ng Linear Equations Using Similar Triangles On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7. Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3). What is the ratio of the rise to the run in the smaller triangle in the diagram? What is the ratio of the rise to the run in the larger triangle in the diagram? What is the equation of the line in slope-intercept form?

Answer:

3

Step-by-step explanation:

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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[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]

[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]

[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\boxed{\mathfrak{answered \: by: \: akbarsdtazm}}}}[/tex]

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

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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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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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".

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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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 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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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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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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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.

The required, there were 644 premium seats and 646 regular seats sold.

Let x be the number of premium seats sold and y be the number of regular seats sold. Then we have two equations:

x + y = 1290 (total seats sold)

30x + 20y = 32240 (total revenue)

We can use the first equation to solve for y in terms of x:

y = 1290 - x

Substituting this into the second equation, we get:

30x + 20(1290 - x) = 32240

Simplifying and solving for x, we get:

x=644

So 644 premium seats were sold. Substituting this into the first equation, we get:

644+ y = 1290

y = 646

So 646 regular seats were sold.

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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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Answer:

-35.7 as a mixed number is -35 and 7/10.

Answer:

Your answer should be [tex]-35 \frac{7}{10}[/tex]

Step-by-step explanation:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.

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:

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

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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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 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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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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The solution of the equation 39=2x+1 is 19

The given equation is 39=2x+1

We have to find the solution of the equation

2x+1=39

Let us find the value of x

Subtract 1 from both sides

2x=38

Divide both sides by 2

x=19

Hence, the solution of the equation 39=2x+1 is 19

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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.

The graph of the table is attached accordingly. It examines the relationship betwen Hours and Height of the tides.

The graph shows that there is very wide variations between the height of the tides.

The relationship cannot said to be inverse or positive

Note, the following are three advantages of graphs: It makes data more attractive and understandable. It aids in the concise summarization of facts. It allows for more accurate data comparison.

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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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