Use Cramer's Rule to solve (if possible) the system of linear equations.

x1 + 2x2 =8
- x1 + x2 = 1

Required:
Find the coefficient matrix.

Given:

Edge of a cubic box = n inches.

He decided to make the box 1 inch taller and 2 inches longer, while keeping its depth at n inches.

To find:

How many cubic inches greater than the box he originally planned to build?

Solution:

Edge of a cubic box is n inches, so the volume of the original cube is:

[tex]V_1=(edge)^3[/tex]

[tex]V_1=n^3[/tex]

According to the given information,

New width of the box = n+1

New length of the box = n+2

New height of the box = n

So, the volume of the new box is:

[tex]V_2=Length\times width\times h[/tex]

[tex]V_2=(n+2)(n+1)n[/tex]

[tex]V_2=(n^2+2n+n+2)n[/tex]

[tex]V_2=(n^2+3n+2)n[/tex]

[tex]V_2=n^3+3n^2+2n[/tex]

Now, the difference between new volume and original volume is:

[tex]V_2-V_1=n^3+3n^2+2n-n^3[/tex]

[tex]V_2-V_1=3n^2+2n[/tex]

So, the volume of new box is 3n^2+2n cubic inches more than the original box.

Therefore, the correct option is A.

Answer:

77.18%

Step-by-step explanation:

115:149*100 =

(115*100):149 =

11500:149 = 77.18

9514 1404 393

Answer:

  (b)  He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.

Step-by-step explanation:

Newton's Law of Cooling says the change in temperature is proportional to the temperature. This relation gives rise to an exponential function describing the temperature.

In this description, the temperature referred to is the difference between the temperature of the object and the temperature of the environment to/from which heat is being transferred.

Juan is only partially correct. The function is exponential, but the temperature that should be used in his equation is not the temperature of the tea, but the temperature difference between the tea and his desk.

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The curve is not linear and not parabolic, excluding the other answer choices.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]V=1000\text{mm}^3[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

I am assuming by the infomation given that the figure is a cube.

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the volume of the cube...}}\\\\S = 10mm; V= s^3\\--------------\\\rightarrow V = 10^3\\\\\rightarrow V = 10 * 10 * 10\\\\\rightarrow \boxed{V=1000\text{mm}^3}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

n(B) = 1350

Step-by-step explanation:

Using Venn sets, we have that:

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

Three values are given in the exercise.

The other is n(B), which we have to find. So

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

[tex]2290 = 1300 + n(B) - 360[/tex]

[tex]940 + n(B) = 2290[/tex]

[tex]n(B) = 2290 - 940 = 1350[/tex]

So

n(B) = 1350

Answer:

-10

Step-by-step explanation:

Step-by-step explanation:

hope it helps

Answer:

I THINK IT IS 74 NOT 4

I HOPE THIS HELPS!!!!!

Answer:

reflected across the y axis: (5,2)

reflected across the x axis: (-2,5)

Answer:

Answer: (5,2) when reflected off the y-axis. (-5,-2) when reflected off the x-axis

Answer:

[tex]2\frac{3}{4} +(-4\frac{1}{4} )=-1\frac{2}{4}[/tex]

Step-by-step explanation:

That's the only equation that makes sense to the number line

Answer:

[tex]A' = (2,0)[/tex]

Step-by-step explanation:

Given

See attachment for ABCD

[tex]k = \frac{1}{2}[/tex] --- the scale factor

Required

The coordinates of A'

From the attachment, we have:

[tex]A = (4,0)[/tex]

So:

[tex]A' = k * A[/tex]

[tex]A' = \frac{1}{2} * (4,0)[/tex]

[tex]A' = (2,0)[/tex]

Answer:

on khan, both are false

Step-by-step explanation:

Answer:

(2) 2,640 ft

Step-by-step explanation:

I'm going to assume that in this question, you are walking 1 full circle around the reservoir. That would mean you need to calculate the circumference of the circular reservoir.

The circumference formula is:

C = ⫪d

C stands for Circumference

d stands for diameter

I will use 22/7 instead of pi, so the formula looks more like this:

C = (22/7)(d)

The diameter is 840 feet, so we will substitute the variable d with 840:

C = (22/7)(840)

You can plug this part into the calculator, but by hand, it'll look something like this:

(22/7)*840 = (22*840)/7

18,480/7 = 2.640

Hope it helps (●'◡'●)

Answer:

B. (-r, 0)

Step-by-step explanation:

W is on the x axis, so the y coordinate is 0.

It is also r away from the origin, so the x coordinate is -r

Hope this helps!

Answer:

the larger number is 69

the smaller number is 16

Step-by-step explanation:

x is the smaller number

y is the larger number

x + y = 85

y - 4x = 5

y = 5 + 4x

x + 5 + 4x = 85

5x = 80

x = 16

y = 69

Answer:

10 pounds of potatoes would cost $15.

Step-by-step explanation:

Set up proportion.

4/6=10/x

simplify 4/6 into 2/3,

2/3=10/x

cross product,

2*x=3*10

2x=30

x=30/2

x=15

lemme just add some to the great reply above,

[tex]\begin{array}{ccll} lbs&\$\\ \cline{1-2} 4&6\\ 10&x \end{array}\implies \cfrac{4}{10}=\cfrac{6}{x}\implies 4x = 60\implies x = \cfrac{60}{4}\implies x = 15[/tex]

Answer:

[tex]\frac{851}{1000}[/tex]

Step-by-step explanation:

First, we can simply multiply that number by 1000, and divide again by 1000 to get a base fraction:

[tex].851\\\\= \frac{1000}{1000} \times .851\\\\= \frac{1000 \times .851}{1000}\\\\= \frac{851}{1000}[/tex]

851 is a secondary prime, having only two factors, both of which are prime.  Those factors are 23 and 37, neither of which is a factor of 1000, so this is already in simplest form.

Answer:

-5 it is

Step-by-step explanation:

Answer:

1/108

Step-by-step explanation:

each denominator triples, so just triple 36.

Answer:

1/108

Step-by-step explanation:

This is a geometric sequence, where each number is 3 times the previous. Normally you would use the actual formula, however you're just asked to pick up on a pattern so just multiplying the second number by 3 works.

Answer:

21

Step-by-step explanation:

7+7+7=21

Answer:

78.5 (I think 90% sure)

Step-by-step explanation:

sum of both scores

75+82 = 157

average for a third test

157÷2=78.5

9514 1404 393

Answer:

  (c)  5x and 3x, and 4 and 1

Step-by-step explanation:

Like terms have the same variable(s) to the same power(s).

The terms of this expression are ...

The like terms are {5x, -3x}, which have the x-variable to the first power, and {4, -1}, which have no variable.

Answer:

Step-by-step explanation:

two points are (-5,-2) and (-1,3)

slope=(3-(-2))/(-1-(-5))=(3+2)/(-1+5)=5/4

Answer:

- 1 - 3(5m + 8) ≥ -85

-1 - 15m - 24 ≥ -85

-15m ≥ -85 + 1 + 24

-15m ≥ 25 - 85

-15m ≥ -60

(-1)(-15)m ≤ -60(-1)

15m ≤ 60

m ≤ 4

Looking at Point A to A', the rectangle moves 5 places to the left which is the x value + 5 and it shifts 1 place down which would be the y value - 1

This gets written as:

(x+5, y-1)

Hello!

x² + 6x + 1 = 0 <=>

<=> x = -6±√6²-4×1×1/2×1 <=>

<=> x = -6±√36-4/2 <=>

<=> x = -6±√32/2 <=>

<=> x = -6±2²√2/2 <=>

<=> x = -6±4√2/2 <=>

<=> x = -6+4√2/2 <=>

and

<=> x = -6-4√2/2 <=>

<=> x = -3+2√2 <=>

and

<=> x = -3-2√2 <=>

x1 = -3-2√2 and x2 = -3+2√2

Good luck! :)

Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.

Answer:

- 0.0943

- 0.386

30.185

Step-by-step explanation:

Given :

ACT:

Mean score, m = 22.5

Standard deviation, σ = 5.3

SAT :

Mean score, m = 526

Standard deviation, σ = 101

1.)

Zscore for ACT score of 22:

Since the distribution is normal ; we use the relation ;

Zscore = (score - mean) / standard deviation

Score = 22

Zscore = (22 - 22.5) / 5.3 = - 0.0943

B.)

Zscore for SAT of 487

Zscore = (score - mean) / standard deviation

Score = 487

Zscore = (487 - 526) / 101 = - 0.386

C.)

ACT score, for ACT Zscore of 1.45

Zscore = (score - mean) / standard deviation

ZScore = 1.45

1.45 = (score - 22.5) / 5.3

1.45 * 5.3 = (score - 22.5)

7.685 = score - 22.5

Score = 7.685 + 22.5

Score = 30.185

Answer:

10^3000

Step-by-step explanation:

1000¹⁰⁰⁰

= (10³)¹⁰⁰⁰

= 10^(3×1000)

= 10³⁰⁰⁰ or 10^3000

Answered by GAUTHMATH

Answer:

x is 10.66

Step-by-step explanation:

What are complementary angles?

They are angles that up to 90

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Hence the value of x is 10.66

Answer:

not 10.66

Step-by-step explanation:

9514 1404 393

Answer:

  y = 2

Step-by-step explanation:

Subtracting the second equation from the third gives ...

  (2z +3x) -(2z -2x) = (-6) -(-6)

  5x = 0

  x = 0

Using this in the third equation, we have ...

  2z +0 = -6

  z = -3

And substituting these values into the first equation, we have ...

  5y -3(0) -4(-3) = 22

  5y = 10 . . . . . subtract 12

  y = 2

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The solution to the system is (x, y, z) = (0, 2, -3).