Use circle K for problems 11-13

1) the supply and demand schedule for Blue-ray movie "Frozen is attached accordingly.

Equilibrium price and quantity are $20 and 40 units respectively.

2) At a price of $30, quantity demand  and supplied are 20 and 60 units respectively

This is an example of supply surplus.

To get the price back to equilibrium, they have to setthe price at $20 /unit

3) at $10 the quantity demand and supplied are 60 units and 20 units respectively.

This is an example of supply shortage.

increasing the price to $20 per unit will help achieve equilibrium.

Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.

Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.

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The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

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Answer:

3 hours and 36 minutes

Step-by-step explanation:

So first divide both things by the Mph (miles per hour)

Skateboard: 8/5= 1.36

Rollerbladoes: 6/3= 2

Now add them up

1.36+2=3.36

Now the 3 is the hour and the 36 is the minutes

Answer:

3x + 4y = 17

Step-by-step explanation:

Espero y te haiga ayudado :)

Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

Answer: a>-13

Step-by-step explanation:

Answer:

a= - 13 .......

.......

.......

.....

.....

Answer:

10%

Step-by-step explanation:

Because 0.1 is equivalent to 1/10 and 10%

Answer:

The squirrel

Step-by-step explanation:

4.5/30 is 0.15 per minute while the squirrel is 4/20 which equals 0.2 per minute. 0.2 is greater than 0.15 making the squirrel faster. Hope this helps!

y'' - 6y' + 9y = 0

If y = C₁ exp(3x) + C₂ x exp(3x), then

y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))

y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))

Substituting these into the DE gives

(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))

… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))

… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))

= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))

… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))

… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)

= 0

so the provided solution does satisfy the DE.

Answer: \(35x < 4-5x+3x^2\) is \(x < \frac{1}{3}\) or \(x > \frac{4}{3}\)

Step-by-step explanation:

A) To generate the table of values, we can substitute different values of x into the equation and solve for y.

x             y

-2        26

-1        12

0         4

1         2

2        10

To plot the graph of the function, we can use the table of values and plot the corresponding points on a graph with a scale of 4 for the y-axis and 2cm to 1 unit along the x-axis. The graph should look like a parabola opening upwards.

c) To solve for the root of the equation 4-5x+3x^2=0, we can use the graph and find the x-coordinate of the point where the graph intersects the x-axis. This point is also known as the x-intercept or the root of the equation. From the graph, we can see that the root is approximately x=0.83.

To solve the equation 3x^2 -5x=2, we can rearrange it to the form 3x^2 -5x-2=0 and factor it as (3x+1)(x-2)=0. This gives us two solutions: x=-1/3 and x=2.

To determine the range of values of x for which 35x​<4-5x+3x^2, we can rearrange the inequality to the form 3x^2-40x+4>0 and factor it as (3x-1)(x-4/3)>0. This means that either (3x-1) and (x-4/3) are both positive or both negative.

When (3x-1)>0 and (x-4/3)>0, we get x>1/3 and x>4/3, which means x>4/3.

When (3x-1)<0 and (x-4/3)<0, we get x<1/3 and x<4/3, which means x<1/3.

Therefore, the range of values of x for which 35x<4-5x+3x^2 is x<1/3 or x>4/3.

Answer: (x+1)^2(x-5)^4(x+2)

Step-by-step explanation: 1. Cancel x  (x+1)^2(x-5)(x+2)(x-5)^3

Use The product Rule: x^a x^b= x ^a+^b and your answer should be (x+1)^2(x-5)^4(x+2)

Answer:

(-4)(3) = -12

(-4+3) = -1

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Answer:

A) 58

Step-by-step explanation:

Mean = Sum of all the data ÷  total number of data

         \(=\frac{52+70+88+15+65}{5}\\\\\\=\frac{290}{5}\\\\\\= 58\)

Answer:

0.29 or 29%

Step-by-step explanation:

There are 7 options per spin. Of which 3 vowels.

For 2 spins, total spins is 14.

conditions:

First spin is 1/7

Second spin is 3/7

so,

4/14 = 0.29 or 29% I think

\(\huge\text{Hey there!}\)

\(\mathsf{\dfrac{5}{6} + \dfrac{3}{9}}\)

\(\mathsf{= \dfrac{5}{6} + \dfrac{3 \div 3}{9 \div 3}}\)

\(\mathsf{= \dfrac{5}{6} + \dfrac{1}{3}}\)

\(\mathsf{= \dfrac{5}{6} + \dfrac{1\times2}{3 \times 2}}\)

\(\mathsf{= \dfrac{5}{6} + \dfrac{2}{6}}\)

\(\mathsf{= \dfrac{5 + 2}{6 + 0}}\)

\(\mathsf{= \dfrac{7}{6}}\)

\(\mathsf{= 1 \dfrac{1}{6}}\)

\(\huge\text{Therefore your answer should be}\)

\(\huge\boxed{\mathsf{\dfrac{7}{6} \ or \ 1 \dfrac{1}{6}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

120 is the number divisible by 6, 8, and 10.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The common multiples to 6, 8, and 10.

6 x 20 =  120

8 x 15 = 120

10 x 12 = 120

So,

120 is divisible by 6, 8, and 10.

Thus,

120 is the number.

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Answer:

4f + 4g

Step-by-step explanation:

Simplify. Distribute 4 to all terms in the first parenthesis by multiplication:

4(f + g) = (4)(f) + (4)(g) = 4f + 4g

4f + 4g is your answer.

~

9514 1404 393

Answer:

 no

Step-by-step explanation:

Using only a straightedge, you cannot measure distance, so cannot ensure that any two distances are the same.

__

The points of interest are on the perpendicular bisector of AB, which can be constructed using a compass and straightedge. The straightedge alone is insufficient.

Answer:

\(5 {x}^{2} \: + \: 8x \: - 2 \: = \: 0\)

Step-by-step explanation:

\(sum \: of roots = - 2 + \frac{1}{5} = - \frac{8}{5} \\ product \: of \: roots = - 2 \times \frac{1}{5} = - \frac{2}{5} \\ from \: general \: equation \\ a {x}^{2} + bx + c = 0 \\ {x}^{2} + \frac{8}{5} x \: - \frac{2}{5} = 0 \\ 5 {x}^{2} \: + \: 8x \: - 2 \: = \: 0\)

Answer: (7x - 2) + (4x) + (5x - 10) = 180

Explanation: The sum of all angles in a triangle is 180º, so you need to make all the angles in the triangle equal to 180º when writing an equation.

Answer: 8.5

Step 1: Multiply by 6 until you reach 51.

6 x 8 = 48.

Step 2: Subtract.

51 - 48 = 3.

Step 3: Convert 3/6 to decimal.

3/6 = .5

Answer = 8.5 times larger

Answer: 8.5

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Step-by-step explanation:

\(\frac{8}{5}\)÷6\(\frac{3}{4}\)

First, simplify the 6\(\frac{3}{4}\) to an improper fraction, which is:

\(\frac{27}{4}\)

Next rewrite the equation using the improper fraction:

\(\frac{8}{5}\)÷\(\frac{27}{4}\)

Now, in order to divide the fraction, we will need to flip the second fraction over, and then multiply the two fractions together. A great way to remember this is the phrase Copy Dot Flip - Copy the first fraction, put a dot for multiplication, and flip the second fraction.

\(\frac{8}{5}\)·\(\frac{4}{27}\)

Finally, multiply together and simplify/reduce if needed:

The final answer is \(\frac{32}{135}\) and no simplification or reduction is needed

Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

The factorization of the expression , the factor are -2 , 1 and 5.

What is factorization?

To factorise an algebraic statement, we first identify the terms' highest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic expression gets expanded in the opposite direction.

Here the given expression is,

=> \(x^3-3x^2-10x-x^2+3x+10=0\)

=> \(x^3-4x^2-7x+10=0\)

=> \(x^3-x^2-3x^2+3x-10x+10=0\)

=> \(x^2(x-1)-3x(x-1)-10(x-1)=0\)

=> \((x-1)(x^2-3x-10)=0\)

=> \((x-1)(x^2-5x+2x-10)=0\)

=>\((x-1)(x(x-5)+2(x-5))=0\)

=> \((x-1)(x-5)(x+2)=0\)

Then x-1=0 , x-5=0 and x+2=0

=> x= 1,5,-2.

Hence the factors of the expression is 1,5 and -2.

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Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

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Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):

We can check our answer by distributing \(-5x\) to the expression inside the parentheses:

\(\therefore\) The answer is \(-5x(x-2)\).

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Answer: none of them are correct

Step-by-step explanation:

BECUASE if it is then it would show it on the nuber line.

Answer:

A

Step-by-step explanation:

Add 3 to each side, there's your answer there.

\(\bf\longrightarrow{F(x) = \displaystyle \int\limits_{0}^{x} \sqrt{4 - {t}^{2} } \: \: dt}\)

\(\bf\longrightarrow{F(x) = \displaystyle \bigg[ \frac{t}{2} \sqrt{ {2}^{2} - {t}^{2} } + \frac{ {2}^{2} }{2} \sin^{ - 1} \frac{t}{2} \bigg] _{0}^{x}}\)

\(\bf\longrightarrow{{F(x) = \displaystyle \bigg[ \frac{x}{2} \sqrt{ 4 - {x}^{2} } + 2\sin^{ - 1} \frac{x}{2} - 0 - 0 \bigg]} }\)

\( \bf\longrightarrow{F(x) = \displaystyle \frac{x}{2} \sqrt{ 4 - {x}^{2} } + 2\sin^{ - 1} \frac{x}{2}}\)