A rectangular pool has an area of 640 square feet. The length is 12 feet shorter than the width. The length of the pool is response area feet and the width of the pool is response area feet.

The temperature on the surface of the planet, based on the equation for the temperature, is 47 degrees Celsius.

The equation given of y = 47 - 5x, is such that every one kilometer that we go from the surface of the planet, the temperature reduces by 5 degrees Celsius.

What this means is that at the surface of the planet the temperature is 47 degrees Celsius because this is the temperature when we have not gone a single kilometer above the surface.

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The rest of the question is:

Note that a change can be an increase or a decrease.

For an increase, use a positive number. For a decrease, use a negative number.

What is the temperature on the surface of the planet?

The relationship between the number of gallons of gas and the cost in dollars is: C. The cost of gas is $3.75 per gallon.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the number of gallons of gas and the cost in dollars on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 7.5/2

Constant of proportionality, k = $3.75.

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Answer: the answer is C just did it

The value of x in the given equation using laws of exponents is; x = -9

We want to solve the problem correctly expressed as;

3^(4x) = 27^(x - 3)

Now, some of the laws of exponents are;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

Now, 27^(x - 3) can also be expressed as;

3^(3(x - 3))

Now, according to power of power rule, if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same. Thus;

3^(3(x - 3)) = 3^(3x - 9)

Thus, we now have;

3^(4x) = 3^(3x - 9)

4x = 3x - 9

3x - 4x = 9

-x = 9

x = -9

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The chef bought a total of 4 1/5 kilograms of beans.

Number of bags of beans the chef bought= 3

Quantity of beans in each bag = 1 2/5 kilograms

Total kilograms of beans bought by the chef= Number of bags of beans the chef bought × Quantity of beans in each bag

= 3 × 1 2/5

= 3 × 7/5

= 21/5

= 4 1/5 kilograms of beans

Ultimately, the chef bought 4 1/5 kilograms of beans.

Complete question:

a chef bought 3 bags of beans. Each bag contains 1 2/5 kilogram of beans. How many kilograms of beans did she buy?

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To find the distance between the man's starting point and his final position, we can use vector addition.

Let's call the man's starting point A and his final position B. We can represent the two legs of his journey as vectors A and B, respectively.

The first leg of his journey, due west, can be represented as a vector of magnitude 4 km in the -x direction.

The second leg of his journey, on a bearing of 197°, can be represented as a vector in the -x and -y direction. We can use trigonometry to find the components of this vector.

The x component of the vector can be found using the formula:

x = magnitude * cos(angle) = d * cos(197°)

The y component of the vector can be found using the formula:

y = magnitude * sin(angle) = d * sin(197°)

where d is the magnitude of the vector (the distance the man traveled in this leg of his journey).

To find the magnitude of the vector, we'll use the Pythagorean theorem:

d^2 = x^2 + y^2

We can substitute the x and y components we found above into this equation to find d:

d^2 = (d * cos(197°))^2 + (d * sin(197°))^2

d^2 = d^2 * (cos^2(197°) + sin^2(197°))

d^2 = d^2

d = sqrt(d^2) = sqrt(d^2)

So the magnitude of the vector is d.

Next, we can add the two vectors to find the total distance from the man's starting point to his final position:

distance = sqrt((4 - d * cos(197°))^2 + (d * sin(197°))^2)

This is the distance the man is from his starting point. To find the exact value, we would need to know the value of d. However, without that information, this is as far as we can take the calculation.

There will be a total of 741 greetings at the mother-daughter tea.

Two or more expressions with an Equal sign is called as Equation.

Let's start by counting the number of greetings between the host mother-daughter pair and the other 19 mother-daughter pairs.

Since each pair only greets once, the host pair will make 19 greetings.

Now we need to count the number of greetings between the 19 guest mothers and the other 19 mother-daughter pairs

Each of the 19 guest mothers will greet 18 other mother-daughter pairs, for a total of 19 x 18 = 342 greetings.

Finally, we need to count the number of greetings between the 19 guest daughters and the 20 mothers

Each of the 19 guest daughters will greet 20 mothers

Total is 19 x 20 = 380 greetings.

By adding all we get 741 greetings

Therefore, there will be a total of 741 greetings at the mother-daughter tea.

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The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

Solution to the quadratic equation

The solution to the quadratic equation is determined as follows;

2x² + 12x - 3 = 0

2x² + 12x = 3

divide through by 2

x² + 6x = ³/₂

take half of coefficient of x, square it and add it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

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Answer:

Let's call the number of cubic yards of mix A that the farmer buys "x", and the number of cubic yards of mix B that the farmer buys "y".

We can write the following constraints based on the minimum monthly requirements:

20x + 10y >= 460 (for acid)

30x + 30y >= 939 (for nitrogen)

5x + 10y >= 200 (for potash)

We also want to minimize the cost, which is given by 25x + 49y.

This is a linear programming problem, which can be solved using simplex method or the graphical method.

By using the graphical method, we find that the optimal solution occurs at x = 11.75 and y = 4.5. This means that the farmer should buy 11.75 cubic yards of mix A and 4.5 cubic yards of mix B to meet the minimum monthly requirements at a minimum cost.

So, the answer to the question is: If mix A costs $25 per cubic yard and mix B costs $40 per cubic yard, the farmer should blend 11.75 yd of mix A & 4.5 yd of mix B to meet the minimum monthly requirements at a minimum cost.

Answer:

The answer

Step-by-step explanation:

Figure 1 figure

3/4

Answer:

120°

Step-by-step explanation:

360 / 12

30 X (5-1)

30 X 4= 120°

The triangles given can be determined to be :

You can use the Pythagorean Theorem and its Converse to determine the type of triangle.

The Pythagorean Theorem and its Converse are basically :

c ² = a² + b ²   This is a right angled triangle

c ² > ( a² + b ² ) This is an obtuse triangle

c ² < ( a² + b ² )

The triangles are :

13 :

26 ² = 24 ² + 10 ²

676 = 676

Right - angled

14 :

20 ² = 13 ² + 6 ²

400 > 205

Obtuse triangle

15 :

17 ² = 16 ² + 3 ²

289 > 265

Obtuse triangle

16 :

32 ² = 29 ² + 24 ²

1, 024 < 1, 417

Acute triangle

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Step-by-step explanation:

Your picture looks blurry however I think the graph passes through the points (0,0)(-1,0) and (3,0) so the equation becomes

[tex](x +1)(x - 3)x[/tex]

[tex] {x}^{3} - 2x {}^{2} - 3x + c[/tex]

Where C is the y intercept.

Since C is 0, our equation becomes

[tex] {x}^{3} - 2 {x}^{2} - 3x[/tex]

Step-by-step explanation:

This symbol is signma, which is the sub of all the X's after plugging them into the equation.

Just to show the pattern, the first 3 numbers on your table are 15, 13, and 13... doing those 3 with Sigma, and simplifying

[tex]( {1 5 - 2)}^{2} + ({13 - 2)}^{2} + {(13 - 2)}^{2} [/tex]

[tex]169 + 121 + 121[/tex]

You would pretty much do that all the way down the list.

After doing so, we wind up with

15, 13, 13, 4, 19, 12, 6, 5, 14

[tex]169 + 121 + 121 + 4 + 289 + 100 + 16 + 9 + 144[/tex]

Adding these together gets your answer of:

[tex]973[/tex]

Answer:

The number is 29.

Step-by-step explanation:

"five times the sum of a number and two" can be represented as 5(x + 2), where x is the number. "nineteen less than six times the number" is the same as 6x - 19. The word "is" determines that these two parts are equal. So, 5(x + 2) = 6x - 19.

Solve:

5x + 10 = 6x - 19

10 = x - 19

x = 29

Check:

5 * (29 + 2) = 5 * 31 = 155

(6 * 29) - 19 = 155

155 = 155

Answer:B

Step-by-step explanation:

Answer:

[tex]sin(P)=\frac{\sqrt{55}}{10}[/tex]

Step-by-step explanation:

The sine function is defined as a ratio of sides: [tex]sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

where the "opposite" side is quite literally the opposite side, if you went straight from the angle, whatever side it's pointing towards is the opposite angle. The hypotenuse... is as the name implies, the hypotenuse. The symbol inside the parenthesis next to the sine is called theta and is just used to represent some angle.

We of course don't know the hypotenuse as it's not given, but we can use the Pythagorean Theorem to solve for the hypotenuse:

[tex]c^2=\sqrt{45}^2+\sqrt{55}^2\\c^2=45+55\\c^2=100\\c=10[/tex]

We do know the opposite side though, it's just the square root of 55, it's directly opposite of the angle P. Plugging in known values we get the following: [tex]sin(P)=\frac{\sqrt{55}}{10}[/tex] and we can't simplify this any further as 45 has no factors which are perfect squares.

In the absence of trade between Glacier and Sequoia, Glacier would consume 8 million pairs of shorts and 48 million pounds of almonds, and Sequoia would consume 15 million pairs of shorts and 20 million pounds of almonds. However, if both countries decide to engage in trade, Glacier could specialize in producing shorts, using 1 million hours of labor per week, and Sequoia could specialize in producing almonds, using 1 million hours of labor per week. This specialization would result in Glacier producing 12 million pairs of shorts and Sequoia producing 24 million pounds of almonds. This would enable each country to consume more of both goods than they could produce in the absence of trade.

The fomulas of the sequence are a(n) = 3200(1.09)^n-1 and a(n) = a(n - 1) * 1.09

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

First term, a = 3200

Increment, r = 9%

To find the explicit formula, we can use the formula for compound interest:

a(n) = a * (1 + r)^n-1

So, we have

a(n) = 3200(1.09)^n-1

For the recursive formula, we have

a(n) = a(n - 1) * 1.09

This is because the product of the current term and the incremnt rate gives the next term

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Step-by-step explanation:

It's a long answer. You have to find the area of the large triangle, the small triangle than subtract the two

A = 1/2(b)(h)

For the big triangle

A = 1/2(16)(4) = 1/2(64) = 32

For the small triangle

A = 1/2(8)(2)

We use 8 and 2 because that's half of 16 and 4, since at the bottom it says A and B are midpoints

A = 1/2(8)(2) = 1/2(16) = 8

Now we subtract

32-8 = 24 units

The equation of the line will be y = -3/4x + 1.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of the line is -3/4 and the y-intercept is 1. The equation of the line can be written as:-

y = mx + c

y = -3/4x + 1

Therefore, the line will have the equation y = -3/4x + 1.

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The reflection of point (-6, -5) across the x-axis will give (-6, 5)

A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or center of the figure.

Given is a point (-6, -5), we need to find the coordinates of the point when it is reflected across the x-axis,

The rule for a reflection across the x-axis -:

The rule for reflecting over the x-axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

i.e, (x, y) → (x, -y)

Therefore,

(-6, -5) → (-6, 5)

Hence, the reflection of point (-6, -5) across the x-axis will give (-6, 5)

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The question is incomplete, the question is solved for:

Reflect point (-6, -5) across x-axis

Answer:

Step-by-step explanation:

To find the distance Tyler needs to swim, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, which is the hypotenuse.

In this case, the two shorter sides of the triangle are 40 feet and 80 feet, and the hypotenuse is the distance Tyler needs to swim to reach Jason. So we can write the equation as follows:

40^2 + 80^2 = d^2

where d is the distance Tyler needs to swim.

Expanding the equation:

1600 + 6400 = d^2

8000 = d^2

Taking the square root of both sides:

d = sqrt(8000) = 80 * sqrt(2)

So, Tyler needs to swim a distance of 80 * sqrt(2) feet, or approximately 113.1 feet, to reach Jason.

if the second number is lower than that's the answer. so in this case kayla

The information regarding the addition is explained below.

Adding 29 + 46:

Student 1: May use the traditional column addition method, lining up the digits in the ones, tens, and hundreds place and carrying over if necessary.

Student 2: May use the breaking apart method, where they break apart the numbers into smaller parts (e.g. 20 + 40) and then add the pieces together.

Student 3: May use a number line, counting up from 29 by the increments of 46 until they reach the sum.

Subtracting 54 - 28:

Student 4: May use the traditional column subtraction method, lining up the digits in the ones, tens, and hundreds place and borrowing if necessary.

Using bundled things to explain regrouping in the addition problem 167 + 59:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the ones as ten ones to make a bundle of ten.

Then add the tens and hundreds place to get the answer 226.

Using bundled things to explain regrouping in the subtraction problem 231 - 67:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the tens as ten tens to make a bundle of a hundred.

Then subtract the hundreds place and the tens place to get the answer 164.

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The Expression with coefficient 4 and -9 is 4j and -9j.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

We have to write the coefficient as 4 and -9.

As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.

So, with coefficient 4 the expression is 4j

and, with coefficient  -9 the expression is -9j.

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Tone is the feeling the author wants the reader to have when reading his or her work. Anaya employs tone to generate the texts "Take the Tortillas out of your poetry" and "Speaking Arabic."

Both authors explore regional cuisine and make use of terminology from various languages.

While Nye's tone is welcoming of mixed cultures, Anaya's tone is sincere towards culture and indignant towards suppression.

The funny tone of Anaya's writing reflects his intention to draw attention to the subject. The laid-back nature of Anaya's delivery is evident.

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The given triangles can be classified based on their sides and angles as:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

Triangles can be classified by both their sides and their angles.

Classification by sides:

Classification by angles:

Thus, using the sides or angles of the given triangles, they are classified as follows:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

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Answer:

The number of books sold were:

Math textbooks: 426
Sociology textbooks = 46

Step-by-step explanation:

Let us use the variable [tex]m[/tex]  to represent the number of math books sold

Let us use the variable [tex]s[/tex]  to represent the number of math books sold

Combined total of 426 math and sociology books were sold is represented by the equation:
[tex]m + s = 426\quad\quad\quad(1)[/tex]

Number of math books sold was 46 more than the number  of sociology textbooks sold is given by
[tex]m - s = 46\quad\quad\quad(2)[/tex]

Adding the equations (1) + (2):
[tex](m + s) + (m - s) = 426 + 46\\\\2m = 472\\\\m = \dfrac{472}{2}\\\\m = 236\\\\[/tex]

Using Equation (1): [tex]m + s = 426[/tex]  we get

[tex]236 + s = 426\\\\s = 426 - 236\\\\s = 190[/tex]