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ivolga24 [154]
3 years ago
9

A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs o

f congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted..
Mathematics
2 answers:
Licemer1 [7]3 years ago
4 0
To verify whether the diagonals are perpendicular to each other, we find the slope of each segment and we can see that the slopes should be opposite reciprocals of each other.This means, these segments are really perpendicular. This theorem can be verified through congruent angles present in the quadrilateral.
blsea [12.9K]3 years ago
3 0

@meerkat18 what is the theorem that is being verified through congruent angles present in the quadrilateral?

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Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$
Viefleur [7K]

QUESTION 1

Given that:

f(x)=2x^2+3x-9,

g(x)=5x+11,

and

h(x)=-3x^2+1

Then;

f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)

f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1

Group similar terms;

f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1

Simplify;

f(x)-g(x)+h(x)=-x^2-2x-19

QUESTION 2

Given that;

f(x)=4x-7.

g(x)=(x+1)^2

and

s(x)=f(x)+g(x)

Substitute the functions;

s(x)=4x-7+(x+1)^2

Substitute x=3

s(3)=4(3)-7+(3+1)^2

s(3)=12-7+(4)^2

s(3)=5+16

s(3)=21

QUESTION 3

Given:

f(x)=3x+2

g(x)=x^2-5x-1

f(g(x))=f(x^2-5x-1)

This implies that;

f(g(x))=3(x^2-5x-1)+2

Expand the parenthesis;

f(g(x))=3x^2-15x-3+2

f(g(x))=3x^2-15x-1

QUESTION 4

The given function is;

f(x)=3(x-6)^2+1

Let

y=3(x-6)^2+1

\Rightarrow y-1=3(x-6)^2

\Rightarrow \frac{y-1}{3}=(x-6)^2

\Rightarrow \sqrt{\frac{y-1}{3}}=x-6

\Rightarrow x=6+\sqrt{\frac{y-1}{3}}

The range is:

\frac{y-1}{3}\ge0

y-1\ge0

y\ge1

The interval notation is;

[1,+\infty)

6 0
3 years ago
True or false: for any function, x=f^-1(y), then y=f(x)
kozerog [31]

YES

We can work out the inverse using Algebra. Put "y" for "f(x)" and solve for x:

<span><span>The function: f(x)=2x+3
</span><span>Put "y" for "f(x)": y=2x+3
</span><span>Subtract 3 from both sides:
 y-3=2x
</span><span>Divide both sides by 2:
 (y-3)/2=x
</span><span>Swap sides: x=(y-3)/2</span><span>  
   </span><span><span>Solution (put "f-1(y)" for "x") :</span> <span>f-1(y)</span>=(y-3)/2</span></span>


6 0
3 years ago
Read 2 more answers
A car was originally purchased in January 2010 for 27000 dollars. The car depreciates at a rate of 18% every year.
Maksim231197 [3]

Answer:

Number of year(n) = 3.4 year (Approx)

Step-by-step explanation:

Given:

Purchase value of car = $27,000

Depreciation rate per year (d) = 18% = 0.18

Future price = half of its original value = $27,000 / 2 = $13,500

Find:

Number of year(n) = ?

Computation:

Future price  =Purchase value(1-d)^n\\\\13,500=27,000(1-0.18)^n\\\\0.5=(0.82)^n\\\\n=3.444(Approx)

Number of year(n) = 3.4 year (Approx)

5 0
3 years ago
Which is greater 1.5 or 1.54
prohojiy [21]
1.54 because 1.5 is the same thing as 1.50
4 0
3 years ago
Read 2 more answers
-3x-6y =0 In Function Form
AlexFokin [52]
Funciton form is f(x)=something
basicallly know that f(x) is the output or y
just solve for y

-3x-6y=0
add 3x to both sides
-6y=3x
divide both sides by -6
y=-1/2x
f(x)=(-1/2)x
4 0
3 years ago
Read 2 more answers
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