Amber has 36 smarties to share among herself and 3 friends. How many smarties will each of them Receive?

A linear equation in two variables of the form ax + by + c = 0, where a, b, c R, a 0, and b 0. By comparing the coefficients of the equations while taking the system of linear equations into consideration, we may determine how many solutions there are. Additionally, we can use a graphical way to determine whether the equation system has a single solution or an infinite number of solutions. This article will teach you how to determine whether a set of equations has an unlimited number of solutions or not.

No Solution or Infinitely Many Solutions to a System of Equations

Let's have a look at the pair of linear equations involving x and y.

A1x + B1y + C1 equals 0; A2x + B2Y + C2 equals 0

Here, a1, b1, c1, and a2 and b2,c2 are real.

Keep in mind that a12 + b12= 0 and a22 + b22 =0.

Case 1: There are infinitely many solutions if (a1/a2) = (b1/b2) = (c1/c2). A dependent pair of linear equations in two variables is the name given to this kind of equation. The lines will cross if we plot this equation's graph.

Case 2. There is no solution if (a1/a2) = (b1/b2) (c1/c2). An inconsistent pair of linear equations is the name given to this kind of equation. The lines on the graph will be parallel.

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Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

Answer:

\(x + {4x}^{2} \)

Step-by-step explanation:

simplify by combining like terms

4x - 3x = x

\(3x ^{2} + {x}^{2} = {4x}^{2} \)

we're left with

\(x + {4x}^{2} \)

Answer:

4x²+x

Step-by-step explanation:

4x-3x+3x²+x²

4x minus 3x is x and 3x² +x² is 4x²

therefore,

4x²+x

Answer:  =

Step-by-step explanation:

83.95% is equal to 83.95% (look at it)

Answer:

=

Step-by-step explanation:

umm 83.95 = 83.95?

Answer:

A

Step-by-step explanation:

To simplify the expression 3 11 5 ÷ 3 − 9 5, let's break it down step by step:

First, let's simplify the division 3 11 5 ÷ 3:

3 11 5 ÷ 3 = (3 × 115) ÷ 3 = 345 ÷ 3 = 115.

Next, let's subtract 9 5 from the result we obtained:

115 - 9 5 = 115 - (9 × 5) = 115 - 45 = 70.

Therefore, the simplified expression is 70.

The correct answer is A. 70.

The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of triangle ABC, hence:

18 ft² = (1/2) * 3 * h

h = 12 ft

Let x represent the height of triangle EFG, hence:

x/12 = 2/3

x = 8 feet

Area of EFG = (1/2) * 2 * 8 = 8 ft²

The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².

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Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

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Notice that

\(7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}\)

\(12=2^2\times3\), so

\(\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}\)

Then taking the positive square root gives

\(\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}\)

so \(\boxed{a=2}\) and \(\boxed{b=1006}\).

The given statement about inequality is true.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.

The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.

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Answer:

Step-by-step explanation:

The quotient log 29 can be rewritten as 1 + log 2.9.

The quotient of two numbers is the result of dividing one number by another. In mathematics, the logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication.

A logarithm is the exponent that a fixed base must be raised to produce a given number. The notation logx (read "log base x") denotes the logarithm of a number with respect to a base x.

Hence, when we say the quotient log 29, it implies that we need to determine the logarithm of 29, which we can represent as log 29, as there is no base specified. In general, we assume the base to be 10.

Now, we have:

`log 29`

To rewrite this quotient, we can consider the following steps:

Step 1: Break the number down into factors

29 is a prime number; it is not divisible by any other number except for 1 and itself. Therefore, we cannot break it down into factors.

Step 2: Find the prime factorization of the divisor

Since the divisor is not provided, we cannot perform this step.

Step 3: Apply the quotient rule of logarithms

The quotient rule of logarithms states that:

log (a / b) = log a - log b

We can use this rule to rewrite `log 29` as follows:

`log 29 = log (10 * 2.9)`

`log 29 = log 10 + log 2.9`

`log 29 = 1 + log 2.9`

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Answer: -5g + 15h - 25 = -5 × (g - h + 5)

Step-by-step explanation:

Step-by-step explanation:

first we do this  -5g = -5 × g

then 15h = 5 × 3h

so, -25 = -5 × 5

when -5g + 15h - 25 = -5 × g - (-5 × 3h) + (-5 × 5)

the answer is = -5 × (g - h + 5)

       According to the Factors of a Negative Number

First The factors of a number entail all of the numbers that can be multiplied by one another to produce that many numbers.

According to The laws of multiplication that the state when a negative number is multiplied by a positive number then also the product will be negative.

Although when the Factors are those numbers. when it is multiplied with together then the result is another number, which is known as a product.

Answer:

so here we minus 5 from 255 to get to 250 and we do it again to get to 245. for reaching the 40th term we should do it 39 times.

so, 255+ (-5) (39) = 255 - 195 = 60

which is our 40th term.

The 40th term of  (255, 250, 245...) is 60.

Calculations :

The formula to find the nth term = \(a_{n}\)  =  -5n + 260

                                                      = \(a_{40}\) x 5n = 260

                                                      = 260 - 200 = 60

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Answer:

243.75

Step-by-step explanation:

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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Answer:

1050

Step-by-step explanation:

Multiply 150 by 7

The sales tax on the Bluray disc player is $17.60.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To calculate the sales tax on the Bluray disc player, we need to add the state tax and county tax to the sale price of the player.

First, we can calculate the amount of the state tax. The state tax rate is 4%, which can be expressed as a decimal by dividing by 100:

State tax rate = 4% = 0.04

To find the amount of state tax, we can multiply the sale price by the state tax rate:

State tax = 0.04 x $219.99 = $8.80

Next, we can calculate the amount of the county tax. The county tax rate is also 4%, so we can use the same method as above to find the county tax:

County tax rate = 4% = 0.04

County tax = 0.04 x $219.99 = $8.80

Now, we can find the total sales tax by adding the state tax and county tax:

Total sales tax = State tax + County tax

= $8.80 + $8.80

= $17.60

Therefore, the sales tax on the Bluray disc player is $17.60.

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(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer:

\(A=1347.7\ cm^2\)

Step-by-step explanation:

Given that,

Radius of a cone, r = 13 cm

Slant height of the cone, l = 20 cm

We need to find the surface area of the cone. The formula for the surface area of the cone is given by :

\(A=\pi rl +\pi r^2\)

Put all the values,

\(A=\pi r(l + r)\\\\A=\pi \times 13(20 + 13)\\\\A=1347.7\ cm^2\)

So, the surface area of the cone is \(1347.7\ cm^2\).

Answer:

x ≈ 11.09

Step-by-step explanation:

Using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

Given

ln(x + 9) = 3 , that is

\(log_{e}\) (x + 9) = 3 , then

x + 9 = e³ ( subtract 9 from both sides )

x = e³ - 9 ≈ 11.09 ( to the nearest hundredth )

Answer:

B, F

Step-by-step explanation:

\(2x^2(x-4)^2=0 \\ \\ \implies x^2=0, (x-4)^2=0 \\ \\ \implies x=0,4\)

If we have:

We know that:

The value for x that satisfy this euqation is 2.51

Answer:

Step-by-step explanation:

→ y² -16y +64

→ y²-8y-8y+64

→ y(y-8) -8(y-8)

→ (y-8) (y-8)

Answer:

Length = X + 3

Step-by-step explanation:

Examples for the length width relationship would go as follows:

Width    Length

1              4

2             5

3             6

4             7

Hope this helps!

-TheBusinessMan

Answer:

Length = x + 3

Step-by-step explanation:

Width = x

Length = 3 + Width

So, Length = 3 + x

So, if Width as a number, then Length will be 3 more than that number.

Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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Answer:

quirky, attention seeker

Step-by-step explanation:

Step-by-step explanation:

if one pump = x

the other pump = 2x

therefore

x + 2x = 8 minutes

3x = 8 minutes

Divide through by 3

x = 8/3 minutes

converting it to seconds

x = 8/3 * 60

x = 160 seconds

therefore

the first pump = 2x = 2 * 160 = 320 seconds

the second pump = x = 160 seconds

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

The answer for blanks in statements are, an x-intercept of 1 , -3, x>1 , increasing , 7.5.

Many mathematical and real-world phenomena are described by functions. Modeling real-world occurrences like population increase, interest rates, or physical motion is frequently done using them. There are many distinct features that functions can have, including continuity, differentiability, and periodicity. Functions can also be linear or nonlinear.

The domain and range of functions are crucial components. The set of all potential input values makes up the domain of a function, whereas the set of all possible output values makes up the range. The behaviour of a function, such as whether it is increasing, decreasing, or constant, can also be used to categorize it. A function's graph shows the relationship between its input and output values graphically.

Function h has an x-intercept of 1 and a y-intercept of -3.  The function is positive for x>1 and increasing on all intervals of x. The average rate of change for the function on the interval [0, 2] is 7.5

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