For each Diagram, write an unsimplified and simplified equation that represents the relationship between x and y.

I need the unsimplified equations on the left side of the chart from what I know it should be equal to the simplified equation across from it.

Answer:

7n - 4

Step-by-step explanation:

The minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To calculate the minimum number of strides that Chao could take to complete a distance of 11.2 km, we need to first convert the distance to meters since the stride length is given in centimeters.

11.2 km = 11,200 meters (1 km = 1000 meters)

Stride length in meters = 70 cm / 100 cm/m = 0.7 m

Now, we can calculate the minimum number of strides as follows,

Minimum number of strides = (Distance covered in meters) / (Stride length in meters)

Minimum number of strides = 11,200 m / 0.7 m ≈ 16,000

Therefore, the minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

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The axis of symmetry of the function is x=-1.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is h(x)=(x+1)²-4.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (-1,-4)

Focus: (-1,-15/4)

Axis of Symmetry: x=-1

Directrix: y= -17/4

Plot the points (-3, 0), (-2, -3), (-1, -4), (0, -3) and (1, 0)

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (1,0),(-3,0)

y-intercept(s): (0,-3)

Therefore, the axis of symmetry of the function is x=-1.

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Answer:

20(4+3)

Step-by-step explanation:

GCF of 80 and 60 = 20

20*4=80

20*3=60

20(4+3)

hope this helps! :)

Answer:

He drove 6 hours.

Step-by-step explanation:

distance = rate times time

300 = 50t  Divide both sides by 50

t = 6

Answer:

Step-by-step explanation:

You want the missing side and the angles for the right triangle with leg BC = 2.7 cm and hypotenuse AB = 3.1 cm.

The cosine of angle B is given by ...

  Cos = Adjacent/Hypotenuse

  cos(B) = CB/AB = 2.7/3.1

Then the angle is ...

  B = arccos(2.7/3.1) ≈ 29.429°

  B ≈ 29°

Angle A is the complement of angle B:

  A = 90° -29°

  A = 61°

The sine ratio is ...

  Sin = Opposite/Hypotenuse

Then side AC can be found from ...

  sin(B) = AC/AB

  AC = AB·sin(B) = 3.1·sin(29.429°) ≈ 1.523

  AC ≈ 1.5 . . . . cm

The triangle solution is ...

__

Additional comment

The mnemonic SOH CAH TOA is intended to help you remember the trig ratios above, in addition to ...

  Tan = Opposite/Adjacent

The cheapest option for Jane is to buy from Suttons Shop, as the total cost is £12, whereas, at Greens Garden Shop, the total cost is £9.98.

To determine the cheapest option, we need to calculate the cost of purchasing 140 liters of compost from each shop.

First, we'll calculate the cost at Suttons Shop:

Jane needs 140 liters of compost, so she needs 140 / 20 = 7 bags of compost.

If she buys 1 bag of compost, it will cost her £2.25.

If she buys 2 bags of compost, it will cost her £3.25.

Since she needs 7 bags of compost, she can buy 3 sets of 2 bags (6 bags) and 1 bag.

So the cost of 6 bags will be 3.25 x 3 = £9.75, and the cost of 1 bag will be 2.25.

The total cost of 7 bags at Suttons Shop will be 9.75 + 2.25 = £12.

Next, we'll calculate the cost at Greens Garden Shop:

Jane needs 140 liters of compost, so she needs 140 / 70 = 2 bags of compost.

Each bag at Greens Garden Shop costs £4.99.

So the total cost of 2 bags at Greens Garden Shop will be 4.99 x 2 = £9.98.

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a) The function would be A(t) = 6000(1 + 0.09)ᵗ

b) The amount in the account in 2012 was approximately $11,737.51.

What is the function model?

In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.

a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:

A(t) = 6000(1 + 0.09)ᵗ

where A(t) is the amount in the account after t years.

b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:

A(8) = 6000(1 + 0.09)⁸

= 6000(1.09)⁸

≈ $11,737.51

Therefore, the amount in the account in 2012 was approximately $11,737.51.

Hence,

a) The function would be A(t) = 6000(1 + 0.09)ᵗ

b) The amount in the account in 2012 was approximately $11,737.51.

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Given the matrix, [tex]\begin{bmatrix}2 & 3 \\3 & 2 \end{bmatrix}[/tex], find its inverse.

First we need to find its determinant which can be done by using the following formula,

[tex]det=\begin{bmatrix}a & b \\c & d \end{bmatrix}=ad-cb[/tex]

Lets call  [tex]\begin{bmatrix}2 & 3 \\3 & 2 \end{bmatrix}[/tex] matrix "A."

So,

[tex]detA=(2)(2)-(3)(3)[/tex]

[tex]\Longrightarrow detA=4-9[/tex]

[tex]\Longrightarrow detA=-5[/tex]

We now have the determinant, we can now use the following formula to determine the inverse matrix,

[tex]A^{-1} =\frac{1}{detA} \begin{bmatrix}d & -b \\-c & a \end{bmatrix}[/tex]

[tex]A^{-1} =-\frac{1}{5} \begin{bmatrix}2 & -3 \\-3 & 2 \end{bmatrix}[/tex]

[tex]\Longrightarrow A^{-1} = \begin{bmatrix}2(-\frac{1}{5}) & -3(-\frac{1}{5}) \\-3(-\frac{1}{5}) & 2(-\frac{1}{5}) \end{bmatrix}[/tex]

[tex]\Longrightarrow A^{-1} = \begin{bmatrix}-\frac{2}{5} & \frac{3}{5} \\\frac{3}{5} & -\frac{2}{5}\end{bmatrix} \therefore \ Sol.[/tex]

*Note* I went a few more steps than the question needed. If you back up two steps on my answer is where they stopped. The last option is correct.

Percentage profit on a chocolate bar is 150%

Profit percentage is a top-level and the most common tool to measure the profitability of a business. It measures the ability of the firm to convert sales into profits. i.e., 20% means the firm has generated a net profit of $20 for every $100 sale.

%profit = (selling price - cost price)/cost price × 100

%profit =( 1.50-0.6)/0.6 × 100

%profit = 0.9/0.6 × 100

= 1.5 × 100

= 150 %

therefore the percentage profit on a chocolate bar is 150%

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The value of a in the equation a + 2 = 3 is 1.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

a + 2 = 3

Subtract 2 from both sides

a + 2 - 2 = 3 - 2

a = 1

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Answer:

D. 3/7, 3:7, or 3 to 7

Step-by-step explanation:

To find the average value of a function on an interval dividing the definite integral [tex]\int\limits^a_b f{(x)} \, dx[/tex] by the length of the interval.

The definition of average value of a function is -"The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function."

When there's a need to find the average value of a function, rather than adding up numbers we can just integrate, and instead of dividing by the number of values we can just divide by the length of the interval.

Adding values → Integration

Number of values → Length of the interval

When we use the length of the interval it makes more sense as we all know intervals have an infinite number of values, so it is more appropriate to use the length of the interval instead.

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The measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠B as follows:

m∠A + m∠B + m∠C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B + 139° = 180°

B = 180° - 139° {subtract 139° from both sides}

m∠B = 41°

12.7/sin90° = a/sin41

a = (12.7 × sin49)/sin90° {cross multiplication}

a = 9.5848

12.7/sin90° = b/sin49

b = (12.7 × sin49)/sin90 {cross multiplication}

b = 8.3319

Therefore, the measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

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$13,000 and $15,000.

mark brainlyest

The number of different outfits that Aldo can create from the shirts and the pairs of pants are 6 outfits.

In this case, Aldo has 2 options for his shirt and 3 options for his pants. To find the total number of outfits, we can multiply these numbers together:

= Number of shirts x Number of pairs of pants

= 2 x 3

= 6 outfits

Therefore, Aldo can create 6 different outfits by choosing a shirt and a pair of pants from the available options.

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Answer:

25/50

will equal to 1/2

The volume of the given 3 - D figure is 156.36 cubic inches.

A volume is a collection of a three dimensional coordinate points enclosed by a two dimensional coordinate points.

Given is the 3 - D figure as shown in the image.

We can write the volume as -

V = πr²h/3 + lbh

V = (3.14 x 3 x 3 x 8)/3 + (9 x 9 x 1)

V = 156.36 cubic inches

Therefore, the volume of the given 3 - D figure is 156.36 cubic inches.

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According to the information, the number sequences would go as follows: arithmetic: 1, 9, 17, 25, 33...; 83, 84, 85, 86, 87... Geometric: 6, 24, 96, 384, 1536...; 1, 6, 36, 216, 1296...; 7, 14, 28, 56, 112...; neither: 4, 9, 16, 25, 36...; 1, 1, 2, 3, 5, 8, 13,...

To identify the sequences that belong to each category, we must take into account the difference between a geometric sequence and an arithmetic sequence. In the case of geometric sequences, they are those sequences made up of numbers that are the result of multiplying the first number by a common factor.

On the other hand, arithmetic sequences are those that are made up of numbers that differ from the previous and the following number by a fixed amount. According to the above, the values would be classified as follows:

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Answer: B: 15,080

Step-by-step explanation:

Alright, let's convert 20% into a decimal: 0.20

Then multiply 0.20 x 75,400  which gets you to 15080

So she needed to pay $15,080 in taxes

As per the density the probability that a density measurement of the post-1982 pennies is 0.3565 g/cm3.

Density is an important physical property that can help identify materials. In this case, we are interested in the density of zinc and how it relates to the post-1982 pennies.

To calculate the probability of a density measurement within 5% of the density of zinc, we need to first determine the range of densities that fall within 5% of the zinc density.

The 5% range of the zinc density is calculated by multiplying the zinc density (7.13 g/cm3) by 5% (0.05), which gives us 0.3565 g/cm3.

The upper and lower limits of this range are then calculated by adding and subtracting this value from the zinc density, respectively.

The upper limit is 7.4865 g/cm3 (7.13 + 0.3565),

while the lower limit is 6.7735 g/cm3 (7.13 - 0.3565).

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Answer:

  36 bottles

Step-by-step explanation:

You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.

The profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.

  profit = selling price - purchase price

  profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle

To make a profit of $120, you need n bottles such that ...

  (10/3)n = 120

  n = 36 . . . . . . . . . multiply by 3/10

The club needs to buy, paint, and sell 36 bottles to raise $120.

12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.

The second smallest number that has 1,2,3,4 and 5 in them is 12354. This number is made up of the digits 1, 2, 3, 4, and 5 in that order. It is the second smallest number because the smallest number that contains these digits is 12345.

To form this number, we start by arranging the digits in descending order, from the largest to the smallest, 5, 4, 3, 2 and 1. We then combine the digits together to form 12354.

12354 is the second smallest number because it contains all the digits 1, 2, 3, 4 and 5 in that order. This number can be used in different ways, such as counting, addition, subtraction, multiplication and division. For example, 12354 divided by 4 equals 3088.75.

The number 12354 can also be used in other ways, such as to represent a date or time. For example, the number 12354 can represent the date 12/3/54, which is December 3, 1954.

In conclusion, 12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.

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a) The missing frequency is 20

b) The modal number of people in a car is 1

c) The median is 3

d) The mean is 0.95

The sum of the frequencies must be 60.

The missing frequency by subtracting the sum of the other frequencies from 60

60 - (28 + 3 + 7 + 1 + 1) = 20

To find the median, we need to arrange the data in order from smallest to largest:

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6

There are 60 numbers in total, so the median is the average of the 30th and 31st numbers:

median = (3 + 3)/2 = 3

The mode is the value with the highest frequency, which is 1.

mean = (1 x 28 + 2 x 20 + 3 x 3 + 4 x 7 + 5 x 1 + 6 x 1) / 60

= (28 + 40 + 9 + 28 + 5 + 6) / 60

= 0.95

Therefore, the missing frequency, mode, median and mean has been found

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The given question is incomplete, the complete question is

Hassan recorded the number of people in 60 passing cars

people 1 2 3 4 5 6

frequency 28 ? 3 7 1 1

a)find the missing frequency

b)median

c)modal

d)mean

In the given case where 860 observations are drawn from a bell-shaped distribution, there are 2 observations of more than 112.

Total number of observations = 860

Mean of the observations = 76

Standard deviation = 18

The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the observations utilizing the Z- score -

Z = X - u/a

Calculating the observations -

Where X = 112 u = 76 and a = 18

Z = 112 - 76/18

= 36/18

= 2

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Answer: 168 in.

Step-by-step explanation:

Feet to inches:

14ft = 168 in.

or

12 x 14 = 168.

Answer: 4 ft 3.8 inches

Step-by-step explanation:

First I converted the measurements to inches to make it easier-

Man - 74in

Tree - 240in

Tree shadow - 168in

240/168 = 74/x

x=51.8

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54    

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

A ratio can be compared by the division of two numbers. For example, the ratio of a and b can be represented as a: b and read as a is to b. Here a: b can be written as a/b

Here we have  

The ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same. The table shows the number of atoms in different quantities of sulfur dioxide.  

The given table is

Sulfur atoms         6     9     12   ___

Oxygen atoms     12    __   ___   54      

Let x, y, and z be the missing values in the table

Given that ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same.  

=> 12/6 = x/9 = y/12 = 54/z    

Now the x, y, and z values can be calculated as follows

Take 12/6 = x/9  

=> 2 = x/9    

=> x = 18  

Take 12/6 = y/12  

=> 2 = y/12

=> y = 24

Take 12/6 = 54/z  

=> 2 = 54/z

=> z = 54/2

=> z = 27    

Therefore,

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54      

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The complete Question is given in the picture

To get by what percent the second number (10) is greater than the first number (5), we can use the following formula:

percent increase = ((new value - old value) / old value) x 100%

So, for the pair of numbers 5 and 10:

percent increase = ((10 - 5) / 5) x 100% = 100%

This means that 10 is 100% greater than 5.

To determine by what percent the first number (5) is less than the second number (10), we can use the following formula:

percent decrease = ((old value - new value) / old value) x 100%

So, for the pair of numbers 5 and 10:

percent decrease = ((10 - 5) / 10) x 100% = 50%

This means that 5 is 50% less than 10.

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Answer:

AC = 16 cm

Step-by-step explanation:

given a tangent and a secant from an external point to the circle, then

the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant, that is

AB × AC = AD²

4x = 8² = 64 ( divide both sides by 4 )

x = AC = 16 cm

Answer:

16 cm

Step-by-step explanation:

tan/sec Theorem

a² = b(b+c)

8² = 4(4+c)

64 = 16 + 4c

48 = 4c

12 = c

12 + 4 = 16 cm