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3 years ago

The scale used on a map is 5 millimeters represents 32 kilometers. How many millimeters represent 160 kilometers?

Mathematics

1 answer:

Anika [276]3 years ago

5 0

Use the proportion formula:

5mm/32= Xmm/160

=22.22 mm

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Help with problems 1 & 3

vlabodo [156]

One side of the rectangle is x=2, the other side is 2x-5
Add up all the four sides: (x+2) +(x+2)+(2x-5)+(2x-5)=54
6x-6=54
x=10

#3: suppose the first integer is x, then the second one is x+2
x(x+2)=255
x^2 +2x -255 =0
factor the quadratic equation: (x+17)(x-15)=0
x=-17, which is impossible, or x=15
so the two positive integers are 15 and 17

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3 years ago

A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0

3 years ago

Toronto FC have lost 25% of their games if they have played 16 games how many would they have lost

bija089 [108]

Answer:

Step-by-step explanation:

4 0

3 years ago

A population of 50 hamsters grows at an annual rate of 40%.

qaws [65]

Answer:

560 hamsters

Step-by-step explanation:

==> 50 + 40% = 70

==> multiply 70 by 8 years

==> 70 × 8

==> 560

4 0

2 years ago

How many triangles can be constructed with sides measuring 1 m, 2 m, and 2 m?

Margaret [11]

Answer: B
Explanation: ONE triangle can be formed.
According to the triangle inequality theorem, the sum of any two sides must be greater or equal than the length of the third side.
Here, the sides are 1 m, 2 m, and 2m. 1m + 2m = 3m > 2m (theorem followed) 2m + 2m = 4m > 1m (theorem followed)
Since, the triangle inequality theorem is followed, Hence, ONE triangle can be formed.

8 0

4 years ago

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