Find the measures of a right triangle with one angle whose measure is 30

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

Consider,

[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]

On taking LCM, we get

[tex]\rm \:  =  \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]

and

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]

So, using these Identities, we get

[tex]\rm \:  =  \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]

So, using this, we get

[tex]\rm \:  =  \: \dfrac{2(7 - 3)}{7 + 3} [/tex]

[tex]\rm \:  =  \: \dfrac{2 \times 4}{10} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{5} [/tex]

Hence,

[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]

Answer:

[tex]P(B) = \frac{4}{18} = \frac{2}{9} = 0.2[/tex]

Step-by-step explanation:

Sample space 2+5+7+4=18

Answer:

4/18 or 2/9

Step-by-step explanation:

The total number of balls = 2 + 5 + 7 + 4 = 18

4 out of the 18 balls are blue ∴ the probability is 4/18 or 2/9

Hope this helps!

Answer:

<1=23

Step-by-step explanation:

If WXZ contains both <1 and <2, and <2 is 4 times <1, then we can set this up as x + 4x = 115

This is easily simplified to 5x = 115

Divide both sides by 5 and you will get x=23

Answer:

120 people would play

Step-by-step explanation:

Answer: James was charged with $180 more for the year that Betty

Step-by-step explanation: So I dont know how your money currency  works sorry, also Ive never done this kind of math problem so I dont know if its right

Answer:(x - 4)(2x + 3)

FOIL = first,outside,inside,last

F -- so multiply first terms in each set....(x)(2x)

O -- multiply outside terms in each set...(3)(x)

I -- multiply inside terms in each set....(-4)(2x)

L -- multiply last terms in each set.......(-4)(3)

Step-by-step explanation:

Answer:

$12.33

Step-by-step explanation:

Since the bill is $68.50, and Jim wants to tip 18%, it will be $80.83 in total

18% = 0.18

since you don't want to DECREASE the bill, it's 1.18

1.18 x 68.5 = 80.83

hope this helped :)

Answer:

Step-by-step explanation:

a

Witch hat = 5

Jack o' lantern = 2

Ghost = 7

Witch Pot = 10

7 x 5 = 35 + 5 = 40

10 x 2 = 20 + 2 = 22

7 + 10 = 17 + 10 = 27

2 x 5 = 10 + 7 = 17

7 + 7 = 14 + 5 = 19

1. 7x5+5=40

2. 10x2+2=22

3. 7+10+10=27

4. 2x5+7=17

5. 7+7+5=19

Answer: 56

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

(p = 2)     = -2

Step-by-step explanation:

Answer:

4hrs 7 minutes and 30 seconds

Step-by-step explanation:

1 7/8 = (1=60) + (7/8 * 60) = 1 : 52:50 time played with Tommy   1 3/4 = (1=60 ) ( (3/4 * 60) = 1:45:00 time played with Nathan   3/2 = (3/2 *60) = 90 = 1:30:00 time played with Chris    Total played with 3 friends = 1:52:50 + 1:45:00+1:30:00= 4:07:50 = 4hrs 7 minutes and 30 seconds

Answer:

[tex]x=-4[/tex]

Step-by-step explanation:

[tex]2(x+6)=4~(Given)\\\\2x+12=4~(Distribute~2~to~x+6)\\\\2x+12-12=4-12~(Subtract~12~on~both~sides)\\\\2x=-8~(Simplify)\\\\\frac{2x}{2}=\frac{-8}{2}~(Divide~2~on~both~sides)\\\\x=-4~(Simplify)[/tex]

Answer:

[tex]\boxed {x=-4}[/tex]

Step-by-step explanation:

[tex]2(x+6)=4[/tex]

Divide both sides by 2 :

Subtract 6 from both sides:

______________________

Answer: y = $35 & 3 weeks

Step-by-step explanation:

Answer:

A) 3 week

B) $35

Step-by-step explanation:

$20-$5=15

$20+$15=35

Answer:

Step-by-step explanation:

h = 3 ft

l*b = 25 sq.ft

Volume = l*b *h

             = 25 * 3

             = 75 cubic feet

Answer:

75ft

Step-by-step explanation:

First you mupilply  [tex]25 x 3 = 75ft[/tex]

and that is it.

Answer:

Third Option: [tex]x=6[/tex] or [tex]x=-3[/tex]

Step-by-step explanation:

[tex]x^2+9x+18=0[/tex]

[tex](x+6)(x+3)=0[/tex]

[tex]x=6[/tex] or [tex]x=-3[/tex]

Answer:

there is not any correct answer among the options.

the answer is

[tex] \frac{ - 21}{45} [/tex]

Simplify the expression!

-7/15

Answer:

x= 17.5

y= 35

Step-by-step explanation:

Steps are in attachment.

Answer:

• For x (Acute angle property)

[tex]{ \rm{(2x + 10) \degree + 30 \degree + 6x=180 \degree}} \\ \\ { \rm{8x + 40=180}} \\ \\ { \rm{8x = 140}} \\ \\ { \boxed{ \underline{ \rm{ \: \: x =17.5 \: \: }}}}[/tex]

• For y ( Interior angle sum of triangles )

[tex]{ \rm{(y + 10) \degree + 6x \degree + 30 \degree = 180 \degree}} \\ \\ { \rm{y + 10 + 30 + (6 \times 17.5) = 180}} \\ \\ { \rm{y +145 = 180 }} \\ \\ { \boxed{ \underline{ \rm{ \: \: y = 35 \: \: }}}}[/tex]

Answer:

Commutative Property

Step-by-step explanation:

Hope it helps. Please mark me brainliest if you would :D

Answer:

1) 14/3 (D)

2) -0.6 (C)

Step-by-step explanation:

1) 5-(2/3)*(2/3//4/3)

2)|-1.2-2.03|-2.03/-2

Answer:

Line a. goes to table 3, line b. goes to table 2, and line c. goes to table 1.

Step-by-step explanation:

Here are the 3 lines graphed (I even labeled each for you) so you can have a bit of a visual.

Hopefully you can find the points on each graph.

(Hint: The x row represents the x coordinate of an ordered pair, and the y row represents the y coordinate of an ordered pair.)

Ordered pairs look like this btw (x,y)

Hope this helps :)

Answer:

Write properties of function:

x intercept/zero: x = 0

Step-by-step explanation:

Write properties of function: Write properties of function:

x intercept/zero:  x = 0

Answer: Write properties of function:

x intercept/zero: x = 0

Answer:

3

Step-by-step explanation:

Answer:

0,1,2,3,4

Step-by-step explanation:

trustttttt meee

Answer:

60%

Step-by-step explanation:

You could make a fraction to help solve for the answer. The denominator is 25 because you add 4 + 15 + 6. The numerator is 15, because it is the number of roses. 15/25 as a percent is 60% because you just times both the numerator and denominator by 4.

Answer:Cell content

Started at 20° and dropped 4° each minute                      -4

Cell content

Started at −20° and rose 1° each minute                              1

Cell content

Started at 20° and dropped 1° each minute                       -1

Cell content

Started at −20° and rose 4° each minute                             1

Step-by-step explanation:

Answer:

Cell content

Started at 20° and dropped 4° each minute                      -4

Cell content

Started at −20° and rose 1° each minute                              1

Cell content

Started at 20° and dropped 1° each minute                       -1

Cell content

Started at −20° and rose 4° each minute                             1

Step-by-step explanation:

Answer:

24-20   311-310     107-110

Step-by-step explanation:

Answer:

nearest tenth

......

24= 20

311=310

107=110..........

Answer:

y= 4/3x+2

Step-by-step explanation:

the y intercept is at 2 and you do rise over run for m

Answer:

9

Step-by-step explanation:

Answer:

If you are doing the same assignment as me then you probably have to choose between either Chanel or Preston and if my math is correct than the right answer would be Chanel.