If P(3,2) and Q(7,10) are the endpoints of the diameter of a circle, what is the area of the circle in square units?

Answer:

See below for a graph

Step-by-step explanation:

Let's call the parent function g(x) = log₅(x), which has a vertical asymptote at x=0, and goes through the points (1, 0), (5, 1), (25, 2).

Then this function is

... f(x) = g(2(x+6)) +2

That is, the function is horizontally compressed by a factor of 2, shifted left 6 units, and shifted up 2 units. This moves the points listed above to ...

... (-5.5, 2), (-3.5, 3), (6.5, 4)

The graph shows the parent function and the listed points in blue, then the transformed function and the corresponding points in red.

Answer:

8 cm

Step-by-step explanation:

... BO/OD = AO/OC = 3/1

Written another way, this is ...

... OD : BO = 1 : 3

Now, BD = OD + BO, so we have

... BD : BO = (OD +BO) : BO = (1 +3) : 3 = 4 : 3

That is, BD = 4/3 × BO

... BD = 4/3 × 6 cm = 8 cm

To find the length of diagonal BD in trapezoid ABCD, we set up an equation using the fact that the diagonals bisect each other. We solve for x and then substitute it into the equation for BD.

To find the length of diagonal BD in trapezoid ABCD, we can use the fact that the diagonals of a trapezoid bisect each other. Let AO = 3x and OC = x. Since the diagonals intersect at point O, we can set up the equation (3x + 6) / x = 3 / 1. Solving for x, we find that x = 1.5. Therefore, BD = 2 * x + 6 = 2 * 1.5 + 6 = 9 cm.

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Answer: Your answer would come out to be 3.5

Step-by-step explanation: it would be 3.5 due to the fact that you have to break these numbers down to the smallest one possible meaning simplify which would result in this equation 7 over 2  

7 over 2 = 3 1 over 2 this equals 3.5      

a ≤ 3

Undo what is done to the variable. The variable is multiplied by 3 and 4 is subtracted from that result. To undo these operations, you add 4, then divide by 3.

... 3a ≤ 9 . . . . 4 is added to both sides of the inequality

... a ≤ 3 . . . . . both sides of the inequality are divided by 3

_____

Comment on solving inequalities

These are the same steps you would use to solve the 2-step equation ...

... 3a -4 = 5

The only difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, you reverse the sense of the comparison (> becomes <, and vice versa; ≥ becomes ≤, and vice versa). You can see this if you consider numbers: 2 > 1. Multiplying by -1 gives -2 < -1.

See the attachment

The expected value of store card transactions will be the product of their average value ($58) and their probability of occurrence (48%).

... $58 × 0.48 = $27.84

Transactions are either "store card" or "without a store card", so the probability of a transaction being made without a store card is

... 1 - 0.48 = 0.52

Using the same computatation as for store card expected value, the expected value of transactions made without a store card is ...

... $74 × 0.52 = $38.48

The expected value of the store's transactions is the sum of the expected values of the different ways transactions can be made:

... $27.84 +38.48 = $66.32

_____

The average value of transactions made without a store card is the weighted average of those made with another card and those made with cash or a gift card. Using c to represent the latter, this weighted sum is ...

... 74 = 0.80 × 70 + 0.20 × c

... 74 -56 = 0.20c . . . . . subtract 56

... 18/0.2 = c = 90 . . . . . divide by the coefficient of c

The average transaction made with cash or a gift card is $90.

Each expected value per transaction should be matched to the correct location on the tree diagram as shown in the image below.

In this exercise, we would use probability to make each of the decisions. The expected value for transactions made with a store card can be determined by multiplying its probability of occurrence (48%) by the average value ($58) as follows;

Expected value per transaction = 58 × 0.48

Expected value per transaction = $27.84

Since transactions are either made with a store card or without a store card, the probability of a transaction being made without a store card is given by;

Probability (without a store card) = 1 - 0.48 = 0.52

In this context, the expected value per transactions made without a store card is given by;

Expected value per transaction = 74 × 0.52

Expected value per transaction = $38.48

... $74 × 0.52 = $

For the store's expected value transactions, we would add each of the expected values calculated above;

Store's expected value transactions = 27.84 + 38.48

Store's expected value transactions = $66.32.

The average transaction value for transactions that are made with cash or a gift card can be calculated by finding the weighted average of all transactions made without a card;

74 = (0.80 × 70) + 0.20 × m

74 = 56 + 0.20m

0.20m = 74 - 56

0.20m = 18

m = 18/0.20

m = $90.

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Answer: [tex]QS=11.8cm[/tex]

Step-by-step explanation:

1. You have the following information:

- The lenght of [tex]RS[/tex] is 2 centimeters.

- The angle m∠S=80°.

- Cos80°=0.17

2. Therefore, you can calculate the lenght of the segment [tex]QS[/tex] as following:

[tex]cos80=\frac{adjacent}{hypotenuse}[/tex]

[tex]adjacent=2cm\\hypotenuse=QS\\cos80=0.17[/tex]

3. Substitute values and solve for [tex]QS[/tex]:

[tex]0.17=\frac{2cm}{QS}\\QS=\frac{2cm}{0.17} \\QS=11.76cm[/tex]

4. To the nearest tenth:

[tex]QS=11.8cm[/tex]

Answer:

D) 91 °F

Step-by-step explanation:

        C = 5/9(F - 32)

      33 = 5/9 (F – 32)     Multiply each side by 9

  9×33 = 5(F- 32)           Divide each side by 5

9×33/5 = F – 32             Add 32 to each side

        F = 9×33/5 + 32

        F = 59.4 + 32

        F = 91 °F

Answer:

Its D

Step-by-step explanation:

USA TP

To find the number of hours Liam volunteered during the first month, we can set up an equation using the given information. By solving the equation, we find that Liam volunteered for 15 hours during the first month.

To solve this problem, we can start by representing the number of hours Liam volunteered in the first month as x. The number of hours volunteered in the next month would be 1 2/3 times x, which can be written as (5/3)x. The total number of hours volunteered is given as 40, so we can write the equation: x + (5/3)x = 40. To solve for x, we can combine the like terms and solve the resulting equation.

Combining the x terms, we get (8/3)x = 40. Solving for x, we divide both sides of the equation by 8/3: x = 40 / (8/3).

Simplifying, we have x = 40 * (3/8) = 15. Therefore, Liam volunteered for 15 hours during the first month.

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By representing the number of hours in the first month as x, we can find the value of x by using the given information and solving the equation. The solution shows that Liam volunteered for 15 hours during the first month.

To solve this problem, we can set up an equation representing the total number of hours Liam volunteered. Let's represent the number of hours he volunteered in the first month as x. According to the problem, he volunteered for 1 2/3 times as many hours in the next month. So, the number of hours he volunteered in the next month is 1 2/3 x. The total number of hours is given as 40. Therefore, we have the equation:

x + 1 2/3 x = 40

To solve for x, we can simplify the equation by converting 1 2/3 to an improper fraction. This gives us:

5/3 x + 1 2/3 x = 40

Combining like terms, we get:

8/3 x = 40

To solve for x, we can multiply both sides of the equation by the reciprocal of 8/3, which is 3/8. This gives us:

x = (40)(3/8) = 15

Therefore, Liam volunteered for 15 hours during the first month.

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Answer:

a. x = 1, y = -2

Step-by-step explanation:

The given equations are 2x + 3y = -4 -------------(1)

x - 2y = 5 -----------------(2)

From the second equation, we get x = 2y + 5

Now plug in x = 2y + 5 in the first equation, we get

2(2y + 5) + 3y = - 4

4y + 10 + 3y = -4

7y + 10 = -4

7y = -14

y = -2

Now plug in y = -2 in x = 2y + 5 to find the x value.

x = 2(-2) + 5

x = -4 + 5

x = 1

Therefore, x = 1, y = -2

Thank you.

18

Put 3 where x is, then do the arithmetic.

... f(x) = x(5x -9)

... f(3) = 3(5·3 -9) = 3(15 -9) = 3·6

... f(3) = 18

_____

Your calculator can do this, too.

21 miles

Big Bird's nest is halfway between Bert's place and Ernie's place, so the distance from the nest to either apartment is the same. Equating those distances, we have ...

... 5x +4 = 15x -30

... 34 = 10x . . . . . . add 30-5x

... 3.4 = x . . . . . . . .divide by 10

The value of x is not the distance. The distance is given by either of the two expressions

Using the first of these, the distance from either apartment to Big Bird's nest is ...

... 5·3.4 +4 = 17 +4 = 21 . . . . miles

Of course, using the second gives the same answer:

... 15·3.4 -30 = 51 -30 = 21

Answer:

D.

Step-by-step explanation:

The coefficient of the leading term tells you how "stretchy" a graph is. Since g(x)'s leading coefficient is 3, and f(x)'s leading coefficient is 9, and they're both [tex]x^{2}[/tex], g is just 3 times f. Then g's constant term is -4, and f's constant term is 0, then g is just f but translated 4 down.

Answer:

Option 4

Step-by-step explanation:

The 3 changing to the 9 stretches the graph vertically by a factor of 3.  The - 4

translates the graph 4 units down .

Its Option 4

as you recall from the pythagorean theorem, which applies only to right-triangles, c² = a² + b².

so, a = 6, b = 8, c = 9...... if that triangle is indeed a right triangle, then 9² = 6² + 8², let's check if that's true.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{6}\\ b=\stackrel{opposite}{8}\\ \end{cases} \\\\\\ 9=\sqrt{6^2+8^2}\implies 9=\sqrt{36+64}\implies 9=\sqrt{100}\implies 9\ne 10~~\bigotimes~~nope[/tex]

Answer:

1/3 3/1 5/6 6/5 8/9 9/8

Step-by-step explanation:

None of the above. All the answers refer to price. The given equation refers to value. We imagine price may stay the same or actually increase year-to-year. The problem statement gives insufficient information to conclude anything about price.

Math is about attention to detail. The equation tells you ...

... The value of the boat decreases by 12% every year.

The value of the boat is multiplied by 0.88 each time X increases by 1. That means the value is 88% of what it was the year before, a decrease of 12%.

(2a^4+5a^3+4) -2a^2

There are 4 terms. Your trinomial could consist of any three of them. Here, we've chosen to use the one with the negative sign as the monomial, because the question asks for a difference.

Answer:

D. 6 hours

Step-by-step explanation:

There are 3 ft in 1 yd, so 400 yd = 1200 ft.

At 200 ft/h, Jim's travel time for 1200 ft will be

... time = distance/speed = (1200 ft)/(200 ft/h) = (1200/200) · ft · (h/ft)

... time = 6 h

A) The problem statement tells you it is a geometric sequence, so you know each term is some multiple of the one before. The first terms of the sequence are given, so you know the first term. The common ratio (the multiplier of interest) is the ratio of the second term to the first (or any term to the one before), -6/2 = -3.

So, the recursive definition is ...

... a_1 = 2

... a_n = -3·a_(n-1)

B) The explicit formula is, in general, ...

... a_n = a_1 · r^(n -1)

where r is the common ratio and a_1 is the first term. Filling in the known values, this is ...

... a_n = 2·(-3)^(n-1)

Answer:

a1=2

an=(an-1)(-3)

Step-by-step explanation:

Hope it helps. :)

Answer:

  B)  Both functions have exactly three x-intercepts.

  C)  The function f(x) is an odd degree function.

  E)  The x intercepts for g(x) are (1, 0); (2, 0) and (-3/2, 0)

Step-by-step explanation:

The function f is a function of degree 3 (there are 3 x-terms in the product contributing to the highest-degree term), so is of odd degree. The leading coefficient in f(x) is the product of the coefficients of x: 1·1·2 = 2, a positive number.

For a polynomial function of odd degree, the general shape of the graph will be "/" if the leading coefficient is positive, and "\" if the leading coefficient is negative. That is, end behaviors will be opposites of each other. Function f has a positive leading coefficient, so its end behavior will be (-∞, -∞) and (+∞, +∞). Function g has end behavior that is (-∞, +∞) and (+∞, -∞), so is not the same. Apparently, g(x) has a negative leading coefficient.

The graph of g(x) shows it to have 3 x-intercepts. They can be read from the graph as (-3/2, 0), (1, 0) and (2, 0). The factoring of f(x) shows it to have 3 x-intercepts, the same number. There is an x-intercept of f(x) for each factor. (The x-intercept value is the value of x that makes the factor zero.)

The function f(x) is of odd degree and has three x-intercepts at -2, 1, and -3/2. The statements regarding the function g(x) cannot be confirmed without further information.

The function given is f(x) = (x+2)(x-1)(2x+3). The degree of the function is 3 as there are three terms multiplied together. Therefore, f(x) is an odd degree function, which makes option C correct.

The x-intercepts of the function occur where y = 0, i.e. where f(x) = 0. Solving this will give the roots or intercepts for x which are -2, 1, and -3/2. This means that the function f(x) has three x-intercepts, which makes option B correct.

Without information or a graph of function g(x), we cannot accurately answer options A, D and E. We cannot know the end behavior, the leading coefficient or the x intercepts for g(x). Therefore, only options B and C are true statements.

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Part A: The exponential function is the best model for the given data. The data shows that every month the number of visitor approximately doubles from previous month. In other words the number is some base value (2, in this case) with the number of month (t) being in the exponent. This the a key characteristic of an exponential growth.  

Part B: (also explained above). Every month the number of visitors approximately doubles. Starting with 5.74 at month 8, the numbers goes up by about the same amount to 12.0 at month 9. At month 10, a similar increase occurs (doubling would be 24, and the data shows 25, so this is all "aproximate"). This trend continues throughout the table.

Part C:

Month 7 will be estimated as half of month 8 (going backward):

Month 7: 5.74/2=2.87

Estimate for month 7 = 2.87 thousand visitors.

Answer:

$1.25

Step-by-step explanation:

Answer:

y = 80 -40x

Step-by-step explanation:

The given equation shows the friend arrives at the restaurant (y=0) when x=2. That is, half the initial distance to the restaurant is covered in each hour of travel time.

If I take 2 hours to travel the 80 miles from my house, my distance will decrease at the rate of 40 miles per hour. My distance from the restaurant can be represented by ...

... y = -40x +80

Answer:

A)55

B)110

Step-by-step explanation:500 /11%=55

55*2=110

The interest is $110 and the amount paid to the bank is $610.

Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest.

It is given that you decide to borrow $500 to go on a trip to whatever land. You go to the bank and borrow the money at 11% for 2 years.

A. The simple interest is,

SI = ( Principle x rate x time ) / 100

SI = ( 500 x 11 x 2 ) / 100

SI = $110

B. The amount paid to the bank after 2 years is,

Amount = P + SI

Amount = $500 + $110 = $610

Therefore, the interest is $110 and the amount paid to the bank is $610.

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Answer:

10 Valentines

Step-by-step explanation:

1/2 = 4/8

3/4 = 6/8

Julie has a total of 4/8 + 6/8 = 10/8 yards of ribbon. If color doesn't matter, she can make 10 Valentines.

_____

10/8 = 10 × 1/8

Answer:

-3c^2 +6

Step-by-step explanation:

The equation will be an identity (0=0) when M is equal to the contents of the parentheses. That polynomial can be used directly, or it can be simplified by combining the c^2 terms.

The contents of parentheses simplify as follows:

... (4c^2 -7c^2 +6) = (c^2(4 -7) +6) = (-3c^2 +6)

Answer:

4c^4-7c^2+6

Step-by-step explanation:

Answer:

7.9

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship of the hypotenuse and the side opposite an angle:

... Sin = Opposite/Hypotenuse

For your geometry, this is ...

... sin(21°) = x/22

Multiplying by 22 gives ...

... x = 22·sin(21°) ≈ 7.9