Which one of the following statements is incorrect?

The drama department was considering two options for the winter production. They used the following equations to represent the p

stellarik [79]

Answer:

Graph D is correct

Step-by-step explanation:

This is complicated because the scales on the x-axis and y-axis are not the same. Graph D has the correct y-intercepts and the correct slopes. The solution is x = 500, where the two lines intersect.

8 0

2 years ago

What is the conjugate of -2 + 8i

topjm [15]

Answer:

-2 - 8i

Step-by-step explanation:

To find the conjugate of a complex number, change the sign of the imaginary part.

The conjugate of -2 + 8i is -2 - 8i.

3 0

2 years ago

ROOTS AND CUBES Can someone please help me answer all 4 following?

Alex Ar [27]

NOTES:

squared (²) means multiply that number by itself 2 times
cubed (³) means multiply that number by itself 3 times
square root (√) means 2 numbers multiplied by itself on the inside simplify to 1 of that number on the outside of the radical
cubed root (∛) means 3 numbers multiplied by itself on the inside simplify to 1 of that number on the outside of the radical

Answer: (C) 41

Step-by-step explanation:

$\quad 6^2+\sqrt[3]{125} \\= 6 \cdot 6+\sqrt[3]{5\cdot 5 \cdot 5}\\= 36 + 5\\= 41$

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Answer: (C) 10

Step-by-step explanation:

$\bigg(\dfrac{7}{3}\times \sqrt[3]{27}-2\bigg)\times \dfrac{1}{5} + \sqrt{81}$

$=\bigg(\dfrac{7}{3}\times \sqrt[3]{3\cdot 3 \cdot 3}-2\bigg)\times \dfrac{1}{5} + \sqrt{9\cdot 9}$

$=\bigg(\dfrac{7}{3}\times3-2\bigg)\times \dfrac{1}{5}+9$

$=(7 - 2)\times \dfrac{1}{5}+9$

$=5 \times \dfrac{1}{5}+ 9$

$= 1 + 9$

$= 10$

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8² = 8 · 8 = 64 11² = 11 · 11 = 121

5³ = 5 · 5 · 5 = 125 3³ = 3 · 3 · 3 = 27

$\sqrt{1600}=\sqrt{40\cdot 40}=40$ $\sqrt[3]{64}=\sqrt[3]{4\cdot 4\cdot 4}=4$

$\sqrt{144}=\sqrt{12\cdot 12}=12$ $\sqrt[3]{8000}=\sqrt[3]{20\cdot 20\cdot 20}=20$

3 0

2 years ago

Solve the following recurrence relation: <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

4 0

2 years ago

If the area around the vegetable garden is of uniform width (labeled with x) and the dimensions of the vegetable garden is 45 fe

Nady [450]

Area of Rectangle = Width × Length

Vegetable Garden
Width = 20
Length = 45
Area of Vegetable Garden = 20×45=900 Sq ft

Area of Entire Garden = Width × Length
Width = 20 + 2x
Length = 45 + 2x
Area = (20 + 2x)(45 + 2x)
(2x + 20)(2x + 45)
4x^2 + 90x + 45x + 900
Area of Entire Garden = 4x^2 + 135x + 900

Area of Flower Garden = Area of Entire Garden - Area of Vegetable Garden

(4x^2 + 135x + 900) - (20 × 45)
4x^2 + 135x + 900 - 900
Area of Flower Garden = 4x^2 + 135x

7 0

2 years ago