Hey there!
Tom's age to Mary's is 3:4; an equivalent ratio is 15:x (x symbolizes Mary's age).
To solve for this, we need to divide our proportions. By that, I mean divide Tom's older age by his younger age. If we do so, we should get a scale factor that we can multiply Mary's younger age by.
15 / 3 = 5
This means that the scale factor of the ages is 5.
x / 4 = 5 (Solving for Mary's unknown age.)
To solve for x, multiply both sides by 4.
x/4 * 4 = x
5 * 4 = 20
x = 20
Mary's age is 20.
I hope this helps!
we have
<u>The system of equations</u>
-------> equation 
-------> equation 
Substitute equation in equation
subtract 
both sides
Divide by 
both sides
the solution is the point 
therefore
the answer is
the solution to the system of equations is the point
Answer: 41 degrees
Step-by-step explanation:
so, we know that a triangle is 180 degrees. since we know that one angle is 80 degrees, we can subtract that from the equation. now, we are trying to find what X is so that we can find the angle. here is how i did it:
i rewrote it and removed the parentheses.
4x + 1 + 4x + 19 = 100
then, i collected like terms and calculated it.
8x + 20 = 100
then, i moved the constant to the right.
8x = 100 - 20
then, i simply calculated it.
8x = 10
solution: x = 10
so, we just insert X into the angle for A. that gets us 4(10) + 1 = angle A
40 + 1 = angle A, hence angle A = 41 degrees.
d) You have a <u>difference of squares</u>:
49y² - 9 = (7y)² - 3²
Recall the identity,
a² - b² = (a - b) (a + b)
So,
49y² - 9 = (7y - 3) (7y + 3)
e) Pull out the common factor 3 from each term:
3x² - 3x - 90 = 3 (x² - x - 30)
Now use the <u>sum-product method</u>. Notice that we can write 30 = 5 • 6, and 5 - 6 = 1, so
3x² - 3x - 90 = 3 (x + 5) (x - 6)
f) Same as in (e), use the <u>sum-product method</u>. Notice that 42 = 7 • 6, and -7 - 6 = -13, so
x² - 13x + 42 = (x - 7) (x - 6)
