Select linear or nonlinear to correctly classify each function.

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:

(x, y) = (-0.3, -1.6)

Step-by-step explanation:

The graph below shows these equations graphed. Their point of intersection is (-0.3, -1.6).

_____

Analytical solution

You can equate the expressions for y to get ...

... 12x +2 = 2x -1

... 10x = -3  . . . . subtract (2x+2)

... x = -0.3 . . . . . divide by 10

... y = 2(-.3)-1 = -1.6 . . . . use the 2nd equation to find y.

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:

63

Step-by-step explanation:

Answer:

25 degrees.

Step-by-step If one of the angles is 38 degrees then in order for the sum to be 63, the answer is 25

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.

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

Step-by-step explanation:

sqrt of 81 is 9 so rational

Sqrt of 89 is irrational

Sqrt of 121 is 11 so rational

Sqrt of 131 is irrational.

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:

y=5

Step-by-step explanation:

1/3(y+7)=(y-1)

I will multiply by 3 on each side to get rid of the fractions

3*1/3(y+7)=(y-1)*3

y+7 = 3*(y-1)

Distribute the 3

y+7 = 3y -3

Subtract y from each side

y-y+7 = 3y-y-3

7 = 2y-3

Add 3 to each side

7+3 = 2y-3+3

10=2y

Divide each side by 2

10/2 = 2y/2

5 =y

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

Answer:

7.9 ft

Step-by-step explanation:

The hypotenuse is the side opposite of the right angle, hence the hypotenuse for this triangle is 11 ft.

Side [tex]x[/tex] is adjacent to the angle given. So we need adjacent and we have hypotenuse. Which trigonometric ratio relates adjacent and hypotenuse? It is COSINE.

Thus, we can write:

[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(44)=\frac{x}{11}[/tex]

Cross multiplying, we can solve for [tex]x[/tex]:

[tex]cos(44)=\frac{x}{11}\\x=cos(44)*11\\x=7.91[/tex]

Rounding to nearest tenth, we have [tex]x=7.9[/tex] ft.

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      

Answer:

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

Step-by-step explanation:

(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: [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:

5

Step-by-step explanation:

It is 5 because no matter how many stamps he sells, he has $5.

Answer:

The y-intercept of Ben's graph is [tex]y = 5[/tex].

Step-by-step explanation:

The function for Ben's amount of money y, depending on the number of stamps sold x, is as follows:

[tex]y = ax + b[/tex]

In which a is the price of each stamp and b is his initial money.

Building the function:

Ben has $5. This means that if he sells no stamps, he is still going to have $5. So [tex]b = 5[/tex].

For each stamp sold, he gains $3. So if sells 1 stamp, he will have $8, if he sells 2, he will have $11. So [tex]a = 3[/tex].

The function is:

[tex]y = 3x + 5[/tex]

Which will be the y-intercept of Ben's graph?

This is the value of y when x = 0.

So

[tex]y = 3*0 + 5 = 5[/tex]

The y-intercept of Ben's graph is [tex]y = 5[/tex].

Answer:

74°

Step-by-step explanation:

The triangle is isosceles and the congruent base angles are 53°. The sum of angles in a triangle is 180°, so the apex angle (∠EDF) will be ...

... 180° - 2×53° = 74°

Answer:

74* is the answer

Step-by-step explanation:

#PLATOFAM

#PLATOLIVESMATTER

#PLATOFAMILY

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

Answer:

1/27

Step-by-step explanation:

The probabaility of rolling a number less than 3 is 2/6 = 1/3, since only two of the six numbers are less than 3.

Assuming the die rolls are independent, the probability of doing this 3 times is the product of the probabilities of doing it each time:

... (1/3)^3 = 1/27

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:

$1.25

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%.

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:

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

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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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:

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.

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. :)