You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?

answers :
a.using a paid membership card to buy it at a 10 percent discount
b.buying it online at a 10 percent discount with a $5 shipping charge
c.buying it at a 10 percent discount without sales tax

x, y (x + 8, y + 2)

Answer:

x = -4 and x = -16.

Step-by-step explanation:

We have the equation,

[tex]x^{2}+20x+100=36[/tex]

i.e. [tex]x^{2}+20x+64=0[/tex]

As the solution of a quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].

On comparing, a = 1, b = 20, c = 64.

So, the solution is,

[tex]x=\frac{-20\pm \sqrt{(20)^{2}-4\times 1\times 64}}{2a\times 1}[/tex].

i.e. [tex]x=\frac{-20\pm \sqrt{400-256}}{2}[/tex].

i.e. [tex]x=\frac{-20\pm \sqrt{144}}{2}[/tex].

i.e. [tex]x=\frac{-20\pm 12}{2}[/tex].

i.e. [tex]x=\frac{-20+12}{2}[/tex] and [tex]x=\frac{-20-12}{2}[/tex].

i.e. [tex]x=\frac{-8}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex].

i.e. x = -4 and x = -16

Thus, the solution of the given equation is x = -4 and x = -16.

The discount is 26%.

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

Given:

Marked price = $25

Selling price = $18.50

So,

Discount = MP - SP

Discount = 25-18.50

Discount = 6.50

Now,

D% = D/MP *100

D% = 6.5 /25*100

D% = 26%

Hence, the discount percent is 26%.

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Answer:

b) Linear Pair

c) Definition of supplementary

d) Substitution; Combine like terms

e) Division Property of Equality

f)  Definition of Right Angle

g) Definition of Perpendicular

Answer:

80.47

Step-by-step explanation:

This is correct! :D

The chef has less than 25.8 pounds of rice.

She takes out 5 pounds to use during the day and stores the rest in containers.

Quantity of rice stored = 25.8 - 5 = 20.8 pounds

Each container can store 2.5 pounds of rice.

Let x represent the number of containers.

The number of containers that can be filled = 20.8/2.5 = 8.32

So, the maximum number of containers the chef will be able to fill with rice is 8

Final answer:

The functions y=x and y=x+5 have the same slope but different y-intercepts. Their graphs are straight lines.

Explanation:

The functions y=x and y=x+5 are related in that they have the same slope of 1. This means that for every increase of 1 in the value of x, the value of y will also increase by 1. However, they have different y-intercepts. The function y=x has a y-intercept of 0, while the function y=x+5 has a y-intercept of 5.

Their graphs are related in that they are both straight lines. The graph of y=x is a line passing through the origin (0,0), while the graph of y=x+5 is a line shifted upward by 5 units compared to the graph of y=x.

Answer: $124.50

Step-by-step explanation:

We are given that the equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.

To find the best estimate of the cost for towing a car 22 miles., we substitute x= 22 in the above equation, we get

Cost of  towing a car 22 miles=[tex]y=4.75(22)+20=[/tex]

[tex]\rightarrow\ y=104.50+20=124.50[/tex]

Therefore, the best estimate of the cost for towing a car 22 miles = $124.50

The number by which the circumference is multiplied is:

                               2

We know that the circumference of the circle in terms of the radius r is given by:

        [tex]\text{Circumference}=2\pi r[/tex]

Now, if the radius is doubled.

i.e.

[tex]r'=2r[/tex]

Hence, the circumference of the new circle is given by:

[tex]\text{Circumference of new circle}=2\pi (2r)\\\\i.e.\\\\\text{Circumference of new circle}=2(2\pi r)[/tex]

i.e.

[tex]\text{Circumference of new circle}=2\times \text{Circumference of original circle}[/tex]

The constant by which the circumference is multiplied is: 2

Answer:

n/(n+1) . . . . n ≠ 1

Step-by-step explanation:

As written, there is no product. There is ony the sum ...

[tex]4\dfrac{n}{4}-4n-\dfrac{1}{n}+1[/tex]

With appropriate parentheses, this becomes the product of rational functions ...

... (4n)/(4n-4)·(n-1)/(n+1)

[tex]=\dfrac{4n(n-1)}{4(n-1)(n+1)}=\dfrac{n}{n+1}[/tex]

_____

At n=1, the product has a "hole" where the denominator of the original expression is zero, so the expression is undefined. Hence the domain of the product must be restricted to n≠1 (as well as n≠-1).

Answer:

[tex]15x^{6}-20x^{5}+10x^4)[/tex]

Step-by-step explanation:

We have been given an expression [tex]-5x^4(-3x^2+4x-2)[/tex] and we are asked to simplify our given expression.

We will use distributive property [tex]a(b+c)=a*b+a*c[/tex] to simplify our given expression.

Upon distributing [tex]-5x^4[/tex] we will get,

[tex](-5x^4*-3x^2)+(-5x^4*4x)-(-5x^4*2)[/tex]

Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,

[tex](15x^{4+2})+(-20x^{4+1})-(-10x^4)[/tex]

[tex](15x^{6})+(-20x^{5})-(-10x^4)[/tex]

[tex]15x^{6}-20x^{5}+10x^4)[/tex]

Therefore, our given expression simplifies to [tex]15x^{6}-20x^{5}+10x^4)[/tex].

Answer:

[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]

And solving for the initial amount [tex] A_o[/tex] we got:

[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]

So then the original price for the car would be approximately 18263.539$

Step-by-step explanation:

For this case we can use the exponential model given by:

[tex] A(t) = A_o e^{bt}[/tex]

Where:

[tex]A_o[/tex] represent the initial amount for the car

[tex]b=-0.07[/tex] represent the exponential growth/decay rate

t represent the number of years. With t =0 at the begin

After 6 year we have that t =6, and we know this condition:

[tex] A(6) = 12000[/tex]

So then we can use the exponential model formula and the condition given and we have this:

[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]

And solving for the initial amount [tex] A_o[/tex] we got:

[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]

So then the original price for the car would be approximately 18263.539$

The domain of Ethan's function f(x) = 2x² + 2x + 4  is all real numbers as it is a quadratic function.

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = 2x² + 2x + 4 represents the temperature of a substance over time. Since temperature is a physical quantity and cannot be negative, the domain of the function must be restricted to non-negative values of x.

To determine the exact domain of the function, we can analyze the expression 2x² + 2x + 4. This expression is always non-negative for any real number x. Therefore, the domain of f(x) = 2x² + 2x + 4 is all real numbers x ≥ 0.

In mathematical notation, the domain of the function can be expressed as:

{x ∈ ℝ | x ≥ 0}

This indicates that the function is defined for all real numbers (ℝ) as long as the value of x is greater than or equal to 0 (x ≥ 0).

Answer:

The perimeter of the first figure is [tex]6\pi +12\sqrt{2}[/tex]

Step-by-step explanation:

Besides that, they got everything right.

Answer:

56 inches is the horizontal distance from the end of the ramp to the back of the truck.

Step-by-step explanation:

Height of the back of the truck =33 inches

Length of the ramp = 65 inches

Length of the end of ramp to the back of the truck =?

In triangle ABC:

AB = 33 inches

BC = ?

AC = 65  inches

[tex]AB^2+BC^2=AC^2[/tex] (Pythagoras theorem)

[tex](33 inches)^2+(BC)^2=(65 inches)^2[/tex]

BC = 56 inches