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ANTONII [103]
2 years ago
8

What is the length of

Mathematics
1 answer:
saveliy_v [14]2 years ago
6 0

Answer:

17 units

Step-by-step explanation:

Because the triangle is isosceles, 2 of its sides are congruent; namely, the two sides that are opposite of the 2 congruent angles are contruent.

Because of the reason stated above, we can see that AC is congruent to BC, meaning that:

x+9=2x-8

-x      -x

9=x-8

+8  +8

17  = x

Notice that BC is equal to x, so 17 is our final answer.

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Samantha gathered the following information on a given day at the dog park.
Luda [366]

The number of dogs that are not puppies is 17, the number of adult dogs without long hair is 6, the number of puppy dogs with long hair is 8 and the number of puppy dogs without long hair is 7.

<h3>What is the information missing?</h3>

To complete the chart it is necessary to determine:

  • Number of dogs that are not puppies.
  • Number of puppies with and without long hair
  • Number of adult dogs without long hair

Number of dogs that are not puppies:

  • 32 (total dogs) - 15 (puppies) = 17 dogs

Adult dogs without long hair:

  • 17 (total adult dogs) - 11 (adult dogs with long hair) = 6 dogs

Puppy dogs with and without long hair

Total of puppy dogs = 15, this number can be obtained by adding 9+6 or 7+8. From these combinations, the only one that meets the rule "There are 6 more dogs that have long hair than dogs that do not have long hair" is 8 puppies with long hair and 7 puppies without long hair.

Note: This question is not written correctly; here is the correct and complete question.

Samantha gathered the following information on a given day at the dog park.

There are 32 dogs playing at the dog park.

15 of the dogs are puppies.

11 of the dogs are not puppies and have long hair.

There are 6 more dogs that have long hair than dogs that do not have long hair.

Fill in the table completely to represent Samantha’s data.

Learn more about dogs in: brainly.com/question/8565422

6 0
2 years ago
If f(x) = 1 - 2x^3, find the inverse of f.
Artyom0805 [142]
Swap x and y's positions

f(x) is another way of saying y, so basically tha initial function is y = 1-2x^3.

Change it up to x = 1-2y^3 and solve for y

X - 1 = - 2y^3

(X - 1)/-2 = y^3

So the cube root of ((x-1)/2) = y
7 0
2 years ago
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
ryzh [129]

First find the critical points of <em>f</em> :

f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7

\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1

\dfrac{\partial f}{\partial y}=6y=0\implies y=0

so the point (1, 0) is the only critical point, at which we have

f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

Find the critical points of <em>g</em> :

\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

\implies\sin t=0\text{ OR }1+5\cos t=0

\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

t=0\implies f(10,0)=155

t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299

t=\pi\implies f(-10,0)=235

t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299

So <em>f</em> has a minimum of -7 and a maximum of 299.

4 0
3 years ago
In each bouquet of flowers, there are 5 roses and 8 white carnations. Complete the table to find how many roses and carnations t
Verizon [17]
40 70 is the right answer ❤️❤️❤️❤️❤️❤️❤️
5 0
3 years ago
The radius of a circle is 16 cm. Find its area in terms of \piπ
Kitty [74]

Answer256pi

Step-by-step explanation:

Area=pi*r^2

=pi*16^2

256pi

3 0
2 years ago
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