The sum of 3x^2 + x + 8 and x^2 - 9 can be expressed as ?

1)

In this question, we have been given Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.

1 minute = 9 liters

⇒ 60 seconds = 9 liters

⇒ 20 seconds = 3 liters

We need to find the amount of water in the tank A

a) when 4 minutes

Given that, 1 minute = 9 liters

Let y1 liters of water in the tank A after 4 minutes

So, we get an equation,

y1 = 9 × 4

y1 = 36 liters

36 + 124 (initial water level) = 160 liters

Hence, 160 liters of water in the tank A after 4 minutes been passed.

b) when 80 seconds

From given information, 20 seconds = 3 liters

Let y2 liters of water in the tank A after 80 seconds

So, we get an equation,

20 (y2) = 3 × 80

y2 = 12 liters

12 + 124 (initial water level) = 136 liters

Hence, 136 liters of water in the tank A after 80 seconds been passed.

Now we need to find the amount of time passed when Tank A contains the following amounts of water.

i) 151 liters

151 - 124 = 27 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t1 be the required time.

so, we get an equation,

9 × t1 = 1 × 27

t1 = 27 / 9

t1 = 3 minutes

This means, 3 minutes have passed when Tank A contains 151 liters of water.

ii) 191.5 liters

191.5 - 124 = 67.5 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t2 be the required time.

so, we get an equation,

9 × t2 = 1 × 67.5

t2 = 67.5 / 9

t2 = 7.5 minutes

t2 = 7 minutes 30 seconds

This means, 7 minutes 30 seconds have passed when Tank A contains 191.5 liters of water.

iii) 270.25 liters

270.25 - 124 = 146.25 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t1 be the required time.

so, we get an equation,

9 × t1 = 1 × 146.25

t3 = 146.25 / 9

t3 = 16.25 minutes

t3 = 16 minutes 15 seconds

This means, 16 minutes 15 seconds have passed when Tank A contains 270.25 liters of water.

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2)

In this question, Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute.

⇒ 1 minute = 2.5 liters of water drained

⇒ 60 seconds = 2.5 liters

⇒ 10 seconds = 0.42 liters

We need to find the amount of water drained from tank B

a) after 30 seconds

Let x1 be the amount of water drained after 30 seconds

Given that, 1 minute = 2.5 liters

So, we get an equation.

10 (x1) = 30 × 0.42

x1 = 3 × 0.42

x1 = 1.26 liters

b) after 7 minutes

Let x2 be the amount of water drained after 30 seconds

Given that, 1 minute = 2.5 liters

So, we get an equation.

x2 = 7 × 2.5

x2 = 17.5 liters

Now, we need to find the time in which the water is draining when Tank B contains

i) 75 liters

80 - 75 = 5 liters of more water drained.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t1 be the required time.

so, we get an equation,

2.5 × t2 = 5

t1 = 5 / 2.5

t1 = 2 minutes

This means, after 2 minutes Tank B contains 5 liters of water.

ii) 32.5 liters

80 - 32.5 = 47.5 liters of more water drained.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t2 be the required time.

so, we get an equation,

2.5 × t2 = 47.5

t2 = 47.5 / 2.5

t2 = 19 minutes

This means, after 19 minutes Tank B contains 32.5 liters of water.

iii) 18 liters

80 - 18 = 62 liters of more water filled.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t3 be the required time.

so, we get an equation,

2.5 × t3 = 62

t3 = 5 / 2.5

t3 = 24.8 minutes

t3 = 24 minutes 48 seconds

This means, after 24 minutes 48 seconds Tank B contains 18 liters of water.

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1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

2.9

Step-by-step explanation:

The answer is 2.9

Step by step:

The three consecutive integers are 4,6,8.

=================================================

Explanation:

There's a gap of 2 units between adjacent neighboring numbers. Consecutive even integers are numbers like 2,4,6,... or 10,12,14,... They are even numbers and they follow one right after another.

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The sum of the first and twice the second is 8 more than the third, so,

first + 2*(second) = (third) + 8

We'll plug in the expressions defined above and solve for x

x + 2*(x+2) = (x+4) + 8

x + 2x+4 = x+4+8

3x+4 = x+12

3x-x = 12-4

2x = 8

x = 8/2

x = 4 is the first number

x+2 = 4+2 = 6 is the second number

x+4 = 4+4 = 8 is the third number and the largest

Answer:

15.6

Step-by-step explanation:

To find the solutions of the equation 2x^2 + x - 6 = 0, we can use the quadratic formula:

What in mathematics is a quadratic equation?

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

In this case, a = 2, b = 1, and c = -6, so we can plug these values into the formula as follows:

x = (-1 +/- sqrt(1^2 - 4(2)(-6))) / (2(2))

x = (-1 +/- sqrt(1 + 48)) / 4

x = (-1 +/- sqrt(49)) / 4

x = (-1 +/- 7) / 4

Thus, the solutions to the equation 2x^2 + x - 6 = 0 are x = -4 and x = 3/2.

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Answer:

Your  picture Is blocked for me

Step-by-step explanation:

Easy to find a great place to work for free

And a taper ratio is a great way for you

The single logarithm value is log (\(x^7 - 5x^6 + 9x^5\) - 5\(x^4\) - 5x³ + 9x² -5x + 1) /  (x³-1).

The power to which a number must be increased in order to obtain another number is known as a logarithm.

For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 10²= 100.

We have log(x+1)³-2log(x+1)+3log(x-1)² -log(x³-1).

Using the property of logarithm

log \(a^m\) = m log a

So, log(x+1)³

= 3  log (x+ 1)

and, 3log(x-1)²

= 6 log(x-1)

Then, log(x+1)³-2log(x+1)+3log(x-1)² - log(x³-1)

=  3  log (x+ 1) - 2 log(x+1) + 6 log(x-1) -  log(x³-1)

= log (x+ 1) + 6 log(x-1) -  log(x³-1)

= log (\(x-1)^6\) (x+ 1) / (x³-1)

= log (\(x^7 - 5x^6 + 9x^5\) - 5\(x^4\) - 5x³ + 9x² -5x + 1) /  (x³-1)

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If you randomly choose two cards from a thoroughly shuffled deck and if you put the first card back in the deck before you draw the second then the probability that the first card is an ace and the second card is a king is 0.59%.

The probability that the first card is an ace and the second card is a king can be calculated as follows,

Initially, divide the expected outcomes by the total possible outcomes

As a deck has a total of 52 cards, the total possible outcomes are considered to be 52

A deck consists of 4 aces and 4 king cards

Hence,

the probability that the first card is an ace = 4 / 52

the probability that the second card is a heart = 4 / 52

The probability that the first card is an ace and the second card is a heart can be determined by multiplying the probability of an ace with the probability of heart,

Probability = (4/52)(4/52)

Probability = 0.0059

Converting into percentage,

Probability = 0.0059 × 100

Probability = 0.59%

Hence the probability that the first card is an ace and the second card is a king is calculated to be 0.59%.

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The correct option would be "None of these" since the projection is an ellipse and not any of the given options (2, 4, 16, or "This option").

To determine the projection of the region D onto the xy-plane, we need to find the intersection curve of the two paraboloids.

First, let's set the two equations equal to each other:

3x² + (12/24)y² = 16 - x²

Next, we simplify the equation:

4x² + (12/24)y² = 16

Multiplying both sides by 24 to eliminate the fraction:

96x² + 12y² = 384

Dividing both sides by 12 to simplify further:

8x² + y² = 32

Now, we can see that this equation represents an elliptical shape in the xy-plane. The equation of an ellipse centered at the origin is:

(x²/a²) + (y²/b²) = 1

Comparing this with our equation, we can deduce that a² = 4 and b² = 32. Taking the square root of both sides, we have a = 2 and b = √32 = 4√2.

So, the semi-major axis is 2 and the semi-minor axis is 4√2. The projection of region D onto the xy-plane is an ellipse with a major axis of length 4 and a minor axis of length 8√2.

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Answer:

Looks like A

Step-by-step explanation:

Answer:

Joshua walked 48 feet in total.

Step-by-step explanation:

To find the total distance we need to sum every distance that he walked. We have:

- First: Joshua walked down the hall to the door = 14 feet

- Second: He continued in a straight line out the door and across the yard to the mailbox = 24 feet

- Third: He came straight back across the yard and stopped to pet his dog = 10 feet

Hence, the total distance is:

\( d_{T} = d_{1} + d_{2} + d_{3} = 14 ft + 24 ft + 10 ft = 48 ft \)

Therefore, Joshua walked 48 feet in total.

I hope it helps you!

Answer:

A, B, and D are congruent

Step-by-step explanation:

ANSWER

If f is a polynomial function and x - 5 is a factor of f, then f(5) = 0

EXPLANATION

When a polynomial fraction is written in factored form,

The values in the factors, x₁, x₂, ..., xₙ are the zeros of the polynomial - also known as roots or x-intercepts.

This means that f evaluated in any of these zeros, the value of the function is zero,

Hence, f(5) = 0 if x - 5 is a factor.

not the correct answer

Step-by-step explanation:

325:5 et 195:5

65 et 39

Answer:

1/2 is left for Sonya when she gets home.

Answer:

1.55 x − 2.16

Step-by-step explanation:

Answer:

1.55 x - 2.16

Step-by-step explanation:

Answer:

I chose 793

you can chose anything from 750-799

Step-by-step explanation:

Those all round to 800

The value of r in the equation r(61/2)=5(61/2)-3.5 is 4.88.

Given an equation r(61/2)=5(61/2)-3.5.

We are required to find the value of r in the equation.

Equation is like a relationship between two or more variable that are expressed in equal to form. The equation of two variables look like ax+by=c. It may be a linear equation, quadratic equation, cubic equation and many more depending on the powers of the variable present in that equation.

In our equation the variable is r.

The equation is given as:

r(61/2)=5(61/2)-3.5

r(61/2)=305/2-3.5

r(61/2)=(305-7)/2

r(61/2)=298/2

r=(298*2)/(2*61)

r=596/122

r=4.88

Hence the value of r in the equation r(61/2)=5(61/2)-3.5 is 4.88.

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Answer:

12cd(2-3c)

Step-by-step explanation:

check:

12cd( 2 - 3c)

12cd(2) - 12cd(3c)

24cd - 36\(c^{2}\)d

Answer:

1.4 meters

Step-by-step explanation:

Given,

Volume of rectangular prism ( V ) = 18.144 cubic meters

Width ( w ) = 2.7 m

Length ( l ) = 4.8 m

To find : d

Here, d is Height ( h ).

Formula : -

V = whl

18.144 = 2.7 x 4.8 x d

18.144 = 12.96 x d

d = 18.144 / 12.96

d = 1.4 meters

\( \huge\fbox\green{ANSWER} \)

\(v = l \times w \times h\)

\(18.144 {m}^{3} = 4.8m \times 2.7m \times d\)

\(18.144 {m}^{3} = 12.96 \times d\)

\( \frac{18.144 {m}^{3} }{12.96 {m}^{2} } = \frac{12.96 {m}^{2} }{12.96 {m}^{2} } \times d\)

\(1.4m = d\)

Answer:

3/8,5/8,9/16,7/16,11/16,5/16,3/4,1/2

Step-by-step explanation:

Answer:

\(8\left(u-v\right)^2-8\left(u-v\right)\)

Step-by-step explanation:

\(\left(u-v\right)\left(u-v\right)=\left(u-v\right)^2\\\left(u-v\right)^2\cdot \:8-8\left(u-v\right)\\=8\left(u-v\right)^2-8\left(u-v\right)\)

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Answer:

point lies on circle

Step-by-step explanation:

Substitute the coordinates of the point into the left side of the equation and if equal to the right side then point lies on circle.

(4 - 1)² + (2 + 2)² = 3² + 4² = 9 + 16 = 25 = right side

Then point (4, 2 ) lies on the circle

The amount of ore (in tons) needed to obtain 126 tons of gold is approximately 1400. Option C is correct.

To determine the amount of ore needed to obtain a specific quantity of gold, we can use the concept of proportions.

Given that the ore contains 9 percent gold, we can set up the following proportion:

9/100 = 126/x

Here, "x" represents the amount of ore in tons that is needed to obtain 126 tons of gold.

By cross-multiplying and solving for "x", we find:

9x = 100 × 126

x = (100 × 126) / 9

x ≈ 1400

Therefore, the amount of ore (in tons) needed to obtain 126 tons of gold is approximately 1400. Option C is correct.

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Answer:

The value of y, when x = 48 is y = 12/5

Step-by-step explanation:

The given parameters are;

x is directly proportional to y

Where x > 0, y > 0

For x = 3. y = 5

Therefore, we have;

x ∝ a·y²

For ,x = 3, when y = 5, we have;

3 = a × 5² = 25·a

∴ a = 25/3

When x = 48, we have;

48 = 25/3×y²

y² = 3/25 × 48 = 144/25

y = √(144/25) = 12/5

y = 12/5

The value of y, when x = 48 is y = 12/5.