Math, some system by elimination

The roots of the quadratic equation y = 5 · x²  + 2 · x + 7 are contained by x = - 1 / 5 ± i √34 / 5.

In this problem we must solve a quadratic equation, whose roots must be found. This can be done by using algebra properties, by completing the square. First, write the entire quadratic equation:

y = 5 · x²  + 2 · x + 7

Second, use algebra properties to find all roots:

y = 5 · [x² + (2 / 5) · x + 7 / 5]

y = 5 · [x² + (2 / 5) · x + 1 / 25] + 5 · (34 / 25)

y = 5 · (x + 1 / 5)² + 34 / 5

Third, use y = 0:

5 · (x + 1 / 5)² + 34 / 5 = 0

5 · (x + 1 / 5)² = - 34 / 5

(x + 1 / 5)² = - 34 / 25

x + 1 / 5 = ± √(- 34) / 5

x = - 1 / 5 ± √(- 34) / 5

x = - 1 / 5 ± i √34 / 5

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The value that lie above 25% of the data of the box plot is 31 and the lower quartile (Q1) = 14 upper quartile (Q3) = 31

Given data ,

The minimum value, which is 14

Now , the lower quartile, which is 16 (25% of the data is below this value)

And , the median, which is 24 (50% of the data is below this value)

Now , the upper Quartile, which is 31 (75% of the data is below this value)

And , the maximum value is 32.

The upper and lower quartiles of a box plot, also known as the 75th percentile (Q3) and 25th percentile (Q1) respectively, represent the range within which the middle 50% of the data falls.

Lower quartile (Q1) = 14

Upper quartile (Q3) = 31

Hence , 25% of the data lie above 31, which is the upper quartile.

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A) The total cost for 45khw of electricity is 27.50c.

B) The total cost for 60khw of electricity is 76.70c.

C) Total cost for 100khw of electricity is 76.70c.

To calculate the cost of electricity for different amounts of kWh, we need to use the sliding scale tariffs provided by the local municipality. Here are the calculations for the given scenarios:

A. For 45 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

There is no electricity used beyond the first 50 kWh, so the total cost is 27.50c.

B. For 60 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

The next 10 kWh cost 0.82c per kWh, so the cost is 10 x 0.82 = 8.20c

The total cost is 27.50c + 8.20c = 35.70c.

C. For 100 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

The next 60 kWh cost 0.82c per kWh, so the cost is 60 x 0.82 = 49.20c

The remaining 40 kWh are not covered by the sliding scale tariff and their cost is unknown.

The total cost is 27.50c + 49.20c = 76.70c.

In summary, the cost of electricity varies depending on the amount of kWh used, and we need to use the sliding scale tariffs to calculate it correctly.

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There are a total of 4 + 3 + 2 + 1 = 10 marbles in the bag. The probability of picking a red marble is the number of red marbles divided by the total number of marbles:

Probability of picking a red marble = 4/10 = 2/5

Therefore, the probability Aisha picks a red marble is 2/5 or 0.4 when written as a decimal.

For a company that charges $5.10 plus 5.747 cents per kilowatt-hour (kWh) for customers using up to 1300 kWh, and charges 5.788 cents per kilowatt-hour (kWh) for the extra kWh used after the first 1300 kWh, if more than 1300 kWh are used, the total charge for 1,300 kWh is $79.811.

The total charge is the product of the multiplication of the unit rate by the total kilowatt-hours used by the customer plus the fixed rate.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication involves the multiplicand, the multiplier, and the product.

Fixed charge = $5.10

Variable charge per kilowatt-hour = 5.747 cents ($0.05747)

Total usage  = 1,300 kWh

The total charge = $79.811 ($5.10 + $0.05747 x 1,300)

Thus, the total charge for 1,300 kWh for the nonextreme weather month is $79.811.

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There are 4 cubes of size 1/4 foot would fill the inside of the prism.

We have to given that;

Height of cuboid = 3 feet

Length of cuboid = 3/4 feet

Width of cuboid = 1/2 feet

We know that;

Volume of cuboid = Length x width x height

Hence,

V = 3/4 x 3 x 1/2

V = 9/8

Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,

= (9/8) ÷ (1/4)

= (9/8) x 4

= 9/2

= 4.5

Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.

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Answer:

3

Step-by-step explanation:

The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

We have,

To convert kilometers (km) to meters (m), we need to multiply the distance by 1000.

a) 1.241 km = 1.241 × 1000 m = 1241 m

b) 6.002 km = 6.002 × 1000 m = 6002 m

c) 5.168 km = 5.168 × 1000 m = 5168 m

d) 3.4 km = 3.4 × 1000 m = 3400 m

e) 21.32 km = 21.32 × 1000 m = 21320 m

f) 0.895 km = 0.895 × 1000 m = 895 m

Therefore,

The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

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The person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

The above problem is asking how much farther a person will travel in one revolution of the Adventure Land ferris wheel compared to one revolution of the Kiddie Land ferris wheel.

The Adventure Land ferris wheel has a diameter of 30 meters, and the Kiddie Land ferris wheel has a diameter of 10 meters.

This means that the circumference of the Adventure Land ferris wheel (the distance traveled in one revolution) is

3.14×30= 94.2 meters

The circumference of the Kiddie Land ferris wheel is

3.14 ×10= 31.4 meters

Here, 94.2-31.4 =62.8 meters

Therefore, the person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

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Answer:

19, 100, and 25

Step-by-step explanation:

Let's call the first number "x", the second number "y", and the third number "z". We know that:

x + y + z = 144   (the sum of three numbers is 144)

We also know that:

x = z - 6   (the first number is 6 less than the third)

y = 4z      (the second number is 4 times the third)

We can substitute the expressions for x and y into the first equation:

x + y + z = 144

(z - 6) + 4z + z = 144

Combining like terms, we get:

6z - 6 = 144

Adding 6 to both sides:

6z = 150

Dividing by 6:

z = 25

Now that we know z, we can use the other equations to find x and y:

x = z - 6 = 25 - 6 = 19

y = 4z = 4(25) = 100

So the three numbers are 19, 100, and 25.

Let first number be a

second number be b

Third number be c

As per the question The first number is 6 less than the third. The second number is 4 times the third.

First number, a = c - 6 ....(i)

second number, b = 4c ....(ii)

Also sum of the three numbers is 144.

a + b + c = 144

c - 6 + 4c + c = 144

c + 4c + c = 144 + 6

6c = 150

c = 150/6

c = 25

Put value of c in equation (i) & (ii)

in equation (i)

a = c - 6

a = 25 - 6

a = 19

in equation (ii)

b = 4c

b = 4 × 25

b = 100

Hence thee required numbers will be 19, 100 and 25.

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[tex]\cos C=\dfrac{CE}{AC}\\=\dfrac{8}{\sqrt{8^2+3^2}}\\=\dfrac{8}{\sqrt{64+9}}\\=\dfrac{8}{\sqrt{73}}\\=\boxed{0,936}[/tex]

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Answer:

8 and -5

Step-by-step explanation:

8 - 5 = 3

(-5) (8)=-40

Answer:

-8,+5

Step-by-step explanation:

-8+5 = 3

-8×+5 = -40

Answer:

2 yards

Step-by-step explanation:

2 yards equals 6 feet because 2x3=6 or 72 inches because 6x12 equals 72. 1 yard is equal to 3 feet.

The probability that a viewer will turn to channel 8 during Jimmy's performance is 2.67%.

The show is 30 minutes long, which is equivalent to 1800 seconds. Jimmy's performance starts at 6:06 pm, which is 366 seconds into the show, and ends at 6:14 pm, which is 414 seconds into the show. Therefore, Jimmy's performance lasts for 48 seconds.

The probability of a viewer turning to channel 8 during Jimmy's performance can be calculated by dividing the length of Jimmy's performance by the length of the entire show:

P = (length of Jimmy's performance) / (length of entire show) = 48 / 1800 = 0.0267

Multiplying by 100 gives the probability as a percentage: 2.67%

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The fraction of the game board that is orange is 1/6

From the question, we have the following parameters that can be used in our computation:

Sections = 6

Orange = 1

using the above as a guide, we have the following:

Fraction = Orange /Total Number of sections

So, we have

Fraction = 1/6

Other forms of the fraction are

Fraction = 2/12 and 3/18

Hence, the fraction is 2/6

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The solution is ,if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.

Here, we have,

given that.

if it takes three people 4 hours to clean a warehouse

now, we have to find that  how long will it take 4 people to clean the warehouse.

i.e. we have,

3 people take to clean = 4 hours

let, 4 people will take to do it x hours.

now, we have,

3 people take to clean = 4 hours

so, 1 people take to clean = 4*3 hours

so, 4 people take to clean = 4*3 / 4 hours

i.e. we get,

x = 4*3 / 4 hours

or, x = 12/4 hours

       = 3 hours

Hence, if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.

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The factorised forms of the Polynomials using difference of squares are;

a). (x - 6) (x + 6)

b). 3 (x - 2) (x + 2).

The factorised forms of the polynomials using the trinomial method are;

a). (x + 3)²

b). 4 (x -5) (x + 3)

Recall that from the difference of squares concept;

a² - b² = (a - b) (a + b) where a² and b² are perfect squares.

Therefore, if we have; x² - 36; we have; x² - 6²

x² - 36 = (x-6) (x + 6).

For, 3x² - 12; = 3 (x² - 4)

= 3 (x -2) (x + 2).

For the trinomials;

x² + 6x + 9;. x² + 3x + 3x + 9

= (x + 3) (x + 3) = (x+3)².

Also, for 4x² - 8x - 60; we have

4 (x² - 2x - 15)

= 4 (x - 5) (x + 3).

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Answer:

t = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

calculate the gradient (slope) of AB using the slope formula and equate to the slope of the perpendicular line.

given line with slope 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex]

calculate [tex]m_{AB}[/tex] using slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (2, - 3 ) and (x₂, y₂ ) = B (- 2, t )

[tex]m_{AB}[/tex] = [tex]\frac{t-(-3)}{-2-2}[/tex] = [tex]\frac{t+3}{-4}[/tex]

equating corresponding slopes

[tex]\frac{t+3}{-4}[/tex] = - [tex]\frac{4}{5}[/tex] ( multiply both sides by - 4 to clear the fraction )

t + 3 = - [tex]\frac{4}{5}[/tex] × - 4 = [tex]\frac{16}{5}[/tex] ( subtract 3 from both sides )

t = [tex]\frac{16}{5}[/tex] - 3 = [tex]\frac{16}{5}[/tex] - [tex]\frac{15}{5}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

D

Step-by-step explanation:

First consider a part of the numerator 5 + 3y2. This can be verbally described as "the sum of 5 and 3 times the square of y".

Then, the entire expression in the numerator, (5 + 3y2)3, can be written as "the cube of the sum of 5 and 3 times the square of y".

Next, consider a part of the denominator (4y), which can be verbally described as "the product of 4 and y".

Then, the entire expression in the denominator, (4y)3, can be written as "the cube of the product of 4 and y".

Dividing the two expressions yields the complete expression shown below.

So, the given expression can be interpreted as "the cube of the sum of 5 and 3 times the square of y divided by the cube of the product of 4 and y".

To be 90% certain that the sample percentage is within 5.5 percentage points of the genuine population percentage, we need to survey at least 384 randomly chosen plane passengers.

To calculate the sample size required for the survey, we can use the formula:

[tex]n = \dfrac{(Z^2 \times p \times q)} { E^2}[/tex]

where:

Z = the z-score associated with the level of confidence (90% in this case), which is 1.645

p = the estimated proportion of passengers who prefer aisle seats (unknown)

q = 1 - p

E = the maximum allowable error (5.5 percentage points)

Since we don't know the proportion of passengers who prefer aisle seats, we can assume a conservative estimate of 50%. This means that p = 0.5 and q = 0.5.

Substituting these values into the formula, we get:

[tex]n = \dfrac{(1.645^2 \times 0.5 \times 0.5)} { (0.055^2) }= 383.8[/tex]

We need to round up to the nearest integer, so the minimum sample size required is:

n = 384

Therefore, we need to survey at least 384 randomly selected air passengers to be 90% confident that the sample percentage is within 5.5 percentage points of the true population percentage.

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The simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

Given information:

f(x) = (log₂(x) + 2) and g(x) = (log₂(x³) - 6)

h(x) = f(x) + g(x) = (log₂(x) + 2) + (log₂(x³) - 6)

Using the rules of logarithms, we can simplify g(x) as follows:

g(x) = log₂(x³) - 6

= 3 log₂(x) - 6.

Now we can substitute this into the expression for h(x):

h(x) = (log₂(x) + 2) + 3 log₂(x) - 6

= 4 log₂(x) - 4

Therefore, the simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

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The study conducted on wild Jackalopes population shows a sample mean weight of 69.9 pounds, with a test statistic of  -1.327 and a p-value of  0.190. Therefore, at a significance level of 0.01, the null hypothesis can be rejected, indicating that the population mean weight is different from 65 pounds. This suggests the population health is in danger, and grants may be needed to re-establish their wild populations.

Pt1

Null Hypothesis The population mean of wild Jackalopes is equal to 69.9 lbs.

Alternative Hypothesis The population mean of wild Jackalopes is not equal to 69.9 lbs.

Test Statistic t = (X - μ) / (s / √n), where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Using a calculator or statistical software, we find that the test statistic is t = -1.327 and the p-value is 0.190.

At the 0.01 significance level, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population mean of wild Jackalopes is different from 69.9 lbs.

Pt2

To show that the population is actually in danger, we could change the null hypothesis to reflect a lower population mean weight. For example:

Null Hypothesis The population mean of wild Jackalopes is equal to 65 lbs.

Alternative Hypothesis The population mean of wild Jackalopes is greater than 65 lbs.

Using the same formula for the test statistic, we find that the test statistic is t = -5.457 and the p-value is 2.29 x 10⁻⁷, which is much smaller than the significance level of 0.01.

At the 0.01 significance level, we reject the null hypothesis. There is strong evidence to conclude that the population mean weight of wild Jackalopes is greater than 65 lbs. This suggests that the health of the population is in danger and that grants to help reestablish wild populations should be pursued.

Our report to the US Fish and Wildlife Service should reflect these findings and suggest taking action to support the health and survival of wild Jackalopes.

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The difference in the students who chose peach pie and apple pie is 46

From the question, we have the following parameters that can be used in our computation:

From the above, we have the percentage difference to be

Difference = 38% - 15%

When the given values are substituted, we have

Difference = 23%

This means that

Students = 23% * 200

Evaluate

Students = 46

Hence, the number of students is 46

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Answer:

Step-by-step explanation:

You want the resultant force equivalent to the two forces ...

There are a number of ways the resultant force can be found. One of them is to add the components of the two forces. Another makes use of the law of cosines:

  r² = u² +v² -2uv·cos(θ)

where θ is the supplement of the angle between the two forces.

  r² = 100² +90² -2·100·90·cos(135°) ≈ 30827.922061

  r ≈ 175.579 ≈ 175.58

The resultant force is about 175.58 pounds.

The angle added to that of v can be found using the law of sines:

  sin(φ)/100 = sin(135°)/175.58

  φ = arcsin(sin(135°)·100/175.58) ≈ 23.749°

The angle East of North is then ...

  55° +23.7° = 78.7°

The direction of the resultant is N 78.7° E.

__

Additional comment

The angles used in the second attachment are bearing angles measured clockwise from north. The rectangular coordinates shown as the sum of the forces represent (north) + (east)i.

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The coordinates of the points B' and C' are B' = (-1, 10) and C' = (-6, -5)

From the question, we have the following parameters that can be used in our computation:

A = (-2, -4)

This point is translated to

A' = (-3, -1)

This means that the rule of transformation is

(x, y) = (x - 1, y + 3)

Given that

B = (0, 7) and C = (-5, -8)

When this transformation is applied on B and C, we have

B' = (0 - 1, 7 + 3) and C' = (-5 - 1, -8 + 3)

Evaluate

B' = (-1, 10) and C' = (-6, -5)

Hence. the coordinates of B' and C' are B' = (-1, 10) and C' = (-6, -5)

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The heart will pumps 31,536 litres in 1 year and pumps 2,207,520 liters in 70 years.

There are 72 heartbeats in a minute.

If heart pumps 7 × 10⁻² litre per heartbeat,

then in 1 min,

7 × 10⁻² x 72 = 5.04 litres/minute

In one year (365 days), the heart pumps:

5.04 x 60 x 24 x 365 = 31,536 litres/year

Hence in 1 year, heart pumps 31,536 litres

In 70 years, the heart would pump:

31,536 x 70 years = 2,207,520 litres

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Answer:

x=144

Step-by-step explanation:

since they are similar their sides have a common ratio

24/x=42/7

7x=42*24

7x=1008

x=144