factor and solve x^2-4x=5

The investment with compound interest earns a greater amount of interest by $486.12 compared to the investment with simple interest.

To determine which investment earns a greater amount of interest, we need to calculate the interest earned in both scenarios and compare the results.

1. Simple Interest:

The formula for simple interest is given by: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.

Using this formula, we can calculate the interest earned with simple interest:

I = 100,000 * 0.03 * 4

I = $12,000

2. Compound Interest:

The formula for compound interest is given by: A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period.

In this case, the interest is compounded annually, so n = 1. Let's calculate the amount earned:

A = 100,000 * (1 + 0.03/1)^(1*4)

A = 100,000 * (1.03)^4

A = $112,486.12

The interest earned in the compound interest scenario is A - P = $112,486.12 - $100,000 = $12,486.12.

The difference between the amounts of interest earned by the two investments is:

$12,486.12 - $12,000 = $486.12.

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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The total weight of the five bags of cat food is approximately 66.1386 pounds.

To determine the weight of the cat food in pounds, we can use the conversion factor that 1 kilogram is approximately equal to 2.20462 pounds.

Given that each bag of cat food has a mass of 6 kilograms, we can calculate the weight of one bag in pounds by multiplying 6 by 2.20462.

[tex]6 kg \times 2.20462 lb/kg = 13.22772 lb[/tex]

Now, to find the total weight of the five bags of cat food, we multiply the weight of one bag by the number of bags:

[tex]13.22772 lb/bag \times 5 bags = 66.1386 lb[/tex]

It's important to note that the provided conversion factor of 2.20462 pounds per kilogram is an approximation, as the exact conversion factor is 2.20462262185 pounds per kilogram.

However, for the purpose of this calculation, we are using the rounded value to one decimal place.

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Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

Answer:

Step-by-step explanation:

If 11 flights were sampled with an 85% on-time arrival rate, the number of flights from the sample that arrived on time would be estimated to be 9.35, which would round to 9 flights.

This can be solved by:

(0.85x11)= 9.35

Since there can't be .35 of a flight, we would round to the nearest whole number, which would just be 9.

The final answer= 9 flights

Given statement solution is :- The angles of ABCD are right angles, which means it is not a rectangle.

To determine if quadrilateral ABCD is a rectangle, we need to examine its properties.

A rectangle is a quadrilateral with four right angles (90 degrees) and opposite sides that are congruent (equal in length). We can verify these conditions for ABCD by analyzing its properties.

First, let's calculate the lengths of the sides of ABCD using the distance formula:

Side AB:

AB = √((x₂ - x₁)² + (y₂ - y₁)²)

= √((5 - 1)² + (6 - 3)²)

= √(4² + 3²)

= √(16 + 9)

= √25

= 5

Side BC:

BC = √((x₂ - x₁)² + (y₂ - y₁)²)

= √((6 - 5)² + (4 - 6)²)

= √(1² + (-2)²)

= √(1 + 4)

= √5

Side CD:

CD = √((x₂ - x₁)² + (y₂ - y₁)²)

= √((2 - 6)² + (1 - 4)²)

= √((-4)² + (-3)²)

= √(16 + 9)

= √25

= 5

Side DA:

DA = √((x₂ - x₁)² + (y₂ - y₁)²)

= √((1 - 2)² + (3 - 1)²)

= √((-1)² + 2²)

= √(1 + 4)

= √5

Now, let's check the angles of the quadrilateral.

Angle A:

Using the slope formula, we can calculate the slopes of AB and AD:

m₁ = (y₂ - y₁) / (x₂ - x₁) = (6 - 3) / (5 - 1) = 3/4

m₂ = (y₂ - y₁) / (x₂ - x₁) = (1 - 3) / (2 - 1) = -2/1

Since the slopes of AB and AD are not negative reciprocals (m₁ * m₂ ≠ -1), angle A is not a right angle.

Similarly, we can calculate the slopes and check the other angles as follows:

Angle B:

Slope of BC: m = (-2) / (1) = -2

Slope of BA: m = (3) / (4) = 3/4

Since the slopes of BC and BA are not negative reciprocals, angle B is not a right angle.

Angle C:

Slope of CD: m = (-3) / (-4) = 3/4

Slope of CB: m = (2) / (-1) = -2

Since the slopes of CD and CB are not negative reciprocals, angle C is not a right angle.

Angle D:

Slope of DA: m = (2) / (-1) = -2

Slope of DC: m = (3) / (4) = 3/4

Since the slopes of DA and DC are not negative reciprocals, angle D is not a right angle.

Based on our calculations, none of the angles of ABCD are right angles, which means it is not a rectangle.

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When Margo places all 6 tiles in a row with sides touching, the length of the row is 4.8 inches.

Margo has 6 tiles of equal size, and each side of the tile measures 0.8 inches. To determine the length of the row when all the tiles are placed together with their sides touching, we need to calculate the total length covered by the tiles.

Since each tile has four sides, and all the sides are touching in a row, we can calculate the total length by multiplying the number of tiles by the length of each side. In this case, the number of tiles is 6, and the length of each side is 0.8 inches.

So, the total length covered by the tiles can be calculated as follows:

Total length = Number of tiles × Length of each side

Total length = 6 × 0.8 inches

Calculating the above expression, we find:

Total length = 4.8 inches

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Alexei's monthly payment is approximately $18.56.

Alexei finances her purchase of a $900 television with a one-year loan that has a fixed annual interest rate of 2.5%. To find Alexei's monthly payment, we can use the formula for calculating monthly loan payments.
The formula for calculating monthly loan payments is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n =number of monthly payments
In this case, the principal loan amount (P) is $900, the annual interest rate (r) is 2.5% (or 0.025 when expressed as a decimal), and the number of monthly payments (n) is 12 (since it is a one-year loan).
First, we need to calculate the monthly interest rate (r) by dividing the annual interest rate by 12: r = 0.025 / 12 = 0.002083.
Next, we can substitute the values into the formula:
M = (900 * 0.002083 * (1 + 0.002083)^12) / ((1 + 0.002083)^12 - 1)
Simplifying the formula gives us:
M = (900 * 0.002083 * 1.002083^12) / (1.002083^12 - 1)
Calculating the values inside the formula gives us:
M = (900 * 0.002083 * 1.026260) / (1.026260 - 1)
Further simplifying the formula gives us:
M = (900 * 0.002083 * 1.026260) / 0.026260
Finally, calculating the expression gives us:
M ≈ 18.56
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The mean absolute deviation is $106.6.

Given the table shows the amount Bill spent on 5 days last week.

DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.

Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,

the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:

Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406

The sum of all absolute deviations is:

10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Hello!

23x = 24

23x/23 = 24/23

x = 24/23

Hello !

Answer:

[tex]\Large \boxed{\sf x=\dfrac{24}{23} }[/tex]

Step-by-step explanation:

We want to find the value of x that verifies the following equation :

[tex]\sf 23x=24[/tex]

We want to isolate x.

Let's divide both sides by 23 :

[tex]\sf \dfrac{23x}{23} =\dfrac{24}{23}[/tex]

[tex]\boxed{\sf x=\dfrac{24}{23} }[/tex]

Have a nice day ;)

Answer:

Step-by-step explanation:

ac=3.14/p==[tex]\beta \alpha[/tex]ty

[tex]13 \leqslant 4x - 3 \leqslant 29 \\ 13 + 3 \leqslant 4x \leqslant 29 + 3 \\ 16 \leqslant 4x \leqslant 32 \\ 16 \div 4 \leqslant x \leqslant 32 \div 4 \\ 4 \leqslant x \leqslant 8[/tex]

Every well-ordered set can be mapped to a unique ordinal number. This mapping preserves the order structure, and the uniqueness arises from the absence of infinite descending chains.

To prove that every well-ordered set is isomorphic to a unique ordinal number, we need to demonstrate two key aspects: (1) that every well-ordered set can be mapped to an ordinal number, and (2) that this mapping is unique, meaning no two different well-ordered sets can be isomorphic to the same ordinal number.

First, let's consider a well-ordered set. By definition, a well-ordered set is a set with a total order relation that satisfies the properties of well-ordering, which include the absence of infinite descending chains.

Now, we can define a mapping from this well-ordered set to an ordinal number. Ordinal numbers represent a specific order type or structure, and they are themselves well-ordered sets. The mapping can be established by assigning each element in the well-ordered set to its corresponding position in the ordinal number based on the order relation.

The key insight is that this mapping is both an isomorphism and unique. It preserves the order structure, meaning that the well-ordered set and the ordinal number have the same order type. Moreover, it is unique because the absence of infinite descending chains ensures that no two different elements in the well-ordered set will map to the same position in the ordinal number.

To illustrate the uniqueness, suppose there were two different well-ordered sets that were isomorphic to the same ordinal number. This would imply that there are two different order structures with the same order type, violating the uniqueness of ordinal numbers.

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Answer:

$880

Step-by-step explanation:

Use the equation:

[tex]P=(1-d)x[/tex] with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

The expression equivalent to (53−√4)12 is 5 to the power of 36.

To find the expression that is equivalent to (53−√4)12, we need to simplify the given expression:

(53−√4)12

First, let's simplify the expression inside the parentheses:

53−√4 = 53−2 = 125−2 = 123

Now, let's substitute this simplified expression back into the original expression:

(123)12

To simplify this expression further, we raise 123 to the power of 12:

(123)12 = 5312 = 5 to the power of (3 * 12) = 5 to the power of 36

Therefore, the expression equivalent to (53−√4)12 is 5 to the power of 36.

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Answer:

[tex]\LARGE\boxed{\sf 5^{\frac{3}{8}}}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\large\text{$\sf \left(\sqrt[4]{5^3}\right)^{\frac{1}{2}}$}[/tex]

To find the equivalent expression, apply exponent rules.

[tex]\textsf{Apply the exponent rule:} \quad \boxed{\sqrt[n]{a^m}=a^{\frac{m}{n}}}[/tex]

[tex]\implies \large\text{$\sf \left(5^{\frac{3}{4}}\right)^{\frac{1}{2}}$}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \boxed{(a^b)^c=a^{bc}}[/tex]

[tex]\implies \large\text{$\sf 5^{\frac{3}{4}\cdot \frac{1}{2}}$}[/tex]

[tex]\implies \large\text{$\sf 5^{\frac{3}{8}}$}[/tex]

Therefore, the equivalent expression to the given expression is:

[tex]\LARGE\boxed{\sf 5^{\frac{3}{8}}}[/tex]

The length of arc RS on circle X is 17.99 centimeters.

To find the length of arc RS on circle X, we need to calculate the circumference of the entire circle and then determine what portion of the circumference is represented by the central angle of 110 degrees.

The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius of circle X is 9 centimeters, so the circumference is C = 2π(9) = 18π centimeters.

To find the length of arc RS, we need to determine what fraction of the entire circumference is represented by the central angle of 110 degrees. A full circle has 360 degrees, so the fraction of the circumference represented by the central angle is 110/360.

To find the length of arc RS, we multiply the fraction of the circumference by the total circumference of the circle. Therefore, the length of arc RS is (110/360) * 18π.

Simplifying the expression, we have (110/360) * 18π = (11/36) * 18π.

Canceling out the common factors, (11/36) * 18π = (11/2)π.

Now, we can approximate the value of π as 3.14. Therefore, the length of arc RS is (11/2) * 3.14.

Calculating the approximate value, we have (11/2) * 3.14 ≈ 17.99 centimeters.

Therefore, the approximate length of arc RS on circle X is approximately 17.99 centimeters.

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Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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The expression 5⁶ ÷ 5⁴ rewritten using positive exponents is 5².

Given the expression in the question:

5⁶ ÷ 5⁴

To rewrite the expression 5⁶ ÷ 5⁴ using a single positive exponent, we can simply apply the exponent rule for division of like bases.

According to exponent rule for division of like bases, when dividing two numbers with similar bases, we can simply subtract the exponents.

That is:

zᵃ ÷ zᵇ = z⁽ᵃ ⁻ ᵇ⁾

Applying this rule: zᵃ ÷ zᵇ = z⁽ᵃ ⁻ ᵇ⁾

5⁶ ÷ 5⁴ = 5⁽ ⁶ ⁻ ⁴ ⁾

Subtract the exponents:

5²

Therefore, the simplified form is 5².

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Answer:

Janna will use 26 marshmallows and 39 graham crackers to make 13

Step-by-step explanation:

S'mores       Marshmallows       Graham Crackers

      4                      8                                12

     13

Look at the first line on the table.

For 4 s'mores, 8 marshmallows are used.

8/4 = 2

2 marshmallows are used per s'more.

For 4 s'mores, 12 graham crackers are used.

12/4 = 3

3 graham crackers are used per s'more.

For 13 s'mores,

13 × 2 = 26

13 × 3 = 39

26 marshmallows and 39 graham crackers are needed.

Complete the table:

S'mores       Marshmallows       Graham Crackers

      4                      8                                12

     13                     26                              39

Answer:

Janna will use 26 marshmallows and 39 graham crackers to make 13

The volume of the given figure above would be = 4,095 yards³.

To calculate the volume of the given figure, it is first divided into two giving rise to a rectangular prism and a trapezoidal prism.

The volume of a rectangular prism= length×width×height

where;

length= 30yrds

width= 9 yards

height= 7 yards

volume= 30×9×7 = 1,890yards³

The volume of a trapezoidal prism= ½(a+b)×h×l

where;

a= 19yd

b= 30yd

h= 10yd

l= 9 yd

volume= ½(19+30)×10×9

= 49×5×9

= 2,205yards³

Therefore, the total volume of the figure would be ;

= 1,890+2,205

= 4,095 yards³

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Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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The vector v with the given magnitude and the same direction as u is v =   -5.65i + 5.65j

A vector is a physical quantity that has both magnitude and direction.

To find the vector v with the given magnitude and the same direction as u. (Give your answers correct to 2 decimal places.) Magnitude: |v|| = 8 , Direction: u = - i + j, we proceed as follows.

The vector v in the direction of u is v = |v|u' where u' is the unit vector in the direction of u

So, u' = u/|uI where |u| = magnitude of vector u = √[(-1)² + 1²] = √(1 + 1) = √2

So, u' = u/|uI

= (- i + j)/√2

So, v = |v|u'

= 8[(- i + j)/√2]

= 8(- i + j)/√2 × √2/√2

= 8(- i + j)√2/(√2 × √2)

= 8(- i + j)√2/2

= 4(- i + j)√2

= 4√2(- i + j)

= 5.65(-1 + j)

= -5.65i + 5.65j

So, v =  -5.65i + 5.65j

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A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

y = [tex]\sqrt{55}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = [tex]\sqrt{55}[/tex]

16 & 81 are the missing frequencies if median and mode are 33.5 and 34.0 respectively.

To determine the missing frequencies, we need to use the information given about the median and mode.

First, let's find the position of the median in the cumulative frequency distribution. The total number of students is given as 230, so the median position will be (230 + 1) / 2 = 115.5. This means that the median falls within the 115th and 116th position in the ordered data.

Next, we need to determine the class interval that contains the median. Looking at the cumulative frequency distribution, we can see that the cumulative frequency just before the median position (115) is 34. This means that the median falls within the 30-39 class interval.

To find the missing frequency (f4) for the 30-39 class interval, we subtract the cumulative frequency of the previous class from the median position:

f4 = 115 - 34 = 81

So, the missing frequency for the 30-39 class interval is 81.

Next, let's determine the mode. The mode is the class interval with the highest frequency. From the given distribution, we can see that the highest frequency is for the 20-29 class interval. However, the mode is given as 34.0, which does not fall within the 20-29 class interval.

To determine the missing frequency (f3) for the 20-29 class interval, we need to distribute the difference in frequencies between the 20-29 and 30-39 class intervals proportionally based on the mode. The difference in frequencies is 81 - 16 = 65.

We can set up the following proportion:

(34 - 20) / (29 - 20) = f3 / (30 - 20)

Simplifying the proportion:

14 / 9 = f3 / 10

Cross-multiplying:

9f3 = 140

Solving for f3:

f3 = 140 / 9 ≈ 15.6

Since frequencies should be whole numbers, we round f3 to the nearest whole number, which is 16.

Therefore, the missing frequencies are:

f3 = 16

f4 = 81

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The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer:

1.5926

Step-by-step explanation:

-We need to first convert the height in feet to inches: Since there are 12 inches in a foot, that means there are 74 inches in a height of 6 foot 2 inches.

-Since the observed height is 74 inches and the mean height is 69.7 inches, we can find the z score by using the following formula:

z = (x-mean) / standard deviation

-We would fill this out like this:

z = (74-69.7) / 2.7

-This equals = 1.592592593

-Rounded to 4 decimal places, this equals 1.5926

Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2