what is the gradient of the straight line AB in the figure above​

The solution for the system of linear equations is: x₁ = -1, x₂ = -3, x₃ = 3 and x₄ = -2

To solve this system of linear equations, we can use the Gaussian elimination method. First, let's represent the system as an augmented matrix:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

| -1 -1  1  0 |  1 |

|  0  0  2 -1 |  4 |

Add the first row to the third row to eliminate x₁ in the third row:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0 -1  3  0 |  6 |

|  0  0  2 -1 |  4 |

Add the second row to the third row to eliminate x₂ in the third row:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0  0  3 -1 |  5 |

|  0  0  2 -1 |  4 |

Divide the third row by 3

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0  0  1 -1/3 |  5/3 |

|  0  0  2 -1 |  4 |

Subtract twice the third row from the fourth row to eliminate x₃ in the fourth row

|  1  0  2  0  |  5  |

|  0  1  0 -1  | -1  |

|  0  0  1 -1/3 |  5/3 |

|  0  0  0 -1/3 |  2/3 |

Multiply the fourth row by -3 to get x₄

|  1  0  2  0  |  5  |

|  0  1  0 -1  | -1  |

|  0  0  1 -1/3 |  5/3 |

|  0  0  0  1  | -2  |

We can use back substitution to find the values of x₁, x₂, and x₃:

x₄ = -2

x₂ - x₄ = -1 which is x₂ = -1 + (-2) = -3

x₃ - (1/3)x₄ = 5/3 therefore; x₃ = 5/3 + (1/3)(-2) = 3

x₁ + 2x₃ = 5 therefore;  x₁ = 5 - 2(3) = -1

The above answer is in response to the full question below;

Solve this system of linear equations

x₁ + 2x₃ = 5

x₂ - x₄ = -1

-x₁ - x₂ + x₃ = 1

2x₃ - x₄ = 4

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Answer:

d. x = 7

Step-by-step explanation:

\(\frac{32}{8} = \frac{28}{x}\)

Cross multiply, the denominator "8" is multiplied by numerator "28", while the numerator "32" is multiplied by denominator "x":

8 * 28 = 224

32 * x = 32x

\(32x = 224\)

Divide both sides by 32:

\(\frac{32}{32} = \frac{224}{32}\)

[x = 7]

Answer:

okbhyuugggfububububhhhukjgyi

Answer:

I think they are correct

Answer:

Step-by-step explanation:

\(A=p(1+rt)\\p=4000\\r=15 \%\\t=\frac{1}{3}years\\\)

∴ \(A=4000[1+(0.15\times\frac{1}{3})]\\A=4,000*0.05\\A= 4,200 (200\\)

Answer:

4,150

Step-by-step explanation:

Answer:

c) +20

Step-by-step explanation:

10 colder goes down

so 30-10= 20

Answer:

the last one

Step-by-step explanation:

it is because there are y² which shows that the it is quadratic equation, not a linear equation

Answer:

last

Step-by-step explanation:

linear are all the equation that have variable x and y to the first degree

the last one as a y^2 so in not linear

Answer: x=1.75

Step-by-step explanation:

Answer:

∠A= ∠E, ∠H = ∠D

and the last one

Step-by-step explanation:

opposite angles are equal, alternative interior angle are equal.

Answer:

∠A = ∠E and ∠H = ∠D.

∠E = ∠H and ∠F = ∠G

Step-by-step explanation:

Angles A and E are one set of corresponding angles and angles H and D are another set.  Corresponding angles are always congruent to each other and thus equal. Therefore, ∠A = ∠E and ∠H = ∠D.

Angles E and H are one set of vertical angles and angles F and G are another set.  Vertical angles are also always congruent to each other and thus equal.  Therefore ∠E = ∠H and ∠F = ∠G

Answer:

A. 42½ units

Step-by-step explanation:

the volume = 5×2×4¼ = 10×4¼ = 42½

Answer:

y = -24x + 8 is changing more quickly

Step-by-step explanation:

the slope of a line illustrates the rate of change

since slope is determined by the coefficient of the 'x' term, we can easily identify it when the equation is in slope-intercept form

the greater the absolute value of the coefficient of the slope is, the steeper the line, or the more rapid the rate of change is

Given the proportion:

Let's determine the terms that are called the means.

In a proportion, the second and third terms are called the means, while the first and last terms are called the extremes.

Let's take the proportion below as an example:

The means are b and c, while the extremes are a and d.

The given proportion can be written as:

Here, the second and third terms are 36 and 2 . Therefore, we can say the means of the proportion are 36 and 2.

ANSWER:

36 and 2

The corresponding element in the range of the function F when 7 is in the domain is 4.6.

The expression for the given function F following as:

F(x) = 6(x) - 19 / 5

The corresponding element in the range of the function F is the output of the function when 7 is input into the function.

To find this output, we can substitute 7 for X in the expression for the function F:

F(7) = 6(7) - 19 / 5

F(7) = 42 - 19 / 5

F(7) = 23 / 5

F(7) = 4.6

Thus, when 7 is in the domain, the equivalent element in the range of the function F is 4.6.

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Answer: P=$7,1333.33

Step-by-step explanation:

Equation: P=A/(1+rt)

Answer:

150 votes

Step-by-step explanation:

If Lucy got 5/6, we can do the following.

(5/6) * 180 = 150

So, Lucy got 150 votes.

Answer:

150

Step-by-step explanation:

We can first divide 180 by 6:

180/6 = 30

Then multiply that by 5:

5 × 30 = 150

Answer:

Solution is given in the photo

The total cost for X hours is the fixed cost of $15 plus the variable cost of $4 per hour which is equal to 4*X, so the total cost is 4*X + 15 

If Margie does not want to spend more than $27 then the inequality is 

4*X + 15 <= 27

4*X <= 12

X <= 3 

If Margie does not want to spend more than $27 then she cannot rent the bicycle for more than 3 hours 

Answer:

Step-by-step explanation:

let's every hour be x

first condition

therefore,

15

therefore

15+4x (as per our is x)

last condition

therefore,

15+4x≤27 (≤ is because as it says"does not want to spend more than $27"

few things about solving inequality

the direction of the inequality won't change

if

the direction of inequality will change

if

\(step - 1 \colon \: define\)

\(15 + 4x \leqslant 27\)

\(step - 2 \colon \: \\ subtract \:15 \: from \: both \: sides\)

\(15 - 15 + 4x \leqslant 27 - 15\)

\(4x \leqslant 12\)

\(step - 3 \colon \: \\ divide \: both \: sides \: by \: 4\)

\( \frac{4x}{4} \leqslant \frac{12}{4} \)

\(x \leqslant 3\)

\( \therefore \: she \: can \: rent \: the \: bicycle \: for \: 3 \: hours\)

Using translation concepts, the equation of the graph of f(x) is given as follows:

\(f(x) = \sqrt{x - 1}\)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Function f(x) is a shift right of one unit of the square root function, hence x -> x - 1 and the equation is given by:

\(f(x) = \sqrt{x - 1}\)

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The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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Answer:

-log_4

Step-by-step explanation:

The value of log1/4 rounded to the nearest hundredth is -0.60

Given the parameter which is needed for our Calculation:

Using a calculator, the value of log1/4 is -0.602059

Rounding to the nearest hundredth, is two digits after the decimal point.

Hence, we have ;

Therefore, log1/4 is -0.60

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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Answer:

-9x^4-1/4x+2

Step-by-step explanation:

To write any polynomial in standard form, we look at the degree of each term. Then, we order each term by degree, from largest to smallest, from left to right.

2 - 9x⁴ - 1/4×​

-9x^4-1/4x+2

Answer:

which revision corrects the inappropriate shift in verb mod? could be,might encounter, use ,would be

Answer:

27.5

Step-by-step explanation:

3 = 7.5

4 = 10

5*7.5=37.5-10=27.5

Seriously. 2=5 contradicts.

The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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