All categories

3 years ago

Solve elimination 5x+y=9 10x-7y=-18

Mathematics

1 answer:

k0ka [10]3 years ago

6 0

To solve this system by addition, notice that if we add these two equations together, neither one of our variables will cancel out.

In this situation, we need to set things up so that when we do add our two equations together, one of the variables will cancel out.

Notice that we have a 10x in our second equation. if we had a -10x in our first equation, then the x's would cancel out.

To create a -10x, we can multiply the top equation by -2 to get a -10x.

From there, rewriting our equation gives us -10x - 2y = -18.

Now the x's cancel. Just add the equations together

now to get the two-step equation -9y = -36.

Solving from here, <em>y = 4</em>.

Now plug y into either one of the equations

to find that x =1.

So our solution is (1,4).

You might be interested in

Find the critical points, domain endpoints, and local extreme values for the function

aliina [53]

Answer:

a) $x = -3$ , b) $x = 0$ , $x = -6$ , c) $x = 0$ , d) $x = -6$

Step-by-step explanation:

a) Let derive the function:

$f'(x) = \frac{10\cdot x \cdot (x+3)-5\cdot x^{2}}{25\cdot (x+3)^{2}}$

$f'(x)$ is undefined when denominator equates to zero. The critical point is:

$x = -3$

b) $f'(x) = 0$ when numerator equates to zero. That is:

$10\cdot x \cdot (x+3) - 5\cdot x^{2} = 0$

$10\cdot x^{2}+30\cdot x -5\cdot x^{2} = 0$

$5\cdot x^{2} + 30\cdot x = 0$

$5\cdot x \cdot (x+6) = 0$

This equation shows two critical points:

$x = 0$ , $x = -6$

c) The critical points found in point b) and the existence of a discontinuity in point a) lead to the conclusion of the existence local minima and maxima. By plotting the function, it is evident that $x = 0$ corresponds to a local maximum. (See Attachment)

d) By plotting the function, it is evident that $x = -6$ corresponds to a local minimum. (See Attachment)

8 0

3 years ago

What is a polynomial function in standard form with zeroes 1, 2, -2. and -3

Juli2301 [7.4K]

<span>A polynomial with the given zeros can be represented as
f(x) = (x-1)(x-2)(x+2)(x+3).
Note that if you set f(x) = 0, then 1,2,-2, and -3 certainly are the solutions. From here, we simply multiply/expand out the polynomial. We can do this in a variety of ways, one of which is taking the left two and right two products separately. We have
(x-1)(x-2) = x^2 - 3x + 2
and
(x+2)(x+3) = x^2 + 5x + 6.
This gives that
f(x) = (x^2 - 3x + 2) (x^2 + 5x + 6).
Expanding this expression out then gives us our answer as
f(x) = x^4 + 2x^3 - 7x^2 - 8x + 12
or answer choice B.</span>

3 0

4 years ago

Amy has 120 acres of peanuts. She risked the soil using a 16-foot disk traveling 4.2 miles per hour.she used 0.62 gallon per acr

lesya [120]

Where is the question?????

3 0

4 years ago

Send the answer from 18 to 23 with process in copy

viktelen [127]

19. Perimeter of rectangle = 2(l + b)

l = 25m

b = 16m

Perimeter of rectangular park = 2 (25 + 16)

= 50 + 32

= 82m

Perimeter of square park = 82m

(given that, perimeter of rectangular and square park are equal)

Perimeter of square = 4a

4a = 82

a = 82/4

a = 20.5m

Area of square park = a²

= 20.5²

= 420.25m²

20. Perimeter of regular hexagon = 6a

a = 2.5

6a = 6 × 2.5

= 15cm

21. Perimeter of regular decagon = 10a

a = 8

10a = 10 × 8

= 80cm

4 0

3 years ago

PLZ HELP ME GEOMETRY<br> question is below

konstantin123 [22]

The missing justification is for the statement that three angles add to a particular angle. The appropriate choice is ...

... c. Angle Addition Postulate

7 0

3 years ago