So it would take A 10 days to do the whole job alone.
What is equation?An equation is a statement that asserts the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in a variety of mathematical contexts, including algebra, calculus, and geometry, as well as in physics, engineering, and many other fields.
Here,
Let's denote A's speed as "a" and B's speed as "b" (in units of work per day). Then, we know that:
In 5 days, A and B together completed the job, so we can write: 5(a + b) = 1 (where 1 represents the whole job).
If A worked at twice the speed (2a) and B worked at half the speed (0.5b), then they would complete the job in 4 days, so we can write: 4(2a + 0.5b) = 1.
We can simplify the second equation by multiplying out the brackets and collecting like terms:
8a + 2b = 1
Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other, and substitute the result into the other equation to find the value of the remaining variable. Let's solve for "b" in terms of "a" from the first equation:
5(a + b) = 1
5b = 1 - 5a
b = (1/5) - a
Now we can substitute this expression for "b" into the second equation:
8a + 2b = 1
8a + 2((1/5) - a) = 1
8a + (2/5) - 2a = 1
6a = (3/5)
a = (1/10)
So A can do 1/10 of the job in one day. To find out how long it would take A to do the whole job alone, we can use the formula:
time = amount of work / rate
Since A can do the whole job alone, the amount of work is 1, and A's rate is 1/10. Therefore:
time = 1 / (1/10)
= 10 days
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
2. How does making tables help you
identify relationships between terms in
patterns?
Answer:
Step-by-step explanation:
well if you know the term than you know the pattern
If 2X = 25 then X = 5, true are false.
Answer:
False
Step-by-step explanation:
The reason for it being false is because 2X = 25 should be divided to by 2 to get to X, which should be half of 25.
therefore X should equal 12.5
what are the answers to these questions?
a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.
b) The domain of V is [0, 3) in interval notation.
c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.
d) The maximum volume is 160/27 cm³.
(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.
Since the height of the box is x cm, the volume of the box can be expressed as
V = x(20-2x)(6-2x) cm³.
(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.
(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get
dV/dx = 4x³ - 52x² + 120x.
Setting dV/dx = 0, we get
x = 0 or x = 3 or x = 10/3.
Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.
We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get
V(0) = V(3) = 0
and
V(10/3) = 160/27.
(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.
So, the length of the box is
20-2(10/3)
= 40/3 cm,
the width of the box is
6-2(10/3)
= 2/3 cm, and
the height of the box is 10/3 cm.
To learn more about volume click on,
https://brainly.com/question/14086100
#SPJ1
For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose the best description of its solution. If the system has exactly one solution, give its solution. (see attached)
The systems of linear equations can be classified as "consistent dependent," "consistent independent," or "inconsistent" as follows:
A. System A = Inconsistent (No solution)
B. System B = Consistent dependent (Indefinitely many solutions)
C. System C = Consistent independent (A unique solution)
How to identify the systems of linear equationsTo identify the systems of linear equations, you first need to note the meaning of the different systems of equations. First, the Consistent dependent has two equations that represent the same line, so they intersect at infinitely many points and any point on the line represents a solution to the system.
Next, the Consistent independent has the two equations represented by two distinct non-parallel lines, so they intersect at exactly one point, which is the unique solution to the system.
Finally, the Inconsistent has two equations that are represented by two distinct parallel lines, so they do not intersect, and there is no solution to the system.
Learn more about the systems of linear equations here:
https://brainly.com/question/14323743
#SPJ1
What is k? k - 9 < - 6
Answer:
Step-by-step explanation:
2
2-9=-7
In negative numbers, the greater number that is negative is less than the smaller negative number. For example, -9<-8. Even though 9 is a bigger number when positive, it's the opposite for negative numbers. While there can be many numbers for k like 0,1, or 2, 1 will probably be the best answer.
Answer:
[tex]\mathrm{k < 3}[/tex]Step-by-step explanation:
[tex]\mathrm{ k - 9 < - 6}[/tex]
Add both sides by 9 :-
[tex]\mathrm{ k - 9+6 < - 6+6}[/tex]Simplify :-
[tex]\mathrm{k < -6+9}[/tex][tex]\mathrm{k < 3}[/tex]___________________
Hope this helps!
what is – 7n + –3 – 6n + 3 + 5 is simpified
Answer:
-13n + 5
Step-by-step explanation:
Give:
– 7n + –3 – 6n + 3 + 5
To Find:
simplify
Explanation:
– 7n + –3 – 6n + 3 + 5
= (-7n - 6n) + (-3 + 3 + 5)
= - 13n + 0 + 5
= -13n + 5
Final Answer:
-13n + 5
WY is a midsegment of AVXZ.
If VZ = 5t + 51 and WY = 11t, what is VZ?
VZ is 92.5. WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.
what is midsegment ?
A midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. It is also known as a midline. The midsegment of a triangle is parallel to the third side of the triangle, and its length is half the length of the third side.
In the given question,
Since WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.
Let's call the length of AX as L. Then, we have:
WY = 11t = 1/2 L
Multiplying both sides by 2, we get:
22t = L
Now, we can use this information to find VZ. Since WY is also parallel to VZ, we have:
WV = VZ
Substituting WV = L/2 and VZ = 5t + 51, we get:
L/2 = 5t + 51
Substituting L = 22t, we get:
22t/2 = 5t + 51
11t = 5t + 51
6t = 51
t = 8.5
Substituting t = 8.5 in the equation for VZ, we get:
VZ = 5t + 51 = 5(8.5) + 51 = 92.5
Therefore, VZ is 92.5.
To know more about midsegment , visit:
https://brainly.com/question/31009210
#SPJ1
A triangle has side lengths of (6.1w + 7.8) centimeters, (1.4w + 8.1) centimeters
and (8.7x + 2.5) centimeters. Which expression represents the perimeter, in
centimeters,
of the triangle?
The expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.
The perimeter of a triangle is the sum of the lengths of its sides. Using the given expressions for the side lengths of the triangle, we can write the perimeter as:
(6.1w + 7.8) + (1.4w + 8.1) + (8.7x + 2.5)
Simplifying and combining like terms, we get:
7.5w + 11.2x + 18.4
Therefore, the expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
NEED HELP ASAP! (10POINTS)
The statement that is true on the linear relationship between the brochures and cost of printing is A. the printing fee is $ 2.50.
How to find the printing fee ?To find the printing fee, find the difference between the total cost of two different numbers of brochures printed.
The printing fee is:
= ( Total cost of 43 - total cost of 40 ) / ( Difference between 43 and 40 )
= ( 607.50 - 600 ) / ( 43 - 40 )
= 7. 50 / 3
= $ 2. 50
Find out more on linear relationships at https://brainly.com/question/30582749
#SPJ1
Please help me with this question
Answer:
Your answer is E) 1/2 , -6 , 5
Step-by-step explanation:
Find the slope between (-6,5) then simplify and you will get 1/2
C & J Realty has received 16 inquiries from prospective home buyers. In how many ways can the inquiries be directed to any two of the firm's real estate agents if each agent handles eight inquiries?
There are 6435 ways to direct the inquiries to any two of the firm's real estate agents.
What is combinations?
Combinations are a mathematical concept used to count the number of ways that a certain number of items can be selected from a larger set of items without regard to the order in which they are selected.
We can use combinations to solve this problem. We need to choose 8 inquiries out of 16 for the first agent, and the remaining 8 inquiries will be handled by the second agent.
The number of ways to choose 8 inquiries out of 16 is:
C(16, 8) = 16! ÷ (8! * (16-8)!) = 12870
This is the number of ways the inquiries can be directed to one agent. Since there are two agents and each handles 8 inquiries, we need to divide this number by 2 to avoid counting each arrangement twice:
12870 ÷2 = 6435
Therefore, there are 6435 ways to direct the inquiries to any two of the firm's real estate agents.
To learn more about Combinations from given link.
https://brainly.com/question/30938605
#SPJ1
In order to save the world. Monnor must find the square of the sum of the roots of the equation: x^2-7x+5=0. What is the answer to Monnor's problem?
The answer to Monnor's problem is NOTA
How to find the answer to Monnor's problem?
For any quadratic equation of the form ax² + bx + c, the sum of roots is given by:
sum of roots = -b/a
In this case, x² - 7x + 5 = 0. Where a = 1 and b = -7. Thus:
sum of roots = -(-7)/1 = 7
Since Monnor must find the square of the sum of the roots of the equation, we have:
square of the sum of the roots = 7² = 49
Thus, the answer to Monnor's problem is NOTA
Learn more about quadratic equation on:
brainly.com/question/1592456
#SPJ1
How to solve -10(x-1.7)=-3 by expanding first
To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.
Expanding -10(x-1.7), we get
-10x + 17 = -3
Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation
-10x + 17 + 10x = -3 + 10x
Simplifying, we get
17 = 10x - 3
Next, we add 3 to both sides of the equation
17 + 3 = 10x - 3 + 3
Simplifying, we get
20 = 10x
Finally, we divide both sides of the equation by 10 to isolate x
20/10 = 10x/10
Simplifying, we get
2 = x
Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.
To know more about distributive property here
https://brainly.com/question/6276874
#SPJ1
Prove the following this:The number of left cosets of a subgroup is equal to the number of its right cosets?
To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.
Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.
First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.
Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.
Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.
Rewrite the quadratic function as a product of linear factors.
f(x) = 16x^2 - 3
help pls
Answer: (4x - √3)(4x + √3).
Step-by-step explanation: Use factoring. The equation (when factored out) is: ax^2 + bx + c. Hence, the equation you wrote rewritten is: 16x^2 + 0x - 3. (√3)(√3) = 3 and (4x)(4x) = 16x^2. It is divisible.
So, the quadratic function f(x) = 16x^2 - 3 can be expressed as a product of linear factors as (4x - √3)(4x + √3).
X 2 3 4 5 6 p(x=x) find the value of p(x>3)
From the given data, we have:
| x | 2 | 3 | 4 | 5 | 6 |
| --- | --- | --- | --- | --- | --- |
| p(x) | | | | | |
We need to find the value of p(x > 3).
We know that the sum of all the probabilities is equal to 1. So, we can find the missing probability by subtracting the sum of the probabilities we know from 1.
p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = 1
We don't know the value of p(x = 2), so we can't directly calculate p(x > 3). But we can find p(x ≤ 3) and subtract it from 1 to get p(x > 3).
p(x ≤ 3) = p(x = 2) + p(x = 3)
To find p(x = 2), we can use the fact that the sum of all the probabilities is 1:
p(x = 2) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6))
Now we can substitute this into the equation for p(x ≤ 3) and solve:
p(x ≤ 3) = p(x = 2) + p(x = 3)
p(x ≤ 3) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6)) + p(x = 3)
p(x ≤ 3) = 1 - (p(x = 4) + p(x = 5) + p(x = 6))
Finally, we can subtract p(x ≤ 3) from 1 to get p(x > 3):
p(x > 3) = 1 - p(x ≤ 3)
p(x > 3) = 1 - (1 - (p(x = 4) + p(x = 5) + p(x = 6)))
p(x > 3) = p(x = 4) + p(x = 5) + p(x = 6)
Therefore, the value of p(x > 3) is the sum of the probabilities for x = 4, 5, and 6.
I really need help please
Valid row operations are:
6R₁+ R₂ → R₃-(1/2) R₁ → R₁R₁ ↔ R₂R₁ ÷ 2 → R₁2R₂ → R₂-1R₃+ R₂ → R₂2R₁ → R₂R₁ + R₂ → R₂What are invalid row operations?Invalid row operations are:
0R₁ → R₁ (this is equivalent to multiplying a row by zero, which is not a valid row operation)
R₃ ÷ 0 → R₃ (division by zero is undefined)
-2 ÷ R₁ → R₁ (division by a variable is not a valid row operation)
2R₁ + R₂ → R₂ (the row operation should be adding multiples of one row to another row, not a combination of multiple rows)
Find out more on valid row operations here: https://brainly.com/question/26320234
#SPJ1
how do you find the base of a rectangle if you only know the height
Step-by-step explanation:
You will have to know more....like the area or the perimeter or the diagonal measure to determine the base if you only have the height.
Help please!!!!
Whoever answers right gets brainliest!
The simplified form of given expression a³/a⁶b⁻¹ is b/a³.
Hence, the correct option is C.
Exponents are a shorthand notation used in mathematics to represent repeated multiplication of a number by itself. The exponent is a small number written to the right and above a base number, and indicates how many times the base should be multiplied by itself.
In the given expression, a³/a⁶b⁻¹
We can apply the rules of exponents, and we get
= a³⁻⁶/b⁻¹
= a⁻³/b⁻¹
= b/a³
Hence, the correct option is C.
To know more about expression here
https://brainly.com/question/5497425
#SPJ1
the front of a refrigerator with a freezer on the bottom . The freezer part on the bottom has a height of 2 feet. The top part has a height of 5 feet.Explain how you find the total area of the front of the frig
The total area of the front of the figure is 21 [tex]feet^{2}[/tex].
What is the area?
The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.
To find the total area we need to add the area of the refrigerator and the area of the freezer.
The top part i.e refrigerator has a height of 5 feet and 3 feet width
Area of the refrigerator section = height * width
= 5 * 3
= 15 [tex]feet^{2}[/tex]
The bottom part i.e freezer has a height of 2 feet and 3 feet width
Area of the refrigerator section = height * width
= 2 * 3
= 6 [tex]feet^{2}[/tex]
The total area of the front of the figure is = Area of the refrigerator section + Area of the freezer section
= 15 + 6 = 21[tex]feet^{2}[/tex]
Learn more about the area here:
https://brainly.com/question/27683633
#SPJ1
Can you please help me with this please please
Answer:
a. 14:8
b. 6:14
Step-by-step explanation:
all books on the shelf = 6+8=14
a. 14:8
b. 6:14
With Bonds, banks pay you back with
O free banking
O a fixed amount
O interest
O stocks
Another Statistics question pls help me
Answer:
55
Step-by-step explanation:
0* .4
28*.5
410*.1
Find the length of the missing side
Answer:
x = 45°
Because there are 180° in a triangle
Plot the foci of this ellipse.
The equation of the ellipse derived as is
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1.
The equation of foci is
F₁ = (h - √(a^2 - b^2), k) , F₂ = (h + √(a^2 - b^2), k)
What is an ellipse?An ellipse is described as a set of points in a plane such that the sum of the distances from each point to two fixed points, called foci, is constant.
We can write the equation of an ellipse as:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
where (h, k) = the center of the ellipse,
a = the semi-major axis,
and b = the semi-minor axis.
The foci of the ellipse are located along the major axis and are equidistant from the center, with a distance of : √(a^2 - b^2).
we know also the formula to find the foci of an ellipse is:
F₁ = (h - √(a^2 - b^2), k)
F₂ = (h + √(a^2 - b^2), k)
The sum of the distances from each point on the ellipse to the foci is constant. The equation can then be written as:
2a = √((x - h + √(a^2 - b^2))^2 + (y - k)^2) + √((x - h - √(a^2 - b^2))^2 + (y - k)^2)
Simplifying, we then can write the equation of the ellipse as:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
To learn more about ellipse at:
https://brainly.com/question/9702250
#SPJ1
A graph is shown.
6987654321
10
0 1 2 3 4 5 6 7 8 9 10
Which ordered pair describes a point that should be removed from the graph so that the graph represents a function?
An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);
3 → 1
1 → 1
In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.
Read more on function here: https://brainly.com/question/27862183
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the slope of the line with a y-intercept = 4, passing through the point (2,8)
Answer: d. m = 2
Step-by-step explanation:
First, we will write a slope-intercept equation using the y-intercept given.
y = mx + 4
Next, we will substitute the given point and solve for m, the slope.
y = mx + 4
(8) = m(2) + 4
4 = 2m
m = 2
Learn more about slope-intercept form equations here:
https://brainly.com/question/27985430
[tex]\boxed{\sf m=2}.[/tex]
Step-by-step explanation:1. Identify the 2 given points.In order to find the slope of any linear equation you need at least 2 points the line passes through. We're explicitly provided one, (2, 8), we just need to figure out the other one.
When the statement says that the line has a y-intercept of 4, it means that at a point with y=4 the function touches the y axis. The only way to touch the y-axis is if the x value is 0. Hence, another given point is (0, 4).
2. Calculate the slope.Formula: [tex]\sf m=\dfrac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
Naming the variables (can be done arbitrarily but always make sure the y's are actual y values from the ordered pairs and that x₁ goes with its corresponding y₁ value from the ordered pair):
[tex]x_{1} =2;\\x_{2} =0;\\y_{1} =8;\\y_{2} =4.[/tex]
Now substituting these values in the formula:
[tex]\sf m=\dfrac{(4)-(8) }{(0) -(2) }=\dfrac{-4}{-2} =\boxed{\sf 2}.[/tex]
Check out the attached image to see the graphed line.
pls answer asap
A traveler has 9 pieces of luggage.
How many ways can the traveler select 3 pieces of luggage for a trip?
Responses
84
84
504
504
60,480
60,480
362,880
Answer:
84
Step-by-step explanation:
Trust me
Answer:
84
Step-by-step explanation:
There are 9 pieces of luggage.
We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left. The third piece can be selected 7 different ways.
9*8*7
504
But order doesn't matter since we are taking 3 pieces.
Divide by (3*2*1)
504/6 = 84
There are 84 different combinations of luggage
The graph shows the total weight of a fish tank, y, as a function of the amount of water in the tank, x
What is the weight of an empty tank?
The weight of the empty tank is given as follows:
4 pounds.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The weight of the empty tank is the intercept of the function, which is of b = 4, hence:
4 pounds.
More can be learned about linear functions at https://brainly.com/question/15602982
#SPJ1
help pleaseeeeeeee
here is the picture is about Row Ops
The result of adding -4 (row 1) to row 3 is determined as (0 - 9 2)|12.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 2 1] | -5
To multiply row by -4, we will multiply each entity by 4 as shown below;
= -4(1 2 1) | -5
= (-4 -8 - 4) |20
To add the result to 3;
(-4 -8 - 4)|20 + (4 - 1 6) | -8
= (0 - 9 2)|12
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.
Learn more about row multiplication here: https://brainly.com/question/31531585
#SPJ1