Mindy has already saved $20 and plans to save $8 each month.Georgette has no money saved yet but plans to to save $5 each month.Will the girls ever have saved the same amount?

Answer:

(i)  [tex]64+192 x^2+240 x^4+160x^6[/tex]

(ii) 1072

Step-by-step explanation:

Part (i)

Using Binomial series formula:

[tex](2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3[/tex]

              [tex]=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6[/tex]

              [tex]=64+192 x^2+240 x^4+160x^6[/tex]

Part (ii)

[tex](1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})[/tex]

               [tex]=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}[/tex]

[tex](2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)[/tex]

[tex]=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...[/tex]

There is no need to keep expanding since the remaining will include the variable.

Therefore, the term independent of x = 64 - 1152 + 2160 = 1072

Answer:

x = - 4

Step-by-step explanation:

i hope its helped. thank you !

Answer:

4/8 or 1/2 rows

Step-by-step explanation:

Hope this helps! ^^

Answer:

F = mg

Step-by-step explanation:

g is the constant of proportionality and force is the product of mass and the acceleration due to gravity

f is directly proportional to m, therefore, f = mg

10

solve:

14 - (2(x) - y)

given x : 3, y : 2, insert the following

[tex]\\ \rm\rightarrowtail 14-(2x-y)[/tex]

[tex]\\ \rm\rightarrowtail 14-2x+y[/tex]

[tex]\\ \rm\rightarrowtail 14-2(3)+2[/tex]

[tex]\\ \rm\rightarrowtail 14-6+2[/tex]

[tex]\\ \rm\rightarrowtail 10[/tex]

Answer:

25

Step-by-step explanation:

First expression: A= k/M

when A = 15 and M = 5, k = A×M = 75

therefore, when M = 4, A = 75/3 = 25

Answer:

23

Step-by-step explanation:

Compatible numbers : numbers that are easy to add, subtract, multiply, or divide mentally.  They are close in value to the actual numbers, although they do not necessary need to be rounded numbers.

-138 is close to -137.56

-6 is close to -6.12

[tex]\implies \dfrac{-138}{-6}[/tex]

Divide the top and bottom by -2:

[tex]\implies \dfrac{69}{3}[/tex]

Divide the top and bottom by 3

[tex]\implies 23[/tex]

If this is too difficult to divide mentally, you could use -140 and -7:

[tex]\implies \dfrac{-140}{-7}[/tex]

As 2 x 7 = 14, then 20 x 7 = 140, so the answer is 20.

Answer:

24

Step-by-step explanation:

The the triangles are similar, the lengths of corresponding sides are in proportion.

15/20 = 18/n

3/4 = 18/n

1/4 = 6/n

n = 4 × 6

n = 24

Answer:

n = 24

Step-by-step explanation:

In similar triangles, corresponding sides are in same ratio.

[tex]\dfrac{n}{18}=\dfrac{20}{15}\\\\\\n=\dfrac{20}{15}*18\\\\\\n = 4*6\\\\n = 24[/tex]

Answer:

Step-by-step explanation:

f(x)=x^4-11x^2-80=x^4-16x^2+5x^2-80

=x²(x²-16)+5(x²-16)

=(x²-16)(x²+5)

=(x-4)(x+4)[x²-(-5)]

=(x-4)(x+4)[x^2-(5i²)]

=(x-4)(x+4)(x-√5 i)(x+√5 i)

so zeros are 4,-4,√5 i,-√5 i

Answer:

g = -3, h = 4.

Step-by-step explanation:

5h - 2g = 26

2h + 2g = 2      Adding the 2 equations:

7h = 28

h = 4.

Substituting for h in the first equation:

5(4) - 2g = 26

-2g = 26 -20 = 6

g = -3.

Step-by-step explanation:

1 case = 24 bottles

365 cases = 365×24 = 8,760 bottles

The miles Peyton's family had travelled when he fell asleep is 770 miles

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.

Miles when Peyton fell asleep = 77% x 1000 = 770 miles

To learn more about percentages, please check: https://brainly.com/question/25764815

Answer: 55.2 cm^2

Step-by-step explanation:

2(4x2.5 + 2.5x1.2 + 1.2x4) = 35.6 cm^2

(2x1.2x4 + 4x2.5) = 19.6 cm^2

(35.6 + 19.6) = 55.2 cm^2

Answer:

Depends on whether you're looking for area or perimeter. Follow the equations below

Step-by-step explanation:

This depends on whether you're being asked to find perimeter of area

Perimeter is equal to 2(length) + 2(width)

In which case perimeter would be 2(4 + w) + 2(w)

Which can be simplified to 8 + 2w + 2w = 4w + 8

However, Area is equal to length times width

Which would be (4 + w) * w = 4w + w^2

Answer:

Step-by-step explanation:

✔ w(4 +w) = 60

The expression for the simplified total gas used is 1.43x.

let the gas used on the way to camp "x"

Then the gas used on the way back can be calculated as follows:

360 / 420 × 0.5 × x

To calculate the total fuel used, We need to add this to the 'x' used on the way.

Therefore,

total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x

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Answer:

14.50

Step-by-step explanation:

i took the quiz on k12 truse me i wish luck

The IQR for these data is 6.25.

Answer choice A is correct.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

To find the IQR, we first need to find the first and third quartiles.

First, we need to order the data from smallest to largest:

10.5, 11, 11.5, 14.5, 14.5, 17, 17, 18, 19

Next, we find the median (middle value) of the data set.

Since we have an odd number of data points, the median is the middle number, which is 14.5.

To find the first quartile (Q1), we need to find the median of the lower half of the data set.

That is, we need to find the median of 10.5, 11, 11.5, and 14.5.

The median of this subset is (11 + 11.5) / 2 = 11.25.

To find the third quartile (Q3), we need to find the median of the upper half of the data set.

That is, we need to find the median of 17, 17, 18, and 19.

The median of this subset is (17 + 18) / 2 = 17.5.

Now we have the first quartile (Q1) = 11.25 and the third quartile (Q3) = 17.5. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

= 17.5 - 11.25

= 6.25

Therefore,

The IQR for these data is 6.25.

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[tex]\text{Let the 3 consecutive numbers be}~ x,~x+1~ \text{and} ~x+2.\\\\\text{According to the condition,}\\\\x+x+1+x+2 = 1146\\\\\implies 3x +3 = 1146\\\\\implies 3(x+1) = 1146\\\\\implies x+1 = \dfrac{1146}3 = 382\\\\\implies x= 382-1 = 381\\\\\text{Now, the numbers are}~ 381,~382~\text{and}~383[/tex]

Answer:

Step-by-step explanation:

Both sin(41) and cos(x) can be represented by the ratio b/c

If the sum of two angles is equal to 90 degrees, then such angles are called complementary angles. The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle. Example:

   40° is the complement of 50°.

   50° is the complement of 40°.

sin (41) = b/c

cos (x) = b/c

∴both sin(41) and cos(x) can be represented by the ratio b/c

x + 41 = 90 (∵ complementary angles)

x = 90-41 = 49

∵ sin 41 = cos x

∴ sin 41 = cos (90-41)

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Answer:

Perimeter=36in

Length of one side=12

Length of the other side=12

Width of one side=6

Width of the other side=6

Step-by-step explanation:

6*2=12, so if the length is 12 half would be six. All of them added up is 36

Answer:

Step-by-step explanation:

[tex]perimeter \: of \: a \: rectangle = 2(2x) + 2(x) \\ 36in = 4x + 2x = 6x \\ \frac{36in}{6} = \frac{6x}{6} \\ x = 6in \\ 2x = 2 \times 6in = 12in[/tex]

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Answer:

The container will hold 190 ft^3 of volume of substance.

if the question means it.

Answer:

Step-by-step explanation:

Scale:- 1box=1units

So

Take one side of each

Scale factor(A to B)

[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]

#6

Scale factor (A to B)

[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]

Scale factor (B to A)

[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]

Answer:

[tex]~[/tex]

Step-by-step explanation:

In given right angled traingle:

[tex]~[/tex]

In ∆ABC,

[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {AC}{AB} = \sin35° \\[/tex]

[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {20}{x} = 0.5736 \\[/tex]

[tex]\: \: \: \: \dashrightarrow \: \: \: \sf x = \dfrac {20}{0.5736} \\[/tex]

[tex]\: \: \: \:{ \pmb{ \pink{ \sf{ \dashrightarrow \: \: \: { x = 34.867 }}}}}[/tex]

Hence,

Total deduction

Now

Earnings after deduction

Total hours:-

You will have to work 110.5 hours to buy the new computer.

A tax is some specific financial amount or some other charged taxpayer by the government in order to fund government spending.

Given is that you have to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are -

FICA (7.65%),

Federal tax withholding (12%)

State tax withholding (8%).

Total money earned after all the deductions -

A{n} = 10 - {7.65% of 10 + 12% of 10 + 8% of 10}

A{n} = 10 - {7.65/100 x 10 + 12/100 x 10 + 8/100 x 10}

A{n} = 10 - {7.65/10 + 12/10 + 8/10}

A{n} = 10 - 2.765

An = 7.235

Cost of new computer = $800.

For 1 hour. you earned $7.235.

Then, you will earn $1 in (1/7.235) hours

So, you will earn $800 in (1/7.235 x 800) = 110.5

Therefore, you will have to work 110.5 hours to buy the new computer.

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Answer:

please see photo for details

Answer:

5b

Step-by-step explanation:

Hope this helps <3

let's recall that d = rt, or namely distance = rate * time.

b = speed of the boat

c = speed of the current

now, we know that going downstream the boat went 16 miles total, that's going only one way, so the distance the boat travels downstream as well as upstream to return is 16 miles flat.

when going downstream, the boat is not really going at "b" speed, is really going at "b + c" speed, because the current is adding its speed to it, so is really going faster than "b".

when going upstream, the boat is not really going at "b" speed" either, is really going slower at "b - c" speed, because the current is against it and thus subtracting speed from "b".

let's take a look at those in a table

[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Downstream&16&b+c&2\\ Upstream&16&b-c&4 \end{array}\qquad \qquad \begin{cases} 16=(b+c)(2)\\\\ 16=(b-c)(4) \end{cases} \\\\\\ \stackrel{16}{(b+c)(2)}~~ = ~~\stackrel{16}{(b-c)(4)}\implies 2b+2c~~ = ~~4b-4c\implies 2c=2b-4c[/tex]

[tex]6c=2b\implies \cfrac{6c}{2}=b\implies \boxed{3c=b} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{16~~ = ~~(\stackrel{b}{3c}+c)(2)}\implies 16=4c(2)\implies 16=8c \\\\\\ \cfrac{16}{8}=c\implies \blacktriangleright \stackrel{mph}{2}=c \blacktriangleleft~\hspace{10em}3(2)=b\implies \blacktriangleright \stackrel{mph}{6}=b \blacktriangleleft[/tex]

Answer:

x= -28

Step-by-step explanation:

1. First you have to add 14 to both sides to get the x by itself. That's always the first thing you have to do. Get x by itself.

2. After that, you should have -x= 28. You can't leave it like that because it is still not simplified. It's basically saying 28 is the opposite of x. What's the opposite of positive? Negative.

3. Therefore, your final answer should be -28

Answer:

x = -28

Step-by-step explanation:

Hey! First, lets establish our equation :)

-14 -x = 14

Now, we are going to get our x alone on a single side, to do this, we are going to add 14 to both sides to be able to cut out -14 on the left side!

-14 -x = 14

+14      +14

     -x = 28

The last thing we have to do is divide both sides by -1 to get x by itself without it being negative!

-x = 28

÷-1  ÷-1

x = -28

So, x, is equal to -28 (negative 28!) :)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Hello! I believe your answer is x= -4 so B

===

Hope this helps and feel free to give feedback

Answer:

x = -4

Step-by-step explanation:

Answer:

Right angle (90°)

Step-by-step explanation:

Because, main Street and Oak Street are crossing each other at 90°.

Hope it helps you in your learning process.

Answer:

right angle

Step-by-step explanation:

because they're perpendicular lines