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3 years ago

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For thousands of years, gold has been considered one of the Earth's most precious metals. One hundred percent pure gold is 24-ka

rat gold, which is
too soft to be made into jewelry. Most gold jewelry is 14-karat gold, approximately 58% gold. If 18-karat gold is 75% gold and 12-karat gold is 50% gold,
how much of each should be used to make a 14-karat gold bracelet weighing 300 grams?
How many grams of 18-karat gold needs to be used to make the bracelet?

1 answer:

Troyanec [42]3 years ago

7 0

The answer is on bitly im about to put the link

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HELP ASAP PLZZZZ

Tcecarenko [31]

QUESTION 1

The given system of equations is

$3d - e = 7...eqn(1)$
$d + e = 5...eqn(2)$

To solve by linear combination, we add equation (1) to equation (2) to get,

$3d + d= 7 + 5$

$4d = 12$

We divide through by 4 to obtain,

$d = \frac{12}{4}$

$d = 3$

We put d=3 into equation (2) to get,

$3+ e = 5$

$e = 5 - 3$

$e = 2$

$\boxed {The \: solution \: is \: (3, 2)}$

QUESTION 2

The given system is

4x + y = 5 ...eqn(1)

3x + y = 3 ...eqn(2)

To solve by linear combination, we subtract equation (2) from equation (1) to eliminate y from the equation.

This will give us,

$4x - 3x = 5 - 3$

This implies that,

$x = 2$

Put x=3 into equation (1) to get,

$4(2) + y = 5$

$8+ y = 5$

$y = 5 - 8$

$y = - 3$

The solution is

$(2,-3)$

QUESTION 3

We want to solve the system;

a – 2b = –2 ....eqn(1)

2a + 2b = 14...eqn(2)

by linear combination.

We need to add equation (1) to equation (2) to eliminate b.

This implies that,

$2a + a = 14 + - 2$

Simplify,

$3a = 12$

Divide both sides by 3 to get,

$a = 4$
Put a=4 into equation (2) to obtain,

$2(4) + 2b = 14$

$8 + 2b = 14$
$2b = 14 - 8$

$2b = 6$

$b = 3$

The ordered pair in the form (a, b) is

$(4,3)$

QUESTION 4

The given system of equations is

11x + 4y = 18 ...eqn(1)

3x + 4y = 2 ...eqn(2)

We subtract equation (2) from equation (1) to get,

$11x - 3x = 18 - 2$

$8x = 16$

$x = 2$

Put x=2 into equation (2) to obtain,

$3(2) + 4y = 2$

This implies that,

$6 + 4y = 2$

$4y = 2 - 6$

$4y = - 4$

$y=-1$

The correct answer is (2,-1).

QUESTION 5

The given system is ;

2d + e = 8...eqn1

d – e = 4...eqn2

We add the two equations to eliminate e.

This implies that,

$2d + d = 8 + 4$

$3d = 12$

We divide both sides by 3 to get,

$d = 4$

We put d=4 into equation (2) to get,

$4 - e = 4$

$- e = 4 - 4$

$- e = 0$

$e = 0$

The solution is

$(4,0)$

7 0

3 years ago

HELP 30 POINTS!!!!!!!!!!!!!!!!!!!!!<br><br><br> Please explain this!!!

finlep [7]

First, multiply the first equation by 3 to get:

$3x+3y=-6$

Then, add the two equations together to get

$8x=16$

We can follow that x=2. Plugging in x=2, we get that y=-4.

Therefore, the solution of (2,-4)

7 0

4 years ago

Read 2 more answers

Solve the following 2(x+3)=x-4

USPshnik [31]

2x + 6 = x - 4
x = -10

6 0

3 years ago

Read 2 more answers

A rescue helicopter flew from its home base for 35 kilometers on a course of 330 degrees to pick up an accident victim. It then

artcher [175]

I've drawn a triangle to represent the journey (see attached.

The angle from Home to Victim to Hospital is:

a = $90 - (360 - 330) = 90- 30 = 60^o$

Using the cos rule, we can solve for the length x:

$a^2 = b^2 +c^2 - 2bccosA
\\x^2 = 35^2+25^2-2(35)(25)cos60
\\x^2 = 1850 - 875
\\x^2 = 975
\\x = \sqrt{975}
\\x = 31.2249...$

Using the cos rule, we can solve for angle b:

$a^2 = b^2 +c^2 - 2bccosA
\\35^2 = 31.22...^2+25^2-2(31.22...)(25)cosb
\\1225 = 975 + 625 - 1561.249...cosb
\\-375 = -1561.249...cosb
\\b = cos^{-1}( \frac{-375}{-1561.249...}) 
\\b = 76.1...$

So the bearing the helicopter has to travel is:

270 - 76.1 = <u>193.9 degrees (1 dp)</u>

And the distance it travels is <u>31.2 km (1 dp)</u>

5 0

3 years ago

John and Jenny together have 45 marbles. Both of them lost 5 marbles each and the product of the number of marbles they now have

Tju [1.3M]

Answer:

124÷2=62

Step-by-step explanation:

Each person has 62 marbles.

The beginning of the problem is not needed to answer the question. The only thing you need to know to answer the question is that they have 124 marbles together.

3 0

3 years ago