Answer/Step-by-step explanation:
If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
A part-time employee worked 4 hours on Monday and 7 hours each day for the next 3 days
At Alan's auto shop, it takes him minutes to do an oil change and minutes to do a tire change. Let be the number of oil changes he does. Let be the number of tire changes he does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Alan can do in less than an hour ( minutes).
Complete question :
At Alan's auto shop, it takes him 9 minutes to do an oil change and 12 minutes to do a tire change. Let x be the number of oil changes he does. Let y be the number of tire changes he does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Alan can do in less than an hour ( minutes).
Answer:
9x + 12y < 120
Step-by-step explanation:
Given that:
Time taken for oil change = 9 minutes
Time taken for tire change = 12 minutes
x = number of oil changes ; y = number of tire changes
Total hours = 1 hour = 60 minutes
Number of oil and Tyre changes possible in less than an hour
(Number of oil changes * time taken) + (number of tire changes * time taken) less than 60 minutes
9x + 12y < 120
Answer:
9x + 12y < 120
Step-by-step explanation:
MA is the bisect or of
Answer:
hum I think it is a bisect
6. A stack of paper is 4.875 cm tall.
How many pieces of paper are in
the stack if each piece is 0.0075 cm
thick?
Answer:
650 pieces of paper
Step-by-step explanation:
each piece is 0.0075 so all you need to do is divide 4.875 by 0.0075
a boat used 1/24 of a gallon of gas to drive 1/3 of a mile.At this rate how many miles can the boat go using 1 gallon of gas.
The answer is:
8 miles
What is the value of x in the equation below?
(9x – 6) = 4x + 10
Answer:
x = 16/5
Step-by-step explanation:
9x – 6 = 4x + 10 <-- Combine like terms on one side
5x = 16 <-- Isolate x
x = 16/5
Answer: 3.2
Step-by-step explanation:
(9x - 6) = 4x + 10
9x - 6 = 4x + 10
9x = 4x + 16
5x = 16
x = 3.2
TAKING TEST PLEASE HELP
Which trigonometric functions have a domain of [–1, 1]?
y = arcsinx and y = arccosx
y = arccosx and y = arctanx
y = arcsinx and y = arctanx
y = arcsecx and y = arccscx
Answer:
A
Step-by-step explanation:
Edge
The trigonometric functions y = arcsinx and y = arccosx have a domain of [–1, 1] option (A) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The domain of a trigonometric function is [-1, 1]
As we know,
The range of the sin x and cos x functions is [-1, 1]
The inverse of the above trigonometric functions are:
arc sin x and arc cos x
The range of sin x and cos x becomes domain.
So the domain of y = arcsinx and y = arccosx is [-1, 1].
Thus, the trigonometric functions y = arcsinx and y = arccosx have a domain of [–1, 1] option (A) is correct.
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Eva's family had a 15,000 gallon swimming pool built. They began filling the pool at 8:00a.m. on Saturday. Every fifteen minutes, Eva recorded the number
in the pool. The pool was being filled at a constant rate. The table shows the first 45 minutes of Eva's data.
Gallons
1,000
2,000
3,000
15
30
45
Minutes
At what rate, in gallons per hour, is the swimming pool being filled?
A. 15 gallons per hour
B. 4000 gallons per hour
C. 66.6 gallons per hour
D. 2000 gallons per hour
Answer: 4,000
Step-by-step explanation:
The solution is Option A.
The rate at which the swimming pool is being filled is 66.6 gallons per hour
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of gallons be = y
Let the time taken be = x
The total volume of the pool = 15000 gallons
The pool is filled at constant rate
Now ,
The coordinate data is given as
The value of A = A ( 15 , 1000 )
The value of B = B ( 30 , 2000 )
The value of C = C ( 45 , 3000 )
Now , the rate at which the swimming pool is filled is given by the slope of the points in the line
So , the slope of the 2 points is given by the formula
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2000 - 1000 ) / ( 30 - 15 )
On simplifying the equation , we get
Slope m = 1000 / 15
Slope m = 66.66 gallons per hour
Therefore , the value of A is 66.6 gallons per hour
Hence ,
The rate at which the swimming pool is being filled is given by the slope of the line where slope m = 66.6 gallons per hour
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An initial population of 460 quail increases at an annual rate of 21%. Write an exponential function
to model the quail population. What will the approximate population be after 3 years?
Answer:
the expected population after 3 years is 863.7009
Step-by-step explanation:
The computation of the expected population after 3 years is shown below
P = P_0 × e^rt
where,
r = 21% = 0.21
t = 3 years
P_0 = 460
Now place these values to the above formula
P = 460 × exp(0.21 × 3)
= 863.7009
hence, the expected population after 3 years is 863.7009
We simply applied the above formula so that the correct value could come
And, the same is to be considered
GOT AN Y INTERCEPT AND GRAPH PROBLEM PLS HELPPPPPP!!! HOPE it's NOT TO HARD TO READDDDDDDDD
Answer:
1) It has a y-intercept of 4
2) A, the rate of change represents how fast the boys run every hour.
If 3 sodas cost $6 then what is the cost per soda??
Answer:
$2 per soda
Step-by-step explanation:
6/3= 2
Find the indicated term of the arithmetic sequence.
22nd term: a1 = 7; d = 4
The 22nd term of the arithmetic sequence is:
.
Answer:
91
Step-by-step explanation:
a(n) = a +(n-1)d
a(n) = 7+(n-1)4
a(22) = 7+(22-1)4
=91
hope this helps
work out and simplify 3/8 - 1/16
Answer:
3x4/8×4-1x2/16x2
12/32-2/32=10/32
hope it helped
Which of the following numbers are perfect . 3364,4489,4358 please solve
Answer:
Below
Step-by-step explanation:
A perfect number is one whose proper divisors add up to that number.
For example, 6 is a perfect number because
Its proper divisors 1, 2 and 3 and 1+2+3 = 6.
First list prime factors:
3364 = 2 * 2 * 29 * 29
Proper divisors are 1, 2, 4, 29, 58, 116, 841, 1682
Sum of these = 2733.
So, 3364 is not a perfect number.
4489 = 67 * 67
Divisors are 1 and 67.
Sum = 68.
So, 4489 is not a perfect number.
4358 =2 * 2179
Divisors are 1 , 2 and 2179.
Sum = 2182.
So, 4358 is not a perfect number.
what is the number which is to be added with 49x square + 4y square to get a perfect square
Answer:
The number which should be added with 49x square + 4y square to get a perfect square is 28xy
Step-by-step explanation:
We need to find the number which is to be added with 49x square + 4y square to get a perfect square.
The expression given is: [tex]49x^2+4y^2[/tex]
For the expression to be perfect square it should be of form: [tex]a^2+2ab+b^2=(a+b)^2[/tex]
Now, we are given [tex]49x^2+4y^2[/tex] and we need to find the middle term
So, solving:
[tex]49x^2+4y^2\\=(7x)^2+(2y)^2+2(7x)(2y)-2(7x)(2y)\\=7x^2+28xy+(2y)^2-28xy\\=(7x+2y)^2-28xy[/tex]
The number which should be added with 49x square + 4y square ([tex]49x^2+4y^2[/tex]) to get a perfect square is 28xy
Which situation leads to a unit cost of $6 per football ticket?
Select one:
1)6 football tickets for $24
2)12 football tickets for $72
3)$6 paid for 6 football tickets
4)$6 paid for 2 football tickets
Answer:
1.) 6 football tickets for $24
Step-by-step explanation:
The situation which leads to a unit cost of $6 per football ticket is; 6 football tickets for $24.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Multiplication is the mathematical operation is used to determine the product of two or more numbers.
We have been given a condition as; a unit cost of $6 per football ticket.
Meaning that;
The cost of one football ticket is 6 dollar
Then The cost of 12 football ticket = 12 x 6 dollar
= 72
Therefore, the situation which leads to a unit cost of $6 per football ticket is; 12 football tickets for $72.
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help i need this soon its 8th grade math
Answer:
50 degrees
Step-by-step explanation:
vertical angles are the same
angle LPM = 180-60-70
angle LPM = 180-130 = 50
angle LPM = angle KPN
50=angle KPN
3. Jackson answered 80o of the questions on his Science test correctly. Colton scored 10
out of 12. Who scored the highest score?
Answer:
i think they both scored the same
Answer:
Colton did.
Step-by-step explanation:
Jack's score was 80%.
Colton got a score of 83.33...
I got Colton's score by solving 10/12.
Find the quotient 17÷3,145
Answer:
0.0054054054
Also simplify to 0.005
Answer:
17÷3,145=0.00540
PLEASE HELP ME What is the least common denominator of the fraction 4 over x plus the fraction 2 x over x minus 1 plus the fraction x plus 3 over 2 x? (6 points)
Group of answer choices
2x − 12
(x− 1),
2(x2 − 1)
2x(x − 1)
Help Pls And Thank you
Answer:
A
Step-by-step explanation:
Total amount of extra money needed to be raised
= $483.62 -$218.25
= $265.37
Since each student raises the same amount and there are 17 students, $265.37 would be shared equally amongst the 17 students.
Amount of money each student must raise
= $265.37 ÷17
= $15.61
Last year Jonathan was 59 and 5/8 inches tall. This year he is 64 and 3/8 inches tall. How many
inches did he grow?
Answer: John grew 4 and 3/4 inches in one year.
Step-by-step explanation:
Start by subtracting 64.375 (64 and 3/8) by 59.625 (59 and 5/8).
Type your numbers into a calculator (both ways can be put into your calculator, but decimals are easier for you to type)
Get your final answer of 4.75.
Hope this helps!
Answer the question in the picture pls WORTH 50 POINTS PLUS BRAINLIEST FOR FIRST CORRECT ANSWER
Answer:
A
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
−y+4≥8
Step 2: Subtract 4 from both sides.
−y+4−4≥8−4
−y≥4
Step 3: Divide both sides by -1.
−y
−1
≥
4
−1
y≤−4
Answer:
12
Step-by-step explanation:
| 4-y| ≥8
Separate into two inequalities, one positive and one negative (remembering to flip the inequality)
4-y ≥8 or 4-y≤ -8
Solve
Subtract 4 from all sides
4-y -4 ≥8-4 or 4-y-4≤ -8-4
-y ≥4 or -y≤ -12
Divide each side by -1, remembering to flip the inequality
y ≤-4 or y ≥12
The smallest positive number is 12
8/9 = 1/3f
what is f
Answer:
f=8/3
Step-by-step explanation:
pls helppp
math work
bleh
Answer:
q = -2
Step-by-step explanation:
when solving 12q >= -24 you get
q >= -2 (12 divides 24 by 2)
therefore q is greater or equal to -2.
Suppose you just deposited $500 into a bank account that has earned 5% interest on the amount you initially
invested. If the new balance is $1,760, what was your initial investment?
Answer:
$1200
Step-by-step explanation:
Let the initial amount that you invested be $ x.
We are told that the new balance after investing $500 is $1760.
Thus, the balance you had before the deposit $500 us;
$1760 - $500 = $1260
So, when the amount invested was $x, the balance was $1260.
Since this money earned 5% interest on the amount you initially
Thus;
$1260 = initial deposit + (5% of inital deposit)
Thus;
x + (5% * x) = 1260
x + (0.05x) = 1260
1.05x = 1260
x = 1260/1.05
x = $1200
What is the image point of (3, – 7) after the transformation D3 o R180° ?
Answer:
Step-by-step explanation:
Here is a guide to help:
Best of luck!
Answer: (9,21)
Step-by-step explanation:
R180 (3,-7) = (-(3),-(-7)) = (-3,7)
D3 (−3,7) = (3 x −3, 3 x 7) = (−9,21)
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $2.70. Today they made $119.60 from the 72 wraps sold. How many of the wraps sold were vegetarian
Answer:
vegetarians= 28
chickens= 44
Step-by-step explanation:
let the number of vegetarians be x
and chickens be y
So
x+2.7y=119.6----------1
x+y=72--------------2
from 2, x= 72-y
put x= 72-y in 1
72-y+2.7y=119.6
-y+2.7y=119.6-72
1.7y=47.6
divide both sides by 1.7
y=47.6/1.7
y=28
put y=28 in 1
x+28=72
y= 72-28
y=44
solve the equation below -2x+16=10
Answer:
x=3
Step-by-step explanation:
8x+5y=-13 3x+4y=10 solve
Answer:
x=−6 and y=7
Step-by-step explanation:
Step: Solve8x+5y=−13for x:
8x+5y=−13
8x+5y+−5y=−13+−5y(Add -5y to both sides)
8x=−5y−13
8x
8
=
−5y−13
8
(Divide both sides by 8)
x=
−5
8
y+
−13
8
Step: Substitute
−5
8
y+
−13
8
forxin3x+4y=10:
3x+4y=10
3(
−5
8
y+
−13
8
)+4y=10
17
8
y+
−39
8
=10(Simplify both sides of the equation)
17
8
y+
−39
8
+
39
8
=10+
39
8
(Add 39/8 to both sides)
17
8
y=
119
8
17
8
y
17
8
=
119
8
17
8
(Divide both sides by 17/8)
y=7
Step: Substitute7foryinx=
−5
8
y+
−13
8
:
x=
−5
8
y+
−13
8
x=
−5
8
(7)+
−13
8
x=−6(Simplify both sides of the equation)Step: Solve8x+5y=−13for x:
8x+5y=−13
8x+5y+−5y=−13+−5y(Add -5y to both sides)
8x=−5y−13
8x
8
=
−5y−13
8
(Divide both sides by 8)
x=
−5
8
y+
−13
8
Step: Substitute
−5
8
y+
−13
8
forxin3x+4y=10:
3x+4y=10
3(
−5
8
y+
−13
8
)+4y=10
17
8
y+
−39
8
=10(Simplify both sides of the equation)
17
8
y+
−39
8
+
39
8
=10+
39
8
(Add 39/8 to both sides)
17
8
y=
119
8
17
8
y
17
8
=
119
8
17
8
(Divide both sides by 17/8)
y=7
Step: Substitute7foryinx=
−5
8
y+
−13
8
:
x=
−5
8
y+
−13
8
x=
−5
8
(7)+
−13
8
x=−6(Simplify both sides of the equation)
Answer: The intersection between these 2 lines are (-6,7)
Source: Desmos Graphing Calculator (look it up its very helpful and gives answers)