Factorise 1 - 25 (a+b)^2

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.

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:

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.

2.14 kilometers of road is built each day

Solution:

Given that road is 10 kilometers long

The crew worked for [tex]4\frac{2}{3}[/tex] days

To find: Kilometers of road build each day

Assume they built the same amount each day

Length of road = 10 km

number of days worked = [tex]4\frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{14}{3}[/tex]

Kilometers of road build each day is given as:

Kilometers of road build each day = total length of road divided by number of days the crew worked

[tex]\rightarrow \frac{10}{\frac{14}{3}}=\frac{10}{1} \times \frac{3}{14}=2.14[/tex]

Thus 2.14 kilometers of road is built each day

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:

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

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-1)/(-2-3)

m=3/-5

m=-3/5

y-y1=m(x-x1)

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

Answer:

The distance cover by Mai's bike is 2 time the distance cover by Noah's bike

Step-by-step explanation:

Given as :

The distance cover by Mai's bike = [tex]d_1[/tex] = 7 [tex]\dfrac{1}{4}[/tex] miles

I.e [tex]d_1[/tex] = [tex]\dfrac{28+1}{4}[/tex] miles

Or, [tex]d_1[/tex] = [tex]\dfrac{29}{4}[/tex] miles

The distance cover by Noah's bike = [tex]d_2[/tex] = 3 [tex]\dfrac{5}{8}[/tex] miles

I.e [tex]d_2[/tex] = [tex]\dfrac{24 + 5}{8}[/tex] miles

Or,  [tex]d_2[/tex] = [tex]\dfrac{29}{8}[/tex] miles

let the number of times that Noah's bike ride was Mai's bike ride = n

So, The distance cover by Mai's bike = n × The distance cover by Noah's bike

Or, [tex]d_[/tex] = n ×  [tex]d_[/tex]

Or, [tex]\dfrac{29}{4}[/tex] miles =  n × [tex]\dfrac{29}{8}[/tex] miles

Or, n = [tex]\frac{\frac{29}{4}}{\frac{29}{8}}[/tex]

∴ n = [tex]\dfrac{8}{4}[/tex]

I.e n = 2

Hence The distance cover by Mai's bike is 2 time the distance cover by Noah's bike  . Answer

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:

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

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:

The probability of winning = 0.001 and hence the expected payoff = $0.

Step-by-step explanation:

There is a lottery contest and there are 1000 entries.

Only one will win and will get a prize of $710. All others would be given nothing.

We have to find the probability of the person winning.

Probability = [tex]\frac{number of favorable events}{total number of events}[/tex]

Number of favorable events = 1

Total number = 1000

So probability of winning the payoff = [tex]\frac{1}{1000}[/tex] = 0.001

Hence the expected payoff = $0

Check the picture below.

Answer:

B, C, D

Step-by-step explanation:

The information given about the teachers is limited to the fact they teach preschool.

B and D. If a teacher has more experience teaching, they are probably better at teaching. Even if the subject is not reading, they gain transferable teaching skills with experience.

C. Although both teachers teach preschool, one may have many more years of experience or other qualifications, which will likely help them to teach better in generally.

A. The samples 30 and 40 students in a typical class are enough to show different students' various learning styles and strengths. The sample size is big enough.

Question:

before last nights game a basketball player has scored an average ( arithmetic mean) of 20 points per game . she scored 25 points in last nights game raising her average go 21 points per game. how many games did she play before last night's game

Answer:

She played 4 games before last night's game

Step-by-step explanation:

Given:

Average of last night basketball games = 20

Points scored in last night game =  25

Rise in average after last night game =  21

To Find:

The number  of games played last night = ?

Solution:

Let the number of games played before last night's game be x

Then

The average of x games =20

That is

[tex]\frac{\text{ Total points scored in x games}}{x}= 20[/tex]

Total  points scored in x games = 20x

In last night game she scored 25 points

So now the total score will be  = 20x+25 and

the number of games will be x+1

Now the

The average of x+1 games = 21

[tex]\frac{20x+25}{x+1}[/tex] =21

[tex]20x+25 =21 \times (x+1) [/tex]

[tex]20x+25 =21x+ 21[/tex]

[tex]25-21 =21x-20x[/tex]

x=4

Answer:

1. Emily scored 60 points in the first round

2. Emily scored minus 30 points in the second round

3. Emily's final score is 15 points.

Step-by-step explanation:

1. Let's review all the information given to us to answer the questions correctly:

Points awarded for a correct answer = 20

Points deducted for a incorrect answer = 10

2. Let's calculate the score of Emily in the first round:

Score = 7 * 20 - 8 * 10

Score = 140 - 80

Score = 60

Emily scored 60 points in the first round

3. Let's calculate the score of Emily in the second round:

Score = 4 * 20 - 11 * 10

Score = 80 - 110

Score = - 30

Emily scored minus 30 points in the second round

4. Let's calculate the final score of Emily:

Final score = (Score 1st round + Score 2nd round)/2

Final score = (60 + - 30)/2

Final score = (60 - 30)/2 = 30/2 = 15

Emily's final score is 15 points.

Answer:

114791256

Step-by-step explanation:

27*17=486

486^3=114791256

Answer:

114791256

Step-by-step explanation:

27*17=486

486^3=114791256

The value of x is 30

Solution:

Given that measure of exterior angle of regular polygon is 2x

The measure of interior angle is 4x

To find: value of x

The sum of an interior angle plus an exterior angle must be equal to 180 degrees (supplementary angles)

measure of exterior angle + measure of interior angle = 180

2x + 4x = 180

6x = 180

x = 30

Finding the measure of an exterior angle

measure of exterior angle = 2x = 2(30) = 60 degrees

Finding the measure of interior angle

measure of interior angle = 4x = 4(30) = 120 degrees

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:

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)}

Domain of the function f(x)=3x^3 is 2,5 what is the function range?

Answer:

The range of given function is {24, 375}

Solution:

Domain of the function is possible input of the function that is "x" and range of the function is possible output of the function that is f(x)

So we can substitute the given domain values of "x" in f(x) and find the range of function

As per the given question:

The domain of the function [tex]f(x) = 3x^3[/tex] is, [2, 5]

We have to find the range of the function

Substitute x = 2 in f(x)

[tex]f(x) = 3x^3[/tex]

[tex]f(2) = 3 (2)^3 = 3(8) = 24[/tex]

Substitute x = 5 in f(x)

[tex]f(5) = 3(5)^3 = 3 \times 125 = 375[/tex]

Therefore range of given function is {24, 375}

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

To know more about equations follow

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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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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:

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:

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:

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 :)

Explanation: All fractions positive or negative are rational numbers so 3/2 must be rational. Another way to think about rational numbers is that if you can turn the number into a fraction, it's rational. Since 3/2 is already in fraction form, it's a rational number.

Answer:

y=4x+8

Step-by-step explanation:

I assume you want this rewritten in slope intercept form. That means we need to isolate the y.

-4x+y=-8

Add 4x to both sides

y=-8+4x

Now let's rewrite it in slope intercept form. Recall slope intercept form is y=mx+b. That means our 'b' (8) must be on the end of the equation.

y=4x+8

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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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.