The system of equations is solved using the linear combination method.

StartLayout 1st row 1st column one-half x + 4 y = 8 right-arrow 2nd column negative 2 (one-half x + 4 y = 8) right-arrow 3rd column negative x minus 8 y = negative 16 2nd row 1st column 3 x + 24 y = 12 right-arrow 2nd column one-third (3 x + 24 y = 12) right arrow x + 8 y = 4 with Bar Underscript 3rd row 3rd column 0 = negative 12 EndLayout

What does 0 = −12 mean regarding the solution to the system?

There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line

if the matrix is invertible.22. \(\left( {\begin{aligned}{*{20}{c}}5&1&{ - 1}\\1&{ - 3}&{ - 2}\\0&5&3\end{aligned}} \right)\) then,  the determinant of the matrix A is -3 (non-zero), the matrix is invertible.

To determine if a matrix is invertible, we need to find its determinant. If the determinant is non-zero, the matrix is invertible. Let's calculate the determinant for the given matrix:

Matrix A = \(\begin{pmatrix} 5 & 1 & -1 \\ 1 & -3 & -2 \\ 0 & 5 & 3 \end{pmatrix}\)

Step 1: Use the first row for cofactor expansion:

Determinant(A) = 5 × Cofactor(1,1) - 1 × Cofactor(1,2) + (-1) × Cofactor(1,3)

Step 2: Calculate the cofactors:

Cofactor(1,1) = Determinant of the 2x2 matrix obtained by removing the first row and first column:

\(\begin{pmatrix} -3 & -2 \\ 5 & 3 \end{pmatrix}\)

Cofactor(1,1) = (-3)(3) - (-2)(5) = -9 + 10 = 1

Cofactor(1,2) = Determinant of the 2x2 matrix obtained by removing the first row and second column:

\(\begin{pmatrix} 1 & -2 \\ 0 & 3 \end{pmatrix}\)

Cofactor(1,2) = (1)(3) - (-2)(0) = 3

Cofactor(1,3) = Determinant of the 2x2 matrix obtained by removing the first row and third column:

\(\begin{pmatrix} 1 & -3 \\ 0 & 5 \end{pmatrix}\)

Cofactor(1,3) = (1)(5) - (-3)(0) = 5

Step 3: Substitute the cofactors back into the formula for Determinant(A):

Determinant(A) = 5 × 1 - 1 × 3 + (-1) × 5 = 5 - 3 - 5 = -3

Since the determinant of the matrix A is -3 (non-zero), the matrix is invertible.

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We have cut out a total of 29370 squares.

First, let's find the greatest possible square that can be cut from the rectangle. This square will have a side length equal to the width of the rectangle, which is 26 units.

After cutting this square from the rectangle, we are left with a smaller rectangle that measures 90 units by (90-26=) 64 units.\

Now we repeat the process and cut out the largest possible square, which has a side length of 64 units.

After cutting out this square, we are left with a rectangle that measures 64 units by (64-26=) 38 units.

We continue this process until we can no longer cut out any more squares.

The side length of the remaining rectangle will be the length of the last square that we cut out.

Let's call this side length x.

At this point, the length of the rectangle is equal to the width, so:

90 - 26 - 64 - 38 - ... - x = x.

Simplifying this equation, we get:

(90 - 26 - 64 - 38 - ...) + x = x

2x = 90 - 26 - 64 - 38 - ...

2x = 90 - (26 + 64 + 38 + ...)

2x = 90 - (26 + 64 + 38 + 26 + 16 + 4 + 2)

2x = 90 - 176

2x = -86

x = -43

Since x cannot be negative, we know that we cannot cut out any more squares.

Therefore, we have cut out a total of:

\(26^2 + 64^2 + 38^2 + ... + (-43)^2\)

To calculate this sum, we can use the formula for the sum of the squares of the first n natural numbers:

\(1^2 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6.\)

We need to find the value of n such that \(n^2\) is equal to \(43^2\)or the closest perfect square below it, which is \(42^2\).

We have:

\(42^2 = 1764.\)

\(43^2 = 1849\)

So n is equal to 42.

Therefore, the sum of the squares of the squares we have cut out is:

\(26^2 + 64^2 + 38^2 + ... + (-43)^2 = 26^2 + 64^2 + 38^2 + ... + 42^2\)

\(= 1^2 + 2^2 + 3^2 + ... + 42^2 - (1^2 + 2^2 + 3^2 + ... + 25^2)\)

\(= 42(42+1)(242+1)/6 - 25(25+1)(225+1)/6.\)

= 29370.

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Answer:

The correct graph is D

Answer:

\(\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}\)

\(\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}\)

\(\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}\)

\(\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}\)

Step-by-step explanation:

Given function:

\(f(x)=2x-1\)

where:

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

f(1) means the value of the function when x = 1.  

Therefore, substitute x = 1 into the given function to find f(1):

\(\begin{aligned}x=1 \implies f(1)&=2(1)-1\\&=2-1\\&=1\end{aligned}\)

\(\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}\)

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

f(4.5) means the value of the function when x = 4.5.

Therefore, substitute x = 4.5 into the given function to find f(4.5):

\(\begin{aligned}x=4.5 \implies f(4.5)&=2(4.5)-1\\&=9-1\\&=8\end{aligned}\)

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "4.5" does not make sense.

\(\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}\)

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

f(10) means the value of the function when x = 10.

Therefore, substitute x = 10 into the given function to find f(10):

\(\begin{aligned}x=10 \implies f(1)&=2(10)-1\\&=20-1\\&=19\end{aligned}\)

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "10" does not make sense.

\(\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}\)

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

The domain of a function is the set of all possible x-values.

As the faces of the six-sided die are labelled 1 to 6, the only possible values of x are 1, 2, 3, 4, 5 and 6.  

\(\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}\)

The domain can also be written as:

\(\{x \in \mathbb{N} \; | \; 1 \leq x \leq 6 \}\)  

or \(\{x \in \mathbb{Z} \; | \; 1 \leq x \leq 6 \}\)

Answer:

\(\boxed{\textsf{ The slope of the line is $\bf{\dfrac{3}{2}}$.}}\)

Step-by-step explanation:

Two points are given to us and we need to find the slope of the line that passes through these two points . The two points are (3,-2) and (9,-2) .As we know that the slope of the line is given by \(\tan\theta\)

Slope of a line is :-

\(\qquad\boxed{\boxed{ \sf Slope =\dfrac{ y_2-y_1}{x_2-x_1}=\tan\theta }}\)

On using this formula we can find the slope of the line .

Putting the respective values :-

\(\sf\implies Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\\sf\implies Slope = \dfrac{ 9-3}{2+2} \\\\\sf\implies Slope =\dfrac{6}{4}\\\\\sf\implies\boxed{\pink{\sf Slope = \dfrac{3}{2} }}\)

Answer:

Its zero -w-

Step-by-step explanation:

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

154 pounds

Step-by-step explanation:

If h=68, then w=5.5(68)-220=374-220=154

Answer:

52.5 gallons a day per person

Step-by-step explanation:

6300 divided by 4 then divided by 30

Answer:

1,575 gallons of water per person per month.

Step-by-step explanation:

Since a family of 4 consumes 6,300 gallons a month, just divide 6,300 by 4. The quotient is 1,575. I hope this helps. Please mark Brainliest :)

Answer:

The total payment is thus $35.75 plus $7.11, or $42.86

Step-by-step explanation:

Note that the sales tax doesn't affect the tip.  The sales tax is 5% of the cost and the tip is 15% of the before tax cost.  We calculate the tax and the tip separately, then add them together and finally add this sum to the cost.

Sales tax:  5% of $35.75:  $1.75

Tip:  15% of $35.75:  $5.36

Adding these two quantities results in $7.11.

The total payment is thus $35.75 plus $7.11, or $42.86

the possible values of x/|x| + y/|y| + z/|z| + xyz/|xyz| are 4, 0, and -4.

To find all possible values of the expression x/|x| + y/|y| + z/|z| + xyz/|xyz|, we need to consider the signs of x, y, and z. Since x, y, and z are nonzero real numbers, they can be either positive or negative.

Case 1: x, y, and z are all positive:

In this case, |x| = x, |y| = y, and |z| = z. So, the expression becomes:

x/|x| + y/|y| + z/|z| + xyz/|xyz| = x/x + y/y + z/z + xyz/xyz = 1 + 1 + 1 + 1 = 4

Case 2: Two of x, y, and z are positive and one is negative:

Without loss of generality, assume x and y are positive, and z is negative. In this case, |x| = x, |y| = y, and |z| = -z. So, the expression becomes:

x/|x| + y/|y| + z/|z| + xyz/|xyz| = x/x + y/y + z/(-z) + xyz/(-xyz) = 1 + 1 - 1 - 1 = 0

Case 3: Two of x, y, and z are negative and one is positive:

Without loss of generality, assume x and y are negative, and z is positive. In this case, |x| = -x, |y| = -y, and |z| = z. So, the expression becomes:

x/|x| + y/|y| + z/|z| + xyz/|xyz| = x/(-x) + y/(-y) + z/z + xyz/xyz = -1 - 1 + 1 + 1 = 0

Case 4: x, y, and z are all negative:

In this case, |x| = -x, |y| = -y, and |z| = -z. So, the expression becomes:

x/|x| + y/|y| + z/|z| + xyz/|xyz| = x/(-x) + y/(-y) + z/(-z) + xyz/(-xyz) = -1 - 1 - 1 - 1 = -4

Therefore, the possible values of x/|x| + y/|y| + z/|z| + xyz/|xyz| are 4, 0, and -4.

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Answer:

17

Step-by-step explanation:

-2(-2) + 9(5) = 49

\(\sqrt{49}\) = 7

10 + 7 = 17

Answer:

£169

Step-by-step explanation:

255/3 = £85

110 x 50 p = 5500 p

255 - 110 = 145 coins which are 20 p

145 x 20 p = 2900 p

5500 p = £55

2900 p = £29

£85 + £55 + £29 = £169

Answer:

I sun 169 ofc

Step-by-step explanation:

Answer: Question 1: 113 & Question 2: 27

Step-by-step explanation:

For question 1 you would add 35+32=67,then you subtract 180-67 to get 113  for your answer & question 2 you would subtract 155-128 to get 27 for the answer

Angles in a triangle add up to 180 degrees.

\(180-35-32=113\)

Angles on a line add up to 180 degrees.

\(p=180-113=67\)

Angles on a line add up to 180 degrees.

\(180-155=25\)

Angles in a triangle add up to 180 degrees.

\(q=180-128-25=27\)

Answer:

4x +1

Step-by-step explanation:

f(x) = 3x - 1

g(x) = x + 2,

(f +g)(x)= 3x-1 + x+2

Combine like terms

          =4x +1

Answer:

(f+g)(x)=4x+1

Step-by-step explanation:

This question asks us to find (f+g)(x), which is equal to adding f(x) and g(x).

f(x)+g(x)

We know that f(x) is 3x-1 and g(x) is x+2.

f(x)=3x-1

g(x)= x+2

(3x-1)+(x+2)

Combine like terms. Add all the terms with a variable, then all the terms without a variable.

(3x+x)+(-1+2)

(4x)+(-1+2)

(4x)+(1)

4x+1

(f+g)(x)=4x+1

A number that represents the property of the sample is the statistics.

Statistics refer to that number that describes a particular property of a sample set of numbers. It is the common property shared by all the numbers of the sample set. It involves the collection of data and information and then categorizing them according to their properties and inferences.

'Mean and proportion' is mathematical calculations that can be carried out on statistic number sets.

Mean refers to the average of the number set that is provided to us. It is calculated by adding the numbers and dividing them by the number of terms.

Proportion refers to the fraction of the number set according to some characteristics shared by the numbers.

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Answer:

x=-31/18

Step-by-step explanation:

As the sales price is 65% off you find the 65% of the original cost and then substract it from the original cost:

The equation that describes the relationship between the time a zebra runs at a speed and the distance it covers is y = 2/3(x).

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Assuming that the relationship between the time a zebra runs at a speed and the distance it covers is a linear one, we can use the formula for the equation of a straight line:

y = mx + b

where y is the distance covered, x is the time the zebra runs at a speed, m is the slope (i.e., the speed of the zebra), and b is the y-intercept (i.e., the distance covered when the zebra is not running).

From the table two points can be formed as (x, y) that are, (3, 2) and (6, 4)

Using these two points, we can find the slope of the line:

m = (y₂ - y₁)/(x₂ - x₁)

 = (4 - 2)/(6 - 3)

 = 2/3

Now as we have the slope m we can use it in point slope form, i.e.

y - y₁ = m(x - x₁)

Using the point (3, 2),

y - 2 = 2/3(x - 3)

y - 2 = 2/3(x) - 2

y  = 2/3(x) - 2 + 2

y  = 2/3(x)

Hence, the equation that describes the relationship between the time a zebra runs at maximum speed and the distance it covers is:

y  = 2/3(x)

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Complete question:

The relationship between the amount of time a zebra run at maximum speed in the distance it covers is shown.

Write an equation to describe this relationship.

The mass of the original sample of phosphorus-32 was approximately 717.7 grams.

To solve this problem, we can use the radioactive decay formula:

A = Ao * 2^(-t/h)

Where:

A = resulting amount after time t

Ao = initial amount (at t=0)

t = time

h = half-life of the substance

In this case, we are given that the half-life of phosphorus-32 is 14.28 days. We want to find the initial mass, represented by Ao.

After approximately 57 days, 55 g of phosphorus-32 remain unchanged. Let's plug these values into the equation:

55 = Ao * 2^(-57/14.28)

To solve for Ao, we can isolate it by dividing both sides of the equation by 2^(-57/14.28):

55 / 2^(-57/14.28) = Ao

Using a calculator to evaluate 2^(-57/14.28), we find that it is approximately 0.07666.

Therefore, the initial mass, Ao, is:

Ao = 55 / 0.07666 ≈ 717.7 g

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Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

Answer:

Below

Step-by-step explanation:

The y-axis intercept occurs when x = 0

  so the first one is y = 21    ( this is the value when x = 0 from table)

the second one shows every 4 increase causes a 3 decrease in y

   so every 4 DECREASE in x causes a +3 INCREASE in y

     decrease x = 4 to   x = 0     increase y = 6 to y = 9

In this problem, we have the sequence

5,9,13,17,21,...

Is an arithmetic sequence

the common difference is d=4

there are 20 terms (rows) in the sequence

Remember that

The rule to find the sum of the first n terms of the arithmetic sequence is equal to

where

n=20

a1=5 ----> first term

d=4

substitute given values

S=860

therefore

Answer:

Please check the explanation.

Step-by-step explanation:

Writing this relation in set notation using curly braces:

{(1, 3), (2, 5), (3, -1), (4, 0), (5, 6)}

The relation clearly indicates that each input is related to exactly one output. In other words, there is no repetition of 'x' values.

Hence, this relation is a function.

We know that the domain is the set of all x values.

Thus, the domain is: {1, 2, 3, 4, 5}

We know that the domain is the set of all y values.

Thus, the range is: {-1, 0, 3, 5, 6}

Given statement solution is :- tan(60°) can be written as the fraction √3/3 using the given special right triangle. Option (c) is correct.

To write tan(60°) as a fraction using a special right triangle, we can use the triangle with side lengths:

a = 1,

b = √3,

c = √3/2.

In this triangle, the angle opposite side a is 30°, and the angle opposite side b is 60°.

We know that tan(theta) is defined as the ratio of the length of the opposite side to the adjacent side. Therefore, in this case, tan(60°) is equal to the ratio of side a to side b.

So, tan(60°) = a/b = 1/√3.

Simplifying the fraction by rationalizing the denominator, we multiply both the numerator and denominator by √3:

tan(60°) = (1/√3) * (√3/√3) = √3/3.

Therefore, tan(60°) can be written as the fraction √3/3 using the given special right triangle.

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The equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

The expression is given as:

9q^ 2 - 2/3(3q - 7) + 5q^2

Open the bracket

9q^ 2 - 2q - 14/3 + 5q^2

Evaluate the like terms

14q^ 2 - 2q - 14/3

Hence, the equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

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Answer:

50

Step-by-step explanation:

Let the number of teachers is t.

60% of t is 30

0.6t = 30

t = 30/0.6

t = 50

Answer:

72%

Step-by-step explanation:

36/50 = 0.72

0.72 x 100 = 72%

Answer:its 5

Step-by-step explanation: cuz

Answer:

RATE

Step-by-step explanation:

Answer:

A. Rate

Step-by-step explanation:

A rate is an example of comparing two different units of measure. For example, miles per hour is a rate because it compares miles, which is a unit of distance, to hours, which is a unit of time.

Hope this helps.