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3 years ago

Is the point (1, -3) a solution to the system? Show all work

Mathematics

1 answer:

Studentka2010 [4]3 years ago

6 0

Answer:

The point P(1,-3) is not a solution to the system.

Step-by-step explanation:

Given $\left \{ {{y-x+2}} \right.$

Let a point be P(1,-3)

Here x = 1 ; y = -3

Substituting the values of x,y in the function

$\left \{ {{y-x+2}} \right.$

For y<x-1

-3 < 1-1

-3<0 (True)

now for,

y>-x+2

-3 > -1 + 2

-3 > 1 (False)

Hence the point is not a solution to the system.

You might be interested in

1. If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter o

scZoUnD [109]

Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) What would happen to the perimeter and area of a figure if the dimensions were changed NON-proportionally? For example, if the length of a rectangle was tripled, but the width did not change? Or if the length was tripled and the width was decreased by a factor of 1/4?

we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

The new figure and the original figure are not similar figures

therefore

Corresponding sides are not proportional and corresponding angles are not congruent

A) If the length of a rectangle was tripled, but the width did not change?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2W ----> P=6L+2W

The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

B) If the length was tripled and the width was decreased by a factor of 1/4?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2(W/4) ----> P=6L+W/2

The perimeter of the new figure and the perimeter of the original figure are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W/4) ----> A=(3/4)LW

The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

4 0

3 years ago

Solve for x:-ax+3b>5

Salsk061 [2.6K]

Our current equation is:
-ax + 3b > 5

Our objective is to solve for x, so let's first get -ax by itself.
Subtract 3b from both sides.

-ax > -3b + 5
Now, we have -a multiplying x, so we need to perform the opposite order of operations (like previously shown with 3b).
Divide both sides by -a.
Remember to flip the inequality when multiplying or dividing by a negative.

x <_ (-3b + 5)/-a is your final answer.

I hope this helps!

7 0

3 years ago

An answer would be nice

liberstina [14]

Answer:

1) 90

Step-by-step explanation:

157.50 / 7 = 22.50 or 270 / 12 = 22.50

22.50 * 4 = 90

5 0

3 years ago

Read 2 more answers

How would I write a function rule f(x) = _x+_ If I have an x and y chart?

san4es73 [151]

Y=ax+b. As simple as that!

3 0

3 years ago

The hypotenuse AB of a right triangle ABC is 5 ft, and one leg, AC, is decreasing at the rate of 2 ft/sec. The rate, in square f

mojhsa [17]

Okay
we have the rate of change of AC = d(AC)/dt = -2
the rate of change od BC = d(BC)/dt
area = (1/2) *AC) (BC)
taking differential on both sides we ge
d(A)/dt = 1/2){ (BC) d(AC)/dt + (AC) d(BC)/dt)}....(1)
again
when AC= 3
applying pythagorous thm
we get
(5)^2 =(3)^2 +(BC)^2
hence we get BC = 4
now we need to find d(BC)/dt
we have
(5)^2 = (AC)^2 +(BC)^2
taking differenial
0=2(AC) d(AC/dt) +2BC d(BC)/dt
that is
d(BC)/dt = -(3) *(-2)/4 ..(at AC =3)
hence
d(BC)/dt = 3/2
substituting these values in equation (1)
d(A)/dt = (1/2) {4 * -2 + 3 *3/2}

which gives
d(A)/dt = -7/4

The rate, in square feet per second, at which the area is changing when AC = 3 is -7/4 ft/sec.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

4 0

3 years ago

Read 2 more answers