ashur solves the following system of linear euations. -3a + 7b = -16. -9a + 5 b = 16 which statement is true about the solution to this system of equations?

Answer:

(x, y ) → (x + 2, y - 4 )

Step-by-step explanation:

Compare the coordinates of 2 corresponding points in the original and the image, that is

B(- 5, 4 ) → B'(- 3, 0 )

To translate from B → B'

We require a shift of 2 units right in the x direction and 4 units down in the y direction, that is

(x, y ) → (x + 2, y - 4 ) ← translation rule

KL is equal to JM because the quadrilateral is a parallelogram.

7x-2=12x-22

5x=20

x=4

KL=7(4)-2=26

answer: x=4, KL=26

Answer:

y= 3x +1

Step-by-step explanation:

Let's write the equation of the line in slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.

Start by finding the slope with the formula below:

[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

Slope

[tex]=\frac{10-(-2)}{3-(-1)}[/tex]

[tex]=\frac{10+2}{3+1}[/tex]

[tex]=\frac{12}{4}[/tex]

= 3

Substitute m= 3 into the equation:

y= 3x +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= -1, y= -2,

-2= 3(-1) +c

-2= -3 +c

c= -2 +3

c= 1

Thus, the equation of the line is y= 3x +1.

_______

Alternatively, we can write the equation in the point-slope form.

[tex]\boxed{y-y_1=m(x-x_1)}[/tex]

Substitute m= 3 and a pair of coordinates into [tex](x_1,y_1)[/tex]:

y -10= 3(x -3)

Additional:

For more questions on writing equations of line, check out:

The equation which passes through the points  (-1,-2)and(3,10) will be y= 3x +1

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Let's write the equation of the line in slope-intercept form. That is, y= mx+c, where m is the slope and c is the y-intercept.

Start by finding the slope with the formula below:

[tex]\rm Slope =\dfrac{y_1-y_2}{x_1-x_2}[/tex]

Slope

[tex]\rm Slope =\dfrac{10-(-2)}{3-(-1)}[/tex]

[tex]\rm Slope=\dfrac{12}{4}[/tex]

Slope = 3

Substitute m= 3 into the equation:

y   =  3x +  c

To find the value of c, substitute a pair of coordinates into the equation.

When x= -1, y= -2,

-2   =   3(-1) +  c

-2= -3  +  c

c  =  -2  +  3

c  =   1

Thus, the equation of the line is y  =   3x +  1.

Alternatively, we can write the equation in the point-slope form.

y  -  y₁  =  m ( x - x₁ )

Substitute m= 3 and a pair of coordinates into :

y  - 10  =  3 ( x  - 3 )

Therefore the equation which passes through the points  (-1,-2)and(3,10) will be y= 3x +1

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Answer:

9 * 10^7.

Step-by-step explanation:

(3 * 10^5) * (3 * 10^2)

= 3 * 3 * 10^5 * 10^2

= 9 *  10^(5+2)

= 9 * 10^7.

Answer:

[tex]25^o[/tex]

Step-by-step explanation:

Let

x ----> the angle in degrees

we know that

[tex]sin(x)=0.42[/tex]

Find the measure of angle x

Using a calculator

[tex]x=sin^{-1}(0.42)=24.83^o[/tex]

Round to the nearest degree

[tex]x=25^o[/tex]

Answer:

10.5 units (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

Note that AB and CD are horizontal lines because A and B have the same y coordinate, and C and D have the same y coordinate. As a result, I can simply subtract their x coordinate values to find length of AB and CD.

Answer:

6 plus or minus square root of 37/2

Step-by-step explanation:

Is the quadratic formula allowed or no?

Answer:

t = 3 ± ½√37

Step-by-step explanation:

0 = -16t² + 96t + 4

This isn't factorable, so complete the square or use quadratic formula.  Completing the square:

16t² − 96t = 4

t² − 6t = 1/4

t² − 6t + 9 = 1/4 + 9

(t − 3)² = 37/4

t − 3 = ±½√37

t = 3 ± ½√37

Answer:

x=1, y=1. (1, 1).

Step-by-step explanation:

4x+6y=10

6x=9y-3

-----------------

4x+6y=10

9y-6x=3

-----------------

4x+6y=10

-6x+9y=3

---------------

simplify -6x+9y=3 into -2x+3y=1

------------------------

4x+6y=10

-2x+3y=1

---------------

4x+6y=10

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

-----------------------

4x+6y=10

-4x+6y=2

---------------

12y=12

y=12/12

y=1

4x+6(1)=10

4x+6=10

4x=10-6

4x=4

x=4/4=1

To solve the system of equations by elimination, multiply one equation by a constant that will create opposite coefficients for one of the variables. Then, combine the equations and solve for the remaining variable.

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations.

In this case, let's eliminate y. We can do this by multiplying the first equation by 3 and the second equation by 6, so that the coefficients of y will be the same but opposite in sign. This gives us:

12x + 18y = 30

36x = 54y - 18

Now subtract the second equation from the first equation:

(12x + 18y) - (36x) = (30) - (54y - 18)

12x + 18y - 36x = -54y + 48

-24x + 18y = -54y + 48

Collect like terms:

-24x - 18y = -54y + 48

Rearrange the equation:

-24x + 54y = 48

The resulting equation is  -24x + 54y = 48.

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I'm assuming there should be a dollar sign here. This is the same as saying "$3 for one pound". A unit rate has some amount per 1 unit of something else. In this case, the 1 unit is 1 pound.

A different example of a unit rate is writing 40 miles per hour. This is the same as saying the car drives 40 miles in 1 hour. The unit here is the "1 hour".

Answer:

Given: $1.00 for 2 lemons $3.00 for every pound $4.00 for 3 slices of pizza $6.0

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x^2 - 98 = 2 * ( x^2 - 49)

          = 2 * (x^2 - 7^2)

          = 2 * (x+7) * (x-7)    {a²-b² = (a+b)(a-b)}

Answer:

9%

Step-by-step explanation:

9/100 = 0.09

To convert to a percent, multiply by 100 and add a percent sign:

0.09 * 100 = 9%

Answer: 9%

Step-by-step explanation:

I Looked it up online.

Answer:

d

Step-by-step explanation:

because 2/5 × 4x=8/5 and 2/5×9=18/5

ita in d

Ralph read 27 books and Homer read 6 books.

Step-by-step explanation:

Given,

Total books read = 33

Let,

Books read by Ralph = x

Books read by Homer = y

According to given statement;

x+y=33     Eqn 1

Ralph read three more than four times as many as Homer.

x = 4y+3    Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex](4y+3)+y=33\\4y+3+y=33\\5y=33-3\\5y=30[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{30}{5}\\y=6[/tex]

Putting y=6 in Eqn 2

[tex]x=4(6)+3\\x=24+3\\x=27[/tex]

Ralph read 27 books and Homer read 6 books.

Keywords: linear equation, substitution method

Learn more about linear equations at:

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Answer:

Step-by-step explanation:

△ABC is isosceles. So ∠3 = ∠4

given 1 ≅ 3.

therefore, 1 ≅ 4

alternate interior angles are equal if only AB//CD

2×11+9

22+9

31

This the the way to solve this answer

Answer:77

Step-bystep explanation:

[9-2]  * [7+4]  

[7]   *    [11]      

7*11=77      

that is your answer plz mark me brainliest :)

Answer:

384 + c = m.

Step-by-step explanation:

You can use another variable such as t to represent "total." I used m to represent total "miles." The variable you use to represent the total shouldn't matter but these two variables make the most sense. 384 for last year's miles plus c, which is this year's miles, equals the total miles. A very simple, straight forward and easy equation to write.

Answer:

[tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].

Step-by-step explanation:

We have to determine that in which quadrant the angle [tex]\theta[/tex] lies if [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].

The horizontal axis i.e. x-axis and the vertical axis i.e. y-axis divides the coordinate plane into four zones, the zone with x and y both positive is the first quadrant and rotating about the origin in anticlockwise we will find 2nd, 3rd and 4th quadrant one by one.

In the first quadrant all the trigonometrical functions [tex]\sin \theta[/tex], [tex]\cos \theta[/tex] and [tex]\tan \theta[/tex] are positive.

In the second quadrant only  [tex]\sin \theta[/tex] is positive.

In the third quadrant only [tex]\tan \theta[/tex] is positive i.e. [tex]\sin \theta[/tex] and [tex]\cos \theta[/tex] are negative.

In the fourth quadrant only [tex]\cos \theta[/tex] is positive.

Therefore, [tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex]. (Answer)

If both sin 0 and cos 0 are negative, the angle 0 lies in the third quadrant because only in this quadrant are both sine and cosine functions negative.

The question asks in which quadrant does 0 lie given that sin 0<0 and cos 0<0. In the context of trigonometric functions in the Cartesian coordinate system, the sin of an angle is negative in the third and fourth quadrants, and the cos function is negative in the second and third quadrants. As such, if both sin 0<0 and cos 0<0, it indicates that the angle 0 must lie in the third quadrant. This is because it is the only quadrant where both the sin and cos of an angle are negative. Therefore, the angle 0 lies in the third quadrant.

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Answer:

The group will need to take a minimum of 5 buses to carry all the people to the trip

Step-by-step explanation:

Given:

Number of 7th grade students going on the trip = 178

Number of chaperones going on the trip = 20

Number of people each bus can hole = 42

To find the number of buses the group will have to take.

Solution:

Let minimum number of buses the group will have to take = [tex]x[/tex]

using unitary method:

If 1 bus can hold = 42 people

Then, [tex]x[/tex] buses can hold = [tex]42x[/tex] people

Total number of people for the trip = [tex]178+20=198[/tex]

The total number of people that can go in [tex]x[/tex] buses must be greater than or equal to 198 in order to carry all the people to the trip.

Thus we have the inequality:

[tex]42x\geq198[/tex]

Solving for [tex]x[/tex]

Dividing both sides by 42.

[tex]\frac{42x}{42}\geq\frac{198}{42}[/tex]

[tex]x\geq4.71\approx 5[/tex]   [As number of buses must be in whole number]

Thus, the group will need to take a minimum of 5 buses to carry all the people to the trip.

The number of buses needed for a field trip is 5 buses.

To determine how many buses are needed for 178 7th grade students and 20 chaperones going to the aquarium, where each bus holds 42 people, we first calculate the total number of passengers: 178 students + 20 chaperones = 198 people. We then divide this total number by the bus capacity. However, since we can't have a fraction of a bus, if there is any remainder after division, we must round up to the next whole number. So the inequality to represent this situation is:

Calculate total passengers:
178 students + 20 chaperones = 198 people

Divide by bus capacity to find the number of buses needed:
198 ÷ 42 = 4.714...

Round up to the next whole number, which means 5 buses will be needed.

Answer:

See explanation

Step-by-step explanation:

a1) Given

[tex]\angle A\cong \angle C\\ \\\angle ABD\cong \angle CDB[/tex]

   Statement               Reason

1. [tex]\angle A\cong \angle C[/tex]   - Given

2. [tex]\angle ABD\cong \angle CDB[/tex]   - Given

3. [tex]\overline{BD}\cong \overline{DB}[/tex]  - Reflexive property

4. [tex]\triangle ABD\cong \triangle CDB[/tex]  - AAS postulate

5. [tex]\overline {AB}\cong \overline{CD}[/tex] - Congruent triangles have congruent corresponding parts

6. [tex]AB=CD[/tex]   - Definition of congruent segments

a2) Given

[tex]\overline{H O}\parallel \overline{E N}\\ \\H W=N W[/tex]

Statement Reason

1. [tex]H W=W N[/tex] - Given

2. [tex]\overline{H O}\parallel \overline{E N}[/tex] - Given

3. [tex]\angle O H W\cong \angle E N W[/tex] - Alternate interior angles theorem (two parallel lines H O and E N are cut by transversal H N)

4. [tex]\angle H W O\cong \angle N W E[/tex] - Vertical angles theorem

5. [tex]\triangle H O W\cong \triangle N E W[/tex] - ASA postulate

b) Given

[tex]PO=PR\\ \\OS=RS\\ \\\angle O\cong \angle R\\ \\m\angle P=90^{\circ}[/tex]

   Statement               Reason

1. [tex]m\angle P=90^{\circ}[/tex]   - Given

2. [tex]\triangle OPE, \triangle RPN[/tex] are right triangles   - Definition of right triangles

3. [tex]\angle O\cong \angle R[/tex]  - Given

4. [tex]PO=PR[/tex]  - Given  

5. [tex]\triangle POE\cong \triangle PRN[/tex]  - HA postulate

6. [tex]OS=RS[/tex] - Given

7. [tex]\angle O\cong \angle R[/tex] - Given

8. [tex]\angle OSN\cong \angle SRE[/tex] - Vertical angles theorem

9. [tex]\triangle SON\cong \triangle SRE[/tex] - ASA postulate

c1) Given

[tex]\overline{SA}\parallel \overline{NE}\\ \\\overline{SE}\parallel \overline{NA}[/tex]

   Statement               Reason

1. [tex]\overline{SA}\parallel \overline{NE}[/tex]   - Given

2. [tex]\angle ENS\cong \angle ASN[/tex]   - Alternate interior angles theorem (two parallel lines SA and NE are cut by transversal SN)

3. [tex]\overline{SE}\parallel \overline{NA}[/tex]  - Given

4. [tex]\angle ESN\cong \angle ANS[/tex]   - Alternate interior angles theorem (two parallel lines SE and NA are cut by transversal SN)  

5. [tex]\overline{SN}\cong \overline{NS}[/tex] - Reflexive property

6. [tex]SN=NS[/tex] - Definition of congruent segments

7. [tex]\triangle ENS\cong \triangle ASN[/tex]  - ASA postulate

8. [tex]\overline{SA}\cong \overline {NE}[/tex]  - Congruent triangles have congruent corresponding parts

9. [tex]SA=NE[/tex]   - Definition of congruent segments

c2) Given

[tex]\angle BTO\cong \angle IWE\\ \\\overline{WI}\cong \overline{BT}\\ \\\overline{OW}\cong \overline{ET}[/tex]

   Statement               Reason

1. [tex]\angle BTO\cong \angle IWE[/tex]   - Given

2. [tex]\overline{WI}\cong \overline{BT}[/tex]   - Given

3. [tex]\overline{OW}\cong \overline{ET}[/tex]  - Given

4. [tex]\overline{WT}\cong \overline{TW}[/tex]   - Reflexive property  

5. [tex]WI=BT[/tex] - Definition of congruent segments

6. [tex]OW=ET[/tex] - Definition of congruent segments

7. [tex]WT=TW[/tex] - Definition of congruent segments

8. [tex]OT=OW+WT[/tex] - Segment addition postulate

9. [tex]WE=WT+TE[/tex] - Segment addition postulate

10. [tex]OW+WT=ET+WT[/tex] - Substitution property

11. [tex]OT=WE[/tex] - Substitution property

12. [tex]\triangle BOT\cong \triangle IEW[/tex]  - SAS postulate

Answer:

What he said

Step-by-step explanation:

Answer:

width of garden=b=10 ft

length of garden=l=10+14=24 ft

Step-by-step explanation:

given area of garden=240 ft^2

length of garden=l

width of garden=b

ac/ ques, l=b+14

area of garden=lb

240 ft^2=(b+14)b

put b=10 form hit and trial method

240=(10+14)10=(24)10=240

width of garden=b=10 ft

length of garden=l=10+14=24 ft answer

Answer:

y + 9 = 6(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 6 and (a, b) = (4, - 9), thus

y - (- 9) = 6(x - 4), that is

y + 9 = 6(x - 4)

Answer:

Hence two ordered pairs can be joined to best draw the line of best fit for this scatter plot are  (0, 14) and (10, 1)

Option B is correct.

Step-by-step explanation:

Answer:

[tex]x=115^o[/tex]

Step-by-step explanation:

Angles Inside a Polygon

A polygon of n sides must have the sum of its internal angles  

[tex]S=180^o(n-2)[/tex]

The polygon shown in the figure has n=5 sides, so the sum of its internal angles is

[tex]S=180^o(5-2)=540^o[/tex]

The construction of the internal angles of the polygon is shown in the image below. The sum of them is

[tex]50+180-x+180-x+360-x+x=540[/tex]

Reducing

[tex]-2x+770=540[/tex]

Solving

[tex]\displaystyle x=\frac{770-540}{2}[/tex]

[tex]\boxed{x=115^o}[/tex]

Answer:

x is 115 degrees

Step-by-step explanation:

Answer:

Package A: [tex]g=18p[/tex] and Package B: [tex]g=12p[/tex]

Step-by-step explanation:

Here is the complete question: A store sells two different packages of glue sticks as described below. Package A : 18 glue sticks. Package B : 12 glue sticks. Write an equation for package A and B that represents the total number of glue sticks is "g" in "p" package.

Given: There are 2 packages .

Package A has 18 glue sticks

Package B has 12 glue sticks

As given let "g" be the total number of glue sticks in "p" packages.

Package A:

Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]

∴ [tex]g=18\times p= 18p[/tex]

∴ [tex]g=18p[/tex]

Package B:

Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]

∴ [tex]g=12\times p= 12p[/tex]

∴ [tex]g=12p[/tex]

Answer:

g(x)=f(x-5)

Step-by-step explanation:

I did this question for my EOC & got it correct.

The equation that relates f(x) with g(x) is g(x) = f(x - 5).

The equation that relates f(x) with g(x) is option D. g(x) = f(x - 5).

Option D represents a translation of the function f(x) in the positive x-direction by a distance of 5 units. This means that every y-value of f(x) at x will now be the y-value of g(x) at (x + 5). The equation g(x) = f(x - 5) precisely captures this relationship between f(x) and g(x).

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Start by simplifying both fractions

[tex]

\dfrac{24}{32}=\dfrac{12}{16}=\dfrac{6}{8}=\dfrac{3}{4} \\

\dfrac{48}{64}=\dfrac{24}{32}=\dfrac{12}{16}=\dfrac{6}{8}=\dfrac{3}{4}

[/tex]

As you can see both fractions simplify to a same value hence the equality

[tex]\dfrac{24}{32}=\dfrac{48}{64}[/tex]

stands.

Hope this helps.

Answer:

(27 - n) times 3 is the expression Kyle should use.

Step-by-step explanation:

If Lee ran for 3 times longer than Kyle ran on Wednesday, then we have to figure out how long Kyle ran on Wednesday. If Kyle ran n fewer minutes than he ran on Tuesday, then we need to figure out how long he ran on Tuesday. If Kyle ran 27 minutes on Tuesday, the we need to subtract n from that to get how long Kyle ran on Wednesday. We can't figure that out with an undefined variable, therefore, that will just have to be 27 - n in the equation. If Lee ran for 3 times that, we need to multiply that by 3. 27 - n would have to be done first, so we will put that in parenthesis. We put all of that together to get (27 - n) times 3. Hope this helps!

Answer:

114791256

Step-by-step explanation:

27*17=486

486^3=114791256

Answer:

114791256

Step-by-step explanation:

27*17=486

486^3=114791256

a) (15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3

b) The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)

c) (2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers

Solution:

Given that,

Use the set of ordered pairs below to answer each question.

{(4, 20),  (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}

So we must find GCF of the ordered pairs

GCF of 4 and 20:

The factors of 4 are: 1, 2, 4

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 4

GCF of 8 and 4:

The factors of 4 are: 1, 2, 4

The factors of 8 are: 1, 2, 4, 8

Then the greatest common factor is 4

GCF of 2 and 3:

The factors of 2 are: 1, 2

The factors of 3 are: 1, 3

Then the greatest common factor is 1

GCF of 15 and 3:

The factors of 3 are: 1, 3

The factors of 15 are: 1, 3, 5, 15

Then the greatest common factor is 3

GCF of 6 and 15:

The factors of 6 are: 1, 2, 3, 6

The factors of 15 are: 1, 3, 5, 15

Then the greatest common factor is 3

GCF of 6 and 30:

The factors of 6 are: 1, 2, 3, 6

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6

GCF of 1 and 5:

The factors of 1 are: 1

The factors of 5 are: 1, 5

Then the greatest common factor is 1

GCF of 6 and 18:

The factors of 6 are: 1, 2, 3, 6

The factors of 18 are: 1, 2, 3, 6, 9, 18

Then the greatest common factor is 6

GCF of 0 and 3:

The factors of 0 are: All Whole Numbers

The factors of 3 are: 1, 3

Then the greatest common factor is 3

Summarizing the results:

(15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3

So let us find the factors of second cordinate and check

For (4, 20) , the factors of 20 are 1, 2, 4, 5, 10, 20

Thus first coordinate 4 is factor of second cordinate

For (8, 4) the factors of 4 are 1, 2, 4

Thus first coordinate is not a factor of second cordinate

For (2, 3), the factors of 3 are 1, 3

Thus first coordinate is not a factor of second cordinate

For (15, 3), the factors of 3 are 1 and 3

Thus first coordinate is not a factor of second cordinate

For (6, 15) , the factors of 15 are 1, 3, 5, 15

Thus first coordinate is not a factor of second cordinate

For (6, 30), the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

Thus first coordinate 6 is factor of second cordinate

For (1, 5) , the factors of 5 are 1 and 5

Thus first coordinate 1 is a factor of second cordinate

For (6, 18) , the factors of 18 are 1, 2, 3, 6, 9, 18

Thus first coordinate 6 is factor of second cordinate

For (0, 3) , the factors of 3 are 1 and 3

Thus first coordinate is not a factor of second cordinate

Summarizing the results:

The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Therefore,

(2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers

To find the ordered pairs with a GCF of 3, divide the second coordinate by the first to find pairs where the first is a factor of the second, and check the second coordinate for prime numbers.

To find the ordered pairs whose first and second coordinates have a greatest common factor of 3, we can go through each pair and check the GCF. The pairs that have a GCF of 3 are (6, 15), (6, 30), and (0, 3).

To find the ordered pairs whose first coordinate is a factor of its second coordinate, we need to divide the second coordinate by the first coordinate and check if the result is a whole number. The pairs that meet this condition are (2, 3), (15, 3), and (0, 3).

To find the ordered pairs whose second coordinate is a prime number, we need to check if the second coordinate is divisible only by 1 and itself. The pair that meets this condition is (2, 3).

Answer:

12 portrait sheets with total cost of $447

Step-by-step explanation:

x sheets ordered

Cameron: 33x + 51 = Lasting Memory : 29x + 99

33x + 51 =  29x + 99

33x - 29x = 99 -51

4x = 48

x = 12 sheets ordered

Total cost: 33 * 12 + 51 = 447

check: 29 * 12 + 99 = 447

Final answer:

Mrs. Burke needs to purchase 12 portrait sheets for the cost to be the same at either studio, and the total cost would be $495.

Explanation:

Mrs. Burke is comparing the costs of family portraits between Cameron Photography and Lasting Memories Company to find out how many portrait sheets will result in the same total cost at either studio. To solve this, we can set up an equation where the total cost at Cameron Photography equals the total cost at Lasting Memories.

Let x be the number of portrait sheets. The total cost at Cameron Photography is given by the expression 33x + 51 (where 33 is the cost per portrait sheet and 51 is the session fee). The total cost at Lasting Memories is expressed as 29x + 99 (with 29 being the cost per portrait sheet and 99 is the session fee).

To find the number of portrait sheets that results in equal costs, we set the two expressions equal to each other:

33x + 51 = 29x + 99

Subtracting 29x from both sides, we get:

4x + 51 = 99

Subtracting 51 from both sides, we get:

4x = 48

Dividing by 4, we find that x = 12. So, Mrs. Burke would need to purchase 12 portrait sheets for the cost to be the same at either studio. Plugging x back into either original cost equation, we find that the total cost at either studio will be 33(12) + 51 = 99(12) + 99 = $495.