Marsha is twice as old as Karli. The sum of their ages seven years ago was 13. How old
are they now?

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]

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:

a

Step-by-step explanation:

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:

[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: 56

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Answer:

Commutative Property

Step-by-step explanation:

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

Answer:

there is not any correct answer among the options.

the answer is

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

Simplify the expression!

-7/15

Answer:

(3b-2a)^2=9b^2-12ab+4a^2

Step-by-step explanation:

Using the formula (a-b)^2=a^2-2ab-b^2, you can plug in the values to get your answer. (Sorry I can't really explain more, it's just using the formula. 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:

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:

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:

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:

y= 4/3x+2

Step-by-step explanation:

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

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.

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:

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:

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:

hey I hope this is clear

Step-by-step explanation:

Answer:

2a^2

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:

24-20   311-310     107-110

Step-by-step explanation:

Answer:

nearest tenth

......

24= 20

311=310

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

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:(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: