Geology in 1668, the Hope diamond was reduced from its original weight by about 45 carats, resulting in a diamond weighing about 67 carats. Write and solve an equation to find how many carats the original diamond weighed. Answer:​

Answers

Answer 1

Answer: W = 112 carats

Step-by-step explanation: Let W be the original weight.

So we have

W - 45 = 67 add 45 to both sides

And that equals 112 carats


Related Questions

Find the slope given the two points:
(3, 70) , (15, 90)

Answers

Answer:

x= 5/3

Step-by-step explanation:

You have given an equal sided triangle with side length a. A straight line connects the center
of the bottom side to the border of the triangle with an angle of α. Derive an expression for
the enclosed area A(α) with respect to the angle (see drawing

Answers

Answer:

Where α is an acute angle (first figure)

The area of the shaded triangle = ((√3)·a²/4)·sin(α)·csc(120 - α))

Where α is an obtuse angle (second figure)

The required area of the shaded region = (√3)·a²/4 + (√3)·a²/4)·sin(α)·sec(α + π/6)

Step-by-step explanation:

Where α is an acute angle (first figure)

The given parameters are;

The given triangle = Equilateral Triangle

Let the sides of the equilateral triangle = 2·a

Therefore;

The measure of each interior angles of the given triangle = 60°

Let c represent the side of the shaded triangle opposite ∠α and b represent the side of the shaded triangle opposite ∠60° and c, represent the third side of the shaded triangle, we have;

The sides of the equilateral triangle = 2·a

By sine rule, we have;

c/sin(α) = b/sin(60°) = a/sin(180 - (60 + α)) = a/sin(120 - α))

b = sin(60°) × a/sin(120 - α)) = (√3)/2 × a/sin(120 - α))

The area of the shaded triangle = 1/2 × a × b × sin(α) = 1/2 × a × (√3)/2 × a/sin(120 - α)) × sin(α) = ((√3)·a²/4)·sin(α)·csc(120 - α))

The area of the shaded triangle = ((√3)·a²/4)·sin(α)·csc(120 - α))

Where α is an obtuse angle (second figure)

The required area of the shaded region = The area of the equilateral triangle - The area of the small unshaded triangle, with base side a and interior angles, (180° - α), 60° and ((180 - (180° - α) - 60°) = ) α - 60°

The area of the unshaded triangle is found as follows;

By sine rule, we have;

c/sin(180° - α) = b/sin(60°) = a/sin(α - 60°)

b = sin(60°) × a/sin(α - 60°) = (√3)/2 × a/sin(α - 60°)

The area of the unshaded triangle = 1/2 × a × b × sin(α) = 1/2 × a × (√3)/2 × a/sin(α - 60°) × sin(α) = -((√3)·a²/4)·sin(α)·sec(α + π/6)

The area of the shaded triangle =  -((√3)·a²/4)·sin(α)·sec(α + π/6)

The required area of the shaded region = 1/2×a²·sin(60°)  - (-((√3)·a²/4)·sin(α)·sec(α + π/6))

The required area of the shaded region = (√3)·a²/4 + (√3)·a²/4)·sin(α)·sec(α + π/6)

I really don’t understand it.

Answers

Answer:

11.1803399

Step-by-step explanation:

By Pythagoras Theorem

[tex] \sqrt{hight {}^{2} + base {}^{2} } [/tex]

[tex] \sqrt{100 + 25} [/tex]

[tex] \sqrt{125} [/tex]

[tex] = = > 11.1803399[/tex]

Answer By,

Zeeshan Khan

What is an equation in slope-intercept form of the line that passes through (6, 10) and is parallel to the graph of y=1/3x−1?

Answers

Given:

The equation of line is

[tex]y=\dfrac{1}{3}x-1[/tex]

To find:

The equation of line in slope-intercept form parallel to given line and passes through (6,10).

Solution:

The slope intercept form of a line is

[tex]y=mx+b[/tex]       ...(i)

where, m is slope and b is y-intercept.

The equation of given line is

[tex]y=\dfrac{1}{3}x-1[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]m=\dfrac{1}{3}[/tex]

Slope of given line is [tex]\dfrac{1}{3}[/tex].

We know that slope of parallel lines are same. So, the slope of required line is [tex]\dfrac{1}{3}[/tex].

Since slope of required line is [tex]\dfrac{1}{3}[/tex] and it passes through (6,10), therefore the equation of line is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-10=\dfrac{1}{3}(x-6)[/tex]

[tex]y-10=\dfrac{1}{3}(x)-\dfrac{1}{3}(6)[/tex]

[tex]y-10=\dfrac{1}{3}(x)-2[/tex]

Add 10 on both sides.

[tex]y-10+10=\dfrac{1}{3}(x)-2+10[/tex]

[tex]y=\dfrac{1}{3}(x)+8[/tex]

Therefore, the required equation of line is [tex]y=\dfrac{1}{3}(x)+8[/tex].

n-7<15 then graph on number line

Answers

Answer:

n<22

Step-by-step explanation: That is the best i can do it

The following is a kite, find LM (hint: you need to use the Pythagorean theorem)

Answers

sorryStep-by-step explanation:

3/8 + 1/8 - 2/7 + 1/4

Answers

Answer:

0.46428571428

Step-by-step explanation:

Answer:

13/28

Step-by-step explanation:

3/8 + 1/8 = 4/8 = 1/2 = 0.5

1/2 - 2/7 = 3/14 = 0.214285714286

3/14 + 1/4 = 13/28 = 0.464285714286

13/28 or 0.464285714286

Hope this helps! <3

negative 3 times x equals?

Answers

Answer:

-3x

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we multiply any negative number in this case -3 times a POSITIVE we will always get a negative. So the positive we can put as x and multiply -3 times x = -3x.

Hope this helps :D

‼️IM GIVING OUT BRAINLIEST ‼️

Elsa used the multiplication table below to write ratios that are equivalent to StartFraction 12 Over 4 EndFraction.

A multiplication table.

One number is missing from the equivalent ratio, as shown.

StartFraction blank Over 12 EndFraction

What is the missing number?
6
18
24
36

Answers

Answer: 24

Step-by-step explanation:

The table shows the mileages x (in thousands of miles) and the selling prices y (in thousands of dollars) of several used automobiles of the same year and model.
Mileage, x: 22 14 18 30 8 24
Price, y: 16 17 17 14 18 15
a.) Use a graphing calculator to find the equation of the line of best fit. Round the slope to the nearest tenth and y-intercept to the nearest integer.
y=
b.) Identify the correlation coefficient. Round to the nearest thousandth.
r=
Interpret the correlation coefficient.
the data show a ___ ___ correlation.

Answers

Answer:

ŷ = -0.18363X + 19.71681

-0.9685

Step-by-step explanation:

Given the data:

Mileage, x: 22 14 18 30 8 24

Price, y: 16 17 17 14 18 15

Using the online regression calculator :

The regression equation obtained is :

ŷ = -0.18363X + 19.71681

Where ;

y = predicted variable

- 0.18363 = slope or gradient

X = predictor variable

19.71681 = intercept

The correlation Coefficient R = -0.9685

This signifies a strong negative relationship between the x and y variable.

The line of best fit has an equation of:

y = -0.1875x + 19.625

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Let x represent the mileages (in thousands of miles) and y the selling prices(in thousands of dollars) of used automobiles.

Plotting the points using geogebra graphing calculator, the line of best fit has an equation of:

y = -0.1875x + 19.625

Therefore the slope is -0.1875 and the y intercept is 19.625

Find out more at: https://brainly.com/question/11324911

Keiko, Juan, and Tony have a total of $80 in their wallets. Keiko has $5 less than Tony. Juan has 3 times what Tony has. How much does each have?

Answers

Answer:

Keiko 12 +  Juan 51 + Tony 17 = $80

Step-by-step explanation:

K + J + T = 80

K=T-5

J=3T

T=T

T-5 + 3T + T = 80

5T -5 = 80  -->  5T = 85 --> T = 17

now that u know T=17, substitute the value of T to find K and J

K=(17)-5 = $12

J=3(17) = $51

T= $17

does anyone do savvas realize

Answers

Answer:

Yes, I do for my Spanish class!

Do you have any questions about it?

Which fraction is equivalent to negative 1 over 6 ? (1 point) 6 over negative 1 negative 6 over 1 negative 6 over negative 1 1 over negative 6 I will give you the brainiest too

Answers

Answer:

1 over negative 6

Step-by-step explanation:

okay so first you said you had negative 1 over 6, this can be written as -1/6.

You then had -6/1 twice and finally you had 1 over negative 6, which can also be written as -1/6.

Ask questions if you are confused

Answer:

1 over negative 6

Step-by-step explanation:

okay so first you said you had negative 1 over 6, this can be written as -1/6.

You then had -6/1 twice and finally you had 1 over negative 6, which can also be written as -1/6.

g(x)=−x+5, solve for x when g(x)=-2

Answers

Step-by-step explanation:

a....................................

9. Choose the correct solution and graph for the inequality.​

Answers

Answer:

x ≤ -9

Step-by-step explanation:

x-3 ≤ -12

x ≤ -12+3 (Isolate x)  

x ≤ -9

4. Two savings accounts each start with a $200 principal and have an interest rate of 5%. One account earns simple interest and the other is compounded annually. Which account will earn more interest over 10 years? How much more?​

Answers

Answer:

The compounded annually account will earn more interest over 10 years

Step-by-step explanation:

The rule of the simple interest is I = Prt, where

P is the original valuer is the rate in decimalt is the time

The rule of the compounded interest is A = P[tex](1+\frac{r}{n})^{nt}[/tex], where

A is the new valueP is the original valuer is the rate in decimaln is the number of periodst is the time

The interest I = A - P

∵ Each account start with $200

P = 200

∵ They have an interest rate of 5%

r = 5% = 5 ÷ 100 = 0.05

∵ One account earns simple interest and the other is compounded  

   annually

n = 1 ⇒ compounded annually

∵ The time is 10 years

t = 10

→ Substitute these values in the two rules above

∵ I = 200(0.05)(10)

∴ I = 100

The simple interest = $100

∵ I = A - P

∵ A = 200[tex](1+\frac{0.05}{1})^{1(10)}[/tex]

∴ A = 325.7789254

∵ I = 325.7789254 - 200

∴ I = 125.7789254

The compounded interest = $125.7789254

∵ The simple interest is $100

∵ The compounded interest is $125.7789254

∵ $125.7789254 > $100

The compounded annually account will earn more interest

   over 10 years

These two triangles are similar what is the length of t?

Answers

Answer:

I think 15

Step-by-step explanation:

Please hurry. Thank you in advance

Answers

Answer:

The value of x in this equation is -23

Step-by-step explanation:

The given equation is:

[tex]-x-8 = 15[/tex]

The given equation is a linear equation in one variable. The solution of the equation requires isolating x on one side of the equation.

Properties of equality will be used to find the solution.

Using Addition property of equality

Adding 8 on both sides

[tex]-x-8+8 = 15+8\\-x = 23[/tex]

Multiplication property of equality

Multiplying both sides by -1

[tex]x = -23[/tex]

Verification:

[tex]-x-8 = 15\\-(-23)-8 = 15\\23-8 = 15\\15 = 15[/tex]

Hence,

The value of x in this equation is -23

You are taking part in a 10 km charity walk. It takes you 3.25 hours to complete the walk. What was your average walking speed, in km per hour? Round your answer to the nearest​

Answers

Answer:

3.077 km/hr (though your question did not specify where to round to)

Step-by-step explanation:

10km/ 3.25 hr

PLEASE ANSWER FAST !!

Answers

Answer:

Obviously condensation

Step-by-step explanation: because it is

What is the difference of the expression (1 + 4i) − (−16 + 9i)?

Answers

Answer:

Step-by-step explanation:

(1+4i)-(-16+9i)

1+4i+16-9i

17-5i

Last month, there were 4 sunny days for every rainy day. If there were 30 days in the month, how many days were rainy? Explain your reasoning

Answers

Answer:

26 because 30-4=26

Step-by-step explanation:

i need help with this question i dont know what to do or what its asking

Answers

What's the question???

Please be more specific on what question you’re asking next time

Miguel is calculating the slope of a line of best-fit in the scatterplot below.

Which pair of points would be best for Miguel to use?
1. P and W
2. Q and V
3. R and U
4. S and T

Answers

Answer:

the answer is B.

Step-by-step explanation: i done the test have a nice day :))))

B)Q and V
Hope this helps!!<3

please solve!

y-2/5y

Answers

3/5y because y is the same as 1y and 1 - 2/5 = 3/5

(6)(-18)(5)= (-18)(6)(5)

Answers

It’s either 5 or true

A right triangle is shown below. What is cos EFD?
Will make BRAINLIEST

Answers

Are you looking for the length from E to F?

The lenngths of the sides of the triangle are in the extended ratio 8:9:10. The primeter of the triangle is 108 cm.What are the lengths of the sides?
The lengths of the sides of the triangle in cm are____?
Please help me!!

Answers

Answer:

I dont know if anyone can answer kinda doesn't make sense

Find the sum of 4.5 x 10^2 and 6 x 10^3 and show work please

Answers

Answer:

6.45 × 10³

Step-by-step explanation:

4.5 × 10² + 6 × 10³ = 0.45 × 10³ + 6 × 10³ = (0.45 + 6) × 10³ = 6.45 × 10³

Answer:

450 and 6000

Step-by-step explanation:

4.5 × 10²

4.5 × 100

450

6 × 10³

6 × 1000

6000

Find the angle measures. Justify you responses.

Given: a//b, m<3= 63 degrees

Find: m<6, m<7

(The < is used as the angle sign)

Answers

Answer:

i think 89

Step-by-step explanation:

Answer:

m∠6 = 117º

m∠7 = 63º

Step-by-step explanation:

m∠3 = m∠7 = 63º(corresponding angles)

180º - m∠3 = m∠6 = 117º (same side interior angles are supplementary)

or

180º-m∠7 = m∠6 = 117º (linear pair)

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