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3 years ago

Simplify. -22-10) - 92

Mathematics

1 answer:

Rzqust [24]3 years ago

5 0

Answer:

2944

Step-by-step explanation:

(-22-10)-92

(-32)-92

2944

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Find the two intersection points

bogdanovich [222]

Answer:

Our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

Step-by-step explanation:

We want to find where the two graphs given by the equations:

$\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1$

Intersect.

When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.

Since the linear equation is easier to solve, solve it for y:

$\displaystyle y = -\frac{3}{4} x + \frac{1}{4}$

Substitute this into the first equation:

$\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16$

Simplify:

$\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16$

Square. We can use the perfect square trinomial pattern:

$\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16$

Multiply both sides by 16:

$(16x^2+32x+16)+(9x^2-54x+81) = 256$

Combine like terms:

$25x^2+-22x+97=256$

Isolate the equation:

$\displaystyle 25x^2 - 22x -159=0$

We can use the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 25, b = -22, and c = -159. Substitute:

$\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}$

Evaluate:

$\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}$

Hence, our two solutions are:

$\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}$

We have our two x-coordinates.

To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

$\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2$

And:

$\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}$

Thus, our two intersection points are:

$\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)$

6 0

3 years ago

PLEASE HURRY FIRST ANSWER WILL BE BRAINLIEST can someone translate these word problems to an actual equation?

Reika [66]

Answer:

1). 9 red 6 fancy 2). 50 shirts 20 pants 3). 62 purple 31 red 4). 19 dimes 9 quarters

Step-by-step explanation:

Most are systems of equations. So, they will have more than one equation.

1). x (Red wrapping paper) y (fancy print paper)

x + y = 15

2x + 4y = 42

Solved: x = 9 y = 6

2). x (shirts) y (pants)

x + y = 70

12x + 30y = 1200

Solved: x = 50 y = 20

3). x (purple) y (red)

I ended up dividing 93 by 3 and then multiplying it by 2 for purple and keeping the other third for red. Not quite sure how to fit this into an equation, its just simple math.

Solved: x = 62 y = 31

4). x (dimes) y (quarters)

.10x + .25y = 4.15

x = y - 10

Solved: x = 19 y = 9

3 0

3 years ago

Two noncongruent triangles, each with side 6 cm and an angle measuring 40 degrees

Svet_ta [14]

Answer:

Two noncongruent triangles, each with side 6 cm and an angle measuring 40 degrees This might be it

Step-by-step explanation: