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3 years ago

Please help! This is for geometry

Mathematics

1 answer:

Lina20 [59]3 years ago

7 0

ACB=90*
ACD=60*
so, DCB=30*
again, CBD= 90*

Now, in triangle CBD,
Tan 60 = CD/BD
Or, (root)3 = CD/5
Or, CD= 5(root)3

Now,
In triangle ACD
Tan. 60 = AD/CD
Or, (Root)3 = (5(root)3/AD)
Or, 5/AD = 1 ( root 3 and root 3 gets cancelled)
so, AD = 5

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Solve AABC. Round your answers to the nearest hundredth, if necessary

Aloiza [94]

Answer:

$C=25^{\circ},\\a\approx 10.72,\\b\approx 11.83$

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be $180-90-65=25^{\circ}$ .

In any triangle, the Law of Sines is given by $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$ .

Therefore, we have:

$\frac{\sin 90^{\circ}}{b}=\frac{\sin 25^{\circ}}{5},\\\\b=\frac{5\sin90^{\circ}}{\sin 25^{\circ}}=11.8310079158\approx \boxed{11.83}$

$\frac{a}{\sin 65^{\circ}}=\frac{5}{\sin25^{\circ}},\\a=\frac{5\sin 65^{\circ}}{\sin25^{\circ}}=10.7225346025\approx \boxed{10.72}$

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3 years ago

What are the ordered pairs of the

9966 [12]

Start by writing the system down, I will use $y$ to represent $f(x)$

$y=x^2-5x+3\wedge y=-3$

Substitute the fact that $y=-3$ into the first equation to get,

$-3=x^2-5x+3$

Simplify into a quadratic form ( $ax^2+bx+c=0$ ),

$x^2-5x+6=0$

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

$x^2+x(m+n)+mn=0$

which then must factor into

$(x+m)(x+n)=0$

And the solutions will be $m,n$ .

Clearly for small coefficients like ours $5,6$ , this is very easy to figure out. To get 5 and 6 we simply say that $m=3, n=2$ .

This fits the definition as $5=3+2$ and $6=2\cdot3$ .

So as mentioned, solutions will equal to $m=3, n=2$ but these are just x-values in the solution pairs of a form $(x,y)$ .

To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.

So the solution pairs are $(2,0)$ and $(3,0)$ .

Hope this helps :)

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3 years ago

The perimeter of a rectangle is 62 m. The length is four more than two times the width. What is the length?

Travka [436]

--------------------------------------------------
Define length and width
--------------------------------------------------
Let x be the width
width = x
Length = 2x + 4

--------------------------------------------------
Formula
--------------------------------------------------
Perimeter = 2(length + width)

--------------------------------------------------
Find Length and width
--------------------------------------------------
62 = 2(2x + 4 + x)
62 = 2(3x + 4) ← combine like terms 
62 = 6x + 8 ← remove bracket 
62 - 8 = 6x ← minus 8 on both sides 
6x = 54 ← swap sides 
x = 54 ÷ 6 ← divide by 6 on both sides
x = 9 m

--------------------------------------------------
Find Length and Width
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Width = x = 9 m
Length = 2x + 4 = 2(9) + 4 = 22 m

--------------------------------------------------
Answer: Length = 22m
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3 years ago

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Find the diameter of a circle with an area of 95.03 square feet.

ra1l [238]

For this case we have that the area of a circle is given by:

$A = \pi * r ^ 2$