Find the value of two numbers if their sum is 12 and their difference is 4
Answers
x + y = 12
Equation 2: Difference:
x - y = 4
Solution:
x + y = 12
x - y = 4
-------------
Add the two equations together:
2x = 16
Divide both sides by 2:
x = 8
Solve for y:
Use equation 1 substituting for x:
x + y = 12
8 + y = 12
Subtract 8 from both sides:
y = 4
Answer:
one number is 8 and the other number is 4.
8 + 4 = 12
8 - 4 = 4
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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The numbers are 8 and 4.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Let the two numbers be M and N.
Now,
The sum is 12 and their difference is 4.
This can be written as,
M + N = 12 _____(1)
M - N = 4 _______(2)
From (1) we get,
M = 12 - N ______(3)
Putting (3) in (2) we get,
M - N = 4
12 - N - N = 4
12 - 2N = 4
Add 2N on both sides.
12 = 4 + 2N
Subtract 4 on both sides.
12 - 4 = 2N
8 = 2N
Divide 2 on both sides.
N = 8/2
N = 4
Now,
Put N = 4 on (3).
M = 12 - 4
M = 8
We can cross-check.
M + N = 12
8 + 4 = 12
12 = 12
M - N = 4
8 - 4 = 4
4 = 4
Proved.
Thus,
The numbers are 8 and 4.
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Related Questions
A. Does the table represent a proportional relationship?
B. If the relationship is proportional, what is the constant of proportionality?
Total wight in pounds. 12 18 30 60
Number of books. 10 15 25 50
Answers
A. Yes the table represents a proportional relationship
B. The constant of proportionality is 1.2
Step-by-step explanation:
Two quantities are proportional if:
One of them is equal to the constant times the other oneIf x and y are proportion, then y = k x, where k is constant∵ Total wight in pounds ⇒ 12 , 18 , 30 , 60
∵ Number of books ⇒ 10 , 15 , 25 , 50
- Divide each two corresponding data to check if all they give
the same constant or not
∵ 12 ÷ 10 = 1.2
∵ 18 ÷ 15 = 1.2
∵ 30 ÷ 25 = 1.2
∵ 60 ÷ 50 = 1.2
- That means the total wight is equal to constant times the
number of books
∴ Total wight = 1.2 Number of books
∴ The total wight and the number of books are in a proportional
relationship
A. Yes the table represents a proportional relationship
∵ Total wight = 1.2 Number of books
∴ The constant of proportionality = 1.2
B. The constant of proportionality is 1.2
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HELP!! which is the measure of wx shown in the diagram below
Answers
Answer:
A. 25°
Step-by-step explanation:
We are given a circle and two intersecting lines of circle meets at s and form an angle 34° at S.
Also, we have W and X points on circle that form a minor arc and T and R makes a major arc of angle 93°.
In order to find the value of minor arc WX, we need to apply following formula:
Subtends angle on intersection of lines = [tex]\frac{Major Arc- Major Arc} {2}[/tex]
Plugging values in above formula, we get
34= [tex]\frac{93 - x }{2}[/tex]
On cross multiplication, we get
34 × 2 = 93-x
68 = 93 -x
x = 93-68
x= 25.
Therefore, measure of arc WX = 25°.Hope this helps and you understand !!!!!!
work out 35% out of £120
Answers
Answer:
42
Step-by-step explanation:
120*35=4200
4200/100=42
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?
Answers
Answer: She earns 482.50
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? *
Answers
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.
How many 60-degree angles does it take to make a full turn?
Answers
Answer:
6
Step-by-step explanation:
360 is a full turn so, 360 divided by 60 is 6
X+2y=4 convert equation from standard form to slope intercept form
Answers
Answer:
y = -(1/2)x + 2
Step-by-step explanation:
2y = -x + 4
y = (-x + 4)/2
y = -(1/2)x + 2
Teri bought 360 rubber band 2 make a bracelet
15% of the bands were white and the rest were red. After using 140 bands to make her 1st bracelet , 20% of the remaining bands were white
How many red bands did teri use on the bracelet
Answers
Answer:
Step-by-step explanation:
No. of white bands = 15% of 360 = (15/100)*360= 54
No.of red bands = 360 - 54 = 306
No. bands remaining = 360 - 140 = 220
No. of remaining white bands = 20% of 220= (20/100)*220 = 44
No. of remaining red bands = 220 - 44 = 176
No. of red band used = No.of red bands - No of remaining bands
= 306 - 176 = 130
Explain how you know that 7/12 is greater than 1/3 but less than 2/3
Answers
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
block 7 math test question 2
Answers
Answer:
The increasing quickly part is B.
The decreasing quickly part is D
The decreasing slowly part is A.
The constant part is C.
And the increasing slowly part is E.
Step-by-step explanation:
See the attached graph.
Here, the graph represents the viewing trend of a reality show. We have to match each phrase to the section of the graph it describes.
Now, the increasing quickly part is B.
The decreasing quickly part is D
The decreasing slowly part is A.
The constant part is C.
And the increasing slowly part is E. ( Answer )
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?
Answers
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.
x+5÷9=3
What is the number where when you add 5 then divide it by 9 it is 3?
Answers
Answer:
22 + 5 ÷ 9 = 3
Proof:
27/9
= 3
the number is 22
3 and19/12 simplified
Answers
Answer:
4 7/12
Step-by-step explanation:
3 19/12 = 3 + 19/12 = 3 + 12/12 + 7/12 = 3 + 1 + 7/12 = 4 7/12
in the equation 6x^2+7x-49 how does 7x become -14x and 21x?
Answers
Answer:
See the explanation.
Step-by-step explanation:
Given function is [tex]6x^2+7x-49[/tex]
We will find its root by factoring.
In any quadratic function of the form [tex]ax^2+bx+c[/tex]
We will two numbers that when multiplied gives [tex]ac[/tex]. And when that two numbers are added it turns to [tex]b[/tex].
So, in [tex]6x^2+7x-49[/tex].
[tex]a=6,\ b=7.\ c=-49[/tex]
And [tex]ac=-294[/tex]
So, we need to find two numbers that when multiplied give [tex]-294[/tex],and when added give [tex]7[/tex].
Now, we can see
[tex]-14\times21=-294\\And\ -14+21=7[/tex]
In this manner, we can rewrite [tex]7x[/tex] as [tex]-14x+21x[/tex].
In the figure, angle D measures 31⁰ and angle A measures 27⁰
1.The measurement of angle B is
A.59⁰
B.63⁰
C.90⁰
2. The measurement of angle F is
A.59⁰
B.63⁰
C.90⁰
Answers
Answer:
1)B:63°
2)A:59°
Step-by-step explanation:
1.ABC is a right triangle at C then angle ACB=90°(right angle)
Angle CAB=27°(see the given)
measure of the angles in any triangle is 180°
then angle CBA=
measure of all the angles - (measure ACB+measure CAB)
=180°-(90°+27°)
=63°
2. Same explanation of angle B:
in the right triangle DEF: angle DEF=90°
angle D=31°(given)
Then measure of angle A=180°-(angle E + angle D)
=180-(90+31)=59°
PLEASE HELP
What is the twenty-first term of the sequence given by
xn = 4n − 3 ?
87
72
81
6
Answers
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
5x/3 + 1/3 =12 find x
Answers
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
X equals 7
Solution
Step 1: simplify both sides of the equation.
5/3 x + 1/3= 12
Step 2: subtract 1/3 from both sides
5/3 x + 1/3 - 1/3 = 12 - 1/3
5/3 x = 35/3
Step 3 : multiply both sides by 3/5
(3/5)(5/3 x)=(3/5)(35/3)
X=7
A rectangle has a width of 8 and a perimeter of 40 what is the length of the rectangle?
Answers
Fiona cut fabric circles for an art project. She recorded the diameters of the circles in the table.
Diameter (cm) Frequency
2 3
2.25 3
2.5 4
2.75 4
3 2
3.5 2
Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots.
Answers
Answer:
2 : 3 dots up
2.25 : 3 dots up
2.5 : 4 dots up
2.75 : 4 dots up
3 : 2 dots up
3.25: 0 dots up
3.5 : 2 dots up
The dot plot for the considered data is plotted based on how many times each observation occured (given by frequencies), as plotted in the image attached.
How does dot plot works?Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
If instead of only observations, the table of unique observation and frequency is given, then we plot dots that many times as the count written in the frequency table.
Thus, if its written that the value 2 has 3 has its frequency, then we plot 3 dots one over the other above the value 2 in the horizontal axis.
For this case, we're given the unique observation to frequency table as:
Diameter (cm) Frequency
2 3
2.25 3
2.5 4
2.75 4
3 2
3.5 2
That means, over the value 2, plot 3 dots (as diameter 2 occured 3 times), and so on, over the value 3.5, plot 2 dots.
The dot plot of the considered data is attached below.
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(889 x 27) + 50 is
than 889 x 27
Answers
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.
9y-4-11y+7
Terms:
Like terms:
Coefficient:
Constants:
Answers
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
What is the slope OF THE GRAPH, not what is A slope, what is THE slope
Answers
Answer:
The slope is -3
Step-by-step explanation:
Hello!
Slope is measured by lattice points on the graph, and the formula is Rise/Run.
To calculate the slope of this graph, we must find two points that intersect coordinates. I will choose coordinates (0,2) and (1,-1).
Now to find the rise, we must find the difference in the y coordinates.
2 - (-1) 2 + 13To find the run, we must find the difference in the x coordinates.
0 - 1-1Now divide:
3/-1-3A 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.
Answers
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
What is equivalent to 8 1/4
Answers
Answer:
33/4
Step-by-step explanation:
8x4 +1 = 33
Answer:
33/4
Step-by-step explanation:
How do I solve systems of equations algebraically
Answers
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
solve the following formula c=1/2f(q+b) for q
Answers
Answer:q= (2C - fb)/f
Step-by-step explanation:
multiplying both sides by 2 we have,
2C = fb + fq,
subtract both sides by fb
fq = 2C - fb,
dividing both sides by f
q= (2C - fb)/f
What is the slope of the line below? Give an exact number
Answers
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]
What is the volume of a shipping cube with dimensions of 2 1/2 feet? 6 3/4 cubic feet 15 5/8 cubic feet 8 1/8 cubic feet
Answers
Answer:
The volume of shipping cube is [tex]15\frac{5}{8}\ cubic\ feet.[/tex]
Step-by-step explanation:
Given:
The dimensions of a shipping cube of 2 1/2 feet.
Now, to find the volume of shipping cube.
Side of cube = [tex]2\frac{1}{2}\ feet.[/tex]
Side = [tex]\frac{5}{2}\ feet[/tex]
So, to get the volume of cube we put formula:
[tex]Volume=(side)^3[/tex]
[tex]Volume=(\frac{5}{2})^3[/tex]
[tex]Volume=\frac{125}{8}[/tex]
[tex]Volume=15\frac{5}{8} \ cubic\ feet.[/tex]
Therefore, the volume of shipping cube is [tex]15\frac{5}{8}\ cubic\ feet.[/tex]
Answer:
b
Step-by-step explanation:
You plant 20 marigold seeds and 12 of them grow into flowers that bloom. If you plant 10 more marigolds, predict how many would bloom?
Answers
Answer:
I would predict that 6 marigolds would bloom
PLZ HURRY! Which mapping diagram represents a function from x → y?
Answers
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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