MATHEMATICS HIGH SCHOOL

Variable g is 8 more than variable w. Variable g is also 4 less than w. Which pair of equations best models the relationship between g and w? A) g=w-8 , q=w+4 B) w=8g , w=g-4 C) g=w+8 , g=w+4 D) w=8g , w=g+4

Answers

Answer 1

Answer:

Answer:

$\Rightarrow g=w+8$

$\Rightarrow w=g-8$

and

$\rightarrow g=w-4$

$\rightarrow w=g+4$

Step-by-step explanation:

We are given that Variable g is 8 more than variable w.

$\Rightarrow g=w+8$

$\Rightarrow w=g-8$

We are also given that

Variable g is also 4 less than w.

$\rightarrow g=w-4$

$\rightarrow w=g+4$

Hence pair of equations best models the relationship between g and w are:

$\Rightarrow g=w+8$

$\Rightarrow w=g-8$

and

$\rightarrow g=w-4$

$\rightarrow w=g+4$

Answer 2

Answer: Given:
Variable g is 8 more than variable w. ⇒ g = w + 8
Variable g is also 4 less than w ⇒ g = w - 4

g = w + 8 or w = g - 8
g = w - 4 or w = g + 4

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Parallel lines never intersect, therefore, do not have a solution. a. True b. False
186 + k = (0 + 358) + 186
If x=4 and y=-2, the value of 1/2xy^2 isa. 32b. 8c. -4d. -8
Renauld has to pay 2 percent in closing costs and 14 percent for the down payment on a purchase of $170,500. Over the life of his loan, he will pay $163,021.87. What is the total cost of his house?. A. $166,431.87. B. $186,891.87. C. $190,301.87

9 miles is approximately equal to 16km. How many km are equal to 63 miles? How many miles are equal to 48km?

Answers

The correct answer is 27 miles!

16 x 7 =112 so 63 miles would equal 112 km
48km equals 21.8258172

If f(x) = x^3 – 2x^2, which expression is equivalent to f(i)?

Answers

f(x) = x³ - 2x².

f(i) = i³ - 2i².

i = √-1.

i³ = (√-1)³ = √-1 * √-1 *√-1 = -1*√-1 = -√-1 = -i

i² = (√-1)² = √-1 * √-1 = -1

f(i) = i³ - 2i² = -i - 2(-1) = -i + 2

f(i) = 2 - i

i=√-1 and all the steps are there

Antoine went on vacation to Las Vegas. His room cost $115.62 each night. His flight there cost $45.70 and his flight home was $32.49. He averaged $15.00 per day on food. On the first day Antoine won $75.00 and on the last day he lost $25.00. If he stayed for 3 months and 4 days, how much did the entire trip (including airfare, food, hotel, and winnings) cost him?

Answers

lets calculate expenses step by step:
room = (3*30 + 4)*115.62 = 10868.28, those are the total days multiplied by the room cost
flight = 45.70 + 32.49 = 78.19
food = (3*30 + 4)*15 = 1410
win = 75
lost = 25
so the total is:
total = room + flight + food + lost - win
= 12306.47
that is the cost of the entire trip, note how we subtracted the win from all other expenses

Which of the following functions are solutions of the differential equation y'' + y = sin(x)?a) y= sinxb) y= cosx
c) y=1/2sinx
d) -1/2xcosx

Answers

Answer:

Option (d)

Step-by-step explanation:

Given,

y" +y=sin x ...........(1)

The particular solution

$y_p=A x sinx +Bx cosx$

$y'_p=Axcosx+Asinx+B cosx-Bxsinx$

$y$

Putting the value of y" and y in equation (1)

$2Acosx-Axsinx-2Bsinx-Bxcosx+Axsinx+Bxcosx = sinx$

$\Rightarrow 2Acosx-2Bsinx=sinx$

Therefore 2A =0 -2B=1

⇒A=0 $\rightarrow B=-(1)/(2)$

Therefore $y_p=-(1)/(2) x cosx$

Final answer:

The solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).

Explanation:

To determine which of the given functions are solutions of the differential equation y'' + y = sin(x), we can substitute each function into the equation and check if it satisfies the equation. Let's go through each option:

Substituting y = sin(x) into the equation, we get -sin(x) + sin(x) = sin(x), which is not true. So, y = sin(x) is not a solution.
Substituting y = cos(x) into the equation, we get -cos(x) + cos(x) = sin(x), which is true. So, y = cos(x) is a solution.
Substituting y = (1/2)sin(x) into the equation, we get -(1/2)sin(x) + (1/2)sin(x) = sin(x), which is true. So, y = (1/2)sin(x) is a solution.
Substituting y = -(1/2)xcos(x) into the equation, we get (-1/2)xcos(x) + (1/2)xcos(x) = sin(x), which is true. So, y = -(1/2)xcos(x) is a solution.

Therefore, the solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).

Learn more about Solutions of a differential equation here:

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A bird was sitting 12 feet from the base of an oak tree and flew 20 feet to reach the top of the tree. How tall is the tree?

Answers

Answer:

It should be 12+20= 32 ft

Step-by-step explanation:

Todd's cube has an edge that measures5 inches. Kara's cube has an edge of3 inches. If Kara's cube was stackedon top of Todd's cube, what wouldbe the total volume of the combinedsolid? ?

Answers

Answer:

152 in³

Step-by-step explanation:

Each cube's volume is the cube of its edge length, so the total volume is ...

(5 in)³ + (3 in)³ = 125 in³ +27 in³ = 152 in³

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