The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-2 and x=3. Use the line segment to determine the average rate of change of the function f(x) on the interval −2≤x≤3

Answer:

Amadi: 20 years old

Chima : 4 years old

Present age of father is 48 years and that of son is 23 years.

Let the age of father be x years

And the son's age be y years

According to the question,

x - y = 25 -----------1

15 Years ago, x= 6( y - 15 )

x= 6y - 90 -------------2

Substituting value of x from equation 2 in equation 1, we get

6y - 90 - y = 25

5y -90 = 25

5y = 25+90

5y= 115

y= 23

Therefore son's age is 23 years and from equation 1 we get x= 25+y = 25+23 = 48 years. So father's age is 48 years.

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Answer:

All except the 3rd

Step-by-step explanation:

Vertical angles are generated by the junction of two straight lines, and they are the opposite of each other. Angles 1 and 3 in the following diagram are vertical angles.

When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, whenever two lines cross or come together, four angles are formed.

According to the Vertical Angles Theorem, vertical angles—angles that are opposite one another and are created when two straight lines cross—are congruent.

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The answer of the given question based on  regular octagon ,the area of the regular octagon with center O is approximately 232.98 square units.

Area is  measure of  amount of space inside  2-dimensional figure or shape, usually measured in square units like square centimeters or square meters. It is calculated by multiplying  length and  width of the figure or a shape.

To find the area of a regular octagon, we need to use the following formula:

A = 2(1 + √2) × s²

Since O is the center of the octagon, we can draw lines from O to each vertex of the octagon. This will divide the octagon into 8 congruent isosceles triangles.

Let's call the length of each side of the octagon "s". Then the base of each triangle will also be "s". We can use the Pythagorean theorem to find the length of the other sides of the triangle:

s²+ s² = (2s)²/2

2s² = 4s² - 4s²/2

2s² = 2s²/2

s² = s²/2

s = √2s/2

Now we can substitute this value of s into the formula for the area of the octagon:

A = 2(1 + √2) × s²

A = 2(1 + √2) × (√2s/2)²

A = 2(1 + √2) × 2s²/4

A = (1 + √2) × s²/2

A = (1 + √2) × (17/2)²/2

A ≈ 232.98 square units

Therefore, the area of the regular octagon with centre O is approximately 232.98 square units.

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Answer:

m∠A = 130

Step-by-step explanation:

Here, In a given figure

m∠A = 2x - 30°

Now, we know that the sum of all angle is 180° on a straight line

So,

2x - 30° + 50° = 180°

2x + 20° = 180°

2x = 180° - 20°

2x = 160°

x = 160° ÷ 2

x = 80°

Here, we get the value of x is 80°

Now,

m∠A = 2x - 30°

m∠A = 2(80°) - 30°

m∠A = 160° - 30°

m∠A = 130

Thus, m∠A = 130

-TheUnknownScientist

Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.

An angle bisector divided an angle into two equal halves.

From the diagram:

Line BD divides angle ABC into two equal halves.

Angle ABD = ( 3x - 7 ) degrees

Angle DBC = 20 degrees

Since angle ABD and DBC are equal haves;

Angle ABD = Angle DBC

Plug in the values:

( 3x - 7 ) = 20

Solve for x:

3x - 7 = 20

Add 7 to both sides:

3x - 7 + 7 = 20 + 7

3x = 27

x = 27/3

x = 9

Therefore, the value of x is 9.

Option A)9 is the correct answer.

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Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Answer:

Step-by-step explanation:

It's a square, 14 by 14 feet.

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

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Lin ran faster because if you convert 2/5=24mins 4/3=80mins and lin would run 2.5 miles in an hour and Noah would run 0.75 miles

If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted

Let A, B and C be events relative to the sample space S.

The sample space is the set of all possible outcomes of the experiment.

The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.

Here we have to plot the each representing events using the Venn diagram representation

Part a

The event is (A ∩ B)'

Plot the Venn diagram

Part b

The event is (A ∪ B)'

Plot Venn diagram

Part c

The event is (A ∩ C) ∪ B

Plot the Venn diagram

Therefore, the Venn diagram of the each event has been plotted

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All four consecutive integers will be 9, 10, 11, and 12 and can be found out by high common sense.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.

For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.

Given that,

8 times the sum of the first and the third  =  8( 1st + 3rd)

40 greater than 10 times the fourth = 40 + 10(4th)

So,

8( 1st + 3rd) = 40 + 10(4th)

Now if we look right and side then it will come out as any number with the unit placed as 0.

So it means on the left side also the unit place must be 0.

By thinking of  1st + 3rd = 10 /20 because at 45 it will be 40 which is not equal to the right-hand side.

Now by hit and trial method, we need to guess it 20 = 9 + 11

Then

8(9 + 11) = 40 + 10(12)

One equation can never give us three unknowns hence it will be the correct way.

Hence so the four consecutive integers will be 9, 10, 11, and 12.

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Answer: m=6, m=-4

Step-by-step explanation:

To solve this proportion, we have to cross multiply.

\(\frac{m-3}{7} =\frac{m}{m+8}\)

\((m-3)(m+8)=7m\)

Now that we have cross multiplied, we actually need to FOIL the left side to expand the equation.

\(m^2+8m-3m-24=7m\)

Combine like terms.

\(m^2+5m-24=7m\)

We can move all terms to one side and then solve for m.

\(m^2-2m-24=0\)

We can actually factor this to:

\((m-6)(m+4)=0\)

We set each factor equal to 0 to find m.

m-6=0

m=6

m+4=0

m=-4

Answer:

In decimal form:

-0.875

Step-by-step explanation:

-7 divided by 8 = -0.875

The matrix operation needed to transform the original matrix (pre-image) is represented by option C. ( \(T' = \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right]\cdot \left[\begin{array}{cccc}-5&-8&-5&-3\\-9&-7&-3&-6\end{array}\right]\). )

The operation used to obtain the image in dash lines is a rotation around the origin, which is defined by following vectorial expression:

\(T' = R\cdot T\) (1)

Where:

Where the original matrix is defined by the following matrix:

\(T = \left[\begin{array}{cccc}x_{1}&x_{2}&...&x_{n}\\y_{1}&y_{2}&...&y_{n}\end{array}\right]\) (2)

And the rotation matrix is:

\(R = \left[\begin{array}{cc}\cos \theta&-\sin \theta\\\sin \theta&\cos \theta\end{array}\right]\) (3)

Where \(\theta\) is the rotation angle, in sexagesimal degrees.

If we know that \(\theta = 180^{\circ}\), \((x_{1}, y_{1}) = (-5, -9)\), \((x_{2},y_{2}) = (-8,-7)\), \((x_{3},y_{3}) = (-5, -3)\) and \((x_{4}, y_{4}) = (-3, -6)\), then the resulting matrix is represented by this entity:

\(T' = \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right]\cdot \left[\begin{array}{cccc}-5&-8&-5&-3\\-9&-7&-3&-6\end{array}\right]\)

The matrix operation \(T' = \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right]\cdot \left[\begin{array}{cccc}-5&-8&-5&-3\\-9&-7&-3&-6\end{array}\right]\) is represented in the graph.

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9514 1404 393

Answer:

  (b)  y/6 = 7/5.25

Step-by-step explanation:

Clockwise from the obtuse angle, the side ratios are ...

  Fig I : Fig II

  4.2 : 3.15

  y : 6

  7 : 5.25

  6 : x

  4 : 3

__

A true proportion will have corresponding parts of these ratios in corresponding places. The only true proportion listed is ...

  \(\dfrac{y}{6}=\dfrac{7}{5.25}\)

Answer:

-5

Step-by-step explanation:

h(x)=3x+1

Let x = -2

h(-2) = 3*-2 +1

        = -6+1

       = -5

Answer: 800 more hours is required to fly an aircraft

Step-by-step explanation:

Answer:

the answer is what I think 46

The solution of the inequality - 1/2x ≥ 4 is shown in Option 2.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

Inequality is,

⇒ - 1/2x ≥  4

Now, We can simplify as;

⇒ - 1/2x ≥  4

⇒ 1/2x ≤ - 4

⇒ x ≤ - 8

When we plot this inequality on a number line,

An arrow starting with a solid point from x = -8 and arrow directing towards negative numbers will represent the given inequality.

Hence, Option (2) will be the answer.

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Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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The mean and the standard deviation, from the frequency table, are given as follows:

The frequency table gives the number of times that each observation appears.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:

Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:

Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.

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