Imagine that you are a teacher grading your students’ assignments. The following questions were turned in with incorrect answers. Trace through the process of solving them to discover where your students made a mistake in their order of operations. Which step of PEMDAS did they do out of order? Explain.

(6-2)^2+12-3^2

The correct answer is 19
student answer 97

Answer:

Equation is 15(x-20) = 945

x = $83

Step-by-step explanation:

The cost of each lesson is $x

The discounted cost = x-20

Since 15 lessons cost 945,

the equation is

15(x-20) = 945

Simplifying by multiplying the term in brackets by 15:

15x - 15(20) = 945

15x - 300 = 945

Adding 300 on both sides isolates the 15 x term

15x = 945 + 300 = 1245

15x = 1245

Dividing both sides by 15 ,
x = 1245/15 = 83

So cost of lesson before discount is $83

The expression is simplified to y ^-7/x^-3

Algebraic expressions are expressions comprising of variables, terms, factors, coefficients, constants.

These expressions are also made up of arithmetic operations such as;

From the information given, we have;

y to the negative seventh power over x to the negative third power

This can be represented as;

Negative seventh power = ^-7

Negative third power = ^-3

Substitute into formula

y ^-7/x^-3

Thus, the expression is simplified to y ^-7/x^-3

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The maximum profit is 800, and the most T-shirts, sweatshirts, and hoodies you should produce is 10.

A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.

based on the available facts;

x= tshirt

y =sweatshirts

10x+20y≤1200

2x+20y≤600

x+y≥50

x≥0

y≥0

so p=6x+20y(objective function)

from above 10x+20y≤1200

20y/20=(-10x/20)+(1200/20)

          y=-1/2+(60)

put y value in all formula

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Answer:

2x + 3y = 13

4x - y = -2

In the second equation, subtract 4x from both sides.

-y = -2 - 4x

Divide both sides by -1.

y = 2 + 4x

Put this into the first equation in place of y.

2x + 3(2 + 4x) = 13

Multiply everything in the parenthesis by 3.

2x + 6 + 12x = 13

Combine like terms.

14x + 6 = 13

Subtract 6 from both sides.

14x = 7

Divide 14 on both sides.

x = 7 / 14

x = 0.5

Put this into the second equation in place of x.

4(0.5) - y = -2

2 - y = -2

Subtract 2 from both sides.

-y = -4

Divide both sides by -1.

y = 4

So x = 0.5 and y = 4.

Step-by-step explanation: I hope this helps.

If hypotenuse of an isosceles right triangle is [tex]4\sqrt{2}[/tex] units, then the area of the triangle is 8 square units

Given,

The hypotenuse of an isosceles triangle =[tex]4\sqrt{2}[/tex]

An isosceles triangle is a triangle that has at least two sides of equal length

Consider the two equal sides as x

According to Pythagoreans theorem

[tex]x^{2} +x^{2} =(4\sqrt{2})^{2} \\2x^{2} =32\\x^2=16[/tex]

x=4 units

We know,

Area of two isosceles right triangle equal to the area of the square with same length

Area of the square = [tex]x^{2} =4^{2}=16[/tex] square units

Then the area of the triangle =[tex]\frac{16}{2}=8[/tex] square units

Hence, if hypotenuse of an isosceles right triangle is [tex]4\sqrt{2}[/tex] units, then the area of the triangle is 8 square units

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Answer:

57,600 ft

Step-by-step explanation:

The solution to the inequality is x < 3.3

The given parameters are:

Perimeter < 18.7 feet

Side lengths: 4.1 ft 4.9 ft 6.4 ft x ft

The perimeter of a shape is the sum of the side lengths

So, we have

Perimeter = 4.1 ft + 4.9 ft + 6.4 ft + x ft

Remove the unit

So, we have

Perimeter = 4.1+ 4.9 + 6.4 + x

Evaluate the sum

Perimeter = 15.4 + x

Recall that

Perimeter < 18.7 feet

So, we have

15.4 + x < 18.7

Subtract 15.4  from both sides

x < 3.3

Hence, the solution to the inequality is x < 3.3

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Answer:

17 / 100 or 1 / 17

Step-by-step explanation:

Hope this helps :)

The required fraction of 17p in  £1 is 17 / 100.

Given that,
To determine the fraction of £1 is 17p.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
£1 = 100p
p = 1 / 100
Multiply by 17 on both sides,
17p = 17 / 100

Thus, the required fraction of 17p in  £1 is 17 / 100.

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Answer:

Your answer would be 17 because 171 divided by 9 is 19, so 323 divided by 19 would be 17.

Answer:

Step-by-step explanation:

Tom made $171 for 9 hours of work. At the same rate, how many hours would he have to work to make 323 ?

171 : 9 = 323 : x

x = 9 * 323 : 171

x = 2907 : 171

x = 17

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

check

171 : 9 = 323 : 17

19 = 19

The distance travel from Fresno to San Bernardino is 224 miles.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

Distance from sacramento to fresno =2x+10

Distance from fresno to san bernardino= 4x + 12

Distance from sacramento to san bernardino = 340.

According to given question we have

Distance from sacramento to fresno+Distance from fresno to san bernardino=Distance from sacramento to san bernardino

2x+10 +4x + 12 =340.

Compare the like terms we get

6x+22=340

Subtract 22 from both sides we get

6x=318

x=53

So,

Distance from sacramento to fresno

=2x+10

=2*53+10

=106+10

=116

Distance from fresno to san bernardino

= 4x + 12

=4*53+12

=224

Therefore, the distance travel from Fresno to San Bernardino is 224 miles.

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Answer:2

Step-by-step explanation:

There is 2 decimal places because you see how many numbers there are behind each of the decimals when multiplying then add them and that’s how many numbers are behind the decimal in the problem

2 digit long multiplication.

__________________________________________

Long multiplication can seem very intimidating, especially if you're multiplying two numbers that are pretty large, or like in this case if you're using decimals. If you take it step by step, though, you'll be able to do long multiplication in no time.

[tex]\frac{\begin{matrix}\:\:&3&4&\:\:\\ \:\:&\:\:&5&6\\ \times \:&\:\:&\:\:&7\end{matrix}}{\begin{matrix}\:\:&3&9&2\end{matrix}}[/tex]

How do we determine where the decimal point goes?

[tex]5.6\mathrm{\:has\:}1\mathrm{\:decimal\:place}[/tex]
[tex]0.7\mathrm{\:has\:}1\mathrm{\:decimal\:place}[/tex]
[tex]\mathrm{Therefore,\:the\:answer\:has\:}2\mathrm{\:decimal\:places}[/tex]
[tex]=3.92[/tex] is your FINAL ANSWER!
__________________________________________
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Hope you have a WONDERFUL day! (:

Answer:

d=rt-g

First, add G to both sides

d=rt-g

+g   +g

----------

dg=rt

Then divide by r since you're solving for t

dg    rt

---=-----

r       r

Your answer should be t=dg/r

Hope this helps!

Step-by-step explanation:

Answer:

a1 = 6 and an = an-1 - 5

a2 = a2-1 - 5 = a1 - 5 = 1

a3 = a3-1 - 5 = a2 - 5 = -4, etc

Step-by-step explanation:

The equation of the parabola is y = (-3/2)x + 1.

The general vertex form of the equation of a parabola is y = a(x - h)2 + k

where (h, k) are the coordinates of the vertex

Here, we are given that vertex = (0, 1)

Thus, the equation of the parabola is-

y = a(x - 0)2 + 1

y = 2ax + 1

Also, we are given that the parabola passes through (12, -17).

Thus, (12, -17) must satisfy the equation of the parabola

⇒ -17 = 2a(12) + 1

-17 = 24a + 1

24a = -17 -1

24a = -18

a = -18/24

a = -3/4

Thus, the equation of the parabola becomes-

y = 2(-3/4)x + 1

y = (-3/2)x + 1

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each input is mapped into only one output, so this is in fact a function.

A relation is a function if and only if each input is mapped into only one output.

Remember that an ordered pair is of the form (x, y), where x is the input and y the output.

In this case, the relation is defined by the ordered pairs:

(6, -2), (2, 2), (4, 1), (-1, 1)

We can see that each input is mapped into only one output, so this is in fact a function.

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Answer:

11/20

Step-by-step explanation:

Answer:

33/60 might be correct.

Step-by-step explanation:

1/4 hours is 15 minutes. 4/5 hours is 48 minutes

48-15=33 more minutes

Step-by-step explanation:

initally dose was 250 mg and then increased to 500 mg.

so, percent increase would be :-

(500-250)/250 * 100

= 1 %

so I guess u are correct.

The percentage increase in the size of the dosa is 100%

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the size of the dosa is increased from 250 to 500.

The amount of increment is:

500 - 250

= 250

The percentage change is given by:

(250/250) × 100%

= 100%

Hence, the percentage increase in the size of the dosa is 100%

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Answer: your mom

(x−5)(x−3)

Answer:

In the picrure

Step-by-step explanation:

Solution of the equation [tex][\frac{1}{5(10x-5)} =(5x-1)][/tex] is [x = (-0.512788205961), (-0.187211794039)].

As per the question statement, our concerned equation is  [tex][\frac{1}{5(10x-5)} =(5x-1)][/tex].

We are required to find the value of "x" that satisfied the equation. First, we will have to convert the given equation to the form of quadratic equation.

[tex][\frac{1}{5(10x-5)} =(5x-1)]\\or, 1=5(10x-5)*(5x-1)\\or, 1=5*5(2x-1)*(5x-1)\\or,1=25[(2x-1)(5x-1)]\\or,1=25(10x^{2} -2x-5x+1)\\or,1=25(10x^{2} -7x+1)\\or,1=250x^{2} -175x+25\\or,250x^{2} -175x+24=0\\[/tex]

Now, [(250x² - 175x + 24) = 0] is in the form of a quadratic equation.

Also, the formula to calculate the solutions of a standard quadratic equation [ax² + bx +c = 0] goes as [tex][x=(\frac{-b+\sqrt{(b^{2}-4ac) } }{2a}), (\frac{-b-\sqrt{(b^{2}-4ac) } }{2a}) ][/tex]

Comparing [ax² + bx +c = 0] with [(250x² - 175x + 24) = 0], we get

(a = 250), (b = 175) and (c = 24), and using these values in the above mentioned formula to calculate the solutions of quadratic equations, we get, [x = (-0.512788205961), (-0.187211794039)].

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As t increases the curve is changing according to the plot points given by the parametric equations.

The coordinates of the points that make up a geometric object, such as a curve or surface, are frequently expressed using parametric equations; in this case, the equations are collectively referred to as a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. It describes a collection of numbers that represent functions with one or more independent variables. The parameters used here are the independent variables. For the representation of the coordinates that make up geometric objects like curves and surfaces, parametric equations are used. Additionally, a curve that is not a function can be drawn using parametric equations.

The equations are

x=1-t²

y=2t-t²,-1≤t≤2

The sketch is in the diagram picture.

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Answer:

Yes because, Maybe because it's sometimes of technology occurs many things such as we no longer using old stuffs and living because. Even the calculator it's similar

i attached a pdf, hopefully it helps you understand!

15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:

it should be 4 3/8 but sorry if it's wrong <3

The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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Answer:

about 230lbs

Step-by-step explanation:

I think

Answer:

v = 11

Step-by-step explanation:

(9v - 3) and 84 are a linear pair and sum to 180° , that is

9v - 3 + 84 = 180

9v + 81 = 180 ( subtract 81 from both sides )

9v = 99 ( divide both sides by 9 )

v = 11