All categories

3 years ago

What is the value of the expression |-5x+12| when x=5

Mathematics

2 answers:

MissTica3 years ago

6 0

First, plug in 5 for x:

| -5 * 5 + 12 | = |-25 + 12| = |-13|

Those two lines are absolute value, which measures the distance from the number to 0 on a number line. This distance is always positive.

The distance from -13 to 0 on a number line is 13. The answer is 13.

Oliga [24]3 years ago

5 0

|-5x + 12|

|-5(5) + 12| = |-25 + 12|

|-25 + 12| = |-13|

|-13| = 13

You might be interested in

A point $(x, y)$ with integer coordinates is randomly selected such that $0 \le x \le 8$ and $0 \le y \le 4$. what is the probab

ahrayia [7]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

A point (x, y) with integer coordinates is randomly selected such that $0 \le x \le 8 \:and\: $0 \le y \le 4$.$

The possible pairs of (x,y) are:

(0,0),(0,1),(0,2),(0,3),(0,4)

(1,0),(1,1),(1,2),(1,3),(1,4)

(2,0),(2,1),(2,2),(2,3),(2,4)

(3,0),(3,1),(3,2),(3,3),(3,4)

(4,0),(4,1),(4,2),(4,3),(4,4)

(5,0),(5,1),(5,2),(5,3),(5,4)

(6,0),(6,1),(6,2),(6,3),(6,4)

(7,0),(7,1),(7,2),(7,3),(7,4)

(8,0),(8,1),(8,2),(8,3),(8,4)

The Total Possible Outcomes n(S)= 45

The pair (x, y) that satisfies the given condition (say event A: $x + y \le 4$ ) are:

$(0,0),(0,1),(0,2),(0,3),(0,4)\\(1,0),(1,1),(1,2),(1,3)\\(2,0),(2,1),(2,2)\\(3,0),(3,1)\\(4,0)$

n(A)=15

Therefore:

$P(A)=\frac{n(A)}{n(S)} =\frac{15}{45} =\frac{1}{3}$

5 0

3 years ago

Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).

lesya [120]

The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted $C$ , which we can parameterize by the vector-valued function,

$\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)$

for $0\le t\le1$ , which has differential

$\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

Then with $x(t)=y(t)=z(t)=1-t$ , we have

$\displaystyle\int_{\mathcal C}\nabla f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\nabla f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r$

$=\displaystyle\int_{t=0}^{t=1}\left(2(1-t)^3e^{(1-t)^2}\,\mathbf i+(1-t)e^{(1-t)^2}\,\mathbf j+(1-t)e^{(1-t)^2}\,\mathbf k\right)\cdot-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)(t^2-2t+2)\,\mathrm dt$

Complete the square in the quadratic term of the integrand: $t^2-2t+2=(t-1)^2+1=(1-t)^2+1$ , then in the integral we substitute $u=1-t$ :

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)((1-t)^2+1)\,\mathrm dt$

$\displaystyle=-2\int_{u=0}^{u=1}e^{u^2}u(u^2+1)\,\mathrm du$

Make another substitution of $v=u^2$ :

$\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv$

Integrate by parts, taking

$r=v+1\implies\mathrm dr=\mathrm dv$

$\mathrm ds=e^v\,\mathrm dv\implies s=e^v$

$\displaystyle=-e^v(v+1)\bigg|_{v=0}^{v=1}+\int_{v=0}^{v=1}e^v\,\mathrm dv$

$\displaystyle=-(2e-1)+(e-1)=-e$

So, we have by the fundamental theorem of calculus that

$\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)$

$\implies-e=f(1,1,1)-2$

$\implies f(1,1,1)=2-e$

3 0

3 years ago

What is the sum of 7 3/16+3/4

muminat

Answer:

7 15/16

Step-by-step explanation:

find the same denominator which is 16

3/4x4/4 = 12/16

7 3/16+12/16= 7 15/16

probably bad explanation but hope it helps.. :)

5 0

2 years ago

Read 2 more answers

In triangle POR, PO = 9cm and PR = 12cm. If

Olin [163]

Answer:

Area of trangle = 1÷2 (9×12×sinRpo)

23= 1÷2 (108×sinRPO)

8 0

3 years ago

A(n) ___________________ variable is a qualitative variable such that there is no meaningful ordering or ranking of the categori

Licemer1 [7]

Answer: c. Nominal

Step-by-step explanation:

Level of measurement determines the nature of description .

The four levels of measurements scales are

1. Nominal scale

Categorize the data on the basis of the quality such as Gender, color, etc.

2. Ordinal scale

Order attributes according to their ranks. For example : 1 < 2 < 3 .

3. Interval scale

Describe the feature of the difference between any two categories. For example : Fahrenheit scale to measure temperature.

4. Ratio scale

Consist of the features of nominal, ordinal, and interval measures but in includes a "true zero" point.

For example : Age.

∴ A<u> nominal</u> variable is a qualitative variable such that there is no meaningful ordering or ranking of the categories.

Hence, the correct answer is c. Nominal .

5 0

2 years ago