Lulu observes that when she dilates a quadrilateral from a center of dilation outside the
quadrilateral, the corresponding sides of the original figure and its dilated image are
parallel. Which statement best explains why this occurs?

Answer:

To determine which investment option would yield the highest return, we can calculate the future value of each investment at a certain age. Let's assume we're looking at the value of each investment at age 65. Option 1: $50 initial investment with an average annual growth rate of 9% starting at age 30 Using a compound interest calculator, we can find that the future value of this investment at age 65 would be approximately $1,338. Option 2: $50 initial investment with an average annual growth rate of 8% starting at age 20 Again, using a compound interest calculator, we can find that the future value of this investment at age 65 would be approximately $1,088. Option 3: $100 initial investment with an average annual growth rate of 7% starting at age 25 Using the same calculator, we can find

0

The solution set of the given inequality is (-4, 4.4)

Here are the steps to follow when solving absolute value inequalities:

Isolate the absolute value expression on the left side of the inequality.

If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

|5t-1| > 21

case 1)

for positive

5t-1 > 21

5t > 22

t > 4.4

for negative

-(5t-1) > 21

-5t+1 > 21

-5t > 20

t< -4

hence the solution set of the given inequality is (-4, 4.4)

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Answer: To find the premium for insuring the goods, we need to determine the total amount of insurance that is needed and then calculate the cost of the insurance based on the given rate.

The total amount of insurance needed is equal to the value of the goods in transit, which is K95 480.

To determine the cost of the insurance, we can use the given rate of K682 for every K27 200 worth of goods. We can set up a proportion:

(K682 / K27 200) = (premium / K95 480)

To solve for the premium, we can cross-multiply and simplify:

K682 * K95 480 = K27 200 * premium

premium = (K682 * K95 480) / K27 200

premium = K1 897.12

Therefore, the premium for insuring the goods is K1 897.12.

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

We want to get an equation with only one variable for it to be able to be solved.

To do this, we will solve the first equation for y.

[tex]x+y=2\\y=2-x[/tex]

Now, we can plug this value of y into the second equation

[tex]7x-y=2\\7x-(2-x)=2\\[/tex]

Finally, we have just one variable, and we can solve for x.

[tex]7x-(2-x)=2\\7x-2+x=2\\8x=4\\x=0.5[/tex]

The period of the sinusoidal function is 4 seconds

The period of a wave is the time it takes for one complete cycle of the wave to occur. In other words, it is the time required for a wave to repeat itself exactly.

The period of a wave is typically denoted by the symbol "T" and is measured in units of time, such as seconds.

In the function plotted the time to complete one oscillation is solved to be 4 seconds

The solution is obtained by taking two successive crests or troughs

using two successive troughs we have

= 5 - 1

= 4

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The vertices οf the given inequalities are (2,0);(-6,0); (0,-1);(0,-3);(-2,-2)

In mathematics, inequality is  a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

The given system οf inequalities are:

2y-x≥ -2

2y+x≥ -6

y≤0

x≤0

Tο find the vertices we must cοnvert the inequality intο an equatiοn.

Sο the equatiοns are:

2y - x= -2-----------------(1)

2y + x= -6----------------(2)

y=0-----------------(3)

x=0 -----------------(4)

Putting the value οf equatiοn (3) in equatiοn (1) and (2) we get,

x=2 and x= -6

Again putting the value οf equatiοn (4) in equatiοn (1) and (2) we get,

y=-1 and y=-3

Sο frοm these the vertices can be written as (2,0);(-6,0) and (0,-1);(0,-3)

Nοw , subtracting equatiοn (2) frοm equatiοn (1) we get,

( 2y - x )-(2y+x)= -2-(-6)

⇒ -2x= 4

⇒x= -2

Putting this value x=-2 in equatiοn (1) we get,

2y-(-2)=-2

⇒2y+2=-2

⇒2y=-4

⇒ y= -2

Hence the vertices οf the given inequalities are (2,0);(-6,0); (0,-1);(0,-3);(-2,-2)

A graph fοr the inequalities is attached belοw.

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Answer:

272.14100

Subtract 47.96 from 320.041

320.041 - 47.96 = 272.14100

Answer:

272.081

Step-by-step explanation:

You're welcome

Answer:

74.43 pounds

Step-by-step explanation:

To find the amount of oxygen needed in the outer tank, we need to first find the volume of the space between the two tanks. This space is a rectangular prism with length 20 feet, width 8 feet, and height 6 feet, but with a rectangular prism removed from the center. The removed prism has length 5 feet, width 4 feet, and height 3 feet.

The volume of the rectangular prism between the two tanks is:

V = (20 x 8 x 6) - (5 x 4 x 3)

V = 960 - 60

V = 900 cubic feet

To find the amount of oxygen needed to fill this space with a density of 0.0827 pounds per cubic foot, we can multiply the volume by the density:

m = V x d

m = 900 x 0.0827

m ≈ 74.43 pounds

Therefore, approximately 74.43 pounds of oxygen is required to meet the density requirement.

Answer: 74 pounds

Step-by-step explanation:

(20*8*6) - (5*4*3)

960-60

v=900 ft3

density=0.0827

mass=0.0827*900

Mass is 74 pounds

It would take the giant tortoise approximately 21.43 hours to travel 3 miles at a rate of 0.14 miles per hour.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.

We can use the formula:

time = distance ÷ speed

where "distance" is the total distance to be traveled and "speed" is the rate of travel.

In this case, the distance is 3 miles and the speed is 0.14 miles per hour. So we can substitute these values into the formula and solve for "time":

time = 3 miles ÷ 0.14 miles per hour

time ≈ 21.43 hours

Therefore, it would take the giant tortoise approximately 21.43 hours to travel 3 miles at a rate of 0.14 miles per hour.

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The equation that can be used to find d, based on the options for the parts of the equation is; (4/5) × d = 260

An equation is a statement of equivalence between expressions.

The specified equation is;  _ _ d = _

The distance of the first part of Alicia's trip = 260 miles

The part of the total distance traveled of the trip represented by the first part of Alicia's trip = 4/5

The total length of Alicia's trip = d

An equation that can be used to find the total length of Alicia's trip therefore is; (4/5) × d = 260

The total distance traveled, d, can be obtained from the above equation when d is made the subject of the equation as follows;

(4/5) × d = 260

d = 260/(4/5) = 260 × 5/4 = 325

The total distance Alicia traveled, d = 325 miles

The correct equation is therefore; (4/5) × d = 260

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The two are similar because both use a percentage as a decimal to get a new price.

1. The function has x-intercepts at x = -2 and x = 3, so the answer is

A.(- 2, 0) * and(3, 0).

2. The y-values are increasing on the interval from x = -3 to x = -1, and from x = 1 to x = 3. So the answer is B, -3 < x < -1.

What is x-intercept?

1. To find the x-intercepts of the quadratic function, we need to find the values of x for which y is equal to 0.

The x-intercept of a function is the point at which the graph of the function intersects the x-axis. At the x-intercept, the value of y (the output of the function) is equal to zero, which means that the corresponding input value of x causes the function to have an output of zero.

From the table, we can see that the function has x-intercepts at x = -2 and x = 3, so the answer is A.

What is an interval?

2. To determine where the function is increasing, we need to look for intervals where the y-values are increasing as x increases.

From the table, we can see that the y-values are increasing on the interval from x = -3 to x = -1, and from x = 1 to x = 3. So the answer is B, -3 < x < -1.

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the radius of the track is approximately 420.38 feet.

Why is it?

The circumference of the circular track is 0.5 miles or 0.5 × 5280 = 2640 feet.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

Therefore, 2640 = 2 × 3.14 × r

Simplifying the equation: 2640 = 6.28r

Dividing both sides by 6.28: r ≈ 420.38 feet

Therefore, the radius of the track is approximately 420.38 feet.

Circumference is the distance around the edge of a circle or any other curved, circular object. It is also the perimeter of the circle. It is calculated by multiplying the diameter of the circle by pi (π), which is a mathematical constant that is approximately equal to 3.14.

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Answer:

17.2 meters

Step-by-step explanation:

We can use the tangent function to solve this problem. Let's denote the height of the tree as h. Then we have the following:

tan(51°) = h / distance from the tree to the end of the shadow

We can find the distance from the tree to the end of the shadow by using the length of the shadow and the angle of elevation of the sun. Since the shadow is 21 meters long, and the angle of elevation of the sun is 51°, we can use the following trigonometric relationship:

tan(51°) = h / distance from the tree to the end of the shadow

tan(51°) = h / x (where x is the distance from the tree to the end of the shadow)

To find x, we can use the following trigonometric relationship:

tan(39°) = h / x (where 39° is the complementary angle to 51°)

We can solve for x by rearranging this equation as follows:

x = h / tan(39°)

Substituting this expression for x into the first equation, we have:

tan(51°) = h / (h / tan(39°))

Simplifying this equation, we get:

h = (21 m) * tan(51°) / tan(39°)

Using a calculator, we find h to be the following:

h = 17.2 meters

Therefore, the height of the tree is approximately 17.2 meters.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.027}{2}\right)^{2\cdot 10}\implies A=4000(1.0135)^{20} \implies \boxed{A \approx 5230.40} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2 \end{cases} \\\\\\ \left(1+\frac{0.027}{2}\right)^{2}-1\implies 1.0135^2-1\approx 0.02718 ~~ \approx ~~ \stackrel{ 0.02718\times 100 }{\boxed{2.718~\%}}[/tex]

Answer:

  step 1

Step-by-step explanation:

You want to know which step in Marta's simplification of 4·log₅(x) +log₅(2x) -log₅(3x) contains an error in application of properties of logarithms.

  log(a^b) = b·log(a)

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  [tex]4\log_5(x)+\log_5(2x)-\log_5(3x)\\\\=\log_5(x^4)+\log_5(2x)-\log_5(3x)\qquad\text{Step 1. Mistake: $4x$ instead of $x^4$}\\\\\log_5(x^4\cdot2x)-\log_5(3x)=\log_5\left(\dfrac{2x^5}{3x}\right)\\\\=\boxed{\log_5\left(\dfrac{2x^4}{3}\right)}[/tex]

Answer:

Step-by-step explanation:

Problem: Imagine a person, John, facing a scheduling conflict due to overlapping appointments.

John had a dentist appointment at 2 PM, which he expected to last an hour, but he also had a meeting scheduled with his colleague at 3 PM.

Why it was difficult: The scheduling conflict made it difficult for John to manage both appointments without disappointing either party.
Math used to solve the problem: John decided to calculate the time it would take him to travel from the dentist's office to the meeting location, considering the appointment duration and travel time.
Dentist appointment: 2 PM - 3 PM

Travel time (calculated using distance and speed): 30 minutes
Meeting time: 3 PM
John realized he would be 30 minutes late for the meeting if he attended the dentist appointment.
Outcome: John decided to reschedule his dentist appointment to an earlier time or another day to avoid the conflict.
Approaching the problem differently next time:

In the future, John could consider using a calendar app to keep track of his appointments and avoid scheduling conflicts.

Additionally, he could factor in the duration of events and travel times when scheduling appointments to ensure he has enough time between engagements.

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Expectation of the gain for the given outcomes on rolling fair dice is:

E = $0.5

The total number of outcomes for such probability experiment is known as the total number of outcomes in probability.

For rolling sum 2 and 12 - {(1,1), (6,6)}

Total number of possible outcomes = 2 (that is 2 and 12)

As, either 2 or 12 will appear. So, there will be 1 gain and one loss.

Gain for rolling 2 or 12 is $12 and for loss $1

Gain = 12 - 1 = $11

For rolling sum 7  - {(1,6),(6,1),(2,5),(5,2),(4,3),(3,4)}

Gain for rolling 7  - $5 and for loss $1

Total number of possible outcomes = 6

Gain = 5 - 1 = $4

For others:

Total number of possible outcomes = 36 - (2+6) = 28

Loss = -$1

Expectation of total gain;

E = (2×11 + 6×4 - 28×1)/36 = 18/36

E = 1/2

E = $0.5

Thus, Expectation of the gain for the given outcomes on rolling fair dice is: E = $0.5

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Complete question:

At this year's State Falr, there was a dice rolling game. If you rolled two dice and got a sum of 2 or 12, you won $12. If you rolled a 7, you won $5. Any other roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent.

The expectation of this game is approximately dollars.

200.55ft³

12×12= 144 (area of the square)

pi×radius² = area of a circle but since it is only half a circle, divide the answer by two and add the area of the semi circle and square for the total area

The steps to find surface area of pyramid using a net of square pyramid is given below.

find the surface area of a square pyramid using a net:

The slant height of a square pyramid can be found using the Pythagorean theorem, where a and b are the length of one side of the base and h is the height of the pyramid:

slant height = √(a² + (1/2×h)²)

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1.Band A: Cost = $500

Band B: Cost $350 + $1.50x

2. The caterer's fixed cost is $150 and the rate per student served is $6.

3.Cost per ticket $12.50

4.we can buy at most 3 bouquets of roses.

What are linear equations?

The first-degree equations are linear equations. The straight line's equation can be found here. ax+by+c=0 is the most common form of a linear equation, where a and b are zeros.

Part 1:

Let x be the number of students.

Band A: Cost = $500

Band B: Cost $350 +$1.50x

The system of equations representing the cost of the two bands is:

CostA = 500

CostB = 350+ 1.5x

Part 2:

Let F be the fixed cost and R be the rate per student served.

From the given information, we can write two equations:

50R + F = 450

150R + F = 1050

Subtracting the first equation from the second, we

get:

100R = 600

Therefore, R = 6.

Substituting R in the first equation, we get:

50(6)+F450

Therefore, F = 150.

So, the caterer's fixed cost is $150 and the rate per student served is $6.

Part 3:

For 100 students:

CostA 500

CostB = 350+ 1.5(100) 500

Both bands have the same cost, but Band A has a lower variable cost.

So, we should choose Band A.

Total cost for 100 students = 500 + 150+ 6(100) =

$1250

Cost per ticket = Total cost / Number of students = 1250/100 = $12.50

For 200 students:

CostA = 500

CostB = 350+ 1.5(200) = 650

Band A still has a lower cost, so we should choose Band A.

Total cost for 200 students 500+ 150 + 6(200) = $1850

Cost per ticket = Total cost / Number of students =

1850/200 $9.25

Part 4:

Let D be the number of bouquets of daisies and R be the number of bouquets of roses.

The cost of daisies is $25 per bouquet and the cost of roses is $35 per bouquet. We want to spend no more than $500, so we can write:

25D +35R < 500

If we buy 15 bouquets of daisies, then we can spend at most $425 on roses:

25(15) + 35Rs 500

375 +35R ≤ 500

35R ≤ 125

If we buy 15 bouquets of daisies, then we can.

Mathematics College spend at most $425 on roses:

25(15)+35R ≤ 500

375 +35R≤ 500

35R ≤ 125

R≤ 3.57

So, we can buy at most 3 bouquets of roses.

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Answer:

the value of T that satisfies the equation 644 204 = 400 000(1+10%) is approximately 6.45.

Step-by-step explanation:

We can simplify the equation 644 204 = 400 000(1+10%) by first simplifying the percentage term on the right-hand side:

10% of 400 000 is equal to 0.1 × 400 000 = 40 000.

So the equation becomes:

644 204 = 400 000(1 + 0.1 × 1)

Now, we can use logarithms to solve for T:

T = log(base 1.1)(644204/400000)

Using a calculator, we can evaluate the right-hand side to be approximately 0.2, so:

T = log(base 1.1)(1.61051)

Using the change of base formula, we can rewrite this as:

T = ln(1.61051) / ln(1.1)

Evaluating the natural logarithms using a calculator, we get:

T ≈ 6.45

The scale factor of the dilation of the square is (b) 18 : 1

To find the scale factor, we need to determine how many times the length of the original square was multiplied to obtain the length of the new square.

The length of the original square is 4.5 meters, and the length of the new square is 81 meters.

Therefore, we need to divide the length of the new square by the length of the original square to find the scale factor:

81 meters ÷ 4.5 meters = 18

So the scale factor is 18:1.

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The equation of circle with endpoints at  (-3, 0) and (3, 0) is x² + y² = 9

The end points (-3, 0) and (3, 0) represent the endpoints of a diameter of the circle. The center of the circle is the midpoint of this diameter. We can find the midpoint of the diameter by averaging the x-coordinates and the y-coordinates of the endpoints:

Midpoint = ((-3 + 3)/2, (0 + 0)/2) = (0, 0)

So the center of the circle is at the point (0, 0). The radius of the circle is half the length of the diameter, which is:

Radius = 1/2 * distance between (-3, 0) and (3, 0)

= 1/2 * 6

= 3

Therefore, the equation of the circle with endpoints at (-3, 0) and (3, 0) is:

(x - 0)² + (y - 0)² = 3²

Simplifying:

x² + y² = 9

So the equation of the circle is x² + y² = 9.

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Answer:

To solve for x in the equation x+8|=-2, we first need to isolate the absolute value expression on the left side of the equation. We can start by subtracting 8 from both sides: x + 8 | = -2 x + 8 - 8 | = -2 - 8 x | = -10 Now we can solve for x by considering the two cases for the absolute value: 1. x + 8 = -10 2. -(x + 8) = -10 Solving for x in each case, we get: 1. x = -18 2. x = 2 Therefore, the solutions for x are -18 and 2.