please help with 4(i)-4(iii). with steps please

The linear equation of the line which passes through the points (-2, -3) and (2, -1) is:

   y + 3 = 0.5 (x + 2)

What is meant by a linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is a straight line equation.

It is of the form: y = mx + c

where m = slope of the line

c = x-intercept of line.

The linear equation of a line is:

y - y₁ = m ( x - x₁)

Given two points on the line

(x₁ , y₁) = (-2, -3)

(x₂ , y₂) = (2, -1)

m = slope of line =  (y₂ - y₁) / (x₂ - x₁) = (-1 - (-3)) / (2 - (-2)) = 2/4 = 1/2

Now substituting this value in the general equation, we can write the equation as:

y - (-3) = 1/2 ( x -(-2))

y + 3 = 0.5 (x + 2)

Therefore the linear equation of the line which passes through the points (-2, -3) and (2, -1) is:

   y + 3 = 0.5 (x + 2)

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Answer:

Step-by-step explanation:

87.5% = 87.5/100 = 875/1000= 7/8

Answer:

-5.5

Step-by-step explanation:

[12*(3/(2^2))]/2-10   [Rewritten to add brackets.

Use PEDMAS to determine order of operation.

P =- parentheses first:

[12*(3/(2^2))]/2-10

[12*(3/(4))]/2-10        [squared the 2]

[12*(3/4)]/2-10          [Removed excess parentheses]

[12*(3/4)]/2-10         [Next parenthses:  12*(3/4)  Divide and Multioply]

[9]/2 - 10                   [Divide and Multiply]

4.5 - 10                     [Add/Subtract]

-5.5                          Result

Answer:

A

Step-by-step explanation:

If you look at the graph it starts at 30 and the next time it lines up on the lines is 3 up and 2 over. Therefore it is 3/2x+30

The  Commutative property Associative property Identity property  property of addition states that the way addends are grouped does not affect their sum.

The commutative property of addition states that the sum is unaffected by the order of the addends. 2+3=3+3

Changing the order of the addends has no effect on the sum, according to the associative property of addition.

(2+3)+4=2+(3+4)

Identity of addition property: Any number is equal to the sum of 0 00 and that number. For instance 0+5=5

According to the commutative property of addition, altering the order of addends has no impact on the sum. 2+3 = 3+2

as 3 rules are there only

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From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.

A function is an argument, concept, or regulation that demonstrates an association between two variables. Functions may be located throughout mathematics and are necessary for the expansion of significant linkages.

If the number of values of the variable 'y' is more than one for a given value of 'x', then it is not a function.

The table is given below.

   x         y

 - 5        20

   0        20

   5        20

  10        20

From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.

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The complete question is attached below.

The height of the building is approximately 79.22 meters, rounded to the nearest meter.

To calculate the angle of elevation, we use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle.

We know that the pole is 3.5 meters tall, and its shadow is 1.77 meters long. We can use this information to calculate the angle of elevation of the sun's rays, which is the angle formed between the horizontal line and the line of sight from the top of the pole to the sun.

In this case, the opposite side is the height of the pole (3.5 meters), and the adjacent side is the length of the shadow (1.77 meters). Therefore, we have:

tan(angle of elevation) = opposite/adjacent = 3.5/1.77

Using a calculator, we can find that the angle of elevation is approximately 63.24 degrees.

Now, we can use this angle to find out the height of the building. We know that the shadow of the building is 43.5 meters long, and we want to find its height, which is the opposite side of the right triangle formed by the angle of elevation and the length of the shadow. Therefore, we have:

tan(63.24 degrees) = opposite/43.5

Solving for the opposite, we get:

opposite = 43.5 * tan(63.24 degrees) = 79.22 meters

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Answer: -3.11111112

Step-by-step explanation:

1 and 5/9 as a decimal is 1.555555556

-1/2 as a decimal is -0.5

1.555555556 divided by -0.5 is -3.11111112

The simplified value is [tex]\frac{7a^{8}+12 }{21a^{5}}[/tex].

What is a mathematical expression?

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is [tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}[/tex].

This can be simplified by cross-multiplying and adding.

[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{5}*a^{3}+4*3}{3*7a^{5}} \\=\frac{7a^{8}+12}{21a^{5}}[/tex].

Therefore the simplified value of the given expression is :

[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{8}+12 }{21a^{5}}[/tex]

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Answer:

Step-by-step explanation:

yes because the montly rate is 6.5%

The number of ways can a train made up consisting of tank cars, box cas and flat cars is 166320

Total number of tank cars = 4

Total number of Box cars = 112

Total number of flat cars = 5

Here we have to apply the concept of combinations

Number of ways of selecting 2 tank car from 5 = [tex]4C_2[/tex]

= 4! / 2!( 4-2) !

= 6

Number of ways of selecting 5 Box cars from 12 = [tex]12C_5[/tex]

= 12! / 5!(12-5)!

= 792

Number of ways of selecting 3 flat cars from 7 = [tex]7C_3[/tex]

= 7! / 3!(7-3)!

= 35

Number of possible ways can a train be made up = 6 × 792 × 35

Multiply the numbers

= 166320

Therefore, the number of possible ways is 166320

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The given question is incomplete, the complete question is :

Freight Train CarsIn a train yard there are 4 tank cars. 12 boxcars, and 7 flatcars. How many ways can a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars?

Bin had 7.25 gallons of gas to start with using the unitary method.

Unitary method is a problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units. In this case, we will use unitary method to find the number of gallons Bin had to start with.

Firstly, we need to find the rate of gas consumption. The slope of the line, which is the change in the gas level over time, gives us this information. Since the slope is -1.25, this means Bin is losing 1.25 gallons of gas per hour.

Next, we need to find the total time Bin has been driving. From the problem, we know that after 1 hour, she had 7.25 gallons left, and after 4 hours, she had 3.5 gallons left. This means that she drove for 3 hours (4-1).

Using the unitary method, we can calculate the total amount of gas Bin had to start with. We know that she lost 1.25 gallons of gas per hour, and she drove for 3 hours. Therefore, she lost a total of 3.75 gallons of gas during the trip.

To find the initial gas level, we need to subtract the amount of gas she lost from the gas level she had at the end of the trip. This gives us:

Initial gas level = Gas level at end of trip + Gas lost during the trip

Initial gas level = 3.5 gallons + 3.75 gallons

Initial gas level = 7.25 gallons

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Complete question:

As Bin is driving her car, she notices that after 1 hour her gas tank has 7.25 gallons left and after 4 hours of driving, it has 3.5 gallons of gas left in it. The rate at which she is LOSING gas is 1.25 gallons....So, the slope is -1.25. How many gallons did she have to START?

A t-test is a statistical test used to determine if there is a significant difference between the means of two groups.

In this case, the two groups being compared are first basemen and all other players, and the variable being measured is salary. By performing a t-test, we can determine if there is a significant difference in the average salary between first basemen and all other players.

To perform a t-test, we first calculate the difference in means between the two groups and divide by the standard error of the difference. The standard error takes into account the variability in the sample and the sample size. The result is the t-statistic, which is then compared to a t-distribution with degrees of freedom equal to the sum of the degrees of freedom of the two groups minus 2. The t-distribution gives us the probability of observing a difference as large or larger than the observed difference by chance if the two groups have the same mean. This probability is known as the p-value.

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Answer: 147m

Step-by-step explanation: the tower's height can be calculated using the following equation: height = (shadow length/pole shadow length) * pole height Therefore, the tower's height is: height = (45.5/1.01) * 2.8 height = 146.5 m The tower's height is approximately 147 m, rounded to the nearest meter

One box of dog food costs $7, while one can of cat food costs $8.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It illustrates that the expressions printed on the left and right sides have an equal relationship.

Some of the components of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. When expressing an equation, the "=" symbol and terms on both sides are a need.

Given data ,

Let the price of a single box of dog food at  x.

Let's say the price of one can of cat food is y.

The cost of 1 box of dog food and 2 cans of cat food is  = $ 23

One can of cat food and two boxes of dog food cost $22, total.

So , the equation will be

1x + 2y = 23                                 ....... (1)

2x + 1y = 22                                  ....... (2)

Equation (1) is multiplied by 2 to get

2x + 4y = 46                                ....... (3)

When equation (2) is subtracted from equation (3), we obtain

3y = 24

value of y is obtained by dividing both sides by 3,

y = $ 8

Equation (1) can be solved by substituting the value of y.

x + [tex]2*8[/tex] = 23

x + 16 = 23

16 is subtracted from both sides, giving us

x = $ 7

Therefore , the value of x is $ 7 and value of y is $ 8

Thus, one package of dog food costs $7, while one can of cat food costs $8.

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Answer:

B. 5/22

----------------------

Total number of students is:

Probability of a first girl is 6 of 12:

Probability of a second girl is 5 of 11 since both numbers reduced by one:

Probability of the two events is:

Correct choice is B.

Each of the quadratic function should be factorized as follows;

x² - 6x + 8 ⇒ (x - 4)(x - 2).

x² - 4x - 32 ⇒ (x - 8)(x + 4).

x² + x - 42 ⇒ (x - 6)(x + 7).

In Mathematics, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Next, we would solve each of the quadratic function by using the factorization method as follows;

x² - 6x + 8 = 0

x² - 4x - 2x + 8 = 0

x(x - 4) - 2(x - 4) = 0

(x - 4)(x - 2) = 0

x² - 4x - 32 = 0

x² - 8x + 4x - 32 = 0

x(x - 8) + 4(x - 8) = 0

(x - 8)(x + 4) = 0

x² + x - 42 = 0

x² - 6x + 7x - 42 = 0

x(x - 6) + 7(x - 6) = 0

(x - 6)(x + 7) = 0

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The value of the unknown side length, BC, in given diagram is 28.3 ft

From the question, we are to determine the value of the unknown side length in the given diagram

By similar triangles theorem, we can write that

AX/XY = AB/BC

From the given information,

AX = 12ft

XY = 17 ft

AB = AX + XB

= 12 ft + 8 ft

= 20 ft

BC = ?

Then, we can write that

12/17 = 20/BC

Cross multiply

12 × BC = 17 × 20

12 × BC = 340

BC = 340/12

BC = 28.3

Hence, the value of BC is 28.3 ft

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The cumulative relative frequency distribution is a useful tool for summarizing data and making comparisons between classes. It can also be used to make predictions about future data values.

A cumulative relative frequency distribution is a table that shows the cumulative relative frequency of a set of data. A cumulative relative frequency is the sum of all relative frequencies up to a certain point in the data set. For example, if the first three entries in a data set are 20, 30, and 10, the cumulative relative frequency of the first entry would be 0.2, the cumulative relative frequency of the second entry would be 0.5, and the cumulative relative frequency of the third entry would be 1.0.

In a cumulative relative frequency distribution, the data is organized into classes, and each class has a relative frequency associated with it. The relative frequency is the fraction of the total number of items in the class compared to the total number of items in the data set. The cumulative relative frequency is the sum of the relative frequencies of all the classes up to that point.

For example, if there are five classes in a data set, the cumulative relative frequency of the first class would be the relative frequency of the first class. The cumulative relative frequency of the second class would be the sum of the relative frequencies of the first and second classes, and so on.

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Answer:

y=7x-8

Step-by-step explanation:

You start off with the equation y= mx+b, where m = the slope (7/1) and b, which is (0,-8). Then you can graph. You first put a dot at (0,-8). Then you count up to 7 and then go to the right 1. You continue the pattern until the line is over the graph. The equation would be y= 7x-8

With the given compound interests, Investment B results in greatest total amount.

What exactly is compound interest?

Compound interest is interest charged on a loan or deposit. It is the most widely utilised idea in our everyday lives. The compound interest for an amount is determined by both the principal and the interest earned over time. This is the primary distinction between compound and simple interest.

Compound interest calculation formula:

A=P(1+r/n)ⁿˣ

Where,

A Equals Amount

P stands for principal.

r = interest rate

n is the number of times interest is compounded each year.

x = time (in years)

Alternatively, the formula may be written as follows:

CI = A – P

Where CI stands for Compound Interest.

Now,

For A

principal = $3000, Rate = 7% compounded semiannualy and time = 7 years

amount=3000(1+7/200)¹⁴

A=3000*1.61

=$4856

For B

 principal = $5000, Rate = 3.2% compounded quaterly and time = 4 years

amount = 5000(1+3.2/400)¹⁶

A=5000*1.13

=$5680

hence,

           Investment B results in greatest total amount.

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The greatest number of autographs that Noelle can own is given as follows:

61 autographs.

The greatest number of of autographs that Noelle can own is 61 autographs, as we would have that:

Owning 62 autographs, the first two statements would be true, which is not possible, as exactly one of the statements is true.

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The required it would cost $12.45 to buy 3 pounds of turkey and 1 1/2 pounds of coleslaw.

The expression model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
To calculate the cost of the turkey, we need to find the price per pound and then multiply it by the number of pounds. The price per pound is,

= $3.50 ÷ (1 1/4 pounds)
= $2.80 per pound

To find the cost of 3 pounds of turkey, we can multiply the price per pound by the number of pounds:

= 3 pounds × $2.80 per pound = $8.40

To find the cost of the coleslaw, we can simply multiply the price per half pound by the number of half pounds,

1 1/2 pounds = 3 half pounds

= 3 half pounds × $1.35 per half pound
= $4.05

Finally, we can add the cost of the turkey and the coleslaw to find the total cost:

$8.40 + $4.05 = $12.45

Therefore, it would cost $12.45 to buy 3 pounds of turkey and 1 1/2 pounds of coleslaw.

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The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.  

The exponential function is a type of mathematical equation that can be used to determine if anything is increasing or decreasing exponentially, such as population, money, or price.

The general form of an exponential function is given by

           f(x) = abˣ   or y = abˣ

Where 'x' is a variable and a and b are constants

Here we have

The graph shows the number of games system sold since 2005.

As we know an exponential function is represented as:  

=> y = abˣ

From the given graph x = 0 and y = 30.5

=> 30.5 = ab⁰  

=> 30.5 = a(1)

=> a = 30.5  

When x = 1, y = 21.35

=> 21.35 = (30.5)(b¹)  

=> b = 0.7

So the required exponential function can be written as

=> y = (30.5)(0.7)ˣ    

Therefore,

The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.    

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For the given system of equations, no solution is possible.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

The system of equations,

-18x + 2y = 8  {equation 1}

y = 9x + 4   {equation 2}

Substitute the value of y from equation 2 to equation 1,

we get,

-18x + 18x + 8 = 8

0 = 0

That means, the lines of the equation are parallel to each other.

Therefore, no solution is possible for the system.

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The variables representing the total cost of the items bought are x and y.

Where X is the total cost of the items bought during the first trip and Y is the total cost of the items bought during the second trip.

Items bought on the first trip:

Boards = 15

Boxes of nails = 3

Total cost = x

Items bought on the second trip:

Boards = 9

Boxes of nails = 1

Total cost = y

Let a piece of board = b

Let a box of nails = n

Let the total cost for the first trip = x

Let the total cost for the second trip = y

x = 15b + 3n

y = 9b + n