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2 years ago

5. Two adjacent, supplementary angles form

Mathematics

1 answer:

marissa [1.9K]2 years ago

7 0

Answer:

linear pair

Step-by-step explanation:

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No need for alink i don't want a link i want a answer please i need hge help

Volgvan

Answer:

48.45

Step-by-step explanation:

6.8 divided by 0.4 is 17.

17 times 2.85 is 48.45

3 0

3 years ago

Solve the equation in the interval [0,2π]. If there is more than one solution write them separated by commas.

zysi [14]

$\large\begin{array}{l} \textsf{Solve the equation for x:}\\\\ \mathsf{(tan\,x)^2+2\,tan\,x-4.76=0}\\\\\\ \textsf{Substitute}\\\\ \mathsf{tan\,x=t\qquad(t\in \mathbb{R})}\\\\\\ \textsf{so the equation becomes}\\\\ \mathsf{t^2+2t-4.76=0}\quad\Rightarrow\quad\begin{cases} \mathsf{a=1}\\\mathsf{b=2}\\\mathsf{c=-4.76} \end{cases} \end{array}$

$\large\begin{array}{l} \textsf{Using the quadratic formula:}\\\\ \mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=2^2-4\cdot 1\cdot (-4.76)}\\\\ \mathsf{\Delta=4+19.04}\\\\ \mathsf{\Delta=23.04}\\\\ \mathsf{\Delta=\dfrac{2\,304}{100}}\\\\ \mathsf{\Delta=\dfrac{\diagup\!\!\!\! 4\cdot 576}{\diagup\!\!\!\! 4\cdot 25}}\\\\ \mathsf{\Delta=\dfrac{24^2}{5^2}} \end{array}$

$\large\begin{array}{l} \mathsf{\Delta=\left(\dfrac{24}{5}\right)^{\!2}}\\\\ \mathsf{\Delta=(4.8)^2}\\\\\\ \mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\ \mathsf{t=\dfrac{-2\pm\sqrt{(4.8)^2}}{2\cdot 1}}\\\\ \mathsf{t=\dfrac{-2\pm 4.8}{2}}\\\\ \mathsf{t=\dfrac{\diagup\!\!\!\! 2\cdot (-1\pm 2.4)}{\diagup\!\!\!\! 2}}\\\\\mathsf{t=-1\pm 2.4} \end{array}$

$\large\begin{array}{l} \begin{array}{rcl} \mathsf{t=-1-2.4}&~\textsf{ or }~&\mathsf{t=-1+2.4}\\\\ \mathsf{t=-3.4}&~\textsf{ or }~&\mathsf{t=1.4} \end{array} \end{array}$

$\large\begin{array}{l} \textsf{Both are valid values for t. Substitute back for }\mathsf{t=tan\,x:}\\\\ \begin{array}{rcl} \mathsf{tan\,x=-3.4}&~\textsf{ or }~&\mathsf{tan\,x=1.4} \end{array}\\\\\\ \textsf{Take the inverse tangent function:}\\\\ \begin{array}{rcl} \mathsf{x=tan^{-1}(-3.4)+k\cdot \pi}&~\textsf{ or }~&\mathsf{x=tan^{-1}(1.4)+k\cdot \pi}\\\\ \mathsf{x=-tan^{-1}(3.4)+k\cdot \pi}&~\textsf{ or }~&\mathsf{x=tan^{-1}(1.4)+k\cdot \pi} \end{array}\\\\\\ \textsf{where k in an integer.} \end{array}$

__________

$\large\begin{array}{l} \textsf{Now, restrict x values to the interval }\mathsf{[0,\,2\pi]:}\\\\ \bullet~~\textsf{For }\mathsf{k=0:}\\\\ \begin{array}{rcl} \mathsf{x=-tan^{-1}(3.4)$

$\large\begin{array}{l} \bullet~~\textsf{For }\mathsf{k=1:}\\\\ \begin{array}{rcl} \mathsf{x=-tan^{-1}(3.4)+\pi}&~\textsf{ or }~&\mathsf{x=tan^{-1}(1.4)+\pi} \end{array}\\\\\\ \boxed{\begin{array}{c}\mathsf{x=-tan^{-1}(3.4)+\pi} \end{array}}\textsf{ is in the 2}^{\mathsf{nd}}\textsf{ quadrant.}\\\\ \mathsf{x\approx 1.86~rad~~(106.39^\circ)}\\\\\\ \boxed{\begin{array}{c}\mathsf{x=tan^{-1}(1.4)+\pi} \end{array}}\textsf{ is in the 3}^{\mathsf{rd}}\textsf{ quadrant.}\\\\ \mathsf{x\approx 4.09~rad~~(234.46^\circ)}\\\\\\ \end{array}$

$\large\begin{array}{l} \bullet~~\textsf{For }\mathsf{k=2:}\\\\ \begin{array}{rcl} \mathsf{x=-tan^{-1}(3.4)+2\pi}&~\textsf{ or }~&\mathsf{x=tan^{-1}(1.4)+2\pi>2\pi~~\textsf{(discard)}} \end{array}\\\\\\ \boxed{\begin{array}{c}\mathsf{x=-tan^{-1}(3.4)+2\pi} \end{array}}\textsf{ is in the 4}^{\mathsf{th}}\textsf{ quadrant.}\\\\ \mathsf{x\approx 5.00~rad~~(286.39^\circ)} \end{array}$

$\large\begin{array}{l} \textsf{Solution set:}\\\\ \mathsf{S=\left\{tan^{-1}(1.4);\,-tan^{-1}(3.4)+\pi;\,tan^{-1}(1.4)+\pi;\,-tan^{-1}(3.4)+2\pi\right\}} \end{array}$

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$\large\textsf{I hope it helps.}$

Tags: <em>trigonometric trig quadratic equation tangent tan solve inverse symmetry parity odd function</em>

6 0

3 years ago

You mid morning break begins at 9:45 am and lasts for 10 minutes. you work for 2 hours and 10 minutes until your lunch break. wh

TiliK225 [7]

9:45 + 10 = 9:55
9:55 + 2:00= 11:55 This is what I got

8 0

4 years ago

A bag contains 12 marbles: 5 are orange, 3 are blue, and the rest are red. If one marble is selected at random from the bag, wha

givi [52]

Answer:

7/12

Step-by-step explanation:

The probability is the number of events out of the number of outcomes. The total number of outcomes is the number of marbles which is 12. The number of events is the number of red or blue marbles which is 3 + 4 = 7. This is true since there are 3 blue listed and since 12 - 5 - 3 = 4 red.

The probability is a ratio or fraction and should be written as 7/ 12.

7 0

3 years ago

On Aaron’s farm, 1/10 of the animals are cows, ⅖ of the animals are chickens,

Ray Of Light [21]

Answer:

There are 5 pigs on Aaron's farm

Step-by-step explanation:

1. Start with 40 animals

2. 1/10 of the animals are cows, so divide 40 by 10 and you will find that 4 of the animals are cows

3. 2/5 of the animals are chickens, so multiple 40 by 2 to get 80 and then divide 80 by 5 and you will find that 16 of the animals are chickens

4. Subtract the 4 cows and 16 chickens from the 40 total animals and you find there are 20 more animals that are neither cows nor chickens

5. Of the 20 remaining animals, 1/4 are pigs, so divide 20 by 4 and you will find that there are 5 pigs

6 0

3 years ago