Answer:
Let x = the number of small boxes purchased
Let y = the number of large boxes purchased
150x+400y&=1950
x=y+2
The system of equations is as follows:
Equation 1: Total nails from small boxes = 150s
Equation 2: Total nails from large boxes = 400l
Equation 3: Total boxes = s + l
Equation 4: Total nails = 150s + 400l = 1950
To determine the number of small boxes and large boxes the contractor purchased, we can set up a system of equations. Let's define the variables: let "s" represent the number of small boxes and "l" represent the number of large boxes.
Now, let's break down the information given into equations:
Equation 1: The total number of nails from the small boxes is 150 times the number of small boxes, which is 150s.
Equation 2: The total number of nails from the large boxes is 400 times the number of large boxes, which is 400l.
Equation 3: The total number of boxes is the sum of small and large boxes, so the total boxes are s (number of small boxes) plus l (number of large boxes).
Given that the contractor bought 2 more small boxes than large boxes and the total number of nails purchased is 1950, we can express this as an equation:
4. Equation 4: The total number of nails purchased is 1950.
Now, we can write the system of equations:
Equation 1: 150s
Equation 2: 400l
Equation 3: s + l
Equation 4: 150s + 400l = 1950
In this system, Equation 1 represents the total number of nails from the small boxes, Equation 2 represents the total number of nails from the large boxes, Equation 3 represents the total number of boxes, and Equation 4 represents the total number of nails purchased.
To find the solution, we can solve this system of equations using various methods, such as substitution or elimination, to determine the values of "s" and "l," representing the number of small and large boxes the contractor purchased, respectively.
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What is the vertex of the graph of f(x) = |x + 3|+ 7? (3,7) (7,3) (-3, 7)(7,-3)
Answer:
vertex (-3 , 7)
Step-by-step explanation:
vertex (h, k) f(x) = a | x - h | + k
f(x) = |x + 3|+ 7 , h = - 3 and k = 7
vertex (-3 , 7)
The value of vertex of the graph would be,
⇒ (-3 , 7)
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
We know that;
Standard form of equation is,
⇒ f(x) = a | x - h | + k
Where, vertex = (h, k)
Here, The equation of graph is,
f(x) = |x + 3|+ 7 ,
And, h = - 3 and k = 7
Thus, The value of vertex of the graph would be,
⇒ (-3 , 7)
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(889 x 27) + 50 is
than 889 x 27
Final answer:
The expression (889 x 27) + 50 is greater than 889 x 27, because adding 50 to any product will always result in a larger number.
Explanation:
The student's question is asking to compare the result of the expression (889 x 27) + 50 with 889 x 27, without actually calculating the precise values.
First, let's evaluate the structure of the expressions. When we have an expression of the form (a x b) + c, adding any number c to the original product of a and b will always result in a value greater than the original product. This is a basic property of arithmetic progression.
Based on this property, we know that (889 x 27) + 50 is definitely greater than 889 x 27 because we are adding a positive number (50) to the original product, hence the sum must be larger.
7. You go out to dinner and the bill is $40 and you want to leave the server a 15% tip. How much of a tip are you going leave?
The tip i will leave is of 6 dollars.
What is percentage ?Percentage is the value per hundredth. Suppose we have 500 dollars and we need find 50% of it.We know 50% of 500 dollars is half of it which is 250 dollars.
To find 50% of 500 dollars we put the the given percentage on numerator and divide by hundred and multiply it by the given amount.
∴ (50/100)×500
= 250 dollars.
According to the given question
You go out to dinner and the bill is $40 and you want to leave the server a 15% tip.
We have to find what is 15% of 40 dollars which is
= (15/100)×40 dollars.
= 6 dollars.
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x+5÷9=3
What is the number where when you add 5 then divide it by 9 it is 3?
Answer:
22 + 5 ÷ 9 = 3
Proof:
27/9
= 3
the number is 22
Find the Quotient.
5,483 ÷ 4
Answer:
1370.75
Step-by-step explanation:
work out 35% out of £120
Answer:
42
Step-by-step explanation:
120*35=4200
4200/100=42
5 A dangerous criminal has escaped from
prison. The police believe he could not have
traveled more than 10 mi in any direction
from the prison. How many square miles
must be searched?
Answer:
314 mile²
Step-by-step explanation:
area = πr² = 3.14 x 10² = 314 mile²
What is equivalent to 8 1/4
Answer:
33/4
Step-by-step explanation:
8x4 +1 = 33
Answer:
33/4
Step-by-step explanation:
How many 60-degree angles does it take to make a full turn?
Answer:
6
Step-by-step explanation:
360 is a full turn so, 360 divided by 60 is 6
How do I solve systems of equations algebraically
Answer:
You solve equations algebraically by using equations to answer and having variables rather than the arithmetic way (doing the work).
Ex: instead of 20÷5=4 (arithmetic), you do
20=5x
How to solve the inequality x+8>2
Answer:
the answer to the inequality is x>-6
Step-by-step explanation:
x+8>2
x>2-8
x>-6
The ratio of boys to girls is 10:7. If there is 84 girls, how many boys are there?
Answer:1
Step-by-step explanation:
What is the slope of the line below? Give an exact number
Answer:
The slope of straight line in the graph is
m = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Slope of a given line is [tex]m = \frac{y_{2}-y_{1} }{x_{2} - x_{1} }[/tex]........(1)
The point (-2,0) lie on x-axis in the graph and another point ( 0, 1) lie on y- axis.
so [tex](x_{1} , y_{1}) = (-2,0) and (x_{2} , y_{2}) = (0,1)[/tex]
substitute these values in equation (1)
[tex]m = \frac{1-0}{0-(-2)}[/tex]
[tex]m = \frac{1}{2}[/tex]
slope of given line is [tex]m = \frac{1}{2}[/tex]
X+2y=4 convert equation from standard form to slope intercept form
Answer:
y = -(1/2)x + 2
Step-by-step explanation:
2y = -x + 4
y = (-x + 4)/2
y = -(1/2)x + 2
Explain how you know that 7/12 is greater than 1/3 but less than 2/3
Answer:
Step-by-step explanation:
7/12 is greater than 1/3 because it has a greater numerator and denominator it is less than 2/3 because the numerator is smaller
1. If two nonvertical lines are parallel, what do we know about their slopes? If two lines are perpendicular and neither is parallel to an axis, what do we know about their slopes? Why must the lines be nonvertical?
Non-vertical parallel lines have equal slopes, while slopes of non-vertical, non-horizontal perpendicular lines are negative reciprocals of each other. Vertical lines are defined as having an infinite slope, thus they must be non-vertical to consider their slopes.
Explanation:When considering the slopes of lines on a graph with perpendicular axes, like the x-axis and the y-axis, we can draw several conclusions about parallel and perpendicular lines. If two non-vertical lines are parallel, their slopes are equal, because the tilt of the lines with respect to the horizontal axis is the same. For example, if we have two equations of lines in the form y = mx + b, where m represents the slope and b represents the y-intercept, parallel lines would have the same value of m.
If two lines are perpendicular and neither line is parallel to an axis, then their slopes are negative reciprocals of one another. This holds true because the product of the slopes of two perpendicular lines is -1. For example, if the slope of one line is a, the slope of the line perpendicular to it will be -1/a.
It is necessary for the lines to be non-vertical because a vertical line does not have a well-defined slope; its slope is considered infinite. Therefore, the definition of perpendicular lines in terms of slope only applies to non-vertical lines.
PLZ HURRY! Which mapping diagram represents a function from x → y?
A function from x to y represents a situation where each x value is linked to a unique y value. This can be represented in a mapping diagram, such as with the points (1,5), (2,10), (3,7), and (4,14). Such a diagram showcases the fact that different x values trigger different y values, demonstrating the dependence of y on x.
Explanation:A function from x to y implies that when the value of x changes, it directly influences the value of y. One way to represent this is through a mapping diagram.
A mapping diagram that represents a function can be visualised as each value of x corresponding to a unique value of y. For example, refer to the following points: (1,5), (2,10), (3,7), and (4,14). Here, every x value is paired with a unique y value. When these points are plotted, there's no x value that corresponds to more than one y value, demonstrating the dependence of y on x.
Therefore, a function from x to y is represented by a mapping diagram where different x values are linked to unique y values, showing the dependency of y values on the x values.
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A company makes a profit of $50 per software program and $35 per video game. The company can produce at most 200 software programs and at most 300 video games per week. Total production cannot exceed 425 items per week. How many items of each kind should be produced per week in order to maximize the profit?
IDENTIFY VARIABLES, STATE OBJECTIVE FUNCTION, AND STATE THE CONSTRAINTS.
Answer:
200- software (x) 225- video game (y) = 425 items
Step-by-step explanation:
software- 200 = $10,000 video-225 = $7,875
total= $17,875
200x + 225y = $17,875
5x/3 + 1/3 =12 find x
Answer:
x = 7.002 or 7
Step-by-step explanation:
5x/3 + 1/3 = 12
- 1/3 - 1/3
5x/3 = 11 2/3
3(5x/3) = 3(11 2/3)
5x = 35.01
x = 7.002 or 7
9y-4-11y+7
Terms:
Like terms:
Coefficient:
Constants:
9y - 4 - 11y + 7
Terms: 9y, -4, -11y, 7
Like terms: 9y and -11y
Coefficient : 9, -11
Constants: 7, -4
Solution:
Given expression is:
9y - 4 - 11y + 7
We have to find the terms, like terms, coefficient and constants
Terms:Each term in the expression is called terms
It includes, numbers, variables also
Terms : 9y and -4 and -11y and 7
Coefficients:A coefficient is a number used to multiply a variable
Here the terms with variables are 9y and -11y
Coefficient : 9, -11
Like terms:"Like terms" are terms whose variables are the same and thier powers is also same
Like terms : 9y and -11y
Constants:The constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number
Constants: 7 and -4
9th grade math thanks
Answer:
Plumber A has greater initial fee
Step-by-step explanation:
Plumber B:
Hourly charge = 160 - 105 = $55
Initial charge = 105 - 55 = $50
Equation: y = 50 + 55x
Answer:
C
Step-by-step explanation:
For plumber A : y = 100 + 30x
For plumber B :
Let the total charge be y
Initial charge be x
Hourly rate be za
For total price = 105 in 1hr
105 = x + a ........(1)
For 160 total charge in 2hrs
160 = x + 2a .........(2)
Substracting (1) from (2)
160 - 105 = 2a - a
55 = a
Substituting a = 55 in (1)
105 = x + a
105 = x + 55
x = 105 - 55
x = 50
:- equation for total charge is
y = 50 + 55a
which is an equation of the line that passes through the points (5,2) and (10,-3)
Answer:
y = x - 4
Step-by-step explanation:
equation of a line can be expressed as
(x - x1)/(x2 - x1) = (y - y1)/(y2 - y1)
(x - 5)/(10 - 5) = (y - 2)/(-3 - 2)
cross multiplying,
-5(x - 5) = 5(y - 2)
clearing the parentheses
-5x + 10 = 5y - 10
hence,
5y = 5x - 20
y = x - 4
PLEASE HELP
What is the twenty-first term of the sequence given by
xn = 4n − 3 ?
87
72
81
6
Answer:
81
Step-by-step explanation:
To find the 21 st term substitute n = 21 into the formula
[tex]x_{21}[/tex] = 4(21) - 3 = 84 - 3 = 81
vanssea earns base salary of $400.00 every week with an additional 5% commission on everything she sells. Vanessa sold $1650.00 worth of items last week. What was Vanessa's total pay last week?
Answer: She earns 482.50
Step-by-step explanation:
A car is purchased with a loan of $8.000 for two years with simple interest. The amount that is paid back is $8,160
Which function represents the interest on this loan after years!
The function that represents the interest on this loan after years is Interest = Principal × Rate × Time.
Explanation:The function that represents the interest on this loan after years can be calculated using the formula for simple interest:
Interest = Principal × Rate × Time
In this case, the principal is $8,000, the rate is unknown, and the time is 2 years. The interest paid back is $8,160, so we can rewrite the formula as:
$8,160 = $8,000 × Rate × 2
Dividing both sides of the equation by $8,000 × 2 gives:
Rate = $8,160 / ($8,000 × 2)
Solving this equation gives a rate of 0.51, or 51%.
The area of a parallelogram increased from 40 to 128 square centimeters what is area percentage?
Answer:
320
Step-by-step explanation:
j u s t a g u e s s b u t i t h i n k i t s r i g h t
To find the area percentage increase when the area of a parallelogram increased from 40 to 128 square centimeters, calculate the percentage change as 220%.
The area percentage increase can be calculated as follows:
Initial area = 40 cm²Final area = 128 cm²Area increase = 128 cm² - 40 cm² = 88 cm²Percentage increase = (Area increase / Initial area) x 100%Substitute the values: Percentage increase = (88 cm² / 40 cm²) x 100% = 220%8/x=14/7 what does x equal
Answer:
when you have two fractions that equal each other you want to solve by using cross multiply
What cross multiply is, is when you multiply diagonally so:
8/x=14/7
you would take 14*x and 8*7
14x=56 (you would then divide each side by 14)
x=4 (14/14=1, 56/14=4)
8/4=14/7
To check your work you could simplify
8/4=2
14/7=2
2=2, which is true
x=4
Hope this helps ;)
Which operations are commutative and
associative?
addition
O subtraction
multiplication
division
Answer:
additionmultiplicationStep-by-step explanation:
When learning about commutative and associative properties, we learn that ...
a + b = b + a . . . . . addition is commutative
ab = ba . . . . . . . . . multiplication is commutative
But we also know that ...
a - b ≠ b - a . . . . . . subtraction is not commutative
a/b ≠ b/a . . . . . . . . division is not commutative
__
We also learn that ...
a + (b+c) = (a+b) +c . . . . addition is associative
a(bc) = (ab)c . . . . . multiplication is associative
And of course, ...
a - (b -c) ≠ (a -b) -c . . . . subtraction is not associative
a/(b/c) ≠ (a/b)/c . . . . . . . division is not associative
_____
However, you can use associative and commutative properties in problems involving subtraction and division if you write the expression properly:
a - (b - c) = a +(-(b -c)) = a +((-b) +c) = (a +(-b)) +c . . . . keeping the sign with the value makes it an addition problem, so the associative property can apply
(a/b)/c = (a(1/b))(1/c) = a(1/b·1/c) = writing the division as multiplication by a reciprocal makes it so the associative property can apply
Answer:
addition
multiplication
Answer would be greatly appreciated. (MATH)
Answer:
6
Step-by-step explanation:
A box of markers weighed 4 2/5 ounces. If a teacher took out 5/8 of the markers, what is the weight of the markers she took out? *
Multiply the weight by the amount they took out:
4 2/5 x 5/8
Rewrite as 22/5 x 5/8
(22 x 5) / (5 x 8)
Simplify:
110/40
Rewrite as a proper fraction:
2 3/4 ounces.