex]
Find the factors of the constant term (15) that add up to the coefficient of the middle term (7). The factors of 15 are 1 and 15, 3 and 5, and 5 and 3. The only pair that adds up to 7 are 3 and 5.
Set the coefficients of the two binomials to 3 and 5, respectively. The expression becomes: [tex](2x^2 + 3x + 5)(5x + 3)[/tex]
Rewrite the binomials using the distributive property: [tex](2x^2 + 3x + 5)(5x + 3) = (2x^2 + 5x + 3x + 15) = 2x(x + 5) + 3(x + 5) = (2x + 3)(x + 5)[/tex]
So, the factors of [tex]2x^2 + 7x + 15[/tex] are [tex](2x + 3)[/tex] and[tex](x + 5)[/tex].
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What is the end behavior of the graph of f x x5 8x4 16x3?
The end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 is asymptotic: it goes towards positive infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity.
The end behavior of the graph of a polynomial function with degree 5 is determined by the leading term, which in this case is x^5. Since the degree of the leading term is odd and the coefficient is positive, the graph of f(x) = x^5 + 8x^4 + 16x^3 will approach positive infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity. This is known as an asymptotic end behavior. As the x-values get larger and larger, the magnitude of the y-values will also get larger and larger, approaching infinity in either direction. This can be seen by looking at the graph of the function, which will have an "S" shape that curves up and to the right (positive infinity) for large positive x-values, and down and to the left (negative infinity) for large negative x-values.
For x > 0, the end behavior is:
f(x) = x5 + 8x4 + 16x3
lim x→∞ f(x) = lim x→∞ x5 + 8x4 + 16x3
lim x→∞ f(x) = lim x→∞ x5
lim x→∞ f(x) = +∞
For x < 0, the end behavior is:
f(x) = x5 + 8x4 + 16x3
lim x→−∞ f(x) = lim x→−∞ x5 + 8x4 + 16x3
lim x→−∞ f(x) = lim x→−∞ x5
lim x→−∞ f(x) = −∞
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Is 6 and 8 and 3/4 True or false?
TRUE: The ratio of 6 and 8 is equivalent to 3/4.
Define the term equivalent ratio?"Two or even more ratios that reflect the same relation as well as comparison of integers are recognized as equivalent ratios," according to the concept of the equivalent ratio. The idea of corresponding fractions is comparable. The term "proportion" also refers to the equivalence of two ratios.The cross multiplication approach and the HCF method can both be used to determine if the supplied ratios be equivalent or not.Remember that the ratio is the same when you multiply both sides of a fraction by a number.
= 3/4
= 3*2 / 4*2
= 6/8
= 6:8
Thus, the ratio of 6 and 8 is equivalent to 3/4.
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Is 6:8 equals 3/4 ? Is it true or false and why?
What is unique array value?
A unique array value is a value that appears only once among all the other values in the given array. Hence the name unique.
What is an array?An array is a set of items, images, or numbers arranged in rows and columns. Arrays are practical illustrations of multiplication ideas.
Why do we need arrays?Arrays are needed in cases where you need to store and manipulate large amounts of data efficiently.
Some of the benefits of using arrays include:
1. Arrays allow you to store a large number of items in a single data structure, which makes it easier to work with large datasets.
2. Arrays allow you to access and modify the items in the array quickly, using the index of the item.
A data structure called an array is used to hold a number of elements together. Each item in an array is recognized by its index, or place within the array. A value that only appears once in an array is considered to be unique array value. Think about the following array, for instance:
[1, 2, 3, 4, 5, 6]
Because each value only occurs once in this array, each value is distinct.
Contrarily, think about the following array:
[1, 2, 3, 3, 4, 5]
Since it appears twice in this array, the number 3 is not unique. Since they only exist once, each of the other values is distinct.
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Willow homework sheet is 3×19 how can you use base 10 blocks to show 3×19
Answer: 27
Step-by-step explanation:
two base ten blocks then 7
What is the slope-intercept form of 5x 2y 10?
The slope-intercept form of a straight line of equation 5x + 2y = 10 is y = (-5/2)x + 5.
The slope-intercept form of a line is:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
To put the equation 5x + 2y = 10 in slope-intercept form, we need to solve for y. We can do this by rearranging the terms and isolating y:
2y = -5x + 10
y = (-5/2)x + (10/2)
Thus, the slope-intercept form of the equation 5x + 2y = 10 is:
y = (-5/2)x + 5
This means that the slope of the line is (-5/2) and the y-intercept is (0,5).
--The question is incomplete, answering to the question below--
"What is the slope-intercept form of 5x + 2y = 10?"
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pleaseee help. im so confused
Solving the inequality [tex]\frac{2x + 4}{2}[/tex] < 6, we get x < 4.
What is Linear Inequality?Linear Inequalities are mathematical expressions which consist of a left hand side and a right hand side connected with inequality signs like <, >, ≤, ≥ and ≠.
They are almost like linear equations when we see it, but the '=' sign in linear equations are substituted with inequality signs like those mentioned earlier.
The expression given here is,
[tex]\frac{2x + 4}{2}[/tex] < 6
Multiplying both sides with 2, we get,
2x + 4 < 6 × 2
2x + 4 < 12
Subtracting both sides with 4, we get,
2x + 4 - 4 < 12 - 4
2x < 8
Dividing both sides by 2,
2x / 2 < 8 / 2
x < 4
Hence the inequality [tex]\frac{2x + 4}{2}[/tex] < 6 results in x < 4.
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Fernando works in the shipping department of a toy manufacturer. Toy cars weigh 3
kilograms apiece and are shipped in a container that weighs 5 kilograms when empty. Toy
trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 10 kilograms.
When packed with toys and ready for shipment, both kinds of containers have the same
number of toys and the same weight. What is the weight of each container?
Write a system of equations, graph them, and type the solution.
The weight of container will be 20 kg
Let x be the number of car toys packed into container. Toy cars weigh 3 kilogram apiece and are shipped in a container that weighs 5 kilograms when empty, then the total weight of container with toy cars is
x.3 + 5 = 3x + 5
The number of toy trucks is also x. Toy trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 10 kilograms, then the total weight of container with toy trucks is
x.2 + 10 = 2x +10
When packed with toys and ready for shipment, both kinds of containers have the same weight. Thus,
3x + 5 = 2x + 10
x = 15
The weight of container = x + 5
= 15 + 5
= 20 kg
Hence, the weight of container will be 20 kg
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Sean and Rachel were both born on April 17. When Sean was 4, his sister Rachel was 2 . Use this information to answer all of the questons in this section.
Answer:
B • r = s - 2
Step-by-step explanation:
Rachel will always be two year younger than Sean. if we substitute the letters with their ages...
[rachel's age] 2 = [ sean's age] 4 - 2
2 = 4 - 2
it can't be A
2 = 4 (two does not equals four)
it can't be C
2 = 4 + 2 (the correct answer is 6, Rachel is not 6 years old)
it can't be D
4 = 2 - 2 (the correct answer is 0. Rachel's not 0 years old as well.
[ also s is the subject in this case. but we are looking for r ]
Answer: B
Step-by-step explanation:
What is the sum of the interior angle of a regular nonagon
The sum of the interior angle of a regular nonagon will be 1,260°.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The interior angle of the polygon is given as,
Interior angle = 180° - 360° / n
And the sum of the interior angle is given as,
Sum of the interior angle = n x (Interior angle)
The number of sides of the regular nonagon is 9. Then the interior angle is given as,
Interior angle = 180° - 360° / 9
Interior angle = 180° - 40°
Interior angle = 140°
Then the sum of the interior angle of a regular nonagon will be given as,
Sum of the interior angle = 9 x 140°
Sum of the interior angle = 1,260°
The sum of the interior angle of a regular nonagon will be 1,260°.
More about the polygon link is given below.
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If a and b are both negative numbers and a>b, what must be true about their absolute values?.
The absolute value of a number is the non-negative distance between the number and zero on a number line, regardless of sign.
This means that the absolute value of a negative number is always positive. Therefore, if a and b both are negative numbers, their absolute values will be positive numbers. If a is greater than b, then the absolute value of a must be greater than the absolute value of b. This can be expressed mathematically as follows:
|a| > |b|
This equation states that the absolute value of a is greater than the absolute value of b. In other words, the distance between a and zero is greater than the distance between b and zero on a number line.
To illustrate this, let’s take an example of two negative numbers, a=-3 and b=-5. The absolute values of these two numbers are 3 and 5 respectively. Since 3 is greater than 5, the absolute value of a is greater than the absolute value of b. This holds true regardless of the sign of the numbers, as long as a is greater than b.
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