Which fraction is between 3/20 and 7/10

lesantik [10]

Answer:

$\huge\boxed{x=8;\ y=1\to(8;\ 1)}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}$

$\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}$

8 0

3 years ago

Read 2 more answers

Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x 4 6x 3y =

wariber [46]

The missing value is 12 in a system of equations with infinitely many solutions conditions.

It is given that in the system of equations there are two equations given:

$\rm y =n -2x+4\\\rm and \\\rm 6x+3y= ?$

It is required to find the missing value in the second equation.

<h3>What is a linear equation?</h3>

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

We have equations:

$\rm y = -2x+4 ....(1)\\ \\\rm 6x+3y= ? ....(2)$

Let's suppose the missing value is 'Z'

We know that the two pairs of equations have infinitely many solutions if and if they have the same coefficients of variables and the same constant on both sides.

From equation (1)

$\rm y = -2x+4 \\\\\rm 2x+y=4$ (multiply both the sides by 3)

$\rm 6x+3y=12$ ...(3)

By comparing the equation (2) and (3), we get

M = 12

Thus, the missing value is 12 in a system of equations with infinitely many solutions conditions.

Learn more about the linear equation.

brainly.com/question/11897796

8 0

2 years ago

A equation for one half and one six

kobusy [5.1K]

What exactly are you looking for?

-TTL

5 0

3 years ago

Read 2 more answers

Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6

Alla [95]

Given:

The expression is:

$2x^3+mx^2+nx+c$

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

$m+n=-6$

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

$P(x)=2x^3+mx^2+nx+c$

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

$P(2)=P(-1)$ ...(i)

Substituting $x=-1$ in the given polynomial.

$P(-1)=2(-1)^3+m(-1)^2+n(-1)+c$

$P(-1)=-2+m-n+c$

Substituting $x=2$ in the given polynomial.

$P(2)=2(2)^3+m(2)^2+n(2)+c$

$P(2)=2(8)+m(4)+2n+c$

$P(2)=16+4m+2n+c$

Now, substitute the values of P(2) and P(-1) in (i), we get

$16+4m+2n+c=-2+m-n+c$

$16+4m+2n+c+2-m+n-c=0$

$18+3m+3n=0$

$3m+3n=-18$

Divide both sides by 3.

$\dfrac{3m+3n}{3}=\dfrac{-18}{3}$

$m+n=-6$

Hence proved.

7 0

3 years ago

student measuring how gasoline prices change records the cost of gas at 10 randomly selected stations in her hometown. One week

k0ka [10]

Answer:

We conclude that he used a paired two-sample t-test.

Step-by-step explanation:

We know that the student measuring how gasoline prices change records the cost of gas at 10 randomly selected stations in her hometown. One week later, she records the price again at the same 10 stations.

We conclude that he used a paired two-sample t-test.

Because at each gas station, the student measured the price of gas twice.

8 0

3 years ago