Solve for a
2x-2=-3x+13
X =

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.

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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A) The inverse of f(x) is f⁻¹(x) = (x² + 9)/3 and B) f is not an inverse of g.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, f(x) = [tex]\sqrt{3x - 9}[/tex].

y = [tex]\sqrt{3x - 9}[/tex].

y² = 3x - 9.

3x = y² + 9.

x = (y² + 9)/3.

y = (x² + 9)/3.

f⁻¹(x) = (x² + 9)/3 and g(x) = 3x² - 9, so f is not an inverse of g.

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Answer: $118.75

Step-by-step explanation: first to see how much one bracelet is, you have to do 71.25/15=4.75. one bracelet is $4.75. so now we multiply 4.75 by 25 to see how much 25 bracelets cost. 4.75x25=118.75. so, if Karen seems all of her bracelets, she can expect to make $118.75.

The required time will be 12.9 years.

What is compound interest?

The interest charged on a loan or deposit is referred to as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.

Given, P = $1700

I = $500

A = P + I = 1700 + 500 = $2200

r = 2% = 0.02

compounded quarterly, n = 4

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

or, 2200 = 1700(1+ (0.02/4))^(4t)

or, 1.294 = 1.005^4t

or, t = 12.9 years

Hence, the required time will be 12.9 years.

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The zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.

What is Cubic equation?

Cubic equations are polynomials of degree3. That means the maximum degree of polynomial is three.

And the standard form of cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c and d are constant coefficients a ≠ 0.

Given that the expression

f(x) = 2x³ + 4x² - 8x - 16

Now we find the roots or zeroes of equation;

for that we will try hit and trial method,

let x = 2

f(x) = 2 (8) - 4 (4) - 8(2) -16

f(x) = 0

That means (x-2) is one of roots of cubic equation.

Now to find other roots of the cubic equation, we will simplify the cubic expression

f(x) = 2x² (x-2) + 8x (x-2) + 8 (x-2)

f(x) = (x-2)  (2x²+ 8x + 8)

Now we will find the roots of quadratic equation (2x²+ 8x + 8).

let g(x) = (2x²+ 8x + 8).

factors of quadratic equation is (x+2) and (x+2).

Therefore the zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.

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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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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:P(3 men) =

Step-by-step explanation:

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

Answer:

A

Step-by-step explanation:

There is no difference between -0 and +0.

So the ans is -3.29 itself.

The inequality that shows when the unicorn gets ahead of the chinchilla is 30s > 100 + 5.75s.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of seconds be represented by s.

The chinchilla is one hundred feet a head of the unicorn and running at a rate of 5.75 feet per second. This will be 100 + 5.75s.

The unicorn is running at a rate of 30 feet

per second. This will be 30s

The inequality will be 30s > 100 + 5.75s.

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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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Answer:

p1 = 95 p2 = 180

Step-by-step explanation:

50 + 90% = 95

95 + 90% = 180

2=3/4,13=1/4,2-3/4=0,13-1/4=0,2-3/4=0*13,13-1/4=0*2

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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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 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:

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 dimensions of the rectangle are 70.5 by 72.5 units.

What is a dimension?

A length measurement that only goes one way. Dimensions include things like width, depth, and height. One dimension is that of a line, two dimensions are found in a square, three dimensions are found in a cube, and one dimension is that of something's height, length, or width. For instance, the room is 26 feet by 15 feet in size.

Solution Explained:
Given,

Area = 143 unit^2

A/Q,

Let length be x and width be x + 2.

So, Area = l X w

      143 = x + x + 2

      143 = 2x + 2

      x = (143 - 2)/2

      x = 70.5

So width = x + 2 = 70.5 + 2 = 72.5

So, the dimensions are 70.5 by 72.5

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Answer:

If you are having trouble understanding the graph, it may be helpful to break it down into smaller pieces. Start by looking at each axis and what it represents. Then, look at each data point and see how it relates to the axes. Finally, look at the overall shape of the graph and what it is trying to tell you. If you are still having trouble understanding the graph, you may want to reach out to someone who is knowledgeable about graphs or data analysis for assistance.

Step-by-step explanation:

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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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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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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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: the answer is 4

Step-by-step explanation:

Answer:

fraction 23/10 that's 2 ³/10

decimal 2.3

The equation of the given function is y = -1/3 x. By using the points through which the line passing through, we can find its equation. Option A is correct.

The equation of the line passing through two points such as (x1, y1) and (x2, y2) is

y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)

From the given graph, the line is passing through the points (0, 0), (-3, 1), and (3, -1).

The equation of the line passing through (-3, 1) and (3, -1) is

y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)

⇒ y - 1 = (-1 - 1)/(3 + 3) × (x + 3)

⇒ y - 1 = -2/6 (x + 3)

⇒ y - 1 = -1/3 (x + 3)

⇒ 3y - 3 = -x - 3

⇒ 3y = -x

⇒ y = -1/3 x

So, option A is correct.

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Answer:

12

Step-by-step explanation:

(3x2) + 6

6 + 6 = 12

Answer:

12

Step-by-step explanation:

3 × 2 is 6

6 + 6 is 12

thus answer is 12

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.