Answer:
(3, 2)
Step-by-step explanation:
I am sure
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
Find the slope of the line below. *
Answer:
-2
Step-by-step explanation:
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.
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
Which simplified ratio correctly compares 12 yard to 20 feet?
A. 5:9
B. 3:5
C. 9:5
D. 5:3
Answer:
The answer is B
Step-by-step explanation:
If you look at the problem you can put 12 and 20 into a ratio like this
12:20
then if you simplify it by like terms say 4
12 divided by 4 is 3
20 divided by 4 is 5
3:5
= B
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
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
A 4-digit number contains at least one even digit. How many such numbers are there? Please help me. I will mark brainliest
Given:
A 4-digit number contains at least one even digit.
To find:
How many such numbers are there?
Solution:
Digits are 0,1,2,3,4,5,6,7,8,9.
Number of odd digits = 5
Number of even digits = 5
4-digit numbers are from 1000 to 9999.
Total number of 4-digit numbers = 9000
Possible ways to get odd digits on all the 4 places is
[tex]5\times 5\times 5\times 5=625[/tex]
It means 625 numbers are their in which all 4 digits are odd.
To find total 4-digit number that contains at least one even digit, subtract the numbers which contains only odd numbers from the total 4-digit numbers.
[tex]9000-625=8375[/tex]
Therefore, total 4-digit number that contains at least one even digit is 8375.
y=5x+1 and y=3x+13
System of equations?
Answer:
(6,31)
Step-by-step explanation:
solve the both equation;
3X+13=5X+1
or, 12=2X
or, X=6
substitute the value of x in the equation;
y=5X+1
or, y=5×6+1
or, y=31
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]
What is the approximate distance between the pints (9, 2) and (4, 8)?
Answer: aproximently d
Step-by-step explanation:
The bright line spectrum of Neon contains a line with the wavelength of 700 nm. What is the
frequency of this light and what color is it?
Answer:
1) The frequency of the light is approximately 4.283 × 10¹⁴ Hz
2) The color of the light is red
Step-by-step explanation:
1) The given parameter;
The wavelength of the line contained in the Neon spectrum, λ = 700 nm = 0.0000007 m = 7.0 × 10⁻⁷ m
The speed of light, v = 299,792,000 m/s
v = f × λ
The frequency, f of the light = v/λ = 299,792,000/(7.0 × 10⁻⁷) ≈ 4.283 × 10¹⁴ Hz
The frequency of the light ≈ 4.283 × 10¹⁴ Hz
2) Given that light with wavelength between 620 - 750 nm constitute red light, we have that the given light with a wavelength of 700 nm is a red light source.
pleaSe i need help brainlist if u get it right
Answer:
62.6
Step-by-step explanation:
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:
Answer these questions
Answer:
1. -1
2. 25°
3. 26 1/4
Step-by-step explanation:
1. 14-8 is 6, -2 - 4 = -6, 6 ÷ -6 is -1
2. 75 + 80 = 155, 180 - 155 = 25°
3. cross multiply 4/5 = 21/x (4x= 105) = 26 1/4 or 105/4
I hope this helped, please mark Brainliest, thank you!
Answer:
What she said
Step-by-step explanation:
1000000000000x1690000000000000000000000000000000000000000000000000000066666666e55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555+3333333333333333333333333333333333333333333444444444444x400
Answer:
oh god my calculator can't handle this
Step-by-step explanation:
so your answer is 3, take it or leave it
No way is that an actual question that you have to do for school. I tried solving it, but my calculator can't take much. Plus, I tried counting how many 0's and 5's and 3's and 4's there were but my tiny brain can't remember no matter what.
I am bored, though, so I did take away all of the extra numbers. I got 691,360 from solving 10 x 1695 + 334 x 40.
You're welcome, I guess.
Pranav is cooking cupcakes. The recipe calls
for 5 cups of sugar. He has already put in 4
cups. How many more cups does he need
to put in?
Answer: 1 cup
Step-by-step explanation:
he has already put in 4, and he needs 5
5-4 = 1
Answer:
Step-by-step explanation:
I more cup
i'm confused with this who knows about this?
Answer:
its C :)
Step-by-step explanation:
Find an
equation for the perpendicular bisector of the line segment whose endpoints
e (-3, -8) and (5,-4).
are
Answer:
[tex]y=-2x-4[/tex]
Step-by-step explanation:
Perpendicular Bisector
The bisector of a segment defined by points (x1,y1) and (x2,y2) must pass by the midpoint of the segment.
The midpoint (xm,ym) is calculated as follows:
[tex]\displaystyle x_m=\frac{x_1+x_2}{2}[/tex]
[tex]\displaystyle y_m=\frac{y_1+y_2}{2}[/tex]
The endpoints of the segment are (-3,-8) and (5,-4), thus the midpoint M is:
[tex]\displaystyle x_m=\frac{-3+5}{2}=1[/tex]
[tex]\displaystyle y_m=\frac{-8-4}{2}=-6[/tex]
Midpoint: M(1,-6)
Let's find the slope of the given segment. The slope can be calculated with the formula:
[tex]\displaystyle m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle m_1=\frac{-4+8}{5+3}=\frac{1}{2}[/tex]
If the bisector is also perpendicular, its slope m2 and the slope of the segment m1 must comply:
[tex]m_1.m_2=-1[/tex]
Solving for m2:
[tex]\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{\frac{1}{2}}=-2[/tex]
Once we have the slope -2 and the point through which our line must pass (1,-6), we compute the equation in its point-slope form:
[tex]y-y_o=m(x-x_o)[/tex]
[tex]y-(-6)=-2(x-1)[/tex]
Operating
[tex]y+6=-2(x-1)[/tex]
[tex]y+6=-2x+2[/tex]
Rearranging
[tex]\boxed{y=-2x-4}[/tex]
[tex]74 \times 54 + 7 \div 20[/tex]
slove this?
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:
I have tried to answer it over and over again but never got the right anser
Answer:
#1) 25 degrees #2) 155 degrees #3) 25 degrees #4) 25 degrees #5) 5x+15= 110
Step-by-step explanation:
basically the use the vertical angle relationship to figure it out
that would mean that 4=155 and 3=1 and since the relationship is straight angle pair it means that 155+ x= 180 180-155= 25
5) CDE= FDG this is the vertical angle rule so 5x+15= 8x-42
solve that by adding like terms, 5x-15= 8x-42 +15 by doing adding to both sides it eliminates the 15 because you added it with the like terms, -42 and got -57
-57+8x= 5x now subtract 8 on both sides, -57= -3x divide and it equals 19
now plug that back into the eqaution of 5x+15 5(19)= 95 + 15= 110
Subtract x2 - 2x - 6 from - 6x + 5
help!!!I don’t get this!!
Answer:
C is the correct answer
Step-by-step explanation:
You would find the answer to that equation by finding the root of 30
So it's C
Hope I helped :)
Please consider Brainliest :)
Solve for a in the proportion.
What is -6 to the second power times -6 to the fifth power
Answer:
2799366
Step-by-step explanation:
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]
Solve for h in the mathematical formula A = 1/2 (a+b)h.
Answer:
Step-by-step explanation:
Ok so the question say if A is a half
(a+b)h
You'll get 1/2+b x h which is the answer but I can't find h because you haven't stayed what h would be.
Adiosss
Solve for w in the proportion.
Answer:
w=40
Step-by-step explanation: