The perimeter of the figure is 18 units. Complete the statements to find the side lengths.


1. Find the distance from A to B. Explain how you found this distance.



2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.


3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.

Step 1: We have the following expression:

Step 2: Fon finding the equivalent expression, we have to factoring the polynomial, this way:

Step 3: Now we have to find two integer numbers that the result of adding them is - 7 and the result of multipliying them is 12

First number: -4

Second number: -3

Therefore, we have now:

2 (x - 4) (x - 3)

Step 4

Answer:

12

Step-by-step explanation:

First, get all of the x values to one side of the equation so that we can solve for x. One way to do this is subtract 5x from both sides.

Now we have this:

4x - 5x = -12.

Simplify:

-x = -12.

We need positive x, so divide both sides by -1.

x = 12.

Hope this helps! :)

The radius(r) of the wheel is;

The perimeter(P) of the wheel is given by the formula below:

The distance travelled by Ivan is 165m.

So, the number(n) of times the wheel is:

Hence, the correct answer is 47.8

Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30

The probability that a student is female given that it is a junior is computed as follows:

The probability that a student is female and junior is:

The probability that a student is a junior is:

Finally, The probability that a student is female given that it is a junior is:

The number of cans is proportional to the number of days, because each day it uses 2 c

Here is the completed table:

Number of bags purchased           Total weight                  Total Cost

1                                                                 4                                  8

2                                                                8                                  16

3                                                                 12                               24

4                                                                  16                              32

5                                                                   20                             40

One bag of cat food weighs 4 pounds. This means that as the bag increases by 1, the weight of the bag increases by 4.

Weight of 1 bag of cat food = 4

Weight of 2 bags of cat food = 4 x 2 = 8

Weight of 3 bags of cat food = 4 x 3 = 12

Weight of 4 bags of cat food = 4 x 4 = 16

Weight of 5 bags of cat food = 4 x 5 = 20

The cost of cat food is $2 per pound.

Cost of a bag of cat food = number of bags bought x weight of one bag x cost per pound

Cost of 1 bag of cat food = 1 x 4 x 2 = 8

Cost of 2 bags of cat food = 2 x 4 x 2  = 16

Cost of 3 bags of cat food = 3 x 4 x 2  = 24

Cost of 4 bags of cat food = 4 x 4 x 2  = 32

Cost of 5 bags of cat food = 5 x 4 x 2  = 40

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option (c) is correct.

An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

Given that,

An expression

1/2bh + 4

There are two terms in the first term b and h are variables and its coefficient is [tex]\frac{1}{2}[/tex] .

In the second term only 4 is a constant term.

It means this expression has two.

(a)  Teemu said, "[tex]\frac{-1}{2}[/tex] is a coefficient"

In the first term [tex]\frac{1}{2}[/tex] is a coefficient of b and h.

(b)  Sammy said, "The entire expression is the sum of 4 terms."

No this expression has only two terms.

Hence, Neither student is correct.

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Answer: Only teemu

Step-by-step explanation: Because 1/2 is the numerical factor in a product involving variables and although sammy said it is the sum of 4 terms, there is 2 in the expression.

Given the function

To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.

We are already given the domain of f, all the real numbers equal or greater than zero.

The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.

Once we find the inverse function, we'll use this concept.

Step 1: Substitute f(x) for y:

Step 2: Swap the variables:

Step 3: Solve for y:

But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:

The probability that a player dealt with four hearts = 0

Probability is defined as the prediction of the occurrence of an event in a stated set.

This can be expressed in proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

From the question given, the 6 sets include the following;

9, 10, jack, queen, king and ace.

There are no hearts given in the set of the event that occurred, therefore, the probability that a player dealt with four hearts = 0.

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Explanation

We are given the following information:

• Amount at the beginning of an investment = $5500

• Percent decrease = 24.6%

We want to determine the decreased amount in dollars and the amount in his account at the end of the year.

We can determine the decreased amount with the formula below:

Therefore, the decreased amount can be calculated as:

Hence, the decreased amount is $1353.

At the end of last year, the amount left in his account can be calculated as follows:

Hence, the year-end amount is $4147.

Each senior citizen ticket costs $7.

One child's ticket costs $14.

Describe algebra.

Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.

S represents the senior citizen ticket cost.

C is the child's ticket cost.

Price is expressed as USD per ticket.

8S + 15C = 266

8S + 8C = 168

Subtract both equations now to get rid of S

8S + 15C = 266

8S + 8C = 168

———————————-

7C = 98

C = 98/7

C = $14

Changing the value of C in the first

8S + 15(14) = 266

8S + 210 = 266

8S = 266 - 210

8S = 56

S = 56 / 8

S = $7

Hence, $7 is the price for senior citizen

And, $14 is the price for child

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The area of the circle is given as:

plugging the value given we have that:

Now, the circumference is given as:

where d is the diameter of the circle. The diameter is twice the raidues, hence the diameter is 38, therefore the circumference is:

Therefore the circumference is 38pi

For the given points, vector in component form equals -6i^ - 7j^ and its magnitude is 9.22

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

Examples of vectors include displacement, velocity, acceleration, force, and others that show both the direction and the size of a quantity. Vector: The displacement is -4 feet, while the velocity is -40 miles per hour. Negative displacement and velocity indicate that the object is travelling counterclockwise.

Vector in component form -

(-4 -2)i^ + (-2-5)j^

= -6i^ - 7j^

Magnitude of the vector equals =

√(-6)² + (-7)² = √85 = 9.22

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Complete Question -

Vector w has its initial point at (2, 5) and its terminal point at (-4, -2). Write the vector in component form and find its magnitude.

The given equation is

First, we subtract 6 on each side.

Then, we divide the inequality by 4.

In a case whereby joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles  the distance she can she run in 40 minutes is  4.31 miles.

This can be solved by the cross multiplication using the rate that given in the question.

We were told that joeita took  58 minutes  of her time to run 6.25 hours miles , then to know the distance she can cover within 40 minutes is

58 minutes  = 6.25 miles

40 minutes = X miles

Let X be the number of miles she want to cover in 40 minutes

we ca cross multiply the expression above as :

( 40 minutes *  6.25 miles ) = (58 minutes  *  X miles)

the X = 4.31 miles

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Remember that the coordinates are written in the form (x,y). Plot the points with the given coordinates: A(1,6), B(1,1) and C(5,1):

Draw a right triangle using the same measures for the legs in order to construct ΔDEF, as described below:

Answer:

75?

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

3 divided by 5

0.6x125

Using linear functions, it is found that:

a) The expression to convert from Fahrenheit to Celsius is: y = 5x/9 - 160/9.

b) The inverse expression is: y = 9x/5 + 32.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function are described as follows:

For the conversion of Fahrenheit to Celsius, we have two points, as follows:

(32,0), (68, 20).

When the input increases by 36, the output increases by 20, hence the slope is calculated as follows:

m = 20/36 = 5/9

Hence:

y = 5/9x + b.

When x = 32, y = 0, hence the intercept b is calculated as follows:

0 = 5/9(32) + b

b = -5 x 32/9

b = -160/9

Hence the equation is:

y = 5/9x - 160/9.

To find the inverse expression, we exchange x and y and then isolate y, as follows:

x = 5/9y - 160/9.

5/9y = x + 160/9

5y = 9x + 160

y = 9x/5 + 32.

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The slope point form is

m is the slope

x1, y1 are the coordinates of a point on the line

The slope of the line is -1

m = -1

point (-5, -4) lies on the line

x1 = -5 and y1 = -4

Let us substitute them in the form above

Remember (-)(-) = (+)

The equation of the line in the slope-point form is y + 4 = -1(x + 5)

Explanations:

Given the following parameters

An initial deposit of Gerard is "d" dollars

For the savings with 5% interest, the interest on "d" dollars will be expressed as;

Get the total savings plus interest in the first account

Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars

For the other account:

Initial deposit = "d" dollars

Interest = $100

Since the interest will be added to the first deposit, hence;

In Tabulated form:

Step 1

From the question, Hailey reads 48 pages of a book

Blake reads half as many as Hailey.

Hence Blake reads;

The answer will be together they read;

Answer; Option C

Assuming Ken gets the same percentage as usuall in these 5 times, we can calculated how many times he did get on base by calculating 60% of 5.

To do this we transform 60% into decimal my dropping the percentage sign and dividing it by 100 and then we multiply the decimal by 5:

So, Ken got on base 3 times.

The profit of the store is represented by the quadratic formula:

Where

P is the profit

x is the number of videos rented

The coefficients of the parabola are:

a= -1 (coefficient of the quadratic term)

b= 90 (coefficient of the x-term)

c=52 (constant)

The value of a is negative, which indicates that the parabola opens downwards and that its maximum value is represented by the vertex.

To determine the maximum profit, you have to determine the coordinates of the vertex.

First, calculate the x-coordinate of the vertex, to do so you have to use the following formula:

Replace it with the values of the coefficients a=-1 and b=90

Second, replace x=45 in the equation to determine the y-coordinate of the vertex:

The y-coordinate of the vertex represents the maximum profit.

So the maximum profit is $2077, the correct option is option A.

The area under a standard normal distribution, which we get on a standard normal table, is the same as the probability on that area.

Thus if the area is 0.125, the probability is 0.125, that is, 12.5%.

Using the concept of volume, 700 milliliters of Solution B was used.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

When dealing with unknowns, the first step is to represent the unknowns using variables, draw up equations based on the available data, and then solve those equations to account for the unknowns.

Volumes of solutions A and B are here which is unknown.

Put these factors in place for us

Let x = the amount of solution A that was mixed in milliliters.

Let y= the amount of solution B that was mixed in milliliters.

The amount of volume utilized for A is 400 ml less than the amount used

for B.

This can be expressed mathematically as y - x = 400.

Or,

- x + y = 400 [1]

The ratios of alcohol in A and B are provided to us.

A contains 12% alcohol, hence its real alcohol content is 12% of x ml.

= 0.12x (12% = 12/100 = 0.12)

Similar to A, B has an alcohol content of 0.20x.

If x of A and y of B are combined, the total alcohol by volume is 0.12x + 0.20y.

and it is said that this amount is 176 ml.

Our second equation is therefore set up as 0.12x + 0.20y = 176 [2].

We create an equation containing only the other term by using both equations and removing either the x or y terms.

We should remove the x term from both equations to create a single equation that just contains the y term because the question only asks us to compute the volume of Solution B that was used.

Review the equations now:

- x + y = 400 [1]

0.12x + 0.20y = 176 [2]

x's coefficients should all be the same:

Increase [1] by 0.12

=> -0.12x + 0.12y =

= 0.12 x 400

=> 0.12x + 0.12y = 48 [3]

By adding [2] and [3], the x word is removed.

0.12x + 0.20y = 176+( -0.12x) + 0.12y = 48

0x + 0.32 y = 224

=> 0,32y = 224

Subtract 0.32 from both sides to get[tex]\frac{0.32y}{0.32}[/tex] = [tex]\frac{224}{0.32}[/tex]

==> y = 700

Therefore, 700 cc of Solution B was utilized.

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Using it's concepts, the point estimates for the population are given as follows:

a) Mean: 97 units sold per month.

b) Standard deviation: 16.06 units sold per month.

In the context of this problem, the 5 observations are given as follows:

97, 110, 89, 97, 92.

Hence the mean is given by:

M = (97 + 110 + 89 + 97 + 92)/5 = 97.

Considering the mean of 97 found above, the standard deviation is given as follows:

[tex]S(X) = \sqrt{\frac{(97 - 97)^2 + (110 - 97)^2 + (89 - 97)^2 + (97 - 97)^2 + (92 - 97)^2}{5}} = 16.06[/tex]

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Given:

an equation is given as y = -8.

Find:

we have to find an equation parallel to the given equation and passing through (-6, -7).

Explanation:

Compare the given equation with y = mx + b,

we find that slope ,m = 0 ,

the equation of the line passing through (-6,-7) is

y - (-7) = m( x - (-6))

y + 7 = 0(x + 6)

y + 7 = 0

y = -7

Therefore, y = -7 is an equation which is parallel to y = -8 and passing through ( -6, -7).

The graph of both y = -8 and its parallel equation y = -7 which passes through (-6, -7) is given as below

Red line represents the equation y = -8

and blue line represents the equation y = -7 passes through the point (-6,-7).

Therefore, the equation of the line parallel to y = -8 and passing through (-6,-7) is y = -7.

Answer:

y2-y1 x2-x1

Step-by-step explanation:

-5-(-1)

--------

0-(-2)

-4

---

2

-2

----

1

1)  The Linear equation that models the average price of a new home is;

y = -800x + 294000.

2) The prediction of the average price of a new hom in the year 2014 is; $256000

We are told that the average price in the year 2004 was $294000

We are told that y is the average price in a home in the year x, where x = 0 represents the year 2004. Thus, this means that the y-intercept is $294000.

Since the line must pass through the points (0, 294000) and (7, 288400), it means that;

Slope = (288400 - 294000)/(7 - 0)

Slope = -5600/7

Slope = -800

Now, we know that the general formula for equation in slope intercept form is; y = mx + c

where; m is slope and c is y-intercept.

Thus;

1) Linear equation is; y = -800x + 294000.

2) For the average price of a new home in the year 2014, this means that x = 2014 - 2004 = 10 years

Thus;

y = -800(10) + 294000

y = $256000

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