Answer:
12 units
Step-by-step explanation:
To find any side length of a right triangle given two side lengths, you would use the pythagorean theorem which is a² + b² = c². In this equation, a and b represents either the height of base of the triangle, and c represents the hypotenuse of the triangle (the diagonal line - in your question it is 13). By plugging in the base and hypotenuse, you get the equation of 5² + b² = 13². 5² is equal to 25 and 13² is equal to 169, so the equation is 25 + b² = 169. Subtract 25 for both sides of the equation and you find that b² = 144. Square both sides and the missing length is 12 because √144 = 12.
Answer:
Keisha bought 3 sandwiches and 5 lemonades.
Equations: x + y = 8 2x + y = 11
Step-by-step explanation:
To solve a problem with two variables, you need to set up a system of equations comparing the two variables and solve using either substitution or elimination. If 'x' represents the number of sandwiches and 'y' represents the number of lemonades, then x + y = 8 because they bought a total of 8 items. Also, the cost of each item is given as well as the total amount of money spent. So, our second equation is: 2x + y = 11. We can use inverse operations to solve for 'y' in the first equation: x + y - x = 8 - x which simplifies to: y = 8 - x. We can then use this expression to substitute in for the variable 'y' in the second equation: 2x + 8 - x = 11.
Combine like terms: x + 8 = 11
Inverse Operations: x +8 - 8 = 11 - 8
Solve: x = 3, so Keisha bought 3 sandwiches
Solve for y: y = 8 - 3 = 5, so Keisha bought 5 lemonades
Answer:
-2 and 4
Step-by-step explanation:
Let's set the larger number to x, and the smaller to y. With these, we can set up our equations.
x = 2y + 8
x + y = 3x - 10
Now, we put the value of x into the second equation.
2y + 8 + y = 3(2y + 8) - 10
Now we can solve for y
3y + 8 = 6y + 24 - 10
3y + 8 = 6y + 14
8 = 3y + 14
-6 = 3y
-2 = y
Now that we have the smaller number, we can put it into the first equation and solve for the larger.
x = 2*-2 + 8
x = -4 + 8
x = 4
So your two numbers are -2 and 4.
Answer:
D. 0.53
Step-by-step explanation:
The answer would be 11.6619037897 because if you make a triangle out of it the sides are 10 and 6 so a^2 + b^2 = c^2 and you get 136 and if you find the square root of that it is <span>11.6619037897</span>
