Answer:
The smallest possible perimeter of the triangle, rounded to the nearest tenth is 72.4 in
Step-by-step explanation:
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
Let
x ------> the length of the remaining side
Applying the triangle inequality theorem
1) x+x > 30
2x > 30
x > 15 in
The perimeter is equal to
P=30+2x
<em>Verify each case</em>
1) For P=41.0 in
substitute in the formula of perimeter and solve for x
41.0=30+2x
2x=41.0-30
x=5.5 in
Is not a solution because the value of x must be greater than 15 inches
2) For P=51.2 in
substitute in the formula of perimeter and solve for x
51.2=30+2x
2x=51.2-30
x=10.6 in
Is not a solution because the value of x must be greater than 15 inches
3) For P=72.4 in
substitute in the formula of perimeter and solve for x
72.4=30+2x
2x=72.4-30
x=21.2 in
Could be a solution because the value of x is greater than 15 inches
4) For P=81.2 in
substitute in the formula of perimeter and solve for x
81.2=30+2x
2x=81.2-30
x=25.6 in
Could be a solution because the value of x is greater than 15 inches
therefore
The smallest possible perimeter of the triangle, rounded to the nearest tenth is 72.4 in
Answer:
10.5 Dollars an hour
Step-by-step explanation:
If he is making 10 dollars an hour then to represent the raise, you would multiply 10 by 5% and add the result onto 10 to get how much he will be making per hour. In this case, 10 x 1.05 would be the equation.
Answer:
C is independent m is dependent.
Step-by-step explanation:
The money is made based on the number cupcakes that are sold.
Distribute the .25 to get .25x + 1 - 3 = 28
Then simplify to get .25x - 2 = 28
Move the two to the right to get .25x = 30
Then divide to leave x: 30 / .25 = 120
X = 120
Answer:
a=3
b=24
Step-by-step explanation:
If 
is a factor of 
, then the factors of must also be factors of .
So what are the factors of ? Well the cool thing here is the coefficient of ![x^2[tex] is 1 so all we have to look for are two numbers that multiply to be -12 and add to be positive 1 which in this case is 4 and -3.-12=4(-3) while 1=4+(-3).So the factored form of [tex]x^2+x-12](https://tex.z-dn.net/?f=x%5E2%5Btex%5D%20is%201%20so%20all%20we%20have%20to%20look%20for%20are%20two%20numbers%20that%20multiply%20to%20be%20-12%20and%20add%20to%20be%20positive%201%20which%20in%20this%20case%20is%204%20and%20-3.%3C%2Fp%3E%3Cp%3E-12%3D4%28-3%29%20while%201%3D4%2B%28-3%29.%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3ESo%20the%20factored%20form%20of%20%5Btex%5Dx%5E2%2Bx-12)
is 
.
The zeros of are therefore x=-4 and x=3. We know those are zeros of by the factor theorem.
So x=-4 and x=3 are also zeros of because we were told that was a factor of it.
This means that when we plug in -4, the result will be 0. It also means when we plug in 3, the result will be 0.
Let's do that.
Equation 1.
Equation 2.
Let's simplify Equation 1 a little bit:
Let's simplify Equation 2 a little bit:
So we have a system of equations to solve:
16a-b=24
9a-b=3
---------- This is setup for elimination because the b's are the same. Let's subtract the equations.
16a-b=24
9a-b= 3
------------------Subtracting now!
7a =21
Divide both sides by 7:
a =3
Now use one the equations with a=3 to find b.
How about 9a-b=3 with a=3.
So plug in 3 for a.
9a-b=3
9(3)-b=3
27-b=3
Subtract 27 on both sides:
-b=-24
Multiply both sides by -1:
b=24
So a=3 and b=24
