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3 years ago

Solve the system using substitution 8x+9y=15 5x-2y=17

1 answer:

8 0

$5x-2y=17\ \ \ \ |-5x\\-2y=-5x+17\ \ \ \ |:(-2)\\y=2.5x-8.5\\\\\text{substitute to the first equation}\\\\9x+9(2.5x-8.5)=17\ \ \ \ |\text{use distributive property}\\9x+22.5x-76.5=17\ \ \ \ |+76.5\\31.5x=93.5\ \ \ \ |:31,5\\x=3\\\\\text{substitute the value of x to the equation}\ y=2.5x-8.5\\\\y=2.5(3)-8.5=7.5-8.5=-1\\\\Answer:\ x=3,\ y=-1\to(3;\ -1)$

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10)<br>Simplify the expression.<br>6(4x + 12) – 9x - 18 - 4(-6)<br>

aleksklad [387]

Answer:

$\boxed{\bold{15x+78}}$

Step By Step Explanation:

Apply Rule - (-a) = a

$\bold{6\left(4x+12\right)-9x-18+4\cdot \:6}$

Multiply: 4 · 6 = 24

$\bold{6\left(4x+12\right)-9x-18+24}$

Expand $\bold{6\left(4x+12\right): \ 24x+72}$

= $\bold{24x+72-9x-18+24}$

Simplify $\bold{24x+72-9x-18+24}$

= $\bold{15x+78}$

━ Mordancy ━

4 0

3 years ago

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$

6 0

3 years ago

Given the graph of g(x), describes the transformation of the parent function f(x)=2^x

salantis [7]

Answer:

The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units

6 0

2 years ago

11. How many different ways can the 16 numbered pool balls be placed in a line on the pool table?

nikklg [1K]

Answer:

The number of ways are 16! or 20,922,789,888,000.

Step-by-step explanation:

Consider the provided information.

We need to determine the number of different ways 16 numbered pool balls be placed in a line on the pool table.

For the first place we have 16 balls.

For the second place we have 15 balls left.

Similarly for the third place we have 14 balls as two balls are already arranged and so on.

Or we can say that this is the permutation of 16 things taking 16 at a time.

Thus the number of ways are: $16!$ or $^{16}P_{16}$

$16!=16\times15\times14\times13......\times2\times1=20,922,789,888,000$

Hence, the number of ways are 16! or 20,922,789,888,000.

7 0

3 years ago

The safety instructions for a 20 foot ladder say the ladder should not be inclined more than 70 degrees with the ground. suppose

Romashka [77]

Answer: the distance of the base of the house to the foot of the ladder is 6.84 feet

Step-by-step explanation:

The scenario is shown in the attached photo.

Right angle triangle ABC is formed when the ladder leans against the wall of the house.

AC = the height of the ladder

AB = x feet = distance of the base of the house to the foot of the ladder

BC is the wall of the building.

To determine x, we will apply trigonometric ratio

Cos # = adjacent/hypotenuse

Where

# = 70 degrees

Hypotenuse = 20

Adjacent = x

Cos 70 = x/20

x = 20cos70

x = 20 × 0.3420

x = 6.84 feets

4 0

3 years ago