Can somebody help me please

Consider this system of equations. x + 2y = 5, –x + 3y = 6 The x- and y-intercepts of the first equation are found below. x-in

vichka [17]

Answer:

Part 1) The x-intercept is the point (-6,0)

Part 2) The y-intercept is the point (0,2)

Step-by-step explanation:

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

we have

$-x+3y=6$

Part 1) Find the x-intercept

For y=0

substitute the value of y in the linear equation and solve for x

$-x+3(0)=6$

$-x=6$

$x=-6$

The x-intercept is the point (-6,0)

Part 2) Find the y-intercept

For x=0

substitute the value of x in the linear equation and solve for y

$-(0)+3y=6$

$3y=6$

$y=2$

The y-intercept is the point (0,2)

7 0

3 years ago

Read 2 more answers

33+34+35+36+...+104 what is the sum of the sequence?

Ray Of Light [21]

This is an arithmetic series, so we know, that:

Sum = (First term + Last term) * Number of terms /2

Here we have:

First term = 33
Last term = 104
Number of terms = 104 - 33 + 1 = 72

and

$S=(33+104)\cdot\dfrac{72}{2}=137\cdot36=\boxed{4932}$

6 0

4 years ago

Sweet t purchased a new pair of jeans to wear at the battle of the bands on sale at 40% off.He saved $20 what was his regular pr

Oliga [24]

If he got the jeans for 40% off he paid 60% of the cost for the jeans. With that you can setup an equation.

20 is 60% of what number

is signifies equals and of signifies multiplication

20 = 0.6*x
x = 20/.6
x = 33.33

The regular price of the jeans is $33.33

8 0

3 years ago

please help me, Prove a quadrilateral with vertices G(1,-1), H(5,1), I(4,3) and J(0,1) is a rectangle using the parallelogram me

mestny [16]

Answer:

Step-by-step explanation:

We are given the coordinates of a quadrilateral that is G(1,-1), H(5,1), I(4,3) and J(0,1).

Now, before proving that this quadrilateral is a rectangle, we will prove that it is a parallelogram. For this, we will prove that the mid points of the diagonals of the quadrilateral are equal, thus

Join JH and GI such that they form the diagonals of the quadrilateral.Now,

JH= $\sqrt{(5-0)^{2}+(1-1)^{2}}=5$ and

GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$

Now, mid point of JH= $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

= $(\frac{5+0}{2},\frac{1+1}{2})=(\frac{5}{2},1)$

Mid point of GI= $(\frac{5}{2},1)$

Since, mid point point of JH and GI are equal, thus GHIJ is a parallelogram.

Now, to prove that it is a rectangle, it is sufficient to prove that it has a right angle by using the Pythagoras theorem.

Thus, From ΔGIJ, we have

$(GI)^{2}=(IJ)^{2}+(JG)^{2}$ (1)

Now, JI= $\sqrt{(4-0)^{2}+(3-1)^{2}}=\sqrt{20}$ and GJ= $\sqrt{(0-1)^{2}+(1+1)^{2}}=\sqrt{5}$

Substituting these values in (1), we get

$5^{2}=(\sqrt{20})^{2}+(\sqrt{5})^{2} }$

$25=20+5$

$25=25$

Thus, GIJ is a right angles triangle.

Hence, GHIJ is a rectangle.

Also, The diagonals GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$ and HJ= $\sqrt{(0-5)^2+(1-1)^2}=5$ are equal, thus, GHIJ is a rectangle.

6 0

3 years ago

What is the value of the function when x = 2?

bekas [8.4K]

Since we have a graph, we could see where '2' is on the x axis.

Since we see that 6 is where the functions value lies, that is the answer.

Answer: When x = 2, y = 6

5 0

3 years ago