Solve the following system of equation graphically 2x+y=-1 and x+2y=4

Answers

Answer 1

Answer: As 2x + y = -1

Then,

y = - 1 - 2x

We can to replace on the bellow equation.

x + 2y = 4

x + 2.( -1 -2x) = 4

Doing the distributive

x + 2.(-1) + 2.(-2x) = 4

x -2 -4x = 4

-3x -2 = 4

-3x = 4 + 2

-3x = 6

x = 6/-3

x = -2
________________

Then, the value of y will be:

y = -1 -2x

y = -1 -2.(-2)

y = -1 + 4

y = 3

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HELP ASAP PLEASE!!!Explain how to tell if a point is a solution for a system of equations.

Answers

Explanation:

When you put the solution values into each equation, the equation becomes a true statement. If all equations become true statements, the point is a solution to the system.

_____

For example, consider the system of equations ...

x + y = 6
x - y = 4

The point (x, y) = (5, 1) is proposed as the solution. When we put those values into the equations, we get ...

5 + 1 = 6 . . . . . true

5 - 1 = 4 . . . . . .true

(x, y) = (5, 1) is the solution to this system of equations. (Since it is a system of two independent linear equations in an equal number of unknowns, we know there is only one solution.)

What is the distance between points (4, -7) and (-5, 9)? Round to the nearest tenth of a unit |____|units

Answers

The correct answer is 18.4. We can use the distance formula to solve this problem.

(x - x)² + (y - y)² = d² Distance formula
(4 + 5)² + (-7 - 9)² = d² Substitute the given values; make sure to always subtract in the same direction (for example, if you had (1, 2) and (3, 4), if you start by subtracting 1 - 3, then subtract 2 - 4 again, not 4 - 2); also remember that when you subtract a negative, you add
9² - 16² = d² Add; remember that when you subtract a positive from a negative, the answer is negative (-7 - 9 = -16), but this doesn't really matter since we're about to square it anyway
81 + 256 = d² Square both numbers; you can use a calculator for this, if you want
337 + d² Add
d = √337 Take the square root of both sides to cancel out the exponent

So, the distance is √337. You can use a calculator to get the estimated answer, which is about 18.4

Hope this helps!

Your answer is -18.4

Hope this helped C;

The employees from maintenance go for coffee together every dayat 9 AM. On Monday, Hector paid $5.45 for three cartons of milk,
four cups of coffee and seven doughnuts. On Tuesday, Guillermo
paid $5.30 for four milks, two coffees, and eight doughnuts. On
Wednesday, Anna paid $5.15 for two milks, five coffees, and six
doughnuts. On Thursday, Alphonse had to pay for five milks, two
coffees, and nine doughnuts. How much change did he get back
from his $10 bill?

Answers

A sugestion: calculate m, c, d from:

3m + 4c + 7d = 5.45;
4m + 2c + 8d = 5.30;
2m + 5c + 6d = 5.15;

Then, calculate 10 - (4m + 2c + 9d);

6. What is the slope of the line pictured?

Answers

Answer:

-1/3

Step-by-step explanation:

We can do this by counting the number of spaces away the points shown are. Starting from the leftmost point, you move down one, or -1, units, and right 3 units. Since slope is defined as rise over run, you can then say that the slope is:

-1/3

Hope this helps!

Evaluate $\rm (3^2+1)/(3^2-1)+(5^2+1)/(5^2-1)+(7^2+1)/(7^2-1)+\ldots+(101^2+1)/(101^2-1) =$
With step by step explanation !

Answers

It's easier to deal with the symbolic sum (in sigma notation),

$\displaystyle\sum_(k=1)^(50)((2k+1)^2+1)/((2k+1)^2-1)$

Expanding the terms in the fraction, computing the quotient, and decomposing into partial fractions gives

$((2k+1)^2+1)/((2k+1)^2-1) = (4k^2 + 4k + 2)/(4k^2 + 4k)$

$=\frac12*(2k^2 + 2k + 1)/(k^2 + k)$

$=\frac12\left(2+\frac1{k(k+1)}\right)$

$=\frac12\left(2 + \frac1k - \frac1{k+1}\right)$

and it's the latter two terms that reveal a telescoping pattern.

In case you need more details about the partial fraction decomposition, we are looking for coefficients a and b such that

$\frac1{k(k+1)}=\frac ak+\frac b{k+1}$

$1 = a(k+1) +bk =(a+b)k+a$

which gives a = 1, and a + b = 0 so that b = -1.

Our sum has been rearranged as

$\displaystyle\frac12\sum_(k=1)^(50)\left(2+\frac1k-\frac1{k+1}\right)=\sum_(k=1)^(50)1+\frac12\sum_(k=1)^(50)\left(\frac1k-\frac1{k+1}\right)=50+\frac12\sum_(k=1)^(50)\left(\frac1k-\frac1{k+1}\right)$

The remaining telescoping sum is

1/2 [(1/1 - 1/2) + (1/2- 1/3) + (1/3- 1/4) + … + (1/48- 1/49) + (1/49- 1/50) + (1/50 - 1/51)]

and you can see how there are pairs of numbers that cancel, so that the sum reduces to

1/2 [1/1 - 1/51] = 1/2 [1 - 1/51] = 1/2 × 50/51 = 25/51

So, our original sum ends up being

$\displaystyle\sum_(k=1)^(50)((2k+1)^2+1)/((2k+1)^2-1) = 50 + (25)/(51) = \boxed{(2575)/(51)}$

9 On Cyber Monday, aTV is priced at
$350.00. How much will
the TV cost after a 6%
sales tax is applied?
tax:

Answers

Answer:

$371

Step-by-step explanation:

350 x 0.06 = 21

350 + 21 = 371

Hope this helped!

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The function f(t) = t2 + 6t − 20 represents a parabola.Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) The function H(t) = −16t2 + 90t + 50 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 28 + 48.8t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points)