Solve the following system of equations graphically: y=3x+4 and y=-2x-5

Answer:

The recursive formula of the arithmetic sequence

[tex]a_{1}=First term of the arithmetic sequence[/tex]

[tex]a_{n}= a_{n-1}+common difference(d)[/tex].

Step-by-step explanation:

A recursive formula is used to find any term of an arithmetic sequence using a function of the preceding term. Each term is the sum of the previous term and the common difference.

To find the recursive formula of the arithmetic sequence

[tex]a_{1}=First term of the arithmetic sequence[/tex]

[tex]a_{n}= a_{n-1}+common difference(d)[/tex]

Answer:

8

Step-by-step explanation:

x-3=5

add the 3 to both sides of the equal sign

x-(3+3)=(5+3)

x=8

Answer: X = 8

Step-by-step explanation: To solve for x in this equation, we want to get x by itself on the left side of the equation. Since 3 is being subtracted from x, to get x by itself, we need to add 3 to the left side of the equation. If we add 3 to the left side, we must also add 3 to the right side.

Notice that on the left side -3 and +3 cancel each other out so we're simply left with x. On the right side, 5 + 3 gives us 8 so we have x = 8.

We can check our answer by substituting 8 back into the original equation. So we have (8) - 3 = 5 or 5 = 5 which is a true statement so our answer is correct.

Answer:

The answer is 10/27

Step-by-step explanation:

5/6 times 4/9 is equal to 10/27

Answer:

Step-by-step explanation:

she works 20 hrs each week....so far, she has worked 5.25 hrs and 5.5 hrs

h = hours remaining

so we are basically taking the total hrs and subtracting the combined hrs she has worked

h = 20 - (5.5 + 5.25) <== ur equation

The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Kendra works 20 hours each week. So far this week, she has worked 5.5 hours on Tuesday and 5.25 hours on Thursday.

Let h be the number of hours remaining for Kendra to work this week.

The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is;

A number of hours remaining for Kendra to work this week = Total number of hours - working on Tuesday - working on Thursday.

h = 20 - 5.5 - 5.25

h = 20 - (5.5 + 5.25)

Hence, the sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).

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Answer:

x=70

Step-by-step explanation:

I'm pretty sure the sum of all angles has to be 360°

and 70+70+40+40=220

so 220+x=360

we figure this out by taking 360-220 which equals 140

and then we divide 140 by 2 which is 70.

To double check, if you add 70+70+40+40+70+70, it equals 360.

The value of x from the given parallelogram is 70°. Therefore, option B is the correct answer.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, ABCD is a parallelogram.

Here, ∠A+∠B+∠C+∠D=360°

70°+x+40°+70°+x+40°=360°

220°+2x=360°

2x=360°-220°

2x=140°

x=70°

Therefore, option B is the correct answer.

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Answer:

The y-coordinate of the original point is negative and the y-coordiinate of the new point is positive.

The transformation is:

[tex](-7.5, 6)[/tex] →  [tex](-7.5, -6)[/tex]

Step-by-step explanation:

For this exercise it is important to remember the definition of "Reflection".

A Reflection is a transformation that consists in folding an figure over a line called "Line of reflection",

In tranformations, the original figure is called "Pre-image" and the figure obtained after the transdformation is called "Image".

Given a point [tex](x,y)[/tex], if this is reflected across the x-axis, the x-coordinate of the point does not change, but the sign of the y-coordinate is transformed into its opposite. Then:

 [tex](x,y)[/tex] →  [tex](x,-y)[/tex]

So, given the new point:

[tex](-7.5, 6)[/tex]

You can determine that the original point is:

[tex](-7.5, -6)[/tex]

Answer:

Youngest Age = 6

Middle Age = 9

Oldest Age = 12

Step-by-step explanation:

Let youngest age be x

Middle one age be y

Oldest age be z

So,

x < y < z

Now lets come up with the equations using the statements.

Three age combined is 27, so we can write:

x + y + z = 27

Oldest is TWICE youngest, so we can write:

z = 2x

Middle is 3 YEARS OLDER than youngest, so we can write:

y = x + 3

Now we replace first equation with 2nd and 3rd, to get:

x + y + z = 27

x + x + 3 + 2x = 27

We can solve this for x:

x + x + 3 + 2x = 27

4x + 3 = 27

4x = 24

x = 24/4

x = 6

Now finding y:

y = x + 3

y = 6 + 3

y = 9

Now finding z:

z = 2x

z = 2(6)

z = 12

Thus,

Youngest Age = 6

Middle Age = 9

Oldest Age = 12

Answer:

270

Step-by-step explanation:

I am not sure if i am correct but i  think you should divide 6,480 by 24 which is 270

Answer:

270 in2

Step-by-step explanation:

Divide 6480 . by 24

Servey says!?: 270 is the awnser!

Answer: The answer is 0.2

Step-by-step explanation:

1 divided by 5 is 0.2 because 1 goes into 5 0.2 times.

Hope this helps!

Two division equations were found for each given multiplication equation. The division equations are the inverse of the multiplication equations, essentially reversing the operation.

The goal is to find two division equations that correspond to each given multiplication equation. Basically, we are undoing or reversing the multiplication operation.

a. 15 x 2/5 = 6

b. 6 x 4/3 = 8

c. 16 x 7/8 = 14

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Answer:

Yes, both expressions for the two method are equivalent.

Step-by-step explanation:

Let the cost of the dress be p as given.

Marta want to evaluate the tax which is proportional to the cost.

8% sales tax will correspond to (8/100)*p=0.08p

Then she will add 0.08 p to p to obtain 0.08p+p= p(0.08+1)= 1.08p

On the other hand, Esther thinks that the cost of the dress, p, should be multiplied by 1.08 to obtain 1.08p at once!

Thus both expressions are equivalent. Only that Martha is wanting to pay much attention to the details , while Esther is a quick one :-)!

Answer:

Victoria Stadium

Step-by-step explanation:

Answer:

whats the answer

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

The length of the diameter is 2.86 cm rounded to 2 DP

Step-by-step explanation:

The formula of the circumference of a circle is

∵ The circumference of a circle is 8.97 cm

- We need to find the diameter of the circle, then we will use

   the 2nd formula of circumference above

∵ The circumference = πd

- Substitute the value of the circumference in the formula

∴ 8.97 = πd

- Subtract both sides by π

∴ 2.855 = d

- Round it to 2 decimal places (to the nearest hundredth)

∴ d = 2.86 cm

The length of the diameter is 2.86 cm rounded to 2 DP

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Solving for x...

3/4x+2=5/4x-6

8=2/4x

8=1/2x

x=16

To find the value of x in the given equation, we can eliminate the fractions, combine like terms, and solve for x. The value of x is 16.

To find the value of x in the equation 3/4x+2=5/4x-6, we need to isolate x on one side of the equation. We can do this by first getting rid of the fractions. Multiplying each term in the equation by the LCD (Least Common Denominator) of 4 will help us eliminate the fractions. Then, we can combine like terms and solve for x.

Finally, we can divide both sides by 2 to solve for x: (32/2) = 2x/2, resulting in x = 16.

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Answer:

The frequency table shows the number of times some people visited a movie theater last year . which set could the frequency table represent?

Step-by-step explanation:

Answer: x = -8 ; y = -6

Step-by-step explanation:

1*x-2*y=4

1*x = 4 + 2*y

x = 4 + 2*y

Now you replace the value of x on the following equation:

-1*x+10*y=8

-1*(4 + 2*y) = 8

-4 - 2*y = 8

-2*y = 8+4

-2*y = 12

y = -12/2

y = -6

You replace the value of y in the previous equation:

x = 4 + 2*y

x = 4 + 2*(-6)

x = 4 - 12

x = -8

                               Question # 1 Solution:

As the expression [tex]13v + 8f +6b+3m[/tex] represents her cost, in dollars for the arrangements when she buys

Which statement is true?

A.The term 13v represents the cost of 13 vases.

B.The coefficient 6 represents the cost of b stems of wood bark.

C.The term 8f represents the cost of f stems of flowers at $8 per stem.

D.The coefficient 3 represents the number of packages of marbles she buys.

Choosing the correct statement:

As the formula for cost of any item can be calculated by multiplying the cost of one item with the total number of items.

So, if f represents the stems of flowers, and the cost of f stems of flowers at $8 per stem. Then according to the formula for cost of any item, the statement C is true i.e. "The term 8f represents the cost of f stems of flowers at $8 per stem" is the correct statement.

                           Question # 2 Solution

As the inequality is given as:

                                12x + 9x - 3 ≤ 3(2x + 14)

and we have to find the value of x.

So,

12x + 9x - 3 ≤ 3(2x + 14)

Step 1: Simplify both sides of the inequality

21x - 3 ≤ 6x + 42

Step 2: Subtract 6x from both sides.

21x - 3 - 6x ≤ 6x + 42 - 6x

15x - 3 ≤ 42

Step 3: Add 3 to both sides.

15x - 3 + 3 ≤ 42 + 3

15x  ≤ 45

Step 4: Divide both sides by 5

15x/5 ≤ 45/5

3x  ≤ 9

x ≤ 9/3

So, x ≤ 9/3 is the right answer. Please note that x ≤ 9/3 can also be written as x ≤ 3.

Hence, option A i.e. x ≤ 9/3 is correct. The solution graph is also attached in figure a.

                               Question # 3 Solution

As we have to find the correct statements from the given graph that represents John's weight (in pounds) as a function of time t, measured in days since January 1, 2017.

So, here are the correct statements that validate the graph:

Keywords: inequality, equation, graph, rate of change, function

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0.024 /yr

Step-by-step explanation:

Without interest, the monthly repayment would be;

5 yrs = 12 months * 5 = 60 months

$4200 / 60

= $70

James, however,  pays $78.40 monthly. The interest therefore is;

Jmaes pays a total of $78 * 60 = $4704 at the end of the 5 years. The formula for finding simple interest is;

A = P(1 + rt)

Where:

   A = Total Accrued Amount (principal + interest)

   P = Principal Amount

   I = Interest Amount

   r = Rate of Interest per year in decimal; r = R/100

   R = Rate of Interest per year as a percent; R = r * 100

   t = Time Period involved in months or years

4704 = 4200 (1 + 5r )

4704 = 4200 + 21000r

504 = 21000r

r = 504/21000

r = 0.024

Interest rate = 0.024 /yr

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Answer:

[tex]A=125.66\ cm^2[/tex]

Step-by-step explanation:

The complete question is

The area of the shaded region is the area inside the larger circle and outside the smaller circle

so

To find out the area of the shaded region subtract the area of the smaller circle from the area of the larger circle

Remember that

The area of the circle is

[tex]A=\pi r^{2}[/tex]

therefore

The area of the shaded region is

[tex]A=\pi [r_1^2-r_2^2][/tex]

where

[tex]r_1=11\ cm[/tex] ---> radius of the larger circle

[tex]r_2=9\ cm[/tex] ---> radius of the smaller circle

assume

[tex]\pi =3.1416[/tex]

substitute

[tex]A=3.1416 [11^2-9^2][/tex]

[tex]A=3.1416 [40][/tex]

[tex]A=125.66\ cm^2[/tex]

Answer:-4

Step-by-step explanation:

a-15=4a-3

a-4a=-3+15

-3a=12

a=-4

Answer:

Jamie has 11/15 yards of Green Felt more than Blue Felt

Step-by-step explanation:

Green felt- Blue felt

= 5/6- 1/10

= 25/30- 3/30  ( taking LCM)

= 25 - 3/30

=22/30

=11/15 yards

LCM= 2*3*5= 30

Factors of 6= 2*3

Factors of 10= 2*5

                      SOLVING QUESTIONS FROM 1ST PAGE

y = -3x - 5

Putting x = -5, and y = 0 in y = -3x - 5

0 = -3(-5) - 5

0 = 15 - 5

0 = 10         ∵Putting B(-5, 0) in y = -3x - 5 does not equate the equation.

As L.H.S ≠ R.H.S

So,

Does this check?

Answer: no        ∵ L.H.S ≠ R.H.S

y = -3x - 5

Putting x = -2, and y = 1 in y = -3x - 5

1 = -3(-2) - 5

1 =  6 - 5

1 = 1         ∵Putting C(-2, 1) in y = -3x - 5 rightly equates the equation.

As L.H.S = R.H.S

So,

Does this check?

Answer: yes      ∵ L.H.S = R.H.S

y = -3x - 5

Putting x = -1, and y = -2 in y = -3x - 5

-2 = -3(-1) - 5

-2 =  3 - 5

-2 = -2       ∵Putting D(-1, -2) in y = -3x - 5 rightly equates the equation.

As L.H.S = R.H.S

So,

Does this check?

Answer: yes       ∵ L.H.S = R.H.S

                         SOLVING QUESTIONS FROM 2ND PAGE

y = -2x + 18

Putting x = 6, and y = 18 in y = -2x + 18

18 = -2(6) + 18

18 = -12 + 18

18 = 6         ∵Putting B(6, 18) in y = -2x + 18 does not equate the equation.

As L.H.S ≠ R.H.S

So,

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

y = 2x + 6

Putting x = 9, and y = 24 in y = 2x + 6

24 = 2(9) + 6

24 = 18 + 6

24 = 24      ∵Putting C(9, 24) in y = 2x + 6 rightly equates the equation.

As L.H.S = R.H.S

So,

Does this check?

Answer: yes       ∵ L.H.S = R.H.S

              SOLVING QUESTIONS FROM 3RD PAGE

y = 3x + 4

Putting x = 2, and y = 7 in y = 3x + 4

7 = 3(2) + 4

7 = 6 + 4

7 = 10         ∵Putting D(2, 7) in y = 3x + 4 does not equate the equation.

As L.H.S ≠ R.H.S

So,

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

                      SOLVING QUESTIONS FROM 4th PAGE

b. Which function could have produced the values in the table.

A. y = 3x + 4                            

B. y = -2x + 18

C. y = 2x + 6

D. y = x + 9

The Table:

x             y

3            12

6            18

9            24

Checking A) y = 3x + 4

Putting (3, 12), (6, 18) and (9, 24) in y = 3x + 4

For (3, 12)

y = 3x + 4

12 = 3(3) + 4

12 = 13   ∵ L.H.S ≠ R.H.S

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

For (6, 18)

18 = 3(6) + 4

18 = 18 + 4

18 = 22   ∵ L.H.S ≠ R.H.S

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

For (9, 24)

24 = 3(9) + 4

24 = 27 + 4

24 = 31   ∵ L.H.S ≠ R.H.S

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

So, the equation y = 3x + 4 could have not produced the all values in the table as the the ordered pairs in table do not satisfy(equate) the equation.

Checking B) y = -2x + 18

Putting (3, 12), (6, 18) and (9, 24) in y = -2x + 18

So, y = -2x + 18 could have not produced all the values in the table, as (6, 18) does not equate the equation.

Checking C) y = 2x + 6

Putting (3, 12), (6, 18) and (9, 24) in y = 2x + 6

So, y = 2x + 6 could have produced the values of in the table as all the orders pairs in the table satisfy/equate the equation.

Checking D) y = x + 9

Putting (3, 12), (6, 18) and (9, 24) in y = x + 9

So, y = x + 9 could have also not produced all the values in the table, as (6, 18) and (9, 24) do not satisfy/equate the equation.

So, from all the verification we conclude that:

HENCE, ONLY y = 2x + 6 COULD HAVE PRODUCED THE VALUES IN THE TABLE AS ALL THE ORDERED PAIRS OF THE TABLE SATISFY/EQUATE THE EQUATION.

                 SOLVING QUESTIONS FROM 5th PAGE

What is the domain and range of the relation?

{(-3, 7), (6, 2), (5, 1), (-9, -6)}

As the given relation is {(-3, 7), (6, 2), (5, 1), (-9, -6)}

The domain is: {-3, 6, 5, -9}

Note: generally, we write the numbers in ascending order for both the domain and range.

The domain could also be written in order as: {-9, -3, 5, 6}

The range is: {7, 2, 1, -6}

The range could also be written in order as: {-6, 1, 2, 7}

Keywords: equation, point, ordered pair, domain, range

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Answer:

Step-by-step explanation:

9,899,399+2082

=9901481

Final answer:

To find out what 9,899,399 increased by 2,082 is, add the two numbers together, resulting in 9,901,481.

Explanation:

The question asks what the result will be if the number 9,899,399 is increased by 2,082. To find the result, we simply need to add the two numbers together. This type of problem involves basic arithmetic operations and is fundamental in understanding how to manipulate and work with numbers.

To calculate the result:

Start with the original number: 9,899,399.

Add the increase: 2,082.

Perform the addition: 9,899,399 + 2,082 = 9,901,481.

Therefore, when the number 9,899,399 is increased by 2,082, the result is 9,901,481.

Answer:

The solution is the point (-5,-3)

Step-by-step explanation:

The complete question is

Consider the linear system of equations y = 2/5x - 1 and 2x -3y + 1 = 0

The solution of the system of equations is?

we have

[tex]y=\frac{2}{5}x-1[/tex] ----> equation A

[tex]2x-3y+1=0[/tex] ----> equation B

Solve by substitution

substitute the equation A in equation B

[tex]2x-3(\frac{2}{5}x-1)+1=0[/tex]

solve for x

[tex]2x-\frac{6}{5}x+3+1=0[/tex]

[tex]2x-\frac{6}{5}x+4=0[/tex]

Multiply by 5 both sides to remove the fraction

[tex]10x-6x+20=0[/tex]

[tex]4x+20=0[/tex]

subtract 20 both sides

[tex]4x=-20[/tex]

divide by 4 both sides

[tex]x=-5[/tex]

Find the value of y

[tex]y=\frac{2}{5}(-5)-1[/tex]

[tex]y=-3[/tex]

The solution is the point (-5,-3)

The question involves solving a system of linear equations from high school algebra. Substituting Y from the first equation into the second and solving for x, we find that x = -5 and Y = -3.

The student is asking about solving a system of linear equations, which is a concept in algebra that falls under high school mathematics. To find the solution to the given linear system, we can use either substitution or elimination methods. Let's use substitution since the first equation has Y isolated.

From the first equation Y = 2/5x - 1, we substitute for Y in the second equation, which gives us 2x - 3(2/5x - 1) + 1 = 0. Simplifying, we get 2x - 6/5x + 3 + 1 = 0, which further simplifies to 4/5x + 4 = 0. Solving for x gives x = -5. Substituting x back into the first equation to find Y yields Y = 2/5(-5) - 1, so Y = -3. Therefore, the solution to the system of equations is x = -5 and Y = -3, which is the point where the two lines intersect.

Answer:

2x + 17

Step-by-step explanation:

Answer:

2(x-17).

Step-by-step explanation:

The given phrase is "two times the difference of a number and 17."

We need to find the expression for given phrase.

Let x be the unknown variable.

Difference is denoted by "-" symbol.

Time is denoted by "×" symbol.

Difference of a number and 17 = x-17

Two times the difference of a number and 17 = 2×(x-17) = 2(x-17)

Therefore, the required expression is 2(x-17).

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]4x+y=3[/tex] ----> Red line

[tex]2x-3y=3[/tex] ---> blue line

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (0.857,-0.429)

The graph in the attached figure

The equation solved for s is s = 4p - 48h

Solution:

Given that equation a company uses to  calculate pay checks is p = 12h +0.25s

Therefore the given equation is:

p = 12h + 0.25s

Where "h" is the number of hours worked

"s" is the total sales

To find: equation for "s"

Let us solve the given equation for "s"

p = 12h + 0.25s

Now move 12h from R.H.S to L.H.S

p - 12h = 0.25s

Now move from 0.25 from R.H.S to L.H.S

[tex]s = \frac{p-12h}{0.25}\\\\s = \frac{p}{0.25} -\frac{12h}{0.25}[/tex]

We know that, [tex]0.25 = \frac{1}{4}[/tex]

[tex]s = \frac{p}{\frac{1}{4}} -\frac{12h}{\frac{1}{4}}\\\\s = p \times \frac{4}{1} - 12h \times \frac{4}{1}\\\\s = 4p - 48h[/tex]

Thus the equation for s is s = 4p - 48h

Answer: 17.5 hope this helps

the answer is 17.5

:D