Answer:
7 quarts of punch
Step-by-step explanation:
62/8 is 7.75,
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
Jill spends $525 for monthly bills. Of this amount she spends 110 on her cell phone bill and 25% on her car payment. The remainder pays her utilities. How much money does she spend on utilities?
Answer:
283.75
Step-by-step explanation:
525/4=131.25
131.25+110=241.25
525-241.25=283.75
Subtract x2 - 2x - 6 from - 6x + 5
pleaSe i need help brainlist if u get it right
Answer:
62.6
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]
How do you evaluate a function.
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.
[tex]74 \times 54 + 7 \div 20[/tex]
slove this?
If you were to roll the
dice two times what is the
probability it will land on a
3 both times?
Answer:
1/36
Step-by-step explanation:
A dice have 6 faces, each face have 1/6 chance to land on, so the chance of landing on 3 two times in a row is 1/6 x 1/6 = 1/36
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:
[tex] \sqrt{47} [/tex]
whats the answer
Step-by-step explanation:
[tex]\sqrt {47}[/tex]
Questions in the photo. Please HELP!
Answer:
Step-by-step explanation: its a
Answer:
No,
No
because every line has to equal 180. (for both of them)
The price of stock market in at 9 AM was 13.17 then the price has been increasing at a rate of 0.11 each hour at noon the price of stuff he was 13.67 it begins to decrease at the rate of 0.12 each hour if the two rates continue and how many hours were the prices of the two stocks with the same
Answer:
2.26 hours
Step-by-step explanation:
Given that:
Stock 1:
Initial price = 13.17
Rate of increase = $0.11 per hour
13.17 + 0.11h - - - (1)
Stock 2 :
Initial price = 13.69
Rate of decrease = 0.12 per hour
13.69 - 0.12h - - (2)
13.17 + 0.11h = 13.69 - 0.12h
0.11h + 0.12h = 13.69 - 13.17
0.23h = 0.52
h = 0.52 / 0.13
h = 2.26 hours
Which of the following best describes the English expression fourteen less
than the quantity of a number plus one?
A. (1 - x) +14
O B. 4 - 1
O C. (x + 1) - 14
D. (x - 1) +14
Answer:
c
Step-by-step explanation:
True or false? You can rely solely upon induction to prove that your conclusion is correct
Answer:
false
Step-by-step explanation:
Answer:
false you will need more info
Step-by-step explanation:
Write the following equation in slope intercept form.
7x-4y=22
y= x+
Answer:
y= -7x+22/-4
Step-by-step explanation:
Answer:
y=7/4x-11/2
Step-by-step explanation:
Move the Y and x values to separate sides
-4y=-7x+22
divide whatever it takes to make y alone (dived by -4)
y=7/4x-11/2
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
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
Jane decided she would spend the
of her money on Sweet Tarts. About how
many pounds of Sweet Tarts did Jane
purchase?
. Between the gum balls, Pixie Sticks, and
that she would spend the rest
Sour Patch Kids, how much money will
Nicholas have left of his allowance?
Answer:
can you comment the real question because this is just gibrish
Step-by-step explanation:
please help me quickly the question is on the image
what is the answer??
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
Find the area of the shape
10 points
1. The retail price of an electric toothbrush is $40. What is the price after
a markdown of 30%?*
Answer:
The answer is 12
Step-by-step explanation:
Simply the expressions
n-7-4n
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
HHHHHHEEEEEEEEELLLLLLLLLPPPPPP
Answer:8 over 4
Step-by-step explanation:
Rise over run
need help, plz answer
Answer:
55 r5
Step-by-step explanation:
Answer:
390/7=55 with a remainder of 5.
Step-by-step explanation:
we can get this answer by subtracting fifty-five sevens from three-hundred ninty.
390-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7=5
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
The square of 356 is 126,736 and the square of 357 is 127,449. What is 3582? Try to solve this problem without multiplying. Show your work.
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
I need some help with geometry.
Answer:
x = 17, angle 1 and 2 = 45
Step-by-step explanation:
Question 13
Find the value of x.
Multiply. Write your answer as a fraction in simplest form.
5/6⋅(−4 1/2)⋅(−2 1/5)=
Answer:
7425
Step-by-step explanation:
First let's make the last two fractions improper.
-4 1/2 = -9/2 -2 1/5 = -11/5
Now we have to find the least common denominator.
[tex]\frac{5}{6} *\frac{-9}{2}*\frac{-11}{5}[/tex]
The least common denominator is 30 because all the denominators can be multiplied by something to get 30.
[tex](\frac{5}{5})*\frac{5}{6}* (\frac{15}{15})*\frac{-9}{2}* (\frac{6}{6})*\frac{-11}{5}[/tex] Simplify
[tex]\frac{25}{30}*\frac{-135}{30}*\frac{-66}{30}[/tex] simply
[tex]\frac{-3375}{30}*\frac{-66}{30}[/tex]
[tex]\frac{222750}{30}[/tex] simply
7425