Factor x^2-6x-7. A.(x-7)(x+1) B.(x-7)(x-1) C.(x+4)(x+7) D.(x+7)(x-1)

Aunty Joan packs a packet of sweets to Alice and Olivia. Alice and Olivia share sweets in the ratio 7:3. Alice gives 3 sweets to

aivan3 [116]

Initially, Alice had 28 sweets and Olivia 12 sweets.

Step-by-step explanation:

First assume that Aunty Joan has x number sweets.

Alice and Olivia shared the x sweets in a ration of 7:3, this means

Alice had 7/10 x sweets and Olivia had 3/10 sweets.

Alice gives 3 sweets to Olivia, Alice will remain with ;

$\frac{7}{10} x-3$

Then the new ratio changes to 5:3 which means Alice will have 5/8 x number of sweets.

Equate the number of sweets for Alice in the two cases, which is

$\frac{5}{8}x=\frac{7}{10} x-3\\ \\\frac{7}{10} x-\frac{5}{8} x=3\\$

$\frac{56x-50x}{80} =3\\\\\\\frac{6}{80} x=3\\\\\\6x=80*3\\\\\\x=240/6\\\\x=40$

So there were 40 sweets at first

Using the ratio of 7:3 then

Alice had 7/10 *40 = 28 sweets

Olivia had 3/10*40= 12 sweets

Alice gave Olivia 3 sweets, so she will remain with 28-3 =25 sweets. Olivia will now have 15 sweets.The new ratio will be 25:15 simplified as 5:3.

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Ratio : brainly.com/question/11095585

Keywords : Ratio

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5 0

3 years ago

A machine for baking hay produces cylindrical bales that are 6 feet in diameter and 5 1/3 feet in height. Which is closest to th

GaryK [48]

We know that
diameter=6 ft----------> r=6/2------> r=3 ft
h=5 1/3 ft------> (5*3+1)/3-----> 16/3 ft
[volume of a cylindrical bales]=pi*r²*h----> pi*3²*16/3---> 150.72 cm³

the answer is the option
B 151 cm³

5 0

2 years ago

A car is driving at 65 kilometers per hour. How far, in meters, does it travel in 4 seconds?

Mumz [18]

Answer:

72.2 m

Step-by-step explanation:

65 km/1 h = (65000 m / 3600s) = 18.05 m/s

Distance = speed * time = 18.05 m/s*4 s = 72.2 m

8 0

3 years ago

Jose receives a $10 gift card for downloading music and wants to determine how many songs he can purchase. Each downloaded song

kvasek [131]

With the $10 gift card, Jose can buy at most 8 songs

x(the number of songs) less than or equal to 8

7 0

2 years ago

Read 2 more answers

Gabby received change worth $2.10. She received 3 more dimes than nickels and 4 less quarters than nickels. How many of each kin

xz_007 [3.2K]

Answer:

Gabby received

7 nickels

10 dimes

3 quarters

Step-by-step explanation:

Let

x----> the number of dimes

y----> the number of nickels

z---> the number of quarters

Remember that

1 dime=$0.10

1 nickel=$0.05

1 quarter=$0.25

we know that

0.10x+0.05y+0.25z=2.10 ------> equation A

x=y+3-----> equation B

z=y-4 -----> equation C

substitute equation B and equation C in equation A and solve for y

0.10(y+3)+0.05y+0.25(y-4)=2.10

0.10y+0.30+0.05y+0.25y-1=2.10

0.40y=2.10-0.30+1

0.40y=2.80

y=7 nickels

Find the value of x

x=y+3 -----> x=7+3=10 dimes

Find the value of z

z=y-4 -----> z=7-4=3 quarters

therefore

Gabby received

7 nickels

10 dimes

3 quarters

6 0

3 years ago