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Rashid [163]
3 years ago
5

One angle of a rhombus measures 102°, and the shorter diagonal is 4 inches long. Approximately how long is the side of the rhomb

us? (Hint: Diagonals of a rhombus bisect the angles.)
2 in.
3 in.
4 in.
5 in.
Mathematics
1 answer:
liq [111]3 years ago
7 0

Answer:

Approximately 3 inches.

Step-by-step explanation:

The shorter diagonal will bisect the 102 degree angle. so we have a triangle  with base angles of 51, vertex 180 - 102 = 78 degrees and base length 4 inches.

Applying the Sine Rule:

4 / sin 78 = x / sin 51  where x = the length of the  side of the rhombus.

x = 4 * sin 51 / sin 78

= 3.17 inches.

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Make a conjecture about the sum of the first 54 positive even numbers
Bogdan [553]
Uhhhhhhhhhh i don’t really know
3 0
3 years ago
Sherman has two sequences . The first sequence is described by the explicit rule f(n) = 15n + 4 and the second sequence is descr
Viktor [21]

Answer:

Step-by-step explanation:

Given the explicit function as

f(n) = 15n+4

The first term of the sequence is at when n= 1

f(1) = 15(1)+4

f(1) = 19

a = 19

Common difference d = f(2)-f(1)

f(2) = 15(2)+4

f(2) = 34

d = 34-19

d = 15

Sum of nth term of an AP = n/2{2a+(n-1)d}

S20 = 20/2{2(19)+(20-1)15)

S20 = 10(38+19(15))

S20 = 10(38+285)

S20 = 10(323)

S20 = 3230.

Sum of the 20th term is 3230

For the explicit function

f(n) = 4n+15

f(1) = 4(1)+15

f(1) = 19

a = 19

Common difference d = f(2)-f(1)

f(2) = 4(2)+15

f(2) = 23

d = 23-19

d = 4

Sum of nth term of an AP = n/2{2a+(n-1)d}

S20 = 20/2{2(19)+(20-1)4)

S20 = 10(38+19(4))

S20 = 10(38+76)

S20 = 10(114)

S20 = 1140

Sum of the 20th terms is 1140

7 0
3 years ago
The unit cube is divided into identical rectangular prisms. What is the volume of one of the identical prisms?
BlackZzzverrR [31]

Answer:

Volume of one prism; (1/16) unit³

Step-by-step explanation:

The given volume of the cube, v₁ = 1 unit cube

The height of the unit cube, h₁ = 1 unit

The length of the unit cube, w₁ = 1 unit

The height of the unit cube, l₁ = 1 unit

The number of identical prism located along the height = 2 identical prism

The number of identical prism located along the width = 2 identical prism

The number of identical prisms located along the length = 4 identical prism

Therefore;

The height of each identical rectangular prism that make up the unit cube, h₂ = h₁/2 = 1/2 unit

Similarly, for each identical rectangular prism, we have;

The width, w₂ = w₁/2 = 1/2 unit

The length, l₂ = l₁/4 = 1/4 unit

The volume of each one of the identical rectangular prism, v₂ = h₂ × w₂ × l₂

∴ v₂ = 1/2 unit × 1/2 unit × 1/4 unit = 1/16 unit³

The volume of one of the identical rectangular prisms = (1/16) unit³.

4 0
2 years ago
You deposit $300 in a savings account. The account earns 2% simple interest per year. What is the interest and balance earned af
kenny6666 [7]

Answer:

$365.70

Step-by-step explanation:

The formula to find this is y = a(1+r)^t\\

For this, a is the initial amount, r is the growth rate percentage (but displayed as a decimal), and t is time.

So to solve, you would do

y = 300(1+0.02)^10\\y = 300(1.02)^10\\y = 365.698325998\\OR\\y = $365.7 in interest

6 0
3 years ago
Craig has a 6 ft by 6 ft square garden in his backyard. He wants to transform the garden into a rectangular shape and reduce the
Yanka [14]
X = 2
So 6 + 2 = 8
6 - 2 = 4
8 x 4 = 32

(6-x)(6+x) = 32
36 - x^2 = 32
-36. -36
-x^2 = -4
X = 2
7 0
3 years ago
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