Answer:
5 weeks
$175
Step-by-step explanation:
Bill owes his mother $300 and plans to pay her $25 every week.
Therefore, after w weeks he has to give her mother more C = 300 - 25w, amount of money.
Steve owes his mother $550 and plans to pay her $75 every week.
Therefore, after w weeks he has to give her mother more C = 550 - 75w, amount of money.
If after w weeks they both will owe their mother the same amount of money, then
300 - 25w = 550 - 75w
⇒ w = 5 weeks. (Answer)
Now, the amount of money will be $(300 - 25 × 5) = $175. (Answer)
<u>A </u><u>pair of shoes</u><u> gives us</u><u> 48 </u><u>different outfits.</u>
What is a linear equation?
- A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
- The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." from Wolfram MathWorld: linear
We will employ the basic counting principle, which states that if one task can be completed in method A and another in way B, then both tasks may be completed in way A*B.
If mom buys 1 shirt, then total shirts(A) = 6+1 =7, total pants(B) = 2 and total shoes (C) = 3
By basic counting principle, number of outfits = A*B*C = 7*2*3 = 42 outfits possible
and
If mom buys 1 pair of shoes, then total shirts(A) = 6, total pants(B) = 2 and total shoes (C) = 3+1 = 4
By basic counting principle, number of outfits = A*B*C = 6*2*4 = 48 outfits possible
hence, buying a pair of shoes gives us 48 different outfits.
Learn more about linear equation
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Answer:
b. Subtracting the base period amount from the analysis period amount, dividing the result by the base period amount, then multiplying that amount by 100%
Step-by-step explanation:
A percentage change can be computed from ...
((new amount) -(old amount))/(old amount) × 100%
This best matches the description of choice B.
_____
<em>Comment on the answer</em>
The formula offered in the question will show the "percent change" from 100 to 103 as 3. It is not 3; rather, it is 3%. The final multiplication must be by 100% in order to arrive at the proper number.
Answer:
10m x 15m
Step-by-step explanation:
You are given some information.
1. The area of the garden: A₁ = 150m²
2. The area of the path: A₂ = 186m²
3. The width of the path: 3m
If the garden has width w and length l, the area of the garden is:
(1) A₁ = l * w
The area of the path is given by:
(2) A₂ = 3l + 3l + 3w + 3w + 4*3*3 = 6l + 6w + 36
Multiplying (2) with l gives:
(3) A₂l = 6l² + 6lw + 36l
Replacing l*w in (3) with A₁ from (1):
(4) A₂l = 6l² + 6A₁ + 36l
Combining:
(5) 6l² + (36 - A₂)l +6A₁ = 0
Simplifying:
(6) l² - 25l + 150 = 0
This equation can be factored:
(7) (l - 10)*(l - 15) = 0
Solving for l we get 2 solutions:
l₁ = 10, l₂ = 15
Using (1) to find w:
w₁ = 15, w₂ = 10
The two solutions are equivalent. The garden has dimensions 10m and 15m.
<span>A parabola that has a horizontal directrix is a parabola that opens up or down.
Here are some of its components:
1) Standard equation of a parabola with a horizontal directrix: (x-h)^2 = 4a(y-k),
a = distance from vertex to focus
2) Vertex at (h,k)
3) Focus(h,k+a)
4) Directrix: y = k-a
5) Axis of symmetry: x = h
A parabola that has a vertical directrix opens to the right or left and is on its side.
Here are some components
1) Standard equation of a parabola with a vertical directrix: (y-k)^2 = 4a(x-h)
2) vertex (h,k)
3) focus (h+a,k)
4) directrix: x = h-a
5) Axis of symmetry: y = k
Hopes this helps :)</span>
