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2 years ago

A balloon is falling. it falls 200 feet each minute. how far will it in 3 minutes?

Mathematics

1 answer:

Morgarella [4.7K]2 years ago

4 0

Answer:

600ft

Step-by-step explanation:

The balloon falls 200 feet in one minute and we need the amount it fell in 3 minutes: 200feet*3minutes = 600 ft

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In the standard x,y plane, a circle has a radius 6 and center (7, 3). The circle intersects the x-axis at (a, 0) and (b, 0). Wha

arsen [322]

Answer: The required value of a+b is 14.

Step-by-step explanation: Given that in the standard xy plane, a circle has a radius 6 and center (7, 3).

The circle intersects the x-axis at (a, 0) and (b, 0).

We are to find the value of a+b.

We know that

the standard equation of a circle with center at (h, k) and radius r units is given by

$(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

For the given circle, we have

(h, k) = (7, 3) and r = 6 units.

So, from equation (i), we get

$(x-7)^2+(y-3)^2=6^2\\\\\Rightarrow (x-7)^2+(y-3)^2=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Since the circle (ii) passes through the points (a, 0) and (b, 0), so let the point be denoted by (c, 0), then we have

$(c-7)^2+(0-3)^2=36\\\\\Rightarrow (c-7)^2+9=36\\\\\Rightarrow (c-7)^2=27\\\\\Rightarrow c-7=\pm3\sqrt3~~~~~~~~~~~~~~~~~~~~~~[\textup{Taking square root on both sides}]\\\\\Rightarrow c=7\pm3\sqrt3$

Therefore, we get

$a=7+3\sqrt3,\\\\b=7-3\sqrt3.$

That is,

$a+b=(7+3\sqrt3)+(7-3\sqrt3)=14.$

Thus, the required value of a+b is 14.

4 0

3 years ago

Enter answer in the space below

almond37 [142]

Put the rest of the info too so ppl could solve it lolll

5 0

3 years ago

Read 2 more answers

Enter the ordered pair that is the solution to the system of equations graphed below please :]

DiKsa [7]

Hello!

Since (1, -2) is the point of intersection, then it is the solution to the system of equations. Let's test our answer to see if it's correct:

$-2 = -4(1) + 2

-2 = -4 + 2

-2 = -2$

But that's only for the first one, let's test for the second one:

$-2 = 1 - 3

-2 = -2$

This is how we know that (1, -2) is the solution to the system of equations. Hope I helped! :3

5 0

4 years ago

PLEASE HELP

Ira Lisetskai [31]

Answer:

5. 27 + 21 = 48

6. 21 - 3 = 18

7. 12 + 9 = 21

Step-by-step explanation:

I could only see these three but I hope this helps :)

3 0

3 years ago

Read 2 more answers

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.

disa [49]

Answer:

f(x): x=4
h(x): x=-2

Step-by-step explanation:

In each case, the axis of symmetry is the vertical line through the vertex.

The equation is in vertex form:

f = a(x -h)² +k . . . . has vertex (h, k)

The x-coordinate of the vertex can be read from the equation: 4. The vertical line with that x-coordinate is ...

x = 4

The vertex is the point where the graph reaches a maximum, (-2, 2). The vertical line with that x-coordinate is ...

x = -2

3 0

3 years ago