3/4 of what number is 8?

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].

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

Answer:

The given system of equations is inconsistent.

Step-by-step explanation:

We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.

[tex]y=-3x+12...(1)[/tex]        

[tex]y=-6x+2...(2)[/tex]

Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.

Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.

Now let us check slope of given lines.

Upon dividing equation (2) by 2 we will get,

[tex]y=-3x+1...(2)[/tex]

We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.

Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.

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.

The complete proof of the theorem in chronological order is;

The proof that when a transversal cut two parallel lines, alternate angles are equal.

1.

Statement: l ∥ m

Reason: Given

2.

Statement: m ∠ 1 = m ∠ 3

Reason: If lines are ∥, corresponding angles are equal.

3.

Statement: m ∠ 2 = m ∠ 3

Reason: Vertical angles are equal

4.

Statement: m ∠ 1 = m ∠ 2

Reason: Substitution

Therefore, alternate exterior angles are equal when a transversal cut two parallel lines,

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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:

[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$

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:

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.

x, y (x + 8, y + 2)

we have been asked to simplify

[tex] (3x-5)-(5x + 1) [/tex]

To Simplify this, we will first open the parenthesis, as below

[tex] (3x-5)-(5x + 1)=3x-5-5x-1\\
\\
\text{take the like terms together and simplify we get}\\
\\
(3x-5)-(5x + 1)=3x-5x-5-1\\
\\
(3x-5)-(5x + 1)=-2x-6\\
\\

[/tex]

Hence the simplified expression is -2x-6

Answer:

-2x-6

Step-by-step explanation:

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

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:

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

Answer:

80.47

Step-by-step explanation:

This is correct! :D

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