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Match the expressions to their limit values.

The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.

Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.

-2(2x + 5) - 3 = -3(x - 1)

To solve this equation, we need to first use the distributive property to expand the left side of the equation.

We have:

-4x-10-3 = -3(x - 1)

-4x-13 = -3(x - 1)

Now, we can group the like terms on the left side and the right side of the equation.

On the left side, we have -4x - 13 and on the right side, we have -3x + 3.

-4x-13 = -3x + 3

To solve for x, we can add 3x to left side of the equation and add 13 to the right side.

This results in the equation:

-4x+ 3x  = 13 + 3

Now, we can add 3x with -4x of the equation to isolate the x-term.

We have:

-x = 16

x = - 16

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2x² - 6x = -7 equation has  imaginary solutions

To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation

x² + 3x - 5 = 0

a = 1, b = 3, c = -5

Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29

The equation has two real solutions

x⁴ - 5x ^ 2 + 3 = 0

This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions

2x² - 6x = -7

2x^2 - 6x + 7 = 0

a = 2, b = -6, c = 7

Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20

Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.

-3x² = -5

Dividing both sides by -3, we get:

x²= 5

a = 1, b = 0, c = -5

Discriminant = 0² - 4(1)(-5) = 20

The equation has two real solutions.

Hence, 2x² - 6x = -7 equation has imaginary solutions

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Answer:

A and D

Step-by-step explanation:

Answer:

A: patients with infectious diseases

D: machines that use radiation

I need that 5+ points if ya know what im sayin ;)

Answer:

Mode is 58 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours

The points which satisfy both the systems are (4, 3) and (-2, 3).Hence, the correct options are (c) (4, 3) and (-2, 3).

A graph is a visual representation of data that shows the relationship between different variables or sets of data. Graphs are used to display complex information in a simple and easy-to-understand way, making it easier for people to analyze and interpret the data.

From the graph, it can be observed that in System 1, the area below the line is the solution region, whereas, in System 2, the area above the line is the solution region.

Therefore, the points which satisfy both the systems are (4, 3) and (-2, 3).Hence, the correct options are (c) (4, 3) and (-2, 3).

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

Answer:

Yes

Step-by-step explanation:

The lines in question have no degree angle to them. Don't let the line in the middle confuse you!

Hope this helps!

The missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

The equation of the function is given as:

y = 5^x

And the x value is given as

x = 2

To determine the missing value, we start by substituting 2 for x in the function y = 5^x

So, we have:

y = 5^2

Evaluate the exponent

y = 25

So, the complete coordinate is (2, 25)

Hence, the missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

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To determine the equation of a line we need to know at least two points the said line passes through or one point and its slope.

We know one point and the equation of a line perpendicular to the one we are looking for.

If two lines are perpendicular, then their slopes are negative reciprocals of each other. This means that the slope of the line we have to establish is the negative inverse of the slope of the line we know.

The given line is:

Its slope is the coefficient that multiplies the x-value, so m=-2/3

To determine the slope of the perpendicular line you have to invert the fraction and multiply it by -1

m₁ is the slope of the known line

m₂ is the slope of the perpendicular line

Now that we have determined the slope of the perpendicular line, we can use the point-slope form to calculate its equation

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point on the line

Using m=3/2 and the point (-3,7) the equation in point-slope form is

To express the equation in the slope-intercept form you have to leave y on the right side of the equation and all other terms on the right side.

-First, distribute the multiplication on the parentheses term:

-Second, pass "-7" to the other side of the equation by applying the opposite operation to both sides of it and simplify the like terms:

The equation of the line that passes through (-3,7) and is perpendicular to y=-2/3x-6 is

Answer:

A=115.6

Step-by-step explanation:

Hey There!

So the first step is to find the formula for area of a trapezoid

\(A = \frac{1}{2} h(b1 +b2)\)

h = height

b1 = base 1

b2 = base 2

now all we do its plug in the values

\(A=\frac{1}{2} 6.8(28.3+5.7)\)

\(6.8x26.3=192.44\\5.7x6.8=38.76\\38.76+192.44=231.2\\\frac{231.2}{2} =115.6\\A=115.6\)

Hope this helps!!

The evaluation of the given Boolean expressions are:

a) A && !B =  false              b) B∥C = true

c) B==C = false                   d) A&&!C = true

e) (B∥C)&&(!A) =  false        f) (A!=B)∥(B!=C)  = true

Information available in the problem:

A = true

B = true

C = true

a) Since A and B are both true, !B (which means "not B") is false. Therefore, A && !B evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

A && !B = true && false = false

b) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true.

Hence,

B∥C = true ∥ false = true

c) Since B is true and C is false, B and C have different values, and therefore B==C will evaluate to false. This is because the equality operator returns true only if its operands have the same value.

Hence,

B==C = true == false = false

d) Since A is true and !C (which means "not C") is true, A&&!C evaluates to true. This is because the logical AND operator returns true only if both of its operands are true.

Hence,

A&&!C = true && !false = true && true = true

e) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true. Therefore, B∥C evaluates to true.

Since A is true and !A (which means "not A") is false, !A evaluates to false.

Therefore, (B∥C)&&(!A) evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

(B∥C)&&(!A) = true && false = false

f) Since A is true and B is true, A!=B (which means "A is not equal to B") is false, because A and B have the same value.

Since B is true and C is false, B!=C (which means "B is not equal to C") is true, because B and C have different values.

Therefore, (A!=B)∥(B!=C) evaluates to true, because the logical OR operator returns true if at least one of its operands is true.

Hence,

(A!=B)∥(B!=C) = false ∥ true = true

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Calista's grade on her last assignment is 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

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Answer:

\(Blue = 12\)

\(Yellow = 9\)

Step-by-step explanation:

Given

\(Blue : Yellow = 4 : 3\)

Required

Determine the number of pints of each to make 21 of green paints

First, calculate the total ratio.

\(Total = 4 + 3\)

\(Total = 7\)

The blue and the yellow pint can be represented individually as:

\(Blue = \frac{4}{7} * Green\)

\(Yellow = \frac{3}{7} * Green\)

Number of blue paint calculated last week is:

\(Blue = \frac{4}{7} * 21\)

\(Blue = {4} * 3\)

\(Blue = 12\)

\(Yellow = \frac{3}{7} * Green\)

\(Yellow = \frac{3}{7} * 21\)

\(Yellow = {3} * 3\)

\(Yellow = 9\)

Answer:

D

Step-by-step explanation:

Let's plug 2 in for x:

18 * 2 - 35 = 36 - 35 = 1

Now, look at the answer choices:

A) Well, 1 is a whole number; it's not a fraction or a decimal. So eliminate A.

B) 1 is not a prime number; the smallest prime number is 2. So eliminate B.

C) 1 is also not a composite number; the smallest composite number is 4. So eliminate C.

D) This is true. 1 is a whole number, but it's not prime or composite, as seen above.

Thus, D is the answer.

~ an aesthetics lover

Answer:

D

Step-by-step explanation: The result is a whole number that is neither prime nor composite.

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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The mean of the distribution is 3

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

According to the first graph,

Given the bar of observations as :

0, 5, 6, 3, 1, 1, 3, 6, 4, 1

Here the Sum of Observations = 30

And the total number of observations = 10

The mean of the distribution = 30/10

The mean of the distribution = 3

According to the second graph,

Given the bar of observations as :

0, 1, 3, 3, 9, 0, 9, 4, 4, 1

Here the Sum of Observations = 34

And the total number of observations = 10

The mean of the distribution = 34/10

The mean of the distribution = 3.4

The mean of the distribution = 4 (closest)

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Answer:

Step-by-step explanation:

3000000000

Answer:

ok so the numbers are 21%, 3/20, 25.6%, 2.24, and .24 we are ordering from least to greatest

Step-by-step explanation: First we need to figure out what 3/20 is and its 0.15 so 3/20 comes first then 0.24 then 2.24 then 21% then 25.6%

The logarithmic equation log(x+9)-logx=3 has a solution of x = 0.0090

From the question, we have the following parameters that can be used in our computation:

log(x+9)-logx=3

Apply the quotient rule

So, we have

log((x + 9/x) = 3

Remove the logarithmic expression

So, we ave

(x + 9)/x = 10^3

Evaluate

(x + 9)/x = 1000

So, we have

1000x = x + 9

Subtract

999x = 9

So, we have

x = 0.0090

Hence, the solution is x = 0.0090

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The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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Answer:

2

Step-by-step explanation:

the leading coefficient is the number in front of the variable with the largest exponent.

here, the largest exponent is 3 in 2x³ and the corresponding coefficient for that is 2

Answer:

Step-by-step explanation:

\(a_{1}=1\\d=-3-1=-4\\a_{n}=a_{1}+(n-1)d\\a_{n}=1+(n-1)(-4)\\a_{n}=1-4n+4\\a_{n}=5-4n\)

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

582.6

Step-by-step explanation:

2/3 x 874 = 582.6

Answer: Y = 17  and X = 43

Step-by-step explanation:

p and r are parallel meaning both angles are the same.

So

3y = 51

divide them by 3

y = 17

Now we take 51 from 180 and we get 129

129 divided by 3x is

x = 43

Answer:

a)

slope = (-4 cm) / (650 cm)

slope ≈ -0.00615

b)  the section of the road measured horizontally is approximately 3983.74 cm long.

Step-by-step explanation:

change in horizontal distance = (change in vertical distance) / slope

change in horizontal distance = (-24.5 cm) / (-0.00615)

change in horizontal distance ≈ 3983.74 cm