A) The change in the volume of solution in the tank after 1 minute is;
-3⁷/₁₅ liters per minute
B) The change in volume of the solution after 15 seconds is; -13/15 liters per minute.
C) What change in the volume of solution in the tank after 15 seconds means is that there is a decrease in the volume of solution in the tank by 13/15 liters per minute.
What is the rate of change?The given parameters of the solution in the tank are;
The rate at which the solution enters the tank, V = 16³/₄ liters per minute
The rate at which the solution leaves the tank = 19⁴/₅ liters per minute
(a) The expression that represents the change in volume in the tank is given as follows;
16³/₄ - 19⁴/₅ = -3⁷/₁₅ liters per minute
b) We want to find the change in volume of the solution after 15 seconds.
15 seconds is equal to 0.25 minutes or 1/4 minutes
Therefore, the change in the volume after 15 seconds is;
-3⁷/₁₅ * 1/4 = -13/15 liters per minute
c) The change in the volume of solution in the tank after 15 seconds is a decrease in the volume of solution in the tank by 13/15 liters per minute.
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Can someone help with #2 and #4
Answer:
2. See below.
4. Domain = {57, 68, 93, 99}
Step-by-step explanation:
Question 2Given relation:
[tex]\{ (1,5),(2,3),(3,2),(4,1),(5,0)\}[/tex]
The given relation is a set of ordered pairs (x, y), where the first element is x and the second element is y.
To express the given relation as a table, enter the x-value of each ordered pair in the left column, and the corresponding y-value of each ordered pair in the right column:
[tex]\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2}1&5\\\cline{1-2}2&3\\\cline{1-2}3&2\\\cline{1-2}4&1\\\cline{1-2}5&0\\\cline{1-2}\end{array}[/tex]
An ordered pair is used to represent the position of a point on the coordinate plane. Therefore, to represent the given relation as a graph, plot each ordered pair on the given coordinate plane.
(See attachment 1).
To represent the given relation as a mapping diagram:
Place the first element of each ordered pair in the left column entitled "Place".Place the second element of each ordered pair in the right column entitled "Points".Connect each ordered pair with an arrow from its first element to its second element to represent the relation between them.(See attachment 2)
Question 4The domain is the set of all x-coordinates.
Therefore, the domain of the given mapping diagram is {57, 68, 93, 99}.
Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.
Maggie made a mistake while combining similar terms of x using vertical angles; the result is -3x rather than 3x, hence the right answer is x = 9.
How do vertical angles work?When two lines intersect, vertical angles are two angles that are opposed by the same vertex and are congruent, meaning they have the same measure.
The vertical angles for this issue are as follows:
4x + 2.
7x - 25.
Since they agree, the following equation may be used to determine the variable x:
4x + 2 = 7x - 25.
The following results from shifting all terms with x to the left side of the equality and all terms that are constant to the right side, with the opposite signal:
4x - 7x = -25 - 2
Combining similar phrases yields the following results:
-3x = -27.
Maggie made a mistake here since 4x - 7x = -3x, thus the proper answer is as follows:
3x = 27
x = 27/3
x = 9.
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step by step solution to 10x-7y=-8
The x and y-intercept of the linear equation 10x - 7y = -8 in an ordered pair form are ( -4/5, 0 ) and ( 0, 8/7 ) respectively.
How to determine the x and y-intercept of the linear equation?The intercept of a line on a graph is simply the point at which it intersects either the x-axis or y-axis.
Given the data in the question;
10x - 7y = -8x-intercept = ?y-intercept = ?To find the x-intercept, substitute in 0 for y and solve for x.
10x - 7y = -8
10x - 7(0) = -8
10x - 0 = -8
10x = -8
Divide both sides by 10
10x/10 = -8/10
x = -8/10
x = -4/5
Therefore, the x-intercept is ( -4/5, 0 ).
To find the y-intercept, substitute in 0 for x and solve for y.
10x - 7y = -8
10(0) - 7y = -8
0 - 7y = -8
-7y = -8
Divide both sides by the coefficient of y
-7y / -7 = -8 / -7
y = -8 / -7
y = 8/7
Therefore, the y-intercept is ( 0, 8/7 ).
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Which describes the range of the parent absolute value function?
{yly} is a real number}
{yly} is an integer}
{yly ≥ 0}
{yly ≤ 0}
Answer:
{ y l y ≥ 0 }
Step-by-step explanation:
The absolute value parent function is:
[tex]f(x) =|x|[/tex]
The absolute value of a number means how far the number is from zero on a number line. Therefore, the absolute value of a number is its positive numerical value.
This means that regardless of the value of x, the value of the absolute value parent function (y-value) will always be positive or zero.
The range of a function is the set of all possible output values (y-values).
Therefore, the set notation that describes the range of the parent absolute value function is:
{ y l y ≥ 0 }Find CE
Given sides are 6, x-5, 14, 2x+3
AB= 6
BC= x-5
CE= 14+2x+3
After conducting some mathematical operations we know that the length of the side CE is 49 units.
What do we mean by mathematical operations?In mathematics, an operation is a function that converts 0 or more input values into a clearly defined output value.The quantity of operands determines the arity of the operation.The order of operations refers to the rules that specify how to solve an expression that requires multiple operations.Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (or PEMDAS) (from left to right).So, the length of CE is:
According to the image, we know that AB + BC = CE. Then,
AB + BC = CE6 + x - 5 = 14 + 2x + 31 + x = 17 + 2x2x - x = 1 - 17x = -16Since length cannot be negative: So, x = 16
Substitute x = 16 in 14 + 2x + 3 to find CE as follows:
14 + 2x + 314 + 2(16) + 314 + 32 + 349Therefore, after conducting some mathematical operations we know that the length of the side CE is 49 units.
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Fill in the blanks-----------
Mr Arnold bought 10 boxes of oranges for $480 Each box had a dozen oranges He later sold the oranges and made a total profit of $120 What was the selling price of one orange? (giving 30 points for this!!
Answer:
5$
Step-by-step explanation:
480$+120$=600$ 600÷120=5
Please help thank you
Answer:y=-9x+3
Step-by-step explanation:
In a y=mx+b equation (slope intercept form) like this one m is the slope and b is the y intercept.
Karen has 48 inches of ribbon. She wants to place the ribbon along the edge of a rectangular frame that is 12 inches wide and 16 inches long. Will Karen have enough ribbon or will she need more? Explain how you know.
Answer:
no
Step-by-step explanation:
12+16+12+16=56
48 is smaller than 56
Using the section of the graph shown, which of
these potential roots of the function should you
test first?
f(x) = 2x³-9x² - 6x + 40
-5
-2
1
8
Polynomial is divisible by x+2, therefore the first root is -2. The second and third roots of the function, we can estimate them utilizing the quadratic equation formula.
What is meant by polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Let the given polynomial function be
F(x)=2x³ - 9x² - 6x + 40, the first potential roots are -2, 4 and 5/2.
Solving for the first root, we divide the given function by x+2 where the result is 2x² - 13x + 40.
Since the given polynomial exists divisible by x+2, therefore the first root exists -2.
For the second and third roots of the function, we can estimate them utilizing the quadratic equation formula.
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4n — 6(3 — n) + _ = 10n —15
Answer:
n • (2n - 5)
——————————————————————
5 • (n - 5) • (3n - 1)
Step-by-step explanation:
4.3 Factoring 3n2 - 16n + 5
The first term is, 3n2 its coefficient is 3 .
The middle term is, -16n its coefficient is -16 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 3 • 5 = 15
Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is -16 .
-15 + -1 = -16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -1
3n2 - 15n - 1n - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
3n • (n-5)
Add up the last 2 terms, pulling out common factors :
1 • (n-5)
Step-5 : Add up the four terms of step 4 :
(3n-1) • (n-5)
Which is the desired factorization
Answer:
n • (2n - 5)
——————————————————————
5 • (n - 5) • (3n - 1)
Step-by-step explanation:
4722x835
Canu show me the work for this i rlly need it
Answer: 3,942,870
Step-by-step explanation:
Answer:
3942870
Step-by-step explanation:
Numerical terms in this expression have been added.
(4722+835= 48557)
(48557) To factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
(59x823 ) The number of times that each prime divides the original integer becomes its exponent in the final result.
In my example,
Prime number 59 to the power of 1 equals 59.
Prime number 823 to the power of 1 equals 823.
Hope this helps you!
is accounting interesting? Help plss more idea
Answer: yes it is interesting because u also know more about finance and you would have a much easier life after this
Step-by-step explanation:
After a recycling awareness program, the number of tons of recyclable material taken to the landfill is reduced by 13 7/10 tons per month. Represent the total change in the tons of recyclable material taken to the landfill after 7 months resulting from the awareness program.
PLSS HELP
Answer:
95 9/10 tonsStep-by-step explanation:
GivenReduction in a month = 13 7/10 tons,Number of months = 7SolutionTotal reduction over the given period is the product of the two numbers above:
13 7/10 * 7 = 13*7 + 7/10*7 = 91 + 49/10 = 91 + 4 9/10 = 95 9/10 tonsHelp pls I need the answer fast and today
Answer:
B.
Step-by-step explanation:
0.264172 is how many gallons are in one liter soooo yeah, the estimation of that is 0.26/1 which is B
13. A rancher wishes to enclose a rectangular corral with 320 feet of fencing. The fencing is only required
on three sides because of an existing stone wall. What are the dimensions of the corral of maximum
area?
The dimensions of the corral of maximum area 80 x 160 feet
What is Area?
Area is a quantity that describes the extent of an area on a plane or curved surface. The area of a planar region or planar region refers to the area of a shape or planar layer, while surface area refers to the area of an open surface or boundary of a three-dimensional object
Set each side perpendicular to the wall x
Parallel to the wall would be 320-2x
the area would be:
A(x) = x (320-2x)
A(x) = 320x-2x ^ 2
It is quadratic with a = -2 and b = 320
The largest area will happen when x = -b / 2a
= -320 / (- 2 * 2)
= 80 feet
so the width will be 80 feet and the length will be:
length = 320-2 * 80
= 160 feet
Hence, The dimensions of the corral of maximum is 80 x 160 feet
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Nicky is making cookies. She needs to add 1 1/2 teaspoons of baking soda, but she can only fined 1/4 teaspoons measuring spoon. How many 1/4 teaspoons measures should she use.
Answer:
6
Step-by-step explanation:
1 and 1/2 is equal to 1 and 2/4, or 6/4. This means that it would take 6 teaspoons to add 1 1/2 teaspoons of baking soda. hope this helps!
Suppose we are given the following.
Line 1 passes through (-2,2) and (2,-8).
Line 2 passes through (0,-1) and (5,6).
Line 3 passes through (4,-7) and (2,-2).
(a) Find the slope of each line.
Slope of Line 1 = 08
Slope of Line 2 =
Slope of Line 3 =
(b) For each pair of lines, determine whether they are
parallel, perpendicular, or neither.
Line 1 and Line 2: OParallel OPerpendicular
Line 1 and Line 3:
Line 2 and Line 3:
Parallel
OParallel
Neither
OPerpendicular Neither
OPerpendicular
Neither
The slope of the line passing through (-2,2) and (2,-8) is -5/2
The ratio of the "vertical difference" to the "vertical change" between (any) two unique points on a line is used to compute slope.
The ratio can also be written as a quotient ("rise over run"), which produces the same number for every 2 different points on same line. A declining line has a negative "rise." The line might be useful, as determined by the slope, or it might appear in a diagram that represents a road or a roof as a narrative or a design.a)The slope of the line passing through (0,-1) and (5,6) is 7/5 .
The slope of the line passing through (4,-7) and (2,-2) is -5/2 .
b) line 1 and line 2 are perpendicular.
line 3 and line 2 are perpendicular.
line 1 and line 3 are parallel .
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Which of the number below are whole numbers?
Answer:
F and D are whole numbers
I need help on algebra 1 rewriting expression with radicals !
It is required to combine the radicals which can be done as follows:
[tex]\begin{gathered} 5\sqrt[]{27}-17\sqrt[]{3}=5\sqrt[]{3\times3\times3}-17\sqrt[]{3} \\ =5\times3\sqrt[]{3}-17\sqrt[]{3} \\ =15\sqrt[]{3}-17\sqrt[]{3} \\ =(15-17)\sqrt[]{3} \\ =-2\sqrt[]{3} \end{gathered}[/tex]Option D is correct.
Evaluate.
10 4/5+(8 3/4−6 1/2)
Enter your answer as a mixed number in simplest form by filling in the boxes.
Step-by-step explanation:
What is an
equation of the line that passes through the points (4, 0) and (3,1)
Your friend uses the order of operations to findthe value of 11(39-3). How could you usethe Distributive Property to show that eithermethod gives the same answer? Explainshowing both methods.
ANSWER AND EXPLANATION:
Given:
[tex]11(39-3)[/tex]Note that the acronym PEMDAS describes the order of operations and each letter stands for;
P - Parentheses
E - Exponents
M/D- Multiplication/Division (from left to right)
A/S - Addition/Subtraction (from left to right)
Following the above order of operations, we can go ahead and solve the expression as seen below;
[tex]\begin{gathered} 11(39-3) \\ =11(36) \\ =396 \end{gathered}[/tex]Using the Distributive Property, we can go ahead and solve the expression as seen below;
[tex]\begin{gathered} 11(39-3) \\ =11*39-11*3 \\ =429-33 \\ =396 \end{gathered}[/tex]We can see from the above that both methods give the same answer.
f(x) = x^2; vertical stretch by a factor of 3 and a reflection in the x-axis, followed
by a translation 3 units down
Answer:
-3x^2-3
Step-by-step explanation:
1: 3x^2
2: -3x^2
3:
y=2x-5 I need help quick
Answer:
5/2
Step-by-step explanation:
4
What is the percent of decrease from 4,097.6 to 3,585.4?
Answer:
= 12.5% decrease
Step-by-step explanation:
Decrease = Original Number - New Number
Then: divide the decrease by the original number and multiply the answer by 100.
% Decrease = Decrease ÷ Original Number × 100
Therefore, the answer is 12.5% decrease
Which is true about the domain and range of a function in the form f(x) = m, where m is a real number greater than 0? The only value that must be in both the domain and range is 0. The only values that must be in both the domain and range are 0 and 1. There are no values that are in the domain and the range. There is an infinite number of values that are in both the domain and range.
There is an infinite number of values that are in both the domain and range.
Here, we are given a function f(x) = m, where m is a real number greater than 0.
For a function, domain is all the input values that the function can take and range is all the output value that the function can take.
Here, all the x values are the domain and the set of all the values that m can take is the range of the function.
Here m can take all values except 0. Whereas there is no constraint on the x values.
Since the range can never have the value 0, options 1 and 2 are eliminated.
Clearly, there can be many values that are both in the domain and range of the given function.
Thus, there is an infinite number of values that are in both the domain and range.
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The expression below shows a sum multiplied by a factor:
3(2+6D)
Which options are equivalent to the expression above?
Select ALL that apply.
A (3 x 2)+(3 x 6d)
B 6+6d
C 3+2+6d
D 2+ (3 x 6d)
E 6+18d
3(2+6d)
Answer:
A and E
Step-by-step explanation:
I see no other correct answer option.
3(2 + 6D) = 3×2 + 3×6D = 6 + 18D
= (3×2)+(3×6D)
with or without brackets this is the same thing as per the priorities of mathematical operations (first multiplications and divisions, and only then secondly additions and subtractions).
You can paint 14 feet in 4 minutes and your friend can paint 18 feet in 6
minutes. How many feet total can you and your friend paint in 22 minutes?
The total feet you and your friend can paint in 22 minutes are 143 feet.
What is the unit rate?A unit rate is the rate for only one of anything. This is expressed as a ratio with a denominator of 1.
Given:
You can paint 14 feet in 4 minutes and your friend can paint 18 feet in 6 minutes.
The unit rate for you = 14/4 = 7/2 feet/min
The unit rate for your friend = 18/6 = 3 feet/min
The total feet you and your friend paint in 22 minutes is,
Multiply the 22 feet with the respective unit rates of you and your friend and add them up,
22×7/2 + 22×3 = 77 + 66 = 143 feet
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compare | -0.125 | and | 0.0125 |
Answer:
| -0.125 | > | 0.0125 |
Step-by-step explanation:
Due to the absolute value signs, the negative sign is null and void. Therefore, 0.125 > 0.0125.
Answer:
0.1375
Step-by-step explanation:
