Let's start by solving the first equation.
a) -3 = 7 + 2t/3
To begin simplifying this equation, we should multiply both sides by 3 to get rid of the denominator on the right side of the equation.
-9 = 7 + 2t
Next, we should subtract 7 from both sides to cancel out the 7 on the right side.
-16 = 2t
Finally, we should divide both sides by 2.
t= -8
Now let's move on to the next equation.
b) 4(5x-2) = 7(2x+3)
Let's use the distributive property to get rid of the parentheses and their coefficients.
20x-8 = 14x + 21
Now, lets subtract 14x from both sides of the equation.
6x - 8 = 21
Next, let's add 8 to both sides of the equation.
6x = 29
And divide both sides by the coefficient of x, which is 6.
x = 29/6 or 4 5/6
Now for the last equation.
C) 2x - 6 = 20 - 2.5x
First, we should add 2.5x to both sides to cancel out the -2.5x on the right side of the equation.
4.5x - 6 = 20
Now, let's add 6 to both sides to get the variable term alone.
4.5x = 26
Finally, we should divide both sides by 4.5 to get x by itself.
x = 5 7/9
Hope this helps! :)
1 -
3 cups left.
2-
David biked a total of 158 miles (option C)
Why?
- First exercise:
To solve the problem we need to consider that for each 1/2 cup of cornmeal, we will have 6 corn muffins.
So, calculating we have:

We can see that, if each 1/2 cups can give us 6 corn muffins, 2 cups can give us 24 corn muffins.

Hence, there are 3 cups left.
- Second exercise:
We can solve the problem by multiplying or adding the fractions according to the number of dots assigned to each one.
So, calculating we have:


Hence, we have that David covered a total 158 miles. (Option C)
Have a nice day!
Answer:
x=0, y=-2
Step-by-step explanation:
Let x=3y+6 be equation 1
and 2x-4y=8 be equation 2
sub equation 1 into equation2,
2(3y+6)-4y=8
6y+12-4y=8
2y=-4
y=-2
sub y=-2 into equation 1,
x=3(-2)+6
x=0
sub is an abbreviation for substitute
For this case we have that every rectangle traingule complies with the Pythagorean theorem:

Where:
c: It is the hypotenuse
b: It's the base
a: It's the height
It is noted that if we replace:

So, we have 
If we evaluate the other options we will obtain wrong results.
Thus, a rectangle triangle can have measurements of:
66 in, 88 in and 110 in respectively
Answer:
Option b