Harmony has 23 cups of pecans to make pecan pie. She needs 3 cups of pecans for each pie.

Mathematics

1 answer:

Andrei [34K]2 years ago

3 0

Answer:

The correct answer is A

Step-by-step explanation:

A is correct because you divide 23 and 3 to equal 7 then you do 7 times 3 to equal 21 cups meaning you have enough pecans to make 7 pies and 2 cups of pecans left over.

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Two terms of a geometric sequence are given. Find the first five terms. Please help asap

Zepler [3.9K]

Answer:

4, 8, 16, 32, 64

Step-by-step explanation:

The nth term of a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

Given

a₇ = 256 and a₁₀ = 2048 , then

a₁ $r^{6}$ = 256 → (1)

a₁ $r^{9}$ = 2048 → (2)

Divide (2) by (1)

$\frac{a_{1}r^{9} }{a_{1}r^{6} }$ = $\frac{2048}{256}$

r³ = 8 ( take the cube root of both sides )

r = $\sqrt[3]{8}$ = 2

Substitute r = 2 into (1)

a₁ × $2^{6}$ = 256

a₁ × 64 = 256 ( divide both sides by 64 )

a₁ = 4

Then

a₁ = 4

a₂ = 2a₁ = 2 × 4 = 8

a₃ = 2a₂ = 2 × 8 = 16

a₄ = 2a₃ = 2 × 16 = 32

a₅ = 2a₄ = 2 × 32 = 64

7 0

2 years ago

20 points!!!!!!!

castortr0y [4]

See the attached figure to better understand the problem
let
L-----> length side of the cuboid
W----> width side of the cuboid
H----> height of the cuboid

we know that
One edge of the cuboid has length 2 cm-----> I'll assume it's L
so
L=2 cm
[volume of a cuboid]=L*W*H-----> 2*W*H
40=2*W*H------> 20=W*H-------> H=20/W------> equation 1

[surface area of a cuboid]=2*[L*W+L*H+W*H]----->2*[2*W+2*H+W*H]

100=2*[2*W+2*H+W*H]---> 50=2*W+2*H+W*H-----> equation 2
substitute 1 in 2
50=2*W+2*[20/W]+W*[20/W]----> 50=2w+(40/W)+20
multiply by W all expresion
50W=2W²+40+20W------> 2W²-30W+40=0

using a graph tool------> to resolve the second order equation
see the attached figure

the solutions are
13.52 cm x 1.48 cm
so the dimensions of the cuboid are
2 cm x 13.52 cm x 1.48 cm
or
2 cm x 1.48 cm x 13.52 cm

Find the length of a diagonal of the cuboid
diagonal=√[(W²+L²+H²)]------> √[(1.48²+2²+13.52²)]-----> 13.75 cm

the answer is
the length of a diagonal of the cuboid is 13.75 cm