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The difference between the functions give:

(f - g)(1) = f(1) - g(1) = -3

For two functions f(x) and g(x), the difference is defined as:

(f - g)(x) = f(x) - g(x).

Then:

(f - g)(1) = f(1) - g(1)

By looking at the given tables, we know that:

f(1) = -2

g(1) = 1

Replacing that we get:

(f - g)(1) = f(1) - g(1) = -2 - 1 = -3

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By subtracting decimals, how much farther she ran on Saturday than on Sunday is determined as: 1.078 kilometers.

When subtracting decimals, the number value is taken into consideration.

Distance ran by Keisha on Saturday = 3.218 kilometers.

Distance ran by Keisha on Sunday = 2.41 kilometers.

Subtract both decimals to determine how much farther she run on Saturday than on Sunday.

3.218 - 2.14 = 1.078 kilometers.

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Answer: x / 5 = 16

x = 80

Answer:

  $47.28

Step-by-step explanation:

The total cost is found by adding the costs of the components.

There is one daisy, at $0.85 each.

There are to carnations at $0.50 each, for a total of 2×$0.50 = $1.00.

The is 6 inches of ribbon. That amount is 1/2 foot, so its cost is ...

  (1/2 ft)×$0.24/ft) = $0.12.

The total cost of the components of one corsage is ...

  daisy cost + carnation cost + ribbon cost = $0.85 +1.00 +0.12 = $1.97

There are 24 corsages, so their total cost will be 24 times this amount, or ...

  24 × $1.97 = $47.28

The total cost of the 24 corsages is $47.28. All the costs of the components required for making a corsage are added to get the total cost of the corsage.

It is given that,

The components and their costs:

The cost of each daise = $0.85

The cost of each carnation = $0.50

The cost of the ribbon per foot = $0.24 (1 foot = 12 inches)

The components for making one single corsage:

One yellow daisy + two pink carnations + 6 inches of ribbon = 1 corsage

Then, calculating the price for one single corsage,

1 × $0.85 + 2 × $0.50 + (1/2) × $0.24 = cost of 1 corsage

⇒ $0.85 + $1 + $0.12

⇒ $1.97

For 24 corsages, the total cost = 24 × $1.97 = $47.28

Therefore, the total cost of the 24 corsages is $47.28.

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Answer:

the answer to the question is 1

Answer:

-26 Is the correct answer

Step-by-step explanation:

Answer:

x + 4

Step-by-step explanation:

Sine the bases are all the same, I can write the equation:

3x+4 = (x-2) 2^3  When we are adding with logs, that means to multiple.  Also, when we have 3 log 2, that can be written as 2^3 or 8 (2x2x2)

3x+4=(x-2)8

3x+4 = 8x-16

4=5x-16

20 = 5x

4=x

Answer:

a=0, 12

Step-by-step explanation:

a=0 and –12+a=0===> a=12

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

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Answer:

angle 8 is congruent to angles 3, 6, and 1

Step-by-step explanation:

If n and q are parallel then corresponding and vertical angles would be congruent. So: angle 8 is congruent to angles 3, 6, and 1.

The standard numbers are obtained from the given numbers as follows;

The standard form of numbers is obtained by expressing the number completely and not using powers of 10

The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;

Number → Standard form

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A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.

-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.

Cardinalities of A and B

It is given that,

A = {n : -14 < n < -5, n ∈ Z}  ............ (1)

B = {h, i, s, x, z} ......... (2)

Thus, from (1),

A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)

Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,

n(A) = 8

n(B) =5

Reason Behind True or False

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The equation of the perpendicular line is y = -2x + 4

The line equation is given as:

2x = 4y - 8

Make y the subject

4y = 2x +8

Divide by 4

y = 0.5x + 2

The slope of the above equation is

m = 0.5

The slopes of perpendicular lines are opposite reciprocals.

This means that, the slope of the perpendicular line is:

n = -1/m

This gives

n = -1/0.5

n = -2

The equation is then calculated as:

y = n(x - x1) + y1

This gives

y = -2(x - 1) + 2

Expand

y = -2x + 2 + 2

Evaluate

y = -2x + 4

Hence, the equation of the perpendicular line is y = -2x + 4

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The ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)

The function is given as:

y = x^2 + 1

the ordered pairs are the x and y values of the function

So, we stet x = 0, 1, 2, 3 and 4

y = 0^2 + 1 = 1

y = 1^2 + 1 = 2

y = 2^2 + 1 = 5

y = 3^2 + 1 = 10

y = 4^2 + 1 = 17

Hence, the ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)

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Answer:

  B.  Completing the square

Step-by-step explanation:

Between the first and second steps shown, the square of half the x-term coefficient was added to both sides. That is a value that makes the polynomial on the left be a "perfect square trinomial."

The process of adding the value required to make the left side a perfect square is called "completing the square."

The resale value of the car after four years is $4820

The given parameters are:

initial value, a = $27,000

Rate, r = 35%

The value of the car each year is represented as:

Value = a *(1 - r)^t

So, we have:

Value = 27000 *(1 - 35%)^t

After four years, we have:

Value = 27000 *(1 - 35%)^4

Evaluate

Value = 4820

Hence, the resale value of the car after four years is $4820

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The paddling rate of Alvin is 9km/hr

Given time against the  river current is 10 hours , speed is 3km/hr

and time with the river current given is 5 hours and the speed is 3km/hr

We need to calculate the paddling rate of Alvin

Let us assume that

r =Alvin's average paddling rate in km/hour

y = speed of the current in km/hour

we know that

speed= distance/time

∴ distance=speed*time

Now,

To Campsite against the current

Speed=(r-y)

∴ Speed=(r-3) ---- (1)

Time=8 hours

Distance=(r-3)*10------ (2)

10r - 30

From Campsite with the current

Speed=(r+y)

∴Speed=(r+3)*5

Time=3 hours

Distance=(r+3)*5----(1)

Equate equation 1 and equation 2

5r +15

because is the same distance

5r + 15 = 10r - 30

5r = 45

r = 9

Hence ,The rate of the paddling rate is 9km/hr

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The function P(x), for the price of the materials for the pen, is 4.18(800/x + x) + 38.

Based on the information, the function P(x), for the price of the materials for the pen will be:

P(x) = 4.18 (2 × 400/x + x) + 38

= 4.18(800/x + x) + 38.

The dimensions will be:

We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.

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If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.

Let's say that each person works at a rate R.

8 people can mow the lawn in 6 hours, then we can write:

(8*R)*6 hours = 1 lawn.

Solving for R:

R = (1/48 lawns per hour).

If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:

(5*R)*T = 1 lawn.

Replacing the value of R:

(5/48 lawns per hour)*T = 1 lawn.

Then we have:

T = (48/5) hours.

We can rewrite that as:

T = (45/5 + 3/5) hours

T = 9 + 3/5 hours.

Then we conclude that the correct option is B.

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The answer choice which is not a step in finding the area of the unknown figure is; Plug all dimensions into the formula: SA=Ixwxh. option B

It follows from the task content that all other steps except Plugging all dimensions into the formula; SA = l×w×h are correct steps.

This is due to the fact that, the formula does not work for all shapes and hence, it can't be generalized for all situations.

The step which is not involved in finding the area of an unknown figure is; Plug all dimensions into the formula: SA=Ixwxh.

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Answer:

B) Plug all dimensions into the formula: SA=Ixwxh.

Step-by-step explanation:

Answer:

(+22x^2+16x+11)/(2x)

The attached image shows the image of A"B"C" after the transformation

The transformation rule states:

A"B"C" = Ro90° (T(-4,3)(ABC))

This implies that one need to rotate the triangle in a 90⁰ clockwise direction, and then one need to translate the triangle.

Using the image shown, the coordinates of ABC are;

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The 90⁰ rule clockwise rotation  will be:

(x,y) -- (y,-x)

So, when translated, it will be:

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

Then the translation of the triangle using T(-4,3):

(x, y) -  (x - 4, y + 3)

So, there is:

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

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Answer: The smallest angle is 35°

Step-by-step explanation:

1 angle: 2x

smallest angle: x

third angle: 2x + 5

all angles in a triangle add up to 180 degrees. Therefore,

2x+x+2x+5 = 180

5x+5=180

5x+5(-5)=180(-5)

5x = 175

5x/5 = 175/5

x = 35

The smallest angle is 35°

Using the normal distribution, the probability is given as follows:

[tex]P(X \geq 10) = 0.0485[/tex].

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution are:

p = 0.5, n = 13.

Hence the mean and the standard deviation are:

Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]

Z = 1.66

Z = 1.66 has a p-value of 0.9515.

1 - 0.9515 = 0.0485, then:

[tex]P(X \geq 10) = 0.0485[/tex].

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Answer: 5.83

Step-by-step explanation:

[tex]\sqrt{(2-5)^2 + (1-6)^2}=\sqrt{34} \approx 5.83[/tex]

Answer:

x = 34

Step-by-step explanation:

The angles x + 12, 100, and x add up to a straight angle, so the sum of their measures is 180°.

(x + 12) + (100) + (x) = 180

x + 12 + 100 + x = 180

2x + 112 = 180

2x = 68

x = 34

Another rigid motions that maps Δ GHJ to ΔKLM is ΔGHJ winding point J rotates 180° in the counterclockwise direction. It then transits south by 10 units and to the right by two units. See the attached image.

Rigid Motion is any method of moving all the points in the plane in such a way that.

There are four forms of rigid motions:

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The regression equation is y =  3.002 + 0.5x and the scatterplot is illustrated.

It should be noted that a scatterplot simply means a type of data that shows the relationship between two numerical variables.

From the information, summation is X is 99, summation Y is 82.5, summation XY is 797.47, and summation X² is 1001.

Now the value of a will be:

= 82.5 - 1001 - 99 - 797.47/(11.1001 - 99²)

= 3.002

b = (11 × 797.47 - 99 × 82.5)/11.1001 - 99²

= 0.5

The regression equation will be:

y = a + bx.

y = 3.002 + 0.5x

There's positive linear correlation between x and y.

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It will take 21 days before there is another day on which he does both.

The lowest common multiple (LCM) of two or more numbers is the lowest possible number which is completely divisible by all the given numbers.

Given,

John goes for a jog every third day and every Saturday he goes to the gym.

That means he goes to the gym on every seventh day, and goes for a jog every third day.

Therefore, he goes for both on the days which are LCM of 3 and 7.

But, LCM of 3 and 7 is 21.

Hence, he goes for both in every 21 days.

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