-4(X-1)+2 which of the following is equivalent to the expression

Answer:

Step-by-step explanation:

Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.

From the first mixture, we have:

12x + 3y = 39

From the second mixture, we have:

16x + 6y = 58

We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:

16x + 6y = 58

(24x + 6y = 78)

-8x = -20

Dividing both sides by -8 gives:

x = 2.5

Substituting this value of x into the first equation, we get:

12(2.5) + 3y = 39

Simplifying, we get:

30 + 3y = 39

Subtracting 30 from both sides gives:

3y = 9

Dividing both sides by 3 gives:

y = 3

Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.

The calculated value of the force of the resistance is 15.62 N

We can use Newton's Second Law of Motion to solve this problem. The formula is:

F = m*a

where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, the brick is falling through water, so there are two forces acting on it:

The net force is the difference between these two forces:

F_net = F_gravity - F_resistance

The weight of the object is:

F_gravity = m*g

So, we have

F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N

Now we can use the formula for net force to find the force of water resistance:

F_net = F_gravity - F_resistance

F_resistance = F_gravity - F_net

F_resistance = 19.62 N - m*a

This gives

F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N

Therefore, the force of water resistance is 15.62 N.

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The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.

Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:

BSA = √(H x M) / 3600

We can rearrange the equation to solve for M:

M = (BSA^2 x 3600) / H

Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:

M = (2.0^2 x 3600) / 165

M = (4 x 3600) / 165

M = 87.27 kg

The above question is in response to the full question as seen in the image;

A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less

than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?

The equation for BSA is BSA = √(H x M)/3600

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The resulting number is 12/5

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it

So, performing the operations,

15/16+15/16×3/5

= 15/16(1+3/5)

= 15/16(8/5)

= 120/80

= 3/2

Now,

3/2+3/2×3/5

= 3/2(1+3/5)

= 3/2(8/5)

= 24/10

= 12/5

Hence, the resulting number is 12/5

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The average rate of change representing the state whose temperature is decreasing slower is given as follows:

-1.5ºF/day.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

For Maine, in 9 days, the temperature fell by 13.5ºF, hence the rate is given as follows:

-13.5/9 = -1.5ºF/day.

For Connecticut, in 2.5 days, the temperature fell by 6.25ºF, hence the rate is given as follows:

-6.25/2.5 = -2.25 ºF/day.

A slower decline is in Maine, as it has a lower rate of change.

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Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.

To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).

by the question.

a. x-3.5>6.9

x>6.9+3.5

x>10.4

b. 6.4>x+3.1

x[tex]\geq 32[/tex]

c. x/4≤8

x≤32

d. 2/3x≤-10

x≤-15

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The area of the shaded region under normal distribution is: 3.51

The standard normal distribution is defined as the normal distribution with a mean of 0 and a standard deviation of 1.

The z-table or the  standard normal table is one that provides the area under the standard normal curve to the left of a specified value, or "z-value". The value for the area is also the probability that the variable is less than the specified z-value.

To the right of -2.25 and to the left of -0.35

From standard normal table, we have the p-values as:

Area to the left of -0.35 = 0.3632

Area to the left of -2.25 = 0.0122

Area of the shaded region = 0.3632 - 0.0122 = 0.351

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Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.

Here,

The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where P is the principal amount (initial investment).

To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.

Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).

Then, we have:

[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]

Dividing both sides by P, we get:

[tex]2= (1 +\frac{r}{n})^{nt}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]

Using the properties of logarithms, we can simplify this expression as:

[tex]ln(2) = n*t * ln(1 + r/n)[/tex]

Dividing both sides by n*ln(1 + r/n), we get:

[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]

Plugging in the values for r and n, we get:

[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]

Solving this expression on a calculator, we get:

t ≈ 13.47 years

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Answer:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of r=11 m and using π = 3.14, we get:

C = 2πr

C = 2 x 3.14 x 11 m

C = 69.08 m

Therefore, the circumference of the circle is 69.08 meters

The angle indicated by a green arc is 54 degrees.

A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.

The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.

To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.

So we have:

The blue arc angle is equal to the sum of the red and green arc angles.

We get the following equation when we plug in the given angle measurements:

98° = 44° + Green arc angle

We can simplify this equation as follows:

Green arc angle = 98° - 44° = 54°

The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.

We currently have:

Green arc angle + 70° + 56° = 180°

We get the following by substituting the value we found for the green arc angle:

54° + 70° + 56° = 180°

We can simplify this equation as follows:

180° - 70° - 56° = 54°

As a result, the angle indicated by a green arc has the value:

It is 54 degrees outside.

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We may conclude after answering the presented question that None of the given quotient equations are true.

What is an equation?

A formula is a statement that two expressions are equal. An equation consists of two sides separated by an algebraic equation (=).  

For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9."

The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements.

[tex]x^2 + 2x - 3 = 0.[/tex] Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.

None of the given quotients are true.

A. 1/2 ÷ 2 = 1/4, not 4.

B. 1/3 ÷ 4 = 1/12, not 4/3.

C. 1/2 ÷ 6 = 1/12, not 1/6.

D. 1/5 ÷ 2 = 1/10, not 10.

E. 1/8 ÷ 3 = 1/24, not 1/3.

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It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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Answer:

Step-by-step explanation: 1. is Yes 2 is no 3. is all 4 is Y and 50 5 is yes and -1

Answer:

1. is 10

2. is 4

3. is 2

?= is 2

Answer: To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations:

y = -3x + 8

y = -2x^2 + 7x

We can set the two equations equal to each other and solve for x:

-3x + 8 = -2x^2 + 7x

This simplifies to:

2x^2 - 10x + 8 = 0

Dividing both sides by 2, we get:

x^2 - 5x + 4 = 0

Factoring the left side, we get:

(x - 1)(x - 4) = 0

So the solutions for x are x = 1 and x = 4.

To find the corresponding values of y, we can substitute these values of x into either equation. Let's use y = -3x + 8:

When x = 1, y = -3(1) + 8 = 5

When x = 4, y = -3(4) + 8 = -4

Therefore, the two skaters might collide at the points (1, 5) and (4, -4).

Step-by-step explanation:

The coordinates of B' after the sequence of transformations are given as follows:

B'(3,-4).

The coordinates of B are given as follows:

B(-3,1).

After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:

B'(3, 1).

The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:

B'(1, -3).

The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:

B'(3,-4).

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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).

In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Finally, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

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Step-by-step explanation:

The measure of angle p is 60°

Answer:

Step-by-step explanation:

An example of an expression with 4 terms where 3 of them are like terms is:

$5x^2 + 7x - 2x^2 + 3x$

To rewrite this expression by combining like terms, we add the coefficients of the terms with the same variables raised to the same power. In this case, the two terms with $x^2$ are like terms, so we can add their coefficients:

$5x^2 - 2x^2 + 7x + 3x = 3x^2 + 10x$

The resulting expression has 2 terms.

Answer: 160

Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.

Since the function is already in standard form (ax^2 + bx + c form) you don't have to change anything and simply rewrite it.

For the vertex, if you have a quadratic function in standard form -b/2a is the x value of the vertex.

-b/2a = -4/(2(2)) = -1

Since we now know the x-value of the vertex we can plug it into the function to find the corresponding y-value.

h(-1) = 2(-1)^2 + 4(-1) - 10 = -12

So, the vertex is at (-1,-12)

Answer:

"Undefined slope"

Step-by-step explanation:

The line is vertical on the graph.

Every point on the line has the same x-coordinate.

If the line crosses the x-axis where x=-7, then the

x-coordinate of every point on the line is -7, and the

equation of the line is

                                     x = -7 .

Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4

To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.

Here are some examples of how we can do this:

5(x - 4/5)

In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.

5x - 20/5

Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.

(25x - 20)/5

In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.

10x/2 - 8/2

This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.

3(5x/3) - 4

In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.

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A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

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Answer:

19.2 ft

Step-by-step explanation:

The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.

When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).

Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.

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The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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The values represents the linear function are:

x y

0 1

1 5

2 9

3 13

4 17

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
The table of values that represents the linear function y=4x+1 is:
x y

0 1

1 5

2 9

3 13

4 17
To generate these values, we can substitute different values of x into the equation y=4x+1 and solve for y.

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Q) which table of values represents the linear function y=4x+1 ?

Answer:

The given equation is 3 + 7x + 11 + 10x = y.

Simplifying the equation, we get:

y = 17x + 14

Comparing with the standard linear equation y = mx + b, we can see that:

m = 17

b = 14

Therefore, m = 17 and b = 14.