The largest single rough diamond ever found, the cullinan diamond, weighed 3106 carats; how much does the diamond weigh in miligrams? in pounds? (1 carat - 0.2 grams)
the diamond weighs mg.
the diamond weighs lbs.

Answer:

[tex] \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]

Step-by-step explanation:

[tex] {(3x + 2)}^{2} + 7 {(3x + 2)} - 8 = 0 \\ \\ plug \: (3x + 2 )= y \\ \\ so \: above \: quadratic \: equation \: \\transforms \: to \\ \\ \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]

Answer:

Question 1) 72

Question 2) 40

Question 3) Both C and D.

Question 4) Both A and C.

Step-by-step explanation:

Question 1)

We are given that:

[tex]\displaystyle \int_1^5f(x)\, dx=8\text{ and we want to find} \int_1^5xf'(x)\, dx[/tex]

We will use integration by parts, given by:

[tex]\displaystyle \int_a^b u\, dv=uv-\int_a^b v\, du[/tex]

We will let:

[tex]u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \Rightarrow v=f(x)[/tex]

Therefore:

[tex]\displaystyle \int_1^5xf'(x)\, dx=xf(x)\Big|_1^5-\int_1^5f(x)\, dx[/tex]

Substitute:

[tex]\displaystyle \int_1^5xf'(x)\, dx=(5(f(5))-(1(f(1))-(8)[/tex]

Evaluate:

[tex]\displaystyle \int_1^5xf'(x)\, dx=75-(-5)-8=72[/tex]

Question 2)

Similarly, we will let:

[tex]\displaystyle u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \text{ so } v=f(x)[/tex]

Hence:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=xf(x)\Big|_0^3-\int_0^3f(x)\, dx[/tex]

Evaluate:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=(3f(3))-(0(f(0))-(2)[/tex]

Thus:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=3(14)-2=40[/tex]

Question 3)

We are given:

[tex]\displaystyle g(x)=\int_4^xf(x)\, dx[/tex]

By the Fundamental Theorem of Calculus:

[tex]g'(x)=f(x)>0[/tex]

The derivative of g is always positive. So, the values of g are always increasing.

The tables that reflect this are C and D.

And there are, as I understand it, no way to determine their exact values. Both C and D are correct.

Question 4)

Similarly, we are given:

[tex]\displaystyle g(x)=\int_{-2}^xf(x)\, dx[/tex]

By the FTC:

[tex]g'(x)=f(x)<0[/tex]

So, g should be decreasing for all x.

The tables that reflect this are A and C.

So, both A and C are correct.

Answer:

The answer is 1 and 4

Step-by-step explanation:

.25 x 4y = Y

36 divided by 4 = 9

Answer:

1.02

Step-by-step explanation:

Answer:

3.764

Step-by-step explanation:

Answer:

what grade is this ?

Step-by-step explanation:

Answer:

area of real bedroom = 32 cm²

hope it helps..

Answer:

Bedroom: 32 cm living room: 81 cm

Step-by-step explanation:

Bedroom: 4 x 8 = 32

Living room : 9 x 9 = 81

( if combining bedroom and living room, it’s 113 cm)(81 + 32 = 113)

Hope this helps

Answer:

The answer is below

Step-by-step explanation:

Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement.

(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)

.The polynomial simplifies to an expression that is a____

A.quadratic

B.liner

C.constany

A.trinomial

B.binomial

C.monomial

with a degree of____

A.1

B.2

C.0

Solution:

A polynomial is an expression involving operations of addition, subtraction, multiplication, exponents which consists of variables and their coefficient. A trinomial is a polynomial consisting of three terms, while a binomial consist of two terms and a monomial consist of one term.

The degree of a polynomial is the highest degree of any of the terms of the polynomial. If it has a degree of 0 it is a constant, a degree of 1 it is linear while for a degree of 2 it is quadratic.

(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)

= (-5x² - 2x + 4) + (8x² - x - 1) + (x² -5x + 2x - 10)

= (-5x² - 2x + 4) + (8x² - x - 1) + (x² - 3x - 10)

= (-5x² + 8x² + x² - 2x - x - 3x + 4 - 1 - 10)

= 4x² - 6x - 7

Therefore:

.The polynomial simplifies to an expression that is a quadratic trinomial of degree 2.

Answer:

35

Step-by-step explanation:

Answer:

15/28 are women

Step-by-step explanation:

2/7 + 1/4 + x = 100%

2/7+1/4= 15/28

9514 1404 393

Answer:

  13/28

Step-by-step explanation:

The fraction that are women is found by subtracting the given fractions from 1.

  1 - 2/7 - 1/4 = 28/28 -8/28 -7/28 = (28 -8 -7)/28 = 13/28

The fraction that are women is 13/28.

Answer:

8.1

Step-by-step explanation:

We denote the number as x.

6 * x = 48.6

We can divide both sides by 6 to get,

x = 8.1

Answer:

8.1

Step-by-step explanation:

Let the unknown number be n.  Translating this statement into symbols, we get:

6n = 48.6

Solving for n by dividing both sides by 6, we get  n = 8.1

The number is 8.1

Answer:

Step-by-step explanation:

the x is 30

60=2x

x=30

Answer:

d

Step-by-step explanation:

its d i think

Answer: 2.71 packs

Step-by-step explanation:

Answer:

It b

Step-by-step explanation:

We know this because 1/2 is 0.5 while 2/3 is 0.67. With this we can say that 1/2 is least than 2/3

Hope this Helped

Answer:

Step-by-step explanation:

(2-4x)+(2-4x)+(-2x+8)=12-10x

Answer:

-3x² -2y² -8xy +5y

34x² + 51xy - 8y + 6y²

7x² - 11xy +12y - 8y²

Step-by-step explanation:

Given:

A: 5x²+3xy +2y

B: 2y²-xy +4x²

С: 12xy+4x²-3y

Find:

1) А-В-С

2) 2A+3B+4C

3) 3A-4B--2C

Computation:

1) А-В-С

5x²+3xy +2y - [2y²-xy +4x²] - [12xy+4x²-3y]

5x²+3xy +2y -2y² +xy -4x² -12xy -4x²+3y

-3x² -2y² -8xy +5y

2) 2A+3B+4C

2[5x²+3xy +2y]+3[2y²-xy +4x²]+4[12xy+4x²-3y]

10x² + 6xy + 4y + 6y² - 3xy + 8x² + 48xy + 16x² - 12y

34x² + 51xy - 8y + 6y²

3) 3A-4B-2C

3[5x²+3xy +2y]-4[2y²-xy +4x²]-2[12xy+4x²-3y]

15x² + 9xy + 6y -8y² + 4xy - 16x² - 24xy - 8x² +6y

7x² - 11xy +12y - 8y²

Answer:

99.7%

Step-by-step explanation:

Given that:

sample size (n) = 655

sample mean ([tex]\overline x[/tex]) = 43.29

Standard deviation [tex]\sigma[/tex] = 2.75

Let's assume we are to estimate the percentage between $33.72 and $51.54

Then;

The test statistics at 33.72 is :

[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]Z = \dfrac{33.72 -43.29}{2.75}[/tex]

[tex]Z = -3.48[/tex]

Z at 51.54

[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]Z = \dfrac{51.54 -43.29}{2.75}[/tex]

[tex]Z = 3.00[/tex]

Using the empirical standard rule, the percentage will be 99.7%

Answer:

x=9

Step-by-step explanation:

3x+9=36

subtract 9 from both sides

3x=27

divide by 3 on both sides

x=9

The solution to the equation 3x + 9 = 36 is x = 9.

To solve the equation 3x + 9 = 36, we'll perform the necessary steps to isolate the variable x on one side of the equation.

Given equation:

3x + 9 = 36

First, we'll subtract 9 from both sides to eliminate the +9 term on the left side:

3x + 9 - 9 = 36 - 9

3x = 27

Next, to isolate the variable x, we divide both sides by 3:

(3x)/3 = 27/3

x = 9

Therefore, the solution to the equation 3x + 9 = 36 is x = 9.

In this equation, we start with an expression involving the variable x and a constant term. By performing algebraic operations, we manipulate the equation to have x on one side and the constant value on the other side. This isolates the variable and provides us with a specific value for x that satisfies the equation. In this case, the value of x is determined to be 9, which can be verified by substituting it back into the original equation to see if it holds true.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ6

Answer:

14x²-41x+15

Step-by-step explanation:

Answer:

8x^3-6x^2-57x+55

Tell me if you would like an explanation If you need one :D

Step-by-step explanation:

[tex]y = - 4[/tex]

[tex]y = - 4[/tex]

Answer:

y=-4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-(-4))/(-6-4)=(-4+4)/-10=0/-10=0

slope is 0

y-y1=m(x-x1) where m=slope

y-(-4)=0(x-4)

y+4=0

y=0-4=-4

y=-4

Answer:

3.24 feet

Step-by-step explanation:

A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 79 . Find the distance between the building and the ladder

We solve the above question using the Trigonometric function of Cosine

cos x = Adjacent/Hypotenuse

Adjacent = x feet

Hypotenuse = 17 ft

The angle = 79°

Hence,

cos 79 = x/17

Cross Multiply

x = cos 79 × 17

x = 3.2437529214.feet

Approximately = 3.24 feet

Therefore, the distance between the ladder and the building = 3.24 feet

Answer:

12/6-1/6=11/6 simplified to 1 5/6

Step-by-step explanation:

to make this easier make sure all fractions have the same denominator 6/3x2/2=12/6 since they now have the same denominator add 12/6+-1/6=11/6

adding a negative(6/3+-1/6) is the same as subtracting a positive(6/3-1/6)

Answer:

1 5/6

hope this helps :)........

Answer:

1) 5 2)7 3)18 4) 14

Step-by-step explanation:

Answer:

t = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

1/4t - 6 = -4

Step 2: Solve for t

Answer:

t=8

Step-by-step explanation:

1/4 = 0.25

0.25t - 6 = -4

0.25t = -4 + 6

0.25t = 2

t = 2/0.25

t = 8

Answer:

B 4456448444424346464646464664646464

Answer:

c I think

Step-by-step explanation:

can you help me with this question In Lines 23 and 24 of his poem "Chicago", Sandburg uses which poetic device? A Simile - a comparison of two unlike things using "like" or "as" B. Metaphor - a comparison of two unlike objects C. Repetition

Answer: 20

Step-by-step explanation: I LOVE THIS I HATE THIS I CAN SEE THIS SO I JUST GEUSSED HOPE IT IS RIGHT BYE

probably it's 8 or 4. and as $8 is the initial fee, that sounds like the starting value. :-)

the line equation you need is the slope intercept form y = mx + b where m = gradient and b = y intercept.

in this case, y = 4x + 8 where x = number of movies seen, and y = total cost in $

for this line m = 4 and b = 8. hence, indeed, the y intercept is 8

Mark as brainlist

Answer:

Step-by-step explanation:

C is a piecewise function because it represents more than one type of deal.

Step-by-step explanation:

= 55 - 2x is the answer .

plz mark my answer as brainlist if you find it useful.

Answer:

Add 5 and 50

−2x + 55

Step-by-step explanation:

Answer:

130

Step-by-step explanation: