Does Anybody Know The Answer?

Answer:

180

Step-by-step explanation:

Consider the equation x + y + z = 15

From algebraic identities, we know that (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

So,

(x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + xz)

From the question, x^2 + y^2 + z^2 = 83 and x + y + z = 15

So,

152 = 83 + 2(xy + yz + xz)

=> 225 – 83 = 2(xy + yz + xz)

Or, xy + yz + xz = 142/2 = 71

Using algebraic identity a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca),

x3 + y3 + z3 – 3xyz = (x + y + z)(x² + y² + z² – (xy + yz + xz))

Now,

x + y + z = 15, x² + y² + z² = 83 and xy + yz + xz = 71

So, x^3 + y^3 + z^3 – 3xyz = 15(83 – 71)

=> x^3 + y^3 + z^3 – 3xyz = 15 × 12

Or, x^3 + y^3 + z^3 – 3xyz = 180

Answered by GAUTHMATH

Answer:

D.

Step-by-step explanation:

f(x) = [tex]\sqrt[3]{4x}[/tex]

g(x) = 2x + 3

[tex]\frac{f}{g}[/tex] (x)  = 'f' divided by 'g'

[tex]\frac{\sqrt[3]{4x} }{2x+3}[/tex]    Substitute.

x cannot be -[tex]\frac{3}{2}[/tex] because that would create a zero in the denominator.

That's a no-no.

It makes it 'undefined'

Answer: -21/2 or -10.5

Step-by-step explanation:

Let x be the number that is going to be subtracted from the rational number

3 × (-8/3) - x = 5/2 ⇒ Write the equation

-8 - x = 5/2 ⇒ Do multiplication

-8 - x + x = 5/2 +x ⇒ Add x on both sides

-8 = 5/2 + x ⇒ Simplify

-8 - 5/2 = 5/2 + x - 5/2 ⇒ Subtract 5/2 on both sides

x = -21/2 = -10.5 ⇒ Simplify

Hope this helps!! :)

Please let me know if you have any questions

Answer:

There are three laws of indices.

Answer:

i have also no idea but plz mark me as brainlist

Answer:

2

Step-by-step explanation:

x + y = 10

y = 8

Substituting in equation,

x + 8 = 10

=>x = 10 - 8

=>x = 2

point slope form:y-2=4(x+1)

then distribute 4 and simplify y-2=4x+4 , y=4x+6 is the slope -y intercept form

then, move 4x on the left side, you get -4x+y=6 , multiply every term by -1, you get 4x-y=-6 which is standard form.

These triangles are congruent by SAS, therefore HI and IJ will be the same length.

3v = v + 60

2v = 60

v = 30

Hope this helps!

Answer:

Hello,

Step-by-step explanation:

Since 4u²+8u=4u(u+2)

Zeroes ={0,-2}

Coefficients={4,8}

But i don't know the relationship.

Answer:

Step-by-step explanation:

If we have 5 terms to the right of the -1 outside the box thing, that means that our original polynomial is a 4th degree (the degree is one lower than the number of terms in order to allow for the constant which has no variable). Set up the synthetic division as shown in the problem. The rule is to bring down the first term, the 1 to the right of the box, multiply it by the number outside, -1, and put that product up under the next number in line inside the box. Like this:

-1 |   1    7     15     9     7

          -1                        

      1  

Now add straight down, multiply the sum by -1 and put that product up under the next term in line, the 15:

-1 |   1     7     15     9     7

            -1     -6              

      1     6  

Then add straight down again, multiply the sum by -1 and put that product up under the next term in line, the 9:

-1 |     1     7     15     9     7

              -1     -6    -9      

        1     6     9

Then do the same thing. Add straight down, multiply the sum by -1 and put the product up under the next term in line, the 7:

-1 |     1     7     15     9     7

              -1     -6    -9     0

        1     6      9     0     7

This is the final result. The last number, the 7 is the remainder, but the rest of it makes up what we call the depressed polynomial and is a polynomial that is one degree less than the degree we started with. So this depressed polynomial is a 3rd degree. The numbers are the coefficients on the x terms:

[tex]1x^3+6x^2+9x+0R7[/tex] or more simply stated:

[tex]x^3+6x^2+9xR7[/tex]

Answer:

$4,208.5

Step-by-step explanation:

The simple interest rate of the college savings account, R = 5.5%

The amount with which the account was opened, P = $500

The amount added each month to her account = $50

The amount in her account after 4 years = Required

The interest on each added $50 is given as follows;

50  × 0.055/12 × (1 + 2 + 3 + ... + 47) = 50  × 0.055/12 × (47/2)(1 + 47) = 258.5

The total amount deposited = 500 + 50 × 47 = $2,850

The total interest = 500×0.55×4 + 50  × 0.055/12 × (47/2)(1 + 47) = 1,358.5

The amount in her account at the end of 4 years, A, is given as follows

A = $2,850 + $1,358.5 = $4,208.5

Answer: -5

Step-by-step explanation:

square brackets mean that you need to select an integer part from the number that does not exceed the original number, that is, if we have a number, that is, if [5,1]=5 or [-5,1]=-6    ;  curly brackets highlight the fractional part {}   [tex]\displaystyle\ \Large \ \boldsymbol{Rules: } \\\\\\\boldsymbol{ if \ x >0 => [x]=x-\{x\}} \\\\\\\boldsymbol{if \ x<0 => [x]=x-1+\{x\}} \\\\\\then \ \ f(-5)=[-5+1]= [-4]=-4-1+0=\boxed{-5}[/tex]                                                                                                              

Answer:

yes it is a function         A

Step-by-step explanation:

Answer:

1. - 8

2. 3

3. - 2

Step-by-step explanation:

1.

80 = - 10b

- 10b = 80

b = 80 / - 10

b = - 8

2.

6 = 2n

2n = 6

n = 6 / 2

n = 3

3.

- 16r = 32

r = 32 / - 16

r = - 2

Answer:

Step-by-step explanation:

55 +80 + ∠C = 180   {Angle  sum property}

135 + ∠C = 180

∠C = 180 - 135

∠C = 45

The side opposite to the biggest angle is the longest side

Biggest angle is ∠B. So the longest side is AC

Smallest angle is ∠C. So, the shortest side is BA

Answer:

B. 11:35 am

Step-by-step explanation:

11:30 a.m. the bottle is 1/4 of the way full.

At what time will the bottle be 1/2 full?

Time required = 1/4 ÷ 1/2

= 0.25/0.5

= 0.5 minutes

Total time required for the bottle be 1/2 full

= 11:30 am + 0.5 minutes

= 11:35 am

B: 11:35 a.m

Answer:

A The bottle was 1/2 full at 11:35 a.m. and doubled again after 5 minutes.

B The bottle was 1/4 full at 11:30 a.m. and doubled twice after 10 minutes.

D Exponential growth involves a constant multiplicative rate of change.

Step-by-step explanation:

Edge 2021

Answer:

a)[tex]X=3300[/tex]

b)[tex]Y=7770[/tex]

Step-by-step explanation:

From the question we are told that:

Number Teachers [tex]T=6[/tex]

Number Student [tex]S=12[/tex]

Number in committee [tex]n=5[/tex]

a) Generally the equation for exactly 3 students on the committee is mathematically given by

[tex]X=^{S}C_3*^{T}C_3[/tex]

[tex]X=^{12}C_3*^{6}C_3[/tex]

[tex]X=3300[/tex]

b) Generally the equation for at least one teacher and at least one student on the committee is mathematically given by

Total Ways-(no of ways of selection no teacher or student)

Where total Ways

[tex]T=^{(6+12)}C_5[/tex]

[tex]T=8568[/tex]

Therefore

[tex]Y=8568-^{6}C_0*^{12}C_5+^{12}C_0*^{6}C_5[/tex]

[tex]Y=8568-798[/tex]

[tex]Y=7770[/tex]

Answer:

-cos α

is the answer-------

Answer:

130 độ

Step-by-step explanation:

góc BOC= góc AOC-góc AOB

=180°-100°=80°

góc MOB = góc AOB/2=100°/2=50°( vì OM là tia phân giác của góc AOB)

góc COM= góc MOB + góc BOC

= 50° + 80°

= 130°

Answer:

the first one

Step-by-step explanation:

check which graph passes through the point (2,4)

Answer:

First graph

Step-by-step explanation:

Edge

Question 2

3rd part and 4th part are equivalent

Question 3

(i) 762,500

(ii) 7625

(iii) 0.007625

Answered by GauthMath please click thank you and comment thanks if you like it.

Answer:

A

Step-by-step explanation:

The correct inequality that represents the given situation is: A.) n - 87 < 320.

The situation states that Samuel played a video game and gained some points. Let's represent the points he gained as 'n'.

Next, it is mentioned that he lost 87 points. To represent this in the inequality, we subtract 87 from the initial points gained, which gives us 'n - 87'.

Finally, the situation specifies that Samuel finished with less than 320 points. This means that the final score, represented by 'n - 87', is less than 320.

This inequality represents that the initial points gained by Samuel (n) minus 87 points is less than 320 points, indicating that his final score is less than 320 points after losing 87 points.

Learn more about equations

https://brainly.com/question/2972832

#SPJ2

Answer:

18

Step-by-step explanation:

The height of the cone is 8, and the diameter is 3. This means that the radius is 3/2, or 1.5. We can plug everything into the formula (using 3 for pi):

[tex]\frac{3(1.5)^2(8)}{3}[/tex]

We can cancel out the 3 from the numerator and the denominator, so we are left with 1.5^2 times 8. 1.5 squared is equal to 2.25, and 2.25 times 8 is equal to 18.

Answer:

System of equations

[tex]x + y = 5[/tex]

[tex]y - 2x = -4[/tex]

[tex](x,y) = (3,2)[/tex] --- solution

See attachment for graph

Step-by-step explanation:

Solving (a): Linear equations with 1 solution

The only condition to this is that, the system must have 1 solution.

Other than that, there is no other condition.

A linear equation is represented as:

[tex]ax + by= c[/tex]

For the equation to have 1 solution;

[tex]a_1 * b_2 \ne a_2 * b_1[/tex]

And example of such equation is:

[tex]x + y = 5[/tex]

[tex]y - 2x = -4[/tex]

Solving (b): The graph

See attachment for graph

The solution is the point of intersection of both lines of the graph. So, we have:

[tex](x,y) = (3,2)[/tex]

Answer:

12

Step-by-step explanation:

117+23=140

140/4 = 35

35-23 = 12

Answer:

3/5

Step-by-step explanation:

1. Establish the Equation: SinA = [tex]\frac{21}{35}[/tex]

2.  simplify [tex]\frac{3}{5}[/tex]

Answer:

sinA = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{21}{35}[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

Step-by-step explanation:

abscissa = x coordinate

ordinate = y coordinate

table:

A( 2,-3)   / (2, -3) / 2/  -3

B(-1,-7)    / (-1, -7) / -1/  -7

C(2,0)    / (2,0)   / 2 / 0

D(-9, 6)  / (-9,6) / -9 / 6

E(2,4) .  / (2,4) .  / 2 / 4

F(0,-5)  /  (0,-5) / 0 / -5