Write the following statement as an equation and solve. Jake Drewrey, owner of Jake's Landscape Service, knows that one of his fertilizer tanks holds four times as many gallons of liquid fertilizer as a second tank. The two tanks together hold 394 gal. If both tanks are filled to capacity, how many gallons of fertilizer does each tank hold?

Math 107 Midterm \[ \text { Unit } 1,6,8,9 \] Please show your work and circle your final answer. 1. Greg has an \( 80: 1 \) scale drawing of the floor plan of his house. On the floor plan, the dimensions of his rectangular living room are \( 1 \frac{7}{8} \) inches by \( 2 \frac{1}{2} \) inches. What is the area of his real living room in square feet?

Which of the following events is Mutually Exclusive? Passing this quiz and passing this class Drawing on the board while listening to music. Going to the zoo and walking. Being outside and being in the classroom.

How many different ways can a captain, assistant captain, and equipment manager be formed from a team of 18 people? (Assume no person can occupy more than one position.)

1- Montrer que : \( \exists!\alpha \in] \frac{-1}{2} ; 0\left[/ \sqrt{\alpha+1}=\frac{-2 \alpha}{\alpha+1}\right. \) 2- On considère la fonction \( h \) de la variable réel \( x \) définie sur \( \mathbb{R} \) par: \( h(x)=x^{3}-x^{2}+3 x+1 \). a- Vérifier que : \( h(\alpha)=0 \). b- Montrer que \( \alpha \) est la seule et unique solution de l'équation: \( h(x)=0 \). c- Montrer que \( h \) admet une fonction réciproque \( h^{-1} \) définie sur un intervalle \( J \) que l'on précisera. d- Montrer que : \( \left(\forall x \in \mathbb{R}^{-}\right)\left(h^{-1}(x)<0\right) \)

1. \( 13=-4 x+9 \)