All categories

4 years ago

Expressions are equivalent to 4 ( 3 j + ( − 4 ) ) − 9

Mathematics

2 answers:

lions [1.4K]4 years ago

7 0

Answer:

12j - 25

Step-by-step explanation:

4(3j-4)-9

12j-16-9

12j-25

LenKa [72]4 years ago

3 0

Answer:

12j - 25

Step-by-step explanation:

I had the exact same question

You might be interested in

Find the area of the region defined by the region defined by the inequality 2|x| + 3|y-1| ≤ 6

EleoNora [17]

If $x$ and $y-1$ have the same sign, then either

$x>0,y>1 \implies 2|x| + 3|y-1| = 2x + 3(y-1)=6 \implies 2x + 3y = 9$

$x$

If $x$ and $y-1$ have opposite sign, then

$x>0,y$

$x1 \implies 2|x| + 3|y-1| = -2x + 3(y-1) = 6 \implies 2x-3y = -9$

This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set

$R = \left\{(x,y) \mid -3\le2x+3y\le9 \text{ and } -9\le2x-3y\le3\right\}$

The area of $R$ is given by the double integral

$\displaystyle \iint_R dx\,dy$

To compute the area, change the variables to

$\begin{cases}u = 2x + 3y \\ v = 2x - 3y\end{cases} \implies \begin{cases}x = \frac14(u+v) \\ y = \frac16(u-v)\end{cases}$

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix}1/4 & 1/4 \\ 1/6 & -1/6\end{bmatrix}$

with determinant $\det(J) = -\frac1{12}$ . Then the integral transforms to

$\displaystyle \iint_R dx\,dy = \iint_R |J| \, du \, dv = \frac1{12} \int_{-3}^9 \int_{-9}^3 dv\, du$

which is 1/12 the area of a square with side length 12. Hence the integral evaluates to

$\displaystyle \iint_R dx\,dy = \frac1{12}\times12^2 = \boxed{12}$ .

5 0

2 years ago

The graph of a line is shown below. What is the equation of a line, in slope intercept form, that is parallel to this line and h

olganol [36]

Answer:

Y=-2/3+1

Step-by-step explanation:

It would be negative because that is where Y is 0

3 0

3 years ago

Please solve #13-14

Serga [27]

Answer:

XZ = 44

KQ = 24

Step-by-step explanation:

XH is half of XZ, and XH is 22x so two times 22x will give you XZ.

XH times two equation - 2(22x)

XZ equation - 43x + 1

Set them equal

2(22x) = 43x + 1

44x = 43x + 1

x = 1

Put x in equation XZ

43(1) + 1 = 44

5 0

3 years ago

What is the initial population of Rock Springs ?

Ostrovityanka [42]

C) 46,200
This is because the 1,900 represents the increase in population in x years.

5 0

3 years ago

In 1997, the average household expenditure for energy was $1,338, according to data obtained from the U.S. Department of Energy.

makvit [3.9K]

Answer:

Null hypothesis H0: µ = $1,338

Alternative hypothesis Ha: µ ≠ $1,338

Which means;

Null hypothesis H0; the average household expenditure for energy is equal to $1,338

Alternative hypothesis Ha; the average household expenditure for energy is not equal to $1,338

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

Therefore, for the case above;

Null hypothesis H0: µ = $1,338

Alternative hypothesis Ha: µ ≠ $1,338

Which means;

Null hypothesis H0; the average household expenditure for energy is equal to $1,338

Alternative hypothesis Ha; the average household expenditure for energy is not equal to $1,338

6 0

3 years ago