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klio [65]
1 year ago
10

The length of the bae of an iocele triangle i x. The length of a leg i 4x−3. The perimeter of the triangle i 66. Find x.

Mathematics
1 answer:
Alexeev081 [22]1 year ago
5 0

Answer:

x = 8

Step-by-step explanation:

since the triangle is isosceles then the 2 legs are congruent, that is both 4x - 3

the perimeter is the sum of the 3 sides , that is

x + 4x - 3 + 4x - 3 = 66

9x - 6 = 66 ( add 6 to both sides )

9x = 72 ( divide both sides by 9 )

x = 8

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Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has
Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0),  Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8  

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

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Answer:

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6 0
3 years ago
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What is interest earned on 3500 invested at 6% compounded quarterly or 12 years
enyata [817]
\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
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n=
\begin{array}{llll}
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t=years\to &12
\end{cases}
\\\\\\
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6 0
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Which of the following is INCORRECT? *
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this option is incorrect

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Step-by-step explanation:

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Angle take 360° in one revolution

6 0
2 years ago
What is 3/8 inch converted to a decimal.
USPshnik [31]
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7 0
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