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3 years ago

HELP GEOMETRY PROOFS

Mathematics

1 answer:

Reptile [31]3 years ago

6 0

Step-by-step explanation:

See the attached for the proof

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A new building is being constructed at UT Austin. It is 200 feet tall, and has a

Mariana [72]

Answer:

Walkway is 3 feet wide.

Step-by-step explanation:

Given:

Length of the building is 150 ft

width of the building is 100 ft

walkway is x ft wide.

Total area(around and including the building) = 16536 square feet

Solution:

Length of the total area will be = length of the building + width of walkway from 2 sides = $150 +2x$

Width of the total area will be = width of the building + width of walkway from 2 sides = $100 +2x$

Now Total area(around and including the building) = Length of the total area $\times$ Width of the total area

$(150+2x)\times(100+2x)=16536\\15000+300x+200x+4x^2=16536\\500x+4x^2=16536-15000\\4(125x+x^2)=1536\\125x+x^2= \frac{1536}{4}=384\\$

$x^2+125x-384=0\\x^2-3x+128x-384=0\\x(x-3)+128(x-3)=0\\(x-3)(x+128)=0\\$

Now solving for both equation we get.

$x+128=0\\x=-128\\x-3=0\\x=3$

Now, We get 2 values for x which -128 and 3 but the width of the building can't be in negative value hence we will consider value of x be 3.

∴ Width of the walkway is 3 ft.

4 0

3 years ago

Read 2 more answers

6x^2-9x +2=0 solve the quadratic equation using the quadratic formula

balu736 [363]

<u>ANSWER: </u>

The roots of $6 x^{2}-9 x+2=0$ are $\frac{9+\sqrt{33}}{4}, \frac{9-\sqrt{33}}{4}$

<u>SOLUTION:</u>

Given, quadratic equation is $6 x^{2}-9 x+2=0$ --- eqn (1)

We need to find the roots of given quadratic equation using quadratic formula.

Quadratic formula for general quadratic equation $a x^{2}+b x+c=0$ is $X=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here, for eqn (1) a = 6, b= -9 and c = 2

$X=\frac{-(-9) \pm \sqrt{(-9)^{2}-4 \times6 \times 2}}{2 x 2}$

$X=\frac{9 \pm \sqrt{81-48}}{4}$

$\begin{array}{l}{X=\frac{9 \pm \sqrt{33}}{4}} \\ {X=\frac{9+\sqrt{33}}{4}, \frac{9-\sqrt{33}}{4}}\end{array}$

Hence the roots of $6 x^{2}-9 x+2=0$ are $\frac{9+\sqrt{33}}{4}, \frac{9-\sqrt{33}}{4}$

6 0

3 years ago

Simplify (-3)(-3)(-3)

Radda [10]

Answer:

-27

Step-by-step explanation:

-3 x -3=9

9 x -3= -27

4 0

3 years ago

Read 2 more answers

If Z= 2+2i, what is z^4?

Dimas [21]

Answer:

assume z is equal to 5.

log(z^4/5) equals log(5^4/5) equals log(5^3) equals 2.096910013.

4 * log(5) - log(5) equals 2.096910013.

they give you the same answer.

this means they're equivalent.

Step-by-step explanation:

7 0

3 years ago

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Vector u has its initial point at (14, -6) and its terminal point at (-4, 7). Write the component form of u and find its magnitu

Thepotemich [5.8K]

$\bf u\implies \begin{cases} (14,-6)\\ (-4,7) \end{cases}\implies (-4-14)~,~(7-(-6)) \\\\\\ (-18) ~,~(7+6)\implies \stackrel{\textit{component form}}{\ \textless \ -18~,~13\ \textgreater \ } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ||u||=\sqrt{a^2+b^2}\implies ||u||=\sqrt{(-18)^2+13^2}\implies ||u||=\sqrt{493}$

3 0

3 years ago