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3 years ago

Please solve the question.

Mathematics

1 answer:

Brrunno [24]3 years ago

7 0

Answer:

a = 125°, b = 20°, c = 35°, d = 90°, e = 55°

Step-by-step explanation:

Quadrilateral PQRS is inscribed in a circle, therefore it is a cyclic quadrilateral.

PQ is diameter, SR is chord and PR is transversal such that:

PQ || SR... (given)

$m\angle PRQ = 90°..(\angle \: inscribed \: in\: semicircle) \\\huge \red {\boxed {\therefore d = 90°}} \\\\m\angle RPQ= m\angle PRS .. (alternate \: \angle s) \\\huge \purple {\boxed {\therefore c = 35°}} \\\\In\: \triangle PQR, \\c + d + e = 180°\\35° + 90° + e = 180°\\125° + e = 180°\\e = 180° - 125°\\\huge \orange {\boxed {\therefore e = 55°}} \\\\a + e = 180°...(opposite \:\angle 's \: of \: cyclic \: quadrilateral) \\a + 55°= 180°\\a = 180°- 55°\\\huge \blue {\boxed {a = 125°}} \\\\In\: \triangle PSR, \\a + b + 35°= 180°\\125° + b + 35° = 180°\\160° + b = 180°\\b = 180° - 160°\\\huge \pink {\boxed {b = 20°}}$

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A tree in leilas backyard has been growing for 3 1/5 years. It is 3/4 meters tall how many meters per year?

IgorC [24]

Answer:

The tree grew 15/64 meters per year.

Step-by-step explanation:

Given

Length of a tree = 3/4 meters

Total time taken by the tree to grow 3/4 taller = 3 1/5 or 16/5 years

To determine

Per year growth of the tree in meters

Per year growth of the tree in meters can be determined by dividing the total length of a tree i.e. 3/4 meters by the total time taken by the tree to get 3/4 taller.

Per year growth of tree = Total Length / Total time to grow

= 3/4 ÷ 16/5

= 3/4 × 5/16

= [3×5] / [4×16]

= 15/64 meters

Therefore, the tree grew 15/64 meters per year.

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3 years ago

Identify the slope and y-intercept of y = -x +1

Brrunno [24]

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3 years ago

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2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

ratelena [41]

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

$x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29$

The associated matrix to the system is

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]$

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]$

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]$

Using backward substitution we have that

$0x_5=-140$ , then $0=-140$ and this is absurd. Then The system is inconsistent.

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4 years ago

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Nataly [62]

Answer: No

Step-by-step explanation: To determine whether 5/3 is rational or irrational, it's important to understand that all fractions positive or negative are rational numbers.

So 5/3 is not an irrational number, it's rational.

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Answer:

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Step-by-step explanation:

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