Answer: Online
Step-by-step explanation:
Find the unit price
(multiply 12.51 and 20.70 by 100 to make it easier to divide)
12.51 divided by 3 = 417
20.70 divided by 5 = 414
Hope this helps!
The value of x is at most 450.
a
x 450
c
x ≤ 450
d
x ≥ 450
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
How do you divide a mixed number into a whole number
Answer:
Rules for division with a mixed number and a whole numberThe mixed number is converted into an improper fraction and the whole number is written as a fraction with denominator 1.
2.Division of the fractions is converted into a multiplication operation by multiplying the improper fraction with the reciprocal of the whole number.
3.The resulting fraction, if required, is written as a mixed number in simplest form.I WILL GIVE YOU EXAMPLES AND LET ME JUST HOPE YOU GET IT ;)Example1: Divide. Write your answer as a mixed number in simplest form. 213÷7 Solution Step 1: First, we write the mixed number 213 as an improper fraction 213=(2×3+1)3=73; 7=71 Step 2: The division is converted into multiplication as follows 213÷7=73÷71=73×17 Step 3: Multiplying numerators and denominators 73×17=(7×1)(3×7)=721 Step 4: 721 can be simplified and written as follows 721=13 Step 5: So, 213÷7=13example2: Divide. Write your answer as a mixed number in simplest form. 5÷134 Solution Step 1: First, we write the mixed number 134 as an improper fraction 134=(1×4+3)4=74; 5=51 Step 2: 5÷134=51÷74=51×47 Step 3: Multiplying numerators and denominators 51×47=(5×4)(1×7)=207 Step 4: 207 can be written as a mixed number as follows 207=267 Step 5: So, 5÷134=267OK HOPE THIS HELPS YOU :')PLEASE MARK ME BRILLIANT :3 THANK YOU -
Answer:First step: Write the whole number and the mixed number as improper fractions.
Second step: Write the reciprocal of the divisor, 2/5, and multiply.
Third step: Simplify, if possible. ...
Fourth step: Perform the simple multiplication of the numerators and the denominators.
Step-by-step explanation:
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?
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:
3 3/5 divided by 18/25
pleaSe i need help brainlist if u get it right
Answer:
62.6
Step-by-step explanation:
5.2sin20xsin?o=....
Answer:
the answer is 0
Step-by-step explanation:
I hope this answer is correct
Write an algebraic expression for the word expression.
the sum of 3 and a number x
The expression is .
Answer:
3 + x
Step-by-step explanation:
Sum means to add, so you would just add 3 and x (since they haven't given an actual number and only a variable).
The sum of the number 3 and the variable x will be (x + 3).
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
In the linear expression, the degree of the variable is one.
The sum of 3 and a number x.
Then the expression will be
⇒ 3 + x
The number 3 is a constant number and the term x is a variable.
The expression (x + 3) is a linear expression because the degree of the expression is one.
The number of the variable is one, then the expression is linear expression of one variable.
Thus, the sum of the number 3 and the variable x will be (x + 3).
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
1. If f(x) = 6x2 and h(x) = 3x, then (f/h)(x)
A2
B2x
C2x2
Which ordered pair is an solution of the equation? Y+5=2(x+1)
Answer:
only -1,-5
got it from khan academy
ls this a function?
1234
2
3
44
Yes
No
Answer:
no
Step-by-step explanation:
this would not be considered a function
If you want to graph the relationship to compare the unit prices, what should the x- axis and the y-axis represent
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
find the linear function from the table
the weekly profit of your cat grooming business is modeled by the expression 2x-15. your profit is more than $55 and at most $105 write your profit as an inequality
Answer:
55 < 2x-15 < 105
Step-by-step explanation:
Just set the equation less than and greater than the variables given
A swimmer is looking for a species of fish along the coast line. She dives 12 feet below the surface of the ocean. Then she dives down 9 more feet. She swims back up 10 feet and down another 6 feet before she finds the species of fish she is looking for. What was the depth at which the swimmer finds the fish?
Answer:
17 feet
Step-by-step explanation:
Given
Downward Movements: 12 feet; 9 feet; 6 feet
Upward Movement: 10 feet
Required
Determine the position at which the swimmer got the fish
First, we need to add up the downward movements;
[tex]Downward = 12ft + 9ft + 6ft[/tex]
[tex]Downward = 27ft[/tex]
Then subtract the upward movement
[tex]Position = Downward - Upward[/tex]
[tex]Position = 27ft - 10ft[/tex]
[tex]Position = 17ft[/tex]
Which sentence contains a word that is misspelled because a silent letter has been left out?
A
She completely forgot the chords to the song.
B
Courtesy costs nothing, but it pays off in huge dividends.
C
Since rent prices in the city were higher than most morgages, she tried to buy a house.
D
Between traffic jams and a lack of nearby parking, we arrived very late to the comic convention downtown.
Answer:
C
Step-by-step explanation:
Morgages is spelled mortgages
Elena goes for a long walk. This graph shows her time and distance traveled throughout the walk.
What was her fastest speed, in miles per hour?
Do not include units (miles per hour) in your answer.
Answer:
Actually it is 4 mph.
Step-by-step explanation:
I know because I had it on a test I just took.
Her fastest speed was 4 miles per hour.
Given that,
Elena goes for a long walk.
This graph shows her time and distance traveled throughout the walk.
We have to find,
What was her fastest speed, in miles per hour?
According to the question,
The graph shows the time and distance traveled throughout the walk.
The distance traveled in every hour is given as follows.
In the given graph at the first point, the distance traveled in 1 hour is 3 miles.At the second point, the distance traveled in 1.5 hours is 0 miles.At the third point, the distance traveled in 2 hours is 5 miles.At the fourth point, the distance traveled in 3 hours is 7 miles.At the fifth point, the distance traveled in 4 hours is 9 miles.Therefore, Her fastest speed was 4 miles per hour.
For more details refer to the link given below.
https://brainly.com/question/24684377
The scissor lift is a device that can lower and raise a platform. the scissor lift can raise the platform at a rate of 2.0 inches per second after t seconds is given by H=2.0t +35. after how many minutes will the lift be at least 50 feet off the ground
Answer:
i thank it is 25 seconds.
Step-by-step explanation:
A car company can make 200 cars per day. How many weeks will it take to
make 5,600 cars?
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
Darryl earns $10 per hour tutoring students. if Darryl tutored for 25 hours this month, how much money did he earn this month
Answer:
danny makes 250 per month
Step-by-step explanation:
Answer:
Darryl earned $250.00 in a month.
Step-by-step explanation:
write each number in standard form and word form
11. 654 thousand, 321
12. five six point nine nine
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!
The question is in the picture. You will get 15 points and brainiest if you answer it. I need it asap as this is due in 12 minutes.
Answer:
constant proportanality is 12 k=12
Step-by-step explanation:
because 5 time 12= 60 and it keep going and going
10x-2x in fewer terms
Answer:
Step-by-step explanations:
10x - 2x
8x
10x - 2x in fewer terms is 8x.
What is Subtraction?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
7/8 divided by 2/3 in simplest form
Answer:
21/16
Step-by-step explanation:
f(x)=-x^2+3 pls help
Answer:
answer = -1
.-(-2)^2 +3 = -4 +3 = -1
Solve for x: u = k + yx
Solve for a in the proportion.
Harriet works at the Mint, where new coins are made. Old and fake coins are also destroyed there. Harriet has 10 bags of $1 coins. All 10 bags contain the same number of coins. Harriet knows that nine bags contain only good coins and that one bag contains only fake coins. The fake coins are all about 0.5 gram short. Harriet has forgotten which bag contains the fake coins.
Harriet has a set of scales for weighing like the ones in the illustration. What is the lowest number of times she can weigh bags on the scales in order to find the bag of fake coins?
Answer:
3 times
Step-by-step explanation:
She would have to weigh the fake coins and another bag of real coins to spot a difference, and then she would need to check another bag to see which was correct. Maybe thats right.
PLEASE ANSWER QUICKLY
Samantha plays on the softball team for her school. She strikes out twice every nine times
she is at bat. If she struck out 14 times this season, how many times was she at bat?
3.1
07
54
O
63
Answer:
63 :)
Step-by-step explanation:
Find the midpoint of the line segment with the given endpoints.
1. (-6,3) and (-6,-1)
2. (-3,-1) and (0,9)
Answer:
1. (-6,1)
2. (-1.5,4)
Step-by-step explanation:
1. (-6,3) and (-6,-1)
Midpoint = [tex](\frac{-6+ -6}{2} , \frac{3 + -1}{2}) = (-6, 1)[/tex]
2. (-3,-1) and (0,9)
Midpoint = [tex](\frac{-3 + 0}{2} , \frac{-1 + 9}{2} ) = (-1.5,4)[/tex]
You buy 4.5 pounds of bananas at $0.49 a pound. You hand the cashier a $20 bill. How much change will you get back
Answer:
You get 17.80 cents back
Step-by-step explanation:
4.5 times 0.49 is 2.20 cents
20 minus 2.20 is 17.80 dollars