Practice and Problem S Subtract using the vertical form. 1. (5g^(2)+6g-10)-(2g^(2)+2g+9)

The polynomial expressions are P(x) = x(x - 5)(x - 2), P(x) = (x + 3)(x + 5)(x - 3)(x + 1), P(x) = (x + 5)(x² - 4x + 5) and P(x) = (x + 5)(x² + 4)

Zeros (1): 0, 5, 2

This means that

Roots: x = 0, x = 5 and x = 2

The equation can be represented as

P(x) = (x - root)

So, we have

P(x) = (x - 0)(x - 5)(x - 2)

Evaluate

P(x) = x(x - 5)(x - 2)

Zeros (2): 0, 5, 2

Here, we have

Roots: x = -3, x = -5, x = 3 and x = -1

Using the form in (a), we have

P(x) = (x + 3)(x + 5)(x - 3)(x + 1)

Zeros (3): 0, 5, 2

Here, we have

Roots: x = -5, x = 2 + i

Using the form used abov]e, we have

P(x) = (x + 5)(x - 2 - i)(x - 2 + i)

Expand

P(x) = (x + 5)((x - 2)² + 1)

So, we have

P(x) = (x + 5)(x² - 4x + 5)

Zeros (4): -1 and 2i

Here, we have

Roots: x = -1, x = 2i

Using the form used abov]e, we have

P(x) = (x + 1)(x - 2i)(x + 2i)

Expand

P(x) = (x + 5)(x² + 4)

Zeros (5):2 mult.2, -4

The zeros here are not clear

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No common factors

For the first set of fractions, the inequality symbol would be <, as 8/9 is less than 10/12. The rationale for this is that when fractions have different denominators, the fraction with the smaller denominator is always less. For the second set of fractions, the inequality symbol would be >, as -5/6 is greater than -6/8. The rationale for this is that when two fractions have the same denominator, the fraction with the larger numerator is always greater. The fractions that are completely simplified are 8/9, -5/6, and -6/8. This is because they cannot be reduced any further as they have no common factors.

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The equation for the given tangent function is f(x) = 3 tan(x - π/2) - 1.

What is Trigonometric function ?

Trigonometric functions are mathematical functions that relate to angles of a right-angled triangle. The three most common trigonometric functions are sine, cosine, and tangent, which are denoted by sin, cos, and tan, respectively.

The general form of a tangent function is given by:

f(x) = A tan(B(x - C)) + D

where A is the amplitude, B is the frequency (inverse of the period), C is the horizontal shift, and D is the vertical shift.

Given the information, we have:

A = 3

period = π

frequency = 1/period = 1/π

horizontal shift = π/2 to the right

vertical shift = down 1

So, we can plug in the values into the general form and get:

f(x) = 3 tan(1(x - π/2)) - 1

Simplifying:

f(x) = 3 tan(x - π/2) - 1

Therefore, the equation for the given tangent function is f(x) = 3 tan(x - π/2) - 1.

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The measures of the angles in the triangle are A = 6.17°,B = 11.50°, C = 162.33° and that's the solution to the triangle using the Law of Sines.

To solve the triangle using the Law of Sines, we can use the following formula:

(a/sin A) = (b/sin B) = (c/sin C)

First, let's convert the given angle B from degrees and minutes to decimal form:

B = 11° 30' = 11.5°

Next, we can plug in the given values into the formula and solve for the unknowns:

(3.7/sin A) = (6.5/sin 11.5°)

Cross-multiplying and rearranging gives us:

sin A = (3.7 * sin 11.5°) / 6.5

Using a calculator, we can find the value of sin A:

sin A = 0.1076

Now, we can use the inverse sine function to find the measure of angle A:

A = sin^-1(0.1076) = 6.17°

Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C:

C = 180° - A - B = 180° - 6.17° - 11.5° = 162.33°

So, the measures of the angles in the triangle are:

A = 6.17°
B = 11.5°
C = 162.33°

Round your answers to two decimal places, we have:

A = 6.17°
B = 11.50°
C = 162.33°

And that's the solution to the triangle using the Law of Sines.

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a) At the time the article was published, the federal minimum wage was $5.85 per hour.

b) According to the US Department of Labor website, the federal minimum wage in 2008 was $6.55 per hour.  

c) To earn the current federal minimum wage of $7.25 per hour, a person must pick up a penny in 4.97 seconds.

d) The phrase "penny dreadful" is a British expression referring to cheaply printed stories of sensational and sometimes gruesome content that were sold for a penny in the 19th century.

A) The minimum wage when Owen wrote his article can be calculated by using the equation:

Minimum wage = (Amount of money earned)/(Amount of time taken to earn it)

In this case, the amount of money earned is $0.01 (the value of a penny) and the amount of time taken to earn it is 6.15 seconds. Therefore:

Minimum wage = ($0.01)/(6.15 seconds) = $0.00162601626 per second

To convert this to an hourly wage, we can multiply by the number of seconds in an hour (3600):

Minimum wage = ($0.00162601626 per second) x (3600 seconds per hour) = $5.85365854 per hour

Minimum wage =  $5.85

B) According to the U.S. Department of Labor, the federal minimum wage in 2008 was $6.55 per hour.

Therefore, Owen's arithmetic was slightly off, as his calculated minimum wage is lower than the actual minimum wage at that time.

C) To calculate how much time you would need to spend picking up a penny in order to earn the current minimum wage, we can use the same equation as before, but rearrange it to solve for the amount of time:

Amount of time = (Amount of money earned)/(Minimum wage)

The current federal minimum wage is $7.25 per hour, or $0.00201388889 per second. Therefore:

Amount of time = ($0.01)/($0.00201388889 per second) = 4.97 seconds

So you would need to spend 4.97 seconds picking up a penny in order to earn the current minimum wage.

D) The phrase "penny dreadful" refers to a type of cheap, sensationalist fiction that was popular in the 19th century. These stories were typically published in weekly installments and sold for a penny each, hence the name "penny dreadful."

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The requried measure of the angle x in at the point of intersection of tangent and secant of the circle is 30°.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

Here,
From the figure the,
From a point, a tangent and a secant are drawn to the circle.
Since an equilateral triangle is formed with the help of a cord intersects the tangent and secant on the circumference of triangle.

Again from the figure, the sum of the angle in the triangle is equal to 180°.
90 - 60 + 180 - 60 + x = 180
30 + 120 + x = 180
x = 30°

Thus, the requried measure of the angle x at the point of intersection of tangent and secant of the circle is 30°.

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A graph that can be used to find the real solution(s) to 3 - 4x = -3 - x² - 4x is shown in the image attached below.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.

Next, we would use an online graphing calculator to plot the given quadratic function 3 - 4x = -3 - x² - 4x as shown in the graph attached below.

By splitting the quadratic function, we have:

y = -3 - x² - 4x

y = 3 - 4x

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A linear function is a polynomial function with a degree of 1, and a degree 4 polynomial function is a polynomial function with a degree of 4. The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. The y-intercept of a graph is the point where the graph crosses the y-axis.

To create the linear function, h(x), we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept can not be 0, we can choose a value for b that is not 0. For example, b = 2. We can also choose a value for m that is not 0, so that h(x) is not a horizontal or vertical line. For example, m = 3. Therefore, h(x) = 3x + 2.

To create the degree 4 polynomial function, P(x), we can use the factored form: P(x) = a(x - r1)(x - r2)(x - r3)(x - r4), where a is the leading coefficient, and r1, r2, r3, and r4 are the zeros of the function. Since the leading coefficient can not be |1|, we can choose a value for a that is not 1 or -1. For example, a = 2. Since one of the factors must be repeated 2 times, we can choose a value for r1 and set r2 equal to r1. For example, r1 = 1 and r2 = 1. Since one of the zeros must be a fraction, we can choose a value for r3 that is a fraction. For example, r3 = 1/2. Since the zeros should have a mix of positive and negative numbers, we can choose a value for r4 that is negative. For example, r4 = -2. Therefore, P(x) = 2(x - 1)(x - 1)(x - 1/2)(x + 2).

To find the points of intersection between h(x) and P(x), we can set h(x) equal to P(x) and solve for x:
3x + 2 = 2(x - 1)(x - 1)(x - 1/2)(x + 2)
This equation can be solved algebraically by expanding the right-hand side and rearranging the terms to form a degree 4 polynomial equation. Then, we can use the Rational Root Theorem and synthetic division to find the possible rational roots of the equation. Once we find the rational roots, we can use them to factor the equation and find the remaining roots. The x-coordinates of the points of intersection are the roots of the equation.

To determine the intervals when h(x)≥P(x), we can use the points of intersection and the signs of h(x) and P(x) on either side of the points of intersection. If h(x) is greater than or equal to P(x) on an interval, then the graph of h(x) is above or coincident with the graph of P(x) on that interval. We can use a sign chart or a graph to determine the intervals when h(x)≥P(x).

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Answer:

1

Step-by-step explanation:

2 power 3 in numerator mean it is 8.

Divide th 2 power 3 in denominator it means 8.

Now upo dividing 8 and 8 it gives 1.

Same it can be understood by any number with exponent 0 is equal to 1.

Solving a quadratic equation we can see that Jason will hit the water after 6 seconds.

We know that the height of Jason is modeled by the quadratic function:

h = - 16x² + 16x + 480

The water is at h = 0, so we need to solve the quadratic equation:

0 = - 16x² + 16x + 480

If we divide all the right side by 16,we will get:

0 = (- 16x² + 16x + 480)/16

0 = -x² + x + 30

Now we can use the quadratic formula to get the solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{-1 \pm 11 }{-2}[/tex]

We only care for the positive solution, which is:

x  = (-1 - 11)/-2 = 6

Jason will hit the water after 6 seconds.

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Answer: 126

Step-by-step explanation:

The total volume of the cheese box can be given by 3bh × L.

A triangular prism is a pοlyhedrοn made up οf twο triangular bases and three rectangular sides. It is a three-dimensiοnal shape that has three side faces and twο base faces, cοnnected tο each οther thrοugh the edges. If the sides are rectangular, then it is called the right triangular prism else it is said tο be an οblique triangular prism.

The volume of a triangular prism is given by = (1/2) × bh × L

where b = base, h = height and L = length

Six identical cheese wedges are packaged in a container shaped like a hexagonal prism, i.e

⇒ 6 × identical cheese wedges

⇒ 6 × (1/2) × bh × L

Total volume of the cheese box:

= 6 × (1/2) × bh × L

= 6 × (1/2) × bh × L

= 3 × bh × L

= 3bh × L

Thus, The total volume of the cheese box can be given by 3bh × L.

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Answer is 240 centigrams = 2400 milligrams, 240 centigrams = 24 decigrams, 240 centigrams = 0.024 kilograms.

Measurement is the process of quantifying an attribute or property of an object or event using a numerical or quantitative scale. The result of a measurement is a number or value that represents the magnitude or amount of the attribute being measured.

Centigrams, milligrams, decigrams, and kilograms are all units of measurement of mass in the metric system.

1 centigram (cg) = 10 milligrams (mg) in the metric system.

240 centigrams =  10×240 milligrams,

So, 240 centigrams is equal to 2400 milligrams.

1 centigram (cg) = 0.1 decigrams (dg)

240 centigrams =  0.1×240 decigrams

So, 240 centigrams is equal to 24 decigrams.

1 centigram (cg) = 0.0001 kilograms (kg)

240 centigrams =  0.0001×240 kilograms

So, 240 centigrams is equal to 0.024 kilograms.

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Therefore , the solution of the given problem of triangle comes out to be NL =  √(100 + 20LM2) * 10 * 4 .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular. The intersection of a quadrilateral's three edges is known as an angle. The sum of a triangle's edges is 180 degrees.

Here,

By removing NP:, we can resolve this system of equations.

NL Equals NP(LM + NL + 5). (5 - LM)

NL = NP(LM - PQ + 5) (LM)

NL(5 - LM) = NP(LM + NL + 5)(LM - PQ + 5) (LM)

By enlarging and condensing, we obtain:

NP = 2NL Plus LM / 5LM

Now that we know this, we can put it into one of the equations to find NL:

(2NL Plus LM / 5LM)

NL = (LM Plus NL + 5) (5 - LM)

By condensing and rearrangeing, we obtain:

(2NL Plus LM) = 0 when (NL2 - 10NL - 5LM2)

The quadratic algorithm yields:

NL =  √(100 + 20LM2) * 10 * 4 alternatively,

=> NL = (10 -  √(100 + 20LM2)) / 4

NL can never be negative, so we pick the positive root:

NL =  √(100 + 20LM2) * 10 * 4

Now that we have this, we can put it into one of the equations to find NP:

NP = 2NL Plus LM / 5LM

NP = 5LM / (2(10 + √100 + 20LM^2)) / 4 + LM)

NP is equal to 5LM / (5 +  √(25 + 5LM2)).

The widths of NP and NL are as follows:

NP is equal to 5LM / (5 + sqrt(25 + 5LM2)).

NL = (10 -  √(100 + 20LM2)) / 4

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the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.

why it is and what is multiple?

a) The number 5,364 can be written as the sum of multiples of powers of 10 as follows:

5,364 = 5 × 1,000 + 3 × 100 + 6 × 10 + 4 × 1

= 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰

(b) If x = 10, then we can write 5,364 as:

5,364 = 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰

= 5x³ + 3x² + 6x + 4

Therefore, the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.

A multiple is a product of a given number and any other whole number. In other words, if a number 'a' can be expressed as the product of another number 'b' and a whole number 'c', then 'a' is a multiple of 'b'. For example, 10 is a multiple of 5 because 10 can be expressed as 5 multiplied by 2. Similarly, 15 is a multiple of 3 because 15 can be expressed as 3 multiplied by 5.

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Answer:

3

Step-by-step explanation:

by the help of Prashant chettri

The sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

To split the given rational expression into a sum of two rational expressions with unlike denominators, we will use the partial fraction decomposition method. Here are the steps:

1. Factor the denominator of the given rational expression: (x^(2)+3x+2) = (x+1)(x+2)
2. Set up the partial fraction decomposition: (2x+3)/(x+1)(x+2) = A/(x+1) + B/(x+2)
3. Multiply both sides of the equation by the common denominator to get rid of the denominators: 2x+3 = A(x+2) + B(x+1)
4. Set up a system of equations by equating the coefficients of the like terms: 2x+3 = (A+B)x + (2A+B)
5. Solve the system of equations to find the values of A and B: A=1, B=1
6. Substitute the values of A and B back into the partial fraction decomposition: (2x+3)/(x+1)(x+2) = 1/(x+1) + 1/(x+2)

Therefore, the sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

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The intersection of sets A and B

The intersection of two sets is the set of elements that are common to both sets. To find the intersection of sets A and B, we simply look for the elements that are in both sets. In this case, the intersection of A and B is {h, o, e}.

The union of two sets is the set of elements that are in either one of the sets or both. To find the union of sets A and B, we simply combine the elements from both sets, making sure to not include any duplicates. In this case, the union of A and B is {h, o, m, e, u, s}.

So, the intersection of sets A and B is {h, o, e} and the union of sets A and B is {h, o, m, e, u, s}.

Here is the solution in HTML:

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When x = 4, y = 320/27.

If y varies directly as x, it means that y = kx, where k is a constant. To find k, we can use the given information:

When x = 3, y = 12

12 = k * 3

k = 4

Now that we know k, we can find y when x = 20:

y = k * x

y = 4 * 20

y = 80

Therefore, when x = 20, y = 80.

25. If y varies directly as the square of x, it means that y = k * x^2, where k is a constant. To find k, we can use the given information:

When x = 2, y = 16

16 = k * 2^2

k = 4

Now that we know k, we can find y when x = 8:

y = k * x^2

y = 4 * 8^2

y = 4 * 64

y = 256

Therefore, when x = 8, y = 256.

26. If y varies directly as the cube of x, it means that y = k * x^3, where k is a constant. To find k, we can use the given information:

When x = 3, y = 5

5 = k * 3^3

k = 5/27

Now that we know k, we can find y when x = 4:

y = k * x^3

y = 5/27 * 4^3

y = 5/27 * 64

y = 320/27

Therefore, when x = 4, y = 320/27.

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65. Find cos tetha, given that sin tetha = 3/5 and tetha is in quadrant II.

We can use the identity cos^2 tetha + sin^2 tetha = 1 to find cos tetha.

cos^2 tetha = 1 - sin^2 tetha

cos^2 tetha = 1 - (3/5)^2

cos^2 tetha = 1 - 9/25

cos^2 tetha = 16/25

cos tetha = ±√(16/25)

cos tetha = ±4/5

Since tetha is in quadrant II, cos tetha is negative. So, cos tetha = -4/5.

66. Find sin tetha, given that cos tetha = 4/5 and tetha is in quadrant IV.

We can use the same identity to find sin tetha.

sin^2 tetha = 1 - cos^2 tetha

sin^2 tetha = 1 - (4/5)^2

sin^2 tetha = 1 - 16/25

sin^2 tetha = 9/25

sin tetha = ±√(9/25)

sin tetha = ±3/5

Since tetha is in quadrant IV, sin tetha is negative. So, sin tetha = -3/5.

67. Find csc tetha, given that cot tetha = -1/2 and tetha is in quadrant IV.

We can use the identity csc^2 tetha = 1 + cot^2 tetha to find csc tetha.

csc^2 tetha = 1 + (-1/2)^2

csc^2 tetha = 1 + 1/4

csc^2 tetha = 5/4

csc tetha = ±√(5/4)

csc tetha = ±√5/2

Since tetha is in quadrant IV, csc tetha is negative. So, csc tetha = -√5/2.

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The volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let us find the volume of the cylinder which has diameter of 22 ft and height of 10 feet.

Diameter=2radius

Radius=22/2=11 feet.

V=πr²h

=3.14×11²×10

=3799.4 cubic feet.

Hence, the volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.

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Answer:

Step-by-step explanation:

1. Figure out which terms are alike. I have separated the like terms using parenthesis for clarification, however, this is not necessary when solving by yourself.

(3y + 4y) + (8 + 2)

2. Combine both sets of like terms however the signs dictate. In this case, add all the signs.

3y + 4y = 7y  

(solve as if there was no constant so if 3 + 4 = 7 then 3y + 4y = 7y)

8 + 2 = 10

3. Put it all together

Final answer: 7y + 10

Note: Understanding how to combine and simplify like terms will be very helpful when you eventually will have to solve for y. When solving an equation you will always want to start by combing and simplifying like terms first.  

It will take 18 years for the Type A and Type B trees to be the same height.

A location in the centre of a line connecting two places is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its ends. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places.

Let us suppose the number of years = y.

The height of the tree of type A is thus,

5 feet + (4 inches/year)(y)

= 5 + 4/12 y feet

= 5 + 1/3 y feet

For the type B:

2 feet + (10 inches/year)(y years)

= 2 + 10/12 y feet

= 2 + 5/6 y feet

To get the height of the two trees as equal we have:

5 + 1/3 y = 2 + 5/6 y

3 + 1/3 y = 5/6 y

3 = 1/6 y

18 = y

Hence, it will take 18 years for the Type A and Type B trees to be the same height.

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To make the trinomial y2 - 18y a perfect square, we need to add a constant that is equal to (18/2)^2 = 81.

This is because a perfect square trinomial is in the form (x + a)^2 = x^2 + 2ax + a^2. In this case, x = y and 2a = -18, so a = -9 and a^2 = 81. So, the trinomial becomes y2 - 18y + 81, which is a perfect square.

To factor the trinomial, we can use the formula (x + a)^2 = x^2 + 2ax + a^2, where x = y and a = -9. So, the trinomial y2 - 18y + 81 can be factored as (y - 9)^2.

Therefore, the proper constant to add to the binomial y2 - 18y to make it a perfect square trinomial is 81, and the factored form of the trinomial is (y - 9)^2.

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Answer:

277

Step-by-step explanation:

Just add lol

Answer:5:7

Step-by-step explanation:

From the given graph it is clear that

The total number of circles = 12

The total number of patterned circles = 5

The total number of plain circles = 7

We need to find the ratio of patterned circles to plain circles.

Substitute patterned circles = 5 and plain circles = 7 in the above formula.

Therefore, the ratio of patterned circles to plain circles is 5:7.

Answer:

a = 6

b = 5

c = -4

Step-by-step explanation:

(2x-1)(3x+4) = [tex]6x^{2}[/tex]+8x-3x-4 = [tex]6x^{2}[/tex]+5x-4

If the equation is [tex]ax^{2}[/tex]+bx+c, then the values of a, b, and c, are 6, 5, and -4 as it makes the equation true.

Using the numbers 1 to 9 (one time each), the boxes can be filled in the following way to make the equation true. 2:2 = 3×3:9 = 4×4 =16.

An arithmetic contrast among two numbers is known as a percentage. Two sets of provided numbers are considered to be approximately equal with respect to one another in conformity with the rules of proportion if they increase or decrease by the same ratio.

We must create the equation to prove the equality by utilizing each of the numerals 1 through 9 once. Any of the numbers between 1 and 9 are equivalent to 1 and 2.

Let the ratio equal 1.

The comparable ratios are therefore 1:1, 2:2, and 3:3.

2:2 = 3×3:9 = 4×4 =16

Therefore, using the numbers 1 to 9 (one time each), the boxes can be filled in the following way to make the equation true. 2:2 = 3×3:9 = 4×4 =16.

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Answer: B' is (1, -2)

Step-by-step explanation:

Point B is (5, 1), so subtract 4 from 5 and subtract 3 from 1 so,

5 - 4 = 1

1 - 3 = -2

B' is (1, -2)

Hope this helps!

The expense E for the production of an item when the price of $74.99 has been established is $3,378,021.86.

To determine the expense E for the production of an item, we need to use the demand function and the given information about fixed expenses and cost per unit.

First, let's plug in the given price of $74.99 into the demand function to find the quantity demanded:

a = 67(74.99) + 74,000

a = 5,024.33 + 74,000

a = 79,024.33

Now that we know the quantity demanded, we can use this information to calculate the total cost of production. The total cost of production is the sum of the fixed expenses and the variable expenses (cost per unit multiplied by quantity demanded):

E = 59,000 + (42.00)(79,024.33)

E = 59,000 + 3,319,021.86

E = 3,378,021.86

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Answer:

Step-by-step explanation:

its 190 because you started on page 4 and you add 186