All categories

3 years ago

2x + 3 (x - 10) = 45 ?? A. X =15 B. X=3 C. X=7 D. X=11

Mathematics

1 answer:

mario62 [17]3 years ago

3 0

Answer:

A. x = 15

Step-by-step explanation:

2x + 3 * (x - 10) = 45

2x + 3x - 30 = 45

5x - 30 = 45

5x = 75

x = 15

You might be interested in

I need help with this word problem.

zloy xaker [14]

Answer:

33 ⅓%

Step-by-step explanation:

Percent means out of 100, so write a proportion:

1 / 3 = x / 100

Solve for x by multiplying both sides by 100:

x = 100 / 3

Reduce:

x = 33 ⅓

The percent of questions he got right is 33 ⅓%.

4 0

3 years ago

Mr. Stubbert wants to buy a $520 sword, and he has a coupon for 15% off.

Oliga [24]

Answer:

the last choice is correct

Step-by-step explanation:

520 - 520(0.15)

6 0

2 years ago

KATRIN_1 [288]

Answer:

pair is

30 and 315

co-prime

7 0

3 years ago

7(x + y) ex2 − y2 dA, R where R is the rectangle enclosed by the lines x − y = 0, x − y = 7, x + y = 0, and x + y = 6

Anastasy [175]

Answer:

$\int\limits {\int\limits_R {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}$

Step-by-step explanation:

Given

$x - y = 0$

$x - y = 7$

$x + y = 0$

$x + y = 6$

Required

Evaluate $\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA$

Let:

$u=x+y$

$v =x - y$

Add both equations

$2x = u + v$

$x = \frac{u+v}{2}$

Subtract both equations

$2y = u-v$

$y = \frac{u-v}{2}$

So:

$x = \frac{u+v}{2}$

$y = \frac{u-v}{2}$

R is defined by the following boundaries:

$0 \le u \le 6$ , $0 \le v \le 7$

$u=x+y$

$\frac{du}{dx} = 1$

$\frac{du}{dy} = 1$

$v =x - y$

$\frac{dv}{dx} = 1$

$\frac{dv}{dy} = -1$

So, we can not set up Jacobian

$j(x,y) =\left[\begin{array}{cc}{\frac{du}{dx}}&{\frac{du}{dy}}\\{\frac{dv}{dx}}&{\frac{dv}{dy}}\end{array}\right]$

This gives:

$j(x,y) =\left[\begin{array}{cc}{1&1\\1&-1\end{array}\right]$

Calculate the determinant

$det\ j = 1 * -1 - 1 * -1$

$det\ j = -1-1$

$det\ j = -2$

Now the integral can be evaluated:

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA$ becomes:

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{x^2 - y^2}} \, *\frac{1}{|det\ j|} * dv\ du$

$x^2 - y^2 = (x + y)(x-y)$

$x^2 - y^2 = uv$

So:

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{|det\ j|}\, dv\ du$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *|\frac{1}{-2}|\, dv\ du$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{2}\, dv\ du$

Remove constants

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 {\int\limits^7_0 {ue^{uv}} \, dv\ du$

Integrate v

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 \frac{1}{u} * {ue^{uv}} |\limits^7_0 du$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 e^{uv} |\limits^7_0 du$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{u*7} - e^{u*0}]du$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{7u} - 1]du$

Integrate u

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7u} - u]|\limits^6_0$

Expand

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -(\frac{1}{7}e^{7*0} - 0)]$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -\frac{1}{7}]$

Open bracket

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} - 6 -\frac{1}{7}]$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} -\frac{43}{7}]$

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{42} -\frac{43}{7}]$

Expand

$\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}$

3 0

3 years ago

A scale drawing of a living room is shown below: A rectangle is shown. The length of the rectangle is labeled 3 inches. The widt

rosijanka [135]

103 ft^2
take 3 and 5 and multiply it by 30
3*30=90
5.5*30=165
then divide them both by 12 to convert inches to feet
90÷12=7.5
165÷12=13.75
then multiply both dividends together
7.5*13.75=103.125
then round to the nearest whole number
103

4 0

2 years ago