Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 6 more square feet than the smaller. What is the width of the rectangles?

Answers

Answer 1
Answer: w-width\n\nl_1=w+1\nl_2=w+2\n\nwl_1=wl_2-6\n\nw(w+1)=w(w+2)-6\nw^2+w=w^2+2w-6\nw^2-w^2+w-2w=-6\n-w=-6\nw=6\leftarrow answer

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The map below shows the length of a proposed land bridge at Phil Hardberger Park. The length of the land bridge is represented by PHin the map below.
P(2,55)
H(32, 15)
On the map, each unit represents 1 yard. To the nearest yard, what is the actual length of the land bridge from P to H?
A 50 yards
B. 150 yards
C. 78 yards
D. 234 yards

Answers

Answer:

A; the actual length of the land bridge from P to H is 50 yards

Step-by-step explanation:

Here in this case, given the coordinates of P and H, we want to calculate the actual length of the distance between the two points.

Mathematically, to calculate this distance, we make use of the distance formula;

D = √(x2-x1)^2 + (y2-y1)^2

In this case, (x1,y1) = (2,55) while (x2,y2) = (32,15)

Substituting these values

D = √(32-2)^2 + (15-55)^2

D = √(-30)^2 + (-40)^2

D = √(900 + 1600)

D = √(2,500)

D = 50 units

Now, we know that each units represent 1 yard, thus 50 units will represent 50 * 1 = 50 yards

Find the area of each parallelogram.

Answers

Answer:

30 and 21

Step-by-step explanation:

Solve the equation. –x + 8 + 3x = x – 6

Answers

First group the coefficients together on their side of the equal sign.
-x + 3x = 2x.

Then, since it is a positive number, subtract it from that side and the other side.

On the other side, the x becomes -x.

Add the 6 from the other side to the 8 to make 14.

14 = -x

Divide both sides by -1, to get the answer.

x = -14
-x+8+3x=x-6
8+2x=x-6
+6 +6
14+2x=x
-2x -2x
14/-1=-x/-1
-14=x

Show that the point (3, 7) lies on the line y = 2x + 1

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Just plug in the point
x = 3 and y = 7
Y = 2(3) + 1
Y = 6 + 1
Y = 7
That’s how to prove it

If 3 dice are rolled at the same time, what is the probability of all 3 dice showing even facevalues? (i.e. all 3 dice showing 2, 4, or 6)

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Total possible outcomes of 3 dice = 6 x 6 x 6 = 216

Total number of ways for all 3 to show even numbers:
222
224
226
242
244
246
262
264
266
.
.
etc.    There 27 of them.

Probability = 27 / 216 = 1/8 = 12.5 percent .

F(x) = 12x - 3x + 12

Find f(10x - 5)

Answers

Answer:

244,140,634

Step-by-step explanation: