All categories

4 years ago

In the diagram shown at the right, a 2-foot-wide flower border surrounds the heart-shaped pond. What is the area of the border?

Mathematics

1 answer:

True [87]4 years ago

6 0

The area is 139.02 sq. ft.

This can be broken into two shapes: a 12 by 12 square and a circle with a diameter of 12. Adding the 2 ft border increases it to a 14 by 14 square and a circle with a radius of 16 (2 on each side).

With border:

Area of square = 14*14 = 196
Area of circle = 3.14(8*8) = 200.96

Together = 396.96

Without border:

Area of square = 12*12 = 144
Area of circle = 3.14(6*6) = 113.04

Together = 257.04

This is a difference of 396.96-257.04 = 139.02 sq. ft.

You might be interested in

HELP ME!!! I've been stuck!

Olin [163]

Answer:

You have to fill the blank squares to complete the table.

See the figure attached and the explantion below.

Explanation:

The figure attached shows the three squares that you have to fill to complete the table to summarize the different theorems to prove triangles are congruent.

1. SAS

SAS stands for Side Angle Side. That means that whenever two sides and the included angle on one triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent.

Thick marks are used to mark the corrsponding parts, sides or angles that are congruent. That is why the two triangles to the first triangles on the image (on the upper square to the right) are marked:

One thick straight mark for two sides that are congruent
Two thick straight marks for the other two sides that are congruent
On thick curved mark for the two angles that are congruent

In that way, the figures show two triangles, with two congruent sides and the included angle congruent, to prove that the two triangles are congruent by the SAS theorem.

2. ASA

ASA stands for Angle Side Angle.

The ASA congruency theorem states that if two angles of a triangle and the included side are congruent, then the two triangles are congruent.

Thus you have to add the legend "Two congruent angles with and included side", which means that if the two angles and the included side on one triangle are congruent to two angles and the included side of other triangles, then both triangles are congruent.

The rule to mark the sides and angles that are congruent is with the use of thick marks. This is how it was done in the drawing of the two triangles in the lower right square:

One thick straight mark for two sides that are congruent
One thick curved mark for two angles that are congruent
Two thick curved marks for the other two angles that are congruent

6 0

3 years ago

A box contains 14 large marbles and 10 small marbles. Each marble is either green or white 8 of the large marbles are green, and

netineya [11]

The probability that the marble is large or white is 0.5714.

<h3>What is probability?</h3>

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Probability of an event is

P(A) = Number of favorable outcomes/ Total Number of outcomes

= n(A)/n(S)

where

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

We have,

Number of large marbles = 14

Number of small marbles = 10

Number of large green marbles = 8 which implies

Number of large white marbles = 14 - 8 = 6

Number of small white marbles = 4 which implies

Number of small green marbles = 10 - 4 = 6.

Now, let

Let X be the event of drawing large marble.

Let Y be the event of drawing small marble.

Let M be the event of drawing white marbles.

Let N be the event of drawing green marbles.

Since only one marble is drawn at a time ,

so P(X) = 14/24

P(Y) = 10/24

P(M) = 10/24

P(N) = 14/24

We have to find the probability that a marble is large or white i.e. P(X∪M).

P(X∪M) = P(X) + P(Y) - P(X∩M)

P(X∩M) = In 14 large marbles 6 are white marbles = 6/14.

P(X∪M) = P(X) + P(Y) - P(X∩M) = 14/24 + 10/24 - 6/14 = 0.5833+0.4167-0.4286 = 0.5714.

Therefore, the probability of drawing large or white marble is 0.5714.

To know more about probability, visit

brainly.com/question/19169117

#SPJ4

3 0

1 year ago

Mario ordered a pizza for dinner when it arrived Mario quickly ate 1/8 of the pizza or Mario's getting napkins his pet poodle at

Leya [2.2K]

Sent a picture of the solution to the problem (s).

6 0

4 years ago

Use the functions f(x) = 2x + 7 and g(x) = 6x − 5 to complete the function operations listed below.

noname [10]

We are given the two functions:

f(x) = 2x + 7

g(x) = 6x – 5

Part A. Find (f + g)(x)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 2 x + 7 + 6 x – 5

(f + g)(x) = 8 x + 2

Part B. Find (f ⋅ g)(x)

(f ⋅ g)(x) = f(x) ⋅ g(x)

(f ⋅ g)(x) = (2 x + 7) (6 x – 5)

(f ⋅ g)(x) = 12 x^2 – 10 x + 42 x – 35

(f ⋅ g)(x) = 12 x^2 + 32 x – 35

Part C. Find f[g(x)]

f[g(x)] = 2 (6 x – 5) + 7

f[g(x)] = 12 x – 10 + 7

f[g(x)] = 12 x - 3

7 0

3 years ago

Which of the following points lie in the solution set to the following system of inequalities?

Oksana_A [137]

A. NOT

(-5, 2) → x = -5, y = 2

y ≤ x - 5 → 2 ≤ -5 - 5 → 2 ≤ -10 FALSE

B. YES

(5, -2) → x = 5, y = -2

y ≤ x - 5 → -2 ≤ 5 - 5 → -2 ≤ 0 TRUE

y ≥ -x - 4 → -2 ≥ -5 - 4 → -2 ≥ -9 TRUE

C. NOT

(-5, -2) → x = -5, y = -2

y ≤ x - 5 → -2 ≤ -5 - 5 → -2 ≤ -10 FALSE

D. NOT

(5, 2) → x = 5, y = 2

y ≤ x - 5 → 2 ≤ 5 - 5 → 2 ≤ 0 FALSE

3 0

3 years ago