The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.

The price f(x), in dollars, of product A after x years is represented by the function below:

f(x) = 0.69(1.03)x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the price f(t), in dollars, of product B after t years:


t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04


Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)

We have proven that line TU is parallel to line VW as shown below. That is, TU || VW

From the question, we are to prove that TU || VW

In the given image,

   Statements           Reasons

1. ST || UV                  Given

2. ∠T ≅ ∠U                Alternate angles

3. ∠T ≅ ∠V                Given

4. ∠U≅ ∠V                 Substitution property

5. TU || VW                 Alternate interior angles theorem

NOTE: If the alternate interior angles formed by a transversal of two lines are equal, then the lines are parallel

Hence, we have proven that line TU is parallel to line VW. That is, TU || VW

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Answer:

a c c

Step-by-step explanation:

The answer is no solution

Explanation:

it depends on how you interpret what's written. The way I initially interpreted it*, I was able to use the quadratic formula to find :

[tex]x=\frac{1}{4}-i\frac{\sqrt{455}}{20},\:x=\frac{1}{4}+i\frac{\sqrt{455}}{20}[/tex]

*I interpreted it as: [tex]x\left(x+3\right)-2\left(-5x+1\right)x=x^2-3\left(4-2x\right)[/tex]

but I don't want to say that this is your correct answer, because there are multiple interpretations (like a lot of interpretations)

{this is mostly in response to other answers}

Assuming that both lines are parallel, we conclude that C = 74°.

Here we can see that both of the lines that go upwards are parallel lines. This means that C and the 74° angles are opposite angles.

Then if we say that x is the angle at the right of the 74°, we must have that:

x + 74° = 180°

x = 180° - 74° = 106°

And we also must have that:

x + C = 106° + C = 180°

Solving for C:

C = 180° - 106° = 74°

C = 74°.

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The area of the octagon having an apothem of 6 meters and a side length of 7 meters is 168 meter square

Using the formula:

Area of an octagon = perimeter * apothem / 2

Note that perimeter of an octagon = 8 a

where a is the length of it's side

Perimeter = 8 * 7

Perimeter = 56 meters

Apothem = 6 meters

Substitute into the formula

Area = 56 * 6/ 2

Area = 336 / 2

Area = 168 meter square

Thus, the area of the octagon is 168 meter square

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Answer:

Do you like having a pet? - statistcal question

Step-by-step explanation:

^^^^

Answer:

13×13×13=2197 that is the answer

Answer:

y = 7 x - 13. y=7x−13. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side.7x-13=y. 7x−13=y. Add 13 to both sides. ... 7x=y+13. 7x=y+13. Divide both sides by 7. ... \frac{7x}{7}=\frac{y+13}{7} 77x​=7y+13​ Dividing by 7 undoes the multiplication by 7.

Step-by-step explanation: hope this helps

Answer:

-7

Step-by-step explanation:

(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).Option C is correct.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given equation;

⇒-8(x+13)=2(x-7)+4x

⇒-8x-13×8 = 2x-2×7+4x

⇒-8x-104=2x-14+4x

⇒-8x-104=6x-14

(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).

Hence, option C is correct.

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Answer:

  (-1, -5)

Step-by-step explanation:

Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.

A point on the shifted graph will be ...

  (x, f(x) -2)

Then for x = -1, the point is ...

  (-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)

The minimum on the shifted curve is M'(-1, -5).

_____

Additional comment

f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.

Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.

In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.

When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.

Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.

Hence option D is correct.

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Answer:

no correlation

Step-by-step explanation:

The correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.

Therefore the correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

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Answer:

See below.

Step-by-Step Explanation:

5) 8x+9-6x-7

8x + 2 - 6x (Subtract the numbers)

2x + 2 (Combine like terms)

2 (x + 1)  (Common factor - Factor by grouping twice)

6) 2y-6+5y+9

2y + 3 + 5y (Add the numbers)

7y + 3 (Combine like terms)

7) 3x+8+4x-9

3x - 1 + 4x (Subtract the numbers)

7x - 1      (Combine like terms)

8) 9y+16-12y+24

9y + 40 - 12y (Add the numbers)

-3y + 40 (Combine like terms)

9) 7g-5-8g+12

7g + 7 - 8g (Add the numbers)

-g + 7 (Combine like terms)

10) 11c-8+5c-8

11c - 16 + 5c (Subtract the numbers)

16c - 16 (Combine like terms)

16 (c - 1)   (Common factor - Factor by grouping twice)

11) 5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)

10x + 15 (Distribute)

12) 5(-2x+3)

-10x + 15 (Distribute)

Hope this helps!

Answer: those are the answers its a long time.

Question  5  Answer: 2(x+1)

8x+9−6x−7

Multiply and combine like terms.

2x+2

Factor out 2.

2(x+1)

Questio 6 Answer : 7y + 3

2y−6+5y+9

Combine 2y and 5y to get 7y.

7y−6+9

Add −6 and 9 to get 3.

7y+3

Question 7  Answer: 3x+8+4x−9

Combine 3x and 4x to get 7x.

7x+8−9

Subtract 9 from 8 to get −1.

7x−1

Question 8 Answer: - 3y + 40

9y+16−12y+24

Combine 9y and −12y to get −3y.

−3y+16+24

Add 16 and 24 to get 40.

−3y+40

Question 9 Answer: -g + 7

7g−5−8g+12

Combine 7g and −8g to get −g.

−g−5+12

Add −5 and 12 to get 7.

−g + 7

Question 10 Answer: 16 ( c - 1 )

11c−8+5c−8

Combine 11c and 5c to get 16c.

16c−8−8

Subtract 8 from −8 to get −16.

16c - 16

Question 11 Answer: 10x +15

5(2x+3)

Use the distributive property to multiply 5 by 2x+3.

10x+15

Question 12 Answer: 15 - 10x

5(−2x+3)

Use the distributive property to multiply 5 by −2x+3.

−10x+15

Answer:

below

Step-by-step explanation:

7(x-3)+2(xy-3y)

I'm positive it's the correct answer

The height of the target is 29 feet.

The correct option is (D)

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The given table path of the thrown ball,

where x represents the horizontal distance and f(x) represents the height of the ball.

Now,

when x = 1.25 feet horizontally, the height will be maximum.

also, the height of the ball at  distance x = 1.25 feet is

f(1.25) = 29 feet.

Hence, height of the target is 29 feet.

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Answer:

D. 29 feet

Step-by-step explanation:

The expected value of the winnings from the game is $4

The payout probability distribution is given as:

Payout ($) 2 4 6 8 10

Probability 0.5 0.2 0.15 0.1 0.05

The expected value is then calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

This gives

E(x) = 2 * 0.5 + 4 * 0.2 + 6 * 0.15 + 8 * 0.1 + 10 * 0.05

Evaluate the expression

E(x) = 4

Hence, the expected value of the winnings from the game is $4

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Answer:

The first option

Step-by-step explanation:

The domain of a rational function should be all real numbers except for when the denominator is equal to 0. To find when the denominator is equal to 0 you simply need to find the zeroes of the denominator... but in this case you can do that through factoring and using the quadratic equation.

So first step is going to be to factor out the GCF, which in this case is x. This gives you the equation. [tex]x(2x^2-x-15)[/tex]. So one of the zeroes is when x=0. Now to find the other two zeroes you can use the quadratic equation which is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\[/tex]. So to find the other zeroes you simply plug the values in. a=2, b=-1, c=-15

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-15)}}{2(2)}\\\\x=\frac{1\pm\sqrt{1-4(2)(-15)}}{4}\\\\x=\frac{1\pm\sqrt{121)}}{4}\\\\x=\frac{1\pm11}{4}\\\\x=\frac{12}{4}\\x=3\\\\x=\frac{-10}{4}\\x=-\frac{5}{2}[/tex]

In the given equation, the value of x is approximately 75°

From the question, we are to determine the value of x

The given equation is

sin x ≈ 0.965926

If sin x ≈ 0.965926

Then,

x ≈ sin⁻¹(0.965926)

∴ x ≈ 75.0°

Hence, the value of x is approximately 75°

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Answer:

the answer is [1, infinity)

Answer:

1. 0

2. undefined

3. -3/2

Step-by-step explanation:

y=-3/2. This value is constant and the x does not change the value at all. so the coordinate are going to be (x, -3/2) so if we take any 2 values you're going to get (-3/2 - (-3/2)) / (x2 - x1) = (-3/2 + 3/2) / (x2 - x1) = (0) / (x2 - x1) which is always going to be 0.

x=-3/2. This value is also constant except the x-value does not vary at all so x2 and x1 are always going to be equal which will result in a 0 as the denominator thus making the slope undefined

y=-3/2x. it's just -3/2 given the slope-intercept form y=mx+b where m is the slope

Answer:

0 underfined 3

—

2

Step-by-step explanation:

SOLVING STEP.

the line y= 3 is parallel to the x-axis,

—

— 2

so the slope is 0

the line x= 3 is perpendicular to the x-axis,

—

— 2

so the slope is underfined

the slope of the line y= 3 x 3

—

— — 2.

2

thank me later

Answer:

D

Step-by-step explanation:

the diagonals of a parallelogram bisect each other , then

2 AE = AC ( substitute values )

2(2x - 5) = 22 ( divide both sides by 2 )

2x - 5 = 11 ( add 5 to both sides )

2x = 16 ( divide both sides by 2 )

x = 8

Answer:

zero (0)

Step-by-step explanation:

-4^0=-1

-1+1=0

Answer:

Part A = 36z² - 9z + 8

Part B = 5z³ + 4z² + 16z - 23

Part c = Yes.

Step-by-step explanation:

Polynomials : Polynomials are algebraic expressions that consist of variables and coefficients.

Trapezium: A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

Given the length of sides :

Side 1: 11z² - 4z + 2

Side 2: -2z + 3 + 12z²

Side 3: 3 - 3z + 13z²

and The perimeter of the trapezoid is 5z³ + 40z² + 7z - 15.

PART A:

The total length of sides 1, 2, and 3 of the trapezoid is obtained by the sum of the trapezoid :

11z² - 4z + 2 + (-2z + 3 + 12z²) + 3 - 3z + 13z²

11z² - 4z + 2 - 2z + 3 + 12z² + 3 - 3z + 13z²

36z² - 9z + 8

PART B:

The length of the fourth side of the trapezoid is given by the difference between the perimeter of the trapezoid and the sum of  length of sides 1, 2, and 3.

5z³ + 40z² + 7z - 15 - 36z² + 9z - 8

5z³ + 4z² + 16z - 23

PART C:

From part A, we can see that the addition of polynomials results in a polynomial.

Likewise, the subtraction of polynomials results in a polynomial.

Therefore, we can say that the polynomials are closed under addition and subtraction.

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Answer:

y=-x+4

Step-by-step explanation:

First use slope formula using 2 points.

(0,3) and (1,2)

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{2-3}{1-0}=\frac{-1}{1} =-1[/tex]

Slope is -1.

Now, use point-slope formula.

y-y1=m(x-x1)

Plug in the information that we have.

y-3=-1(x-0)

Use distributive property.

y-3=-x+1

Add 3 to both sides.

y=-x+4

It is now in slope-intercept form.

Hope this helps!

If not, I am sorry.

Theta has a reference angle of 30° and is in Quadrant I or II.

Sin(theta) = ½

Basic angle: 30

The acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle sandwiched between the terminal side and the x-axis.

Angles: 30,

180-30 = 150

Because sin is positive in quadrants 1 and 2.

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Solution: X=6

Detailed explanation:

In this problem we're asked to find "x" or the unknown.

The first step is to subtract 11x from both sides.

[tex]---\mapsto\boldsymbol{-11x+79=13}[/tex]

Next, subtract 79 from both sides.

[tex]---\mapsto\boldsymbol{-11x=-66}[/tex]

To finish this off, divide both sides by -11.

[tex]---\mapsto\boldsymbol{x=6}[/tex]

Voila! There's our answer!

___________________

Hope I helped.  Best wishes.

Reach far. Aim high. Dream big.

___________________

[tex]\large\green\longrightarrow \tt \large \:79 \: = \: 11x \: + \: 13[/tex]

[tex]\large\green\longrightarrow \tt \large \:79 \: - \: 13 \: = \: 11x[/tex]

[tex]\large\green\longrightarrow \tt \large \:66 \: = \: 11x[/tex]

[tex]\large\green\longrightarrow \tt \large \: \frac{ \cancel{66} \: \: ^{ \pink6} }{ \cancel{11}} \: = \: x \\ [/tex]

[tex]\large\green\longrightarrow \tt \large \:6 \: = \: x[/tex]

Hence , the value of x is 6

Answer:

$3.43

Step-by-step explanation:

Cost per pound means how much you are paying for one pound of the item. In this question it says a pound of cheese costs 3.43, therefore each pound of cheese costs 3.43. We can also use the equation 3.43x where x represents the amount of pounds you are purchasing. Just multiply the two and you will get a cost for any amount (pounds) of cheese.

Answer:

y = 7/6x - 62/3

Step-by-step explanation:

The equation for slope:

y = mx + b

m is the slope and b is the y-intercept

y = 7/6x + b

-9 = 7/6(10) + b

-9 = 35/3 + b

-62/3 = b

Answer:

m=-3

Step-by-step explanation:

Since the lines are parallel to each other, their gradients are equal.

∴ gradient of green line = gradient of red line

∴ m = -3

Solution: slope=-3

Detailed explanation:

This little problem asks us to find the slope of the line. Let's do this!

[tex]\searrow[/tex]

This is what parallel lines look like:

<------------------------------------------------------------------------------------------------------->

<------------------------------------------------------------------------------------------------------->

The two lines above will never intercept each other.

And that's what parallel lines are - they are lines that never intercept.

They can be vertical, horizontal, or diagonal, it doesn't matter. As long as both of them have the same slope and never intercept each other.

So, since parallel lines have identical slopes, the slope of the red line = slope of the green line (the problem provides us that both lines are parallel)

Slope of the red line = -3

Voila! There's our answer!

__________________________

Hope I helped! Best wishes!

Reach far. Aim high. Dream big.

"reflection"

__________________________