The domain of the function to know the number of cars remaining on any day during the month is [0, 40]. The maximum and minimum values are 120 and 0 respectively.
The domain is the all inputted value for which the function is defined. All the x values are domain of a function.
Now, finding the domain of the function,
We know that, the number of cars cannot be negative, so
[tex]f(x)\geq0\\120-3x\geq0\\3x\leq120\\x\leq40[/tex]
The number of cars should be greater than 0, so x > 0.
So, the domain will be [0, 40].
The maximum value is given by putting x = 0,
[tex]f(0)=120-3(0)\\=120[/tex]
The minimum value is given by putting x = 40,
[tex]f(40)=120-3\times40\\=120-120\\=0[/tex]
Therefore, the domain of the function f(x)=120-3x to know the number of cars remaining on any day during the month is [0, 40]. The maximum and minimum values are 120 and 0 respectively.
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Calculate 18.75 x 11.54 a) exact value b. corrected to 1 d.p c. corrected to 2 s.f
Step-by-step explanation:
18.75 x 11.54
= 216.375
216.375 is the correct answer
james scored 30 out of 90 in a music test.he scored 48 out of 150 in drama test scored 35 out of 120 in an art test.in which test james score the highest
Answer:
music test
Step-by-step explanation:
divide each one and find the highest answer.
If x = 1 and y = 2 is a solution to the simultaneous equation ax + by = 2 and bx + a^(2)y = 10, find the possible values of a and b.
Answer:
a = - 2, [tex]\frac{9}{4}[/tex] , b = 2, - [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Since x = 1, y = 2 is a solution to the equations , then substitute these values into the 2 equations and solve for a and b
a + 2b = 2 → (1)
b + 2a² = 10 → (2)
In (1) subtract 2b from both sides
a = 2 - 2b → (3)
Substitute a = 2 - 2b into (2)
b + 2(2 - 2b)² = 10 ← expand parenthesis using FOIL
b + 2(4 - 8b + 4b²) = 10 ( simplify left side )
b + 8 - 16b + 8b² = 10 ( subtract 10 from both sides )
8b² - 15b - 2 = 0
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 8 × - 2 = - 16 and sum = - 15
The factors are - 16 and + 1
Use these factors to split the b- term
8b² - 16b + b - 2 = 0 ( factor first/second and third/fourth terms )
8b(b - 2) + 1(b - 2) = 0 ← factor out (b - 2) from each term
(b - 2)(8b + 1) = 0
Equate each factor to zero and solve for b
b - 2 = 0 ⇒ b = 2
8b + 1 = 0 ⇒ 8b = - 1 ⇒ b = - [tex]\frac{1}{8}[/tex]
Substitute these values into (3) and evaluate for a
b = 2 ⇒ a = 2 - 2(2) = 2 - 4 = - 2
b = - [tex]\frac{1}{8}[/tex] ⇒ a = 2 - 2(- [tex]\frac{1}{8}[/tex] ) = 2 + [tex]\frac{1}{4}[/tex] = 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{9}{4}[/tex]
The possible values of a and b are 8, -3 or 9/4 , -1/8 respectively.
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equations are,
ax + by = 2 (1)
and bx + a²y = 10 (2)
Also, x = 1 and y = 2 are the solution of the equation,
Substitute x = 1 and y = 2in equation (1),
a(1) + b(2) = 2
a + 2b = 2 (3)
Further substitute x = 1 and y = 2 in equation (2),
b(1) + a²(2) = 10
2a² + b = 10 (4)
By solving equation (3) and (4),
The possible values of a are 8 and 9/4.
And possible value of b are -3 and -1/8.
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What is the answer to 27 · 64?
Answer:
1728
Step-by-step explanation:
27
64
-----------
108
1620
1728
Answer:
1728
Step-by-step explanation:
27•64= 0108+162 =1728
PLEASE CAN SOMEONE HELP ME
Answer:
u=ABCDEF
Step-by-step explanation:
Solución
10x-3x=11+10
Answer: x=3
Step-by-step explanation:
PLEASE NO LINKS OR NEGATIVITY
answer the following question
While moving up on the rope-way, I noticed that the seat place in the opposite direction was numbered as 95. Behind it was number 0, then 1, 2 and so on. My seat place was numbered as 66. What number should I meet when I am in the middle of my one-way route?
The seat in the middle of the one-way route is 34
The seats are given as:
[tex]First= 0[/tex] --- the first seat behind the seat number 95
[tex]Last= 66[/tex] --- my seat
The seat number half-way would be:
[tex]Half = \frac{Last - First}{2} + 1[/tex]
This gives
[tex]Half = \frac{66- 0}{2} + 1[/tex]
Subtract 0 from 66
[tex]Half = \frac{66}{2} + 1[/tex]
Divide 66 by 2
[tex]Half = 33 + 1[/tex]
Add 33 and 1
[tex]Half = 34[/tex]
Hence, the seat in the middle of the one-way route is 34
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Write an equation in slope-intercept form that describes the line through the points (-2,6) and (3, 1).
Answer:
y=-x+4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-6)/(3-(-2))
m=-5/(3+2)
m=-5/5
m=-1
y-y1=m(x-x1)
y-6=-1(x-(-2))
y-6=-(x+2)
y-6=-x-2
y=-x-2+6
y=-x+4
182,000/907 step by step please
Answer:
200 R 600
or
200 600/907
Step-by-step explanation:
0 0 0 2 0 0
9 0 7 1 8 2 0 0 0
− 0
1 8
− 0
1 8 2
− 0
1 8 2 0
− 1 8 1 4
6 0
− 0
6 0 0
− 0
6 0 0
i need help on this assignment
Answer:
the answer is 10
Step-by-step explanation:
by the why want to be friends??
Answer:
10
Step-by-step explanation:
Which of these shapes have an area
Answer:
Shape 2 and 3
Step-by-step explanation:
shape 1 is not enclosed so it cannot have area
ayy yo who want smok wit me
Choose the inequality that could be used to solve the following problem.
Three times a number is at most negative six.
(A) 3x ≤ -6
(B) 3x < -6
(C) 3x ≥ -6
(D) 3x > -6
Answer:
I believe the answer is A
Step-by-step explanation:
three times x can be equal to, but never greater than -6
Answer:
A. 3x ≤ -6
Step-by-step explanation:
the sentence ‘3x is at most -6
means that the most 3x is allowed to be is -6
it can be -6 or any number less than -6
So, the phrase 3x is at most -6
’ means ‘
3x ≤ -6
A Freight Train Travels 144 miles in 6 hours.How Far will it travel in 15 hours
Please help me out kindda hard
Hello there, there are multiple ways of solving this problem, let me show you.
[tex]{\huge{\boxed{\mathbb{QUESTION}}}}}[/tex]
A Freight Train Travels 144 miles in 6 hours. How Far will it travel in 15 hours?
_________________
For this problem I will show you 2 methods.
[tex]{\huge{\boxed{\mathbb{METHOD\:ONE}}[/tex]
Cross multiplication, cross multiplication involves algebra to use.
Let x be our answer for this problem. Here is our it would look like
[tex]\frac{6}{144}=\frac{15}{x}[/tex], now we will cross multiply, here is what it'd look like now.
[tex]6x=2160[/tex], then do simple algebra and divide both sides by 6. and then we get [tex]x=360[/tex] miles in 15 hours.
_________________
[tex]{\huge{\boxed{\mathbb{METHOD\:TWO}}[/tex]
For method two we can look for the unit rate. Also known as our rate for one.
divide 144 by 6 and we get 24, then multiply it by 15 and we get 360.
_________________
[tex]{\huge{\boxed{\mathbb{EXACT\:ANSWER}}[/tex]
360 miles in 15 hours.
Have a good day :) !Please help with this I will give brainliest
Answer:
I beleave its 27
Step-by-step explanation:
Kareem has $20,000 in his savings account that earns 5% annually. How much interest will he earn in one year?
Answer:
1000
Step-by-step explanation:
5% of my 20000 is 1000 so 21000 total or 1000 anually
Ethan and Alex ordered 1,263 pizzas for the school. They wanted to share them equally with each class.If there are 34 classes, how many pizzas will each class get?
1. A hat store tracks the state of college and professional team hats for m, months. The number of
college hats sold is represented by (6m+3). The number of professional hats sold is represented by
(5m-2). Write an expressions to show how many more college hats were sold than professional hats.
Then evaluate the expression if m equals 10.
NYS
2. Which expression is equivalents to the expression -3(4x-2)-
2x ? Explain the process you used to find your solution.
A. -8x
B. -16%
C. -14x-2
D. -14x + 6
3. A square scrapbooking page has a perimeter of (8x+20) inches. What is the length of one side of the
scrapbooking page? Show your work.
1) The expression representing how many more college hats were sold than professional hats is [tex]m+5[/tex]
when [tex]m=10[/tex], [tex]15[/tex] more college hats were sold
2) The equivalent expression to [tex]-3(4x-2)-2x[/tex] is [tex]-14x+6[/tex]. The explanation is found in the steps below
3) The length of one side of the square scrapbooking page will be
[tex](2x+5)\text{ inches}[/tex]. The working is shown below.
1) According to the question, [tex]m[/tex] is the number of months hats were sold.
[tex]6m+3[/tex] is the number of college hats sold in [tex]m[/tex] months
[tex]5m-2[/tex] is the number of professional hats sold in [tex]m[/tex] months
Since [tex]6m+3>5m-2[/tex] when [tex]m>0[/tex]
the expression representing how many more college hats were sold than professional hats is
[tex](6m+3)-(5m-2)\\=6m+3-5m+2\\=m+5[/tex]
when the number of months hats were sold is [tex]10[/tex], [tex]m=10[/tex], and
[tex]m+5=(10)+5=15hats[/tex]
[tex]15[/tex] more college hats were sold in [tex]10[/tex] months
2) To get the equivalent expression to [tex]-3(4x-2)-2x[/tex], carry out the steps below
remove brackets
[tex]-12x+6-2x[/tex]
arrange like terms
[tex]-12x-2x+6[/tex]
simplify like terms
[tex]-14x+6[/tex]
The answer is (D)
3) Let the length of one side of the square be [tex]s[/tex]
The perimeter will be
[tex]4s=8x+20[/tex]
making [tex]s[/tex] the subject of the formula
[tex]\dfrac{4s}{4}=\dfrac{8x+20}{4}\\\\s=(2x+5)\text{ inches}[/tex]
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please solve quickly for 50 points
find the value of A
help please
Answer:
a= 6
Step-by-step explanation:
(7a-4)= 38
7×6= 42
42-4= 38
Evelyn can run 3 miles in 40 minutes
Answer:
m= 4.5 miles
Step-by-step explanation:
Let the number of miles Evelyn can run be m and can be modeled by the equation below
m= kx
Where x Is the Minutes
When m= 3
x= 40
3= k40
k= 3/40
If x= 60
m=3/40(60)
m = (60*3)/40
m= 180/40
m= 4.5 miles
Which of the following is the missing reason? Statements Reasons two thirds times x plus 7 equals negative 5 Given 2x 21 = â’15 Multiplication Property of Equality 2x = â’36 Subtraction Property of Equality x = â’18 ? Division Property of Equality Distributive Property Addition Property of Equality Subtraction Property of Equality.
The correct option is B. Distributive property
Given,
[tex]\frac{2}{3} x+7=-5\\[/tex]
On solving the above equation,
multiplying both sides by 3 we, get
[tex]2x+21=-15[/tex]
now subtracting 21 from both the sides,
[tex]2x=-36\\[/tex]
dividing both the sides by 2 we get,
[tex]x=-18[/tex]
Since in the above steps we follow all the giving property except the distributive property.
Hence the correct option is B. Distributive property.
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1.1046 rounded to the nearest whole number
Answer:
1
Step-by-step explanation:
Answer is 1
cuz nearest whole number, just check the next number that is nearest, that in this case is the decimal 1, hence, if it's 5 or above add a one to the whole number, if not then just write it as it is. in this case the nearest number is less than five so we just write it as 1.0000 or just 1
Select the correct answer.
You're trying to determine how much money it would cost to hire a lawn mowing company to cut your grass. Your yard
measures 8,712 square feet. The lawn mowing company charges a base rate of $30, plus $20 for every tenth of an
acre. You determine that it will cost $70 to hire the lawn mowing company. Which sentence best describes this price
estimate?
A. The price should be $50 because you have a 0.1 acre yard.
B. The price should be $50 because you have a 0.2 acre yard.
C. The price should be $90 because you have a 0.3 acre yard.
D.
The price estimate is accurate,
Find the range for the measure of the third side of a triangle given the measures of two sides.
18 ft and 23 ft
The range for the measure of the third side of the triangle is (5, 38).
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
Two sides of the triangle are 18 ft and 23 ft.
Let the third side of the triangle is x cm.
Since, the third side is greater than the difference of the remaining sides and less than the sum of the two sides.
Implies that,
23 - 18 < x < 23 + 18
5 < x < 38
The range of the third side varies from (5, 38).
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fill in the table of values for y=2x+3
Answer:
2 4 2 y-3
•
•
•
•
•
Yan po answer
help please! very important
What type of slope does the graph have!
Answer:
it either has a postive slope (when lines go uphill from left to right)
a negative slope (when lines go downhill from left to right)
a zero slope (when lines are horizontal)
or a undefined slope (when lines are vertical)
Step-by-step explanation:
hope this helps
Answer:
a negative slope of -2
Explanation:
slope = (y2-y1)/(x2-x1)
points (1,1) (0,3)
x1 = 0 y1 = 3
x2 = 1 y2 = 1
(1-3)/(1-0) = -2/1 = -2