Graph y minus 3 equal one half (x+2)

In ΔJKL, k = 9.6 cm, l = 2.7 cm and ∠J=43°. Find ∠L, to the nearest 10th of a degree.

Bogdan [553]

Answer:

L = 10.64°

Step-by-step explanation:

From the given information:

In triangle JKL;

line k = 9.6 cm

line l = 2.7 cm; &

angle J = 43°

we are to find angle L = ???

We can use the sine rule to determine angle L:

i.e

$\dfrac{j}{SIn \ J} = \dfrac{l}{ SIn \ L}$

Using Pythagoras rule to find j

i,e

j² = k² + l²

j² = 9.6²+ 2.7²

j² = 92.16 + 7.29

j² = 99.45

$j = \sqrt{99.45}$

j = 9.97

∴

$\dfrac{9.97}{Sin \ 43} = \dfrac{2.7}{ Sin \ L}$

${9.97 \times Sin (L ) = (2.7 \times Sin \ 43)$

$= Sin \ L = \dfrac{ (2.7 \times Sin \ 43)}{9.97 } \\ \\ = Sin \ L = \dfrac{ (2.7 \times 0.6819)}{9.97 } \\ \\ = Sin \ L = 0.18466 \\ \\ L = Sin^{-1} (0.18466) \\ \\ L = 10.64 ^0$

3 0

3 years ago

Opposite angles of a parallelogram are congruent. a. True b. False

AlexFokin [52]

Correct answer is true

4 0

3 years ago

Mike took clothes to the cleaners three times last month. First, brought 4 shirts and of slacks and paid $11.45. Then brought

GenaCL600 [577]

Complete Question:

Mike took clothes to the cleaners three times last month. First, brought 4 shirts and 1 pair of slacks and paid $11.45. Then brought 7 shirts, 2 pairs of slacks, and 2 sports and paid $35.39. Finally, brought 5 shirts and 2 sports and paid $21.43 . How much was charged for each shirt, each pair of slacks, and each sports coat?

Answer:

The charges

For each Shirt = $1.49

For each pair of slacks = $5.49

For each sports coat = $6.99

Step-by-step explanation:

Let Shirt = a

Let pair of slacks = b

Let sports coat = c

First, brought 4 shirts and 1 pair of slacks and paid $11.45

= 4a + b = 11.45 ..........Equation 1

b = 11.45 - 4a

Then brought 7 shirts, 2 pairs of slacks, and 2 sports and paid $35.39

= 7a + 2b + 2c = 35.39.........Equation 2

5 shirts and 2 sports and paid $21.43

5a + 2c = 21.43............Equation 3

Hence:

4a + b = 11.45 ..........Equation 1

7a + 2b + 2c = 35.39.........Equation 2

Using elimination method

Multiply Equation 2 by the coefficient of b = 1 in Equation 1

Multiply Equation 1 by the coefficient of b = 2 in Equation 2

8a + 2b = 22.9 .......Equation 4

7a + 2b + 2c = 35.39.........Equation 2

Subtracting Equation 2 from Equation 4

= a - 2c = -12.49 ........Equation 5

a = -12.49 + 2c

Subtituting -12.49 + 2c for a in Equation 3

5a + 2c = 21.43............Equation 3

5(-12.49 + 2c) + 2c = 21.43

= -62.45 + 10c + 2c = 21.43

Collecting like terms

10c + 2c = 21.43 + 62.45

12c = 83.88

c = 83.88/12

c = 6.99

5a + 2c = 21.43............Equation 3

Substituting 6.99 for c in Equation 3

5a + 2(6.99) = 21.43

5a + 13.98 = 21.43

5a = 21.43 - 13.98

5a = 7.45

a = 7.45/5

a = 1.49

4a + b = 11.45 ..........Equation 1

Substituting 1.49 for a in Equation 1

4(1.49) + b = 11.45

b = 11.45 - 4(1.49)

b = 11.45 - 5.96

b = 5.49

Therefore, since the charges

For each shirt = a

The charges for each Shirt = $1.49

For each pair of slacks = b

The charges for each pair of slacks = $5.49

For each sports coat = c

The charges for each sports coat = $6.99

3 0

2 years ago

The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle

ra1l [238]

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use w to represent the width, the length will be 6 more than 2 times w.

Hence, the length is $2w+6$ .

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

$A=w(2w+6)$

We can also substitute 40 in for A as it's given in the question.

$40 = w(2w+6)$

Distributing w by multiplying it by both terms in the parentheses, we get

$40 = 2w^2+6w$

We can make the equation simpler by dividing both sides by 2.

$20 = w^2+3w$

Subtracting both sides by 20 will make the left-hand side 0.

$0=w^2+3w-20$

Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

$w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}$

$w= \frac{-3\pm\sqrt{9+80}}{2}$

$w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}$

Since the second solution results in a negative number, it cannot be the length of w.

$w=\frac{-3+\sqrt{89}}{2}\approx3.217$

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

$l=2(3.217)+6$

$l=12.434$

The length of this rectangle is 12.434 cm.

6 0

1 year ago

In integers how to know if minus (-) 1 upon 2 is greater or minus (-) 1 is greater???

kogti [31]

Answer:

1/2 is 0.5 so -1/2=-0.5

-0.5 is greater than -1

use a number line

Step-by-step explanation:

4 0

2 years ago

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