Consider the following figure:

Answer:

[tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

1) Convert [tex]4\frac{1}{3}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]\frac{4\times3+1}{3} -1\frac{2}{3}[/tex]

2) Simplify 4 * 3 to 12.

[tex]\frac{12+1}{3}[/tex]

3) Simplify 12 + 1 to 13.

[tex]\frac{13}{3} -1\frac{2}{3}[/tex]

4) Convert [tex]1\frac{2}{3}[/tex]   to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]\frac{13}{3} -\frac{1\times3+2}{3}[/tex]

5) Simplify 1 * 3 to 3.

[tex]\frac{13}{3} -\frac{3+2}{3}[/tex]

6) Simplify 3 + 2 to 5.

[tex]\frac{13}{3} -\frac{5}{3}[/tex]

7) Join the denominators.

[tex]\frac{13-5}{3}[/tex]

8) Simplify.

[tex]\frac{8}{3}[/tex]

9) Convert to mixed fraction.

[tex]2\frac{2}{3}[/tex]

(Decimal Form: 2.666667)

Thank you,
Eddie

If the formula, =MID("ABCDEFGHI",3,4) is used, the result yielded would be CDEF.

When using the =MID function on a spreadsheet, the number after the text in the formula would show the position of the text from the left that the function would begin to count from.

The text in the third position from the left as shown in ABCDEFGHI is C so we need to start counting from letter C.

The second number in the function would then show the number of texts that needs to be counted and selected from the row of letters. That number is 4.

So from the letter C, you'll count 4 letters including the letter C itself.

The result you get would therefore be C, D, E, F which are the four letters from C.

In conclusion, the formula =MID("ABCDEFGHI",3,4) would yield the result, "C, D, E, F,."

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The number of years she had her investment is after 3 years

From the question, the given parameters are:

The number of years (T) is calculated from the following simple interest formula

I = PRT

Substitute the given parameters in the above equation

20.64 = 400 * 1.72% * t

Express 1.72% as decimal without percentage

20.64 = 400 * 0.0172 * t

Evaluate the product

20.64 = 6.88 * t

Divide both sides by 6.88

20.64/6.88 = 6.88/6.88 * t

Evaluate the quotient

3 = t

Rewrite the equation as

t = 3

This means that she had her investment after 3 years

Hence, the number of years she had her investment is after 3 years

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Answer:

  14(cos(125°) +i·sin(125°))

Step-by-step explanation:

The product of two complex numbers is the product of their magnitudes at an angle equal to the sum of their angles.

For A = a·cis(α) and B = b·cis(β), the product AB is ...

  AB = (a·cis(α))·(b·cis(β)) = ab·cis(α+β)

where "cis(x)" stands for the sum (cos(x) +i·sin(x)).

The product of interest is ...

  Z1·Z2 = (7cis(15°))·(2cis(110°)) = (7·2)cis(15°+110°)

  Z1·Z2 = 14cis(125°) = 14(cos(125°) +i·sin(125°))

Based on the given task content about the average hourly rate, Dominique's average hourly rate is $0.26.

Average hourly rate = Regular rate of Dominique's payment ÷ Number of hours worked

= $14 / 54 hours

= 0.25925925925925

Approximately,

Average hourly rate = $0.26

Therefore, Dominique's average hourly rate is $0.26

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Answer:

18

Step-by-step explanation:

For this problem, you have to look at the ratios of the corresponding sides.

Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18

Answer:

290 + 5m = 985

Step-by-step explanation:

Given information:

From the given information, we can create the following equation:

Initial payment plus extra amount each month for 5 months equals total payment.

⇒ 290 + 5m = 985

To solve the equation:

Subtract 290 from both sides:

⇒ 290 + 5m - 290 = 985 - 290

⇒ 5m = 695

Divide both sides by 5:

⇒ 5m ÷ 5 = 695 ÷ 5

⇒ m = 139

Therefore, the extra amount George paid each month was $139.

Answer: [tex]\Large\boxed{290+5m=985}[/tex]

Step-by-step explanation:

Given information

Initial cost = $290

Total cost = $985

Number of months = 5 months

Cost each month = ?

Set variable

Let [ m ] be the cost each month

The equation in verble sense

Initial paid + Extra each month = Total cost

Convert verbal equation to mathematical sense

$290 + 5m = $290

Therefore, to find the extra amount paid each month, the equation is [tex]\Large\boxed{290+5m=985}[/tex]

---------------------------------------------------------------------------------------------------------

EXTRA The following will be solving the derived equation, please ignore this part if it is useless for you.

Given equation

290 + 5m = 985

Subtract 290 on both sides

290 + 5m - 290 = 985 - 290

5m = 695

Divide 5 on both sides

5m / 5 = 695 / 5

m = $139

Hope this helps!! :)

Please let me know if you have any questions

The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;

D = 6371 + (343)×2

Hence, we have; diameter, D = 7057 km.

Hence, the distance travelled after 8 revolutions is;

C = 8 × πd

C = 8 × 3.14 × 7057

C = 177,271.8 km.

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The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units

As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.

Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).

Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)

Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).

Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).

This is the coordinates for A'.

Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.

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Area equals Length times Width.

since the width of this equation is 5 units Longer then its Length

W = L + 5

To put this area in a equation we could say

L(L+5)=A
Simplify the equation, L^2 + 5L = A.

Step-by-step explanation:

this just means that the first function with input value x = 0 is calculated. that result becomes the input value x for the second function. and that result becomes the input value x for the 3rd function. and that result is then our result.

to answer a and b we only need to look at the main operation of each function :

the first one uses only basic multiplication and subtraction.

the second one uses squaring.

the third one is a 1/x operation.

a.

since the final result is a negative number (-31), the second function with the square operation cannot be last.

because a square operation always delivers a positive result.

+a × +a = +a²

-a × -a = +a²

remember, for a square operation we multiply the same number by itself. therefore we cannot mix signs like -a × +a, because then they would not be the same numbers anymore.

b.

since the initial input value is 0, the third function (1/x) cannot be the first, because 1/0 is not defined.

c.

because of the "large" -32 term in the first function I guess that this will be the last one to create such a low negative result of -31.

since 1/x cannot be first, (x - 2)² is then first. that makes 1/x second, and (4x - 32) third, as mentioned.

let's try :

x = 0

(x - 2)² = (0 - 2)² = (-2)² = 4

x = 4

1/x = 1/4

x = 1/4

4x - 32 = 4×1/4 - 32 = 1 - 32 = -31

hurrah ! we are correct !

The inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]x=g(y)=-\frac{y}{3}+1[/tex].

Here, the given function is [tex]f(x)=-3x+3[/tex].

Then we get:

[tex]y=-3x+3\\\Longrightarrow x=-\frac{y}{3}+1[/tex]

Thus, the inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]g(x)=-\frac{x}{3}+1[/tex].

The graph representing this inverse function is given as follows:

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Answer:

252

Step-by-step explanation:

using a brute force method in c++

#include <stdio.h>

int main(){

int a, b, c, n = 0;

for(a = 1; a <= 9; a++)

 for(b = 0; b <= 9; b++)

  for(c = 0; c <= 9; c++)

   if((a==3 || b==3 || c==3)) n++;

printf("%d\n", n);

}

Answer:

It is a rational number.

Step-by-step explanation:

A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.

Hi :)

Below is the difference between rational & irrational numbers

Evidently,

Let's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]

Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.

Thus

[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

y=2

-5(2)²-3(2)-2

-5(4)-3(2)-2

-20-6-2

=12

Katrina would pay less amount of interest on the nonsubsidized student loan

The total interest paid on the nonsubsidized loan is $3,860.80

What is monthly compounding?

Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.

In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.

In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:

FV=PV*(1+r/n)^(n*t)

FV=balance after 2 years=unknown

PV=loan amount

r=annual interest rate

n=number of times interest is compounded annually=12

t=number of years before repayments commence=2

Non-subsidized loan:

FV=$29,000*(1+2.5%/12)^(12*2)

FV=$30,485.28

Subsidized loan:

FV=$29,000*(1+4.5%/12)^(12*2)

FV=$31,725.71

Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly  payments would occur at the end of each month:

PV=PMT*(1-(1+r)^-N/r

PV=balance of loan after 2 years

PMT=monthly payment=unknown

r=monthly interest rate=annual interest rate/12

N=number of monthly payments in 6 years=12*6=72

Non-subsidized loan:

$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)

PMT=$456.40

total monthly payments=$456.40*72

total monthly payments=$32,860.80

Interest= total monthly payments-loan

interest=$32,860.80-$29,000

interest=$3,860.80

Subsidized loan:

$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)

PMT=$503.61

total monthly payments=$503.61 *72

total monthly payments=$36,259.92

Interest= total monthly payments-loan

interest=$36,259.92 -$29,000

interest=$7,259.92

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Answer:

[tex]y=\dfrac{8}{7}x - \dfrac{23}{7}[/tex]

Step-by-step explanation:

Rearranging the terms, we get [tex]7y=8x-23[/tex]. Dividing both sides by 7, we get [tex]\dfrac{7y}{7} = \dfrac{8x-23}{7}[/tex], so [tex]\boxed{y=\dfrac{8}{7}x - \dfrac{23}{7}}[/tex]

Answer:

y = [tex]\frac{8}{7}[/tex]x -[tex]\frac{23}{7}[/tex]

Step-by-step explanation:

You are changing this to the slope-intercept form of a line.

y = mx + b

8x -7y = 23  Subtract 8x from both sides of the equation

-7y = -8x + 23  Divide both sides of the equation by -7

y = [tex]\frac{-8}{-7}[/tex]  - [tex]\frac{23}{7}[/tex]  

[tex]\frac{-8}{-7}[/tex] is the same as [tex]\frac{8}{7}[/tex]

y = [tex]\frac{8}{7}[/tex]x - [tex]\frac{23}{7}[/tex]

The dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height if the storage shed is to be built in the shape of a box with a square base.

It is defined as a three-dimensional space enclosed by an object or thing.

It is given that:

A storage shed is to be built in the shape of a box with a square base.

It is to have a volume of 729 cubic feet.

Let x be the length of the base

Let y be the height of the box.

V = 729 cubic feet

The base is square:

l = w = x

V = x²y

y =  729/x²

Cost of the base = $8x²

Cost of the roof = 3x²

Cost of the sides = 4(5.50)xy

= 22xy

Total cost

C= 8x² + 3x² + 22xy

C = 11x² + 22x(729/x²)

C = 11x² + 16038/x

Find the first derivative:

dC/dx = 22x - 16038/x²

Equate; dC/dx = 0

22x - 16038/x² = 0

22x = 16038/x²

22x³ =16038

x³ = 729

x = 9

y = 729/(9)² = 9

Length of base = 9 ft

Width of base  = 9 ft

Height of box = 9 ft

Thus, the dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height.

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The third side of the triangle falls between (50, 60).

Inequality triangle theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, the other two sides are 5 cm and 55 cm. The range of the third side x can be computed using inequality triangle theorem.

Hence,

x < 5 + 55

x < 60

And,

x > 55 - 5

x > 50

Therefore, 50 < x < 60.

Hence, the third side of the triangle falls between (50, 60).

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Answer: None of these are correct

Step-by-step explanation:

I believe that the equation is showing transitive property.

Answer:

f(–5)=–4

Step-by-step explanation:

as it is defined

1. The sentences translated to equations looks like:

a) 4x = 32.

b) x + 6y = 43.

c) 3x + 7 = 9x - 4.

d) 76 - 2x = 8x.

2. The equations translated to sentences looks like:

a) The sum of 16 and 9 times x is 50.

b) The sum of the square of x and 6 times y is 4 times w.

c) Three times x is 52.

d) Five-sixth is equal to the product of -10 and x.

Practice Part 1: Translate sentence to equation

a)Four times a number is thirty-two.

Assuming the number to be x, we get the equation, 4x = 32.

b)The sum of and six times  is equal to forty-three.

The sentence, when translated to an equation looks like, x + 6y = 43.

c)The sum of 7 and three times  equals the difference of 9 times  and 4.

The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.

d)Two times  less than 76 is equal to the product of 8 and

The sentence, when translated to an equation looks like, 76 - 2x = 8x.

Practice Part 2: Translate equation into sentence

a) 9x + 16 = 50.

- The sentence for the given equation is, the sum of 16 and 9 times x is 50.

b) x² + 6y = 4w.

- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.

c) 3x = 52.

- The sentence for the given equation is, three times x is 52.

d) 5/6 = -10x.

- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.

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Answer:

  x = 23; not extraneous

Step-by-step explanation:

A solution is extraneous if it does not satisfy the original equation. Extraneous solutions can sometimes be introduced in the process of solving radical and rational function equations.

Squaring both sides of the given equation, we get ...

  √(3x +12) = 9

  3x +12 = 81 . . . . . . square both sides

  x +4 = 27 . . . . . . . divide by 3

  x = 23 . . . . . . . . . . subtract 4

There is only one solution, and it satisfies the equation:

  √(3×23 +12) = √81 = 9

The solution x = 23 is not extraneous.

Answer: x = 23; not extraneous

Step-by-step explanation:

1. The master budget variance for July was $3,900, and this variance was favorable.

2. The July sales volume variances in terms of contribution margin and operating income are $2,800 F and $3,900 F, respectively.

3. The July flexible-budget variances in terms of contribution margin and operating income are $5,550 F and $6,650 F, respectively.

4.  Flexible budgets for the following output levels are:

                                                     3,560 units        3,980 units

Sales revenue                           $53,400               $59,700

Variable manufacturing costs     14,240                  15,920

Fixed manufacturing costs         12,460                   13,930

Variable selling and

administrative expenses             7,120                    7,960

Fixed selling and

administrative expenses            9,100                     9,100

Operating Income                   $10,480                $12,790

                                             Actual Master      Budget   Per Unit  Variance

Units                                               3,500          4,000                          500 U

Sales revenue                          $ 54,300    $ 60,000       $15.00  $ 5,700 U

Variable manufacturing costs    10,000         16,000          4.00     6,000 F

Fixed manufacturing costs         13,000         14,000          3.50      1,000 F

Variable selling and

administrative expenses            6,500           8,000         2.00      1,500 F

Contribution margin               $24,800       $22,000                    $2,800 F

Fixed selling and

administrative expenses           8,000            9,100                        1,100 F

Total costs                              $37,500        $47,100

Operating income                  $16,800        $12,900                    $3,900 F

Sales volume variance:

Revenue per unit                   $15.51            $15.00         $0.51 F

                                             Actual Master      Budget    Variance

Units                                               3,500          3,500            U

Sales revenue                          $ 54,300    $ 52,500       $ 1,800 F

Variable manufacturing costs    10,000         14,000         4,000 F

Fixed manufacturing costs         13,000         12,250            750  U

Variable selling and

administrative expenses            6,500           7,000           500 F

Contribution margin               $24,800        $19,250      $5,550 F

Fixed selling and

administrative expenses           8,000            9,100          1,100 F

Operating income                  $16,800         $10,150      $6,650 F

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Quadrilateral is a family of plane shapes that have four straight sides. Thus the sum of their internal angles is [tex]360^{o}[/tex]. Examples include rectangle, square, rhombus, trapezium, and kite.

A kite is a plane shape that has its adjacent sides to have equal measures.

The given diagram in the question is a kite that has its specific properties compared to other quadrilaterals.

Thus, the required proof is stated below:

Given: ΔCAV and ΔCEV

Prove that: ΔCAV ≅ ΔCEV

Then,

CE ≅ CA (length of side property of a kite)

EV ≅ AV (length of side property of a kite)

<ACV ≅ <ECV (bisected property of a given angle)

<AVC ≅ <EVC (bisected property of a given angle)

CV is a common side to ΔCAV and ΔCEV

Therefore it can be deduced that;

ΔCAV ≅ ΔCEV (Angle-Angle-Side congruent theorem)

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Put the equation in standard linear form.

[tex]x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}[/tex]

Find the integrating factor.

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5[/tex]

Multiply both sides by [tex]\mu[/tex].

[tex](t+5) x'(t) + x(t) = 5(t+5)e^{5t}[/tex]

Now the left side the derivative of a product,

[tex]\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}[/tex]

Integrate both sides.

[tex](t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt[/tex]

On the right side, integrate by parts.

[tex](t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C[/tex]

Solve for [tex]x(t)[/tex].

[tex]\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}[/tex]

Answer:

5/16

Step-by-step explanation:

assuming you mean 5(1/2) = 8x

5(1/2) is the same as 5/2

so, 5/2 = 8x

5 = 16x

x= 5/16

El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.

En esta pregunta debemos encontrar el volumen remanente entre el espacio de una caja cúbica y una esfera introducida en el elemento anterior. El volumen remanente es igual a sustraer el volumen de la pelota del volumen de la caja.

Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:

Cubo

V = l³

V = (4 cm)³

V = 64 cm³

Esfera

V' = (4π / 3) · R³

V' = (4π / 3) · (2 cm)³

V' ≈ 33.5103 cm³

Segundo, determinamos la diferencia de volumen entre los dos elementos:

V'' = V - V'

V'' = 64 cm³ - 33.5103 cm³

V'' = 30.4897 cm³

El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.

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Answer:

54°

Step-by-step explanation:

Opposite angles of a parallelogram are congruent, so;

[tex]9x+9=8x+14 \\ \\ x=5 \\ \\ m\angle S=9(5)+9=54^{\circ}[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

In a Parallelogram, opposite angles are equal, so we infer that :

[tex] \qquad❖ \: \sf \:9x + 9 = 8x + 14 [/tex]

[tex] \qquad❖ \: \sf \:9x - 8x = 14 - 9[/tex]

[tex] \qquad❖ \: \sf \:x = 5 \degree[/tex]

Next,

Measure of Angle S is :

[tex] \qquad❖ \: \sf \:9x + 9[/tex]

[tex] \qquad❖ \: \sf \:9(5) + 9[/tex]

[tex] \qquad❖ \: \sf \:45 + 9[/tex]

[tex] \qquad❖ \: \sf \:54 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]