Answer the following correctly

Mathematics

1 answer:

Lerok [7]3 years ago

8 0

Answer: The last option is the correct Answer

The initial value is 2

Step-by-step explanation: The equation of line passes through the origin is represented by: y = mx where m is the slope or unit rate .

Then by definition.

m = 2

Slope on the line is 2.

the unit rate is 2.

Also, the constant of proportionality is 2.

Therefore, the statement which is not true for the equation y=2x represents a set of data is: The initial value is 2.

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Help me pls.

salantis [7]

Answer:

1. 424

2.471

3.512

Step-by-step explanation:

1. 10×12+8×10+8×13+8×15

=120+80+104+120

=424

2. 5×24+9×24+9×15+9×15

=120+216+135

=471

3. 24×16+2×24+2×20+2×20

=384+48+40+40

=512

3 0

3 years ago

A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

Let $(x,y)$ be any point on the parabola. Then, from the definition of a parabola,

Distance of $(x,y)$ from focus = Distance of $(x,y)$ from directrix.

Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$