Answer:
D E + E F greater-than D F
5 less-than D F less-than 13
Triangle D E F is a scalene triangle
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
we have the triangle EDF
where
![ED=4\ units\\EF=9\ units](https://tex.z-dn.net/?f=ED%3D4%5C%20units%5C%5CEF%3D9%5C%20units)
<u><em>Applying the triangle inequality theorem</em></u>
1)
![ED+EF > DF\\4+9 > DF\\13 > DF\\DF < 13\ units](https://tex.z-dn.net/?f=ED%2BEF%20%3E%20DF%5C%5C4%2B9%20%3E%20DF%5C%5C13%20%3E%20DF%5C%5CDF%20%3C%2013%5C%20units)
2)
![ED+DF > EF\\4+DF > 9\\DF > 5\ units](https://tex.z-dn.net/?f=ED%2BDF%20%3E%20EF%5C%5C4%2BDF%20%3E%209%5C%5CDF%20%3E%205%5C%20units)
so
The length of DF is the interval -----> (5,13)
The triangle DEF is a scalene triangle (the three length sides are different)
therefore
<em>The statements that are true are</em>
D E + E F greater-than D F
5 less-than D F less-than 13
Triangle D E F is a scalene triangle
The future worth (F) of the current investment (P) with the compounded interest of i is calculated through the formula,
F = P x (1 + i)^n
Substituting the known values and the given values,
y = 360(1 + 0.03)^x
Simplifying,
y = 360(1.03)^x
Thus, the answer is letter D.
Answer:
Part 1) ![f(x)=4x+3](https://tex.z-dn.net/?f=f%28x%29%3D4x%2B3)
Part 2) ![f(x)=2x+1](https://tex.z-dn.net/?f=f%28x%29%3D2x%2B1)
Part 3) ![f(x)=x-4](https://tex.z-dn.net/?f=f%28x%29%3Dx-4)
Step-by-step explanation:
<em>Table 1</em>
step 1
Find the slope
take two points from the data in the table
(0,3) and (3,15)
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute
![m=\frac{15-3}{3-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B15-3%7D%7B3-0%7D)
![m=\frac{12}{3}=4](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B12%7D%7B3%7D%3D4)
step 2
Find the linear function in slope intercept form
![f(x)=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
we have
![m=4\\b=3](https://tex.z-dn.net/?f=m%3D4%5C%5Cb%3D3)
substitute
![f(x)=4x+3](https://tex.z-dn.net/?f=f%28x%29%3D4x%2B3)
<em>Table 2</em>
step 1
Find the slope
take two points from the data in the table
(2,5) and (5,11)
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute
![m=\frac{11-5}{5-2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B11-5%7D%7B5-2%7D)
![m=\frac{6}{3}=2](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B6%7D%7B3%7D%3D2)
step 2
Find the linear function in slope intercept form
![f(x)=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
we have
![m=2\\point\ (2,5)](https://tex.z-dn.net/?f=m%3D2%5C%5Cpoint%5C%20%282%2C5%29)
Solve for b
substitute
![5=2(2)+b\\b=5-4\\b=1](https://tex.z-dn.net/?f=5%3D2%282%29%2Bb%5C%5Cb%3D5-4%5C%5Cb%3D1)
therefore
![f(x)=2x+1](https://tex.z-dn.net/?f=f%28x%29%3D2x%2B1)
<em>Table 3</em>
step 1
Find the slope
take two points from the data in the table
(5,1) and (8,4)
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute
![m=\frac{4-1}{8-5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4-1%7D%7B8-5%7D)
![m=\frac{3}{3}=1](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B3%7D%3D1)
step 2
Find the linear function in slope intercept form
![f(x)=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
we have
![m=1\\point\ (5,1)](https://tex.z-dn.net/?f=m%3D1%5C%5Cpoint%5C%20%285%2C1%29)
Solve for b
substitute
![1=1(5)+b\\b=1-5\\b=-4](https://tex.z-dn.net/?f=1%3D1%285%29%2Bb%5C%5Cb%3D1-5%5C%5Cb%3D-4)
therefore
![f(x)=x-4](https://tex.z-dn.net/?f=f%28x%29%3Dx-4)
Answer:
+ 5, - 5
Step-by-step explanation:
p^2 - 8 = 17
p^2 = 17 + 8
p^2 = 25
= 5 x 5
p^2 = 5^2
p = ± 5
The answer is 5 ik beciase i did it