Find the missing side lengths.

Step-by-step explanation:

Principal Amount = $150,000

Rate of appreciation per year = 6%

Appreciated amount = $150,000×6/100

= 6×1500 = $9,000 per year

in 7 years(2020) , the appreciated amount becomes = $9000×7yrs

= $63,000

Thus the value in 2020 = $150,000+$63,000

= $213,000

Answer:

a₅ = 37

Step-by-step explanation:

The term to term rule ' subtract 3 ' is the common difference d of an arithmetic sequence with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁₂ = 16, then

a₁ + 11d = 16 ← substitute d = - 3

a₁ + 11(- 3) = 16

a₁ - 33 = 16 ( add 33 to both sides )

a₁ = 49 , then

a₅ = 49 + (4 × - 3) = 49 - 12 = 37

The measure of each angle are

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

<4 = 134

So, <4 = <2 = 134 (Vertical opposite angle)

<4= <8= 134 (Corresponding Angle)

<1 + <4 = 180 (Linear Pair)

<1 = 180-134

<1 = 46

<1 = <3= 46 (Vertical opposite angle)

<2= <6= 164 (Corresponding Angle)

<3= <7 (Corresponding Angle)

<1= <5 (Corresponding Angle)

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Answer:

25ml of wallpaper remover

Step-by-step explanation:

(y = amount of wallpaper remover)

4500×4 = 18000

18000:600

750    : y

18000y = 600×750

18000y = 450000

y = 450000÷18000

y = 25

Answer:

5 hours

Step-by-step explanation:

Let x represent the amount of hours that ralph can do.

Let y represent the money he earned.

Let m represent how much he earns per hour.

Let b represent the initial fee

y=mx+b

y=33x + 24

189=33x+24

Solve for x:

189=33x+24

165 = 33x

x=5

Answer:

750 J

Step-by-step explanation:

Answer:

It will be worth about £885.59.

Step-by-step explanation:

The art piece originally costs £600.

And it appreciates at a rate of 3.97% each year.

And we want to find the value of the art after 10 years.

We can write an exponential function to model the situation. The standard exponential function is given by:

\(f(t)=a(r)^t\)

Where t is the time in years.

Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.

103.97% = 1.0397. So, r = 1.0397:

\(f(t)=a(1.0397)^t\)

Our a is the initial value. Therefore:

\(f(t)=600(1.0397)^t\)

Then the value of the piece of art after 10 years is:

\(f(t)=600(1.0397)^{10}=885.5879...\approx \pounds 885.59\)

It will be worth about £885.59 after 10 years.

Answer:

885.59

Step-by-step explanation:

1. 600 + 23.82

2. 623.82 + 24.77

3. 648.59 +25.75

4. 674.34 + 26.77

5. 701.11 + 27.83

6. 728.94 + 28.94

7. 757.88 + 30.09

8. 787.97 + 31.28

9. 819.25 + 32.52

10. 851.77 + 33.82

After 10 years the art valued for 885.59 British Pounds.

Answer:

Step-by-step explanation:

 8,000  

+ 700  

+ 80  

+ 5  

The number n = 8,785 in expanded form is A = (8 x 1000) + (7 x 100) + (8 x 10) + (5 x 1)

Brackets should be expanded in the following ways to factorize an expression

For an expression of the form A = a ( b + c ) , the expanded version is given by A = ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket

For an expression of the form A = ( a + b ) ( c + d ) , the expanded version is given by A = ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Given data ,

Let the expression be represented as A

Now , the value of A is

n = 8,785

Now , the value of n in the expanded form is given by factorizing ,

8,785 in expanded form is:

8,000 + 700 + 80 + 5

or

(8 x 1000) + (7 x 100) + (8 x 10) + (5 x 1)

Hence , the expression is A = (8 x 1000) + (7 x 100) + (8 x 10) + (5 x 1)

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The circumference of a circle with diameter 379 can be found using the formula:

C = πd

where d is the diameter of the circle. Substituting the given value of d, we get:

C = 3.14 x 379

C ≈ 1191.06

Rounding to the hundredths place, the circumference is approximately 1191.06 units of length (e.g. inches, centimeters, etc.).

Therefore, the answer to fill in the blank is 1191.06.

Answer:Gemma has more bottle caps.

Step-by-step explanation:

The limit of the given function as x approaches infinity is infinity.

To find the limit of the given function as x approaches infinity, we need to analyze the behavior of the function for very large values of x.

First, we can observe that the term 49x^2 dominates the other terms in the function as x gets very large. This is because the square of any number grows much faster than a linear function (x) or a constant function (-7x).

Therefore, we can simplify the given function as follows:

lim x→[infinity] (49x^2 + x − 7x) = lim x→[infinity] 49x^2

Now we can directly evaluate the limit by applying the rule that states if a function is of the form ax^n where a and n are constants and x approachesinfinity, then the limit is infinity if n > 0 and negative infinity if n < 0.

In this case, a = 49 and n = 2, which is greater than 0. Therefore, the limit as x approaches infinity is infinity.

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Answer:

33

I hope this helps!

Answer:

B

Step-by-step explanation: I just did it on edge

Answer:

The answer is B.

Remark

We have to figure out which of the graphs is not linear if they were graphed.

Eliminations

The last one is the graph of

y = 22 - 2x which is still a straight line.

D is linear.

The second last one is the table for

y = 3x which is a straight line going through the origin.

The second from the top is not easily deciphered.

The line I get is y = - x - 3 which is linear or a straight line.

The top one is

y = x^2 which is not linear at all

Answer A <<<<<

The work done the force is determined as -4·xy  +  4y - 4x.

The work done the force is determined from the dot product of the force and displacement of the object.

Mathematically, the formula for work done is given as;

W = F·d

where;

The displacement of the object is calculated as follows;

d = (-3, 3 ) - (1, - 1)

d = (-3 - 1, 3 - - 1)

d = (-4, 4)

The given force;

F = xyi + (y - x)j

The dot product of the force and displacement is calculated as;

W = F.d

W = -4·xy  +  4y - 4x

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Starting with part a, question (i):

Find the average rate of change in both populations between 2002 and 2012.

Recall that the average rate of change of a function f(x) in the interval [ a, b] is given by the quotient:

rate of change = ( f(b) - f(a) ) / (b - a)

Therefore, for our population P1 case on the years 2002 and 2012 we have:

[ P1(2012) - P1(2002) ] / (2012 - 2002) = [62 - 42] / 10 = 20 / 10 = 2

for population P2 we have:

22 [72 - 82] /10 = -10/10 = -1

You can proceed doing the same process for the other cases (ii) and (iii).

Case (ii)Now part b of the problem:

Rate of change between 2002 and 2019:

99 [ 76 - 42] / ( 17) = 534 / 17 = 2

2(929 9[ 65 - 82] / 17 = -17 / 17 = -1

Case (iii)

Rate of change between 2007 and 2019:

9797 [76 - 52] / 12 = 24/12 = 2

22 [65 - 77] / 12 = -12 / 12 = -1

We see that the rates of change for each population remained constant over the years.

What we noticed in the table regarding both populations, is that while population P1 is increasing over the years, population P2 is going down in numbers year after year.

We can say therefore that P1 is INCREASING, while P2 is DECREASING. And that the rate of change they experienced was constant over the years.

Answer:

3/20

Step-by-step explanation:

There are 60 children in a club. In the club, the ratio of the number of girls to the number of boys is 3:1

Step 1

We find the number of girls and boys

The ratio is given as:

Girls : Boys

3:1

The sum of Proportion = 3 + 1 = 4

The number of girls

= 3/4 × 60 children

= 45 girls

The Number of boys

= 1/4 × 60 children

= 15 boys

Step 2

From the question, we are told:

3/5 of the girls play a musical instrument.

The number of girls that play Instruments is calculated as:

3/5 × Number of girls

= 3/5 × 45 girls

= 27 girls

4/5 of the boys play a musical

instrument.

The number of boys that play Instruments is calculated as:

4/5 × Number of boys

= 4/5 × 15 boys

= 12 boys

Step 3

The fraction of the 60 children that play a musical instrument is calculated as:

Sum of boys and girls that play a musical instrument/ 60 children

= 27 girls + 12 boys/60

= 39/60

= 3/20

The fraction of the 60 children that play a musical instrument is 3/20

Answer: 250 ≤ 100+5x

150≤5x divide by 5

30≤x

It will take 30 weeks to earn enough.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

f=120p

f=120(16)

f= 1920

Answer:

74 pounds

Step-by-step explanation:

g=2s

b=s+5

b=42

s=b-5

=42-5

=37

g=2×37

=74 pounds

Used the names as letters and work in an algabraic way.

The best answer that describes the meaning of the multiplicities next to the number 1 in the preceding diagram is: the number 1 represents the solution that repeats thrice.

A multiplicity is a mathematical concept used to describe the number of times a value appears as a root of a polynomial equation. The number of times a specific value appears as a root of a polynomial is referred to as the multiplicity of that value.

In the given diagram, the number 1 represents the solution of the equation x = 1. The multiplicities of the number 1 are represented by the number 3.

Therefore, the number 1 has a multiplicity of 3. This means that the solution of the equation x = 1 repeats thrice. This can be better understood by looking at the graph of the equation.

The graph of the equation x = 1 is a vertical line that intersects the x-axis at 1.

Since the equation has a multiplicity of 3, the vertical line intersects the x-axis three times.

This means that the point (1, 0) occurs three times on the graph. This is shown in the diagram as three dots along the x-axis.

Therefore, the meaning of the multiplicities next to the number 1 in the preceding diagram is that the number 1 represents the solution that repeats thrice.

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Answer:

3.54x10^1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The approximations for the integral ∫₀² \(e^x\) / (1 + x²) dx using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with n = 10 are:

Trapezoidal Rule: 2.308664

Midpoint Rule: 2.362634

Simpson's Rule: 2.335206

Trapezoidal Rule:

Using the Trapezoidal Rule formula:

∫₀²\(e^x / (1 + x^2) dx = (h / 2) [f(0) + 2f(0.2) + 2f(0.4) + ... + 2f(1.8) + f(2)]\)

where h = 0.2 is the width of each subinterval.

We evaluate \(f(x) = e^x / (1 + x^2)\) at each subinterval midpoint:

\(f(0) = e^0 / (1 + 0^2) = 1\\f(0.2) = e^{0.2} / (1 + 0.2^2)\\f(0.4) = e^{0.4} / (1 + 0.4^2)\\...\\f(1.8) = e^{1.8} / (1 + 1.8^2)\\f(2) = e^2 / (1 + 2^2)\)

Substituting the values into the formula:

∫₀² \(e^x / (1 + x^2) dx = (0.2 / 2) [1 + 2f(0.2) + 2f(0.4) + ... + 2f(1.8) + f(2)]\)

Evaluating each term and summing them up:

∫₀² \(e^x / (1 + x^2) dx = (0.2 / 2) [1 + 2(1.221402) + 2(1.298464) + ... + 2(3.425647) + 7.389056]\)

Round the final result to six decimal places:

∫₀² \(e^x / (1 + x^2) dx = 2.308664\)

Midpoint Rule:

Using the Midpoint Rule formula:

∫₀² \(e^x\) / (1 + x²) dx ≈ h [f(x₁/₂) + f(x₃/₂) + ... + f(xₙ₋₁/₂)]

where h = 0.2 is the width of each subinterval.

Evaluating f(x) = \(e^x\) / (1 + x²) at each midpoint:

f(0.1) ≈ \(e^{0.1}\) / (1 + 0.1²)

f(0.3) ≈ \(e^{0.3}\) / (1 + 0.3²)

...

f(1.9) ≈ \(e^{1.9}\) / (1 + 1.9²)

Substituting the values into the formula and summing them up:

∫₀² \(e^x\) / (1 + x²) dx ≈ 0.2 [f(0.1) + f(0.3) + ... + f(1.9)]

Round the final result to six decimal places:

∫₀² \(e^x\) / (1 + x²) dx ≈ 2.362634

Simpson's Rule:

Using Simpson's Rule formula:

∫₀² \(e^x\)/ (1 + x²) dx ≈ (h / 3) [f(0) + 4f(0.2) + 2f(0.4) + 4f(0.6) + ... + 2f(1.8) + 4f(2)]

where h = 0.2 is the width of each subinterval.

Evaluating f(x) = \(e^x\)/ (1 + x²) at each point:

f(0) ≈ \(e^0\) / (1 + 0²) = 1

f(0.2) ≈ \(e^{0.2}\) / (1 + 0.2²)

f(0.4) ≈ \(e^{0.4}\) / (1 + 0.4²)

...

f(1.8) ≈ \(e^{1.8}\) / (1 + 1.8²)

f(2) ≈ \(e^2\)/ (1 + 2²)

Substituting the values into the formula and summing them up:

∫₀² \(e^x\) / (1 + x²) dx ≈ (0.2 / 3) [1 + 4f(0.2) + 2f(0.4) + 4f(0.6) + ... + 2f(1.8) + 4f(2)]

Round the final result to six decimal places:

∫₀² \(e^x\) / (1 + x²) dx ≈ 2.335206

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Answer:  Selling price, x, = 8.3333 units

Step-by-step explanation:

We can find the vertex by one of two methods:

1)  Take the derivative of the equation and set it to zero.  The derivative gives us the slope at any point x.  The vertex has a slope of zero (it changes direction).

y=-6x^2 + 100x– 180

y' = -12x + 100

0 = -12x + 100

12x = 100

x = 8.333

2) Graph the function and locate the vertex.  Attached.

The vertex of the parabola is (8.33, 236.66).

A plane curve produced by a moving point such that its separation from a fixed point equals that of a fixed line is a parabola.

Given, the expression;

y = -6x² +100x - 180,

where x = selling price of each soccer ball and y = daily profit from soccer balls.

A parabola's vertex is the location where its symmetry line and parabola intersect.

To find the vertex of a parabola:

Step  1: Compare the equation of the parabola with the standard form

y = ax² + bx + c.

By comparing,

y = -6x² +100x - 180 with the above equation, a = -6, b = 100, and c =-180.

Step - 2: Find the x-coordinate of the vertex using the formula,

h = -b/2a

Then we get,

h = -(100) / (2 × -6)

h = 8.33

Step - 3: To find the y-coordinate (k) of the vertex,

substitute x = h in the expression, y = -6x² +100x - 180.

Then k = -6(8.33 x 8.33) + 100(8.33) -180

k = 236.66

Step - 4: Write the vertex (h, k) as an ordered pair.

The vertex = (h, k) = (8.33, 236.66).

Therefore, (8.33, 236.66) is the vertex of the parabola.

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Answer:

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

The greatest value of the function is - 3.

Hi :)

We'll use sohcahtoa to solve this problem

\(\large\boxed{\boxed{\begin{tabular} {c|1} \sf{ Sohcahtoa} & \sf{Formulas} \\\cline{1-2} \\\ \sf{Soh} & \sf{Opp/hyp} \\\sf{Cah} & \sf{Adj/hyp} \\\sf{Toa} & \sf{Opp/adj} \end{tabular}}}}\)

Thus

The function that equals \(\sf{\dfrac{7}{25}}\) besides \(\sin B\) is :

\(\tt{Learn\:More;Work\;Harder}\)

:)

Answer:

Step-by-step explanation:

I need the statements please.

A. K = 0. B. No value. No value of K can make ab=ba, since a and b are not equal.

A. K = 1. When k = 1, ab = ba because the product of any two numbers is the same regardless of the order in which they are multiplied.

B. No value. If k is not equal to 1, then ab will not be equal to ba. This is because the order in which numbers are multiplied affects the product. For example, if a = 2 and b = 3, then ab = 6 and ba = 6. However, if k = 2, then ab = 12 and ba = 18, which are not equal.

It is important to note that the commutative property of multiplication states that the product of any two numbers is the same regardless of the order in which they are multiplied. This means that ab = ba for any values of a and b. However, the question is asking for the values of k that will make ab = ba, so we must consider the effect of k on the product of a and b.

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