Answer:
The cost of 1 medium smoothie = $3.38
Step-by-step explanation:
Cost of 1 jumbo smoothie = $4.95
⇒ Cost 2 Jumbo Smoothies = 2 x $4.95 = $9.9
Let us assume the cost of 1 medium smoothie = m
Now, the Cost of 2 jumbo smoothie and 1 medium smoothie + $0.15
= 4 (cost of 1 medium smoothie)
⇒ $9.9 + m + $0.15 = 4 m
or, 10.15 = 4 m - m
or, 3 m = 10.15
⇒ m = 10.15/3 = 3.38
or, m = 3.38
Hence, the cost of 1 medium smoothie = $3.38
Answer:
14.8
Step-by-step explanation:
2 + 5 × 4 - 8 - (-4/5)
Solve for brackets.
2 + 5 × 4 - 8 + 4/5
Multiply.
2 + 20 - 8 + 4/5
Add or subtract.
= 74/5
Answer:
![k = 5](https://tex.z-dn.net/?f=k%20%3D%205)
Step-by-step explanation:
Given
![g(x) = f(x) + k](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%29%20%2B%20k)
Required
Determine the value of k
First, we need to determine the equation of g(x)
Start by calculating the slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Where x and y are two corresponding values:
![(x_1,y_1) = (1,1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281%2C1%29)
![(x_2,y_2) = (0,-3)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%280%2C-3%29)
The slope (m) is:
![m = \frac{-3- 1}{0 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-3-%201%7D%7B0%20-%201%7D)
![m = \frac{-4}{- 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-4%7D%7B-%201%7D)
![m = 4](https://tex.z-dn.net/?f=m%20%3D%204)
The equation is calculated using:
![y - y_1 = m(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m%28x%20-%20x_1%29)
Where
and ![(x_1,y_1) = (1,1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281%2C1%29)
![y - 1 = 4(x - 1)](https://tex.z-dn.net/?f=y%20-%201%20%3D%204%28x%20-%201%29)
![y - 1 = 4x - 4](https://tex.z-dn.net/?f=y%20-%201%20%3D%204x%20-%204)
Make y the subject of formula
![y = 4x - 4 + 1](https://tex.z-dn.net/?f=y%20%3D%204x%20-%204%20%2B%201)
![y = 4x - 3](https://tex.z-dn.net/?f=y%20%3D%204x%20-%203)
So:
![f(x) = 4x - 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%20-%203)
Next, we determine the equation of f(x)
Start by calculating the slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Where x and y are two corresponding values:
![(x_1,y_1) = (-1,-2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-1%2C-2%29)
![(x_2,y_2) = (0,2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%280%2C2%29)
The slope (m) is:
![m = \frac{2- (-2)}{0 - (-1)}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2-%20%28-2%29%7D%7B0%20-%20%28-1%29%7D)
![m = \frac{2+2}{0+1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2%2B2%7D%7B0%2B1%7D)
![m = \frac{4}{1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B4%7D%7B1%7D)
![m = 4](https://tex.z-dn.net/?f=m%20%3D%204)
The equation is calculated using:
![y - y_1 = m(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m%28x%20-%20x_1%29)
Where
and ![(x_1,y_1) = (-1,-2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-1%2C-2%29)
![y - (-2) = 4(x - (-1))](https://tex.z-dn.net/?f=y%20-%20%28-2%29%20%3D%204%28x%20-%20%28-1%29%29)
![y + 2 = 4(x +1)](https://tex.z-dn.net/?f=y%20%2B%202%20%3D%204%28x%20%2B1%29)
![y + 2 = 4x +4](https://tex.z-dn.net/?f=y%20%2B%202%20%3D%204x%20%2B4)
Make y the subject of formula
![y = 4x + 4 - 2](https://tex.z-dn.net/?f=y%20%3D%204x%20%2B%204%20-%202)
![y = 4x + 2](https://tex.z-dn.net/?f=y%20%3D%204x%20%2B%202)
So:
![g(x) = 4x + 2](https://tex.z-dn.net/?f=g%28x%29%20%3D%204x%20%2B%202)
Recall that
![g(x) = f(x) + k](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%29%20%2B%20k)
Make k the subject
![k = g(x) - f(x)](https://tex.z-dn.net/?f=k%20%3D%20g%28x%29%20-%20f%28x%29)
Substitute values for g(x) and f(x)
![k = 4x + 2 - (4x - 3)](https://tex.z-dn.net/?f=k%20%3D%204x%20%2B%202%20-%20%284x%20-%203%29)
![k = 4x + 2 - 4x + 3](https://tex.z-dn.net/?f=k%20%3D%204x%20%2B%202%20-%204x%20%2B%203)
![k = 4x - 4x+ 2 + 3](https://tex.z-dn.net/?f=k%20%3D%204x%20-%204x%2B%202%20%20%2B%203)
![k = 5](https://tex.z-dn.net/?f=k%20%3D%205)
<h2>
Answer:</h2>
The simplified form of the given polynomial equation is:
![-2x^2-x+7](https://tex.z-dn.net/?f=-2x%5E2-x%2B7)
<h2>
Step-by-step explanation:</h2>
We are asked to simplify the given polynomial expression in terms of the variable x.
The algebraic expression is given as:
![(-9x^2+2x+13)-(-7x^2+3x+6)](https://tex.z-dn.net/?f=%28-9x%5E2%2B2x%2B13%29-%28-7x%5E2%2B3x%2B6%29)
On taking out the terms from both the brackets the sign of the terms of the second bracket gets interchanged as there is a negative sign preceding it.
Hence, we get the expression as:
![=-9x^2+2x+13+7x^2-3x-6\\](https://tex.z-dn.net/?f=%3D-9x%5E2%2B2x%2B13%2B7x%5E2-3x-6%5C%5C)
Now on combining the like terms we get:
![=-9x^2+7x^2+2x-3x+13-6\\\\\\=-2x^2-x+7](https://tex.z-dn.net/?f=%3D-9x%5E2%2B7x%5E2%2B2x-3x%2B13-6%5C%5C%5C%5C%5C%5C%3D-2x%5E2-x%2B7)