Which one of the following numbers is a multiple of 8

Stephen, Gavin and Jim share some sweets in the ratio 4:1:2. Stephen gets 30 more sweets than Jim. How many sweets are there alt

Kamila [148]

Answer:

105 sweets

Step-by-step explanation:

There are 4 + 1 + 2 = 7 parts in total

Stephen gets 4 parts (or 4x)

Jim gets gets 2 parts (or 2x)

Given,

Stephen gets 30 more than Jim, we can write:

Stephen = Jim + 30

or

4x = 2x + 30

We can solve for "x":

$4x = 2x + 30\\4x-2x=30\\2x=30\\x=15$

There are 7 parts of sweets altogether (or 7x), we know x so:

There are:

7 * 15 = 105 sweets altogether

7 0

3 years ago

What is the area of a triangle whose vertices are D(3, 3) , E(3, −1) , and F(−2, −5) What is the area of the rectangle?

RideAnS [48]

Answer:

The area of the triangle with the given vertices is 10 square units

Step-by-step explanation:

x y

D 3 3

E 3 -1

F -2 -5

D 3 3

Area: A=Abs [(xd ye + xe yf + xf yd) - (yd xe + ye xf + yf xd)] /2

Absolute value: Abs

A = Abs { [(3)(-1)+(3)(-5)+(-2)(3)] - [(3)(3)+(-1)(-2)+(-5)(3)] } / 2

A = Abs [ (-3-15-6)-(9+2-15) ] / 2

A = Abs [ (-24)-(-4) ] / 2

A = Abs ( -24+4) / 2

A = Abs (-20) / 2

A = 20 / 2

A = 10 square units

4 0

3 years ago

The volume of a cylinder is 54π cubic inches and the height is 6 inches. Find the radius.

Anika [276]

Answer:

The radius of the cylinder is 3 inches.

Step-by-step explanation:

For any given cylinder, the volume can be expressed as:

volume = $\pi$ $r^{2}$ h

where r is the radius of its circular surface, and h is its height.

Given that: volume = 54π cubic inches, and the height = 6 inches.

then,

54 $\pi$ = $\pi$ x $r^{2}$ x 6

54 $\pi$ = 6 $\pi$ $r^{2}$

$r^{2}$ = $\frac{54\pi }{6\pi }$

= 9

r = $\sqrt{9}$

r = 3

The radius of the cylinder is 3 inches.

8 0

3 years ago

John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages

oksano4ka [1.4K]

Answer:

John’s age is 8 years

Step-by-step explanation:

Let

x -----> John’s father's age

y -----> John’s age

z -----> John’s sister's age

we know that

$x=5y$ -----> equation A

$y=2z$

$z=y/2$ -----> equation B

$(x+2)+(y+2)+(z+2)=58$

$x+y+z+6=58$

$x+y+z=52$ -----> equation C

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

$5y+y+y/2=52$

Multiply by 2 both sides to remove the fraction

$10y+2y+y=104$

$13y=104$

$y=8$

Find the value of x

$x=5(8)=40$

Find the value of z

$z=8/2=4$

therefore

John’s father's age is 40 years

John’s age is 8 years

John’s sister's age is 4 years

7 0

3 years ago

A bag of candy containing 320 pieces is to be divided up into 18 smaller bags for distribution with fourteen left over. How many

nikitadnepr [17]

Answer:

17

Step-by-step explanation:

A bag of candy contains 320 pieces

It is to be divided into 18 smaller bags with fourteen left over

Therefore the pieces that will go in each bag after the distributorn can be calculated as follows

= 320/18

= 17 remainder 14

Hence 17 pieces of candy will be in each bags

5 0

3 years ago