2x-y + 2z = -6
-3y +z = -2
2x-3z=4
Enter your answer, in the form (z, y, z), in the boxes in simplest terms

Based on the calculations, the sum of the areas of the rectangles is equal to: A. 0.25 square unit.

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

By critically observing the figure (see attachment), we can logically deduce the following information:

Width of rectangle A = 2 units

Width of rectangle B = 2 units.

Width of rectangle C = 4 units.

Next, we would determine the length and area of each of the rectangle.

The length of the first rectangle is given by:

Length of rectangle, y = 3^-x

Length of rectangle, y(0) = 3⁻⁰ = 1 units.

Length of rectangle, y = 3^-x

Length of rectangle, y(2) = 3⁻² = 0.11 unit.

Area of first rectangle = 2(0.11)

Area of first rectangle = 0.22 square unit.

For the second rectangle, we have:

Length of second rectangle, y = 3^-x

Length of second rectangle, y(4) = 3⁻⁴ = 0.012 unit.

Area of second rectangle = 2(0.012)

Area of second rectangle = 0.025 square unit.

For the third rectangle, we have:

Length of third rectangle, y = 3^-x

Length of third rectangle, y(8) = 3⁻⁸ = 0.00015 unit.

Area of third rectangle = 4(0.00015)

Area of third rectangle = 0.0006 square unit.

Now, we can calculate the sum of the areas of the rectangles:

Total area = 0.22 square unit + 0.025 square unit + 0.0006 square unit.

Total area = 0.246 ≈ 0.25 square unit.

Total area of rectangle = 0.25 square unit.

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Complete Question:

Figure 3 shows the graph of y = 3^−x and three inscribed rectangles. What is the sum of the areas of the rectangles?

[a] 0.25

[b] 0.50

[c] 2.45

[d] 6.26

[e] 12.68

The equation that best represents the depth of the pond each week is,

[tex]y=10(1.03)^{x}[/tex]

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation.

Given:

The given equation is,

[tex]y=P(1+r)^{x} \;\;\;\;\;-------equation(1)[/tex]

Depth of the pond, P = 10 feet deep

Rate of pond increase, r = 3% = 0.03

Substitute the value of P and r in the equation (1),

[tex]y=10(1+0.03)^{x}[/tex]

Therefore, The equation that best represents the depth of the pond each week is,

[tex]y=10(1.03)^{x}[/tex]

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Hence the change that Jasmine is going to receive from the expenditure on the rice is $14.4

The price of the white long grain rice  = 0.70 dollars

The price of the brown jasmine rice is 2.10 dollars

The quantity that was bought from each is 1.25 and 2.25

Hence we would have the total expenses as

0.70 dollars x  1.25 and

2.10 dollars x  2.25

= 0.875 + 4.725

= 5.6 dollars

Hence the total expenditure that Jasmine has done is 5.6 dollars. The difference would be the change that he would receive.

= $20 - $5.6

= $14.4

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Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, 1 km has approximately 39,283.2 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

From the problem, the conversion factors are given as

1 kilometer = 0.62 mile

36 inches = 1 yard

1 mile = 1760 yards

To convert 1 kilometer into inches, first, convert 1 kilometer to miles using the conversion factor, 1 kilometer = 0.62 mile

1 km = 0.62 miles

Then, convert miles to yards using the conversion factor, 1 mile = 1760 yards

1 km = 0.62 miles = 0.62 (1760 yards)

1 km = 0.62 miles = 1091.2 yards

Lastly, convert yards to inches using the conversion factor, 36 inches = 1 yard

1 km = 0.62 miles = 1091.2 yards = 1091.2 (36 inches)

1 km = 0.62 miles = 1091.2 yards = 39,283.2 inches

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The boiling point of water is 256 °F warmer than the boiling point of liquid propane.

In the question, we are given that the boiling point of a liquid is the temperature at which the liquid starts to boil. The boiling point of water is 212°F. Propane gas is used for cooking in gas grills. Liquid propane has a boiling point of -44°F.

We are asked to find how much warmer the boiling point of water is than the boiling point of liquid propane.

To find the warmth of the boiling point of water in comparison to the boiling point of liquid propane, we subtract the boiling of liquid propane from the boiling point of the water.

Thus, The warmer the boiling point of water is in comparison to the boiling point of liquid propane = The boiling point of water - The boiling point of liquid propane,

or, The warmer the boiling point of water is in comparison to the boiling point of liquid propane = 212 °F - ( -44 °F),

or, The warmer the boiling point of water is in comparison to the boiling point of liquid propane = 212 °F + 44 °F = 256  °F.

Thus, the boiling point of water is 256 °F warmer than the boiling point of liquid propane.

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The fraction of the solution present in the contaminant is 3/5.

First, we convert 50% to fractions.

Changing a percentage to a fraction is equivalent to dividing a number by 100.

500% = 500/100

Taking this into account, we get 3/(500/100).

Then, when we divide a number by a fraction, we multiply the result by the inverse of the fraction.

= 3/(500/100)

= 3 x 100/500

Further simplifying;

= 300/500

= 3/5

Therefore, the value of the fraction of contaminant solution is 3/5.

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[tex]\fbox{x = - 4} \: \sf or \: \fbox{ x = 2}[/tex]

Step-by-step explanation:

[tex] \frac{x}{2} = \frac{4}{x} - 1[/tex]

multiply whole equation with 2x,

[tex] \hookrightarrow\frac{x}{2} \times 2x = ( \frac{4}{x} \times 2x) - (1 \times 2x)[/tex]

[tex]\hookrightarrow {x}^{2} = 8 - 2x[/tex]

Rearranging above equation and making a quadratic equation,

[tex]\hookrightarrow {x}^{2} + 2x - 8 = 0[/tex]

Comparing above equation with, ax²+bx+c,

a =1, b=2, c= -8

Using formula,

[tex]x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

Substituting the given values,

[tex]x = \frac{ - 2 ± \sqrt{ {2}^{2} - 4 \times 1 \times ( - 8)} }{2 \times 1}[/tex]

[tex]x = \frac{ - 2 ± \sqrt{ 4+32} }{2}[/tex]

[tex]x = \frac{ - 2 ± 6 }{2}[/tex]

[tex]x = \frac{ - 2 + 6}{2} = \frac{4}{2} = 2[/tex]

or

[tex]x = \frac{ - 2 - 6}{2} = \frac{ -8}{2} = - 4[/tex]

[tex] \fbox{x = -4} \: \sf or \: \fbox{ x = 2}[/tex]

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Answer:

-$83

Step-by-step explanation:

Create an equation to model Nina's balance.

[tex]40-63+80-140=-83[/tex]

The length of the hypotenuse in this right-angled triangle =  6.98 cm².

The Pythagorean theorem states that the total of the squares on the legs of a right triangle equals the square upon that hypotenuse (the side opposite the right angle)—or, in popular algebraic notation, a2 + b2 = c2.

The basic formula for calculating the area of a triangle is the half square product of its base as well as height, i.e., A = 1/2 b h. This formula applies to all triangles, whether they are scalene triangles, isosceles triangles, or equilateral triangles.

Hypotenuse (c) = 8 cm

Base (b) = 3.9 cm

Length =

C² = (a² + b³)

a² = C² - b²

a = √((8)² - (3.9)²)

  = 6.98 cm²

The length of the hypotenuse in this right-angled triangle =  6.98 cm².

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Answer:Algebra 2 is the third math course in high school and will guide you through among other things linear equations, inequalities, graphs, matrices, polynomials and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, sequences and series, probability and trigonometry.

Answer:

ask his mom she probobaly weighs more

Step-by-step explanation:

The pressure of the circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top =  287.23 N/m².

A force seems to be an influence that could also cause an object's motion to change. A force can cause a mass item's velocity or acceleration to alter. The force can be expressed intuitively as a push or perhaps a pull. Because it has both magnitude and direction a force is a vector quantity.

The force applied against the surface of an item per unit area across which that force is spread is referred to as pressure (symbol: p or P).

Force = 810N

Radius of the circular table = 90cm.

Pressures  = force /area

Finding the area of circular table = πr²

                                                       = π x 90 x 10⁻² (1 cm = 10⁻²)

                                                       = 2.82 m²

substituting the value in the formula.

Pressures  = force /area

                  = 810/2.82

                  = 287.23 N/m²

The pressure of the circular table top has a radius of 90 cm. A force of 810 N is applied to the whole table top =  287.23 N/m²

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The equation which can be used to solve the the average number of miles he would have to ride to meet his target is 28.7 = 17 + 3x.

The solve equation is x = 3.9 miles.

He wants to ride his bicycle 28.7 miles this week.

He has already ridden 17 miles.

He rides for 3 more days.

The equation which can be used to determine the average number of miles he would have to ride to meet his target can be calculated as follows:

The total distance to ride is 28.7 miles.

Therefore,

28.7 = 17 + 3x

where

Therefore,

28.7 = 17 + 3x

subtract 17 from both sides of the equation

28.7 = 17 + 3x

28.7 - 17 = 17 - 17 + 3x

11.7 = 3x

divide both sides by 3

3x / 3 = 11.7 / 3

x = 11.7  /3

x = 3.9

Therefore, he needs to travels 3.9 miles daily for 3 days.

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You can see that JL = LK  and  MK ≅ JL, hence according to the transitive property, we can conclude that LK ≅ MK

A midpoint is a point that divides a line of a segment into two equal parts. It also means that the point bisects the given line.

If the point L is the midpoint of JK, then;

JL + LK = JK and;

JL = LK .........1

Similarly, K intersects MK at K, then;

MK ≅ JL..........2

From equation 1 and 2, you can see that JL = LK  and  MK ≅ JL, hence according to the transitive property, we can conclude that LK ≅ MK

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Answer:

y = - 5x - 7

Step-by-step explanation:

A line has a function:

y = ax + b

Because the line has a slope of - 5

=> a = - 5

=> y = - 5x + b

Because the line goes through point (- 1; - 2)

=> - 2 = (- 5).(- 1) + b

=> 5 + b = - 2

=> b = - 7

=> The slope intercept from of the line:

y = - 5x - 7

The baseball team can bring 11 players to the tournament based on their budget.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of players the team can bring to the tournament. They rented a bus for $856.50 and budgeted $24.75 per player for meals, hence:

24.75x + 856.5 = 1128.75

x = 11

The baseball team can bring 11 players to the tournament based on their budget.

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Answer its the first one

Step-by-step explanation:

Answer: itll be 2/3 im pretty sure

Step-by-step explanation:

Answer:

53/3

Step-by-step explanation:

[tex]x \: + 1 - \frac{2}{3} = 18 \\ x \: - \frac{2}{3} = 18 - 1 \\ x - \frac{2}{3} = 17 \\ x = \frac{17}{1} + \frac{2}{3} \\ x = \frac{51 + 2}{3} \\ x = \frac{53}{3} \\ check \\ \frac{53}{3} + \frac{1}{1} \\ = \frac{53 + 3}{3} \\ = \frac{56}{3} - \frac{2}{3} \\ = \frac{56 - 2}{3} \\ x = \frac{54}{3} \\ x \: = 18[/tex]

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Ashley and her four friends will need 5 hours and 19.57 minutes to make 1575 bags if Ashley takes 2/3 of a minute and each friend takes 75% longer.

The first sexagesimal fraction of an hour, or one-fifth of an hour, or 60 seconds, is known as the minute. On rare occasions, due to leap seconds, a minute in the UTC time zone has 61 seconds (A negative leap second might be inserted, producing a minute of 59 seconds; however, this has never occurred in more than 40 years under this system.) The minute can be used with SI units even if it isn't a SI unit. Minute or minutes is represented by the SI unit min (without a dot). Occasionally, people would slangy refer to minutes of time by the prime symbol.

Calculations:

For a bag, Ashley needs about 2/3 of a minute.

= Ashley prepare bag in 1 minute = 3/2  

Her friends takes 75%  Longer to prepare a bag

time taken by her friends =  2/3  + (75/100)(2/3)

= (2/3)( 1  + 3/4)

= (2/3)(7/4)

= 7/6  Minutes

Her one friend prepare bag in 1 minute =  6/7

Bag prepared by Ashley & her 4 friend in 1 Minute

=  3/2  +  4*6/7

=  (21 + 48)/14

= 69/14  Bag

69/14   Bag prepared in 1 minute

1 Bag prepared in    14/69   minutes

1575  bags prepared  in   1575  * 14/69

= 319.57 minutes

= 5 hrs  19.57 Minutes

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The answer to the problem of logical reasoning will be:

8 + 9 × 4 = 8 + 36 = 44

By hit and trial method, we get that:

The value of bag will be 4.

The value of book will be 9

The value of pencil will be 5.

We get that:

4 + 9 × 4 = 4 + 36 = 40

Which is true

2(8) + 8 × 4 = 16 + 32 = 48

Which is true

9 + 8 + 2(8) = 9 + 8 + 16 = 33

Which is true

So, we get that:

8 + 9 × 4 = 8 + 36 = 44

Therefore, the answer to the problem of logical reasoning will be:

8 + 9 × 4 = 8 + 36 = 44

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Answer:

Step-by-step explanation:

f(x)=3(x+7)³-9

1. Let's graph the function у=3х³

2. Shift the graph of the function to the left by 7 units along the х-axis

3. Slide the graph of the function down 9 units along the y-axis

Answer:

1) Constant

2) Decreasing

3) Increasing

Step-by-step explanation:

1) Graphically, we can say that a function is constant if we see a flat line, which means that the range is the same throughout its domain, in this case we have one flat line, therefore it is a constant function

2) The graph is going down as it moves from left to right in all the domain, that means it's decreasing

3) The graph is going up as it moves from left to right in all the domain, that means it's increasing.

Bianca should play with her phone for 1.5 hours to use the entire battery.

Bianca spent 1/2 of an hour playing on her phone which used up 1/3 of her phone's battery.

Then,

Therefore, Bianca should play with her phone for 1.5 hours to use the entire battery.

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

Work Shown:

A = 18 take bio

B = 13 take Spanish

C = 5 take both

A+B-C = 18+13 - 5 = 26 students total

------------------------------

Another approach:

18 take bio and 5 take both, so 18-5 = 13 take bio only

13 take Spanish and 5 take both, so 13-5 = 8 take Spanish only

We then have 13+8+5 = 26 students

Both methods only work when each student is in either bio, Spanish, or both. We cannot have a student who is in neither class.

The given data is quantitative, continuous, ratio.

Quantitative data is information that is expressed as counts or numbers, each of which has a specific numerical value. Data is any measurable information that may be used by academics for statistical analysis and mathematical computations so that they can derive practical conclusions.

Quantitative information provides answers to inquiries like "How many?," "How often?," and "How much?" Mathematical approaches may be used to easily verify and assess this data.

If a continuous variable has a meaningful zero point, it is regarded as a ratio (i.e., as in age or distance).

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Answer:

5

Tips to Add Negative and Positive Numbers:

1.) Adding a negative number to a positive number is subtracting it.

example: 5 + (-3) = 5 - 3

2.) Adding a positive number to a smaller negative number is subtracting the smaller number by the larger one.

example: -3 + 5 = 5 - 3

3.) Adding a positive number to a larger negative number is having the positive number subtracted by the larger negative.

example: -5 + 3 = 3 - 5  (but the final answer needs a negative sign)

4.) Adding a negative number to another negative number is adding the numbers together, but with a negative sign in the final calculation.

example: -3 + (-2) = 3 + 2  (but the final answer needs a negative sign)

5.) I think you know how to add two positive numbers

(I know the wording of the tips can be confusing, so make sure to look at the examples if you don't understand)

The slope associated with points (2, 6) and (-1, 3) is 1 so it is not a negative slope.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

Given the points,

(2, 6) and (-1, 3)

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

So,

Slope = (3 - 6)/(-1 - 2)

Slope = (-3)/(-3) = 1

Hence "Slope of the given points is +1 so it is positive".

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