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)
36 x 3/9.
3/9 = 0.33
0.33 x 36 = 12
The matching is given below.
- Doubling ⇒ 2
- Quadrupling ⇒ 4
- Tripling ⇒ 3
- Halving ⇒ 1/2
<h3>What is an exponent?</h3>
Let a be the initial value and x be the power of the exponent function and b be the increasing factor. The exponent is given as
y = a(b)ˣ
You are asked to write exponential equations from word problems.
We know that factor 2 represents doubling, factor 4 represents quadrupling, factor 3 represents tripling, and factor 1/2 represents halving.
Then the matching is given below.
- Doubling ⇒ 2
- Quadrupling ⇒ 4
- Tripling ⇒ 3
- Halving ⇒ 1/2
More about the exponent link is given below.
brainly.com/question/5497425
#SPJ1
Answer:
Step-by-step explanation:

The rope tied to the tree will make a triangle.
The height of the triangle = 180cm
The base of the triangle = 200cm
to find how much rope you need, work out the hypotenuse using Pythagoras:
180^2 + 200^2 = 72400
√72400 = 269.0724809
This is the length of rope he needs, however you need to +30 as this is what he will need when he ties the rope:
269.0724809 + 30 = 299.0724809
299.0724809 is less than the 270cm of rope he has, so he would need more.