Answer:
The correct answer is 25.2 in.
Step-by-step explanation:
It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.
2 inches of the ribbon are frayed so actual length = 58 inches
Please refer to the attached image for the ribbon.
A is at 0
C is at 60
B is at 2
P is the point to divide the remaining ribbon in the ratio 2:3.
Part AB of the ribbon is frayed.
BP: PC = 2:3
Let BP = 2
and PC = 3
Now, BP + PC = BC = 58 = 2 + 3 = 5
So,
BP = 
Location of the Cut = 2 + 23.2 = <em>25.2 inches</em>
<em></em>
Alternatively, we can use the formula directly:
m: n is the ratio 2:3
Answer:
The graph has a domain of all real numbers.
The graph has a y-intercept at 
.
The graph has an x-intercept at 
.
Step-by-step explanation:
Given: The graph is ![y=\sqrt[3]{x-1}+2](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2)
The domain of a function is a set of input values for which the function is real and defined.
Thus, the graph has a domain of 
.
To find the y-intercept: To find the y-intercept, substitute 
in .
![\begin{aligned}y &=\sqrt[3]{x-1}+2 \\&=\sqrt[3]{0-1}+2 \\&=-1+2 \\&=1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dy%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2%20%5C%5C%26%3D%5Csqrt%5B3%5D%7B0-1%7D%2B2%20%5C%5C%26%3D-1%2B2%20%5C%5C%26%3D1%5Cend%7Baligned%7D)
Thus, the y-intercept is
To find the x-intercept: To find the x-intercept, substitute 
in .
![\begin{aligned}y &=\sqrt[3]{x-1}+2 \\0 &=\sqrt[3]{x-1}+2 \\-2 &=\sqrt[3]{x-1} \\(-2)^{3} &=(\sqrt[3]{x-1})^{3} \\-8 &=x-1 \\-7 &=x\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dy%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2%20%5C%5C0%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2%20%5C%5C-2%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%20%5C%5C%28-2%29%5E%7B3%7D%20%26%3D%28%5Csqrt%5B3%5D%7Bx-1%7D%29%5E%7B3%7D%20%5C%5C-8%20%26%3Dx-1%20%5C%5C-7%20%26%3Dx%5Cend%7Baligned%7D)
Thus, the x-intercept is
Answer:
a) 952
b) 136
Step-by-step explanation:
<u>Ratio of b:g = 3:4, based on this we have:</u>
- Number of boys = 3x
- Number of girls = 4x
- Total number of pupils = 3x+4x = 7x
<u>Number of spectacle wearers:</u>
- 1/3*3x + 3/8*4x = x + 3/2x = 2.5x
<u>Number of those not wearing spectacles:</u>
<u>And this number equals to 612, then we can find the value of x:</u>
- 4.5 x = 612
- x= 612/4.5
- x= 136
a) T<u>otal number of pupils:</u>
b)<u> The difference in the number of boys and girls:</u>
Answer:
2/3
Step-by-step explanation:
The slope of a line can be computed as:
where
is the increment along the y-direction
is the increment along the x-direction
We can choose the following two points to calculate the slope of the line shown:
(0,1) and (3,3)
Therefore, the slope of the line is
Two lines are said to be parallel if they have same slope: therefore, a line parallel to the one shown should also have slope of 2/3.
Answer:
Step-by-step explanation:
We have been given a triangle. We are asked to find the value of x for our given triangle.
We can see that measures of both angles with red mark are equal.
The angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Using angle bisector theorem, we can set an equation as:
Therefore, the value of x is 5.
