Richard and Stephen win some money and share it in the ratio 1:3. Richard gets £14. How much did Stephen get?

Mathematics

1 answer:

LenaWriter [7]3 years ago

5 0

Well depending on who has what ratio Stephen could have £42 or £4.66

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In the figure, TS = 8, SR = 4, and QR = 2, what is the length of PQ?

Sauron [17]

Answer:

d. 22

Step-by-step explanation:

(PQ + QR) × QR = (TS + SR) × SR => two secants intersecting theorem

PQ = ?

QR = 2

TS = 8

SR = 4

Plug in the values

(PQ + 2) × 2 = (8 + 4) × 4

2PQ + 4 = 12 × 4

2PQ + 4 = 48

2PQ + 4 - 4 = 48 - 4

2PQ = 44

2PQ/2 = 44/2

PQ = 22

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3 years ago

If you were to solve the system using the addition method, what would you multiply the first equation by in order to make the x'

Inessa05 [86]

2 times 2=4
multiply first equation by 2 to get
-4x+6y=12
then add to get

-4x+6y=12
<u>4x-2y=8 +</u>
0x+4y=20

4y=20
y=5

sub back
-2x+3y=6
-2x+3(5)=6
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-2x=-9
x=9/2=4.5

the number to multiply by is 2

7 0

3 years ago

Given two vectors A=2i+3j+4k,B=i-2j+3k find the magnitude and direction of sum<br>(physics question)

Law Incorporation [45]

Answer:

$Magnitude =\sqrt{59} \\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}}$

Step-by-step explanation:

A=2i+3j+4k

B=i-2j+3k

Sum of the vectors:

A + B = 2i+3j+4k + i-2j+3k = 3i + j + 7k

$Magnitude =\sqrt{3^2 + 1^2+ 7^2} \\\\Magnitude =\sqrt{9+1+49} \\\\Magnitude =\sqrt{59}$

Direction of the sum of the vectors:

$\widehat{A + B} =\frac{\overrightarrow{A + B}}{Magnitude\: of \:\overrightarrow{A + B}} \\\\\widehat{A + B} =\frac{3i + j + 7k}{\sqrt {59}} \\\\\widehat{A + B} =\frac{3}{\sqrt {59}} i +\frac{1}{\sqrt {59}} j+\frac{7}{\sqrt {59}} k\\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}} \\\\$