MATHEMATICS HIGH SCHOOL

4 An alloy is a mixture of metals. Most of the gold used in jewellery is an alloy of pure gold and other metals which are added to make the gold harder. Pure gold is 24 carats (ct), so 18 carat parts pure gold 18 gold is an alloy of gold and other metals in the ratio 18:6. In other words, 18/24 parts pure gold and 6/24 other metals. a. A jeweller makes an 18 ct gold alloy using three grams of pure gold. What mass of other metals does she add?
b . An 18 ct gold chain contains four grams of pure gold. How much other metal does it contain? c. What is the ratio of gold to other metals in 14 ct gold?
d. What is the ratio of gold to other metals in 9 ct gold?

Answers

Answer 1

Answer:

To calculate the mass of other metals in each scenario, we need to use the given ratios.

Given:

- Pure gold is 24 carats (ct).

- 18 carat gold is an alloy of gold and other metals in the ratio 18:6 (18/24 parts pure gold and 6/24 other metals).

a. A jeweller makes an 18 ct gold alloy using three grams of pure gold. What mass of other metals does she add?

First, let's find the mass of other metals in the 18 ct gold alloy.

18 ct gold contains 18/24 parts pure gold and 6/24 parts other metals. So, if the jeweller uses 3 grams of pure gold, the amount of other metals in the alloy can be calculated as follows:

Mass of other metals = (6/24) * 3 grams

Mass of other metals = (1/4) * 3 grams

Mass of other metals = 3/4 grams

b. An 18 ct gold chain contains four grams of pure gold. How much other metal does it contain?

Similarly, for the 18 ct gold chain containing 4 grams of pure gold:

Mass of other metals = (6/24) * 4 grams

Mass of other metals = (1/4) * 4 grams

Mass of other metals = 4/4 grams

Mass of other metals = 1 gram

c. What is the ratio of gold to other metals in 14 ct gold?

For 14 ct gold, the ratio of gold to other metals is 14:10 (since 14 + 10 = 24, and gold is 14 out of 24 parts, while other metals are 10 out of 24 parts).

d. What is the ratio of gold to other metals in 9 ct gold?

For 9 ct gold, the ratio of gold to other metals is 9:15 (since 9 + 15 = 24, and gold is 9 out of 24 parts, while other metals are 15 out of 24 parts).

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Which fraction is equivalent to 72%?
A. 7/200
B. 18/25
C. 9/25
D. 7 1/5

Answers

B 18/25
18/25=x/100
x=1800/25=72%

Write the equation of the given line in standard form y=ax+b:The line containing the midpoints of the legs of a right triangle ABC where A (-5,5), B (1,1) and C (3,4) are the vertices.

Answers

Find the distance between the sets of points.
Use this to determine which sides are the legs.

A to B = sqrt(52) = 7.2111
A to C = sqrt(50) = 7.07106
B to C = sqrt(65)= 8.622577

B to C is hypotenuse

midpoint of A to B is (-2,3)
midpoint of A to C is (-1, 4.5)

The line we are solving for contains these midpoints, so we have to solve for the slope between them and use point-slope form to make the equation of the line.
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The area of a rectangle is 38.25 square yards and its base is 9 yards. What is the height? Do not round your answer.h = ________ yd

Answers

Answer:

4.25 yards

Step-by-step explanation:

Area of rectangle = Base x Height

Height = Area of Rectangle ÷ Base

In this case, Area =38.25 sq yards and Base = 9 yards

Height = 38.25 ÷ 9 = 4.25 yards

hi! your answer is 4.25. (also hope this helps everyone who finds this in search for the answer)

Is 7x+y+3=y a linear equation. also is this in standard form

Answers

Answer:

Hi! The correct answer is 7x=-3!

Step-by-step explanation:

~Write in standard form~

Final answer:

The equation 7x+y+3=y is a linear equation as it consists of variables to the first degree, but it's not in the standard form. Upon rearranging, the standard form will be 7x - 3 = 0.

Explanation:

Yes, the equation 7x+y+3=y is a linear equation because it represents a straight line when plotted on a graph. This is because it consists only of the first degree variables (that is, variables raised to the power of 1) of x and y, which define linear equations. However, it is not in the standard form. The standard form of a linear equation is usually written as Ax + By = C, where A, B, and C are constants and x and y are variables, and A and B are not both zero. Therefore, to express this equation in standard form, we need to rewrite it, resulting in the equation 7x + y - y - 3 = 0 or 7x - 3 = 0.

Learn more about Linear Equations here:

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If m + 4n = 2n + 8m ; what is the ratio of n to m ?a) 1:4, b) 1:-4, c) -4:1, d) 2:7, e) 7:2

Answers

m + 4n = 2n + 8m

To answer the ratio, massage this equation around to find ' n/m ' .

Let's subtract 'm' from each side:

4n = 2n + 7m

Subtract '2n' from each side:

2n = 7m

Divide each side by 'm' :
2 (n/m) = 7

Divide each side by 2 :

n/m = 7/2 . . . . . there's your ratio. That's choice-'e'.

$m + 4n = 2n + 8m\n 7m=2n\n m=(2)/(7)n\n\n (n)/(m)=(n)/((2)/(7)n)=(7)/(2)$

Four employees can wash 20 service vehicles in 5 hours. how long would it tke 5 employees to wash the same number of vehicles?

Answers

So the employee rate for washing cars turns out to be 4*5 = 20 man hours to wash 20 vehicles which is 1 vehicle per hour per employee.
5 employees will wash 5 vehicles in 1 hour
5 employees will wash 20 vehicles in 1*4 = 4 hours.

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