Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15

No, the expression 3x + 5y - 2200 is not a quadratic expression.

A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.

It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.

"3x + 5y - 2" is a linear expression, not a quadratic expression.

In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.

The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.

It is a first-degree polynomial, meaning that the highest power of the variable is 1.

Linear expressions often have a graph that is a straight line.

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No. The expression, 3x + 5y - 2, is not quadratic.

The expression "3x+5y-2" is a linear expression, not quadratic.

Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.

The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.

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To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer:

1 1/8 of a mile.

Step-by-step explanation:

The distance around the track is one quarter of a mile. Therefore, if you run around the track 4 times, you will have ran 1 mile, as 4 * 1/4 = 1. You would also run the other 1/2 of the lap, and to find that distance, you would multiply 1/2 * 1/4, because you only ran 1/2 of a lap and not one whole lap, which would come out to 1/8 of a mile. So, your final answer would be 1 + 1/8 of a mile, which comes out to 1 and 1/8 of a mile.

The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.

1. Start with the quadratic function: y = x² - 4x + 3.

2. Determine the value of x for which you want to find the value of y.

3. Substitute the given value of x into the equation.

4. Perform the necessary calculations to simplify the expression.

5. Evaluate the expression to find the value of y.

For example, let's find the value of y when x = 2:

1. Start with the quadratic function: y = x² - 4x + 3.

2. We want to find the value of y when x = 2.

3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.

4. Simplify the expression: y = 4 - 8 + 3.

5. Perform the necessary calculations: y = -1.

6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.

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The value of b in the Problem given is 0.5

The given problem can be represented mathematically as below :

We can find be in the expression thus :

4 = 8b

divide both sides by 8 in other to isolate b

4/8 = 8b/8

0.5 = b

Therefore, value of b in the expression is 1/2.

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The profit percent made by the green grocer on the sale of the grapefruits is 50%.

To calculate the profit percent, we need to determine the profit made on the sale of the grapefruits.

The grocer buys a box of 150 grapefruits for $12, which means the cost of each grapefruit is $12/150 = $0.08.

The grocer sells each grapefruit for 12 cents, which is $0.12.

The profit made on each grapefruit is the selling price minus the cost price: $0.12 - $0.08 = $0.04.

Now, we can calculate the total profit by multiplying the profit per grapefruit by the number of grapefruits: $0.04 * 150 = $6.

To find the profit percent, we divide the profit by the cost price and multiply by 100: ($6 / $12) * 100 = 50%.

Therefore, the profit percent is 50%.

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Answer: 21.15 ft²

Step-by-step explanation:

We can use the formula for the area of a triangle:

(b×h)/2

In this case, the base is 9 and the height is 4.7.

So, we substitute the variables with the numbers in this problem.

(9 × 4.7)/2

9 × 4.7 = 42.3

42.3/2 = 21.15

So, our final answer is 21.15 ft²

Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

The area of the given rectangle is determined by multiplying its length of 13 units by its width of 2 units, resulting in an area of 26 square units.

To find the area of the rectangle, we need to multiply its length by its width. The length of the rectangle is given as 13 units and the width is given as 2 units.

The formula to calculate the area of a rectangle is: Area = Length × Width.

Using the given measurements, we substitute the values into the formula:

Area = 13 × 2 = 26 square units.

Therefore, the area of the given rectangle is 26 square units.

To provide a more detailed explanation, the area of a rectangle represents the total amount of space enclosed by its four sides. In this case, the rectangle has a length of 13 units and a width of 2 units. When we multiply the length by the width, we are essentially finding the product of the two dimensions, which gives us the total area.

The resulting area of 26 square units implies that within the boundaries of the rectangle, there are 26 square units of space. It is important to note that the unit of measurement used for the length and width should be consistent to ensure the accuracy of the area calculation.

In summary, the area of the given rectangle is determined by multiplying its length of 13 units by its width of 2 units, resulting in an area of 26 square units.

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Answer: Step-by-step work:

40,328

77

3,105 (Carry the 3)

27,468

302,976

1,609,432

Add the numbers horizontally:

2,943,941

So, 40,328 * 77 = 2,943,941

The remainder when divided by 10 is:

2,943,941 % 10 = 1

Therefore, the remainder is 1.

More concisely:

40,328 * 77 = 2,943,941

2,943,941 % 10 = 1

So the remainder when 2,943,941 is divided by 10 is 1.

Hope this helps! Let me know if you have any other questions

Step-by-step explanation:

Answer:

Step-by-step explanation:

The transformation used to show congruence between polygon ABCDE and its image is a translation of 6 units to the left and 1 unit down.

To show that polygon ABCDE and its image are congruent, we need to determine which transformation was used. In this case, the transformation that can be used to show congruence is a translation.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. Since the image of A' is at (-4, 2) and the image of D' is at (-2, 1), we can see that the polygon was shifted 6 units to the left and 1 unit down.

Therefore, the transformation used is a translation of -6 units in the x-direction and -1 unit in the y-direction. This translation preserves the shape and size of the polygon, making ABCDE congruent to its image.

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Answer:

[tex]\dfrac{120}{169}[/tex]

Step-by-step explanation:

Find the exact value of the given trigonometric expression.

[tex]\sin(2\sin^{-1}(\frac{12}{13} ))= \ ??\\\\\hrule[/tex]

The method I am about to show you will allow you to complete this problem without the use of a calculator. Although, memorization of the trigonometric identities is essential.

Apply the following double-angle identity.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\sin(2A)=2\sin(A)\cos(A)\end{array}\right}[/tex]

[tex]\sin(2\sin^{-1}(\frac{12}{13} ))\\\\\\ \\\Longrightarrow 2\sin(\sin^{-1}(\frac{12}{13} ))\cos(\sin^{-1}(\frac{12}{13} ))\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{1-(\frac{12}{13} )^2} \Big)\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{1-(\frac{12}{13} )^2} \Big)\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{1-\frac{144}{169}}} \Big)\\\\\\ \\\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\sqrt{\dfrac{25}{169}}} \Big)[/tex]

[tex]\Longrightarrow 2\Big(\dfrac{12}{13}\Big)\Big(\dfrac{5}{13} } \Big)\\\\\\\\\Longrightarrow \boxed{\boxed{\frac{120}{169} }}[/tex]

Thus, the problem is solved.

Answer:

77 units^2

Step-by-step explanation:

Since the formula for the area of a parallelogram is Area = Base x Height, you can multiply the Base (11) by the Height (7)

So, A = (7) x (11) = 77 units^2

The 8 in this case is not necessary. You only need the base and height. Hope this helps!

Answer:

Therefore, the amount (future value) of the ordinary annuity is approximately $19,446.27.

Step-by-step explanation:

We can use the formula:

FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)

where we will consider :

FV is the future value,

P is the periodic payment,

r is the interest rate per period,

n is the number of compounding periods per year, and

t is the number of years.

Now given :

P = $1300 (payment per semiannual period)

r = 4.5% per year (or 0.045 as a decimal)

n = 2 (compounded semiannually)

t = 8 years

Plugging in these values into the formula, we will be getting:

FV = 1300 * [(1 + 0.045/2)^(2*8) - 1] / (0.045/2)

Calculating this expression will give us the future value (amount) of the ordinary annuity:

FV = 1300 * [(1 + 0.0225)^(16) - 1] / 0.0225

FV ≈ $19,446.27 (rounded to the nearest cent)

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Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

A scale is just another way of saying what we want to count by on our graph.

Step-by-step explanation:

A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.

Answer:

The area of the complex figure is approximately 210.92 square units.

Step-by-step explanation:

Let's calculate the area of the complex figure with the given information.

We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.

1. Equilateral Triangle:

The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:

Area of Equilateral Triangle = (base^2 * √3) / 4

In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.

Area of Equilateral Triangle = (13^2 * √3) / 4

Area of Equilateral Triangle ≈ 42.42 square units

2. Right Triangle:

The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).

Area of Right Triangle = (base * height) / 2

In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).

Area of Right Triangle = (5 * 5) / 2

Area of Right Triangle = 12.5 square units

3. Rectangle:

The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).

Area of Rectangle = length * width

Area of Rectangle = 13 * 12

Area of Rectangle = 156 square units

Now, to get the total area of the complex figure, we add the areas of each component:

Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle

Total Area = 42.42 + 12.5 + 156

Total Area ≈ 210.92 square units

Therefore, the area of the complex figure is approximately 210.92 square units.

Answer:

If the tickets are priced at $20 each, the total amount of money taken in would be $88,000.

Step-by-step explanation:

To write the number of tickets sold, n, as a function of the ticket price, p, we can use the given information that for every $1 increase in price, 200 tickets go unsold.

Let's define the slope of the line as the decrease in tickets per dollar increase in price. Since 200 tickets go unsold for every $1 increase, the slope of the line is -200.

Now, let's find the equation of the line through the given points: (12, 6000), (13, 5800), (14, 5600), and so on.

Using the point-slope form of a linear equation, we have:

n - 6000 = -200(p - 12)

Simplifying the equation, we get:

n - 6000 = -200p + 2400

Rearranging the equation to solve for n, we have:

n = -200p + 8400

This equation represents the number of tickets sold, n, as a function of the ticket price, p.

To find how much money will be taken in if the tickets are $20 each, we substitute p = 20 into the equation:

n = -200(20) + 8400

n = -4000 + 8400

n = 4400

If the tickets are $20 each, the number of tickets sold would be 4400. To calculate the total amount of money taken in, we multiply the number of tickets sold by the ticket price:

Money taken in = Number of tickets sold * Ticket price

Money taken in = 4400 * $20

Money taken in = $88,000

Hope this helps.

Answer:

It's 1

Step-by-step explanation:

any number or expression divided by itself is 1

Answer:

1

Step-by-step explanation:

The expression (x + 4) / (4 + x) simplifies to 1 because no matter what value you choose for x, when you add 4 to it and add the same value to 4, you always get the same result in the numerator and denominator, making them cancel out and equal to 1.

Answer:

y = (-1/6)x represents a proportional relationship.

The calculated value of the rate of the graph is 0.8

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

The graph

Where, we have

(0, -16) and (20, 0)

The rate of the graph is calculated as

Rate = Change in y/x

using the above as a guide, we have the following:

Rate = (0 + 16)/(20 - 0)

Evaluate

Rate = 0.8

Hence, the rate is 0.8

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The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.

For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).

Applying this transformation to each vertex of triangle NMO, we get:

N' = (2(-1) - (-5), 2) = (5, 2)

M' = (2(-1) - (-2), 1) = (2, 1)

O' = (2(-1) - (-3), 3) = (3, 3)

The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

The formulas for the piecewise function graphed below are:
f(x) =  x + 3  for -2 ≤ x < 0, 3 for 0 ≤ x < 2, -2x + 7 for  2 ≤ x ≤ 4.

The piecewise function graph provided consists of three distinct pieces.

To give the formulas for each piece, we can break it down as follows:
For the left piece:
The left piece of the graph starts at x = -2 and ends at x = 0. It appears to be a linear function with a positive slope. Let's call this function f₁(x).
The formula for the left piece, f₁(x), can be written as:
f₁(x) = mx + b
To find the slope (m) and y-intercept (b), we can use two points on the graph.

From the graph, we can see that when x = -2, y = 1. And when x = 0, y = 3.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 1) / (0 - (-2))
m = 2 / 2
m = 1
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
1 = 1(-2) + b
1 = -2 + b
b = 1 + 2
b = 3
Therefore, the formula for the left piece is:
f₁(x) = x + 3
For the middle piece:
The middle piece of the graph starts at x = 0 and ends at x = 2. It appears to be a horizontal line.

Let's call this function f₂(x).
The formula for the middle piece, f₂(x), can be written as:
f₂(x) = c
To find the value of c, we can observe that the y-values of this piece are all equal to 3.

Therefore, the formula for the middle piece is simply:
f₂(x) = 3

When x = 2, y = 3. And when x = 4, y = -1.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (-1 - 3) / (4 - 2)
m = -4 / 2
m = -2
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
3 = -2(2) + b
3 = -4 + b
b = 3 + 4
b = 7
Therefore, the formula for the right piece is:
f₃(x) = -2x + 7
To summarize, the formulas for the piecewise function graphed below are:
f(x) =
x + 3     for       -2 ≤ x < 0
3           for       0 ≤ x < 2
-2x + 7   for      2 ≤ x ≤ 4

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