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3 years ago

6

A dilation has been performed on ΔABC. The length of segment BC is 5 cm and the length of segment BC' is 30 cm. If segment AC ha

s a length of 12 cm, what is the length of segment A'B'?

1 answer:

borishaifa [10]3 years ago

7 0

If we try to find the scale factor by dividing 30 by 5 to get 6cm, then multiply 12 by 6 and we get A'B' = 72cm
: D

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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

3. Janet is flying a kite on a string that is 75m long. The kite is 62m above the ground. Estimate the distance between Janet an

konstantin123 [22]

Answer: a) It will be a right triangle with a hypotenuse of 75 and a vertical leg that is 62.
b) The length of the kite string is 75 (given in the problem). However, I believe you are looking for the distance from the spot on the ground beneath the kite to Janet. That is about 42.2 m.

To find the missing distance in the right triangle. You have to use the Pythagorean Theorem. I set it up and solve it below.

a^2 + b^2 = c^2
x^2 + 62^2 = 75^2
x^2 + 3844 = 5625
x^2 = 1781
x = 42.2 (about)

3 0

3 years ago

Writ all the factors other than 1 and the number itself <br><br><br>for 5th grade

Vinil7 [7]

Answer:

A prime number has exactly two factors, 1 and itself. For example, 13 is a prime number because the only factors of 13 are 1 and 13

<em>if this is what you are looking for..</em>

8 0

1 year ago

For the differential equations dydx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to thi

julsineya [31]

Answer:

1. (-4,6) there is no a solution to the equation through this point

2. (2,−6) there is no a solution to the equation through this point

3. (−5,39) there is a solution to the equation through this point

4. (−1,45) there is a solution to the equation through this point

Step-by-step explanation:

Using the existence and uniqueness theorem:

Let:

$F(x,y)=\sqrt{y^2-36} \\\\and\\\\\frac{\partial F}{\partial y} =\frac{y}{\sqrt{y^2-36} }$

Now, let's find the domain of $F(x,y)$ , due to the square root:

$y^2-36 \geq 0\\\\y^2\geq 36\\\\y \geq 6\hspace{12}or\hspace{12}y\leq-6$

So the domain of the function is:

$y \in R\hspace{12}y\geq6\hspace{12}or\hspace{12}y\leq-6$

Now, due to the fraction $\frac{\partial F}{\partial y}$ the denominator must be also different from 0, so:

$y^2-36\neq0\\\\y \neq \pm6$

So, the theorem tells us that for each $y_0\in R:\hspace{12}y_0>6\hspace{12}or\hspace{12}y_0$ there exists a unique solution defined in an open interval around $x_0$ .

1. (-4,6) there is no a solution to the equation through this point because $y_0=6$

2. (2,−6) there is no a solution to the equation through this point because

$y_0=-6$

3. (−5,39) there is a solution to the equation through this point because

$y_0>6$

4. (−1,45) there is a solution to the equation through this point because

$y_0>6$

6 0

3 years ago

50 qt = ___gal ____qt

jenyasd209 [6]

Answer:

12 gallons 2 quarts

Step-by-step explanation:

4 0

3 years ago