How many solutions are there for the system of equations shown on the graph?
A. No solution
B. One solution
C. Two solutions
D. Infinitely many solutions
Answers
Answer:
D
Step-by-step explanation:
There can be infinite solutions
Related Questions
The value of x is at most 450.
a
x 450
c
x ≤ 450
d
x ≥ 450
Answers
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
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?
Answers
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:
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?
Answers
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.
7/8 divided by 2/3 in simplest form
Answers
Answer:
21/16
Step-by-step explanation:
5.2sin20xsin?o=....
Answers
Answer:
the answer is 0
Step-by-step explanation:
I hope this answer is correct
Hope this helps segsy pig
Simplify
Rewrite the expression in the form 9^n
9•9^2= ___
Answers
Answer:
9^3
Step-by-step explanation:
Since you are given 9^2 already and have to multiply that result by yet another nine, then your problem is 9^3
Hope this helps!
pleaSe i need help brainlist if u get it right
Answers
Answer:
62.6
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?
Answers
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]
Of the 1,400 students enrolled at a Middle School, 40% of students enrolled are in the 6th grade. How many students are enrolled in 6th grade? Explain how you got your answer.
Answers
Answer:
560 students
Step-by-step explanation:
1400*.40=560 students in 6th grade
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.
Answers
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
If you want to graph the relationship to compare the unit prices, what should the x- axis and the y-axis represent
Answers
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
Solve for x: u = k + yx
Answers
=
u
y
−
k
y
is the answer
x= u/y - k/y
Find the midpoint of the line segment with the given endpoints.
1. (-6,3) and (-6,-1)
2. (-3,-1) and (0,9)
Answers
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
Answers
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
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?
Answers
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.
1. If f(x) = 6x2 and h(x) = 3x, then (f/h)(x)
A2
B2x
C2x2
Answers
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
Answers
Answer:
63 :)
Step-by-step explanation:
Please help me. Hurry, linear equations.
Answers
Answer:
Let's simplify step-by-step.
3−3/4x−1/4x−7
=3+ −3/4x+ −1/4x+ −7
Combine Like Terms:
=3+ −3/4x+ −1/4x+ −7
=(−3/4x+ −1/4x)+(3+ −7)
=−x+ −4
Answer:=−x−4
Step-by-step explanation:
answer:-4
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.
Answers
Answer:
C
Step-by-step explanation:
Morgages is spelled mortgages
Morgages is spelled wrong. It’s actually spelled mortgages.
What is the approximate distance between the pints (9, 2) and (4, 8)?
Answers
Answer: aproximently d
Step-by-step explanation:
Write an algebraic expression for the word expression.
the sum of 3 and a number x
The expression is .
Answers
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
Solve for a in the proportion.
Answers
10x-2x in fewer terms
Answers
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
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
Answers
Answer:
55 < 2x-15 < 105
Step-by-step explanation:
Just set the equation less than and greater than the variables given
Darryl earns $10 per hour tutoring students. if Darryl tutored for 25 hours this month, how much money did he earn this month
Answers
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
Answers
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!
f(x)=-x^2+3 pls help
Answers
Answer:
answer = -1
.-(-2)^2 +3 = -4 +3 = -1
Solve for h in the mathematical formula A = 1/2 (a+b)h.
Answers
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
A car company can make 200 cars per day. How many weeks will it take to
make 5,600 cars?
Answers
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
Help PLEASE!
Which statement is true about the equation 7(2+5x)=3x+14
7
(
2
+
5
x
)
=
3
x
+
14
?
The equation has infinitely many solutions.
The equation has infinitely many solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution because x=0
.
Answers
Answer:
the first answer is correct Edge 2020
Step-by-step explanation:
Answer:
Step-by-step explanation:
-6