Find the area of the figure given to the right. The hexagon is regular. Round to the nearest whole number.

Solution:

Using the Maclaurin series;

Thus;

ANSWER: 1.22

We are asked to study a graph of car performance and give details about the dependent and independent variables. Here is the graph in question:

Our control point is: the info given: 55 miles per gallon gave 20 mi/gallon gas usage. We see clearly that point on the graph, located at (55, 20) on the red line.

Therefore, the gas performance, is the quantity we are studying and it is the "DEPENDENT" variable. As such, it should be graphed on the veritical axis as it is on the graph provided.

The INDEPENDENT variable is the speed we are trying (in the first case the 55 mph (miles per hour) . This variable is what is plotted on the horiontal axis.

Given the shape of the graph: we see it as a line decreasing as we go at higher speeds, the better performance (more miles per gallon) will be obtained as we reduce the speed (going towards 45 miles per hour or even less). Notice that at the beginning of the horizontal axis (for about a 35 mph speed) we see the maximum height of the line at around 27 miles per gallon. So to answer the last question: We could get better gas mileage if we reduce the travelling speed at 35 miles per hour.

The term is the word that is used to represent the added and subtracted parts of an expression.

When one is writing a mathematical expression, they would have to make use of numbers, variables as well as symbols in the equation that is being written.

The operators that are written are seen to be connected through the use of symbols of multiplication, addition or otherwise.

The parts of the expression that are known to be fully connected to the addition as well as the subtraction is what is referred to as terms.

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Answer:

See below

Step-by-step explanation:

Answer:

1,800 im not sure tho

Step-by-step explanation:

Given:

The function f(x) = log(x) and f(x) = log(x - 2).

Required:

What transformtaion have been made from parent function?

Explanation:

The graph of the function,

The graph of f(x) = log(x - 2) shifted to 2 units in the x - direction.

Answer:

Option A is correct.

The slope of the line passing through the given points is equal to -5/7.

A slope is also known as gradient and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (-1 - 4)/(4 - (-3))

Slope = -5/(4 + 3)

Slope = -5/7

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This is the graph of the parent function:

But translated 2 units up. Therefore, the equation of this graph is given by:

0.7768

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Although part of your question is missing, the complete question is "determine the pattern then write the decimal to complete the decimal grid 0.34 0.65 as shown in a grid".  

The decimals in  given pattern is 0.23, 0.24, 0.25, 0.34, 0.43, 0.44, 0.45, 0.54 , 0.63, 0.64, 0.65.

In the decimal grid, there are 5 horizontal rows and 3 vertical columns. In each row, the next element increases by 0.01 and In each column, the next element increases by 0.10.  

So in the first row, the elements are 0.23, 0.24, 0.25

The given element below that  is given as 0.34

The elements in the next row are 0.43, 0.44, 0.45

The element in the fourth row is 0.54

The elements of the last row are 0.63 and 0.65

Hence, completing the pattern missing elements are 0.23, 0.24, 0.25, 0.43, 0.44, 0.45, 0.54 and 0.63

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A composite number is a positive integer that has more than two factors, for example, 4, it can be expressed as 2x2=4 and 1x4=4.

Then, the answer is a number with multiple factors

SOLUTION

Venn Diagram for the problem is shown below

Now from the Venn Diagram the number at the center of the intersection of all three circles is 6. This represents the number of students that liked all three subjects.

Number that liked Math and Science is 18, So number that liked "Math and Science only", will be 18 (all the people that like Math and Science) minus 6 (numbers that liked all three subjects). This becomes 12.

This was how 4 (numbers that liked science and social studies

We could start by drawing the triangle we are given. However, it would be better to draw the triangle after the y-axis reflection. To calculate the y-axis reflection, we first think as follows

We see that the reflected point is at the same height as the original point. This means that the y coordinate should remain the same. So, the only thing that changed is the x coordinate. This suggests that, to calculate the reflection about the y-axis, we simply multiply by -1 the first coordinate. So, after the reflection we get the points

P'(-3*(-1),9)=(3,9)

Q'(-3*(-1),5)=(3,5)

R'(-7*(-1),5) =(7,5)

Now, if we plot this points we get

So, if we rotate this 180° we would get the following

So the new points after rotating 180°, would be

P''(-3,-9)

Q''(-3,-5)

R''(-7,-5)

Answer:

Let you be "x"

and your sister be "y"

when you are 2 your sister is twice your

x=2 y=4

so your sister is 2 year older than you

now you're 40 so your sister would be

Step-by-step explanation:

When I was 2 my sister was twice my ag Now I'm 40 then my sister age is 80.

\

Two or more expressions with an Equal sign is called as Equation.

Given,

When I was 2 years my sister was twice of my age.

Let us consider the ages by using a equation like this

x/y------>X represents my age/ y represents my sister age

x/y ----->2/4=40/a

a is the age of sister when i was 40.

Now let us solve 2/4=40/a

One by two equal to forty by a.

Apply cross multiplication

2a=160

Divide both sides by 2

a=80

Hence, if I'm 40, my sister is 80 years old.

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Answer:

3

Explanation:

Given the logarithmic expression:

First, express 64 as a power of 4:

Next, apply the power law of logarithms:

Finally, by the unity law:

The result of the evaluation is 3.

Answer: b) and a)

Step-by-step explanation:

Cause absolute value is the opposite of the number

We have the next function

In 1960, x=0

In 1965, x=5

In 1966, x=6

In 1967, x=7

In 1968, x=8

As we can see the year with the least value is 1966

Legs are mentioned below.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A triangle's side is one of its legs. The term "leg" for a right triangle typically refers to a side other than the one across from the right angle (which is termed the hypotenuse). The word catheti also refers to legs.

Given,

a) AB and BC

AB = height

BC = base

b) AC and BC

AC = hypotenuse

c) BC and AC

BC = Base

AC =  hypotenuse

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The solution to each equation involving absolute values:

In this exercise we have eight cases of equations involving absolute values. The definition of absolute value is:

|x| = a, where x = a, for x ≥ 0 and - x = a, for x < a.

Now we proceed to resolve on each case:

Case 1

|k| = 8

k = 8 ∨ - k = 8

k = 8 ∨ k = - 8

Case 2

|x| = 7

k = 7 ∨ - k = 7

k = 7 ∨ k = - 7

Case 3

|a + 2| = 8

a + 2 = 8 ∨ - a - 2 = 8

a = 6 ∨ a = - 10

Case 4

|8 · n| / 10 = 2

|8 · n| = 20

8 · n = 20 ∨ - 8 · n = 20

n = 20 / 8 ∨ n = - 20 / 8

n = 10 / 4 ∨ n = - 10 / 4

n = 5 / 2 ∨ n = - 5 / 2

Case 5

|- m + 9| = 13

- m + 9 = 13 ∨ m - 9 = 13

m = - 4 ∨ m = 22

Case 6

|7 - 5 · x| = 27

7 - 5 · x = 27 ∨ - 7 + 5 · x = 27

5 · x = - 20 ∨ 5 · x = 34

x = - 4 ∨ x = 34 / 5

Case 7

|2 · x + 7| / 5 = 5

|2 · x + 7| = 25

2 · x + 7 = 25 ∨ - 2 · x - 7 = 25

2 · x = 18 ∨ 2 · x = - 32

x = 9 ∨ x = - 16

Case 8

|- 3 - 5 · a| / 9 = 1

|- 3 - 5 · a| = 9

- 3 - 5 · a = 9 ∨ 3 + 5 · a = 9

5 · a = - 12 ∨ 5 · a = 6

a = - 12 / 5 ∨ a = 6 / 5

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Point C is reflected across a line AB such that it maps to point D.

Points C and D are then connected to form a line CD.

Let us draw a figure to better understand the problem

As you can see from the above figure,

We have reflected the point C across the line AB and the reflected point is mapped to point D.

Then we connected the point C to point D using the red color to form line CD.

The line CD is perpendicular to line AB.

All other options depend on the exact scenario which means they may or may not be true.

But we can be sure about option D that it must always be true.

Therefore, option D is the correct answer.

Tarik is 0.75 miles away from the store.

It should be noted that based on the information given, the expression has been given for the hours used.

In this case, the minutes used was:

= 7.15am - 7.00am

= 15 minutes

This will be changed to hour

15 minutes = 15/60 = 0.25 hour.

The expression given is:

= 3(x - 0.5)

where x = hours used 0.25

= 3(x - 0.5)

= 3(0.25 - 0.5)

= 3(-0.25)

= -0.75

He is 0.75 miles away.

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When x=9, y=81.

To find the proportionality constant take the ratio of y/x.

Thus, the proportionality constant is 9.

The relation between y and x can be determined as,

Thus, the required relationship between x and y is y=9x.

SOLUTION:

From the given geometric sequence gives

The common ratio. reduce

Simplifying this gives

Therefore the common ratio is r=3

To solve this type of question we need to form 2 equations of 2 variables and solve them to find the 2 variables

Let x is the number of the large drinks and y is the number of the medium drinks

Since the restaurant sold 52 drinks, then

Since the cost of the large drink is $2.75 each, then

The cost of the large drinks is 2.75(x)

Since the cost of the medium drink is $2.15 each, then

The cost of the medium drinks is 2.15(y)

Since the total cost of them is $131.60, then

Add 2.75(x) and 2.15(y) and equate the sum by 131.60

Now we have a system of equations to solve it

Multiply equation (1) by -2.75 to make x equal in values of the two equations and different in signs to eliminate it

Add equations (2) and (3)

Divide both sides by -0.6

They sold 19 medium drinks yesterday

Solution

Part a

For the first part we have two points (2,4) and (4,10)

We can find the slope like this:

And then the intercept would be:

4= 3*2 +b

b= 4-6= -2

Then the answer is:

y= 3x -2

Part b

f(-4)=18 and f(4) =2

The slope is:

2= -2*4 +b

b= 2+8=10

y= -2x+10

Part c

x intercept at (-5,0) and the y intercept (0,4)

And using the y intercept we have:

4= 4/5*0 +b

b= 4

y= 4/5x +4

To find the area of the trapezoid, we will use the formula below:

where a and b are the base and h is the height.

From the diagram given, a=7 , b=17 and h = 5.

Substitute the values into the formula and evaluate.

That is;

Hence, the area of the trapezoid is 60 yd².

This can be solved using permutations

What are permutations?

A permutation of a set in mathematics is a loosely defined organization of its members into a sequence or linear order, or, if the set is already sorted, a rearranging of its elements. The act or process of shifting the linear order of an ordered set is often referred to as "permutation." Permutations are distinct from combinations, which are random picks of certain members of a collection. For example, there are six permutations of the set 1, 2, 3 represented as tuples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 1, 2). (3, 2, 1). Permutations include anagrams of words with various letters.

No. of ways using permutation = ¹⁷P₅ = 742560

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Explanation

We can infer that the Literary Digest poll was wrong because it was biased.

We are told that the poll used lists of telephone and automobile owners to select their sample which doesn't give a full representation of all those who will vote in the election.

So we can infer that the problem with the Literary Digest poll is that it was Biased

The equation of the line is x = 2

The slope of the line is given as

Slope = Undefined

This can be rewritten as

m = Undefined

The point on the line is also given as

(x, y) = (2, 1)

For a line with an undefined slope, it means that:

The line is a vertical line

The equations of all vertical lines are represented as

x = x₁

In this case,

(x₁, y₁) = (2, 1)

Remove the y-coordinate

x₁ = 2

Substitute x₁ = 2 in the equation x = x₁

So, we have

x = 2

Hence, the line has an equation of x = 2

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Let's call the votes John recieved x

If Sam recieved 20% more votes than John, it means that the total votes Sam recieved are 1.20x

We know that the total amount of votes add up to 99. Thereby,

Thereby, John recieved 45 votes in total