The expression 12x+8 represents the perimeter of a square write 12x+8 as a product then tell what expression represents one side of the square.

Answer:

Part A: 8.4 minutes per mile

Part B: 38 minutes

Explanation on Part B: (put it in your own context)

8.4 + 1.1 = 9.5 minutes per mile

As 9.5 * 4 = 38 minutes

Enjoy ;)

Answer:

yes

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

I passed 7th grade with a B

The solution to the given system of equations using different methods are as follows:

(a) Naïve Gauss elimination: x = -1, y = 2, z = 0.

(b) Gauss elimination with partial pivoting: x = -1, y = 2, z = 0.

(c) Gauss-Jordan elimination without partial pivoting: x = -1, y = 2, z = 0.

(a) To solve the system of equations using naïve Gauss elimination, we perform the following steps:

1. Multiply the first equation by 6 and the third equation by 21 to eliminate x.

6x + 6y - 6z = -18

-63x + 84y + 21z = 21

2. Add the modified first equation to the second equation to eliminate x.

6x + 2y + 2z = 2

0x + 86y + 15z = 4

3: Solve the resulting system of equations.

6x + 2y + 2z = 2     (Equation 1)

0x + 86y + 15z = 4   (Equation 2)

From Equation 1, we have:

6x = 2 - 2y - 2z

x = (2 - 2y - 2z)/6

x = (1 - y - z)/3

Substituting the value of x in Equation 2, we have:

0(1 - y - z)/3 + 86y + 15z = 4

86y + 15z = 4

15z = 4 - 86y

z = (4 - 86y)/15

4. Now, we can substitute the obtained values of x and z back into the first equation to find y:

(1 - y - z)/3 + y - (4 - 86y)/15 - 3 = -3

Solving this equation, we get y = 2.

5. Substituting the values of y and z back into x, we have:

x = (1 - 2 - (4 - 86*2)/15)/3

x = -1

Therefore, the solution to the given system of equations using naïve Gauss elimination is x = -1, y = 2, z = 0.

(b) To solve the system of equations using Gauss elimination with partial pivoting, we'll perform the following steps:

1: Rearrange the equations to form an augmented matrix:

[1, 1, -1 | -3]

[6, 2, 2 | 2]

[-3, 4, 1 | 1]

2: Find the pivot element by selecting the row with the largest absolute value in the first column. Swap rows if necessary:

[6, 2, 2 | 2]

[1, 1, -1 | -3]

[-3, 4, 1 | 1]

3: Perform row operations to create zeros below the pivot element in the first column:

R2 = R2 - (1/6)R1

R3 = R3 + (1/2)R1

The new matrix becomes:

[6, 2, 2 | 2]

[0, 5/3, -5/3 | -17/3]

[0, 5, 7/2 | 5/2]

4: Continue row operations to eliminate the second variable from the third row:

R3 = R3 - (5/3)R2

The matrix after this step is:

[6, 2, 2 | 2]

[0, 5/3, -5/3 | -17/3]

[0, 0, 32/3 | 22/3]

5: Back-substitution to find the values of the variables:

z = (22/3) / (32/3) = 0

y = (-17/3 - (-5/3)z) / (5/3) = 2

x = (2 - 2y + z) / 6 = -1

Main Answer:

The solution to the given system of equations using Gauss-Jordan elimination without partial pivoting is:

x = -1

y = 2

z = 0

The solution is x = -1, y = 2, and z = 0.

(c) To solve the system of equations using Gauss-Jordan elimination without partial pivoting, we'll perform the following steps:

1: Rearrange the equations to form an augmented matrix:

[1, 1, -1 | -3]

[6, 2, 2 | 2]

[-3, 4, 1 | 1]

2: Perform row operations to create zeros above and below the pivot element in the first column:

R2 = R2 - 6R1

R3 = R3 + 3R1

The new matrix becomes:

[1, 1, -1 | -3]

[0, -4, 8 | 20]

[0, 7, -2 | -8]

3: Continue row operations to create a diagonal matrix with ones on the main diagonal and zeros elsewhere:

R1 = R1 + R2

R3 = R3 + (7/4)R2

The matrix after this step is:

[1, -3, 7 | 17]

[0, -4, 8 | 20]

[0, 0, 1 | -1]

4: Further simplify the matrix to get the final solution:

R1 = R1 + 3R3

R2 = R2 - 2R3

The matrix becomes:

[1, 0, 0 | -1]

[0, -4, 0 | 2]

[0, 0, 1 | -1]

The solution is x = -1, y = 2, and z = 0.

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Equation and solution of equation :

17.25 + p(17.50) = 69.75

17.25 + 17.50p = 69.75

17.50x = 69.75 - 17.25

17.50p = 52.50

p = 52.50/17.50

p = 3

So three people can go to the amusement park (assuming that they are all travelling together in the same car).

The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

A group of friends wants to go to the amusement park. they have $69.75 to spend on parking and admission. Parking is $17.25, and tickets cost $17.50 per person, including tax.

Let p be the number of people. Then the equation is given as,

17.50p + 17.25 = 69.75

The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.

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Answer:

\(10\sqrt{2}\)

Step-by-step explanation:

The diagonal of any square with side length \(s\) is equal to \(s\sqrt{2}\). Since the side length of the square is 10, the diagonal must be \(\boxed{10\sqrt{2}}\).

To support and prove this:

The diagonal creates two 45-45-90 triangles, with the diagonal being the hypotenuse of both of these triangles. The Pythagorean Theorem states that in any triangle, the sum of the squares of both legs is equal to the square of the hypotenuse (\(a^2+b^2=c^2\)).

Call the diagonal \(d\). In these two triangles, both legs are equal to 10 (the side lengths of the square), and the hypotenuse is the diagonal. Thus, we have:

\(10^2+10^2=d^2,\\100+100=d^2,\\d^2=200,\\d=\sqrt{200}=\sqrt{100}\cdot \sqrt{2}=\boxed{10\sqrt{2}}\)

Answer:

Step-by-step explanation:

The side making up the top triangle is also 10.

a^2 + b^2 = x^2             Pythagoras

Givens

a = b                              Property of a square

a = 10

b = 10

Solution

10^2 + 10^2 = x^2

100 + 100 = x^2

x^2 = 200

x^2 = 2 * 100

sqrt(x^2) = sqrt(2 * 100)

x = 10*sqrt(2)

The elimination method is a method for solving systems of linear equations.

The method of elimination  consists of removing the same variable from two equations and then finding the value of the other variable that is not eliminated after taking the difference between the two equations.

An equation of the form Ax By = C. Here x and y are variables and A, B and C are constants.

To solve the variables of the given equations by elimination method Let's look at a short comprehensible example.

2x + y = 7 ------> (1)

x + y = 5 -------> (2)

To eliminate 'y', subtract (1) - (2),

2x + y - x - y = 7 - 5

x = 2

Substitute x = 2 in equation(1),

2(2) + y = 7

4 + y = 7

y = 3

Therefore, x = 2, y = 3

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The values of (x - 1/x) = √32 and  x² + 1/x² = 34.

Algebraic identities are mathematical equations or expressions that hold true for all values of the variables involved.

Using some algebraic identities we can solve the given problem. Here are some commonly used algebraic identities:

=> (a + b)² = a² + b² + 2ab

=> (a - b)² = a² + b² - 2ab

Here we have

=> x+1/x = 6  

Do squaring on both sides

=> (x + 1/x)² = 36

As we know (a + b)² = a² + b² + 2ab

=> x² + 1/x² + 2x (1/x)  = 36  

=> x² + 1/x² + 2 = 36  

=> x² + 1/x²  = 36 - 2

=>  x² + 1/x² = 34  ---- (1)

As we know (a - b)² = a² + b² - 2ab

=> (x - 1/x)² = x² + 1/x² - 2 x(1/x)

=> (x - 1/x)² = x² + 1/x² - 2  

=> (x - 1/x)² = 34 - 2     [ From  (1) ]

=> (x - 1/x) = √32

Therefore,

The values of (x - 1/x) = √32 and  x² + 1/x² = 34.

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Answer:

Step-by-step explanation:

Unfortunately, I cannot answer this question without additional information about the distances traveled and the time taken by Reiko to travel from point A to point B and back to point A.

The speed at which Reiko traveled is calculated as distance divided by time. Therefore, we need to know both the distance and time for each leg of the journey to determine the speed.

Without this information, it is not possible to determine whether Reiko traveled from A to B at a speed greater than 40 miles per hour.

As per the given Ratio difference between the amount of money spent and the amount of money saved in a week is $2.

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.

The ratio formula can be used to represent a ratio as a fraction. For any two quantities, say a and b, the ratio formula is a:b = a/b. Because a and b are separate amounts for two portions, the total quantity is given as (a + b).

et 5x be the money he spends and 4x be the amount he saves

therefore, 5x+4x= 18

9x= 18

x= 18/9= 2

Tom spends, 5×2 = $10

and he saves, 4×2= $8

Difference, = $10-$8= $2

Therefore, as per the given ratio in the question difference between the amount of money spent and the amount of money saved in a week is $2.

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Tom receives $18 from his father in a week. The ratio of the amount of

the money he spends to the amount of money he saves in a week is 5:4

What is the difference between the amount of money spent and

amount of money saved in a week?

For the given number 395,621 round off it to nearest ten thousand is equal to 400,000.

As given in the question,

Given number is equal to :

395,621

Round off the given number 395,621 to nearest ten thousand is given by:

395,621 = 300,000 + 95,621

Ten thousand is represented by 95,621 for the given number

95621 is in between two numbers

90,000< 95,621 < 100,000

95,621 is more closer to 100,000

After rounding it off to the nearest ten thousand

300,000+ 100,000 = 400,000

Therefore, for the given number 395,621 round off it to nearest ten thousand is equal to 400,000.

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Answer:

they are skewed i believe

Answer:

parallel

Step-by-step explanation:

they are parallel because AB and DE match with each other in a parallel form

The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

Given that,

The function is f(x)= (x-5)³(x+2)²

We have to find at which root does the graph function touch the x-axis.

We know that,

Mathematical calculus' core component is functions. The unique forms of relationships are the functions. When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x.

Take the function

f(x) = (x-5)³(x+2)²

f(x) = 0 if a curve touches the x-axis.

⇒ (x - 5)³(x + 2)² = 0.

But if ab = 0

So, a=0 and b=0

⇒ (x - 5)³ = 0 and (x + 2)² = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x=5 and x=-2.

Therefore, The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

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The latest sentence of proof by using the triangle congruence method we can conclude that f+e=c, \(a^{2} + b^{2} = c^{2}\).

Given that ΔABC and ΔCBD are right triangles

Therefore, one angle of both triangle is of 90°

So, ∠B is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Consequently, ∠A is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Similarly, When two triangles are similar then their corresponding angles are equal and their corresponding sides are also equal.

Therefore , the two proportions can be rewritten as

a² = cf ( equation 1 )

b² = ce ( equation 2 )

By adding b² on both side of equation 1 then we can write equation 1 as

\(a^{2} + b^{2} = b^{2}+cf\)

\(a^{2} + b^{2} = ce+cf\)

Because b² and ce are equal and substitute on the right side of equation 1

Using the converse of distributive property  in above equation then we get a new equation. That is,

\(a^{2} +b^{2} = c(f+e)\)

Because distributive property is a(b+c)=a(b+ac)

a² + b² = c²

Because e + f = c²

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Answer:

x=5 ; x=1

Step-by-step explanation:

plug in:

2(x^2+2) -3 = (2x-3)^2 +2

simplify:

2x^2 + 1 = 4x^2- 12x + 10

Move everything to one side:

2x^2 + 1 = 4x^2- 12x + 10 ---> 0= 2x^2 -12x +10

Factor

2(x-5)(x-1)=0

x=5

x=1

Spermatophyta and Bryophyta differ in terms of their mode of reproduction, presence of vascular tissues, dominance of generation, plant structure, and habitat preferences.

Spermatophyta and Bryophyta are two distinct groups of plants with several differences. Here are five differences between them:

Reproduction: Spermatophyta (seed plants) reproduce through seeds, while Bryophyta (mosses and liverworts) reproduce through spores.

Vascular Tissue: Spermatophyta possess well-developed vascular tissues, including xylem and phloem, that transport water, nutrients, and sugars throughout the plant. In contrast, Bryophyta lack true vascular tissues and rely on diffusion to transport water and nutrients.

Dominant Generation: In Spermatophyta, the sporophyte generation is dominant and larger in size, while the gametophyte generation is reduced. Bryophyta, on the other hand, have a dominant gametophyte generation, which is the visible leafy part of the plant, while the sporophyte generation is smaller and dependent on the gametophyte.

Structure: Spermatophyta exhibit well-differentiated plant structures, including roots, stems, and leaves. In Bryophyta, these structures are simpler and lack true roots, stems, and leaves. Instead, they have rhizoids for anchorage and absorption.

Habitat: Spermatophyta can be found in diverse terrestrial environments, ranging from deserts to forests, while Bryophyta are typically found in moist and shady habitats, such as damp soil, rocks, or tree bark.

These differences reflect the varied adaptations and ecological roles of these two plant groups.

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Answer:

Ans = 65

Step-by-step explanation:

2x3 + 5x + 9

2x3 + 5x10 + 9

6 + 50 + 9

56 + 9

= 65

When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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Answer: h=39

Step-by-step explanation:

1. First we have to divide $612.50 by $12.50 because Chandra needs to earn this much money, and she earns $12.50 every hour.

2. 612.50/12.50=49

3. Chandra needs to work 39 hours to earn $612.50.

4. h=39

Answer:

x=9

Step-by-step explanation:

Since we know that 4x=36, we would have to do the inverse operation of the multiplication to isolate the variable. Thus, we do 4x/4 and 36/4. (Since you have to do it on both sides.)

Which would equal to x=9.

In equation form:

4x=36

÷4 ÷4

-----------

x = 9

Hope this helps!!! ^^

Based on the information provided about the scatterplot, we can draw a conclusion by analyzing the data points and their correlation with individual's weight and time it takes to raise their pulse rate to 140 beats per minute.

Step 1: Observe the scatterplot and identify the patterns or trends in the data.

Step 2: Compare the o's (females) and the +'s (males) to see if there are noticeable differences or similarities in the data.

Step 3: Determine if there is a positive, negative, or no correlation between weight and time taken to reach 140 beats per minute.

Step 4: Based on the observations, draw a conclusion about the most accurate statement regarding the data. Unfortunately, I cannot see the scatterplot itself, so I am unable to provide you with the most accurate conclusion.

However, using these steps, you can analyze the scatterplot and determine the correct conclusion.

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Answer: F 15.57

Step-by-step explanation:

2.86+1.57= 4.43

20-4.43=15.57

Answer:  (-4,0)

Step-by-step explanation:

y = 1/2x +2  

x = -4

y = 1/2(-4) + 2    [To find the solution, we use x=-4 to solve for y, so plug in -4 for x]

y = -2 + 2

y = 0

And we use y = 0, to find the x.

0 = 1/2x + 2

-2 = 1/2x            [Subtract 2 from both side]

1/2x = -2             [Rewrite it]

    x =  -2 / (1/2)

    x = -4

So we find the solution (-4,0)

Answer:

Yes

Step-by-step explanation:

This is already tough due to 33 being an odd number of people. And obviously, an amount of people can't be a decimal.

So in order to do this, simply divide 33/3 which is 11. This would mean there would be 3 people per classroom.

3 people in each of the 11 classrooms!

That's it, solved!

Thank you,

Eddie

Answer:the answer is -0.5 pound(s)

Step-by-step explanation:

Negative values means the cat's weight decreased from the previous month.

Positive values means the cat's weight increased from the previous month.

We want how much change in the last 3 months cat had gone though. We simply add up the changes.

-0.7 + 0.5 - 0.3 = -0.5

This means the cat's total weight change in all three months is decrease of 0.5 pounds.

Answer:

The function displayed in the table is best described as an Exponential Decay Function.

Step-by-step explanation:

            First, the main difference between a linear and an exponential function is the shape of its graph, as well as the presence of either a constant ratio or a constant rate of change.

            Linear functions are functions with a base function of  \(f(x)=mx+b\), which has a constant rate of change (\(m\)), and the shape of its graph will be a straight line.

            Exponential functions on the other hand use the base function \(f(x)=a^x\), where \(a\) is the constant ratio of the function, and its graph is curved and has a horizontal asymptote that the graph will approach but never touch as it either increases or decreases to positive or negative infinity respectively.

            The function in the problem gives you four points that are on its graph: (-2, 540), (-1, 270), (0, 135), and (1, 67.5). Using these points, you can determine whether it is a linear or exponential function. You can tell that when the x-value increases by 1, the f(x) value is divided by 2, or multiplied by \(\frac{1}{2}\). Since there is a constant ratio instead of a constant rate of change in the function, you would know that the function in the table is an exponential function. Since the function is also constantly decreasing, the function would be best described as an Exponential Decay Function.

Have a great day! Feel free to let me know if you have any more questions :)

The sum of the series converges to 7 / (1 + 2z), and the domain for which it converges is -1/2 < z < 1/2.

To find the sum of the given geometric series\(7−14z+28z^2−56z^3+\)⋯, we need to first identify the first term (a) and the common ratio (r).
Step 1: Identify the first term (a)
The first term is 7.
Step 2: Identify the common ratio (r)
Observe the series and find the ratio between consecutive terms:
-14z / 7 = -2z
\(28z^2 / -14z = -2z\)
\(-56z^3 / 28z^2 = -2z\)
The common ratio is -2z.
Step 3: Determine the convergence of the series
A geometric series converges when the absolute value of the common ratio (|r|) is less than 1:
| -2z | < 1
To solve for the domain of z, we need to find the values for which this inequality holds:
-1 < -2z < 1
Divide all parts of the inequality by -2, and remember to reverse the inequality signs when dividing by a negative number:
1/2 > z > -1/2
Step 4: Find the sum of the converging series
For a converging geometric series, the sum can be calculated using the formula:
sum = a / (1 - r)
Plug in the values of a and r:
sum = 7 / (1 - (-2z))

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