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3 years ago

Carran is building a fence around his rectangular yard. The fence will cover the front and the 2 sides of the yard. The

Mathematics

1 answer:

dolphi86 [110]3 years ago

7 0

9514 1404 393

Answer:

sides: 12 feet
front: 28 feet

Step-by-step explanation:

Let x represent the length of one side of the yard. Then the width of the yard is 2x+4, and the perimeter is ...

P = 2(L +W) . . . . . . . . . . formula for perimeter of a rectangle

80 = 2(x + (2x+4)) . . . . . with values from the problem filled in

40 = 3x +4 . . . . . . . . divide by 2, collect terms

36 = 3x . . . . . . . . . subtract 4

12 = x . . . . . . . . . divide by 3. This is the length of the side fence.

2x +4 = 2(12) +4 = 28

The fence is 12 feet on the sides and 28 feet on the front. (Its total length is 52 feet.)

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Quadrilateral ABCD is inscribed in the circle. If m∠A = 95°, what also must be true?

makvit [3.9K]

Opposite angles in a cyclic quadrilateral add up to 180 degrees .
So the angle opposite angle A ( that is angle C) must be 180-95 = 85 degrees

7 0

3 years ago

. Three types of shirts sold at a store cost $9.00, $11.00, and $12.50. One day, the store sells a total of 23 shirts and makes

lbvjy [14]

Answer:

X + 3y = 23

9x + 36y = 243

11 shirts sold at $9.0 per shirt, 4 shirts sold at $11 per shirt and 8 shirts sold at $12.5 per shirt

Step-by-step explanation:

-----Since we are told to assume that the number of shirts sold for $9.00 each is x, that of $11.00 is y and also that of $12.50 is z.

9x + 11y + 12.5z = 243

9x + 11y + 12.5(2y) = 243

9x + 36y = 243_______ equation 1

----- The statement also read that One day, the store sells a total of 23 shirts and makes $243 on the sales. TWICE AS MANY SHIRTS WERE SOLD FOR $12.50 THAN WERE SOLD FOR $11.00

Z = 2y

x + y + z = 23

X + y + 2y = 23

X + 3y = 23_____ equation 2

Now multiply the above by 9 to have this equation's "x" sharing the same coefficient with that of equation 1

9x + 27 = 207 will be the new one___equation 3

-----Subtract equation 3 from 1 and we have

9x + 36y = 243____ equation 1

9x + 27y = 207____ equation 3

9y = 36

Y = 4

-----Substitute y = 4 in equation 2

X + 3y = 23

X + 4(3) = 23

X + 12 = 23

X = 23 - 12

X = 11

-----Remember that x + y + z = 23

11 + 4 + z = 23

15 + z = 23

Z = 23 - 15

Z = 8.

So therefore, x =11 shirts, y = 4 shirts and z = 8 shirts

4 0

3 years ago

Identify the factors of 9x^2+24x+16

Goryan [66]

Hi friend,

This is a perfect square trinomial.

It can be recognised because it is of the form:

a^2−2ab+b^2=(a−b)^2

with a=3x and b=4

9x2−24x+16=(3x)2−(2⋅(3x)⋅4)+42

=(3x−4)2

6 0

3 years ago

X^2 - 10x - 20 = 0, which number would have to be added to "complete the square"?

Airida [17]

Answer:

Step-by-step explanation:

When you're completing the square you're adding (b/2)^2 which in this case is (-5)^2 or 25. This is because when you rewrite it as a square binomial you write it in the form (x+(b/2))^2 which is going to result in x^2+b+(b/2)^2. Since you need to reach 25 you need to add 45 since the last value is at -20.

3 0

2 years ago

Read 2 more answers

Two number cubes are rolled. What is the probability of rolling a sum of 9 or a sum that is even?

Murljashka [212]

Well I don't know !
Let's figure it out together.

Each cube can land in 6 different ways, so the total number
of possible results with two cubes is (6 x 6) = 36 .

Now we need to figure out how many of those 36 possibilities
meet your specifications ... either 9 or any even number.

Ways to make 9 :

3 . . . 6
6 . . . 3
4 . . . 5
5 . . . 4

Four ways to make 9.
____________________________

Ways to make an even number:

1 . . . 1
3 . . . 1
1 . . . 3
2 . . . 2
5 . . . 1
1 . . . 5
6 . . . 2
2 . . . 6
6 . . . 4
4 . . . 6
6 . . . 6

Eleven ways to make an even number.
_____________________

Total number of ways to succeed = (4 + 11) = 15 ways

So the probability of succeeding (rolling 9 or an even number)
is

15 / 36 = 5 / 12 = 0.41666... = (41 and 2/3) % .

8 0

4 years ago

Read 2 more answers