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Licemer1 [7]
3 years ago
15

How does the function f(x) = a ln x compare to the parent function when |a| > 1?

Mathematics
1 answer:
VladimirAG [237]3 years ago
5 0

Answer: The graph is stretched.

Step-by-step explanation:

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Find the perimeter of Triangle ABC with the verticies A(-5,5) B(3,-5) and C(-5,1
finlep [7]

Hello!
 
Let's calculate a distance between two points using the Pythagorean theorem:<span>

</span>d ^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2

Data:

x_B = 3 &#10;&#10;x_A = -5 &#10;&#10;y_B = -5 &#10;&#10;y_A = 5 &#10;&#10;d_ {AB} =?

Solving: distance from A to B

d^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2 &#10;&#10;d^ 2_ {AB} = (3 - (-5)) ^ 2 + (-5 - 5) ^ 2 &#10;&#10;d^ 2_ {AB} = (8) ^ 2 + (-10) ^ 2 &#10;&#10;d^ 2_ {AB} = 64 + 100 &#10;&#10;d^ 2_ {AB} = 164 &#10;&#10;d_{AB} = \sqrt {164} &#10;&#10;d_{AB} = \sqrt {2 ^ 2 * 41} &#10;&#10;\boxed {d_ {AB} = 2 \sqrt {41}}

<span>Solving:
 
distance from A to C</span>

d ^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2

Data:

x_C = -5&#10; &#10;x_A = -5&#10; &#10;y_C = 1 &#10;&#10;y_A = 5 &#10;&#10;d_ {AC} =?


d^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2 &#10;&#10;d^ 2_ {AC} = (-5 - (-5)) ^ 2 + (1 - 5) ^ 2 &#10;&#10;d^ 2_ {AC} = (0) ^ 2 + (-4) ^ 2  &#10;&#10;d^ 2_ {AC} = 0 + 16  &#10;&#10;d^ 2_ {AC} = 16 &#10;&#10;d_ {AC} = \sqrt {16} &#10;&#10;\boxed {d_ {AC} = 4}&#10;<span>
</span>

Solving:

distance from B to C

d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2

Data:

x_C = -5 &#10;&#10;x_B = 3 &#10;&#10;y_C = 1 &#10;&#10;y_B = -5 &#10;&#10;d_ {BC} =?


d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2&#10; &#10;d^ 2_ {BC} = (-5 - 3) ^ 2 + (1 - (-5)) ^ 2&#10;&#10;d^ 2_ {BC} = (-8) ^ 2 + (6) ^ 2  &#10;&#10;d^ 2_ {BC} = 64 + 36&#10;&#10;d^ 2_ {BC} = 100 &#10;&#10;d_ {BC} = \sqrt {100}&#10;&#10;\boxed {d_ {BC} = 10}

<span>Now let's calculate the perimeter of the triangle ABC, knowing that the perimeter is the sum of the sides, then:
</span>
p = d_ {AB} + d_ {AC} + d_ {BC}  &#10;&#10;

p = 2\sqrt {41} + 4 + 10

&#10;\boxed {\boxed {p = 14 + 2 \sqrt {41}}} \end {array}} \qquad \quad \checkmark
8 0
3 years ago
A hang glider is soaring over a 100-acre area that consists of thick forest and open fields. In the diagram below, the forested
Sonbull [250]

Answer:0.8 :)))

Step-by-step explanation:

8 0
3 years ago
Solve for x:a(a²+b²)x²+b²x-a​
m_a_m_a [10]

Answer:

x = a/(a² + b²) or x = -1/a  

Step-by-step explanation:

a(a²+ b²)x² + b²x - a =0

Use the quadratic equation formula:

x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} =\dfrac{-b\pm\sqrt{D}}{2a}

1. Evaluate the discriminant D

D = b² - 4ac = b⁴ - 4a(a² + b²)(-a) = b⁴ + 4a⁴ + 4a²b²  = (b² + 2a²)²

2. Solve for x

\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-b^{2}\pm\sqrt{(b^{2}+2a^{2})^{2}}}{2a(a^{2} + b^{2})}\\\\ & = & \dfrac{-b^{2}\pm(b^{2}+ 2a^{2})}{2a(a^{2} + b^{2})}\\\\x = \dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}\\\\x =\dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\\end{array}

\begin{array}{rcl}x = \large \boxed{\mathbf{\dfrac{a}{a^{2} + b^{2}}}}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2b^{2}- 2a^{2}}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2(a^{2}+ b^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\large \boxed{\mathbf{-\dfrac{1}{a}}}\\\\\end{array}

5 0
3 years ago
One number exceeds another by 44. the sum of the numbers is 24. what are the​ numbers?
baherus [9]

Let, the numbers = x,y

x+y= 24   1st eqn

x-y = 44   2nd eqn

24-y-y = 44

-2y = 44-24

y = 20/-2 = -10

substitute that in equation 1st x = 24+10 = 34

so, the numbers would be 34 & -10



4 0
3 years ago
Is 0.102 less than 3/7
Bond [772]

it is less than

3/7 ⇒ 0.42857142857

3 0
3 years ago
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