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Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Therefore, the journey to Kumasi required more petrol by simplifying the fractions.

To compare the amount of petrol used for the journeys to Kumasi and Accra, we'll calculate the fractions of the full tank of petrol used for each journey.

Let's assume that the full tank of petrol has a capacity of 1 unit.

Othniel used 2/5 of the full tank of petrol to travel to Kumasi.

The fraction of the full tank of petrol used for the journey to Kumasi is 2/5, which is equivalent to 0.4.

Othniel used 2/6 of the full tank of petrol to travel to Accra.

To compare the fractions accurately, we need to make the denominators equal. Since the least common multiple (LCM) of 5 and 6 is 30, we'll convert the fractions to have a denominator of 30.

Converting the fraction 2/5 to have a denominator of 30:

(2/5) * (6/6) = 12/30

Converting the fraction 2/6 to have a denominator of 30:

(2/6) * (5/5) = 10/30.

Comparing the fractions, we find that Othniel used 12/30 of the full tank of petrol to travel to Kumasi and 10/30 of the full tank of petrol to travel to Accra.

Since 12/30 is greater than 10/30, the journey to Kumasi required more petrol.

Simplifying the fractions, we have:

Journey to Kumasi: 12/30 = 2/5.

Journey to Accra: 10/30 = 1/3.

Therefore, the journey to Kumasi required more petrol than the journey to Accra.

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Answer:

Okay, so what is the question?

Answer:

   Tornado: clouds, strong wind, rain, hail.

   Hurricane or cyclone: strong wind, heavy rain.

   Blizzard: heavy snow, ice, cold temperatures.

   Dust storm: strong winds, arid conditions.

   Flood: heavy rainfall.

   Hail storm: cold or warm temperatures, rain, ice.

   Ice storm: freezing rain.Step-by-step explanation:

Answer:

x = 19 or x = 13

Step-by-step explanation:

Solve for x over the real numbers:

2 x^2 - 64 x + 494 = 0

Divide both sides by 2:

x^2 - 32 x + 247 = 0

Subtract 247 from both sides:

x^2 - 32 x = -247

Add 256 to both sides:

x^2 - 32 x + 256 = 9

Write the left hand side as a square:

(x - 16)^2 = 9

Take the square root of both sides:

x - 16 = 3 or x - 16 = -3

Add 16 to both sides:

x = 19 or x - 16 = -3

Add 16 to both sides:

Answer: x = 19 or x = 13

Answer:

C is correct.

Answer:

Sana takes 10 minutes longer than Ali in bathroom

Step-by-step explanation:

Given:

Ali Showers, brushes teeth 20 minutes

Thus, Ali takes 20 minutes time in bathroom

Sana Takes a bath, brushes teeth ½ hour

1 hour has 60 minutes

1/2 hour has 60/2=30 minutes

Thus, Sana takes 30 minutes time in bathroom.

Time, taken more by sana than Ali = 30 minutes - 20 minutes = 10 minutes

.

Thus, Sana takes 10 minutes longer than Ali in bathroom.

Answer:

By definition, the perimeter of a polygon is calculated by taking the sum of all side lengths of a particular polygon. You can also find the perimeter of all polygons, whether they are regular or irregular polygons

Step-by-step explanation:

Step-by-step explanation:

the perimeter of the polygon below is 152 cm calculate a

Answer: 28x-2

Step-by-step explanation:

First, you get rid of the parentheses. Since the symbol is +, nothing really changes: 12x - 3 + 16x +1

Then, you combine like terms to get your answer: 28x-2

Answer:

28x−2

Step-by-step explanation:

Combine 12x and 16x to get 28x.

28x−3+1

Add −3 and 1 to get −2.

28x−2

28x−2

Factor out 2.

2(14x−1)

Answer:

$3050.48

Step-by-step explanation:

If 4% is compounded quarterly, that means it's 1% every quarter. since we have 5 years, that's 1.01^20, which is approx. 1.2202. We multiply this by the orignal $2500, so our investment at the end of 5 years is $3050.48 (rounded to nearest cent)

The amount of money that Tia's investment would be worth at the end of 5 years is equal to $3050.5.

Given the following data:

To determine how much is the investment worth at the end of 5 years:

Mathematically, compound interest is given by the formula:

\(A = P(1 + \frac{r}{n})^{nt}\)

Where;

Substituting the given parameters into the formula, we have;

\(A = 2500(1 + \frac{0.04}{4})^{4\times 5}\\\\A = 2500(1 +0.01)^{20}\\\\A = 2500(1.01)^{20}\\\\A = 2500(1.2202)\)

Future value, A = $3050.5

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Answer:

c ≥ 10 dozen

Step-by-step explanation:

Victor wants to have at least 10 dozen cookies for the bake sale.

In layman terms it can be understood as that Victor wants either  10 dozen cookies or more than that such as 11, 12, 13, 50 , 100 whatever number is greater than 10.

Let the no. of dozen of cookies wanted by him is c

according to condition

if victor wants  either 10 dozen cookies

it can be represented mathematically as

c = 10 dozen  (1)

_____________________________________

If victor wants no. of dozens of cookies greater than 10 .

it can be written as

c >10  dozen (2) (">" is symbol for greater than . expression simply means value of x should be greater than 10)

______________________________________________

now combining  equation one and two, we have

c ≥ 10 dozen . It can means that x can take value starting from 10 to any no greater than..

Answer:

Higher

Step-by-step explanation:

$34.89 + $43.65 = 79.84

79.84 is 0.46 less than 80

The complex roots of the equations are:

Part B: Solving equations using the quadratic formula:

5. x² + 4x + 6 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (-4 ± √(4² - 4(1)(6))) / (2(1))

Simplifying: x = (-4 ± √(-8)) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

6. x² - 4x + 13 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (4 ± √((-4)² - 4(1)(13))) / (2(1))

Simplifying: x = (4 ± √(-36)) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

7. x² + 49 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (0 ± √(0² - 4(1)(49))) / (2(1))

Simplifying: x = ±√(-196) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

8. x² - 6x + 4 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (6 ± √((-6)² - 4(1)(4))) / (2(1))

Simplifying: x = (6 ± √(20)) / 2

Simplifying further: x = 3 ± √5

The equation has two real solutions.

9. x² + 2 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (0 ± √(0² - 4(1)(2))) / (2(1))

Simplifying: x = ±√(-8) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

10. x² + 8 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (0 ± √(0² - 4(1)(8))) / (2(1))

Simplifying: x = ±√(-32) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

11. x² + 16 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (0 ± √(0² - 4(1)(16))) / (2(1))

Simplifying: x = ±√(-64) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

12. x² + 2x + 3 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (-2 ± √(2² - 4(1)(3))) / (2(1))

Simplifying: x = (-2 ± √(-8)) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

13. x² + 5x + 8 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (-5 ± √(5² - 4(1)(8))) / (2(1))

Simplifying: x = (-5 ± √(25 - 32)) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

14. x² - 3x + 4 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (3 ± √((-3)² - 4(1)(4))) / (2(1))

Simplifying: x = (3 ± √(9 - 16)) / 2

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

15. 2x² - 3x = -3

To solve this equation, first rearrange it to the form ax² + bx + c = 0:

2x² - 3x + 3 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values: x = (3 ± √((-3)² - 4(2)(3))) / (2(2))

Simplifying: x = (3 ± √(9 - 24)) / 4

Since the discriminant is negative, there are no real solutions. The equation has two complex roots.

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Answer:

C. 3x + 2(2x + 3) = 9

Step-by-step explanation:

We are given the following relation:

y = 2x + 3

And we want to substitute into:

3x + 2y = 9.

So

\(3x + 2(2x + 3) = 9\)

Which is given by option C.

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

a) 15yd

b)2.45ft

Step-by-step explanation:

P = perimeter, l=length and w = width of the rectangle

P = 2l+2w

a) 40 = 2l+2(5)

40 = 2l+10

30=2l

15=l

b) 18.4 = 2(6.75) + 2w

18.4 = 13.5+2w

4.9=2w

2.45=w

Answer:

x ≤ –6 and x ≥ 1

Step-by-step explanation:

Answer:

\(y = 3x + 4 = 3(0) + 4 = 4\)

13 friends make up 48.1%

14 friends make 51.8%

51.8-48.1 = 3.7

3.7% decrease

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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Answer:

375 feet

Step-by-step explanation:

Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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Answer:

20200

Step-by-step explanation:

As you're in a hurry, I can give it later? xx

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Two equivalent expressions to  3x + 3(x+y) are:

Two expressions are equivalent if we can rewrite one into the other, in such a way that  we only use algebra to do so.

Here we start with the expression:

3x + 3(x + y)

If we take 3 as a common factor, then we can write:

3x + 3(x + y) = 3*(x + (x + y)) = 3*(x + x + y)

That is an equivalent expression, now if we simplify this:

3*(x + x + y) = 3*(2x + y)

Distribute that product.

3*(2x + y) = 6x + 3y

These is other equivalent expression.

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2 on division by 3/7 yields 14/3.

For the division of two fractions, we need to multiply the first fraction with the reciprocal of the second. Reciprocal of a fraction means interchanging the numerator and denominator ie, the reciprocal of a is 1/a, the reciprocal of p/q = q/p, and so on.

For example, if a/b and c/d are the fractions the a/b ÷ c/d = a/b x d/c =ad/bc.

Implementing the same method to solve this question,

We have 2/1 = 2 as the first and 3/7 as the second fraction. Thus,

2 ÷3/7 =2 x 7/3 = 14/3. So 14/3 is the answer.

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Answer:

the perimeter is 13yd + 13yd + 5yd +5yd = 36yd

the area is 5yd + 5yd = 10yd, 10yd × 12yd ÷ 2 = 60yd

Answer: 9/4

Step-by-step explanation:

Reciprocal means flip the fraction

The reciprocal of 4/9  is  9/4

Answer: the rciprocal is 9/4

Step-by-step explanation:

The answer is D.

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