Step-by-step explanation:
for some reason the equation at the top says 7(x+2) but both of the equations at the bottom say 7(x-2)... I'm just going to do 7(x-2)
Emmanuels Work:
7(x-2)=91
distribute the 7 by multiplying both x and -2 by it
7x-14=91
add 14 to both sides
7x=105
divide both sides by 7
x=15
Mauricio's Work:
7(x-2)=91
to get rid of the 7 multiplication, divide both sides by 7
x-2=13
add 2 to both sides
x=15
Answer:
Domain: [0, 40]
Range: [0, 20]
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
- Range is the set of y-values that are outputted by function f(x)
- Interval Notation - [a, b] denotes inclusive, (a, b) denotes exclusive
Step-by-step explanation:
According to the graph, we see that our x-values span from 0 to 40. Since both are closed dots, they are included in the domain:
Interval Notation [0, 40]
Inequality Notation 0 ≤ x ≤ 40
According to the graph, we see that our y-values span from 0 to 20. Since both are closed dots, they are included in the range:
Interval Notation [0, 20]
Inequality Notation 0 ≤ y ≤ 20
Answer:
Surface Area = 150
Step-by-step explanation:
The surface area of this triangular prism is the sum of area of all the sides.
Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)
- Triangle 1 area:

- Triangle 2 area:

- Lateral surface 1 (rectangle):

- Lateral surface 2 (rectangle):

- Bottom surface (rectangle):

Summing all these gives us the total surface area.
Total surface area = 
**** <em>The triangle shown is divided into half by the perpendicular line (3cm) to the base. So the base is divided in half (4 cm and 4 cm).</em>
<em>Now, we have a right triangle with one leg 4 cm and another leg 3 cm. How do we get the hypotenuse? We use </em><em>Pythagorean Theorem</em><em>. Which is:</em>
<em>
</em>
<em>Hence, the side length of the hypotenuse is 5 [used above in the calculation]</em>
Answer:
65 miles per hour
Step-by-step explanation:
520 divided by 8