184.8 calories :)
the grams are both 100, meaning we can use percentages. banana: 70% of 86 (.7*86=?) is 60.2 calories. yogurt: 140% of 89 (1.4*89=?) is 124.6 calories. 60.2+124.6=184.8 calories
Answer:
![A=37.5\ units^2](https://tex.z-dn.net/?f=A%3D37.5%5C%20units%5E2)
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
![A=\frac{1}{2}[b1+b2]h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Bb1%2Bb2%5Dh)
where
b1 and b2 are the parallel bases
h is the height of trapezoid (perpendicular distance between the two parallel bases)
In this problem the area is equal to
![A=\frac{1}{2}[BC+AD]AB](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5BBC%2BAD%5DAB)
we have the coordinates
![A(-3,2),B(1,5),C(7,-3),D(0,-2)](https://tex.z-dn.net/?f=A%28-3%2C2%29%2CB%281%2C5%29%2CC%287%2C-3%29%2CD%280%2C-2%29)
the formula to calculate the distance between two points is equal to
step 1
Find the distance AB
![A(-3,2),B(1,5](https://tex.z-dn.net/?f=A%28-3%2C2%29%2CB%281%2C5)
substitute in the formula
step 2
Find the distance BC
![B(1,5),C(7,-3)](https://tex.z-dn.net/?f=B%281%2C5%29%2CC%287%2C-3%29)
substitute in the formula
step 3
Find the distance AD
![A(-3,2),D(0,-2)](https://tex.z-dn.net/?f=A%28-3%2C2%29%2CD%280%2C-2%29)
substitute in the formula
step 4
Find the area
![A=\frac{1}{2}[BC+AD]AB](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5BBC%2BAD%5DAB)
substitute the values
![A=\frac{1}{2}[10+5]5](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5B10%2B5%5D5)
![A=37.5\ units^2](https://tex.z-dn.net/?f=A%3D37.5%5C%20units%5E2)
(17-7)*2=weekly allowance
so her weekly allowance is 20
Answer:
![f(g(-4)) = 18](https://tex.z-dn.net/?f=f%28g%28-4%29%29%20%3D%2018)
Step-by-step explanation:
Given
![f(x) = 4x + 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%20%2B%206)
![g(x) = x^2 + x - 9](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20%2B%20x%20-%209)
Required
Find f(g(-4))
First, calculate f(g(x))
We have:
![f(x) = 4x + 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%20%2B%206)
![f(g(x)) = 4g(x) + 6](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%204g%28x%29%20%2B%206)
Substitute: ![g(x) = x^2 + x - 9](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20%2B%20x%20-%209)
![f(g(x)) = 4[x^2 + x - 9] + 6](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%204%5Bx%5E2%20%2B%20x%20-%209%5D%20%2B%206)
Open bracket
![f(g(x)) = 4x^2 + 4x - 36 + 6](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%204x%5E2%20%2B%204x%20-%2036%20%2B%206)
![f(g(x)) = 4x^2 + 4x-30](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%204x%5E2%20%2B%204x-30)
Substitute
for ![x](https://tex.z-dn.net/?f=x)
![f(g(-4)) = 4*(-4)^2 + 4*(-4)-30](https://tex.z-dn.net/?f=f%28g%28-4%29%29%20%3D%204%2A%28-4%29%5E2%20%2B%204%2A%28-4%29-30)
![f(g(-4)) = 64 -16 -30](https://tex.z-dn.net/?f=f%28g%28-4%29%29%20%3D%2064%20-16%20-30)
![f(g(-4)) = 18](https://tex.z-dn.net/?f=f%28g%28-4%29%29%20%3D%2018)
Answer:-74
Step-by-step explanation: When you are in the megatives, less is more! So -74 is actually greater then -75