Problem: Four students tried to write 12x + 3y=9 in equivalent y= mx + b form.
Question: Did each student get an equation that is equivalent to the original Ax + By=C form?
If so, explain the reasoning for each step. If not, tell what errors the students made.

Answer:

1

Step-by-step explanation:

Add 4+1=5 then do 5÷5=1

Answer:16

Step-by-step explanation: -4(5 - 1) is 16.

Answer:

the answer is -16

Step-by-step explanation:

z(x-1)

-4(5-1)

-4(4)

-16

Answer: f= -3x^2-x-1/ x

Step-by-step explanation:

Answer: 8a + 2b + 19 is the answer

Answer:

= 8a +2b + 19

Step-by-step explanation:

Combine Like Terms:

(12a + −4a) + (3b + −b) + (19)

=8a + 2b + 19

Answer:

Sham Rock is searching for a four-leaf clover in a field. He finds 2 four-leaf clovers during the first 12 minutes of his search. If Sham spends a total of 180 minutes searching in the field, predict the number of four-leaf clovers he will find.

Step-by-step explanation:

Answer:

245,564people

Step-by-step explanation:

The population of Algebra City is approximately 314,159 people, but the rate decreases at 2.7% each year. About how many people will live in Algebra City in 9 years?

We solve for the above question using the formula for Exponential decrease. =

P(t).= Po(1 - r)^t

Where

P(t) = ?

Po = Initial population = 314159

r = 2.7% = 0.027

t = time = 9 years

P(t) = 314159(1 - 0.027)⁹

= 245564.2088

Approximately to the nearest whole number = 245,564people

\(\huge\text{Hey there!}\)

\(\huge\textbf{Keep in mind:}\)

\(\large\textbf{When you hear or see the word \boxed{quotient} in mathematics}\\\large\textbf{usually it means the RESULT/ANSWER of a division}\\\large\textbf{equation.}\)

\(\huge\textbf{Assuming:}\)

\(\mathbf{\dfrac{1}{3}}\)

\(\mathbf{\dfrac{1\leftarrow \boxed{\mathsf{dividend}}}{3\leftarrow \boxed{\mathsf{divisor}}} = result \leftarrow \boxed{\mathsf{quotient}}}\)

\(\mathbf{1 \leftarrow \boxed{\rm{dividend}} \div 3 \leftarrow \boxed{\rm{divisor}} = result\leftarrow \boxed{\rm{quotient}}}\)

\(\uparrow\huge\textbf{Simplify \& you'll have the quotient}\uparrow\)

\(\mathbf{Quotient \rightarrow 0.333333333}\)

\(\mathbf{Quotient \approx 0}\)

\(\huge\textbf{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{0}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer: 19.

Step-by-step explanation:

9 -3 / 1/3 + 1

6 / 1/3  +  1

(6 * 3/1)  + 1   also written as (6 * 3)  +  1

18   +  1

= 19.

Answer:

Step-by-step explanation:

V = w h l

V = 7.5 * 7.5 * 6

V = 337.5cubic feet * 0.05

V = 16.875Lbs

V = 17Lbs (Rounded to nearest pound)

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

To know more about concave mirror Visit:

https://brainly.com/question/31379461

#SPJ11

The height of Corbin's model given the actual height of the monument and the scale of the model is 6.04 inches.

A scale model is smaller representation of a bigger object / drawing. The scale model is reduced by constant dimensions.

The height of Corbin's model = 604 / 100 = 6.04 inches

To learn more about scale models, please check: https://brainly.com/question/20213755

#SPJ1

Answer:

8 hours

Step-by-step explanation:

72 miles per hour

576/72= 8

The sum of all the angles of a triangle is 180 degrees

We see that Line HI and JI are equal in length meaning that triangle HIJ is an isosceles triangle. This means that the two angles of unknown measure are both x.

So lets now set up our equation:

  \(x + x + 74 = 180\\2x = 106\\x = 53\)

Thus x is 53 degrees

Hope that helps!

Answer:

\(x = 6\)

Step-by-step explanation:

\(7x + 6 + 2x = 60 \\9x + 6 = 60\)

add \(-6\) to both sides

\(9x + 6 - 6 = 60 - 6 \\9x = 54\)

Divide both sides by \(9\)

\(\frac{9x}{9} = \frac{54}{9}\)

\(x = 6\)

According to the equation, the weight of box in ounces is 64.

Firstly let us represent the weight of box with w. Now, the formula to be used for calculation of the weight of box is -

The weight of box in ounces = weight of box in pounds × number of ounces in one pound/one

Keeping the values in formula to find the value of weight of box in ounces.

The weight of box in ounces = 4 × 16/1

Performing multiplication and division on Right Hand Side of the equation to find the weight of box in ounces

The weight of box in ounces = 64 ounces

Thus, the weight of box in ounces is 64.

Learn more about pounds -

https://brainly.com/question/10618309

#SPJ4

To calculate the future value (FV) of $200 under different compounding periods, we can use the formula for compound interest:

FV = P(1 + r/n)^(nt)

where:

FV = Future Value

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Number of years

Given:

P = $200

r = 4% = 0.04

t = 6 years

a. Compounded annually:

n = 1

FV = 200(1 + 0.04/1)^(1*6) = $200(1.04)^6 ≈ $251.63

b. Compounded semiannually:

n = 2

FV = 200(1 + 0.04/2)^(2*6) = $200(1.02)^12 ≈ $253.72

c. Compounded quarterly:

n = 4

FV = 200(1 + 0.04/4)^(4*6) = $200(1.01)^24 ≈ $254.92

d. Compounded monthly:

n = 12

FV = 200(1 + 0.04/12)^(12*6) = $200(1.0033)^72 ≈ $255.23

e. Compounded daily:

n = 365

FV = 200(1 + 0.04/365)^(365*6) = $200(1.0001096)^2190 ≈ $255.26

f. The observed pattern of future values (FVs) increasing with more frequent compounding is due to the effect of compounding interest more frequently. As the compounding periods increase (annually, semiannually, quarterly, monthly, daily), the interest is added to the principal more often, allowing for more significant growth over time. This compounding effect leads to slightly higher FVs as the compounding periods become more frequent.

To learn more about investment : brainly.com/question/14921083

#SPJ11

The slope-intercept form of the linear equation will be y = 6x - 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The points are given below.

(-1, -10) and (3, 14)

The equation of the line that passes through the points (-1, -10) and (3, 14) will be given as,

(y + 10) = [(14 + 10) / (3 + 1)](x + 1)

y + 10 = 6(x + 1)

y + 10 = 6x + 6

y = 6x - 4

The slope-intercept form of the linear equation will be y = 6x - 4.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

Answer:

121

Step-by-step explanation:

10(3)^2-7(3)+10=121

Brillianst please!!!

Answer:

a = 45

Step-by-step explanation:

Start by changing the fractions so they share a common denominator to combine like-terms:

6/10a - 5/10a = 9/2

1/10a = 9/2

Multiply both sides by 10 to isolate a.

a = 90/2

a = 45

Congruent angles simply means angles that are equal. A triangle has three angles . Since one of the angle is given as 98 degree, the other 2 angles which are congruents are therefore equal. The total angle of a triangle is equals to 180 degree. Therefore,

x = 41 degree

The second term of the finding sequence is 25.

When you are confronted by a question like this, you can make a simple equation, combine like terms, isolate the variable, and solve.

"5 consecutive odd numbers" basically means x + (x + 2) + (x + 4) + (x + 6) + (x + 8). Each time you add 2 more to ensure there are no even numbers. Otherwise, it wouldn't be only consecutive odd numbers.

We are told the sum of these numbers is 135. This means x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

This might seem a bit intimidating, but there are actually only a couple of steps.

Combine like terms.

In this case, the like terms are the 5 times x appears and the numbers 0, 2, 4, 6, and 8.

x + x + x + x + x = 5 • x, or 5x.

0 + 2 + 4 + 6 + 8 = 20

So by combining like terms, we can simplify (x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135 down to just 5x + 20 = 135.

Isolate the variable.

Now we just have to isolate x. The value of x is the lowest term in the sequence.

5x + 20 = 135

To isolate x, first subtract 20 from both sides. Then, divide both sides by 5.

5x + 20 - 20 = 5x

135 - 20 = 115

5x = 115

5x / 5 = x

115 / 5 = 23

x = 23

The lowest term in the sequence is 23.

Identify all numbers in the sequence.

Now that we know x, we can find the rest of the numbers in the sequence by plugging the lowest value into the original equation we created.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

(23 + 0) + (23 + 2) + (23 + 4) + (23 + 6) + (23 + 8) = 135

23 + 0 = 23 This is the first and lowest term in the sequence.

23 + 2 = 25 This is the second term in the sequence.

23 + 4 = 27 This is the third term in the sequence.

23 + 6 = 29 This is the fourth term in the sequence.

23 + 8 = 31 This is the fifth and last term in the sequence.

Now we know the sequence is 23, 25, 27, 29, 31.

Finding the Answer:

To find the answer, locate the second term in this sequence.

23, 25, 27, 29, 31

The second term is 25.

The complete question is-

The sum of 5 consecutive odd numbers is 135. What is the second number in this sequence?

learn more about the sequence,

https://brainly.com/question/30262438

#SPJ4

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

Learn more on monthly payment here;

https://brainly.com/question/25599836

#SPJ1

Answer:

4(0.5-3)=n-0.25(12-8n)

2-12=n-3+2n

-10=-3+3n

-10+3=3n

-7=3n

n=-2.3

Answer: n= -7/3

Step-by-step explanation:

4(0.5 - 3) = n - 0.25(12 -8n)  solve for n .

2 - 12 = n - 3 + 2n  

 -10 = 3n - 3

+ 3           +3

n = -7/3

Answer:

7/20

Step-by-step explanation:

because it is 2 minutes of news for every/ 20 minutes of music.

The answer is 7/20.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

local radio station WMTH schedules 2 minutes of news for every 20 minutes of music

now, we get,

because it is 2 minutes of news for every/ 20 minutes of music.

To learn more on ratio click:

brainly.com/question/13419413

#SPJ2

Answer:

nsjdbkskskdnskksmsnsjdnnnnndjdnnndndnj

Fashion trends influence people's tastes and preferences in clothing.

Fashion trends have a significant impact on the demand for clothing and fashion accessories. They play a crucial role in shaping people's tastes and preferences, which directly affect their purchasing decisions. As fashion trends change, consumers are influenced to adopt new styles, designs, and aesthetics, leading to shifts in their demand for clothing items.

Fashion trends are a non price determinant of demand because they operate independently of the price of the products. Unlike factors like price, income, or availability, fashion trends do not directly affect the quantity demanded at a given price. Instead, they influence consumers' preferences, attitudes, and perceptions towards different clothing options, leading to changes in the overall demand for fashion products.

Fashion trends can create a sense of novelty, social acceptance, and personal expression, driving consumers to seek out specific styles or brands that align with the current trends. This influence on people's tastes and preferences in clothing can result in shifts in demand curves as consumer preferences change over time. Therefore, fashion trends are a significant nonprice determinant of demand in the fashion industry.

Learn more about price here:

https://brainly.com/question/19091385

#SPJ11

Answer:

y=1/2×+4

Step-by-step explanation:

i think that the answer