A bank account balance, b, for an account starting with s dollars, earning an annual interest rate,

dlinn [17]

1. Ans: Option (B) $-6x^4$

Explanation:
Given: $2x^4 - 8x^4$
Take the common out:
=> $x^4(2 - 8)$

Hence: => $[tex]-6x^4$ [/tex] (Option B)

2. Ans: Option (D) $-3y^5$

Explanation:
Given: $6y^5 - 9y^5$
Take the common term(s) out:
=> $y^5(6-9)$

Hence: => $-3y^5$ (Option D)

3. Ans: Option (B) $9x^2 - 12x + 6$ quadratic trinomial

Explanation:
Given: $6 - 12x + 13x^2 - 4x^2$

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> $13x^2 - 4x^2 - 12x + 6$
=> $9x^2 - 12x + 6$ (Option B)

4. Ans: Option (C) $7.3x^2 + 0.8x + 1.3$

Explanation:
In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

Common guppies: $3.1x^2 +6.0x + 0.3$ 
Endler's guppies: $4.2x^2 - 5.2x + 1.0$
(add both)
-----------------------------------------------------------------
Total number: $7.3x^2 +0.8x + 1.3$
-----------------------------------------------------------------
Hence the ans is Option(C) $7.3x^2 + 0.8x + 1.3$

5. Ans: Option (D) $2x^2(133 - 18 \pi )$

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = $266x^2$

Now the area of the circular fountain:
Area of the Circular Fountain = $\pi r^2$
Since, r=6x
Therefore,
Area of the Circular Fountain = $\pi (6x)^2 = 36 \pi x^2$

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = $266x^2$ - $36 \pi x^2$
=> Final area of the Yard = $2x^2(133 - 18 \pi)$ (Option D)

6. Ans: Option (A) $56x^2$

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = $60x^2$

Now the area of the stadium:
Area of the stadium = 1x * 4x = $4x^2$

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= $60x^2$ - $4x^2$
=> Final area of the lot = $56x^2$ (Option A)

-i

4 0

4 years ago

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a vector V is inclined to an angle OX at 45degree and OY at 60degreee find its inclination to OZ, find its magnitude if V is 12u

Delicious77 [7]

If α, β, and γ are the angles with respect to OX, OY, and OZ, respectively, then their cosines satisfy the relationship
cos(α)² + cos(β)² + cos(γ)² = 1

Part A
For α = 45° and β = 60°, γ can be found from
cos(45°)² + cos(60°)² + cos(γ)² = 1
cos(γ)² = 1 - (1/√2)² - (1/2)² = 1/4
cos(γ) = ±1/2
γ = 60° or 120°
The inclination of V to OZ is 60° or 120°.

In rectangular coordinates,
V = (12cos(45°))i + (12cos(60°))j ± (12cos(60°))k
V = (6√2)i + 6j ± 6k

Part B
For V = 2i +3j +4k, the direction cosines and angles are
cos(α) = 2/||V|| = 2/√(2²+3²+4²) = 2/√29
α ≈ 68.2°
cos(β) = 3/√29
β ≈ 56.1°
cos(γ) = 4/√29
γ = 42.0°

7 0

3 years ago

a proportional relationship is represented by the equation 2x=18y . If y=x , where k is the constant of proportionality, then wh

liubo4ka [24]

Answer: $\bold{k=\dfrac{1}{9}}$

Step-by-step explanation:

The constant of proportionality is y = kx. Solve the given equation for "y" to find k-value in front of "x".

18y = 2x

$\dfrac{18y}{18}=\dfrac{2x}{18}$

$y=\dfrac{1}{9}x$

$k=\dfrac{1}{9}$

8 0

3 years ago

Today, Barry wants to write at least 50 pages of his research paper. Barry wrote 18 pages this morning. Barry averages about 8 p

Sever21 [200]

Answer:

The answer is

Step-by-step explanation:

4 0

3 years ago

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A new roll of insulated electrical wire has 200 feet of wire. Mr.S needs pieces that are 6 1/4 feet long. How many full pieces o

lisov135 [29]

$200 \div 6 \dfrac{1}{4} \\ = 200 \div \dfrac{25}{4} \\ = 200 \times \dfrac{4}{25} \\ = 32$

Answer : He can cut 32 full pieces.

Hope this helps. - M

7 0

3 years ago

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