Charles has $10.00 and is heading to the store. He has to buy milk for his Mom that costs $2.75, and gets to use
the rest of his money to buy gatorade that cost $1.75. How many bottles of gatorades can he buy?

Answer:

Replace all the (x) values with the Values "-1, 0, 2" to get your answers

Step-by-step explanation:

        4(-1)+4  (-1) < 0

f(-1)=  4(-1)+4  (-1) > 0

f(-1)= 4x+4 x < 0

f(0)= 4x +8 x>/_ 0

f(2)= 4x +8 x>/_ 0

The given statement in the form of inequality is given as -

c - 6 > 24.

An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > c

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the statement as -

"Six subtracted from c is greater than 24"

We can write the inequality as -

c - 6 > 24

Therefore, the given statement in the form of inequality is given as -

c - 6 > 24.

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{Question in english -

Six subtracted from c is greater than 24}

Answer:

40

Step-by-step explanation:

Area = Base * height

A = 8 * 5

A = 40

Answer:

40

Step-by-step explanation:

A=b×perpendicular height

=8×5

=40

Answer:

no

Step-by-step explanation:

side needs to be a bit bigger than that

Answer:

-243.97

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

total angle inside quadrilateral = 360°

x+2x+90+30 = 360

3x = 360-120

3x = 240

x = 80°

The answers to the questions on linear combination have been solved below

1. We can start by multiplying both sides by -2 to eliminate the x-term:

2x + 4y = 0

-2(2x + 4y) = -2(0)

-4x - 8y = 0

Now, we have:

-4x - 8y = 0

9x + 4y = 28

We can now use linear combination by adding these two equations to eliminate the y-term:

(-4x - 8y) + (9x + 4y) = 0 + 28

5x = 28

Dividing both sides by 5, we get:

x = 28/5

Now, we can substitute this value of x into either of the original equations to solve for y. Let's use the second equation:

2x + 4y = 0

2(28/5) + 4y = 0

56/5 + 4y = 0

4y = -56/5

y = -14/5

Therefore, the solution to the system of equations is:

x = 28/5

y = -14/5

We can check that these values satisfy both equations:

9x4y = 28

9(28/5)(-14/5) = 28

-352/25 = 28/25 (true)

2x + 4y = 0

2(28/5) + 4(-14/5) = 0

56/5 - 56/5 = 0 (true)

Therefore, the solution is verified.

2. The system of equations is:

5x + 3y = 41

3x - 6y = 9

We can simplify the second equation by dividing both sides by 3:

3x - 6y = 9

x - 2y = 3

Now we can use linear combination by multiplying the first equation by 2 to eliminate the y-term:

2(5x + 3y) = 2(41)

10x + 6y = 82

(x - 2y) + (10x + 6y) = 3 + 82

11x = 85

Dividing both sides by 11, we get:

x = 85/11

Now we can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:

5x + 3y = 41

5(85/11) + 3y = 41

425/11 + 3y = 41

3y = 41 - 425/11

3y = (451 - 425)/11

y = 26/33

Therefore, the solution to the system of equations is:

x = 85/11

y = 26/33

We can check that these values satisfy both equations:

5x + 3y = 41

5(85/11) + 3(26/33) = 41

425/11 + 26/11 = 41

451/11 = 41 (true)

3x - 6y = 9

3(85/11) - 6(26/33) = 9

255/11 - 52/11 = 9

203/11 = 9 (true)

Therefore, the solution is verified.

3.

3(x - 2y) = 3(-8)

3x - 6y = -24

3x - 6y = -12

3x - 6y = -24

Subtracting the second equation from the first equation, we get:

0 = 12

This is a contradiction, since 0 cannot equal 12. Therefore, there is no solution that satisfies both equations.

This means that the system is inconsistent, and there are no solutions.

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The correct answer is E) Two of the responses above are correct:

The measurement(s) that would help determine absolute dates by radiometric means are the accumulation of the daughter isotope and the loss of parent isotopes. These two measurements are crucial in radiometric dating methods, which rely on the decay of radioactive isotopes in rocks and minerals over time.

In radiometric dating, scientists measure the ratio of parent isotopes to daughter isotopes in a sample. The parent isotopes decay at a known rate, converting into daughter isotopes. By determining the amount of parent isotope that has decayed and the accumulation of daughter isotope, scientists can calculate the age of the sample.

For example, if a rock sample contains a radioactive isotope with a half-life of 1 million years, and 75% of the parent isotope has decayed into the daughter isotope, it can be inferred that the rock is approximately 2 million years old (since two half-lives have passed).

Therefore, the correct answer is E) Two of the responses above are correct: the accumulation of the daughter isotope and the loss of parent isotopes are measurements that help determine absolute dates by radiometric means.

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Answer:

11x² - x + 10

Step-by-step explanation:

Given

(5x² + 2x + 1) + (6x² - 3x + 9 ) ← remove both parenthesis

= 5x² + 2x + 1 + 6x² - 3x + 9 ← collect like terms

= 11x² - x + 10

Answer:

speed

time

faster

greater

You can fill in these words in the blanks.

Answer:

Step-by-step explanation:

Without more input from you, it's hard to find an exact value for b.  However, b may take on a large range of values.  b = 10 and b = -3 (chosen arbitrarily) are acceptable choices.

Take a look at the quadratic formula.  The discriminant is b^2 - 4ac.  There is nothing about this equation that restricts or forbids the use of any value of b.

Answer:

Step 1: Move the decimal point so that you have a number that is between 1 and 10. ...

Step 2: Count the number of decimal places moved in Step 1 . ...

Step 3: Write as a product of the number (found in Step 1) and 10 raised to the power of the count (found in Step 2).

Step-by-step explanation:

There are 120 different ways to order 5 people in line at the ice cream truck.

To find the number of ways to order a group of people in line, we can use the formula for permutations, which is $n!$, where n is the number of people in the group.

In this case, we are ordering 5 people in line at the ice cream truck. Using the formula for permutations, we can calculate the number of ways to order these 5 people as $5! = 120$.

Therefore, there are 120 different ways to order 5 people in line at the ice cream truck.

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The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Let \(n=0\). Then \(0^3 = 0\) but 0 > 0 is a false statement.

The set of all strings accepted by M is an infinite decidable subset of L.

Every infinite Turing-recognizable language has an infinite decidable subset.

Let's prove this theorem.

We must know the properties of the Turing recognizable language before the proof. A language is considered Turing recognizable if a Turing machine M accepts all strings in the language, and either rejects or loops forever on all strings not in the language. We can define that any language is infinite if it contains infinite strings.

Similarly, the set of all strings in the language is infinite if the language is infinite.

Let us suppose that L is an infinite Turing-recognizable language over the alphabet Σ. It implies that there exists a Turing machine M that accepts all the strings in L. We need to consider the following facts to prove that every infinite Turing-recognizable language has an infinite decidable subset:

If a Turing machine accepts an infinite number of strings in a language L, then it accepts at least one infinite subset of the language.

Suppose that a Turing machine accepts a language L, then the set of all strings accepted by the Turing machine is decidable.

Now, let's construct a new Turing machine M′ that works in the following manner:

In the first step, M' simulates M on the input w.

In this step, M' generates the strings of Σ* in some order.

In this step, for each string generated in step 2, M' runs M on that string. If M accepts that string, then M' outputs the string.

Suppose that there are only finite strings of L that are accepted by M. It implies that M has an infinite loop on all other strings not in L.

since M′ generates the strings of Σ* in some order, M′ will eventually simulate M on the string w for which M has an infinite loop.

Therefore, M′ will be in an infinite loop and will never halt.

So, the set of all strings accepted by M is infinite. We can say that the set of all strings accepted by M is an infinite decidable subset of L.

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To conduct a follow-up study that would provide 95% confidence that the point estimate is correct to within +0.08 of the population proportion, the required sample size can be calculated using the formula:

n = [(z^2 * p * q) / E^2]

Where:

z = z-score corresponding to the desired confidence level (1.96 for 95% confidence level)

p = point estimate of the population proportion (0.43 in this case)

q = 1 - p

E = acceptable sampling error (0.08 in this case)

Substituting the values, we get:

n = [(1.96^2 * 0.43 * 0.57) / 0.08^2] = 148.15

Rounding up to the nearest integer, we get a required sample size of 148 consumers.

To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within +0.08 of the population proportion, we need to use a z-score of 2.58 (corresponding to 99% confidence level) in the formula. Substituting the values, we get:

n = [(2.58^2 * 0.43 * 0.57) / 0.08^2] = 266.85

Rounding up to the nearest integer, we get a required sample size of 267 consumers.

To conduct a follow-up study that would provide 95% confidence that the point estimate is correct to within +0.02 of the population proportion, we need to use the same formula with a different value of E. Substituting the values, we get:

n = [(1.96^2 * 0.43 * 0.57) / 0.02^2] = 1,462.41

Rounding up to the nearest integer, we get a required sample size of 1,463 consumers.

To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within +0.02 of the population proportion, we need to use a z-score of 2.58 in the formula. Substituting the values, we get:

n = [(2.58^2 * 0.43 * 0.57) / 0.02^2] = 6,614.51

Rounding up to the nearest integer, we get a required sample size of 6,615 consumers. The sample size requirements increase as the desired confidence level increases or as the acceptable sampling error decreases. This means that a larger sample size is needed to achieve a higher level of confidence or a smaller margin of error. For example, increasing the desired confidence level from 95% to 99% or decreasing the acceptable sampling error from 0.08 to 0.02 will result in a significant increase in the required sample size. Therefore, researchers need to carefully balance the trade-offs between the desired level of confidence, the acceptable sampling error, and the available resources (time, budget, etc.) to determine an appropriate sample size for their study.

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Answer:

There's no c in your uploaded question

the values of x and y that satisfy the system of equations are x = -14/11 and y = 13/11.

To solve the system of linear equations using one of the three methods (elimination, substitution, or matrix inversion), let's first check the rank of matrix A and [A b].

The matrix A is a 3x2 matrix:

A = [2 3]

[-1 4]

[5 -6]

To find the rank of A, we can perform row operations to reduce the matrix to row-echelon form. The rank of A is equal to the number of non-zero rows in its row-echelon form.

Performing row operations on A, we have:

Row 2 = Row 2 + 0.5 * Row 1

Row 3 = Row 3 - 2.5 * Row 1

The row-echelon form of A is:

A = [2 3]

[0 5]

[0 -21]

Since A has two non-zero rows, the rank of A is 2.

Next, we check the rank of [A b]. The vector b is a 3x1 vector:

b = [1]

[6]

[-3]

We can append vector b as an additional column to matrix A:

[A b] = [2 3 1]

[-1 4 6]

[5 -6 -3]

Performing row operations on [A b], we have:

Row 2 = Row 2 + Row 1

Row 3 = Row 3 - 2 * Row 1

The row-echelon form of [A b] is:

[A b] = [2 3 1]

[0 7 7]

[0 -12 -5]

Since [A b] has two non-zero rows, the rank of [A b] is also 2.

Since the rank of A and [A b] are both 2, we can proceed with solving the system of linear equations using any of the three methods.

Let's use the method of matrix inversion to solve the system.

The system of equations can be written as a matrix equation:

Ax = b

To find x, we can multiply both sides of the equation by the inverse of A:

\(A^(-1) * A * x = A^(-1) * b\)

\(I * x = A^(-1) * b\)

\(x = A^(-1) * b\)

To find the inverse of A, we can use the formula:

\(A^(-1) = (1 / (ad - bc)) * [d -b][-c a]\)

Plugging in the values of matrix A, we have:

\(A^(-1) = (1 / (2 * 4 - 3 * -1)) * [4 -3][1 2]\)

Calculating the inverse of A, we have:

A^(-1) = (1 / 11) * [4 -3]

[1 2]

Multiplying A^(-1) by vector b, we have:

\(x = (1 / 11) * [4 -3] * [1][6][-3]\)

Calculating the product, we get:

x = (1 / 11) * [4 * 1 + -3 * 6]

[1 * 1 + 2 * 6]

Simplifying, we have:

x = (1 / 11) * [-14]

[13]

Therefore, the solution to the system of linear equations is:

x = -14/11

y = 13/11

Hence, the values of x and y that satisfy the system of equations are x = -14/11 and y = 13/11.

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Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{The\ slope\ of\ a\ line\ passing\ through\ the\ points\ (x_1,y_1)\ and\ (y_2,y_1)\ is\ given\ by:}\\\mathrm{Slope(m)=\frac{y_2-y_1}{x_2-x_1}}\\\\\mathrm{According\ to\ the\ question,}\\\mathrm{(x_1,y_1)=(0,-2)}\\\mathrm{(x_2,y_2)=(-2,-8)}\)

\(\mathrm{Therefore\ the\ slope=\frac{-8-(-2)}{-2-0}=\frac{-8+2}{-2}=3}\)

Answer:

(-5,-13)

Step-by-step explanation:

Find the vertex of the parabola y=1/5x^2+2x−8.  

In this equation a=15  and b = 2.  

x= -2/2(1/5) = -2/2/5 = -2/1 * 5/2 = -5

Substitute −5 into the equation y=1/5x^2+2x−8

y=1/5(−5)^2+2(−5)−8

y=5−10−8

y=−13

The vertex is (−5 , −13)

The parallel sides are AB and CD while the area of the Trapezium is 240cm²

A.)

Parallel sides are directly opposite one another and their lines never meet. lines AB and CD.

Therefore, the two parallel sides are AB and CD

B.)

Area of Trapezium = Area of Rectangle + Area of Triangle

Area of rectangle = Length * width

Area of rectangle = 6 * 16 = 96 cm²

Area of Triangle = 1/2*base*height

Area of Triangle= 1/2 * 18 * 16

Area of Triangle = 144 cm²

Hence, area of Trapezium is 240 cm²

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Answer: C. 51%

Step-by-step explanation:

Answer:

-625

Step-by-step explanation:

Here we are basically multiplying each term by -5. So if you want two more terms, you would go like this...

5 × -5 = -25

-25 × -5 = 125

125 × -5 = -625

-625 × -5 = 3125

and so on!!!

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⇒First in the diagram you can choose two points that will assist you in finding the the slope/gradient of the equation.

⇒Choosing two points from the diagram we get (1,1) and (2,3)

⇒Note you can use two points of your choice you would still get the same gradient/slope/

Gradient and slope are one and the same thing.

\(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\\)

⇒\(m=\frac{3-1}{2-1} \\m=\frac{2}{1} \\m=2\)

⇒In this case the gradient from the calculation is 2.

⇒The general equation to get the equation of a straight line is y=mx+c ,Note this is a straight line. we cans see that from the diagram.

I will use the point (1,1) in the p[lace (x,y) and m=2 to find the value of c

\(1=2(1)+c\\1=2+c\\1-2=c\\c=-1\)

As a results the equation of the straight line is y=2x-1

Answer:

y = 2x - 1

Step-by-step explanation:

In order to find the equation of a line, we need to first find the coordinates of two points that the line passes through.  Using the coordinates, we then have to calculate the line's gradient. Finally, we need to find the y-intercept of the line and use it and the gradient to find the line's equation.

The y-intercept (c) of a line is the y-coordinate of the point where the line crosses the y-axis. From the graph, we can see that the line given passes through the y-axis where the y-coordinate is -1. Therefore the y-intercept is -1:

c = -1

From the graph shown, we can see that the line passes through the points (3, 5) and (1, 1). Therefore, we can calculate the gradient of the line using the following formula:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\),

where m is the line's gradient and (x₁, y₁) and (x₂, y₂) are points on the line.

Therefore, the gradient,

m = \(\frac{5 - 1}{3 - 1}\)

   = 2

Now that we have the gradient  and y-intercept of the line, we can use the following formula to find the equation of the line:

\(\boxed{y = mx + c}\)

⇒ y = 2x + (-1)

⇒ y = 2x - 1

Therefore, the equation of the line shown is y = 2x - 1.

Step-by-step explanation:

area of figure = 5x² + 3

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Step-by-step explanation:

It is given that,

-2.2 × 3.7 = 8.14

The first number is -2.2

The second number is 3.7

We know that, (-) × (+) = - (the answer is a negative)

If we multiply -2.2 and 3.7, we will get -8.14.

But in the given case, the answer is 8.18 instead of -8.14. Hence, this is the only error.

Answer:

3/8

Step-by-step explanation:

simply multiply 1/8 by 3/1

3X1 is 3 and 8X1 is 8 so 3/8

Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

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The rate of change and the initial value, can be found to be B. initial value : 1 , rate of change : 1.

The initial value is the first x - value that is on the linear relationship. In this case, that initial value would be 1.

The rate of change can be found by the formula:

= Change in y / Change in x

= ( 4 - 2 ) / ( 5 - 3 )

= 2 / 2

= 1

The rate of change is therefore 1.

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