what is the first of four consecutive numbers if their sum is 2006

The solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).

Herein we find a system formed by one linear equation and one nonlinear equation (quadratic equation). First, we equalize the two equations to eliminate the variable y:

2 · x² - 5 · x - 7 = 2 · x + 2

2 · x² - 7 · x - 9 = 0

2 · [x² - (7 / 2) · x - 9 / 2] = 0

2 · (x - 9 / 2) · (x + 1)

There are two solutions to x: x₁ = 9 / 2, x₂ = - 1. And the solutions for y are:

y₁ = 2 · (9 / 2) + 2

y₁ = 11

y₂ = 2 · (- 1) + 2

y₂ = 0

Then, the solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).

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(2,3) is a solution to the system of equations.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Consider the system of equations,

2x - 3y = - 5                                                                                 --------(1)

4x - 4y = - 4                                                                                 --------(2)

Multiplying equation (1) with 2.

4x - 6y = - 10

4x - 4y = - 4

Now, subtracting the above equations:

4x - 6y - ( 4x - 4y) = - 10 + 4

4x - 6y - 4x + 4y = - 6

- 2y = - 6

2y = 6

y = 3

Then,

4x - 4y = - 4

4x - 4 × 3 = - 4

4x - 12 = - 4

Adding 12 on both sides of the equation,

4x - 12 + 12 = - 4 + 12

4x = 8

x = ( 8/4 )

x = 2

Therefore, (x, y) = ( 2, 3) is a solution to the system of equations.

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Answer:

Yes

Step-by-step explanation:

The probability of rolling a 3 first, then an even number, is 1/12.

So, in the given situation the first roll has no effect on the second roll because they are separate events.

Because they are independent, the probabilities of the two events can be multiplied.

Now, we will multiply the two probabilities as follows:

Therefore, the probability of rolling a 3 first, followed by rolling an even number is 1/12.

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Answer:

the correct answer is O. x ≤ 1

Step-by-step explanation:

the rest are wrong because of the equal to sign in inequalities

Answer:

4736 because count add them together or do it your way

Answer: I'm pretty sure its 14.

Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14

Answer:

[tex]5^{14/5}[/tex]

Step-by-step explanation:

[tex]\frac{5^3}{5^{1/5}} \\ \\ 5^{3-\frac{1}{5}} \\ \\ =5^{14/5}[/tex]

A coefficient in the algebraic expression is: 5

The constant is: 12

A variable is: x

A term in the algebraic expression can be: 5x or 12.

An algebraic expression consist of terms, which can be:

Thus, given the algebraic expression, 5x + 12, the following parts of the algebraic expression can be identified as shown below:

A coefficient in the algebraic expression is: 5 (tis is the number multiplied by the variable x)

The constant is: 12 (this is the number standing alone)

A variable is: x (this is the alphabet in the algebraic expression)

A term in the algebraic expression can be: 5x or 12.

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Answer:

x = 36

y = 15

Step-by-step explanation:

127 - 52 = 75

75 / 5 = 15

2x + 3 = 5(15)

2x + 3 = 75

2x = 72

x = 36

Given function y =45(0.974)ˣ is a function of exponential decay and percentage rate of decrease is 2.6%.

The exponential function is an function f(x) = a(b)ˣ

a = initial amount when x= 0

b= base that is multiplied and it is greater than 0

And x is the variable in the exponent

When b> 1 , the values of this function goes up and up and then this function shows exponential growth.

When 0< b< 1, the values of this function becomes smaller as x increases then this function shows exponential decay.

And r is the percentage rate of change where b =r +1

Given function is y = f(x) = 45(0.974)ˣ

When we compare it with standard function f(x) = a(b)ˣ

we get a = 45 and b =0.974

As b is between 0 and 1 in this case, therefore this function is exponential decay.

b =r+ 1

therefore r = b-1 = 0.974-1 = -0.026

converting 0.026 to percentage we get -0.026*100= -2.6% ( negative sign shows decrease)

Therefore, we can say that the given function represents exponential decay function and rate of decrease is 2.6%

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The solution by using the quadratic formula is,

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

What is Quadratic formula?

To solve a quadratic equation ax²+ bx + c = 0 , we use the quadratic formula,

x = - b ± √b² - 4ac / 2a

The given expression is;

- 2x² + 4x = 5

Now, The given equation is solve by using Quadratic formula as;

- 2x² + 4x = 5

Move terms to the left side

- 2x² + 4x - 5 = 0

- ( 2x² - 4x + 5 ) = 0

2x² - 4x + 5 = 0

Compare with quadratic equation ax²+ bx + c = 0 we get;

a = 2, b = -4, c = 5

Since, Quadratic formula is,

x = - b ± √b² - 4ac / 2a

Hence, Substituting all the values of a, b and c in quadratic formula we get;

x = - (-4) ± √(-4)² - 4*2*5 / 2*2

x = 4 ± √16 - 40 / 4

x = 4 ± √-24 / 4

x = 4 ± 2√-6 / 4             ( Since, i = √-1  )

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

So, The solution by using the quadratic formula is,

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

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Answer:

If they all had to equal 360 when put together then the answer would be 22. If they All had to equal 180 when put together, then the answer would be 2.

Step-by-step explanation:

The directions are not quite clear but I have two answers just in case.

The journal entries to record (a) the payroll and (b) the employer's payroll tax expense for the month are as follows:

a) The payroll:

Debit Sales salaries $125,000

Debit Office salaries 35,000

Credit:

 Federal income tax withholding payable 32,300

 Medical insurance withholding payable 7,370

 Social security tax withholding payable 10,200

 Medicare tax withholding payable 2,550

 Cash $107,580

b) The employer's payroll tax expense:

Debit Payroll Tax Expense $975

Credit:

 Federal Unemployment Tax Payable $200

 State Unemployment Tax Payable $775

SUTA = 3.1% of $25,000 = $775

FUTA = 0.8% of $25,000 = $200

Sales salaries $125,000

Federal income tax withheld 32,300

Office salaries 35,000

Medical insurance withheld 7,370

Social security tax withheld 10,200

Medicare tax withheld 2,550

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The rate of change of the linear function for the given table is determined as: C. 120.

A linear relationship function is represented as a straight line graph which can be expressed as a linear equation in slope-intercept form as, y = mx + b.

The rate of change of the function is represented as m, which is also the slope of the graph, and the y-intercept is b.

A linear function has a rate of change/slope which can be found using the formula:

m = y2 - y1/x2 - x1.

Given the set of table values that represents a linear function below, we can use two pairs of values to find the rate of change as follows:

(0.5, 60) = (x1, y1)

(1.5, 180) = (x2, y2)

Plug in the values

Rate of change (m) = (180 - 60)/(1.5 - 0.5)

Rate of change (m) = (120)/(1)

Rate of change (m) = 120

Therefore, the rate of change of the linear function for the given table is determined as: C. 120.

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Answer:

3

Step-by-step explanation:

See the attached image.

Answer:

  -7 ≤ x ≤ -4

Step-by-step explanation:

You want a compound inequality that expresses the same relation as a number line graph with solid dots at -7 and -4, and shading between.

The graph shown is indicating values of x lie between -7 and -4, including those values. As an inequality, this is written ...

  -7 ≤ x ≤ -4

Check the picture below.

Answer:

In order to round 25.691 to the greatest place or the nearest whole number, first start at the last digit behind the decimal, in the case, being the 1. When it comes to things like this, if the digit is 4&under meaning its the number 4,3,2,1 or 0. If it is 5&up, that means it could be 5-9, making the digit go up (but if its 2, then the digit just goes away, you wont have to worry about that one specific number).

Next step is to round the 9 which makes the 6 go up one digit (meaning it turns into a 7). Now, when you round the seven, it will make the whole number go up one digit, but if you want to round that as well, to start, it's first rounding equaled up to 26. If you're rounding it to a whole tens number, it would be 30. I hope that this helps you understand this subject or topic much better! :3

Step-by-step explanation:

Answer:

152x-52

Step-by-step explanation:

The value of the expression after division is A = 100

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2³ ( 152 / 8 ) - 52   be equation (1)

On dividing the equation by 8 in the expression , we get

On simplifying the equation , we get

A = 8 ( 19 ) - 52

On further simplification , we get

A = 152 - 52

A = 100

Therefore , the value of A is after the division is 100

Hence , the equation is A = 100

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Answer:Average Speed = 126.6 mph

Step-by-step explanation:

Answer:

1.) 85+ (-10) = 95 is false.

2.)  5x+7 = 17 is false.

3.) -8(-2) - 7 = 14 – 5 is false.

Step-by-step explanation:

1. is false because since 85 ≠ 95, then 85 + ( - 10) = 95 is false.

2. is false because since 12 ≠ 17, then 5x + 7 = 17 is false.

3. is false because since -15 ≠ 14, then -8( - 2) - 7 = 14–5 is false.

Answer: c=√29

Step-by-step explanation:

We use Pythagoras' theorem:

[tex]c^2=5^2+2^2\\c^2=5*5+2*2\\c^2=25+4\\c^2=29\\[/tex]

Extract the square root of both parts of the equation:

[tex]\sqrt{c^2}=\sqrt{29} \\ c=\sqrt{29}[/tex]

25 percent of the original price was saved during the purchase of the futon bed

The percent of the original price that is saved can be calculated as follows

The original price is $700

The new price is $525

The first step is to calculate the percentage change

= 700-525

= 175

Therefore the percent saved can be calculated as follows

= 175/700 × 100

= 0.25 × 100

= 25

Hence 25 percent of the original price was saved

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Find the altitude of the top of the hill by adding the difference to the altitude of the check point 3:

Find the difference between the two altitudes:

You got it correct.

Answer: 4/5

Step-by-step explanation:

7/15 + 1/3

(7/15 x 1/1) (1/3 x 5/5) = ?

7/15 + 5/15 = ?

7+5/15 = 12/15

12/15 both sides divided by 3 = 4/5

therefore
7/15 + 1/3 = 4/5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{7}{15} + \dfrac{1}{3}}[/tex]

[tex]\mathsf{= \dfrac{7}{15} + \dfrac{1\times5}{3\times5}}[/tex]

[tex]\mathsf{= \dfrac{7}{15} + \dfrac{5}{15}}[/tex]

[tex]\mathsf{= \dfrac{7 + 5}{15 - 0}}[/tex]

[tex]\mathsf{= \dfrac{12}{15}}[/tex]

[tex]\mathsf{= \dfrac{12\div3}{15\div 3}}[/tex]

[tex]\mathsf{= \dfrac{4}{5}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{4}{5}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

|3.7−(−1.5)|

The initially reported temperature was 3.7 however the temperature changed to -1.5.

Answer:b B

Step-by-step explanation:or a