Dimitri determined that the ordered pair (2, –2) is a solution to the system of linear equations 7x + 9y = –4 and 5x – 2y = 6 as shown. Equation 1: 7 x + 9 y = negative 4. 7 (2) + 9 (negative 2) = negative 4. 14 + (negative 18) = negative 4. Negative 4 = negative 4. Equation 2: 5 x minus 2 y = 6. 5 (2) minus 2 (negative 2) = 6. 10 minus 4 = 6. 6 = 6. What was Dimitri’s mistake? He mixed up the coordinates of the ordered pair when substituting it into the equations 7x + 9y = –4 and 5x – 2y = 6. He checked the equation 7x + 9y = –4 first when he should have checked 5 x minus 2 y = 6 first. He made a mistake in his calculations when substituting the ordered pair into the equation 7x + 9y = –4 and simplifying. He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.

The value of function f (x) at x = 3 is,

⇒ f (3) = - 22

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = - 2x² - 4

Now, Put x = 3 in above function we get;

⇒ f (x) = - 2x² - 4

Put x = 3;

⇒ f (3) = - 2 (3)² - 4

⇒ f (3) = - 2 x 9 - 4

⇒ f (3) = - 18 - 4

⇒ f (3) = - 22

Thus, The value of function f (x) at x = 3 is,

⇒ f (3) = - 22

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Answer:

When new, the scooter cost $900

Step-by-step explanation:

The complete question in the attached figure

we have

[tex]A(t)=900(0.85)^t[/tex]

This is a exponential function of the form

[tex]A(t)=a(b)^t[/tex]

where

A(t) ----> represent the value of a motor scooter

t ----> the number of years after it was purchased

a ---> represent the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

b=(1+r)

In this problem we have

[tex]a=\$900\\b=0.85[/tex]

The base b is less than 1

That means ----> is a exponential decay function (is a decreasing function)

Find the percent rate of change

[tex]b=(1+r)\\0.85=1+r\\r=0.85-1\\r=-0.15[/tex]

Convert to percentage (multiply by 100)

[tex]r=-15\%[/tex] ---> negative means is a decreasing function

Verify each statements

case A) When new, the scooter cost $765.

The statement is false

Because the original value of the scooter was $900

case B) When new, the scooter cost $900

The statement is true (see the explanation)

case C) The scooter’s value is decreasing at a rate of 85%  each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15%  each year (see the explanation)

case D) The scooter’s value is decreasing at a rate of  0.15% each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15%  each year (see the explanation)

Answer:

Step-by-step explanation:

(14)

Given :

y = [tex]\frac{1}{2}[/tex][tex](x-3)^{2}[/tex] - 6

comparing with the standard form :

y = a[tex](x-h)^{2}[/tex] + k

vertex = ( h , k )

Focus = (h , k+14a )

Directrix = y = k

comparing the equation and the standard form ;

Vertex = ( 3 , -6 )

Focus = ( 3 , -6+14{1/2} )

Focus = ( 3 , 1)

Directrix ⇒ y = -6

(19)

[tex]x^{2}[/tex] + [tex]4y^{2}[/tex] = 13 .............. equation 1

[tex]x^{2}[/tex] - [tex]4y^{2}[/tex] = 5  ..................... equation 2

add equation 1 and 2

2[tex]x^{2}[/tex] = 18

divide through by 2

[tex]x^{2}[/tex] = 9

x = ±3

substitute x = 3 into equation 1

[tex]3^{2}[/tex] + 4[tex]y^{2}[/tex] = 13

9 +4[tex]y^{2}[/tex] = 13

4[tex]y^{2}[/tex] = 13 - 9

4[tex]y^{2}[/tex] = 4

[tex]y^{2}[/tex] = 1

y = ±1

Therefore , the solution is ( 3 , 1 ) or (-3 , -1 )

Answer:

  14) vertex: (3, -6); focus: (3, -5.5); directrix: y = -6.5

  17) see below for a graph

  19) (±3, ±1) — four points

  20) see below for the work

Step-by-step explanation:

14) The vertex form of a quadratic equation can be written as ...

  [tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex]

This parabola will have its vertex at (h, k), its focus at (h, k+p), and its directrix at y=k-p.

The given equation is ...

  y = 1/2(x -3)² -6

Comparing this to the form above, we see that ...

  4p = 2, h = 3, k = -6

From this, we can find the value of p to be ...

  p = 2/4 = 1/2 . . . . divide the above equation by 4

Now, we know the parameters of the parabola are ...

_____

17) The equation of the parabola is given as ...

  y = 1/4(x -1)² +5

Comparing the given equation to the form shown in the above problem, we see that ...

So the parameters of the parabola are ...

The graph is shown below.

_____

20) It is convenient to show the solution steps before showing the solution. Hence we show problem 20 (steps) before problem 19 (solution).

The given system of equations is ...

The two equations can be added to give ...

  (x² +4y²) +(x² -4y²) = (13) +(5)

  2x² = 18 . . . . . . eliminate parentheses, collect terms

  x² = 9 . . . . . . . . divide by 2

  x = ±3 . . . . . . . . take the square root

__

The second equation can be subtracted from the first to give ...

  (x² +4y²) -(x² -4y²) = (13) -(5)

  8y² = 8 . . . . . . . eliminate parentheses, collect terms

  y² = 1 . . . . . . . . . divide by 8

  y = ±1 . . . . . . . . . take the square root

_____

19) Based on the above, the four solutions to the given system of equations are ...

  (3, 1), (3, -1), (-3, 1), (-3, -1)

__

A graph is shown in the second attachment.

There are 2100 cups in the package.

Step-by-step explanation:

Given,

Number of green cups in package = 630

This represent 30% of the total package.

Let,

x represent the total number of cups in package.

30% of x = 630

[tex]\frac{30}{100}*x=630\\0.30x=630[/tex]

Dividing both sides by 0.30

[tex]\frac{0.30x}{0.30}=\frac{630}{0.30}\\x=2100[/tex]

There are 2100 cups in the package.

Keywords: percentage, division

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Final answer:

Each carrot cost $2.10, found by dividing the total cost of $10.50 by the number of carrots, which is 5.

Explanation:

The student’s question relates to the basic concept of unit price in mathematics. Joe bought 5 carrots for a total of $10.50. To find out how much each carrot cost, we divide the total cost by the number of carrots.

Here’s the calculation step-by-step:

Determine the total cost of the carrots, which is $10.50.

Determine the number of carrots bought, which is 5 carrots.

Divide the total cost by the number of carrots: $10.50 / 5 = $2.10.

So, each carrot costs $2.10 when expressed as a decimal to the nearest hundredth.

Answer:

q = 177/13

Step-by-step explanation:

3q - 16q = 7 + 2(-89 – 3)

-13q = 7 + 2(-92)

-13q = 7 - 184

-13q = -177

q = (-177)/(-13)

q = 177/13

Answer:

720°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 ( number of sides of a hexagon ), thus

sum = 180° × 4 = 720°

The sum of the measures of the interior angles of a hexagon is [tex]720^{\circ}[/tex]

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain. The bounded plane region, the bounding circuit, or the two together, may be called a polygon. A hexagon is a six-sided polygon or [tex]6-[/tex]gon. Interior angles are those that lie inside a polygon.

The total of the internal angles of any simple hexagon is [tex]\boldsymbol{720^{\circ}}[/tex]

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1. Geometric Sequence

2. [tex]a_n = a_{n-1} * 3[/tex]

3. [tex]a_n = 6 * (3)^{n-1}[/tex]

Step-by-step explanation:

Given sequence is:

6, 18, 54, 162,....

Here

[tex]a_1 =6\\a_2 = 18\\a_3 = 54[/tex]

(a) Is this an arithmetic or geometric sequence?

We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.

We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r

[tex]r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3[/tex]

As the common ratio is same, the given sequence is a geometric sequence.

(b) How can you find the next number in the sequence?

Recursive formulas are used to find the next number in sequence using previous term

Recursive formula for a geometric sequence is given by:

[tex]a_n = a_{n-1} * r[/tex]

In case of given sequence,

[tex]a_n = a_{n-1} * 3[/tex]

So to find the 5th term

[tex]a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486[/tex]

(c) Give the rule you would use to find the 20th week.

In order to find the pushups for 20th week, explicit formul for sequence will be used.

The general form of explicit formula is given by:

[tex]a_n = a_1 * r^{n-1}[/tex]

Putting the values of a_1 and r

[tex]a_n = 6 * (3)^{n-1}[/tex]

Hence,

1. Geometric Sequence

2. [tex]a_n = a_{n-1} * 3[/tex]

3. [tex]a_n = 6 * (3)^{n-1}[/tex]

Keywords: Geometric sequence, common ratio

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Answer:

I believe that it would just be 20% of the $45 which would mean that you would have to pay $36 a month.

Hope this is helpful!

The cost to you per month, after the landlord's contribution, is $36.

If you buy both Liability and Contents insurance, and take advantage of the landlord's offer to pay 20% of the cost, the cost to you per month can be calculated as follows:

Let's assume the cost of Liability insurance is represented by 'L' and the cost of Contents insurance is represented by 'C'.

According to the information given, if you buy both insurances at the same time, the cost is $45 per month.

This means: L + C = $45

The landlord is willing to pay 20% of the cost, which is equal to 20% of ($45). To calculate this amount:

20% of $45 = (20/100) x $45 = $9

So, the landlord will pay $9 towards the cost of both insurances.

Now, if you subtract the landlord's contribution from the total cost, you'll get the amount you have to pay:

(L + C) - $9 = $45 - $9 = $36

Therefore, the cost to you per month, after the landlord's contribution, is $36.

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Answer:

the answer is 4x-3

Step-by-step explanation:

To simplify the expression 3x + 4(x - 6) - 3(x - 7), distribute the multiplication across the parentheses, combine like terms, and simplify to get the final result: 4x - 3.

To simplify the expression 3x + 4(x - 6) - 3(x - 7), follow these steps:

Distribute the 4 into the second parenthesis: 4  imes x - 4  imes 6 which gives 4x - 24.

Distribute the -3 into the third parenthesis: -3  imes x + (-3)  imes (-7) which gives -3x + 21.

Combine like terms with the rest of the expression: 3x + (4x - 24) + (-3x + 21).

Add/subtract the x terms and constant terms: 3x + 4x - 3x (which simplifies to 4x) and -24 + 21 (which simplifies to -3).

The simplified form of the expression is 4x - 3.

Answer:

Step-by-step explanation:

|x-4|<13.

The above equation means, whatever the actual value of x is, the value of (x - 4) must be greater than - 13 and less than 13.

Hence, -13 < x - 4 < 13 or, -9 < x < 17. The value of x will be in between -9 and 17. The value of x can not be -9 or 17.

Answer: time = 3.15 hrs

Step-by-step explanation:

distance = 63km

speed = 20km/hr

time = ?

speed = distance / time

therefore :

time = distance / speed

time = 63/20

time = 3.15 hours

Answer: 3 for whole numbers, but if you want to be exact, 3 and 3/20 (three and three twentieths)

Step-by-step explanation:

20 times 3 is 60, and there is 3 left so you would make it a fraction since it won't divide into 20.

Answer:

Cash assets is the answer

Answer:

the slope is 4/5

Step-by-step explanation:

because i learn that

Answer:

12

Step-by-step explanation:

4(2+1)

4*3

12

Answer:

substitute n in bigger equation with 2.

4(2+1)

4×3=12

Well, what is the story?

sure, what. you will have to do is to fomulate the links between the human brain and what a computer does, i prefer a mind map, then find the common procedures and use it in your answer

Answer:

54.

Step-by-step explanation:

Start at 60 and subtract 6. That leaves you with 54.

The 60th term in the arithmetic sequence -6, -3, 0, 3, ... can be determined using the formula of an arithmetic sequence, which results in a value of 171.

An arithmetic sequence, also known as an , is a sequence of numbers in which each term is obtained by adding a fixed constant to the previous term. In simpler terms, it's a sequence where the difference between any two consecutive terms is always the same.

The given sequence is an arithmetic progression where each term differs from the previous term by a constant value. In this case, the common difference[tex](\(d\))[/tex]between consecutive terms is 3.

To find the 60th term of this sequence, we can use the formula for the nth term of an arithmetic sequence:

[tex]\[a_n = a_1 + (n - 1) \cdot d\][/tex]

Here,[tex]\(a_n\)[/tex]represents the nth term, \(a_1\) is the first term, \(n\) is the term number we want to find, and \(d\) is the common difference.

In this sequence:

- The first term [tex](\(a_1\)) is -6.[/tex]

- The common difference [tex](\(d\)) is 3.[/tex]

- We want to find the 60th term, so [tex]\(n = 60\).\\[/tex]

Now, we can substitute these values into the formula:

[tex]\[a_{60} = -6 + (60 - 1) \cdot 3\][/tex]

[tex]\[a_{60} = -6 + 59 \cdot 3\][/tex]

[tex]\[a_{60} = -6 + 177\][/tex]

[tex]\[a_{60} = 171\][/tex]

Therefore, the 60th term in this arithmetic sequence is 171. This means that if you continued the sequence, the 60th term would be 171 units greater than the first term (-6), following the pattern of adding 3 at each step.

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Answer:

Are you VSCO??

Step-by-step explanation:

The greatest common factor is simply which factors of each number are shared between them. Factors are numbers that multiply together to get a certain number.

For example, a) 2x, 4

The factors of 2x are 2 and x

The factors of 4 are 2 and 2

The factors that are shared between them is 2, so the greatest common factor is 2 in this case.

For 2x^2, 4x it's easier to write it out:

The factors of 2x^2 are 2, x, x

The factors of 4x are 2, 2, x

Because they both have 2 and x, the greatest common factor is 2x in this case.

Answer:

The number of viruses was 2 times greater than bacteria.

Step-by-step explanation:

The number of viruses was [tex]2*10^9[/tex], and the number of bacteria was [tex]1*10^9[/tex].

To find how many times was the virus number greater than the bacteria number, we just divide the virus number by bacteria number:

[tex]\frac{ virus\:number }{bacteria\:number} =\frac{2*10^9 }{1*10^9} = 2*\frac{10^9}{10^9} =2[/tex]

Viruses are 2 times greater.

Answer:

Viruses are 2 times of the bacteria.

Step-by-step explanation:

Given:

Number of viruses = [tex]2\times 10^9[/tex]

Number of bacteria = [tex]1\times 10^9[/tex]

We have to found how many times viruses are greater than the bacteria.

To find how many times,we can divide both the numbers to compare its values.

Lets

Numerator = Number of viruses

Denominator = Number of bacteria

Dividing both we have,

⇒ [tex]\frac{2\times 10^9}{1\times 10^9}[/tex]

⇒ [tex]2\times 10^(^9^-^9)[/tex] ...[tex]\frac{ab^x}{cb^y}=\frac{ab^x^-^y}{c}[/tex]

⇒ [tex]2\times 10^0[/tex]       ...[tex]a^0=1[/tex]

⇒ [tex]2[/tex]

So the viruses are 2 times of the bacteria.

Answer:

Step-by-step explanation:

so he needs to collect at least 120 cans....and he already has 64

c + 64 > = 120 (thats a greater then or equal sign)

c > = 120 - 64

c > = 56....he needs to collect at least 56 more

To represent the number of cans that Xander must still collect to reach at least 120 cans, use the inequality c >= 120 - 64. The solution to the inequality is c >= 56.

To represent the number of cans that Xander must still collect to reach at least 120 cans, we can use the inequality:

c >= 120 - 64

This inequality represents that Xander must collect a number of cans that is greater than or equal to the difference between the desired total (120) and the number of cans he has already collected (64).

The solution to the inequality is:

c >= 56

This means that Xander must still collect at least 56 more cans to reach his goal.

Answer:

a=$1.75 per candy bar

b=$1.74 per candy bar

c=$1.71 per candy bar

d=$1.73 per candy bar

Option C is the better buy.

Hope this helps!

Answer:

Step-by-step explanation:

to find the x intercept, sub in 0 for y and solve for x

-6x + 4y = 96

-6x + 4(0) = 96

-6x = 96

x = -96/6

x = -16.....ur x intercept is -16 or (-16,0) <===

to find the y intercept, sub in 0 for x and solve for y

-6x + 4y = 96

-6(0) + 4y = 96

4y = 96

y = 96/4

y = 24....so ur y int is 24 or (0,24) <===

[tex]\text{Find the x and y intercepts:}\\\\\text{x intercepts:}\\\\\text{Plug in 0 to y}\\\\-6x+4(0)=96\\\\\text{Solve:}\\\\-6x+4(0)=96\\\\-6x=96\\\\\text{Divide both sides by -6}\\\\\boxed{x=(-16,0)}\\\\\text{y intercept:}\\\\\text{Plug in 0 to x}\\\\-6(0)+4y=96[/tex]

[tex]\text{Solve:}\\\\-6(0)+4y=96\\\\4y=96\\\\\text{Divide both sides by 4}\\\\\boxed{y=(0,24)}[/tex]

Convert the fraction to a decimal:

1/25 = 0.04

Multiply by 100 to get the percent:

0.04 x 100 = 4%

The fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have a fraction:

= 1/25

In decimal:

= 0.04

In percent:

= 0.04×100

= 4%

Thus, the fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.

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Answer:

domain: {0, 5, 9, 32} range: {2,3,4,7}

Step-by-step explanation:

we know that

For a set of ordered pairs, the first elements of each ordered pair represents the domain of the function and second elements of each ordered pair represents the range of the function.  

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

In this problem we have

values of x ----> [tex]\{0,5,9,32\}[/tex]

values of y ----> [tex]\{2,3,4,7\}[/tex]

therefore

domain: {0, 5, 9, 32} range: {2,3,4,7}

Answer:

Yes, they are congruent

Step-by-step explanation:

Yes, they are congruent because all the side and angle lengths are congruent.

Answer:

Yes

Step-by-step explanation:

Answer:

Yes it is 15

Step-by-step explanation:

30/2 =15

Answer:

Yes, you are right! The answer is 15!  :)

Step-by-step explanation:

2y = 30

Divide by two to get y on it's own.

y = 15

The larger number is 97 and smaller number is 22.

Step-by-step explanation:

Let,

The two numbers are x and y.

According to given statement;

x+y=119      Eqn 1

y-4x=9       Eqn 2

Subtracting Eqn 2 from Eqn 1

[tex](x+y)-(y-4x)=119-9\\x+y-y+4x=110\\5x=110[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5}=\frac{110}{5}\\x=22[/tex]

Putting x=22 in Eqn 1

[tex]22+y=119\\y=119-22\\y=97[/tex]

The larger number is 97 and smaller number is 22.

Keywords: linear equation, elimination method

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Answer:

coupon b offers $10.50 off whereas the other is only for $10 off

Step-by-step explanation:

25%*42=10.5