The equation of proportional situation is y = ax.
Therefore your answer is y = 14x
6 painters can paint the fence in 15 hours. How long would it take 5 workers to do the same job? 12.5 is not the right answer
Answer:
It will take them 18 hours.
Step-by-step explanation:
To find the answer of this, you must first multiply the amount of people by the time:
6 * 15 = 90
Then to find the time it takes 5 workers, divide this by 5:
90 ÷ 5 = 18
So it will take them 18 hours!
Help plzzz....………………….…....................................
Answer:
C
Step-by-step explanation:
You automatically know that it is not A. The dot is filled in on the number line, so it must have a line under the inequality mark.
The number line says that x is greater than or equal to 2.5
Key:
gtoet means greater than or equal to
ltoet means less than or equal to.
B:
3x + 2 gtoet 17
3x gtoet 15
x gtoet 5
This is incorrect. X is not gtoet 5.
C:
12 + 4x gtoet 22
4x gtoet 10
x gtoet 2.5
This is correct. X is gtoet 2.5
D:
-6x - 15 gtoet 0
-6x gtoet 15
(The sign switches in this one because you are dividing by a negative)
x ltoet 2.5
Incorrect. X is not ltoet 2.5
Monkey Chunks cereal is normally $3.25 per box but today it’s on sale for 25% off. What is the new price and round to the nearest penny? PLEASE HELP!!!!
Answer:
$2.44
Step-by-step explanation:
Change the percentage into a decimal. Move the decimal point to the left two place values.
25% = 25/100 = 0.25
Multiply the two numbers:
3.25 x 0.25 = 0.8125
Subtract the number gotten from the original number. Remember to first simplify.
0.8125 = 0.81
3.25 - 0.81 = 2.44
$2.44 is your new price.
~
For a school play, 739 tickets valued at $857 were sold. Some cost $1 and others cost a $1.50. How many $1 tickets were sold?
if someone could explain how you set it up and why that would really help me
Answer:
503 $1 tickets sold.
Step-by-step explanation:
Use two equations
Let x = number of $1 tickets sold
Let y = number of $1.50 tickets sold
x + y = 739
1x + (1.5)y = 857
First equation ==> y = 739 - x
Plug this into the second equation
x + (1.5)(739 - x) = 857
x + 1108.5 - 1.5x = 857
- 0.5x = -251.5
x = 503
There were 503 $1 tickets sold.
To find the number of $1.50 tickets, just plug this value of x into either one of the equations.
(503) + y = 739 (739 - 503 = 236)
y = 236
There were 236 $1.50 tickets sold.
A system of linear equations and using the elimination method, we found out that 503 $1 tickets were sold for the school play.
To solve the problem involving the tickets sold for the school play, we need to set up a system of linear equations.
First, let’s define our variables: let x be the number of $1 tickets and y be the number of $1.50 tickets sold. Based on the problem, we can create the following equations:
x + y = 739 (total number of tickets sold)
1×x + 1.5×y = $857 (total amount of money collected)
We can solve this system of equations using either the substitution method or the elimination method. For this example, let's use the elimination method and multiply equation (1) by -1.5 to eliminate y when we add the two equations:
-1.5x - 1.5y = -1108.5 (After multiplying equation (1) by -1.5)
1x + 1.5y = 857 (Original equation (2))
By adding the two equations, we get:
-0.5x = -251.5
Now we divide both sides by -0.5 to find the value of x:
x = 503
So, 503 $1 tickets were sold for the school play.
A rectangle has a length of 6 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. Graph a system of linear equations to find x .
The value of x is the point of intersection of the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]
The value of x is 3
The given parameters are:
[tex]\mathbf{Length = 6}[/tex]
[tex]\mathbf{Width = x}[/tex]
The perimeter is calculated as:
[tex]\mathbf{P =2 \times (Length + Width)}[/tex]
So, we have:
[tex]\mathbf{P =2 \times (6 + x)}[/tex]
Expand
[tex]\mathbf{P =12 + 2x}[/tex]
The area is calculated as:
[tex]\mathbf{P = Length \times Width}[/tex]
So, we have:
[tex]\mathbf{A =6 \times x}[/tex]
[tex]\mathbf{A =6x}[/tex]
See attachment for the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]
From the attached graph, the lines of both functions meet at x =3.
Hence, the value of x is 3
Read more about linear equations at:
https://brainly.com/question/11897796
Suppose that 216 students attended school one day, and 62 percent of them ate the school's breakfast. How many students ate the school's breakfast that day? Round your answer to the nearest whole number
Answer:
Given the statement:Suppose that 216 students attended school one day, and 62 percent of them ate the school's breakfast.
Total number of students attended school = 216 students.
and 62% of them ate the school breakfast that day.
Now, to calculate the number of students ate the breakfast that day.
Proportion states that the two ratios or fraction are equal.
Let x represents the number of students ate the breakfast that day.
then, by using proportion;
[tex]\frac{62}{100}=\frac{x}{216}[/tex]
Multiply both sides by 216 we get;
[tex]x = \frac{62}{100} \times 216[/tex]
Simplify:
[tex]x = 133.92[/tex]
therefore, the number of students ate the school breakfast that day(to the nearest whole number) is, 134 students.
Which is equivalent to (-2ab^3) (-3a^2b^5)
Answer:
6 a^3 b^8
Hope That Helps!
Solve for y in terms of x.
2/3y - 4 = x
y = x + 6
y = -x + 4
y = -x + 6
y = x + 4
Answer:
[tex]y=\frac{3}{2} x+6[/tex]
Step-by-step explanation:
We are given the following equation and we are supposed to solve y in terms of x. It simpler terms, it means that we have to make y the subject of the equation while x being used in it as it is:
[tex]\frac{2}{3} y-4=x[/tex]
Taking the constant 4 to the side where x is to get:
[tex]\frac{2}{3} y=x+4[/tex]
Multiplying the denominator 3 to the other side of the equation to get:
[tex]2y=3x+12[/tex]
Isolating y to make it the subject:
[tex]y=\frac{3}{2} x+\frac{12}{2}\\ \\y=\frac{3}{2} x+6[/tex]
what is the importance of the quadratic formula?
Answer:
It solves all quadratic equations for any real or imaginary solutions.
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.
which of the following trigonometric equations is false for x?
a) sin x = 2 /√5
b) cos x = -0.1439
c) cos² x + sin² x = 1
d) sec x = √3 / 4
e) tan x = -100
Please help!
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −3
0 0
1 3
g(x)
g(x) = 7x + 2
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Answer:
A) slope of f(x) = 3 , slope of g(x) = 7
B) y intercept of f(x) is 0 and g(x) is 2
So g(x) has greater y intercept
Step-by-step explanation:
Lets find equation of f(x) using the given table
LEts take two points from the table (0,0) (1,3)
[tex]slope = \frac{y_2-y_1}{x_2-x_1} = \frac{3-0}{1-0} = 3[/tex]
we use equation y=mx+b
where m is the slope and b is the y intercept
we got m = 3, we use (0,0) and find out b
y=mx+b
0 = 3(0) + b
so b=0
So equation for f(x)= 3x +0
slope =3 and y intercept = 0
For equation g(x) = 7x +2 , slope = 7 and y intercept = 2
solve and show your work 3.6(5×4)÷3+5.0=
Answer:
1.5 - 1 1/5 = 3
10
= 0.3
Step-by-step explanation:
The quantity, y, varies directly as x. When y=10 x=6
The quantity y is directly proportional to x, indicated by the equation y = (5/3)x, found by determining the constant of proportionality (k = 5/3) given that y=10 when x=6.
Explanation:The problem states that the quantity, y, varies directly as x.
In mathematical terms, this relationship can be represented as y = kx, where k is the constant of proportionality.
Given that when y=10, x=6, we can find k by substituting these values into our formula, yielding 10 = k*6.
Solving for k, we get k = 10/6 or k = 5/3.
Therefore, the equation that describes how y varies directly as x is y = (5/3)x.
This equation tells us that for every unit increase in x, y increases by 5/3 units, illustrating a direct proportionality relationship between the two quantities.
This relationship can be depicted as a straight line through the origin (0,0) on a graph, where k also represents the slope of the line.
Name
Score
John
2
Hank
-1
Tammy
-2
Sami
0
Gil
1
One day five golfers made the scores shown. Ordered from GREATEST to LEAST they are
Answer:
John > Gil > Sami > Hank > Tammy
Step-by-step explanation:
It might help if we draw a number line like the one below.
Then we can see that John > Gil > Sami > Hank > Tammy.
Final answer:
The golf scores from greatest to least are John (2), Gil (1), Sami (0), Hank (-1), Tammy (-2).
Explanation:
The student is asking to order the golf scores from greatest to least. When comparing numbers, the higher a number's value, the greater it is. In this context, negative scores are lower than zero or positive scores. Here's how the scores are ordered:
John: 2
Gil: 1
Sami: 0
Hank: -1
Tammy: -2
This order reflects the scores from highest to lowest, with John having the highest score and Tammy the lowest.
Of 300 tickets,240 were sold to sixth grade students what percent of the total number of tickets sold were sold to sixth grade students?
Answer:
80%
Step-by-step explanation:
to find the percentage of tickets sold to sixth grade students
percent sold = [tex]\frac{numbersold}{numberof tickets}[/tex] × 100%
= [tex]\frac{240}{300}[/tex] × 100% = 80%
Answer:
80%
Step-by-step explanation:
To find the percentage sold to sixth graders, take the number sold to sixth graders over the total
percentage to sixth graders = tickets sold to sixth graders/ total tickets
The total tickets are 300
Tickets to sixth graders is 240
Substitute it in
percentage to sixth graders = 240/300
=24/30
=4/5
=.8
Multiply this by 100 to give the percent
80%
a weekly salary of $325 plus a 6.5% commission on sales at a store. How much would she make in a work week if she sold $4800 worth of merchandise?
Answer: $637
Step-by-step explanation:
Find the amount she makes in commission 4,800 x 0.065=312
add the weekly salary and commission to get her total earnings
325+312= 637
Answer:
Income = 637
Step-by-step explanation:
Income = weekly salary + commission
commission = 6.5% * sales
commission = .065* 4800
= 312
Income = weekly salary + commission
Income = 325+312
Income = 637
Please help look at the picture
Answer:
y = - 5x - 1
Step-by-step explanation:
The first thing to do (always) is pay attention to x =0. That at least gives you a partial answer. y = y' - 1. when you put 0 in for whatever y' is you get 0. What about the other numbers? How did they come about.
We have another clue. Whenever you put in a positive number for x, you get a negative answer for y. That's interesting. So y' has a minus sign associated with it.
y = -ax - 1 Make a>0 so there is only 1 minus sign. x cannot have an even power, because an even power would make everything positive except the -1.
So we'll start with y= - ax - 1 We'll also make the assumption that a = 1
y = - x - 1 That won't work. a >1 otherwise x = 2 won't give - 11
y = -ax - 1
let x = 2
let y = - 11 Solve for a
y = - ax - 1
- 11 = -a*-2 - 1 add 1 to both sides
-11 + 1 = - a(-2) - 1 + 1
- 10 = -2a Divide by - 2
- 10/-2 = -2a/-2
a = 5
Answer: y = - 5x - 1
Can anyone help me plz ?? Lakita has 66 water bottles for the 5K race participants. In addition, she is planning to buy boxes of water bottles that have 12 water bottles each. All of the boxes cost the same. Lakita can buy up to 5 boxes of water bottles given the amount of money she has.Write a function to describe how many water bottles will Lakita buy.Find a reasonable domain and range for the function.
We can see here that the function can be written as:
f(x) = 66 + (12 × x)
To determine how many water bottles Lakita will buy, we need to consider the number of water bottles she already has (66) and the number of boxes she can afford to buy (up to 5). Each box contains 12 water bottles.
We can create a function to represent this situation:
Let's define:
x = the number of boxes Lakita will buy
The total number of water bottles Lakita will have is:
Total number of water bottles = 66 + (12 × x)
The reasonable domain for this function is 0 ≤ x ≤ 5, as Lakita can buy up to 5 boxes of water bottles.
The range of the function represents the total number of water bottles Lakita will have, which depends on the value of x. The range can be expressed as:
Range: 66 ≤ Total number of water bottles ≤ 126
So, the function can be written as:
f(x) = 66 + (12 × x)
Where:
x = the number of boxes Lakita will buy, and
f(x) = the total number of water bottles she will have.
What is the probability that a student prefers chocolate given that the students is a girl?
Answer:
The probability is 1/2.
Step-by-step explanation:
There are a total of 40 girls that are surveyed and 20 prefer chocolate. If you write that as a fraction 20/40, it simplifies to 1/2.
If a line passes through the points (1,3) and (-2,-9), the equation of the line is y-3=4(x-__)
Answer:
y - 3 = 4(x - 1)
Step-by-step explanation:
This is point slope form, which looks like this:
[tex]y-y_{1}=m(x-x_{1})[/tex]
Because a 3 is used for the y value, we know the coordinate point we are using is (1, 3). All we need to do is plug the x value in.
y - 3 = 4(x - 1)
the base of a cylinder has a radius of 5 inches what measurement is needed to find the volume of the cylinder
Answer:
height
Step-by-step explanation:
the volume (V) of a cylinder is calculated using the formula
V = πr²h
where r is the radius and h the height
given the radius then the height is the required measurement needed
A married couple wishing to file their taxes jointly, claim their children, as well as medical expenses must file their taxes using which form?
Answer:
I believe it is a 1040 tax form
Step-by-step explanation:
Final answer:
A married couple should use IRS Form 1040 to file their taxes jointly, claim dependents like children, and deduct medical expenses.
Explanation:
A married couple wishing to file their taxes jointly, claim their children, and deduct medical expenses should use the IRS Form 1040. This is the standard Income Tax Return form for individuals in the US. The Form 1040 allows taxpayers to report their income, claim tax deductions and credits, and calculate the amount of tax owed or refund due.
When filing a joint return, you are also able to claim dependents, which may include children, and report medical expenses that can be deducted if they exceed a certain percentage of your adjusted gross income. While there are different variations, such as 1040A or 1040EZ, the full 1040 form is necessary when claiming detailed deductions such as medical expenses.
Suppose LM ∥ KN , KL ∥ NM , h1=5, h2=6, and the perimeter of KLMN is 42. Find the area of KLMN.
To find the area of KLMN, we need to determine the length and width of the quadrilateral. We can do this by setting up and solving equations using the given information. By substituting the values and solving the equations, we find that the area of KLMN is 90 square units.
Explanation:To find the area of KLMN, we need to determine the length and width of the quadrilateral. Since LM is parallel to KN, we know that LM = KN. Similarly, KL is parallel to NM, so KL = NM. Let's call the length of KLMN as L and the width as W. The perimeter of KLMN is 42, so we have L + KL + KN + NM = 42. Since KL = NM, we can rewrite the equation as L + 2KL + 2NM = 42.
We are also given the heights h1 and h2, which represents the vertical distance between the parallel sides. In this case, h1 = 5 and h2 = 6. The formula for the area of a quadrilateral is A = L * h1. Therefore, A = L * 5. We need to find the value of L to calculate the area.
Using the information given, we can set up the following equations:
L + 2KL + 2NM = 42
KL = NM
L * 5 = A
To solve these equations, we'll use substitution. Since KL = NM, we can substitute KL as NM in the first equation. This gives us:
L + 2NM + 2NM = 42
Simplifying the equation, we get:
L + 4NM = 42
Since h2 = 6 and h2 = NM, we can substitute NM as 6 in the equation:
L + 4(6) = 42
Simplifying further, we get:
L + 24 = 42
Subtracting 24 from both sides:
L = 18
Now that we know the value of L, we can calculate the area using the formula: A = L * h1. Substituting the values we have:
A = 18 * 5 = 90
Therefore, the area of KLMN is 90 square units.
Learn more about Area of a Quadrilateral here:https://brainly.com/question/39164410
#SPJ12
A rectangular prism with a volume of 2 cubic units is filled with cubes with side lengths of 1/4 unit. How many 1/4 unit cubes does it take to fill the prism
Answer:
128
Step-by-step explanation:
Method A.
The volume of the prism is 2 cubic units.
Each cube has side length of 1/4 unit.
The volume of each cube is (1/4)^3 cubic unit.
The volume of each cube is 1/64 cubic unit.
To find the number of cubes that fit in the prism, we divide the volume of the prism by the volume of one cube.
(2 cubic units)/(1/64 cubic units) =
= 2/(1/64)
= 2 * 64
= 128
Method B.
Imagine that the prism has side lengths 1 unit, 1 unit, and 2 units (which does result in a 2 cubic unit volume.) Since each cube has side length 1/4 unit, then you can fit 4 cubes by 4 cubes by 8 cubes in the prism. Then the number of cubes is: 4 * 4 * 8 = 128
Answer:
128 cubes.
Step-by-step explanation:
Volume of each cube = (1/4)^3 = 1/64 cubic units.
Number of cubes that will fill the prism
= 2 / 1/64
= 2*42
= 128 answer
Please help me answer this correctly
Answer:
see explanation
Step-by-step explanation:
using A = bh with b = 2x + 1 and h = x + 1, then
(2x + 1)(x + 1) = 28 ← expand factors on left
2x² + 3x + 1 = 28 ( subtract 28 from both sides )
2x² + 3x - 27 = 0 ← in standard form
To factorise, consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x term
product = 2 × - 27 = - 54 and sum = + 3
The factors are - 6 and + 9
Use these factors to split the middle term
2x² - 6x + 9x - 27 = 0 ( factor first/second and third/fourth terms )
2x(x - 3) + 9(x - 3) = 0 ( take out the factor (x - 3) )
(x - 3)(2x + 9) = 0
equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
2x + 9 = 0 ⇒ x = - [tex]\frac{9}{2}[/tex]
however x > 0 ⇒ x = 3
base = 2x + 1 = (2 × 3) + 1 = 7 units and height = x + 1 = 3 + 1 = 4 units
Point A lies on the circle and has an x-coordinate of 3.
Answer:
y = √7
Step-by-step explanation:
This circle has a center at (0,0) and a radius of 4 so its equation is:-
x^2 + y^2 = 16
when x= -3, (-3)^2 + y^2 = 16
9 + y^2 = 16
y^2 = 7
y = √7
What is the equation of a line that is parallel to y= 3 5 x−7 y=35x−7 and passes through (15, 8) (15, 8)
Answer:
The equation of this line would be y = 35x - 517
Step-by-step explanation:
In order to find this equation we must first find the slope of the original line. The original slope (the coefficient of x) is 35, which means the new slope will also be 35 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.
y - y1 = m(x - x1)
y - 8 = 35(x - 15)
y - 8 = 35x - 525
y = 35x - 517
The equation of the line parallel to y = 35x - 7 and passing through the point (15, 8) is y = 35x - 517.
Explanation:To find the equation of a line that is parallel to y = 35x - 7 and passes through the point (15, 8), we need to determine the slope of the original line.
Since the given line is in the form y = mx + b, where m is the slope, we can see that the slope of the given line is 35.
Since parallel lines have the same slope, the slope of the line we're looking for is also 35.
Now we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the values, we have y - 8 = 35(x - 15).
Expanding and simplifying, we get y - 8 = 35x - 525.
Finally, rearranging the equation, we find the equation of the line is y = 35x - 517.
The pattern 0.73, 083 , 0.93
Answer:
1.03
Step-by-step explanation:
I think the pattern is adding .1 So then next one is 1.03
Answer:
+0.10
Step-by-step explanation:
0.73+0.10= 0.83+0.10=0.93 etc
have a great day!
Karin wants to use the distributive property to mentally find the value of 19 x 42+ 19x 58. Which expression can she use?
19 x (42 + 58) or 19*(42 + 58) is the expression she can use. You factor out the common term 19. The distributive rule says that we can multiply the outer 19 with each term inside to get the original expression again.
Write an integer for each situation. 3 miles below sea level u may solve the other ones?
"3 miles below sea level" may be written as -3. The negative indicates you are below sea level. Going above sea level means the value would be positive.
"earning 45 dollars" can be written as +45 or simply 45. If you lost 45 dollars, then it would be -45. If you are in debt 45 dollars, then it would be -45.
"moving back 5 spaces" is represented by -5 whereas moving forward 5 spaces is +5 or simply 5.