All categories

4 years ago

-x + 4y = 10 and x - 3y = 11 using substitution

Mathematics

2 answers:

11111nata11111 [884]4 years ago

4 0

Answer:

y = 21

x = 74

Step-by-step explanation:

-x + 4y = 10

x - 3y = 11

Let the first eqn be eqn 1 and the second be eqn 2

- x + 4y = 10 --------eqn 1

x - 3y = 11 ----------eqn 2

From eqn 1, make x the subject of the formula

Carrying x over the equal to in order to change the sign from - to +

4y - 10 = x

Substitute the value of x in eqn 2

4y - 10 - 3y = 11

Collecting like terms

4y - 3y = 11 + 10

y = 21

The value of y is 21

Then, substitute the value of y into eqn 1

-x + 4y = 10

-x + 4(21) = 10

-x + 84 = 10

84 -10 = x

In order to get rid of the - sign

x = 74

Therefore,

x = 74

y = 21

Anuta_ua [19.1K]4 years ago

3 0

Answer:

Step-by-step explanation:

hello : -x + 4y = 10 ....(*)

x - 3y = 11...(**)

add(*) and(**) : y=21

put this value in(**) : x -3(21) = 11

x= 74

You might be interested in

I WILL MAKE YOU THE BRAINLIEST EASY QUESTION

Marizza181 [45]

Answer:

B.) 3.65, 3 2/3, 3.7

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

In your random sample of 25 Chips Ahoy bags, you find a mean of 985 chips per bag, with a standard deviation of 10 chips. Run a

stealth61 [152]

Answer:

The p -value is less than 0.001.

Step-by-step explanation:

Given information:

Sample size = 25 chips

Sample mean = 985

Sample standard deviation = 10

Let as assume that sample is distributed normally.

The formula for test statistic

$t=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}$

where,

$\overline{x}$ is sample mean

μ is population mean.

s is sample standard deviation.

n is sample size.

The value of test statistic is

$t=\frac{985-1000}{\frac{10}{\sqrt{25}}}$

$t=-7.5$

The p-value is

$p=2\times p(t$

Therefore the p -value is less than 0.001.

6 0

4 years ago

A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so

Debora [2.8K]

Let $A(t)$ = amount of salt (in pounds) in the tank at time $t$ (in minutes). Then $A(0) = 11$ .

Salt flows in at a rate

$\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}$

and flows out at a rate

$\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}$

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

$\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}$

which I'll solve with the integrating factor method.

$\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95$

$-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}$

$\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}$

Integrate both sides. By the fundamental theorem of calculus,

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}$

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)$

$\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}$

$\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}$

$\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}$

After 1 hour = 60 minutes, the tank will contain

$A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131$

pounds of salt.

7 0

2 years ago

Find all values of k so that each trinomial <br> 2 x^2+ kx+12

n200080 [17]

K can be 10,11,14,25

Work
(2x+4)(X+3)
(2x+3(X+4)
(2x+6)(X+2)
(2x+2)(X+6)
(2x+1)(X+12)
(2x+12)(X+1)

6 0

4 years ago

Which graph represents the function f(x))=2•(1/3)^x

prisoha [69]

Answer:

The one in the right top hand corner. It shows one arrow pointing up and one to the right.

Step-by-step explanation:

I can't really explain it.

5 0

2 years ago