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Using substitution method, the best initial step in solving the equation is solve the first equation for x.

The equation can be solved by substitution method as follows:

2x + 3y = -12

6x + y = 18

Hence, let's make y the subject of the formula in equation(ii)

6x + y = 18

y = -6x + 18

We have to substitute the value of y in equation(i)

2x + 3y = -12

2x + 3(-6x + 18) = -12

2x - 18x + 54 = -12

- 16x + 54 = -12

-16x = - 12 - 54

- 16x = -66

x = 66 / 16

x = 33 / 8

Therefore,

6(33 / 8) + y = 18

99 / 4 + y = 18

y = 18 - 99 / 4

y = - 27 / 4

From the solving above the best step to solve the equation is solving the first equation for x.

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Answer: [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]

Step-by-step explanation:

Using the vertex form, the equation is

[tex]y=a \left(x-\frac{1}{2} \right)^2 +1[/tex]

Substituting in the coordinates (2, -8) to solve for a,

[tex]-8=a \left(2-\frac{1}{2} \right)^2 +1\\\\-8=\frac{9}{4}a+1\\\\-9=\frac{9}{4}a\\\\a=-4[/tex]

So, the equation is [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]

The total cost of the hire purchase for the bicycle is  $19,145.

The difference between the hire purchase price and the cost price for the bicycle is  $2,825.50

The difference as a percentage of cash price 17.31%.

The total cost of the hire purchase is the sum of the deposit and the total monthly instalment.

Total cost of the hire purchase = amount deposited + total instalment paid

Total instalment paid = number of month x payment per month

$1224.50 x 10 = $12,245

Total cost of the hire purchase = $6,900 +  $12,245 = $19,145

The difference = cost of hire purchase + cash price

$19,145 - $16 319.50 = $2,825.50

The difference as a percentage of cash price = (2,825.50 / $16,319.50) x 100 = 17.31%

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The advantages may be of using the method of completing the square to solve quadratic equations to estimate the values of x and y roots without calculating them.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Using Completing the square.

1. First of all we can find the minimum or maximum of the equation immediately.

2. Second is to cuts out the need to use the given ones (a, b, c) in the quadratic formula.

3. It allows estimating the values of x and y roots without calculating them.

Then Estimating on a test is a very valuable asset.

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The law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.

Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.

It is given that:

The statement is:

If you have a cat, then it will chase mice.

As we know, from the definition of the Law of Syllogism, the legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.

Your cat will chase mice.

The Law of syllogism makes this argument true.

Thus, the law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.

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Answer:46

Step-by-step explanation:

Answer:

  C) no: The packs of socks are marked up to $7 and then discounted to $4.20

Step-by-step explanation:

You want to know the price of a $5 pair of socks after markup by 40%, and again after that price is marked down 40%.

When the $5 cost is marked up by 40%, the resulting price is ...

  $5 + 0.40×5 = $5 +2 = $7.

The socks are marked up to $7.

When the $7 price is marked down by 40%, the resulting price is ...

  $7 - 0.40×7 = $7.00 -2.80 = $4.20

The socks are discounted to $4.20.

The example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because it will not occur.

The probability is the branch of mathematics that shows the occurrence of the random event. The value of the probability varies from 0 to 1.

The equation of the probability is

Probability = Number of favorable outcomes / Total number of outcomes

The probability of getting number number 7 when you throw a die once is zero. Because when you throw a die the possible outcomes are 1, 2, 3, 4, 5 and 6. We wont get number 7. Therefore the probability is zero

Hence, the example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because  it will not occur.

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Answer:4

Step-by-step explanation:

Answer:a) Given :

51 pounds of seed  can be planted in = 9 acre field.

Per pound of seed =

We can convert 9/51 in simplest fraction by dividing top and bottom by 3.

We get

Therefore, 3/17 of an acrs can be planted per pound of seed.

b) $10 amount = 16 pounds of sugar.

$1 amount = 16/10 = 1.6 pounds of sugar.

Therefore, 1.6 pounds of sugar she got per dollar.

Step-by-step explanation:

Answer:

6/3=2

30/10=3

Step-by-step explanation:

For simple division like this, you can look and see how many times 3 can go into 6, and 10 into 30.

Answer:

slope of 1/2

Step-by-step explanation:

x-2y=-18

First, get the equation in slope intercept form

y = mx+b  where m is the slope and b is the y-intercept

-2y = -x -18

Divide each side by -2

y = 1/2 x + 9

The slope is 1/2

Parallel lines have the same slope, so lines that are parallel will have a slope of 1/2

For the function f(x) =[tex]\sqrt{8x+10}[/tex] the inverse function [tex]f^{-1}[/tex](x) = [tex]\frac{x^2-10}{8}[/tex] x≥ 0 as can be calculated through the inverse function's formula.

In mathematics, any kind of inverse is a function that serves to “undo” any other function. That is, if f(x) produces y, then while putting y into the inverse off it produces the output x.

To find the inverse of a function, write the function y as a function of x i.e., y = f(x) and then solve for x as a function of y.

Inverse operations are seen as opposite operations that provides undo to each other. For example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse operations.

Every one-to-one function f has an inverse; this inverse is denoted by f−1 and read aloud as 'f inverse'. A function and its inverse 'undo' each other: one function does something, the other undoes it.

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The three relations given all represent functions because each has exactly one y-value that corresponds to each x-value.

A relation can be defined as a function if the x-values (input/domain element) each has exactly one y-value (output value/range element) that is related to or it corresponds to.

A function can have two x-values that have the same y-value but cannot have two y-values that corresponds to one x-value.

In the first relation showing a graph, each x-value on the graph has exactly one y-value it corresponds to. Therefore, it is a function.

In the second relation that is represented by the set of ordered pairs, every x-value also have only one y-value it is related to. Therefore, it represents a function.

The third function given shows a table of values of a relation that has exactly only one y-value that is assigned or related to each x-value. This also is a relation that represents a function.

Therefore, all three relations represent functions.

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48×35. By using standard algorithm we got 1680.

Given that,

48×35

We have to find the multiplication of the numbers by standard algorithm.

Standard algorithm is nothing but the words "Standard" and "Algorithm" make up the standard algorithm. Standard refers to the standard or standard way of doing anything, such as eating, bathing, or brushing one's teeth. Algorithms are nothing more than a task's sequential execution. As a result, solving a problem step by step is a common algorithm in mathematics. You will discover what a standard algorithm is in this article, along with the addition, subtraction, multiplication, and division standard algorithms.

If you don't use the standard algorithm , your answers will be incorrect.

48×35=1680

Therefore, By using standard algorithm we got 1680.

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The last month's payment for White family can be algebraically expressed as;

⇒ 2665 - d - 11m.

What is an expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

Cost of a new pool table = $2,665

Down payment = d dollars

And, The monthly payment = m dollars.

Since, we have to given a duration of twelve months, we will have to subtract one month from 12 to give, 11 months.

Hence, We can formulate an algebraic equation as;

2665 - d - 11m.

Thus, The last month's payment for White family can be algebraically expressed as;

⇒ 2665 - d - 11m.

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The side of square is 216 units and side of cube is 36 units.

According to question we have given that Sally has a cube of some length in units. Let the length of side of cube is S units .

As we know , Area of cube = 6 (side)²= 6S² square units.

Volume of cube = (side)³ = S³ cubic units

Then, as given area in square units of cube = 1/6 of volume of cube in cubic units . That is 6S²= 1/6 S³ => S = 36 units

Area of cube with side 36 units = 6×36²=46656 square units

Volume of cube with side 36 units = 36 ³ cubic units

So, the side of cube is 36 units.

Also, the number of square units in area of Square = number of cubic units in volume of cube

Area of square (S²) = 46656

Side of square = sqrt (46656 ) = 216 units

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Answer:

it would be 11^8

Step-by-step explanation:

i dont see this as an option but i believe that there was a mistake i dont believe that any of theese are correct

Total outcome is 50 [because the number produced by the machine is from 1 to 50]

Question a:

Multiple of 10 are 10, 20, 30, 40, 50

There are five possible outcomes for multiple of 10

P(Multiple of 10) = 5/50 = 1/10

Question b:

Number 1 to 50 will be all the outcomes that are not 100

There are 50 possible outcomes

P(not 100) = 50/50 = 1

Question c:

Multiple of 4 that are less than 50 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

There  are 12 possible outcomes for multiple of 4

We want 'not multiple of 4' so we need to do 50 - 12 = 38 outcomes

P(not a multiple of 4) = 38/50 = 19/25

Question d:

One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9

There are 9 possible outcomes

P(one-digit number) = 9/50

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Answer:

64°

Step-by-step explanation:

it's a right angle (90°) so u take away the other angle (26°) which gets you 64°

ANSWER

EXPLANATION

Given;

c) Hence;

In decimal form;

d)

Answer:

1.01

Step-by-step explanation:

14.14/14

14/14=1

0.14/14=0.01

1+0.01=1.01

Answer:

y = 4x+2

Step-by-step explanation:

To find an equation that runs through (-4,1) and (4,3) first find the difference between the two y numbers and x number to find the slope. between the two y numbers you go left or right 8 units, and difference between the two x numbers, which is 2. making the slope 4. looking at a graph and marking the two points, draw a line connecting the two given points, find the y intercept. the y intercept is at coordinates (0, 2) making the y intercept 2. making that into an equation is y = 4x + 2

Answer:

0.875 inches

Step-by-step explanation:

Pretty easy. Just divide how many inches thick the boards are by how many there are: inches-thick/amount

Now substitute 10.5/12 and find your answer

0.875 inches thick per board

The correct option D) Add 48 to 52 is the conjecture that describes for the  7th term in the sequence.

For the given question, the sequence is given as;

4, 20, 36, 52,

Where, the first term a₁ is 4.

Second term a₂ is 20 and,

Third term a₃ is 36

Common difference d for each case is;

d = a₂ - a₁

d = 20 - 4 = 16

d = a₃ - a₂

d = 36 - 20 = 16

as, common difference is same, the sequence is said to be in AP.

Then, the formula for finding the 7th term is -

a₇ = a₁ + 6d

a₇ = 4 + 6×16

a₇ = 100

Now, this 7th term from the options can be found as;

Add 48 to 52 = 100.

Thus, the conjecture that describes for the 7th term in the sequence is add 48 to 52.

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one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. then the probability of all 5 questions prepared for appears is 2

Recall : nCr = n! ÷ (n-r)!r!

The total possible outcome ; 5 questions out of 10

10C5 = 10! ÷ 5!5! = (10*9*8*7*6)÷(5*4*3*2*1) = 252

Required outcome :

All 5 questions set being from the 9 questions covered and 0 from the 1

left uncovered

9C5 * 1C0

9C5 = 9! ÷ 4!5! = (9*8*7*6) ÷ (4*3*2*1) = 126

1C0 = 1! ÷ 1!0! = 1

Probability = required outcome / Total possible outcomes

P(All 5 questions prepared for appears) :

[9C5 * 1C0] ÷ 10C5

(126 * 1) / 252

= 126/ 252

=2

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3:5 is equivalent to Aiyana’s ratio

Since 3 and 5 are both prime numbers, you must multiply them by the same number (or any other integer) in order to have a ratio that is the same as Aiyana's. Ex 3:5=6:10=9:15 etc. The three ratios are identical.

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

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Answer:

s:[-2,-3] is the answer

The set S:{ - 2 , - 3 } will make the inequality 2p - 8 < 5p + 4 true

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

The set S : { - 2 , - 3 , - 4 , - 5 }

The inequality relation is 2p - 8 < 5p + 4

Now , substituting the value from set S in the inequality , we get

When p = - 2 :

2p − 8 < 5p + 4

2(-2) − 8 < 5(-2) + 4

-4 − 8 < -10 + 4

-12 < -6  TRUE

When p = - 3

2p − 8 < 5p + 4

2(-3) − 8 < 5(-3) + 4

-6 − 8 < -15 + 4

-14 < -11  TRUE

When p = - 4

2p − 8 < 5p + 4

2(-4) − 8 < 5(-4) + 4

-8 − 8 < -20 + 4

-16 < -16  FALSE

When p = - 5

2p − 8 < 5p + 4

2(-5) − 8 < 5(-5) + 4

-10 − 8 < -25 + 4

-18 < -21  FALSE

Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation

Hence , the set S:{ -2,-3 } is the solution

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[tex]\sqrt[3]{27x^6y^4}\implies \sqrt[3]{3^3 (x^2)^3 y^3 y^1}\implies 3x^2 y\sqrt[3]{y}[/tex]