1. Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, y, after x days. In how many days will the water level be 26 feet?
Slope(m)=
y-intercept(b)=
equation y=
Answer=
Slope = -0.5
Y-intercept = 34
Equation: y = -0.5x + 34
Answer = It will take 16 days for the water level to be 26 feet.
The question is an illustration of a linear function.
The equation of the function is: [tex]\mathbf{y = 34- 0.5 x}[/tex]The number of days to reach 26ft is 16The given parameters are:
[tex]\mathbf{Level = 34ft}[/tex]
[tex]\mathbf{Rate = -0.5ft/day}[/tex]
The equation of the function is:
[tex]\mathbf{y = Level +Rate \times x}[/tex]
Where:
y represents the water level
x represents the number of days
So, we have:
[tex]\mathbf{y = 34- 0.5 \times x}[/tex]
[tex]\mathbf{y = 34- 0.5 x}[/tex]
A linear equation is represented as;
[tex]\mathbf{y = mx + b}[/tex]
So, by comparison:
[tex]\mathbf{Slope(m) = -0.5}[/tex]
[tex]\mathbf{y-intercept (b) = 34}[/tex]
When the water level is 26, it means y = 26.
So, we have:
[tex]\mathbf{y = 34- 0.5 x}[/tex]
[tex]\mathbf{26 = 34 - 0.5x}[/tex]
Collect like terms
[tex]\mathbf{26 - 34= - 0.5x}[/tex]
[tex]\mathbf{-8= - 0.5x}[/tex]
Divide both sides by -0.5
[tex]\mathbf{16= x}[/tex]
Rewrite as:
[tex]\mathbf{x = 16}[/tex]
Hence, the number of days to reach 26ft is 16
Read more about linear functions at:
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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
mr.ortega sandwich shop sells and 6 inch sandwich for 3.30 and a 12 inch sandwich for 7.20 he wants to find out which sandwich is the better deal
Answer:
the 6 inch is a better deal because it is 55 cents per inch while the 12 inch is 60 cents per inch
Write 25/60 and 8/20 as fractions in simplest form. Then determine whether the ratios form a proportion
Answer:
8/20= 4/5
25/60= 5/12
Step-by-step explanation:
8÷4
Answer:
25/60 = 5/12
8/20 = 2/5
The Ratios do not form a proportion
Step-by-step explanation:
25/60:
25 ÷ 5/60 ÷ 5
= 5/12
8/20:
8 ÷ 4/20 ÷ 4
= 2/5
5/12 ≠ 2/5
The ratios are not proportional.
An electronics company is changing its internet advertising from a banner advertisement to a pop-up advertisement. The cost of the banner advertisement in dollars is represented by the function C(n) = 0.30n + 5.00 where 'n' is the average number of hits per hour and $5.00 is just a flat-rate cost.
1.) The cost of the pop-up advertisement will double the cost per hit. The equation for this new cost function will be D(n) =
2.) This change does/does not shift the function vertically and/or horizontally.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Cost function of banner advertisement:
C(n) = 0.30n + 5.00
n = average number of hits per hour
5 = flat rate
From the function, C(n), the cost per hit is the slope value of the function ; which is 0.30
1.) If the cost of pop-up advert will double the cost per hit, the cost function for pop-up advert will be :
D(n) = 2(0.30n) + 5
D(n) = 0.60n + 5.00
B.) This change in cost per hit has resulted in change in slope which is defined as :
[Rise / run = vertical change / horizontal change].
Hence, both vertical and horizontal change has occurred.
Find the value of x and m
Answer:
x=5 m=3
Step-by-step explanation:
Find the additive inverse of -1/8
Answer:
1/8
Step-by-step explanation:
(Dont mind me, just need to add more characters LOL)
9- 3(2x + 7) + 4x – 45
Answer:
−2x−57
Hope this helps!
Name the property illustrated by the equation.
-6xy + 0 = -6xy
Answer:
identity
Step-by-step explanation:
Answer:
identity
Step-by-step explanation:
Solve for x and y in the triangles.
(please help me I will pick brainly)
Answer:
52
38
Step-by-step explanation:
Find an equivalent fraction for the decimal: .57
sk
A radio station requires DJs to play 4 commercials for every 36 songs they play. What is the unit rate of songs to commercials?
Answer:
The correct answer for this question is that the unit rate is 5:1.
Step-by-step explanation:
We can work this out by simplifying down the 2 commercials to every 10 songs ration, so that 10:2 becomes 5:1. We can work this out by halving the original ratio to simplify it.
the area of a square garage is 121 square feet. will it fit a car that measures 13 feet long? explain
Answer:
It won't because the area is length times height. So 11 x 11. So some of the car will be hanging out of the garage.
Step-by-step explanation:
Help me please) Bro Im dumb Help
Answer:
The answer is 69 degrees.
Step-by-step explanation:
All you have to do is take the higher temperature and subtract it by the lower one.
f(x)=2x-6 find f(-2)
NEED ANSWER ASAP
(5x + 6x3 + 2x) - (3x - 2x3 - 7x2) is equivalent to:
8x3 + 12x2 - X
B
4x3 -- 5x2 - x
C
-4x3 + x2 + 6x
2x3 + 4x2 -- 5x
Answer:
A- 8x^3 + 12x^2 - x
Step-by-step explanation:
The symbol ^ with a 2 is squared and ^ with 3 means cubed.
1. Add a 1 before the parenthesis on both sides. Now, the equation should look like 1(5x^2 + 6x^3 + 2x) -1(3x - 2x^3 - 7x^2).
2. Now we should distribute. 1 × 5x^2 + 1 × 6x^3 + 1 × 2x -1 × 3x + -1 × -2x^3 + -1 × -7x^2.
3. Now the equation should be simplified.
1 × 5x^2 = 5x^2
1 × 6x^3 = 6x^3
1 × 2x = 2x
-1 × 3x = -3x
-1 × -2x^3 + -1 = 2x^3 -1. In this equation, there is a +- sign together, which is the same as a - sign.
-1 × -7x^2 = 7x^2
4. The new equation is 5x^2 + 6x^3 + 2x - 3x + 2x^3 - 1 + 7x^2
5. Now you can combine the like terms. 5x^2 and 7x^2 can be added, so 5x^2 + 7x^2 is equal to 12x^2. Also, 6x^3 and 2x^3 can be added, so 6x^3 + 2x^3 is equal to 8x^3. Lastly, 2x and -3x can be combined, so 2x - 3x is equal to -1x or -x.
6. So, the simplified equation is 12x^2 + 8x^3 -x. You can also write it as 8x^3 + 12x^2 - x. So, A is the answer.
Is 6.825 rational or irrational
Answer:
rational since all decimals that terminate are rational here is a sheet to help
6.825 is rational number.
What are rational numbers?A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.
Given number: 6.825
Now, we know Terminating decimals like 0.35, 0.7116, 0.9768, etc., are rational numbers.
So, we can see that 6.825 is terminating decimal.
Learn more about rational and irrational number here:
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2m - 7 + m = 10 + 3m
Answer:
no solutionStep-by-step explanation:
2m - 7 + m = 10 + 3m
3m - 3m = 10 + 17
0 = 17
therefore, there is no solution
Answer: no solution
Like the other answer said, no solutions avaliable.
Jill converted the equation of the line 15x-4y=-2 into slope-intercept form and found the slope and y-intercept of the line
as follows.
What was her Mistake?
She Mixed Up the slope and the y-intercept.
She got the sign of the slope wrong.
She git the sign of the y-intercept wrong.
She found reciprocals of the slope and the y-intercept.
ASAP Please Right Answer
Answer:
She got the sign of the slope wrong
Step-by-step explanation:
She did [tex]\frac{-4y}{-4} = \frac{-2-15x}{-4}[/tex] and turned that into [tex]\frac{-2}{-4}-\frac{-15x}{-4}[/tex], which is wrong, because she did the negative twice. Therefore, she mixed up the sign of the slope.
Please mark brainliest if this helped you!
Answer:
she got the sign of slope wrong
Step-by-step explanation:
took test on edg
What is the value of x?
Answer:
90
Step-by-step explanation:
Answer:
x=95 degrees
Step-by-step explanation:
All of the angles in a triangle add up to 180, so 45+50+(180-x)=180.
Open the parenthesis, and you get 45+50+180-x=180.
Then subtract 180 from both sides, so 45+50-x=0.
Simplify that to 95-x=0, and add x to both sides.
x=95
Also, you can use exterior angles theorem, which states that 45+50=x.
That's the shorter way.
please help meeeeeeeeeeeeeeeeeeee
Answer:
Im pretty sure it's D
Step-by-step explanation:
Srry if Im wrong.
Plz mark brainliest
You hang two strings of decorative lights. Strand 1: changes between red and blue every 15 seconds. Strand 2: changes between green and gold every 18 seconds. Both strands just changed color. After how many seconds will the strands change color at the same time again?
Answer:
The strands change color at the same time again after 90 seconds
Step-by-step explanation:
We are told:
Strand 1: changes between red and blue every 15 seconds.
Strand 2: changes between green and gold every 18 seconds.
To solve for this question, we use the LCM method.
Step 1
List multiples of each number until the first common multiple is found.
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120
Multiples of 18:
18, 36, 54, 72, 90, 108, 126
Therefore,
LCM(15, 18) = 90
The first common multiple is 90, and this is the lowest common multiple.
Therefore, the strands will change color at the same time again after 90 seconds.
Solve for t. 100-3t=76
Answer:
8
Step-by-step explanation:
100-3t=76
-3t=-24
t=8
Answer:
t=8
Step-by-step explanation:
100 - 3t = 76
-100 -100
-3t = -24
/-3 /-3
t = 8
Hope this helps!
what is the domain or range of y = one-fourth x minus 6
Answer:
domain and range will be ( negative infinity, positive infinity
Solve for v.
42 =3v- 15
Simplify your answer as much as possible.
Step-by-step explanation:
42=3v-15
We move all terms to the left:
42-(3v-15)=0
We get rid of parentheses
-3v+15+42=0
We add all the numbers together, and all the variables
-3v+57=0
We move all terms containing v to the left, all other terms to the right
-3v=-57
v=-57/-3
v=+19
Answer:
v= +19
Step-by-step explanation:
.In a fruit basket, there are 8 bananas and 4 apples. What is the unit rate for bananas to apples?
Answer:
2:1
Step-by-step explanation:
Answer:
2 bananas per apple
Step-by-step explanation:
х
у
-1
1
0
2.
1
4
2
8
3
16
Using the table from Question 7, select 1 other possible representation,
4
Of(-1) =1
f(n) = f(n-1)-2
Of(-1) = 1
f(n) = f (n − 1) +
Of(-1) = 1
f(n) = f(n-1) + 2
of(-1) = 1
f(n) = f (2) - n-1
Answer:
1,7 so you can do add to get to it
The airplane model scale on the box says that 4 cm represents 5 m. The actual wing measures 6.4 m by 16.95 m. What are the dimensions of the model wing?
Answer:
Dimensions of model wing is 5.12 cm * 13.56 cm
Step-by-step explanation:
Here, we are told that in the model we have 4 cm representing 5 m
So if 4 cm rep 5 m
x cm rep 6.4 m
4 * 6.4 = 5 * x
25.6 = 5x
x = 25.6/5
x = 5.12 cm
4 cm rep 5 m
x cm rep 16.95 m
4 * 16.95 = 5 * x
x = (4 *16.95)/5
x = 13.56 cm
y = 2x – 5
X Y
0 y1
2 y2
5 y3
7 y4
y1=?
y2=?
y3=?
y4=?
Answer:
y1 = -5
y2 = -1
y3 = 5
y4 = 9
Step-by-step explanation:
The equation of the table is
y = 2x - 5
The table is
→ x → y
→ 0 → y1
→ 2 → y2
→ 5 → y3
→ 7 → y4
To complete the table by finding the values of y substitute every x in the equation by its value to find the corresponding y
∵ y = 2x - 5
∵ x = 0
→ Substitute x by 0
∴ y1 = 2(0) - 5
∴ y1 = 0 - 5
∴ y1 = -5
∵ y = 2x - 5
∵ x = 2
→ Substitute x by 2
∴ y2 = 2(2) - 5
∴ y2 = 4 - 5
∴ y2 = -1
∵ y = 2x - 5
∵ x = 5
→ Substitute x by 5
∴ y3 = 2(5) - 5
∴ y3 = 10 - 5
∴ y3 = 5
∵ y = 2x - 5
∵ x = 7
→ Substitute x by 7
∴ y4 = 2(7) - 5
∴ y4 = 14 - 5
∴ y4 = 9
Answer:
(D) y2 and y4
Step-by-step explanation:
Laila read 36 pages in 4 hours. Which expression can be used to find the number of pages she read per hour?
StartFraction 36 hours Over 4 pages EndFraction
StartFraction 4 pages Over 36 hours EndFraction
StartFraction 4 hours Over 36 pages EndFraction
StartFraction 36 pages Over 4 hours EndFraction
Answer:
D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
