The expression (m + 8) - (5m + 11) simplifies to -4m - 3.
How to subtract the expresisonsFrom the question, we have the following parameters that can be used in our computation:
Subtract 5m + 11 and m + 8
To subtract (5m + 11) from (m + 8), we need to distribute the negative sign to each term inside the first set of parentheses:
(m + 8) - (5m + 11)
Open the brackets
= m + 8 - 5m - 11
Evaluate the like terms
= -4m - 3
Hence, (m + 8) - (5m + 11) simplifies to -4m - 3.
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A bag contains 8 green marbles and 32 blue marbles. If a representative sample contains 2 green marbles, then how many blue marbles would you expect it to contain? Explain
Because the ratio of green marbles to blue marbles is 1:4
The number of blue marbles in the representative sample which contains 2 green marbles is 8.
What is meant by a representative sample?
A subset of a population that aims to correctly reflect the traits of the larger group is called a representative sample. Because the results accurately mirror those you would get from interviewing the full population, it is known as a representative sample.
Because samples comprise more manageable, smaller representations of the broader group, they are helpful in statistical analysis when population numbers are huge.
Given the total number of green and blue marbles is 8 and 32 respectively.
So the ratio of green marbles to blue marbles = 8:32 = 1:4
Now, this ratio is maintained when we form a representative sample.
Given there are 2 green marbles in a representative sample.
Then the number of blue marbles x is:
2 : x = 1 : 4
2 : x = 2 : 8
x = 8
Therefore the number of blue marbles in the representative sample is 8.
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{y=1/2x−4
{ y=−2x+1
What is the y-
coordinate for the solution to the system of equations?
The y-coordinate for the solution to the system of equations is y = -3.
What is substitution method?The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.
Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be chosen over other algebraic methods for straightforward equations that don't require complicated calculations.
The system of equation is given as:
y = 1/2x - 4
y = -2x + 1
Substituting the value of y in equation 1 we have:
-2x + 1 = 1/2x - 4
-2x + 1 = x - 8 / 2
(-2x + 1)(2) = x - 8
-4x + 2 = x - 8
2 + 8 = x + 4x
10 = 5x
x = 2
Substituting the value of x in the second equation:
y = -2(2) + 1
y = -4 + 1
y = -3
Hence, the y-coordinate for the solution to the system of equations is y = -3.
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etry E.7 Find the distance between a point and a line GWC
Q Search
Line & has equation y=x+1. Find the distance between t and the point V(-5-6).
Round your answer to the nearest tenth.
Submit
Work it
The distance between the line and the point is 2 units
How do we calculate the distance between a line and a point?A perpendicular line will give the shortest distance between a point and a line.
From the equation of the line y = x+1. Therefore the slope is 1
using the equation (y-y1) = m(x-x1)
equation of the line joining the point and the line
= y-(-6) = -1(x - (-5)
= y+6 = -x-5
y = -x-11
x-1 = -x-11
2x = -10
x = -5
y = -5+1
y = -4
(x,y) = (-5,-4)
d = √ -5-(-5)²+ -4-(-6)²
d = √ 0+ 4
d = √4
d = 2 unit
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A quantity with an initial value of 3600 decays continuously at a rate of 80% per year.
What is the value of the quantity after 0.2 decades, to the nearest hundredth?
Answer:
Step-by-step explanation:
The decay rate of 80% per year means that after each year, the value of the quantity decreases by 80/100 * 3600 = 2880.
To find the value of the quantity after 0.2 decades, we need to multiply the number of years by 10, since a decade is equal to 10 years. In this case, 0.2 decades is equal to 0.2 * 10 = 2 years.
The value of the quantity after 2 years can be found using the formula:
3600 * (1 - 0.8)^2
Plugging in the values, we get:
3600 * (1 - 0.8)^2 = 3600 * (0.2)^2 = 3600 * 0.04 = 144
So, the value of the quantity after 0.2 decades, to the nearest hundredth, is 144.
Answer: 726.83
Step-by-step explanation:
A positive integer is 3 less than another. If the sum of the reciprocal of the smaller and
twice the reciprocal of the larger is 9/10 then find the two integer
Answer:
Step-by-step explanation:
Let the smaller integer be x, then the larger integer is x + 3.
The sum of the reciprocal of the smaller and twice the reciprocal of the larger is 9/10:
1/x + 2/(x + 3) = 9/10
Expanding both sides:
10/x + 20/(x + 3) = 90/10
Combining like terms on the left side:
(10 + 20)/(x(x + 3)) = 90/10
30/(x(x + 3)) = 9/10
Cross multiplying both sides:
30 * 10 = 9 * (x(x + 3))
300 = 9x(x + 3)
Expanding the right side:
300 = 9x^2 + 27x
Subtracting 27x from both sides:
273 = 9x^2 + 27x - 27x
273 = 9x^2
Taking the square root of both sides:
√273 = √(9x^2)
√273 = 3x
Dividing both sides by 3:
√273/3 = x
The smaller integer is √273/3 and the larger integer is √273/3 + 3.
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For the linear equation 3x + y = 9 we have:
x-intercept (3, 0)y-intercept (0, 9).How to find the x and y-intercepts?Here we want to find the two intercepts for the linear equation:
3x + y = 9
First, the x-intercept is the point that we get when we evaluate on y = 0.
3x + 0 = 9
3x = 9
x = 9/3
x = 3
Then we get: x-intercept (3, 0)
And for the y-intercept we need to evaluate in x = 0.
3*0 + y = 9
y = 9
Then the y-intercept is (0, 9).
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