Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ When I entered the last answer, it was incorrect.

a) The exponential function defining the monthly cell phones sold is given as follows: y = 450(1.0475)^t.

b) The predicted amounts are given as follows:

The general format of an exponential function is given as follows:

y = ab^x.

In which:

The parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 450(1.0475)^x.

Then the amounts are given as follows:

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The given statement " the notation "f(x)" is another way of representing y-values in a function" is true because f (x) and y are the same things.

The notation f(x), read as "f of x", indicates a function named f. It reflects that 'y is a function of x'. The letter 'x' refers to the input value or independent variable. While the letter 'y' is replaced by f(x) and it refers to the output value or dependent variable.

The notation 'f (x)' is exactly the same as that of 'y'. Even on graphs, y-axis can be labelled with 'f (x)'.

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Answer:

mn = 20ft is the answer (I hope it helps)

Answer:

12.5

Step-by-step explanation:

The average midterm exam grade for the entire class is 82.

The middle value in a set of numbers is the average, which is calculated by dividing the total of all the values by the number of values.

Here given that,

Math class contains 18 twelve graders.

Also contains 4 eleventh graders

Total number of students = 18 + 4 = 22

Total marks of students in the twelve grade = 18 x 83 = 1494

Total marks of students in the eleventh grade = 4 x 79 = 316

Total marks = 1494 + 316 = 1810

Therefore to find the average grade of midterm exam is :

1810 / 22 = 82.2

Therefore the average grade on the midterm exam for the entire class is 82.

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The team Pie Peace made pies at a rate of 4.5 per hour

The complete data is,

Team                   Pies        Hours

Crusty                   28            8

Pie Peace             27            6

Fab bakers           20            4

Yum                      26            5

We have from the table provided,

In 8 hours, Team Crusty produced 28 pies.

In 6 hours, Team Pie Peace produced 27 pies.

In 4 hours, Team Crusty produced 20 pies.

In 5 hours, Team Crusty produced 26 pies.

We must divide the number of pies produced by the total time required in order to determine the rate of pies produced.

As a result,

28 pies divided by 8 hours equals 3.5 pies per hour for Team Crusty.

4.5 pies per hour or Team Pie Peace = 27 pies in 6 hours.

20 pies divided by 4 hours yields 5 pies each hour for Team Crusty.

26 pies divided by 5 hours yields 5.2 pies per hour for Team Crusty.

Therefore, team Pie Peace made pies at a rate of 4.5 per hour

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The value of the equation is x² - x - 1 = 0

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x - ( 1/x ) = 1   be equation (1)

On simplifying the equation , we get

( x² - 1 ) / x = 1

Multiply by x on both sides of the equation , we get

x² - 1 = x

Subtracting x on both sides of the equation , we get

x² - x - 1 = 0

Now , given that ( x / ( x² + 3x - 1 ) ) = 1/4

On simplifying the equation , we get

Cross multiplying the equation , we get

4x = ( x² + 3x - 1 )

Subtracting 4x on both sides of the equation , we get

x² - x - 1 = 0

Hence , the equation is x² - x - 1 = 0

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Answer: the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.

Step-by-step explanation:

The conversion from Fahrenheit to Celsius is C = 5/9 (F-32).

First, we substitute Pat's temperature of 99.3 degrees Fahrenheit into the equation:

C = 5/9 (99.3-32)

C = 5/9 * 67.3

C = 37.3 degrees Celsius

So the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.

Answer:

37.4 degrees

Step-by-step explanation:

C = 5/9 (F-32)

F = 99.3 so plug F into the equation

C = 5/9 (99.3 - 32)

C = 5/9 (67.3)

5/9 in a calculator = .555 repeating

.555 x 67.3 = 37.35

Rounded = 37.4 degrees

The answers to each part is -

Given is to find -

We can write the expression as -

{x} = [tex]5\frac{1}{3} - 3\frac{2}{3}[/tex]

{x} = 16/3 - 11/3

{x} = 5/3

We can write the expression as -

{x} = [tex]8\frac{4}{7} - 7\frac{5}{7}[/tex]

{x} = 60/7 - 54/7

{x} = 6/7

Therefore, the answers to each part is -

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Answer:

-27

10x +8.

Step-by-step explanation:

x² - 9 ÷ x² - 4x - 5

=x²+5x+4 x² - 2x - 15

x² - 9 × x² - 2x - 15

=x² +5x +4 x² - 4x - 5

-9 × 3

=5x. 4. 2

-27.

=10x + 8 .

The same line of equations can be written in two different ways in a dependent equation. The lines that appear when we graph dependent equations are the same.

The solutions to these kinds of equations are infinite rather than fixed.

When the same line is written in two different ways, a dependent system of equations has infinite possible solutions. When attempting to solve for a system of equations, these two scenarios arise. When working through a system of equations, you'll need to keep track of a few words from your vocabulary.

A system of equations is formed by the two equations y=2x+5 and y=4x+3. The system's solution is the ordered pair that results from resolving both equations. One solution, an infinite number of solutions, or nothing at all can be found for a system of two linear equations.

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mc008-1 jpg 3456 has a degree of 3840.

A degree is a unit of measurement for angles. It is not a SI unit because radians are the SI unit for measuring angles. In general, we measure angles in degrees with a protractor in geometry.

A degree is a unit of measurement for expressing the measurement of an angle. Angles are typically measured in two different units: radians and degrees. Angles are always measured in degrees in practical geometry.

A degree is denoted by the symbol °. (degree symbol). A complete angle in degrees is 360 degrees (sometimes written as 360°), which equals one complete rotation.

As a result, 3456/0.9 = 3840

As a result, mc008-1 jpg 3456 has a degree of 3840.

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Answer:

First, there are NO 5-digit pin codes that include the digits 7, 2, 4, 6, 9, and 3. But, there are 720 pin codes that include 5 out of the 6 digits.

Step-by-step explanation:

Answer: x = 1

Step-by-step explanation:

5(3x-1) = 10

Use distributive property and multiply 5 times 3x and 5 times -1.

15x-5 = 10

Move -5 to the right of the equal sign making it positive.

15x = 10+5

Solve.

15x = 15

Divide both sides of the equal side by 15.

15x÷15 = 15÷15

Solve.

x=1

Hope this helps :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5(3x - 1) = 10}[/tex]

[tex]\mathsf{5(3x) + 5(-1) = 10}[/tex]

[tex]\mathsf{15x - 5 = 10}[/tex]

[tex]\textbf{ADD 5 to BOTH SIDES}[/tex]

[tex]\mathsf{15x - 5 + 5 = 10 + 5}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{15x = 10 + 5}[/tex]

[tex]\mathsf{15x = 15}[/tex]

[tex]\textbf{DIVIDE 15 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{15x}{15} = \dfrac{15}{15}}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{x = \dfrac{15}{15}}[/tex]

[tex]\mathsf{x = 1}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 1}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex]-5x+13[/tex]

Step-by-step explanation:

[tex](-2x+9)-(3x-4)\\=-2x+9-3x+4\\=-5x+13[/tex]

A pound of apples and a pound of oranges each cost $2.50.

Pound is a unit of weight or mass commonly used in the imperial system of measurement. It is equal to 0.453 kilograms and 16 ounces. It is also known as the avoirdupois pound, which is the most commonly used today. In some contexts, the term "pound" may also refer to a unit of currency, the British Pound Sterling (GBP).

This can be determined by subtracting Gina's total cost from Tom's total cost.
Tom's cost was $8.00, and Gina's cost was $5.00, so 8.00 - 5.00 = 3.00. Since Tom bought 3 pounds of apples more than Gina and the same amount of oranges, the cost of the extra apples is $3.00.
Since each pound of apples and oranges costs the same amount,
then $3.00 divided by 3 pounds is $1.00,
so each pound of apples and oranges costs $2.50.

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The midsegment of a trapezoid with only the coordinates given can be determine by following steps 1,2 and 3 below

The midsegment of a trapezoid is a line segment that connects the midpoints of the two parallel sides of the trapezoid.

To solve for the midsegment of a trapezoid with only the coordinates given, you can use the following steps:

1. Find the coordinates of the midpoints of the two parallel sides of the trapezoid. To do this, you need the coordinates of the four vertices of the trapezoid. For example, if the trapezoid has vertices A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4), the midpoints of the two parallel sides are:

Midpoint of AB: ((x1 + x2)/2, (y1 + y2)/2)

Midpoint of CD: ((x3 + x4)/2, (y3 + y4)/2)

2. Use the coordinates of the two midpoints found in step 1 to find the equation of the line that contains the midsegment. The slope of the midsegment is the average of the slopes of the two parallel sides of the trapezoid.

The equation of the line can be written in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1))

3. Once you have the equation of the line you can use it to find the y-intercept b and the slope m.

For example:

Trapezoid with coordinates A(2,3), B(4,4) , C(7,5) and D(5,6)

Midpoint of AB: (3,3.5)

Midpoint of CD: (6,5.5)

Slope of AB = (y2-y1)/(x2-x1) = (4-3)/(4-2) = 1/2

Slope of CD = (y4-y3)/(x4-x3) = (6-5)/(5-7) = -1/2

Midsegment slope = (1/2 + (-1/2))/2 = 0

The equation of the midsegment line is y = 0x+b

by using the point (3,3.5)

we can find the value of b = 3.5

Thus, the equation of midsegment is y = 0x + 3.5

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A straight line with a positive and constant slope can be represented by the system of equation 2x + 3y = 5 and 4x + 6y = 7.

The line is a linear equation, which is a line of constant slope. The slope of the line is determined by the coefficients of the variables in the equation.

It can be calculated by dividing the coefficient of the x-term by the coefficient of the y-term. In this example, the slope of the line is calculated by dividing 2/3, which is equal to 0.67.

This indicates that the line has a positive slope. The line is a line of best fit, meaning that it will pass through all the points defined by the two equations. The line will also pass through the point of intersection of the two equations, which is the point (2,1).

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Option (1) and (3) indicate a net of a pyramid with a square base.

Having a square base and four lateral sides, a square pyramid is a type of pyramid in geometry. Having three or more triangle faces that meet above the base and a base, a pyramid is a type of polyhedron (the apex). It is called a pentahedron because a square pyramid is a three-dimensional object with a total of five faces.

We must determine which of the provided diagrams best depicts the net of a square-based pyramid.

Think about the overall net that depicts the pyramid with a square base (as shown in figure 1)

Triangle 3 and triangle 2 are flipped to the left to create the diagram (3).

Diagram (1) is produced by flipping triangles 1 and 3 to their opposite sides.

As a result, Option (1) and (3) indicate a net of a pyramid with a square base.

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The product of 6x4 is 24.

A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied. For instance, the sum of 6 and 5 is 30. (the result of multiplication).

Integers, natural numbers, fractions, real numbers, complex numbers, and quaternions are examples of typical special instances where it is possible to define the product of two numbers or the multiplication of two numbers.

In linear algebra, there are numerous different types of products. Some of them have names that sound confusingly close but have very distinct meanings (outside product, external product), while others have names that sound completely different but basically imply the same thing (outer product, tensor product, Kronecker product). These are briefly discussed in the sections that follow.

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Answer:

2 dollers

Step-by-step explanation:

120$ +194$ divided by C square is e square so in conclution the sum will eventually be 4$ and 4$÷2= 2$

Answer:

We are given that the mass of a cube, M, is proportional to the cube of the length of its edge, L. This means that we can write the relationship between M and L as:

M = kL^3

where k is the proportionality constant.

We are also given that when the length of the cube's edge is 35 cm, the mass of the cube is 40 kg. So we can use this information to find the value of the proportionality constant k.

35 cm = 0.35 m (converting cm to m)

Now we can substitute the given values into the equation and find k:

40 = k(0.35)^3

k = 40 / (0.35)^3

Now that we have the value of k, we can use it to find the mass of the cube when the length of its edge is 0.6 m.

M = kL^3

M = 40 / (0.35)^3 * (0.6)^3

M = 40 / (0.35)^3 * (0.216)

M = 40 / (0.003375) * (0.216)

M = 40 / 0.00726 * 0.216

M = 40 / 0.015856

M = 2511.53 kg (to 2 decimal places)

So the mass of the cube when the length of its edge is 0.6m is 2511.53kg

The answer would be M = 204.6 kg

The mass of the cube, M, is given by the equation M = kL^3, where k is the proportionality constant.

Given that M = 40 kg when L = 0.35 m, we can find k by substituting these values into the equation:

40 = k(0.35)^3

k = 40 / (0.35)^3

= 40 / 0.0421875

= 947.125

To find M when L = 0.6 m, we can substitute this value of L into the equation:

M = 947.125 * (0.6)^3

= 947.125 * 0.216

= 204.6

The given information is that M is proportional to the cube of L. This means that the mass of the cube is directly proportional to the cube of the length of its edge. The proportionality constant k is found by using the given values of M and L, and then using that constant value we can find the mass when we know the length of the edge.

We have found the mass of the cube when the length of its edge is 0.6m is 204.6 kg by using the proportionality constant and equation we have derived from the given information.

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The 10th term of the sequence is -131072.

What is a geometric sequence?

A geometric sequence is a sequence of numbers such that the quotient between any two consecutive terms is a constant called the common ratio.

This sequence appears to be a geometric sequence with a common ratio of -4.

To find the nth term of a geometric sequence, we can use the formula:

[tex]a_n = a_1 * r^{n-1}[/tex]

where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the position of the term in the sequence.

So, in this case:

[tex]a_10 = 5 * (-4)^(10-1) = 5 * (-4)^9 = 5 * -262144 = -131072[/tex]

Therefore, the 10th term of the sequence is -131072.

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T = 2000/r expresses the amount of time it will take to fill the pool.

The volume of liquid that can be poured, dispensed, or eaten in an hour is measured in gallons per hour.

It gauges how quickly a liquid may travel from one location to another. The flow rate of liquids in pipes, tanks, and other vessels can be determined using the rate of r gallons per hour.

The flow rate of liquids through pumps and other mechanical devices can also be measured using this technique.

You may calculate the amount of liquid utilized or consumed in an hour using the rate of r gallons per hour.

This can be useful for estimating how much water will be consumed over a certain length of time.

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Answer:

[tex]\boxed{\bf q=30}[/tex]

Step-by-step explanation:

[tex]\bf q+19 > 49[/tex]

Subtract 19 from both sides:-

[tex]\bf q+19-19 > 49-19[/tex]

[tex]\bf q=30[/tex]

________________

Hope this helps!

Have a great day!

Answer:

q>30

Step-by-step explanation:

This question tests on Inequality.

Given Information from the question, we have to make sure the left side of the inequality has only q, which is the variable, then we will simplify it.

[tex]q + 19 > 49 \\ q + 19 - 19 > 49 - 19 \\ q > 30[/tex]

Therefore the inequality is q>30.

According to the definition of Avogadro's number , the correct statement is (d) Avogadro’s number is 6.02×10²³ , which equals the number of items in one mole.

The Avogadro number or Avogadro constant is the number of units present in one mole of any substance is .

The Avogadro number is equal to 6.022140857 × 10²³ .

The Avogadro number creates a bridge between the macroscopic world and microscopic world by relating the amount of substance to number of particles.

Therefore , the correct statement is (d) .

The given question is incomplete , the complete question is

What is the correct statement about Avogadro's number ?

(a) Avogadro’s number is 8.31, which equals the number of items in one mole.

(b) Avogadro’s number is 1.60×10¹⁹ , which equals the number of items in one mole.

(c) Avogadro’s number is 1.38×10²³, which equals the number of items in one mole.

(d) Avogadro’s number is 6.02×10²³ , which equals the number of items in one mole.

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The inverse of a linear graph can be graphed by x and y coordinates.

When a function is stated in the form which is y = mx + b, where m and b are real integers and m is not equal to 0, the function is said to be linear.  The variables in this equation are x and y, while the coefficients are m and b. A linear graph is the graph of a linear function, where a linear function has a straight line as its graph; its slope is m and its y-intercept is (0,b). The inverse of a linear graph can be thus created as -

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To find the intermediate step in the form of (x+a)=b for the equation x^2+5x+11=13x, we need to first move all the terms to one side of the equation.

x^2+5x+11 = 13x

x^2 - 8x + 11 = 0

To solve this equation, we can factor it.

x^2 - 8x + 11 = 0

(x-11)(x-1) = 0

So, we have two solutions for x: x = 11 and x = 1

To find the intermediate step in the form of (x+a)=b, we can write each solution as (x+a)=b

x = 11, so (x+(-11)) = 11

x = 1, so (x+(-1)) = 1

So, the intermediate step in the form of (x+a)=b for the equation x^2+5x+11=13x is:

(x-11) = 11 and (x-1) = 1