you buy x packs of pencils, twice as many packs of erasers, and three times as many rolls of tape. write an expression in simplest form for the total amount spent.

pencils cost 1.85
erasers cost 3.15
tape cost 2.50

The domain and the range of the piecewise function in this problem are given as follows:

The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:

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Answer:

graph attached

Step-by-step explanation:

The statement which must be true about D, the discriminant of function h is D =0 hence, option (D) must be correct.

When working with quadratic equations, the discriminant is commonly calculated to investigate the kind of roots. Even though it is difficult to ascertain a discriminant for any polynomial, there exist methods for collecting the discriminant of cubic and quadratic equations that reduce our approach.

The discriminant function gives us an idea about the nature of the solution whether it is real or not if real then how much will be the solution?

If D > 0 then there will be 2 real solutions.

If D = 0 then there will be 1 real solution.

If D < 0 then there will be 2 imaginary solutions.

Given that function, h has an interception it means there will be a real solution. Hence, D = 0 will be the correct answer.

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A Sinusoid is a cyclic function. The equation of the sinusoid shown in the graph is y=2Cos(2πx/3).

The general equation of the sinusoid shown is given by the following equation,

\(y = a\ \cos\left(\frac{2\pi x}{b}\right)\)

where a is the amplitude of the graph, and b is the length of a complete cycle.

In the given graph the amplitude of the function is 2, while the length of the cycle is (2π/3). Therefore, The equation of the sinusoid shown in the graph can be written as,

\(y = 2 \cos\left(\dfrac{2\pi x}{3}\right)\)

Hence, the equation of the sinusoid shown in the graph is y=2Cos(2πx/3).

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Answer:

C! y=2cos(3x)

Step-by-step explanation:

6 and 4 tis is correct beacause it is

The width of the room is 7 meters and its length will be (7 + 2) = 9 meters.

We have a rectangular room which is 2 meters longer than it is width with it’s perimeter is 16 meters.

We have to determine the dimensions of this room.

The Perimeter of rectangle is -

P = 2(L + B)

According to the questions -

Perimeter = 16

Assume the width to be x.

Then its length will be (x + 2) meters.

Substituting the values, we get -

P = 2(L + B)

16 = 2(x + x + 2)

x + x + 2 = 16

2x + 2 = 16

2x = 14

x = 7

Hence, the width of the room is 7 meters and its length will be (7 + 2) = 9 meters.

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:4/5

Step-by-step explanation: thats the slope

Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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Answer:

B can

Step-by-step explanation:

126 and 79 are not divisible by 5, only numbers that end in 0 or 5 can

Answer: Option A

Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]

Step-by-step explanation:

It should be noted that, the VaR for a 3-year period with a 2.5 percent probability is Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]. Therefore, option A only is correct while other options are wrong

Answer:

A: Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]

Step-by-step explanation:

Answer:

On a number line, 1/6 would land in the exact middle between 0 and 2/6

Step-by-step explanation:

Not too sure what your question meant, but I hope my answer helped!

If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)

x²- 12x + 11 = 0

subtract 11 from both-side

x² - 12x = -11

Add square of half of the coefficient of x to both-side

x² - 12x + (-6)² = -11 + (-6)²

(x- 6)² = -11 + 36

(x-6)² =25

Take the square root of both-side

x - 6 = ±5

add 6 to both-side

x = ±5 + 6

Either x = 5 + 6 or x = -5+6

x = 11 or x = 1

Answer:

if you convert inches to cm...

Step-by-step explanation:

9inch=22.86cm

12inch=30.48cm

V=TTr²h

TT= 3.14

V= 3.14×22.86²×30.48

V= 50014.6cm³

if you don't convert inches to cm...

V=TTr²h

V=3.14 ×9×12

V=339.12cm³

Answer:

There are 3 twos in 6.

Step-by-step explanation:

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

Answer:

24/6=x

where x is the number of students in every group

Step-by-step explanation:

there's 24 kids in total

you want to divide them into 6 groups

24/6

Answer:

?= 105

Step-by-step explanation:

I saw the straight angle the two triangles formed, so I immediately knew that that is 180 degrees. I took 180-75 to get 105

The width of the deck given that the entire deck needs 40 feet to trim is 8 feet

Let's assume the width of the rectangular deck is "w".

The perimeter of the deck can be calculated by using the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

Here, the length of the deck is given as 12 feet.

So, P = 2(12 + w)

We also know that the total trim required is 40 feet.

So, P = 40 feet

Equating both the expressions for P, we get:

2(12 + w) = 40

Simplifying the equation, we get:

24 + 2w = 40

2w = 16

w = 8

Therefore, the width of the deck is 8 feet.

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The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

From the question, we have the following parameters that can be used in our computation:

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

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The value of the equation is b = 30 , which is greater than 25

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

b x ( 5/6 ) = 25   be equation (1)

On simplifying the equation , we get

Multiply by 6 on both sides of the equation , we get

5b = 25 x 6

5b = 150

Divide by 5 on both sides of the equation , we get

b = 150 / 5

b = 30

So , the value of b is 30 and is greater than 25

b > 25

Hence , the equation is b = 30

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Answer:

\(y=\frac{1}{3}x-2\)

Step-by-step explanation:

Given the information, we can use the point-slope form to find the equation for the line:  \(y-y_{1}=m(x-x_{1})\)

\(y-(-4)=\frac{1}{3}x(x-(-6) )\)

Isolating y and combining like terms gives us \(y=\frac{1}{3}x-2\)

Answer:

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

Step-by-step explanation:

Given that the total cost of manufacturing by the company is $15000.

Let x be the number of gallons the company sells.

It is also mentioned that the company earns $10 on each gallon.

So the total profit will be the the difference of the selling cost of gallons and manufacturing cost

Mathematically,

\(10x-15000\)

Now it is mentioned that the profit should be at least 50000 dollars which means the profit can be minimally 50000 and also can be greater than it so

\(10x-15000 \geq 50000\)

The number of gallons can be found by solving the obtained inequality.

Hence,

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

Answer:

x = 2

As x = 12/6 = 2

Step-by-step explanation:

3x-4+3x-8

3x+3x-4-8

= 6x-12

FACTORISING for check and set to zero

6(x-2)

6x -12 = 0

Cancel out left by adding 12 to both sides then applying /6 to both sides to cancel 6 left side.

6x--12 + 12 = 0 + 12

6x / 6  =  12  / 6

x = 12/6

x = 2

or balance as grouping by separation  = multiply at end by  -1

3x+3x = --4 - 8

6x  = - 12

x = - 12/6

x = - 2

x = - 2  ( -1 )

x  = 2