Answer: (3a + 1) (a + 3)
Step-by-step explanation:
<u>Concept:</u>
Here, we need to know the idea of factorization.
It is like "splitting" an expression into a multiplication of simpler expressions. Factoring is also the opposite of Expanding.
<u>Solve:</u>
Given = 3a² + 10a + 3
<em>STEP ONE: separate 3a² into two terms</em>
3a
a
<em>STEP TWO: separate 3 into two terms</em>
3
1
<em>STEP THREE: match the four terms in ways that when doing cross-multiplication, the result will give us 10a.</em>
3a 1
a 3
When cross multiply, 3a × 3 + 1 × a = 10a
<em>STEP FOUR: combine the expression horizontally to get the final factorized expression.</em>
3a ⇒ 1
a ⇒ 3
(3a + 1) (a + 3)
Hope this helps!! :)
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Answer:
By S.S.S. congruence property; ΔTZW ≅ ΔVZU
Step-by-step explanation:
Given:
TUVW is a rectangle.
To Prove : TZW ≅ UZV
Proof:
Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.
So,
And also TV and WU are the diagonals of the rectangle.
And the diagonals of rectangle bisects each other.
Therefore;
Now In ΔTZW and ΔVZU
TW = UV (from 1)
TZ = ZV (from 2)
WZ = ZU (from 3)
So, by S.S.S. congruence property;
ΔTZW ≅ ΔVZU
Hence proved.
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
Answer: -6p - 78
Step-by-step explanation:
-5 (3p + 3) + 9(-7 + p)
-15p -15 - 63 + 9p
-6p-78
