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3 years ago

CAN SOMEONE PLEASE DO THIS AND SHOW WORK!!!! I’m sooo confused!!!!

Mathematics

1 answer:

Otrada [13]3 years ago

6 0

The measure of triangle ABD is 50°

Step-by-step explanation:

Given:

Triangle ABD is formed by tangent and secant

minor arcs AC=68°, CD=124°

To find:

the measure of triangle ABD

Solution:

Angle Formed by Tangent and Secant = 1/2*(difference of Intercepted Arcs)

The intercepted arcs are AC and AD.

We know that minor arc AC + minor arc CD + minor arc AD = 360°

So using this formula AD = 360° - minor arc AC - minor arc CD

AD = 360° -68°-124°

arc AD = 168°

Substituting in the above formula,

∠ ABD = 1/2*(minor arc AD - minor arc AC)

∠ ABD =1/2*(168 - 68)

∠ABD= 50°

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Solve the following system of equations by substitution. Show all steps.

Alinara [238K]

Answer:

Given system of equations:

$\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}$

To solve by substitution, equate the equations and solve for x:

$\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}$

Therefore, the x-values of the solution are $x = 0$ and $x = 4$ .

To find the y-values of the solution, substitute the found values of x into the functions:

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$g(4)=-2(4)+3=-5$

Therefore, the solutions to the given system of equations are:

$(0, 3)$ and $(4, -5)$

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2 years ago

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Olenka [21]

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