We know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)
Let
A------> Lincoln, NE
B------> Boulder, CO
C------> third city
we know that
in the triangle ABC
AB=500 miles
BC=200 miles
AC=x
Applying the Triangle Inequality Theorem
1) 500+200 > x------> 700 > x------> x < 700 miles
2) 200+x > 500----> x > 500-200------> x > 300 miles
the solution for x is
300 < x < 700
the interval is------> (300,700)
the possible distances, d, in miles, between Lincoln, NE, and the third city, are in the range between 300 and 700 miles
By applying concepts of <em>linear</em> functions, the graphs are related to the following expressions:
- (4/7) · x + 2
- x + 2
- (1/7) · x + 2
- - (1/7) · x + 2
- - x + 2
<h3>How to match a line with a given linear function</h3>
Graphically speaking, lines are described by <em>linear</em> functions, a kind of polynomials of grade 1, whose standard form is presented below:
y = m · x + b (1)
Where:
- x - Independent variable
- y - Dependent variable
- m - Slope
- b - Intercept
Please notice that the slope is represented graphically by the change in the y-variable divided by the change in the x-variable and the intercept is the location where the line passes through the y-axis. Hence, the <em>resulting</em> expressions are shown in this order:
- (4/7) · x + 2
- x + 2
- (1/7) · x + 2
- - (1/7) · x + 2
- - x + 2
To learn more on linear functions: brainly.com/question/9330192
#SPJ1
Answer:
19.2cm²
Step-by-step explanation:
Given parameters:
Radius of the circle = 7cm
Angle subtended by the arc = 45°
Unknown:
Area of the sector = ?
Solution:
To find the area of the sector, use the expression below;
Area of sector = 
where r is the radius ;
Insert the parameters and solve;
Area of sector = 
x 
x 7²
Area of sector = 19.2cm²
Answer:
-3
Step-by-step explanation:
Let n = number of glasses needed
1 glass gives us 1*0.4 = 0.4 liters of water
2 glasses give us 2*0.4 = 0.8 liters
3 glasses give us 3*0.4 = 1.2 liters
4 glasses give us 4*0.4 = 1.6 liters
and so on...
In general,
n glasses give us n*0.4 = 0.4*n liters of water
So 0.4*n is going to be the same as 3.4 as we want to fill the 3.4 liter pitcher.
Set 0.4*n equal to 3.4 and solve for n
0.4*n = 3.4
0.4*n/0.4 = 3.4/0.4 <<--- divide both sides by 0.4
n = 8.5
If we want n to be a whole number, then round up to the nearest whole number. So we'll need 9 full glasses of water to fill the 3.4 liter pitcher. There is extra water in this case which isn't used.
So the answer is either 8.5 or 9 depending on if your teacher wants you to round to the nearest whole number.
