A couch, a love seat, and a chair cost $1565. The couch costs twice as much as the chair, and the live seat costs $400 more than the couch. Find the cost of the love seat, the couch, and the chair.

Relative maxima and relative minima are called relative extrema.

Given:

The given statement is:

Relative maxima and relative minima are called relative_____.

To find:

The correct word to fill the given blank.

Explanation:

Relative maxima: If the function changes from increasing to decreasing, then the turning point is known as relative maxima.

Relative minima: If the function changes from decreasing to increasing, then the turning point is known as relative minima.

Relative extrema: The turning points relative maxima and relative minima are known as relative extrema.

Therefore, the relative maxima and relative minima are called relative extrema.

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Answer:

The given equation of the curve is

 y= x² - 36

To find it's inverse we have to convert y in terms of x.

So, adding 36 to both sides of equation

→ y + 36=x² -36 + 36

→ y + 36 = x²

→ x² = y+ 36

→ x =[tex]\pm[/tex][tex]\sqrt{y+36}[/tex]

Now, to find inverse you can replace x by y, so by replacing x by y, the above equation becomes

y =[tex]\pm\sqrt{x+36}[/tex]

Second option is correct.

Answer:

Your answer would be D.

Step-by-step explanation:

Answer:

Closed circle on -108 and shaded to the left, I took the same lesson and got 100%

Step-by-step explanation:

But your missing part of the question, it's how would you graph the solution set of x/-6 ≤ -18?

For this case we define the following variable:

x: unknown number

We then have the following equation:

[tex]- \sqrt {41} x = 1[/tex]

From here, we clear the value of x.

We have then:

[tex]x = - \frac {1} {\sqrt {41}}[/tex]

Answer:

An irrational number that can be multiplied by negative square root of 41 to get a product that equals 1 is:

[tex]x = - \frac {1} {\sqrt {41}}[/tex]

Final answer:

The slope-intercept equation of the line that passes through (1, 2) and (3, 4) is y = x + 1, with a slope of 1 and a y-intercept of 1.

Explanation:

To find the slope-intercept equation of a line that passes through the points (1, 2) and (3, 4), we first need to determine the slope of the line. We use the formula for the slope (m) given by the change in y over the change in x, or Δy/Δx. Calculating the slope, we get:

m = (4 - 2) / (3 - 1) = 2 / 2 = 1.

Now we have the slope, we can use the slope-intercept form of the line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in one of the points, say (1, 2), into this equation gives us:

2 = (1)(1) + b

Which simplifies to:

b = 2 - 1 = 1

So the y-intercept (b) is 1. Therefore, the slope-intercept equation of the line is:

y = x + 1

The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.

The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:

Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.

Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.

However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.

Answer:

[tex]y=1(x-5)^2 + 3[/tex]

Step-by-step explanation:

Given : from the graph vertex is (5,3)

Also graph passes through point (8,12)

We use vertex form of quadratic equation

General vertex form is

[tex]y=a(x-h)^2 + k[/tex]

vertex is (5,3)

h= 5 and k =3

So equation becomes [tex]y=a(x-5)^2 + 3[/tex]

Now we need to find out 'a'

We use (8,12) to find out 'a'

Plug in x=8 and y = 12

[tex]12=a(8-5)^2 + 3[/tex]

[tex]12=a(3)^2 + 3[/tex]

12= 9a + 3

subtract 3 on both sides

9 = 9a

divide both sides by 9

so a=1

Final equation is

[tex]y=1(x-5)^2 + 3[/tex]

An equation of the function of this graph is equal to [tex]y=1(x-5)^2 + 3[/tex]

Given the following data:

The vertex form of a quadratic equation can be used to write an equation of the function of a graph.

Mathematically, the vertex form of a quadratic equation is given by this formula:

[tex]y=a(x-h)^2 + k[/tex]

Substituting the given parameters into the formula, we have;

[tex]12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1[/tex]

a = 1.

For the equation:

[tex]y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3[/tex]

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The interval notation is:

0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

The  second and third car seats are suitable.

The number lines shows the weights of the car seats which is designed for in comparison the weight of the 32lb child.

Three car seats are designed as follows:

As the seat designed for a child upto and including 30 lb would not be suitable for 32 lb child. Because 32lb is more than the 30 lb.

Now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 32lb.

The interval notation is:

0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

The  second and third car seats are suitable.

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It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We need to find the unit fractions to convert 15 days into seconds.

1 day = 24 hour

1 hour = 60 minutes.

1 minutes = 60 seconds

Therefore, 24 hours = 24 x 60 x 60  = 86400 seconds

There are 86400 seconds in one day.

Then 15 days = 15 x 86400 = 1,296,000

Hence, It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.

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Answer:

(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares

Step-by-step explanation:

The formula for difference of squares

[tex]a^2 - b^2 =(a+b)(a-b)[/tex]

(–7x + 4)(–7x + 4) both parenthesis having same terms so this will not result in difference of squares

(–7x + 4)(4 – 7x) both parenthesis having same terms so this will not result in difference of squares

(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares

(–7x + 4)(7x – 4) sign changes for both terms in both parenthesis so this will not result in difference of squares

The value of f(q+1) is 2(q-1).

A relation or expression involving one or more variables.

Given that, f(x) = 2x - 4

When x = q+1

f(q+1) = 2(q+1) - 4

f(q+1) = 2q + 2 - 4

f(q+1) = 2q - 2

f(q+1) = 2(q-1)

Hence, the value of f(x) when x = (q+1) is 2(q-1)

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The measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°

From the diagram, we can observe that angles 6 and 7 are vertically opposite angles.

From one of the angle theorems, we have that vertically opposite angles are equal

That means,

measure of ∠ 6 = measure of ∠ 7

From the question,

we have that, m6 = (11x + 8)° and m7 = (12x – 4)°

Since, the measures of angles 6 and 7 are equal, then we can write that

(11x + 8)° = (12x – 4)°

Now, determine the value of x, we will solve the equation

11x + 8 = 12x – 4  

First, subtract 11x from both sides

11x - 11x + 8 = 12x - 11x - 4

8 = x - 4

Now, add 4 to both sides

8 + 4 = x -4 +4

12 = x

∴ x = 12

Now, we will determine the measure of ∠6

m ∠6 = (11x + 8)°

Put x = 12

∴ m ∠6 = (11(12) + 8)°

m ∠6 = (132 + 8)°

m ∠6 = 140°

To determine the measure of ∠4, m4, we will first determine the measure of ∠8.

From the diagram,

m ∠6 + m ∠8 = 180° (Sum of angles on a straight line)

∴ 140° + m ∠8 = 180°

Then,

m ∠8 = 180° - 140°

m ∠8 = 40°

From the diagram, we can observe that angles 4 and 8 are corresponding angles.

Also, from one of the angle theorems, we have that corresponding angles are equal.

Hence, the measure of ∠ 4 equals the measure of ∠ 8.

From above, m ∠8 = 40°

∴ m ∠4 = 40°

Hence, the measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°

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