Anita began solving the system ​ {x+y=8, x−y=2 ​ by writing 2x=10 .

Which property justifies this step?


Division Property of Equality

Multiplication Property of Equality

Addition Property of Equality

Substitution Property of Equality

in the number line, the end points are DG, and the point in between is O

DG = 88

DO = 5x + 12

OG = 2x

Set the equation. The two parts (DO & OG) are equal to the whole (DG)

2x + 5x + 12 = 88

Simplify. Combine like terms

(2x + 5x) + 12 = 88

7x + 12 = 88

Isolate the x. Remember to do the opposite of PEMDAS. Subtract 12 from both sides

7x + 12 (-12) = 88 (-12)

7x = 76

Isolate the x. Divide 7 from both sides:

7x/7 = 76/7

x = 76/7

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

Find DO. Plug in "76/7" for x:

DO = 5x + 12

DO = 5(76/7) + 12

Simplify. Remember to follow PEMDAS. Multiply 76 with 5

DO =  380/7 + 12

Next, divide 380 with 7

DO = 54.29 (rounded)

Finally, add

DO  = 54.29 + 12

DO = 66.29

66.29 is your answer

hope this helps

Answer:

13.33

Step-by-step explanation:

Answer:

0

4z^5

Step-by-step explanation:

We are asked to

Simplify m - {n - [p + (m + n - p)]}.

For that we remove first internal bracket and then next in the same order.

= m - {n - [p + m + n - p]}. (by removing the inner bracket)

Now we simplify the term inside by cancelling p

=  m - {n - [ m + n ]}.  Next is multiply by - the term m+n.

= m-[n-m-n].  Now n cancels out.

=m-(m) = 0

Finally we get 0 as answer.

0

2m

-2m + 2p

2.Select the correct difference.

-3z^ 5 - (-7z^ 5)

= 3z^5+7z^5

= 4z^5

Answer:

A) (0, 2)

Step-by-step explanation:

Rewriting the second equation to the same form as the first, it becomes

... 1/2y = x + 1

... y = 2x + 2

Now, it is clear that both equations have the same y-intercept at y=2, so that is the solution.

... (x, y) = (0, 2)

c : evaluate using order of operations ( pemdas )

Option: C is the correct answer.

 C-   Evaluate using order of operations

We know that while solving a algebraic expression we must follow the rule:

                       PEMDAS

whose full form is:

  Parenthesis , Exponents,Multiplication division addition and subtraction.

This means that parenthesis is to be solved first then the preference is given to the exponent, then division and multiplication are treated at the same level and the last preferred operation is addition and subtraction.

     Hence, the correct answer is:

          Option: C

answer will be equal to 3250 divided by 250 which is 13

The expression would be m - 4 because if Marty ran 4 more miles than Shana, that means that Shana ran 4 less miles than Marty.

The four inequalities are less than, less than or equal to, greater than, and greater than or equal to. Less than means that a number is less than the other number. For example, if you say 4 is less than 7 it is because 4 is less than 7 by 3 which makes 7 value more than 4. For less than or equal to, it means that the number or variable is less than or the same number as the other number. For example, if you say x is less than or equal to 9, that means that x is less than 9 or equal to 9. For greater than, it means that the variable is greater than the other number. For example, if x if greater than 10 than the variable has to be greater than 10 or 11 and so on. For greater than or equal to, it means that the variable is greater than the other number or equal to that number. For example, if x is greater than or equal to 12, then x is greater than 12 or 13 and up or x is equal to 12 or x is 12.

Answer: He needs to answer 20 emails.

Step-by-step explanation:

Given : Jim has answered 7 e-mails .  (1)

This  is 35% of the e-mails he must answer .

We can write 35% as 0.35.

Let x be the number of emails  he need to answer.

Then, Number of mails he has answered = 0.35x  (2)

From (1) and (2), we have

[tex]0.35=7\\\\\Rightarrow\ x=\dfrac{7}{0.35}=\dfrac{700}{35}=20[/tex]

Hence, he needs to answer 20 emails.

Answer:

[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]

Step-by-step explanation:

We are given that an expression

[tex]x^4+10x^2+25[/tex]

We have to find the factorize the expression completely over the cmplex number.

[tex](x^2+5)^2[/tex]

Using identity [tex](a+b)^2=a^2+b^2+2ab[/tex]

[tex](x^2+5)(x^2+5)[/tex]

Substitute each factor equal to zero.

[tex]x^2+5=0[/tex] ,[tex]x^2+5=0[/tex]

[tex]x^2=-5[/tex]

[tex]x=\pm \sqrt{-5}=\pm i \sqrt 5[/tex]

[tex]x=i\sqrt 5[/tex] and [tex]x=-i\sqrt 5[/tex]

[tex]x-i\sqrt 5=0[/tex] and [tex]x+i\sqrt 5=0[/tex]

The factor of second term is also same

Therefore, the factors of the   expression completely is given by

[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]

The solution to the quadratic equation is ±5i

Given the expression below:

x^4+10x^2+25 = 0

Let P = x^2

Substituting into the expression, we will have;

P^2 + 10P + 25 = 0

Factorizing the expression, we will have:

P^2 + 10P + 25 = 0

P^2 + 5P+ 5P + 25 = 0

P(P+5) + 5(P + 5) = 0

(P+5)(P+5) = 0

P = - 5 twice

Substitute into the given substitute

x^2 = -5

x = √-5

x = ±5i

Hence the solution to the quadratic equation is ±5i

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When the product of two numbers is 40 and one of the numbers is 8/15, the other number can be found by dividing 40 by 8/15, which is 937.5.

The question is asking for the other number when the product of two numbers is 40 and one of the numbers is given as 8/15. To answer this, we need to use the concept that the product of two numbers is equal to one number multiplied by the other. Therefore, to find the missing number, we need to divide 40 (the product) by the given number (8/15).

So, the calculation will look like this: 40 ÷ (8/15) = 7500/8 = 937.5.

Thus, the other number is 937.5 .

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it should be about 4-5 hours because her mom sleeps half the time that Mei sleeps!! you are welcome!

Answer:

9x^2 − 42xy + 49y^2

Step-by-step explanation:

The product of [tex](3x + 7y)^2[/tex] is: D)[tex]9x^2 + 42xy + 49y^2[/tex]

The product of (3x + 7y)^2 can be found using the formula for squaring a binomial:

(3x + 7y)^2 = (3x + 7y)(3x + 7y)

To calculate this product, you can use the distributive property (FOIL method):

(3x + 7y)(3x + 7y) = (3x * 3x) + (3x * 7y) + (7y * 3x) + (7y * 7y)

Now, simplify each term:

(9x^2) + (21xy) + (21xy) + (49y^2)

Combine like terms:

9x^2 + 42xy + 49y^2

So, the product of [tex](3x + 7y)^2[/tex] is:

D)[tex]9x^2 + 42xy + 49y^2[/tex]

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Answer:

it is a neg slope

Step-by-step explanation:

a. is Substitution Property

b. might be definition of supplementary angles

Answer:

B is the sum of adjacent angles is 180 degrees

Step-by-step explanation:

It is showing you that m∠3 and m∠4 "=" 180

(1)

(f+g)(x) = 6x^2+2x-7+4x-3=6x^2+6x-10

(f-g)(x)=6x^2+2x-7-4x+3 = 6x^2-2x-4

(2)

(f+g)(x)=2x-3x+1-2x=-3x+1

(f-g)(x)=2x-3x-1+2x=x-1

I think it is B. If you drew a graph of this and the x axis was time and the y axis is the  enrollment then you would get 3  different x values and  1 y value. That's still a function. I've drawn it below.

Given condition is: Sam took out an 80/20 mortgage on a $205,000 home.

Here, 80/20 refers to 80% mortgage amount means it will be paid as mortgage and 20% loan amount.

So, to find the amount financed under the first mortgage, we will find 80% of 205000.

[tex]\frac{80}{100}\times205000[/tex]

= $164000

Hence, option A is the correct answer.

Answer:

Quotient = x^4 + x^3 + x^2 + x + 1

Remainder = 0

Step-by-step explanation:

(x^5 +1) is divided by (x - 1) as shown below:

(x^5 +1) / (x - 1)

where x^5 is divided by (x - 1) when multiplied by x^4 (quotient) to give x^4 - 1.

Now x^4 - 1 is divided by is divided by (x - 1) when multiplied by x^3 (quotient) to give x^3 - 1.

Then again x^3 - 1 is divided by (x - 1) when multiplied with x^2 (quotient) to give x^2 -1.

x^2 - 1 is divided by (x - 1) when multiplied by x to give (x - 1).

Lastly, (x - 1) is divided by (x - 1) when multiplied by 1 to cancel the terms with remainder 0.

Hello...

Students - 30

Boys - 13

Girls - ?

30 - 13 = 17

There are 17 girls!

Percentage:

17 / 30 = 0.56666666667...

= 56.6...

Answer:

56% are girls

44% are boys

56.66% is the percentage of the class are girls.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.

Given:

Total students= 30

Number of boys= 13

Number of girls = 30- 13 = 17

So, percentage of the class are girls

= 17 /30 x 100

= 0.56666x 100

= 56.66%

Hence, 56.66% is the percentage of the class are girls.

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Hey there!!

What is the area of a rectangle?

The area of a rectangle = Length × Breadth

Given :

Length is 6m longer than the width.

Hence, length = 6 + breadth

Area = ( 6 + breadth ) ( breadth )

Area = 6 breadth + breadth²

Area = 775

Hence, 775 = 6 breadth + breadth²

( Let's take the breadth as ' b ' )

775 = 6b + b²

... b² + 6b - 775 = 0

... b² - 25b + 31b - 775 = 0

... b ( b - 25 ) + 31 ( b - 25 ) = 0

... ( b + 31 ) ( b -25 ) = 0

There are two solutions found :

b + 31 = 0 and b - 25 = 0

Hence,

b = -31 and b = 25

As the values can not be in negatives, we take 25

Hence, the value of the breadth is 25.

Length = 6 + b

Length = 31

Hence, the value of the length = 31

Hope my answer helps!!

Use distributive property:

(a + b)(c + d) = ac + ad + bc + bd

(x - 2)(x - 5) = (x)(x) + (x)(-5) + (-2)(x) + (-2)(-5) = x² - 5x - 2x + 10

60 times 0.14 = 8.4

You would give $8.40 as a tip of 14% from a bill of $60

Final answer:

To calculate a 14% tip on a $60 bill, you multiply 0.14 by $60, resulting in a tip of $8.40.

Explanation:

To find out how much a 14% tip is on a $60 bill, we need to convert the percentage into a decimal by dividing by 100.

This gives us 0.14 as the decimal form of 14%.

We then multiply this decimal by the total bill amount to calculate the tip: 0.14 × $60 = $8.40

Therefore, the tip would be $8.40.

Directrix:

If the vertex of the parabola is at (0, 0) and the focus is (0, -4) which is 4 units down then the directrix will be the line 4 units UP.

Answer: y = 4

Equation of parabola:

[tex]y = \frac{1}{4p}x^{2}[/tex]  ; where p is the distance from the vertex to the focus.

As stated above, the focus is 4 units down, so p = -4

[tex]y = \frac{1}{4(-4)}x^{2}[/tex]

[tex]y = \frac{1}{-16}x^{2}[/tex]

Answer: [tex]y = -\frac{1}{16}x^{2}[/tex]

Your answer is 28x^2-37x+12

1) Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd

28x^2-21x-16x+12

2) Collect like terms

28x^2+(-21-16x)+12

3) Simplify

28x^2-37x+12

Use FOIL

28x-21x-16x+12

-9x+12

Answer:

The metric system is based on the number 10.

Step-by-step explanation:

We have been given an incomplete statement. We are asked to fill in the blank for given statement.

The metric system is based on the number ___.

We know that metric system is an alternative system of measurement used in most countries including the United States. This system includes prefixes like kilo-, hecto-, deka-, deci-, centi-, and milli.

The metric system is based on number 10 as all these units are based on power of 10.

Therefore, option C is the correct choice.

The metric system is based on the number 10.

Here, we have,

The metric system is a decimal-based system of measurement that is widely used around the world. It is designed to be a coherent and consistent system, with units of measurement that are related to each other by powers of 10.

In the metric system, there is a base unit for each quantity being measured, such as meters for length, grams for mass, and liters for volume. The prefixes are then used to indicate multiples or fractions of the base unit. These prefixes are based on powers of 10, which allows for easy conversions between different units within the system.

For example, when we go from a larger unit to a smaller unit within the same measurement category, we move the decimal point to the right by powers of 10. Likewise, when we go from a smaller unit to a larger unit, we move the decimal point to the left by powers of 10.

This decimal-based nature of the metric system makes it highly convenient for scientific and everyday use, as it simplifies calculations and conversions.

The metric system is based on number 10 as all these units are based on power of 10.

Therefore, option C is the correct choice.

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Area of Parallelogram ABCD is equivalent to the area of rectangle AXBY.

Area of rectangle AXBY= Length AX * Length AB= 3 ft * 4√2 ft = 12√2 sq.ft.

Thus Area of Parallelogram is 12√2 sq.ft.

Answer:

The ratio of dogs to animals  [tex]\frac{9}{16}[/tex].

Step-by-step explanation:

If the shelter captures 9 dogs they also catch 7 cats.

So,

the total number of Animals = Total number of Dogs + Total number of Cats

                                                = [tex]9+7[/tex]

                                                 =[tex]16[/tex]

Therefore,

The ratio of dogs to animals    = Number of Dogs / Total number of animals

                                                   = [tex]\frac{9}{16}[/tex]

7/16

7 is dog 9 is cat

7+9=16