How is seeing the parts of a partitioned number line the same as seeing the parts of a partitioned rectangle? How is it different?

Answer: The problem can be visualized with the help of the following diagram:

Therefore the building height can be determined by using the pythagorean theorem, the steps are as follows:

Therefore the ladder reaches 9.9ft up the wall.

we have that

the algebraic expression that represents this situation is

15-(9+2.65+1.35+2(1.74))

therefore

George needs to put a parenthesis before the 9

The company has different staff with different salaries scale

No of employees Salary

14 $21,000

11 $23,800

18 $26,300

4 $32,000

5 $39,500

1 $145,700

To find mean

Mean = summation of salary x no of employees / Total number of employees

14 x 21000 = 294, 000

11 x 23,800 = 261,800

18 x 26,300 = 473,400

4 x 32,000 = 128,000

5 x 39,500 = 197,500

1 x 145,700= 145,700

Frequency = 14 + 11 + 18 + 4 + 5 + 1

Frequency = 53

Mean = 28, 309.43

Mode is the highest number of employees salaries that appear most

From the table, The highest number is 18

18 number of the employees received 26, 300

The mode is $26,300

To calculate the median

Firstly, get the total number of employees in the company

The total number = 14 + 18 + 11 + 4 + 5 + 1

Total number of employees = 53

Median = total number + 1 / 2

Median = 53 + 1 /2

Median = 54/2

Median = 27th position

This implies fall between the 27th position of the employee

The median is $26, 300

The rule for a dilation by a factor of k using the origin as the center of dilation, is:

In the options A and B, additions and substractions are involved. Then, they cannot be the rule of a dilation about the origin.

In the options C and D, we can see that both are dilations about the origin. The factor used in the option C is 5/4, while the factor used in the option D is 0.9.

Nevertheless, notice that 5/4 is greater than 1 and 0.9 is smaller than 1.

Then, the dilation from option C would produce a bigger polygon, while the dilation from option D will produce a smaller polygon.

Since the polygon must be a smaller one, then the rule that could represent this dilation is:

Which corresponds to option D.

Midpoint : (6,1)

Point A : (4,8)

Point B (xb,by)

Midpoint (xm, my)=( x1+x2) /2 , ( y1+y2)/2

So:

xm= 6 = (4+xb) /2

6 = (4+xb) /2

Solve for xb

6 x 2 = 4+ xb

12 = 4+xb

12-4 = xb

8 = xb

For Yb:

my= 1 = (8+yb) /2

1 = (8+yb) /2

Solve for yb

1(2) = 8+yb

2 = 8+ yb

2-8 = yb

-6 = yb

Coordinate of B = (xb,yb) = (8,-6)

to rotate 90 degrees counterclockwise we must transform the points like this

and then invert the sign of the y-coordinate or the second coordinate of each point, so the total transformation is

now, transform each point

we know that

The slope is undefined, when we have a vertical line

therefore

1900 tiles are needed to cover the worktop.

From the question, we have

The surface area of the worktop is 3.04m squared.

The worktop is to be covered with square tiles each measuring 4cm by 4cm.

Number of tiles = (3.04*10000)/(4*4)

=1900

Multiplication:

To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.

Complete question:

The worktop is to be covered with square tiles, each measuring 4 cm by 4 cm. How many tiles are needed to cover the worktop?The surface area of the worktop is 3.04m squared.

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The equation of the given line is

Where: The slope is -1/3

Perpendicular lines have additive reciprocal slopes which means if the slope of one of them is m, then the slope of the other is -1/m

Then the slope of the perpendicular line to the given line is 3

So, we have to look for the graph of positive slope

The graphs of A and D have positive slopes because the directions of the lines are increasing from left to right

Then we have to find the slope of each line to find the correct choice

Since the slope of the line is 3, then the y part increases 3 units for 1 part increases of x

We can see that in graph A

The answer is A

Given:

y = 5x - 10

y = x + 6

To find:

We need to find the value of x and y from the above equations.

Length of pendant including silver border is = 23/24 inch

The width of the pendant including the silver border is = 5/6 inch

When adding two fractions with the same denominator (lower number), just add the numerator (upper number) and leave the denominator unchanged if the fractions are like. To add fractions with different denominators, you must rewrite the fractions so that they have a common denominator before computing the sum.

For the given case,

The length of the pendant including the silver border is

(5/8)+ (1/3) = (15+8)/24

= 23/24 inch

The width of the pendant including the silver border is

(1/2) + (1/3) = (3 + 2)/6

= 5/6 inch

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Given

Two points (8,6) and (3,−6)

Find

distance between the two points

Explanation

Distance between the two points is given by

so , distance between (8,6) and (3,−6) is

Final Answer

Therefore , the distance between these two points is 13

The quadratic function is given by the following expression:

The direction at which the graph opens is determined by the signal of the number multiplying x². If the number is positive then the graph opens upwards, if it is negative it opens downward. In this case it is negative so it opens donward.

The vertex of a quadratic expression can be found by the following expression:

Where a is the number multiplying "x²", while b is the number multiplying "x". Applying the data from the problem we have:

To find the value of "y" for the vertex we need to apply the coordinate for x on the expression. We have:

The coordinates of the vertex are (-1,4).

To sketch a graph we need to find the x-intercept and y-intercept of the function. These are given when f(x) = 0 and x=0 respectively. Let's find these points.

The x intercept happens in two points -3 and 1, while the y intercept happens in the point 3. With this and the vertex we can sketch the function.

Answer:

5400 feet

Explanation:

The distance the ball travels each time it was hit = 361.87 feet

First, this distance is rounded to the nearest ten feet.

Multiply 360 by 15 hits:

The total amount of distance the ball will travel after 15 hits is 5400 feet.

The Law of Cosines is:

Where "a", "b" and "c" are sides of the triangle and "C" is the angle opposite side "c".

In this case you know that:

Then, you can substitute values as following:

Finally, evaluating, you get that the answer is:

Check the picture below.

so let's get "h" and thus we can get the area of the trapezoid.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{17^2 - 8^2}=h\implies \sqrt{225}=h\implies 15=h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=15\\ a=12\\ b=20 \end{cases}\implies A=\cfrac{15(12+20)}{2}\implies A=240~m^2[/tex]

well, for that, that'd be 2 can plus some more for the remaining 40 m², so I'd think 3 cans will do it,

[tex]\pounds 19.75\cdot \stackrel{cans}{3}\implies \text{\LARGE \pounds 59.25}[/tex]

The schematic diagram below represents the path followed by the glider,

The point A represents the location of the airport.

Observe that the path of the glider forms a right angled triangle ABC.

So the hypotenuse AC can be calculated by using Pythagoras Theorem as,

Thus, the distance of the glider's last leg back to the airport is 17 miles.

So the second option is the correct choice.

We have that for seven and a half hours, you get 72$, then we have the following rule of three:

then we have that:

therefore, for each hour, you get $9.6

So, for 40 hours we have:

finally, we have that for 40 hours you get $384

The Solution:

Given:

Required:

To construct a bisector of each of the given lines.

Steps:

1. Take your compass and put the pin on one end of the line, and then expand the compass to at least more than half the length of the line ( but not greater than the length of the line).

2. Make an arc on the upper side and the lower side of the middle of the line, and then repeat the process when you take the pin mouth of the compass to the other end of the given line.

3. Connect the pairs of intersections of the arcs to make a straight line.

The straight is the required bisector.

Below is an example with the first line:

The first step is to find how many cups of flour she has left to bake the cookies after baking the cake. To do it, substract the amount of flour she needs for the cake to the total amount of flour she decided to use.

She has 10.5 cups of flour to bake the cookies. To find how many tray of cookies, solve the following equation for x:

She can make 21/5 trays of cookies. Written as a mixed number it is 4 1/5, it means she can make 4 1/5 or less trays of cookies.

The least expensive house in the 100,000 range, given the stem and lead plot on house sale prices, is $120, 000.

The stem and leaf plot on the house sale prices is given such that the stem is in hundreds of thousands and the leaf is in ten thousands.

This means that if you have a stem of 0 and a leaf of 2, the house price is:

= 0 + 20,000

= $20,000

A stem of 3 and a leaf of 4 means the house price is:

= 300,000 + 40,000

= $340,000

The cheapest house in the 100,000 range is the leaf value of 2 which means the least expensive house is:
= 100,000 + 20,000

= $120,000

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To solve the equation for p, we can first apply the cross product method, that is, we multiply the numerator and denominator that each line of the "X" connects.

Then, we have:

Now, we divide by 11 from both sides of the equation:

Therefore, the value of p that satisfies the given equation is 8/11 or 0.72.

Answer:

  fails the vertical line test: not a function

Step-by-step explanation:

You want to know how to tell if a relation is a function or not.

A relation is a map between values of the independent variable (input, x) and values of the dependent variable (output, y). Such a map can be represented many ways, including a table, graph, set of ordered pairs, dual number lines, or even a diagram showing inputs and outputs. The attachment shows such a diagram.

A relation does not need to be between numbers. Tokens of any kind can be used for input and output identifiers.

A function is a relation in which each input corresponds (maps) to exactly one output.

The relation shown on the left of the attachment is not a function because the first (top) input item (A) maps to more than one output item (B).

When a relation is expressed as ordered pairs (x, y) or a table, it will be a function if and only if no x-value is repeated.

When a relation is expressed as a graph, it will be a function if and only if no vertical line intersects more than one point on the graph. (This is the "vertical line test.")

Explanation

Step 1

the area of a circle is given by:

so, the area of teh walkway will be the difference of areas

Step 2

expand the polynomius:

therefore, the answer is

I hope this helps you

We have the next linear equation y=5x+1​

For the first row,

y=11

we substitute the value in the equation

11=5x+1

we clear x in order to know the value of x

5x=11-1

x=10/5

x=2

For the second row

x=4

we substitute the value in the equation

y=5(4)+1

y=20+1

y=21

For the third row

y=31

we substitute the value in the equation

31=5x+1

5x=31-1

5x=30

x=6

For the fourth row

x=8

we substitute the value in the equation

y=5(8)+1

y=40+1

y=41

The table of the equation

x y

2 11

4 21

6 31

8 41

Answer: Graph the value of b first on the Y - axis

The slope - intercept form of equation is

y = mx + b

where m = slope , and b = intercept

You graph the value of b on the Y - axis

The decimal forms of rational numbers can be finite, i.e. have a non infinite number of digits. In case they have infinite digits then these are periodic. This means that there's a patron of digits that is repeated infinitely.

Irrational numbers on the other hand can only have infinite digits on their decimal form and they are not periodic.

m∠D = 28º , m∠C= 109º

1) Given that these triangles are congruent, we can state that the angles of both are equal, and their sides as well.

2) Let's check on the picture:

Since the triangles are congruent, we can state that m∠D = m∠A, and m∠C = m∠F

So m∠D = 28º Since 62 and 28 are complementary angles

And

m∠C = 109º Since m∠EFM and ∠EFD are supplementary

To multiply these numbers, the first step is to writhe "-8" as an improper fraction, to do so, divide it by 1

Next is to solve the multiplication, to do so, first multiply the first two terms of the multiplication:

The multiplication is between two negative numbers, when you multiply two negative numbers, the minus signs cancel each other and turn into a positive value, this is called "double-negative"

Next multiply the result by the third fraction -2/5

This time you are multiplying a positive and a negative number, so the result of the calculation will be negative

Final step is to simplify the result, both 144 and 15 are divisible by 3, so divide the numerator and denominator by 3 to simplify the result to the simplest form:

Given:

6(y + 4)

Let's find the equivalent expression.

To find the equivalent expression, apply distributive property.

Distribute 6 to the numbers in the parentheses.

We have:

6(y + 4)

= 6(y) + 6(4)

= 6y + 24

Therefore, the equivalent expression is: ^