A line is definitely by the equation y = -x + 3 which shows the graph of this line ?

Answer:

B. Square both sides of the equation.

Step-by-step explanation:

You cannot do anything to the equation unless you square both sides to eliminate the square root on the left (squaring each individual term of the equation does not help; you need to square the entire square root to eliminate it).

Hope this helps!

Answer: 752

Step-by-step explanation:

Given that,

Margin of error = 3% = 0.03

confidence level = 90% = 0.90

therefore from the z-table

z = 1.645

Now since no prior estimate of p is given, so we say p = 0.5

Sample size required will be

n = 1.645² × 0.5 ×(1-0.5) / 0.03² = 751.67

n = 751.67 ≈ 752

[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]

Answer:

1/13

Step-by-step explanation:

Answer:

I always factor out the -1 so my leading coefficient is 1

Step-by-step explanation:

-x^2 + 10x -24

I always factor out the -1 so my leading coefficient is 1

-1 ( x^2 -10x +24)

Then what 2 terms multiply to 24 and add to -10

-6*-4 = 24

-6+-4 = -10

-1( x-6)(x-4)

The company must produce and sell 350 dishwashers in order to maximize profit.

To determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.

The profit (P) is given by the equation:

P(x) = Revenue - Cost

The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):

Revenue = p * x

The cost is given by the function C(x):

Cost = C(x)

Therefore, the profit function can be expressed as:

P(x) = p * x - C(x)

Substituting the given expressions for p and C(x):

P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)

Expanding and simplifying the equation:

P(x) = 420x - 0.3x² - 5000 - 0.3x²

Combining like terms:

P(x) = -0.6x² + 420x - 5000

To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:

x = -b / (2a)

In our case, a = -0.6 and b = 420:

x = -420 / (2 * -0.6)

x = -420 / (-1.2)

x = 350

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350 dishwashers must the company produce and sell in order to maximize profit.

Maxima means a point at which the function attains the maximum value.

Given the following information:

Price per dishwasher, p = 420 - 0.3x

Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2

Profit= Total Selling price- Total Cost Price

Total Selling price of x dishwasher, S.P= xp

S.P=x(420 - 0.3x)

S.P=420x - 0.3x²

Profit= 420x - 0.3x² - ( 5000 + 0.3x²)

Profit= 420x - 0.3x² - 5000 - 0.3x²

Profit=  -0.6x²+420x-5000

So, profit, f(x)=-0.6x²+420x-5000

To determine the value of x so that maximum profit is possible:

1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.

2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.

[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]

Calculating the value of x by transposing,

x=420/1.2

x=350

To check maxima, calculating second derivative.

[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]

2nd derivative is negative, it means that x=350 is the point of maxima.

Thus, a company must produce and sell 350 dishwashers in order to maximize profit.

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Answer:

25 students

Step-by-step explanation:

Given the equation of the best line of fit, [tex] y = 0.677x + 1.77 [/tex] , the number of students predicted to be in the matching band, if we have 35 students in the concert band, can be approximated by plugging in 35 as "x" in the equation of the best line of fit, and solve for "y". y would give us the predicted number of students to expect in the marching band.

[tex] y = 0.677(35) + 1.77 [/tex]

[tex] y = 23.695 + 1.77 [/tex]

[tex] y = 25.465 [/tex]

The approximated number of to be in the marching band, with 35 students in the concert band is roughly 25 students.

Answer:25 students

Step-by-step explanation:

Answer:

x=5y-3

Step-by-step explanation:

[tex]4x+12=20y\\4x=20y-12\\x=\frac{20y-12}{4} \\x=\frac{20y}{4}- \frac{12}{4} \\x=5y-3[/tex]

Answer:

Monthly Loan Payment

Loan Amount (P) = $6,000

Monthly Interest Rate (n) = 0.75% per month [9.00% / 12 Months]

Number of months (n) = 36 Months [3 Years x 12 months]

Monthly Loan Payment = [P x {r (1+r)n} ] / [( 1+r)n – 1]

= [$6,000 x {0.0075 x (1 + 0.0075)36}] / [(1 + 0.0075)36 – 1]

= [$6,000 x {0.0075 x 1.308645}] / [1.308645 – 1]

= [$6,000 x 0.009815] / 0.308645

= $58.89 / 0.308645

= $190.80

Monthly Loan Amortization Schedule

“Therefore, the total interest paid during the first year will be $465.99”

HOPE this example helps

Answer:

11 / 12 or 0.9167

Step-by-step explanation:

Given:

3/4 + 1/6

Find:

Value with expression

Computation:

"3/4 added to number 1/6"

3/4 + 1/6

By taking LCM

[9 + 2] / 12

11 / 12 or 0.9167

Answer:

4 2/3 :)

Step-by-step explanation:

The total paint in the bucket in the simplified mixed fraction is [tex]6\frac{2}{3}[/tex] pints.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A housepainter mixed [tex]3\frac{1}{2}[/tex] pints of blue paint in a bucket with [tex]1\frac{1}{6}[/tex] pints of white paint.

So, The total paint in the bucket is the sum of the pints of both paints which

is, = [tex](3\frac{1}{2} + 1\frac{1}{6})[/tex] pints.

[tex]= (\frac{7}{2} + \frac{7}{6})[/tex] pints.

[tex]= \frac{21 + 7}{6}[/tex] pints.

[tex]= \frac{28}{6}[/tex] pints.

[tex]= 6\frac{2}{3}[/tex] pints.

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Answer:

The answer is option 2.

Step-by-step explanation:

Quadratic function is always written in the form of ax² + bx + c where the highest power of x is 2.

In the options above :

Option 1 is Cubic function.

Option 2 is Quadratic function.

Option 3 and 4 are Linear function.

Answer:

I guess....

Step-by-step explanation:

option 2............

Answer:

The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Step-by-step explanation:

A firm has the​ marginal-demand function [tex]D' x = \dfrac{-1200}{\sqrt{25-x^2 } }[/tex].

Find the demand function given that D = 16,000 when x = $4 per unit.

What we are required to do  is to find the demand function D(x);

If we integrate D'(x) with respect to x ; we have :

[tex]\int\limits \ D'(x) \, dx = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

Let represent   t  with [tex]\sqrt{25-x^2}}[/tex]

The differential of t with respect to x is :

[tex]\dfrac{dt}{dx}= \dfrac{1}{2 \sqrt{25-x^2}}}(-2x)[/tex]

[tex]\dfrac{dt}{dx}= \dfrac{-x}{ \sqrt{25-x^2}}}[/tex]

[tex]{dt}= \dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]

replacing the value of  [tex]\dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]  for dt in   [tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

So; we can say :

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits{\dfrac{- x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits \ dt[/tex]

[tex]D(x) = 1200t+ C[/tex]

Let's Recall that :

t  = [tex]\sqrt{25-x^2}}[/tex]

Now;

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex]

GIven that:

D = 16,000 when x = $4 per unit.

i.e

D(4) = 16000

SO;

[tex]D(x) = 1200(\sqrt{25-x^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-4^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-16}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{9}})+ C[/tex]

[tex]D(4) = 1200(3}})+ C[/tex]

16000 = 1200 (3) + C

16000 = 3600 + C

16000 - 3600 = C

C = 12400

replacing the value of C = 12400 into [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex], we have:

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

∴ The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Answer:

Step-by-step explanation:

Fog=2(g)+1

2(3x+2+4)+1

2{3x+6)+1

6x+12+1

=6x+13

Fog(-2)=6(-2)+13

-12+13

=1

Gof=3(f)+2+4

=3(2x+1)+6

6x+3+6

=6x+9

Gof(-2)=6(-2)+9

-12+9

=-3

Answer:

Expected Value of $2:

Expected Value of $2:

Win, 0.3333 x $3 = $1

Plus

Loss, 0.6667 x -$2 = -$1.33

Expected value = ($0.33)

Step-by-step explanation:

Probability of a win = 2/6 = 0.3333

Probability of a loss = 4/6 = 0.6667

Expected Value of $2:

Win, 0.3333 x $3 = $1

Plus

Loss, 0.6667 x -$2 = -$1.33

Expected value = ($0.33)

The casino game player's expected value is computed by multiplying each of the possible outcomes by the likelihood (probability) of each outcome and then adding up the values.  The sum of the values is the expected value, which amounts to a loss of $0.33.

Answer:

25872 ways

Step-by-step explanation:

We're choosing 5 women from a group of 11 and 3 men from a group of 8. We don't care about what order they are picked and so we'll use the combination formula, which is:

n!/(k!)(n-k)! with n as population and k as picks.

We'll multiply the results together. (8! / (3!)(8-3)!) * (11! / (5!)(11-5)!)

That equals: (8! / (3!)(5!) ) * (11! / (5!)(6!)) = 40320/(6x120) * 39916800/ (120x720)

56 * 462 = 25872

Answer:

a = 10 1/4

Step-by-step explanation:

So with the following equation,

4/5a - 8 = 1/5,

we need to use the commutative property.

Which is the moving of whole numbers or variables.

So we add 8 to both sides.

4/5a = 41/5

Divide 4/5 by both sides

a = 10 1/4

So on of the equations could look like a = 10 1/4

Thus,

a = 10 1/4 could be one of the equations given which are equal to 4/5a - 8 = 1/5.

Hope this helps :)

Answer:

[tex]\huge\boxed{a=\dfrac{41}{4}=10\dfrac{1}{4}=10.25}[/tex]

Step-by-step explanation:

[tex]\dfrac{4}{5}a-8=\dfrac{1}{5}\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup\cdot\dfrac{4}{5\!\!\!\!\diagup}a-(5)(8)=5\!\!\!\!\diagup\cdot\dfrac{1}{5\!\!\!\!\diagup}\\\\4a-40=1\qquad\text{add 40 to both sides}\\\\4a-40+40=1+40\\\\4a=41\qquad\text{divide both sides by 4}\\\\\dfrac{4a}{4}=\dfrac{41}{4}\\\\a=10.25[/tex]

Answer:

0.65463

Step-by-step explanation:

From the given question:

It is stated that 2% of the parts are defective (D) out of 50 parts

Therefore the probability of the defectives;

i.e  p(defectives) = [tex]\dfrac{N(D)}{N(S)}[/tex]

p(defectives) = [tex]\dfrac{2}{50}[/tex]

p(defectives) = 0.04

The probability of the failure is the P(Non-defectives)

p(Non-defectives) =  1 - P(defectives)

p(Non-defectives) =  1 - 0.04

p(Non-defectives) =  0.96

Also , Let Y be the number of non -defective out of the 52 stock parts.

and we need Y ≥ 50

P( Y ≥ 50) , n = 52 , p = 0.96

P( Y ≥ 50) = P(50 ≤ Y ≤ 52) = P(Y = 50, 51, 52)

= P(Y = 50) + P(Y =51) + P(Y=52)    (disjoint events)

P(Y = 50) = [tex](^{52}_{50}) ( 0.96)^{50}(1-0.96)^2[/tex]

[tex]P(Y = 50) = 1326 (0.96)^{50}(0.04)^2[/tex]

P(Y = 50) = 0.27557

P(Y = 51) =[tex](^{52}_{51}) ( 0.96)^{51}(1-0.96)^1[/tex]

[tex]P(Y = 51) = 52(0.96)^{51}(0.04)^1[/tex]

P(Y = 51) = 0.25936

(Y = 52) =[tex](^{52}_{52}) ( 0.96)^{52}(1-0.96)^0[/tex]

[tex]P(Y = 52) = 1*(0.96)^{52}(0.04)^0[/tex]

P(Y = 52) = 0.1197

∴

P(Y = 50) + P(Y =51) + P(Y=52) = 0.27557 + 0.25936 + 0.1197

P(Y = 50) + P(Y =51) + P(Y=52) = 0.65463

Answer:

[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]

Step-by-step explanation:

1 dime = 10 cents

1 nickel = 5 cents

So,

If there are 15 dimes

=> 15 dimes = 15*10 cents

=> 15 dimes = 150 cents

=> 15 dimes = $1.5

Rest is $0.5

So, for $0.5 we have 10 nickels coins

=> 10 nickels = 10*5

=> 10 nickels = 50 cents

=> 10 nickel coins = $0.5

Together it makes $2.00

Answer:

The answer would be 27π

Step-by-step explanation:

the area is 36pi and the shaded region is 3/4 of the circle, as a 90 degree angle is 1/4 of a 360 degree circle. 3/4 of 36pi is 27pi

Answer:

27π

Step-by-step explanation:

Imagine that this circle was complete. As you can see, only 3 / 4th of the circle remains, with respect to this whole circle. This is not an assumption, though it does appear so. The portion missing forms a right angle with the radii, and thus by definition, that portion is a quarter of a circle.

________

The simplest approach is to assume this circle to be complete, and solve for that area - provided the radii being 6 inches. Afterward we can take 3 / 4th of this area, solving for the area of the shaded region. After all, this circle is 3 / 4ths of our " complete circle. "

Area of an Imaginary " Complete Circle " = π[tex]r^2[/tex] = π[tex](6)^2[/tex] = 36π,

Area of Shaded Region ( 3 / 4th of the " Complete Circle " ) = [tex]\frac{3}{4}[/tex]( 36π ) = 27π

27π is the exact area of the shaded region. If you want an approximated area, take π as 3.14, or a similar quantity to that.

Answer:

4x² + 30x - 2 = 0

Step-by-step explanation:

Given:

Area = 58 square feet

Width = 7 feet

Length = 8 feet

Since the area is 58, writing the equation, we have:

(8 + 2x)(7 + 2x) = 58

Now expand the equation:

56 + 16x + 14x + 4x² = 58

56 + 30x + 4x² = 58

Collect like terms:

30x + 4x² + 56 - 58 = 0

30x + 4x² - 2 = 0

Rearrange the equation to a proper quadratic equation:

4x² + 30x - 2 = 0

The quadratic equation that can be used to determine the thickness of the frame, x is 4x² + 30x - 2 = 0

Answer:

853.8cm^3

Step-by-step explanation:

[tex]h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3[/tex]

Answer:

26^7=8 031 810 176

Step-by-step explanation:

The word has 7 letters. So the word have 7 places where any of 26 letters can be placed.

Any of 26 letters can stay at 1st place

Any of 26 letters can stay at 2-nd place (because letters can be repeated)

Any of 26 letters can stay at 3rd place  

Any of 26 letters can stay at 4th place

Any of 26 letters can stay at 5th place

Any of 26 letters can stay at 6th place

Any of 26 letters can stay at 7th place  

So N= 26*26*26*26*26*26*26=26^7=8 031 810 176

Answer:

the percentage of people who have an IQ between 115 and 140 is 16.79%

Step-by-step explanation:

From the information given:

We are to  determine the percentage of people who have an IQ between 115 and 140.

i.e

P(115 < X < 140) = P( X  ≤ 140) - P( X  ≤ 115)

[tex]P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})[/tex]

[tex]P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})[/tex]

[tex]P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})[/tex]

[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)[/tex]

[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)[/tex]

From Z tables :

[tex]P(115 < X < 140) = 0.9938-0.8259[/tex]

[tex]P(115 < X < 140) = 0.1679[/tex]

Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%

Using the normal distribution, it is found that 82.02% of people who have an IQ between 115 and 140.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The proportion of people who have an IQ between 115 and 140 is the p-value of Z when X = 140 subtracted by the p-value of Z when X = 115, hence:

X = 140:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140 - 100}{16}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a p-value of 0.9938.

X = 115:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{115 - 100}{16}[/tex]

[tex]Z = -0.94[/tex]

[tex]Z = -0.94[/tex] has a p-value of 0.1736.

0.9938 - 0.1736 = 0.8202.

0.8202 = 82.02% of people who have an IQ between 115 and 140.

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Answer:

It is a weak negative correlation, and it is likely causal.

Step-by-step explanation:

Correlation coefficient can be said to be a statistical value that shows the relationship between two variables.

Here, the correlation coefficient is 0.26 which means that the magnitude of correlation is low and it causes a weak correlation.

Here, since one variable increases as the other variable decreases, the correlation is said to be negative and weak. We can see that the more a player golf's, the lower the number to required strokes. This would result in a negative slope.

Therefore, It is a weak negative correlation, and it is likely

causal.

Answer:

The correct answer is B on edge 2020.

Step-by-step explanation:

Answer:

The full production costs are:

ABC = $22,900,000

PQR = $1,700,000

Step-by-step explanation:

Traditional costing method is a costing method that allocates or applies overhead based on a particular metric determined by a company. It therefore add both direct cost of production and production overheads absorbed to obtain the full cost of production.

Since production overheads in this question is absorbed on demand sales basis, the full production costs for ABC and PQR can be computed as follows:

ANZ Corporation

Computation of Full Production Costs

Particulars                                      ABC                 PQR    

Sales demand                             30,000             15,000

Cost                                                   $                        $    

Direct cost:

Direct materials cost (w.1)        1,350,000           900,000

Direct labor cost (w.2)                900,000          600,000  

Total direct cost                     22,500,000        1,500,000

Indirect cost:

Production overhead (w.3)        400,000          200,000

Full production cost            22,900,000        1,700,000

Workings:

w.1: Computation of direct material cost

Direct material cost = Direct material cost per unit * Sales demand

Therefore;

ABC Direct material cost = $45 * 30,000 = $1,350,000

PQR Direct material cost = $60 * 15,000 = $900,000

w.2: Computation of direct labor cost

Direct labor cost = Direct labor cost per unit * Sales demand

Therefore;

ABC Direct material cost = $30 * 30,000 = $900,000

PQR Direct material cost = $40 * 15,000 = $600,000

w.3: Allocation of production overhead

Production overheads allocated to a model = Production overheads * (Model's Sales Demand / Total Sales demand)

Total Sales demand = 30,000 + 15,000 = 45,000

Therefore, we have:

Production overhead allocated to ABC = $600,000 * (30,000 / 45,000) = $400,000

Production overhead allocated to PQR = $600,000 * (15,000 / 45,000) = $200,000

Answer:

105°

Step-by-step explanation:

Supplementary angle of 75° = 180° - 75° = 105°

Answer:

105°

Step-by-step explanation:

angle given is 75°

= 180° - 75°

= 105°

Hey there! :)

Answer:

118 children

58 students

59 adults

Step-by-step explanation:

We can solve this problem by setting up a system of equations:

Let a = adults

2a = children (since double the # of adults were children), and

s = students

Set up the equations:

1704 = 5(2a) + 7s + 12(a)

1704 = 10a + 7s + 12a

235 = 2a + a + s

Simplify the equations:

1704 = 22a + 7s

235 = 3a + s

Subtract the bottom equation from the top by multiplying the bottom equation by 7 to eliminate the 's' variable:

1704 = 22a + 7s

7(235 = 3a + s)

1704 = 22a + 7s

1645 = 21a + 7s

---------------------- (Subtract)

59 = a

This is the number of adults. Substitute this number into an equation to solve for the number of students:

235 = 3(59) + s

235 = 177 + s

s = 58.

Since the number of children is equivalent to 2a, solve:

2(59) = 118 children.

Therefore, the values for each group are:

118 children

59 adults

58 students.

Answer:

adults: 59, students:58 and children 118

Step-by-step explanation:

let A for adults, and C = children and S for students

There are half as many adults as there are children=

A=C/2 , C=2A

A+C+S=235 or

A+2A+S=235 first equation

3A+S=235

12A+5C+7S =1704 or

12A+10A+7S=1704

22A + 7S=1704 second equation

3A+S=235 first

solve by addition and elimination

22A+7S=1704

21 A+7S=1645 subtract two equations

A=59 adults

C=2A=2(59)=118

substitute in :A+S+C=235

S=235-(118+59)=58

check: 5C+7S+12A=1704

5(118)+7(58)+12(59)=1704

Answer:

-1

Step-by-step explanation:

Thanks

The product of expression (2 + √5) (2 - √5) is,

⇒ (2 + √5) (2 - √5) = - 1

We have to given that,

An expression to simplify,

⇒ (2 + √5) (2 - √5)

Now, We can simplify it by using formula,

⇒ (a - b) (a + b) = a² - b²

Hence, We get;

⇒ (2 + √5) (2 - √5)

⇒ (2² - √5²)

⇒ 4 - 5

⇒ - 1

Therefore, The product of expression (2 + √5) (2 - √5) is,

⇒ (2 + √5) (2 - √5) = - 1

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Answer:

[tex]\huge\boxed{z=3}[/tex]

Step-by-step explanation:

If two polygons are similar, then corresponding sides are in proportion.

The corresponding sides:

4 → x

y → 15

3 → w

2 → 6

z → 9

therefore:

[tex]\dfrac{z}{9}=\dfrac{2}{6}[/tex]         cross multiply

[tex](z)(6)=(9)(2)[/tex]

[tex]6z=18[/tex]         divide both sides by 6

[tex]z=3[/tex]

Answer:

Step-by-step explanation: