5. Answer: see explanation
<u>Step-by-step explanation:</u>
If the roots are m and 3m, then x = m and x = 3m
⇒ x - m = 0 and x - 3m = 0
⇒ (x - m)(x - 3m) = 0
⇒ x² - 4mx + 3m² = 0
Since x² + px + q = 0 then p = -4m and q = 3m²
3p² = 3(-4m)² 16q = 16(3m²)
= 3(16m²) = 48m²
= 48m²
3p² = 48m² = 16q ⇒ 3p² = 16q
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6. Answer: 8 or 18
<u>Step-by-step explanation:</u>
The Area of the entire rectangle (A = L × w) is 12 × 10 = 120
The Area of the shaded region is 72, so the Area of the non-shaded region is 120 - 72 = 48.
There are two non-shaded triangles.
- Bigger non-shaded Δ: L = 12-x, w = 10 ⇒

- Smaller non-shaded Δ: L = x, w = x ⇒

Combine the Areas of both triangles and set it equal to the Area of the non-shaded region:

Area of ΔBEF:

Answer:
77 seeds
Step-by-step explanation:
Given that:
Number of seed planted in each big pot = 9
Number of big pots = 2
Total number of seeds planted in bigbpot:
Number of big pots * number of seed per pot
= 2 * 9 = 18 seeds
Total Number of seeds planted in small pot = 59 seed
Number of seeds planted in small pot + Number of seeds planted in big pot
59 seeds + 18 seeds
= 77 seeds
Answer:
8 sq inches
Step-by-step explanation:
the label covers only one part of the juice box.
Area of juice label=area of rectangle
2 in*4 in=8 square inches.
Answer:
Expected Number=71
Variance =4959
Standard Deviation= 70.42
Step-by-step explanation:
Expected Number = E (x) = np
Here p = 0.71 and q= 1- 0.71= 0.29 n= 100
Expected Number = E (x) = np = 0.71*100= 71
b) The Variance and Standard Deviation for the number of these tweets with no reaction
Suppose the number of tweets are hundred then the number of tweets with no reaction would be 71 .
Variance = E(x²) - [E(x)]² = (100)²- (71)²= 10000- 5041= 4959
Standard Deviation= √4959= 70.42
Answer:
To get the function g, shift f up by 3 units and to the right by 9 units.
Step-by-step explanation:
The given functions are
If f(x) is a parent function, then g(x) can be written in the form of f(x) as
...(1)
The translation is defined as
... (2)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
It means, to get the function g, shift f up by 3 units and to the right by 9 units.