Logan used 12 centimeters of tape to wrap 4 presents. How much tape will Logan need in all if he had wrap 8 presents? Assume the relationship is directly proportional.

Answer:   x = -3 + √3     or     x = -3 - √3

Step-by-step explanation:

X²+6x+6

now breaking 6x into 2x and 3x we get ,

X²+3x+2x+6

taking x common and 2 common we get ,

x(x+3)+2(x+3)

taking (x+3) common

(x+3) (x+2)

so comparing with zero to get values of x ,

either

x+3=0

x=-3

or x+2=0

x=-2

Answer:

Junior PSAT

Training Packet

2016-17

Math Department  

Answer Key

Section 3: Math Test — No Calculator

QUESTION 1.

Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4.

Dividing both sides of 5x = 4 by 5 yields x =

_4

5

. Te value of x can now be

substituted into the expression 10x + 3, giving 10 ( _4

5 ) + 3 = 11.

Alternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and

10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.

Choices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10,

contradicting the given equation, 5x + 6 = 10. For example, choice A is

incorrect because if the value of 10x + 3 were 4, then it would follow that

x = 0.1, and the value of 5x + 6 would be 6.5, not 10.

QUESTION 2.

Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0.

Ten, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives

5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting

2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Terefore, the solution to the

given system of equations is (2, −2).

Alternatively, the equation x + y = 0 can be rewritten as x = −y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. Te value of y can then

be found in the same way as before.

Choices A, C, and D are incorrect because when the given values of x and

y are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the

equations are not true. Tese answers may result from sign errors or other

computational errors.

QUESTION 3.

Choice A is correct. Te price of the job, in dollars, is calculated using

the expression 60 + 12nh, where 60 is a fxed price and 12nh depends on the

number of landscapers, n, working the job and the number of hours, h, the job

takes those n landscapers. Since nh is the total number of hours of work done

when n landscapers work h hours, the cost of the job increases by $12 for each

hour a landscaper works. Terefore, of the choices given, the best interpretation

of the number 12 is that the company charges $12 per hour for each landscaper.

Choice B is incorrect because the number of landscapers that will work each

job is represented by n in the equation, not by the number 12. Choice C is

incorrect because the price of the job increases by 12n dollars each hour,

which will not be equal to 12 dollars unless n = 1. Choice D is incorrect

because the total number of hours each landscaper works is equal to h. Te

number of hours each landscaper works in a day is not provided.

QUESTION 4.

Choice A is correct. If a polynomial expression is in the form (x)2

+ 2(x)(y) +

(y)2

, then it is equivalent to (x + y)2

. Because 9a4

+ 12a2

b2

+ 4b4

= (3a2

)2

+

2(3a2

)(2b2

) + (2b2

)2

, it can be rewritten as (3a2

+ 2b2

)2

.

Choice B is incorrect. Te expression (3a + 2b)4

is equivalent to the product

(3a + 2b)(3a + 2b)(3a + 2b)(3a + 2b). Tis product will contain the term

4(3a)3

(2b) = 216a3

b. However, the given polynomial, 9a4

+ 12a2

b2

+ 4b4

,

does not contain the term 216a3

b. Terefore, 9a4

+ 12a2

b2

+ 4b4 ≠ (3a + 2b)4

.

Choice C is incorrect. Te expression (9a2

+ 4b2

)2

is equivalent to the

product (9a2

+ 4b2

)(9a2

+ 4b2

). Tis product will contain the term (9a2

)

(9a2

Answer:

that looks hard

Step-by-step explanation:

b

Answer:

-3n-7

Step-by-step explanation:

n-7-4n

and then u combine like terms and u get

-3n-7

Answer:

-3n-7

Step-by-step explanation:

n also means 1n

Answer:

the answer is 0

Step-by-step explanation:

I hope this answer is correct

Answer:will hope it help to find the answer with an unqualified

Step-by-step explanation:

Answer:

Step-by-step explanations:

10x - 2x

8x

10x - 2x in fewer terms is 8x.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

Given is an expression 10x - 2x.

We have to find the difference of these two expressions.

We can add or subtract only the like terms.

Like terms are terms which consist of same kind of variables.

Here 10x and 2x have same variable x.

So they can be subtracted.

10x - 2x = x(10 - 2) = 8x

Hence the difference of 10x and 2x is 8x.

To learn more about Subtraction, click on the link given below :

https://brainly.com/question/1927340

#SPJ3

Answer:

4 weeks

Step-by-step explanation:

5,600/200 = 28

28/7 = 4

Answer:

4 weeks

Step-by-step explanation:

200x7=1400

5600/1400=4

Answer:

The answer is 12

Step-by-step explanation:

Answer:

it represents the following

read in my explanation

Step-by-step explanation:

A bar chart is a graph with rectangular bars. The graph usually compares different categories. Although the graphs can be plotted vertically (bars standing up) or horizontally (bars laying flat from left to right), the most usual type of bar graph is vertical.

The horizontal (x) axis represents the categories; The vertical (y) axis represents a value for those categories. In the graph below, the values are percentages.

Answer:

The unit price in this situation is the approximate cost per pound of clementines. So, the x-axis should represent the number of pounds. The y-axis should represent the cost.

Step-by-step explanation:

Plato correct answer word for word

Answer:

Step-by-step explanation:

The weights in pounds of the defensive linemen were :

254,311, 297, 323, 260, 242, 300, 252, 303, 274

Ascending order: 242 ,252 ,254 ,260 ,274 ,297 ,300 ,303 ,311 ,323

The weights in pounds of the offensive linemen were :

310 ,315, 305, 318, 298, 301, 321, 332, 320

Ascending order:298 ,301 ,305 ,310 ,315 ,318 ,320 ,321 ,332

a)

Offensive line       Stem        Defensive line

                               24     |            2

                               25     |            2 , 4

                               26     |            0

                               27     |            4

         8             |      29     |           7

      1,5              |      30     |           0,3

     0,5,8           |      31      |           1

     0,1               |      32     |           3

      2                |      33     |

Five number summary of offensive line:

1) minimum: 298

2) maximum: 332

3)

Lower quartile:298 ,301 ,305 ,310

Q1 is the median of lower quartile

[tex]Q1=\frac{301+305}{2}=303[/tex]

4)

Upper quartile:318 ,320 ,321 ,332

Q3 is the median of upper quartile

[tex]Q3=\frac{320+321}{2}=320.5[/tex]

5)

Q2 is the median

 298 ,301 ,305 ,310 ,315 ,318 ,320 ,321 ,332

Mid value =[tex]\frac{9+1}{2}[/tex]=5th term = 315

Q2=315

Five number summary of defensive line:

1) minimum: 242

2) maximum: 323

3)

Lower quartile:242 ,252 ,254 ,260 ,274

Q1 is the median of lower quartile

Q1=254

4)

Upper quartile:297 ,300 ,303 ,311 ,323

Q3 is the median of upper quartile

Q3=303

5)

Q2 is the median

 242 ,252 ,254 ,260 ,274 ,297 ,300 ,303 ,311 ,323

Mid value =\frac{274+297}{2}=285.5

Q2=285.5

c) Mean weight of offensive line = [tex]\frac{298+301+305+310+315+318+320+321+332}{9}=313.33[/tex]

Mean weight of defensive line = [tex]\frac{242+252+254+260+274+297+300+303+311+323}{10}=281.6[/tex]

Mean weight of offensive line is more

So, Offensive group of players tends to be heavier

Answer:

constant proportanality is 12 k=12

Step-by-step explanation:

because 5 time 12= 60 and it keep going and going

Answer:

21/16

Step-by-step explanation:

Answer:

[tex]x = 4y[/tex]

Step-by-step explanation:

Given

[tex]y = kx[/tex]

See attachment for options.

Required

Determine which of the options answers the question

Analyzing the option one after the other:

[tex]\frac{x}{y} = 4[/tex]

Multiply through by y

[tex]y * \frac{x}{y} = 4 * y[/tex]

[tex]x = 4y[/tex]

Divide through by 4

[tex]\frac{x}{4} = \frac{4y}{4}[/tex]

[tex]\frac{x}{4} = y[/tex]

This can be rewritten as

[tex]y = \frac{x}{4}[/tex]

[tex]y = \frac{1}{4} x[/tex]

By comparison with [tex]y = kx[/tex]

we have:

[tex]y = y[/tex]

[tex]x = x[/tex]

[tex]k = \frac{1}{4}[/tex]

Hence: this answers the question.

Answer:

x=2

Step-by-step explanation:

12=12 2=2

the sides have the same x

Answer:

Step-by-step explanation:

The number of rectangles and combinations:

Total

Now the number of,

Rectangles and combinations are,

→ 1 rectangle = 6

→ 2 rectangles = 5

→ 3 rectangles = 4

→ 4 rectangles = 3

→ 5 rectangles = 2

→ 6 rectangles = 1

Then the total number is,

→ 6+5+4 + 3+2+1

→ 15 + 6 = 21

Hence, total number is 21.

Answer:

to evaluate a function, substitute the input

Step-by-step explanation:

(the given number or expression) for the function variable (place holder, x) replace the x with the number or expression. 1. given function f (x)=3x -5 finf (f) 4.

Answer:

danny makes 250 per month

Step-by-step explanation:

Answer:

Darryl earned $250.00 in a month.

Step-by-step explanation:

Answer:

162 is greater than 130.. if that's what your are talking about..

Answer:

After 2 hours the Red Cross raises $250 and after 6 hours it raised a total of $785. What's the average rate of change in terms of dollars per hour? Add answer. Log in to add ... If we start with 5 cells, and each cell divides in two every 15 minutes, how many total after 1 hour? if you what 3x +2/w is than you ...

Step-by-step explanation:

Step-by-step explanation:

Given data

Let the cheese be x

And strawberry be y

So

6x+6y=96-------1

x+4y=52----------2

Solving 1 and 2 simultaneously

Let us multiply equation 2 by 6 we have

6x+6y=96

6x+24y=312

-0-18y=-216

18y=216

y=216/18

y=12

Put y=12 in equation 2

x+4*2=52----------2

x+8=52

x=52-8

x=44

cheese =44

strawberry =12

Answer:

The problem to get 358² is solved by adding 357 twice and then add 1 to the value of 357²

Step-by-step explanation:

The given information are;

The square of 356 = 126,736

The square of 357 = 127,449

We note that 357² = (356 + 1)² = 356² + 2×356 + 1 = 126,763 + 712 + 1 = 127,449

We can write the above equation as follows;

357² = (356 + 1)² = 356² + 356 + 356 + 1 = 126,763 + 712 + 1 = 127,449

357² = 127,449

Similarly, we have;

358² = (357 + 1)² = 357² + 357 + 357 + 1 = 128,164

358² =  128,164

We can also look at the question as forming squares with tiles

To form the square tile with 358 units per side, we add an extra row and column of 357 tiles each. Completing the figure with an extra tile at the top right or left corner

Therefore, the area of the 358 unit per side square = The area of the 357 unit per side + 357 + 357 + 1 =  128,164

11. 654,321

12. 56.99

Answer:

11. Standard form: 654,321

12. Standard form: 56.99

Word Form:

11. Six hundred fifty four thousand, three hundred twenty one

12. Fifty six point ninety nine

I hope this helps!

Answer:

55 < 2x-15 < 105

Step-by-step explanation:

Just set the equation less than and greater than the variables given

Answer:

false

Step-by-step explanation:

Answer:

false you will need more info

Step-by-step explanation:

Answer:

only -1,-5

got it from khan academy