Situation 1: In Lakeville, Melinda’s television cable bill is a flat rate of $50 per month, plus $1.50 for every movie she rents. After one month of service, her bill is $66.25.

Situation 2: In Oceanside, Kimberly’s television cable bill is a flat rate of $60 dollars per month, plus $1.25 for every movie she rents.

If you were to model these two situations with equations to solve for all the unknowns, what similarities and differences would the equations have? Can you solve for all the unknowns in both situations?

Answer:

f⁻¹(x) = (4x)/5

Step-by-step explanation:

f(x) = 2x - 3x/4.

Assume y=f(x). Therefore:

y = 2x - 3x/4.

Make x the subject in the above equation.

y = (2x(4) - 3x)/4.

y = 5x/4.

4y = 5x.

(4y)/5 = x.

x = (4y)/5.

Therefore:

f(y) = (4y)/5.

Replace y with x.

f⁻¹(x) = (4x)/5.

Therefore, the inverse of f(x) = 2x - 3x/4 is f⁻¹(x) = (4x)/5!!!

The line segment drawn from point A to point A′, after reflecting the triangle over the y-axis, is perpendicular to the y-axis. This is because the reflection mirrors the image across the y-axis resulting a right-angle formation between the line segment and the axis.

The line segment drawn from point A to point A′, after a reflection of Triangle HAM over the y-axis, would be perpendicular to the y-axis. This is because in a reflection over the y-axis, the x-coordinates of the points change sign and the y-coordinates stay the same. This procedure mirrors the image over the y-axis and creates a segment from A to A′ that is perpendicular to the y-axis and bisects the distance between A and A′.

This idea correlates to the vector concept in physics where components of the vector may be viewed as sides of a right triangle. Much like in that context, the line segment from A to A′ and the y-axis form a right angle, hence they are perpendicular.

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Answer:

see below

Step-by-step explanation:

g(x) = x^3 − x^2 − 4x + 4

We know the graph will have up to 3 zero's because it is a cubic

g(x) = x^3 − x^2 − 4^x + 4

I will factor by grouping, taking an x^2 from the first 2 terms and -4 from the last 2 terms

  g(x)=  x^2(x-1) -4(x-1)

Now factor out x-1

  g(x)= (x-1)(x^2 -4)

We can factor the (x^2-4) as a difference of squares

g(x) = (x-1) (x-2)(x+2)

Using the zero product property

0= (x-1) (x-2)(x+2)

x-1 =0   x-2 =0   x+2=0

We have zeros at x=1   x=2  and x=-2

Then we can plot points to determine where the function is between the points We will pick negative infinity 0 1.5 and infinity

at g(-inf) =  -inf  because x^3 dominates and that goes to -infinity

at g(0) = 0+000+4 =4

at g(1.5) =-.875

at  g(inf)=because x^3 dominates and that goes to infinity

Answer:

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

We have f(x) = 3ˣ + 10 and g(x) = 2x - 4. Substitute:

(f - g)(x) = (3ˣ + 10) - (2x - 4) = 3ˣ + 10 - 2x - (-4) = 3ˣ + 10 - 2x + 4

(f - g)(x) = 3ˣ - 2x + 14

Answer:

−6 < x  < 9

Step-by-step explanation:

−7 < x − 1 < 8

Add 1 to all sides

−7+1 < x − 1+1 < 8+1

−6 < x  < 9

Answer: [tex]-6<x<9[/tex]

Step-by-step explanation:

You have the following expression provided in the exercise:

[tex]-7 < x - 1 < 8[/tex]

Then, in this case, in order to solve the expression, it is necessary to add 1 to both sides.

Therefore, applying the procedure mentioned before, you get that the solution is the following:

[tex]-7 < x - 1 < 8\\\\-7 +(1)< x < 8+(1)\\\\-6<x<9[/tex]

Answer:

A.  The angle measures are 30°, 60°, and 90°.

on edge

Step-by-step explanation:

If the question provides the angles of a triangle as 30°, 60°, and 90°, or 45°, 45°, and 90°, we are dealing with a right triangle. Depending on the measures of the angles, the triangle can be classified as either a 30-60-90 triangle or a 45-45-90 isosceles right triangle. Without sufficient information, the exact measures of the angles cannot be determined.

When considering a triangle with angle measures provided as options, we recall the fundamental property that the sum of internal angles in any triangle is 180 degrees. The question presents three possible sets of angle measures:

Both of the first two options include a 90° angle, indicating that we are dealing with a right triangle. Right triangles have specific properties and can be classified as either 30-60-90 or 45-45-90 triangles, depending on the measures of the other two angles. A 30-60-90 triangle has angles in the ratio of 1:2:√3, and a 45-45-90 triangle, also called an isosceles right triangle, has two angles of 45° each. The third option implies insufficient information to determine the exact measures of all angles.

Answer: -5

Step-by-step explanation:

You start with 50.

Then subtract the 3 transactions: 50-(3×5)=50-15=35

Then you subtract the 2 ills: 35-(2×20)=35-40=-5

And that's how get the answer!

Answer:

Option C is correct.

Step-by-step explanation:

We need to find the polynomial function in standard form with zeros at –6, 2, and 5

If a is a zero of polynomial then x-a is the factor of polynomial

So, (x+6)(x-2)(x-5) are factors of polynomial.

Multiplying these factors to find the standard polynomial function

(x+6)(x-2)(x-5)

We need to solve this:

(x+6)(x^2-5x-2x+10)

(x+6)(x^2-7x+10)

x^3-7x^2+10x+6x^2-42x+60

x^3-7x^2+6x^2+10x-42x+60

x^3-x^2-32x+60

So, Option C f(x) = x3 – x2 – 32x + 60 is correct.

Answer:

option A is correct

Step-by-step explanation:

gradpoint

Answer:

Option D. It's a perfect square trinomial.

Step-by-step explanation:

(a) 36x² - 4x + 16

= (6x)² - 2(2x) + (4)²

It's not a perfect square trinomial

(b) 16x² - 8x + 36

= (4x)² - 2x(4x) + (6)²

It's not a perfect square trinomial

(c) 25x² + 9x + 4

= (5x)² + 2[tex](\frac{9}{2}x)[/tex] + (2)²

It's not a perfect square trinomial

(d) 4x² + 20x + 25

= (2x)² + 2(10x) + (5)²

= (2x+5)²

It's a perfect square trinomial.

Answer:

the answer is d indeed pls like it up and give 5 stars

Step-by-step explanation:

Answer:

(f+g)(x)= 5x-11

(f-g)(x)= x-3

The value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

It is required to find the value of   (f+g)(x) and (f-g)(x).

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The functions are

f(x) = 3x - 7

g(x) = 2x - 4

We have to find the value of the function (f + g)(x) and  (f-g)(x) we get

According to given question we have,

The value of the function (f +g)(x)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 3x - 7 + 2x - 4

(f + g)(x) = 5x - 11

The value of the function (f - g)(x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 3x - 7 - (2x - 4)

(f - g)(x) = 3x - 7 - 2x + 4

(f - g)(x) = x - 3

Therefore,  the value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

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Answer:

C

Step-by-step explanation:

Since the triangle is right with hypotenuse h

Use Pythagoras' identity to solve for h

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

h² = ( 5[tex]\sqrt{2}[/tex] )² + ( 5[tex]\sqrt{2}[/tex] )²

   = 50 + 5 0 = 100

Take the square root of both sides

h = [tex]\sqrt{100}[/tex] = 10 → C

Answer:

The correct answer option is C. Both A and B.

Step-by-step explanation:

We are given a figure of a rectangle which when transformed changes it length of two sides AB and DC to AB' and DC'.

By looking at the figure, we can conclude that the transformation has changed the lengths of some sides of the given figure as well as changed the area of the figure.

Therefore, the correct answer option is C.

Answer:

x=3 or x= 1/3

Step-by-step explanation:

Let the number = x

The reciprocal of the number = 1/x

According to the given statement:

x+1/x=10/3

x²+1/x=10/3

3(x²+1)=10x

3x²+3=10x

Move 10x to the L.H.S

3x²-10x+3=0

Break the middle term:

3x²-9x-x+3=0

3x(x-3)-1(x-3)=0

(x-3)(3x-1)=0

x-3=0 , 3x-1=0

x=0+3 ,  3x=0+1

x=3    , 3x=1

x=3    ,x = 1/3

So x=3 or x= 1/3 ....

Answer:

Part A) [tex]\$42,888.48[/tex]  

Part B) [tex]A=\$22,304[/tex]

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12[/tex]  

substitute in the formula above  

[tex]A=8,500(1+\frac{0.0812}{12})^{12*20}[/tex]  

[tex]A=8,500(1.0068)^{240}[/tex]  

[tex]A=\$42,888.48[/tex]  

Part B) What if the deposit were compounded monthly with simple interest?  

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=20\ years\\ P=\$8,500\\r=0.0812[/tex]

substitute in the formula above

[tex]A=8,500(1+0.0812*20)[/tex]

[tex]A=\$22,304[/tex]

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

[tex]A(t)=8,500(1.0068)^{12t}[/tex] ------> equation A

[tex]A(t)=8,500(1+0.0812t)[/tex]  -----> equation B

using a graphing tool  

see the attached figure  

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.

The retirement account will be worth $27,627.24 after 20 years with compound interest and $23,180 with simple interest. Compound interest grows at a faster rate and becomes better than simple interest when the compounding periods are more frequent.

To calculate the value of the retirement account after 20 years with compound interest, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal deposit, r is the interest rate, n is the number of times compounded per year, and t is the number of years. In this case, P = $8,500, r = 8.12%, n = 12 (monthly compounding), and t = 20. Plugging in these values, we get A = $8,500(1 + 0.0812/12)^(12*20) = $27,627.24.

If the deposit were compounded monthly with simple interest, we can use the formula A = P + (P*r*t), where A is the final amount, P is the principal deposit, r is the interest rate, and t is the number of years. In this case, P = $8,500, r = 8.12%, and t = 20. Plugging in these values, we get A = $8,500 + ($8,500 * 0.0812 * 20) = $23,180.

To compare the two situations on a graph, we can plot the value of the retirement account over time for both compound and simple interest. We would see that the compound interest account grows at a faster rate and reaches a higher value compared to the simple interest account. Compound interest becomes better than simple interest when the compounding periods are more frequent, as it allows the interest to be reinvested more often and generate additional earnings.

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Based on parallelogram ABCD shown below, the values of x and y include;

x = 17 units.

y = 10 units.

In Euclidean Geometry, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that has two equal and parallel opposite sides.

Generally speaking, a parallelogram has both pairs of opposite sides parallel to each other and the opposite angles (vertical angles) are congruent:

AB ║ CD

AB = CD

3x - 9 = 42

3x = 42 + 9

3x = 51

x = 51/3

x = 17 units.

Next, we would determine the value of y as follows;

4y - 3 = 37

4y = 37 + 3

4y = 40

y = 40/4

y = 10 units.

Complete Question:

Use parallelogram ABCD. What are the values of x and y?

Answer:

The correct answer is the second one

Step-by-step explanation:

Line BE and ED are congruent because they are the same length and E is the mid line.

Answer:

second option is correct

Step-by-step explanation:

By the given

ΔDEC≅ΔBEC

which means triangle DEC is congruent to triangle BEC

then by CPCTC (corresponding parts of congruent triangle are congruent)

there every side and angle of DEC will be equal to BEC

⇒BE= DE (by CPCTC)

hence second option is correct

9m = 4.5

divide by 9 for 9m and 4.5

9m/9= 4.5/9

m= 0.5

3v= -105

divide by 3 for 3v and -105

3v/3=- 105/3

v= -35

17m = 85

divide by 17 for 17m and 85

17m/17= 85/17

m= 5

Answers: 0.5,-35 and 5

Answer:

1885 plate appearances

Step-by-step explanation:

546 plate appearances + 627 plate appearances + 712 plate appearances = 1885 plate appearances

Answer:

1885

Step-by-step explanation:

546+627+712=1885

The answer is:

[tex]u+v=-1+2i[/tex]

To solve the problem, we just need to consider that the variable "u" and "v" represents different expressions, and then, perform the operation and add the like terms.

We must remember that the like terms are the terms that share the same variable and the same exponent.

We have that:

[tex]u=1+3i\\v=-2-i[/tex]

So, calculating we have:

[tex]u+v=(1+3i)+(-2-i)=(1-2)+(3i-i)=-1+2i[/tex]

Hence, we have that:

[tex]u+v=-1+2i[/tex]

Have a nice day!

Answer:

x = 19

Step-by-step explanation:

Question: find x such that f(x) = 2/3

Given f(x) = (-1/3) x + 7

equate the value of f(x) to be 2/3

hence,

(2/3) = (-1/3)x + 7 (multiply both sides by 3)

(3) (2/3)  = (3) (-1/3)x + (3) 7

2 = -x + 21

x = 21 - 2

x = 19

So to get the output value 2/3 we will input x = 19

A mathematical relationship from a set of inputs to a set of outputs is called a function.

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

Clearly, all the values of x and f(x) are satisfying it.

Now, the output is given as 2/3.

So, we can write,

[tex]\frac{2}{3} = -\frac{x}{3} + 7[/tex]

⇒  [tex]\frac{2}{3}-7 = -\frac{x}{3}[/tex]   ( changing the side of 7)

⇒ [tex]-\frac{19}{3} = - \frac{x}{3}[/tex]

⇒ x = 19

So to get the output value 2/3 we will input x = 19

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Answer:

Step-by-step explanation:So to me I would trust the medical journal published in 1982. Back then they were more people that studied those kind of things. And back then there was like people finding out different  types of plants and medical resources. (hope this helps you)..:)

Answer:

The correct answer will be option- C

Step-by-step explanation:

A research journal is considered as the reliable or credible source of the research as the research articles published in the journal are always verified by the peer-group which includes the scientists.

The peer-group verifies the credibility of the research paper by checking and correcting the steps of the scientific method and checking the eligibility of the collected data and the conclusions drawn from it.

Therefore, Nick should use a medical journal published in 1982 as the credible source for him and thus option- C is the correct answer.

Answer:

[tex]\$620.07[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=2\ years\\A=\$700\\ r=0.0625\\n=1[/tex]  

substitute in the formula above  and solve for P

[tex]700=P*(1+\frac{0.0625}{1})^{2}[/tex]  

[tex]700=P*(1.0625)^{2}[/tex]  

[tex]P=700/(1.0625)^{2}[/tex]  

[tex]P=\$620.07[/tex]  

[tex]\huge{\boxed{\frac{1}{20}}}[/tex]

To convert from a decimal to a percentage, multiply the decimal by [tex]100[/tex].  [tex]0.05*100=5[/tex], so the percentage equivalent is [tex]5\%[/tex].

Percentages are fractions when you use a denominator of [tex]100[/tex], so [tex]5\%[/tex] is the same as [tex]\frac{5}{100}[/tex].  Divide the numerator and denominator each by [tex]5[/tex] to get the fraction in simplest form, which is [tex]\frac{1}{20}[/tex].

Answer:

c=13.2 units

Step-by-step explanation:

step 1

Find the measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

A+B+C=180°

substitute the given values

16°+49°+C=180°

65°+C=180°

C=180°-65°=115°

step 2

Find the measure of c

Applying the law of sines

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

substitute the given values and solve for c

c/sin(115°)=4/sin(16°)

c=4(sin(115°))/sin(16°)

c=13.2 units

Answer:

[tex]\large\boxed{2x^2-14x+7}[/tex]

Step-by-step explanation:

[tex](4x^2-5x + 1)-(2x^2+9x-6)\\\\=4x^2-5x+1-2x^2-9x-(-6)\\\\=4x^2-5x+1-2x^2-9x+6\qquad\text{combine like terms}\\\\=(4x^2-2x^2)+(-5x-9x)+(1+6)\\\\=2x^2-14x+7[/tex]

Answer:

The answer is option B. which is 2x^2 - 14 + 7.

Remember to reverse the signs.

Answer:

B is the center of the circle.

Step-by-step explanation:

Given is a circle in the picture.

A is the point on the circle.

Y is another point on the circle

AY is hence the chord

B is equidistant from the circumference

B is the center of the circle.

Point B is established as the center of the circle because it is equidistant from the circumference. This property defines B as the central point from which all points on the circle are equally distant, confirming its role as the circle's center.

In the given scenario, the information provided indicates that point B is equidistant from the circumference of the circle. This property characterizes point B as the center of the circle.

To articulate this differently, since B is equidistant from any point on the circle, it serves as the central point from which all points on the circle are equally distant.

Therefore, B is unequivocally identified as the center of the circle. This conclusion is drawn from the fact that the center of a circle possesses the unique property of being equidistant from all points on its circumference.

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Answer:

A 3

Step-by-step explanation:

y-9 = 3(x-9)

This is in point slope form

y-y1 = m(x-x1)

where (x1,y1) is the point and m is the slope

A point on the line is (9,9) and the slope is 3

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

To express solutions to inequalities using interval notation.

I prefer to express solutions to inequalities using interval notation. Both formats are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

Hence, To express solutions to inequalities using interval notation.

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1. Commutative property of adfition

2. Multiplicative inverse

3. Associative property of addition

4. Distributive property

5. Additive identity

Answer:

1-------------- Commutative property of addition

You can commute the terms in a addition, so doesn't matter wat therm goes left or right,

2 ------------ is multiplicative inverse

Each number X has another number Y so X*Y=1

3-------------- Associative property of addition

When you have parentheses in this type of addition, the order in what you do te equation doesn't matter

4 ------------- distributive property

You can distribute the multiplication here, so x(a +b) = x*a + x*b

5 ------------ Additive identity

There exist one number a so for every number x, x+a = x, and the number a is te zero.