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2 years ago

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A rectangle with perimeter 198 cm is divided into five congruent rectangles. What is the perimeter of one of the five congruent

rectangles?

1 answer:

Yanka [14]2 years ago

3 0

P = 198 cm

P/5 = 198 cm/5

P/5 = 39.60 cm

I believe this is the perimeter of one of the 5 congruent rectangles.

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HELP ASAP In two or more complete sentences, Explain how you would find the equation of a parabola, given the coordinate of the

kvasek [131]

In the general case in Cartesian coordinates, you would use the definition of a parabola as the locus of points equidistant from the focus and directrix. The equation would equate the square of the distance from a general point (x, y) to the focus with the square of the distance from that point to the directrix line.

Suppose the focus is located at (h, k) and the equation of the directrix is ax+by+c=0. The expression for the square of the distance from (x, y) to the point (h, k) is ...
(d₁)² = (x-h)²+(y-k)²
The expression for the square of the distance from (x, y) to the directrix line is
(d₂)² = (ax+by+c)²/(a²+b²)

Equating these expressions gives the equation of the parabola.
(x-h)²+(y-k)² = (ax+by+c)²/(a²+b²)

When the directrix is parallel with one of the axes, one of the coefficents "a" or "b" is zero and the equation becomes much simpler. Often, it would be easier to make use of the formula (for a directrix parallel to the x-axis):
y = 1/(4p)*(x -h)² +k
where the (h, k) here is the vertex, the point halfway between the focus and directrix, and "p" is the (signed) distance from the focus to the vertex. (p is positive when the focus is above or to the right of the vertex.)

4 0

2 years ago

Johnny works on multiple jobs for his uncle. Johnny is paid a one-time fee of $245.00 for all of his jobs. His uncle also pays h

Ede4ka [16]

From the above problem, we can create the equation:

P = 245 + 20 t

where P is the total payment that Johnny receives and t is the total time he worked

Given that P = 2245, so find for t:

2245 = 245 + 20 t

t = 100 hours

7 0

2 years ago

Write an equation perpendicular to x-4y=20 that passes through the point 2,-5

marshall27 [118]

Answer:

4x +y = 3

Step-by-step explanation:

Perpendicular lines have slopes that are the negative reciprocals of one another. When the equation of the line is written in standard form like this, the equation of the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Doing this much would give you ...

4x +y = (constant)

Note that we have chosen to make the equation read 4x+y, not -4x-y. The reason is that "standard form" requires the leading coefficient to be positive.

Now, you just need to make sure the constant is appropriate for the point you want the line to go through. So, it needs to be ...

4(2) +(-5) = constant = 3

The line of interest has equation ...

4x + y = 3

3 0

2 years ago

Alicia has 6 paintings she wants to hang side by side on her wall.

gayaneshka [121]

<u>Answer:</u>

A) 720 ways

B) 15 ways

C) 6 ways

<u>Step-by-step explanation:</u>

A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Alicia can arrange her paintings in 720 ways.

B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:

$P(n, r) = \frac{n!}{r!(n-r)!}$

$= \frac{6!}{4!(6-4)!} = 15$

Therefore, Alicia can choose any 4 of her paintings in 15 ways.

C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways

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2 years ago

a jogger runs 218 meters eastward then 72 meters westard then 62 meters eastward and finally 184 meters westward. For this motio

iris [78.8K]

Answer:

<u>Total distance = 536 m</u>

<u>Total displacement = 24 m</u>

Step-by-step explanation:

<u>Distance and Displacement</u>

A moving object constantly travels for some distance at defined periods of time. The total moved distance is the sum of each individual distance the object traveled. It can be written as:

dtotal=d1+d2+d3+...+dn

This sum is obtained independently of the direction the object moves.

The displacement only takes into consideration the initial and final points of the path defined by the object in its moving. The displacement, unlike distance, is a vectorial magnitude and can be even zero if the object starts and ends the movement at the same point.

For the question at hand, it's not known if the requirement is about the distance or the displacement, so we will compute both.

To compute the distance, we just add all the distances:

dtotal= 218 m + 72 m + 62 m + 184 m = 536 m

To compute the displacement, we must establish a positive direction as desired. Let's choose the east as the positive direction. Any movement eastward is considered positive and any movement westward is negative. We mentioned the displacement is a vector, but since we only have movement in the x-axis, we can only manage the signs. Thus, the total displacement is:

xtotal = 218 m - 72 m + 62 m -- 184 m = 24 m

Since the result is positive, the jogger stopped 24 meters eastward form the original point.

4 0

2 years ago