Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.

The rate of change of the width of the rectangle at that instant is 3.8 inches/sec.

Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).

A crossed rectangle is a crossed quadrilateral made up of two opposing sides and the two diagonals of a rectangle. It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic,  with opposite sides of equal length and equal angles that are not right angles.

We have,

W=width of the rectangle

H=height of the rectangle

A=Area of the rectangle

We know that,

A=W×H

A=20, W=4

20=4×H

H=5 inches

dA/dt=7 (inches)²/sec

dH/dt= -3 inches/sec

dA/dt=W.(dH/dt)+H×dW/dt

dA/dt=4(-3)+5(dW/dt)

7=-12+5(dW/dt)

dW/dt=19/5

dW/dt=3.8 inches/sec

Therefore, the rate of change of the width of the rectangle at that instant is 3.8 inches/sec.

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Answer:

A

Step-by-step explanation:

There is no difference between -0 and +0.

So the ans is -3.29 itself.

Answer:

Step-by-step explanation:

The maximun value (63) is located at point (1, 2).

Check attached image 1.

The purple coloured area represents the resulting area of possible answers that meet all the requirements established by the restrictions within the cartesian plane.

In this step, we need to look for extreme values, these are normally found on the edges and corner of the area drawn by all the restrictions.

Check attached image 2 to see the extreme values.

Point A is located at: (-3, -2)

Point B is located at: (-3, -4)

Point C is located at: (3, -4)

Point D is located at: (1, 2)

Given function: [tex]P=10x+6y+41[/tex]

Since we are tryong to obtain the point where there is a maximun value for function "P", we need to evaluate all the extreme points and choose the one that makes the function return the maximum value out of all 4 points.

Evaluating the points:

[tex]P(-3, -2)=10(-3)+6(-2)+41=-1\\ \\P(-3, -4)=10(-3)+6(-4)+41=-13\\ \\P(3, -4)=10(3)+6(-4)+41=47\\ \\P(1, 2)=10(1)+6(2)+41=63[/tex]

The maximun value (63) is located at point (1, 2).

There's a different method called "Simplex" that can also be used to solve these type of optimization problems. It's more complicated but can be useful when working with more than 2 variables.

The system of linear inequalities is graphed is y≥3x-2; x+2y ≤4. Hence option b is the correct.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The graph consists of two inequalities.

Since the graph lines are solid, thus the inequality sign either "less than or equal" or "greater than or equal".

First find the equation of line.

One line passes through the points (0,2) and (4,0).

The equation of line that passes through the point (a,0) and (0,b) is

x/a + y/b = 1

The equation of the line is x/4 + y/2 =1

(x + 2y)/4 = 1

x + 2y = 4

The equation of the inequality will be either x + 2y ≤ 4 or x + 2y ≥ 4.

Putting x =0  and y = 0 in x + 2y ≤ 4

0 + 0 ≤ 4

0≤ 4 (true)

In the graph (0,0) includes in the shaded region. Therefore the inequality is  x + 2y ≤ 4.

The second line passes through the points (0,-2) and (3,7).

If a line passes through the points (x₁, y₁) and (x₂, y₂), then the equation of line is y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).

The equation of the line is

y - 7 = (7 + 2)/(3 - 0)(x - 3)

y - 7 = 3x -9

y = 3x - 2

The equation of the inequality will be either y ≥ 3x-2 and  y ≤ 3x-2:

Putting x =0  and y = 0 in y ≥ 3x-2

0 ≥ 0-2

0 ≥ -2 true

In the graph (0,0) includes in the shaded region. Therefore the inequality is y ≥ 3x-2.

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The Greatest Number of orders were in the month = September

The Numbers of orders increased in month = August to September

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

According to the given information

From graph

We got to know

In may , orders = 3150

In June , orders = 3050

In July , orders = 2900

In August , orders = 3200

In September , orders = 3250

a) The Greatest Number of orders were in the month = September

b) The Numbers of orders increased in month = August to September

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The value of x would be 11° and the value of y would be 6.

What are congruent triangles?

Two triangles are congruent if all of their sides are the same - so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.

ΔRWS ≅ ΔTUV

As both triangles are congruent then we can say that

∠S ≅ ∠V

so ∠S = 29°

Now in ΔRWS,

By using the sum of all angles of the triangle property, we can write

∠R +∠W + ∠S = 180°

(8x - 27)° + 90° + 29° = 180°

8x = 180° - 92°

8x  = 88°

x = 88/8

x = 11°

Now Side RS ≅ Side TV

         3y + 7 = 25

         3y = 25 - 7

         3y = 18

            y = 18/3

            y = 6

Hence, the value of x would be 11° and the value of y would be 6.

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The Greek letter rho represents the correlation between two numerical variables for a population.

What is Rho?

The amount of money an option will lose or gain with a 1% change in interest rates is how Rho, which gauges an option's sensitivity to changes in the risk-free rate of interest (the interest rate paid on US Treasury bills), is calculated.

How is rho determined?

Rho's exact formula is challenging. The first derivative of the option's value with regard to the risk-free rate is however used to compute it.

                           Rho calculates the anticipated change in price of an option for a 1% change in the risk-free rate of a US Treasury bill.

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You will need 51.2 lbs of the cheaper candy and 4 lbs of the expensive candy.

A equation is supposed to be straight condition in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight conditions in two factors

Let x be number of pounds of cheaper candy and y represent that of expensive candy.

Then, x + y = 55.2----(1)

And

2x + 8.9y = 55.2(2.5) = 138

2x + 8.9y = 138---------(2)

On solving above two equation, we get

x = 51.2

y = 4

Thus, cheaper candy are of 51.2 ib and expensive are of 4 ib

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Answer:V = 550 ft^3

Step-by-step explanation:

The volume of a cylinder is

V = pi r^2 h

We know the radius is 2.5 and the height is 28

V = 3.14 * (2.5)^2 * 28

V =549.5 ft^3

Rounding to the nearest whole number

V = 550 ft^3

The disadvantage of piece rate pay is that the cost of producing higher quantities of a product can be a reduction in the quality of the items produced.

Piece rate is any type of job in which a worker is paid a set amount for each unit produced or action performed, regardless of time. Some employees may be paid on a piece rate or on a commission basis.

Employees are paid on a piece rate, and commission payments are based on results rather than an hourly or weekly pay rate. This means that the employee's weekly pay will vary depending on how much work they do. One of the drawbacks of piece rate pay is that the cost of producing larger quantities of a product may result in a decrease in the quality of the items produced.

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The volume of a cone with diameter 11.5 inches and a height of 15 inches is  519 in³.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreases to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, A cone with a radius of 11.5 inches and a height of 15 inches.

Now, The diameter is 11.5 inches, hence radius is 11.5/2 = 5.75 inches.

We know the volume of a cone is (1/3)πr²h.

∴  The volume of a cone is = (1/3)×π×(5.75)²×15 inch³.

= 519 in³.

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Answer:

g(x)= -x^2 - 3

Step-by-step explanation:

We know the vertex is (0, -3) and the parabola is opening downward that means the a value has to be negative. And if you know the transformation that -3 moves the parabola down by 3 units as f(x) represents the parent function y= x^2

The graph of the system of equations is shown below, and the solution is: (6, 1).

When a system of equations are plotted on a graph, the lines of the two equations in the system will intersect at a point. The coordinates of that point represents the solution of the system of equations.

In the graph shown below in the attachment, the red line represents the line 3x - y = 17, which has a slope of 3 and intercepts the y-axis at -17.

The green line represents the equation, x + 4y = 10, which has a slope of -1/4 and a y-intercept of 2.5.

Both lines intersect at point (6, 1).

Therefore, the solution is (6, 1)

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Step-by-step explanation:

The equation y=10x+5 is in the y=mx+b format, where m is the slope and b is the y-intercept.

The slope is 10 and the y-intercept is 5.

Since x represent the number of hours picking berries, y would represent the total number of berries picked.

Y-intercept (or the initial amount) is 5, and slope (aka rate of change) is 10.

y=10x+5                   replace x to 1 so it means that one hour has passed

y=10(1)+5                  simplify

y=10+5

y=15                         y represents the total number of berries picked

That means 15 berries would be picked in one hour.

I uploaded an image of how the graph would look like.

Answer:

Step-by-step explanation:

The inverse of f(x) =  ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5

What is inverse of function?

Change y in for the f(x) :

y = ∛5x + 5

Switch the x and y

x³ = 5y + 5

x³ - 5 = 5y

y = ( x³ - 5 ) / 5

f⁻¹ = ( x³ - 5 ) / 5

Hence, The inverse of f(x) =  ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5

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Hello,

I hope you and your family are doing well!

To find the mean of a set of numbers, you need to add up all of the numbers and divide the sum by the total number of numbers in the set.

In this case, the mean would be calculated as follows:

(678 + 592 + 652 + 800 + 502 + 396 + 502 + 301) / 8 = 515.25

So the mean of this data set is 515.25.

The mean is a measure of the central tendency of a data set and can be used to represent the entire set of numbers by giving a single value that is representative of the set as a whole. It is also known as the average.

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Answer: x=3

Step-by-step explanation:

When you plug in each number only 3 is the right answer.

A. 8(-4)-4=2(2(-4)+4)

-36=8 False

B. 8(12)-4=2(2(12)+4)

92=56 False

C. 8(0)-4=2(2(0)+4)

-4=8 False

D. 8(3)-4=2(2(3)+4)

20=20 True

The required measures of angles are:

∠MJL =  78°

∠JLP = 28°

What is incenter ?

One of the triangle's centers where the bisectors of the inner angles converge is known as the incline. The incenter is often referred to as the incircle's center in a triangle. An incenter might have several distinct types of characteristics.

The junction point of the central axis, which is the center of the triangle's inscribed circle, places this point at an equal distance from each of the triangle's sides. Since the biggest circle that might fit within a triangle is the incenter, it is also referred to as the center of the triangle's circle.

In the figure,

∠PJL = ∠MJP = 39°

∠MJL = ∠PJL +  ∠MJP  = 39° + 39° = 78°

∠PLK = 28°

∠JLP =∠PLK  = 28°

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The required measures of angles are:

∠MJL =  78°

∠JLP = 28°

What is the incenter of a triangle?

The inclination is one of the triangle's centers where the inner angles' bisectors converge. The incenter is frequently referred to as the triangle's incircle's center. Multiple different types of features could apply to an incenter.

This point lies at an equal distance from each of the triangle's sides because it is the intersection point of the central axis, which is also the center of the inscribed circle. The incenter is also referred to as the triangle's circle's center since it is the largest circle that could possibly fit inside a triangle.

In the figure,

∠PJL = ∠MJP = 39°

∠MJL = ∠PJL +  ∠MJP  = 39° + 39° = 78°

∠PLK = 28°

∠JLP =∠PLK  = 28°

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Answer:

[tex]\textsf{A)} \quad -\dfrac{9}{5}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given sum:

[tex]\displaystyle \sum^{\infty}_{n=1} -3\left(\dfrac{3}{8}\right)^n[/tex]

Therefore, the first term in the series is:

[tex]a_1=-3\left(\dfrac{3}{8}\right)^1=-\dfrac{9}{8}[/tex]

The common ratio, r, is:

[tex]r=\dfrac{3}{8}[/tex]

Substitute the first term, a, and common ratio, r, into the formula:

[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{1-\frac{3}{8}}[/tex]

[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{\frac{5}{8}}[/tex]

[tex]\implies S_{\infty}=-\dfrac{9}{5}[/tex]

Therefore, the sum of the given series is:

Answer:

2/7 ​≈0.285714286

Step-by-step explanation: 3/7−1/7

Since 3/7​ and 1/7​ have the same denominator, subtract them by subtracting their numerators.

3−1​ over 7

Subtract 1 from 3 to get 2.

2/7

the Factor

so 2/7 ≈0.285714286

Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:

Arc QR = 48°

Arc RS = 96°

Arc QPS = 216°

Arc PSR = 186°

Arc SRQ = 144°

The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.

Find arc PSR:

Arc PSR = 2(93) [based on the inscribed angle theorem]

Arc PSR = 186°

Find arc QR:

Arc QR = 360 - arc PQ - arc PSR

Substitute

Arc QR = 360 - 126 - 186

Arc QR = 48°

The value of ARC QR is 48

Arc RS = arc PSR - arc PS

Arc RS = 186 - 90

Arc RS = 96°

The value of ARC RS is 96

Arc QPS = 126 + 90

Arc QPS = 216°

Arc PSR = arc PS + arc RS

Arc PSR = 90 + 96

Arc PSR = 186°

Arc SRQ = arc RS + arc QR

Arc SRQ = 96 + 48

Arc SRQ = 144°

Therefore the value of ARC QR is 48° and ARC RS is 96°

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a. The coordinates of vertex B is (-3, -4)

b. The coordinates of vertex A' is (3,8)

What do you mean by rotation 180° about the origin?

The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).

Solution:

a. Current coordinate of vertex B is (3, 4).

  After rotating it 180° it becomes B (-3 , -4)

b. After translation the coordinates of vertex A is (5-2,4+4)

Coordinates of vertex A is (3,8)

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If ΔA B C is rotated 180° about the origin, the coordinates of B' (-3, -4)

b. The coordinates of vertex A' is (3,8)

What do you mean by rotation 180° about the origin?

The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).

Solution:

a. Current coordinate of vertex B is (3, 4).

 After rotating it 180° it becomes B (-3 , -4)

b. After translation the coordinates of vertex A is (5-2,4+4)

Coordinates of vertex A is (3,8)

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Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0

The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be

y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)

y + 8 = -5x + 5

y = - 5x - 3

The equation that best represents a line perpendicular will be y = - 5x - 3.

Answer:

p1 = 95 p2 = 180

Step-by-step explanation:

50 + 90% = 95

95 + 90% = 180

Answer:

Step-by-step explanation:

You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.

We can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...

  m = ∆a/∆p = 100/(-1) = -100

The y-intercept (b) can be found by solving the slope-intercept equation for b:

  y = mx +b

  b = y - mx

For (x, y) = (3.50, 250), the value of 'b' is ...

  b = 250 -(-100)(3.50) = 600

The slope-intercept equation for 'a' in terms of p is ...

  a = -100p +600

The value of 'a' for p = 1.50 is ...

  a = -100(1.50) +600

  a = 450

They will sell 450 items if the price per item is $1.50.

Answer:

Just by multiplying the extraction by the output per kilo for each mine and then summing it. The question asks to express it in millions and you have 8.2 million units

Step-by-step explanation:

Hope it helps

Answer:P(3 men) =

Step-by-step explanation: