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OLEGan [10]
3 years ago
6

Determine the strongest classification for quadrilateral ABCD with vertices at A(1, 2), B(3, 5), C(5, 3), and D(2, 1). The quadr

ilateral is a because .

Mathematics
1 answer:
Vlada [557]3 years ago
8 0

This is all i could come up with

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HELP 40 POINTS
Tom [10]
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0
3 years ago
X+5/2 + x−3/3 =3 1/6
Nataly [62]
The answer is x=-1/2
3 0
3 years ago
Read 2 more answers
Ms. Hagan invested twice as much money in an account that pays 7% interest as she did in an account that pays 6% in interest. He
Karo-lina-s [1.5K]

Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

Step-by-step explanation:

Let P be the initial amount she invested in an account that pays 6% interest.

Then, amount invested in other account = 2P

Simple interest = Principal x rate x time

After one year, for the first account,

Interest = P(0.06)(1)  = 0.06P

For second account,

Interest = (2P)(0.07)(1)=0.14P

Total interest = 0.06P+0.14P=1000

\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000

2P = 2(5000)=10000

Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

7 0
3 years ago
Please answer ASAP (math)
SSSSS [86.1K]

Answer: Undefined

Step-by-step explanation:

Replace x with -5

8 0
2 years ago
The distance from Jason’s house to the school is 0.5 kilometers. What is the distance in meters
Sedaia [141]

Answer: 500 miles

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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