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2 years ago

What is the length of leg s of the triangle below?

Mathematics

1 answer:

Phoenix [80]2 years ago

8 0

Answer:

option A

Step-by-step explanation:

take 45 degree as reference angle

using sin rule

sin 45 = opposite / hypotenuse

$\frac{1}{\sqrt{2} }$ = s/ $8\sqrt{2}$

$\frac{1}{\sqrt{2} } *8\sqrt{2}$ = s

root 2 and root 2 gets cancel

8 = s

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What are the quotient and remainder of (5x^4-3x^2-4x+6) / (x-7)?

Phantasy [73]

Use long or synthetic division

The correct choice is B

7 0

3 years ago

PLEASE HELP MEEEE READ AND ANSWER

Lena [83]

Answer:

A. 8/3

B. -27/35

Step-by-step explanation:

keep change flip

keep the first fraction the same, change division to multiplication, and flip the other fraction.For example 1/4 becomes 4/1.

5 0

2 years ago

Use the augmented matrix method to solve the following system of equations. Your answers may be given as decimals or fractions.

Alexandra [31]

Answer:

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

Step-by-step explanation:

Given equations are

x - 2y - z = 2

x + 3y - 2z = 4

-x + 2y + 3z = 2

from the given equations the augmented matrix can be written as

$\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right]$

$R_2=>R_2-R_1\ and\ R_3=>R_3+R_1$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right]$

$R_2=>\dfrac{R_2}{5}$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right]$

$R_1=>R_1+2.R_2$

$=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$R_3=>\dfrac{R_3}{2}$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right]$

$R_1=>R_1+\dfrac{7}{5}R_3\ and\ R_2+\dfrac{1}{5}R_3$

$=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right]$

So, from the above augmented matrix, we can write

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

7 0

3 years ago

A rectangle is twice as long as it is wide. it's width is 5 1/2 cm. find the area of the rectangle.

Dmitry [639]

<span>A rectangle is twice as long as it is wide. it's width is 5 1/2 cm. find the area of the rectangle.</span>

answer: 60 1/2 cm.

4 0

2 years ago

Which of the following polynomial functions is graphed below? OA. f(x) = (x - 2) ^ 2 * (x + 3) * (x - 1) O B. f(x) = (x + 2) ^ 2

laila [671]

The function of the polynomial is (b) $f(x) = (x + 2) ^ 2 * (x - 3) * (x + 1)$

From the graph, we have the following highlights

The graph crosses the x-axis at x = -1 and x = 3
The graph touches the x-axis at x = -2

The above highlights mean that:

The function has a multiplicity of 1 at x = -1 and x = 3
The function has a multiplicity of 2 at x = -2

So, the function of the polynomial is:

$f(x) =a(x + 2)^2(x + 1)(x - 3)$

Assume a = 1.

So, we have:

$f(x) =1(x + 2)^2(x + 1)(x - 3)$

Multiply

$f(x) =(x + 2)^2(x + 1)(x - 3)$

Hence, the function of the polynomial is (b) $f(x) = (x + 2) ^ 2 * (x - 3) * (x + 1)$

Read more about polynomial graphs at:

brainly.com/question/8878887

8 0

2 years ago