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1 year ago

12

Polygon ABCDE has the vertices A(2, 8), B(4, 12), C(10, 12), D(8, 8), and E(6, 6). Polygon MNOPQ has the vertices M(-2, 8), N(-4

, 12), O(-10, 12), P(-8, 8), and Q(-6, 6).
A transformation or sequence of transformations that can be performed on polygon ABCDE to show that it is congruent to polygon MNOPQ is a
The length of the wooden plank is meters. How many -meter pieces can Joe saw from the wooden plank?

1 answer:

Leto [7]1 year ago

9 0

A transformation that can be performed on polygon ABCDE is a reflection over the y-axis.
The image of a polygon by a reflection its mirror image. The reflected image has the same size as the original.
It means that polygon ABCDE is congruent to polygon MNPQ.

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A scale drawing of a rectangular park is 5 inches wide and 7 inches ong. The actal prake is 280 yards long. What is the area of

Roman55 [17]

Given:

A scale drawing of a rectangular park is 5 inches wide and 7 inches long.

The actual park is 280 yards long.

To find:

The area of the actual park.

Solution:

Length of drawing = 7 inches

Length of actual park = 280 yards

The scale factor is

7 inches : 280 yards

1 inches : 40 yards

The width of the drawing is 5 inches. So, the width of actual part is

$40\times 5=200 yards$

The area of the actual park is

$Area=Length \times width$

$Area=280\times 200$

$Area=56000$

Therefore, the area of the actual park is 56000 sq. yards.

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2 years ago

Solve the system of linear equations using multiplication.

Anna71 [15]

Answer:

$(8,-1)$

Step-by-step explanation:

The given system is:

$3x+3y=21$

$6x+12y=36$

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

$x+y=7$

$x+2y=6$

We could solve the first equation for $x$ and replace the second $x$ with that.

Let's do that.

$x+y=7$

Subtract $y$ on both sides:

$x=7-y$

So we are replacing the second $x$ in the second equation with $(7-y)$ which gives us:

$(7-y)+2y=6$

$7-y+2y=6$

$7+y=6$

$y=6-7$

$y=-1$

Now recall the first equation we arranged so that $x$ was the subject. I'm referring to $x=7-y$ .

We can now find $x$ given that $y=-1$ using the equation $x=7-y$ .

Let's do that.

$x=7-y$ with $y=-1$ :

$x=7-(-1)$

$x=7+1$

$x=8$

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

$3x+3y=21$ with $(x,y)=(8,-1)$ :

$3(8)+3(-1)=21$

$24+(-3)=21$

$21=21$ is a true equation so the "solution" looks promising still.

$6x+12y=36$ with $(x,y)=(8,-1)$ :

$6(8)+12(-1)=36$

$48+(-12)=36$

$36=36$ is also true so the solution has been verified since both equations render true for that point.

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2 years ago

Read 2 more answers

Joey wants to build a rectangular garden. He plans to use a side of a river for one side of the garden, he will not place fencin

jonny [76]

We let x and y be the measures of the sides of the rectangular garden. The perimeter subtracted with the other side should be equal to 92.

<span> 2x + y = 92</span>

The value of y in terms of x is equal to,

<span> y = 92 – 2x</span>

The area is the product of the two sides,

<span> A = xy</span>

Substituting,

<span> A = x (92 – 2x) = 92x – 2x2</span>

Solving for the derivative and equating to zero,

<span> 0 = 92 – 4x ; x = 23</span>

Therefore, the area of the garden is,

<span> A = 23(92 – 2(23)) = 1058 yard<span>2</span></span>

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2 years ago

Read 2 more answers

Tim has an after-school delivery service that he provides for several small retailers in town. He uses his bicycle and charges $

nlexa [21]

Answer:

<em>$4.84</em>

<em></em>

Step-by-step explanation:

Given that

For delivery within $1\frac{1}2$ mi, charges = $1.25

For delivery within $1\frac{1}2$ mi - $1\frac{3}4$ mi, charges = $1.70

For delivery within $1\frac{3}4$ mi - 2 mi, charges = $2.15

and

so on.

i.e.

For delivery within 2 mi - 2 $\frac{1}4$ mi, charges = $2.60

For delivery within 2 $\frac{1}4$ mi - 2 $\frac{1}2$ mi, charges = $3.05

For delivery within 2 $\frac{1}2$ mi - 2 $\frac{3}4$ mi, charges = $3.50

For delivery within 2 $\frac{3}4$ mi - 3 mi, charges = $3.95

For delivery within 3 mi - 3 $\frac{1}4$ mi, charges = $4.40

So, every 0.25 mi or $\frac{1}4$ mi increase in distance, there is an increase of $0.45 in the charges.

It is given that there is increase of 10% in the rates.

i.e. for every 0.25 mi increase in distance, there is an increase of 0.45*1.10 = $0.495 in the charges.

The distance of $3\frac{1}8$ miles lies within the range 3 mi - 3 $\frac{1}4$ mi.

So actual charges after increase of 10%

$\Rightarrow \$4.40 \times \dfrac{110}{100}\\\Rightarrow \$4.40 \times 1.10\\\Rightarrow \bold{\$4.84}$

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2 years ago

What number comes next 16, 06, 68, 88,

inessss [21]

So the given series is "16, 06, 68, 88, __"

Count all the cyclical opening in each of these numbers. For example in 16, there is a one cyclical loop present in it(the one in 6), similarly in 06 it is two(one in zero and one in 6), going ahead, in 68 it is 3(one in 6 and two in 8).

From here on things become simple: hence, the cyclical figures in these equations written down becomes 1,2,3,4,_,3.

Let's now try solving the above sequence, going by the logical reasoning the only number that can fill in the gap should be 4.

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2 years ago