The division property of equality informs us quite simply that if we divide both sides of an equation by the same number, then the resulting equation is unaltered. This is known as the distributive property of equality.
How can we make sense of this information?It is important to keep in mind that the value of a fraction is always equivalent to the numerator of the fraction if the denominator of the fraction is 1 and the numerator of the fraction is anything other than zero.
To speak in terms of fractions is to refer to numbers that are not whole.
The value of the numerator in a fraction is determined by whether or not the numerator is nonzero and whether or not the denominator is 1.
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Determine which equation is false based on the solution set.
S:{3}
−28 = 2(4p − 4)
5(b + 3) = 30
7 = 3y − 2
one third times x plus 18 equals 19
Based on the solution set S:{3} the equation which is false is
-28 =2(4p -4).
As given in the question,
Given solution set S:{3}
Equation which is false based on the solution set
1. −28 = 2(4p − 4)
Divide by 2 from both the sides
⇒ -14 = 4p -4
⇒ p = -10/4 ≠ 3
2. 5(b + 3) = 30
Divide by 5 from both the sides
⇒b + 3 =6
⇒ b = 3
3. 7 = 3y − 2
⇒ 3y = 9
⇒ y = 3
4. One third times x plus 18 equals 19
(1/3)x + 18 = 19
⇒(1/3)x =1
⇒x =3
Therefore, based on the solution set S:{3} the equation which is false is
-28 =2(4p -4).
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Factor by grouping
xy-9x-3y+27
The factored expression of the expression given as xy - 9x - 3y + 27 is (x - 3)(y - 9)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to factor the expression by grouping?The expression is given as
xy - 9x - 3y + 27
Factor out the common factor from the expression
So, we have
xy - 9x - 3y + 27 = x(y - 9) - 3(y - 9)
Factor out (y - 9) from the expression
So, we have
xy - 9x - 3y + 27 = (x - 3)(y - 9)
The expression above cannot be further simplified
This means that the expression has been completely factored and cannot be further factored
Hence, the equivalent expression of the expression given as xy - 9x - 3y + 27 when it is factored by grouping is (x - 3)(y - 9)
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(03.06 LC)
Choose the equation below that represents the line that passes through the point (-2,-1)
and has a slope of 5.
The line that passes through the point (-2,-1) and has a slope of 5. The equation of the line is y + 1 = 5(x + 2).
What is slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
Using the slope and 1 point format: (y- y₁) = m(x - x₁)
where m = slope = 5, and point is (x₁, y₁). In this case point (x₁, y₁) = (-2, -1)
x₁ = -2, y₁ = -1
Using: (y- y₁) = m(x - x₁)
y - -1 = 5(x - -2)
y + 1 = 5(x + 2).
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Which table of ordered pairs represents a proportional relationship?
need help ASAP!!
Answer:
Table 3 represents a proportional relationship
============================
Proportional relationship has the form of:
y = kx, where k- coefficient of proportionalityThe value of k should be same for any pair of coordinates:
k = y/xLet's test it for each tableTable 1k = 8/4 = 2k = 11/7 ≠ 2k = 14/10 ≠ 2NoTable 2k = 25/5 = 5k = 49/7 = 7 ≠ 5k = 81/9 = 9 ≠ 5NoTable 3k = 3/6 = 1/2k = 5/10 = 1/2k = 7/14 = 1/2YesTable 4k = 3/6 = 1/2k = 11/8 ≠ 1/2k = 18/13 ≠ 1/2NoA cord of wood is a pile 8 feet long, 4 feet wide, and 4 feet high. Find the volume of a cord of wood.
128 feet³ is the volume of a cord of wood.
What is volume in maths?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."l = 8 feet
b = 4 feet
h = 4 feet
volume of a cord of wood = l × b × h
= 8 × 4 × 4
= 128 feet³
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HELP
Determine which equation is false based on the solution set. S:{3}
−28 = 2(4p − 4)
5(b + 3) = 30
7 = 3y − 2
1/3 x + 18 = 19
If the solution set S ={3}, then the equation 1 is false
The solution set S = {3}
Equation 1
-28 = 2(4p-4)
4p-4 = -28/2
4p-4 = -14
4p = -14+4
4p = -10
p = -10/4
p = -5/2
This equation is false
Equation 2
5(b+3) = 30
b+3 = 30/5
b+3 = 6
b = 6-3
b = 3
This equation is true
Equation 3
7 = 3y-2
3y = 7+2
3y = 9
y = 9/3
y = 3
This equation is true
Equation 4
(1/3)x+18 = 19
(1/3)x = 19-18
(1/3)x = 1
x = 1 ÷1/3
x = 1×3
x = 3
This equation is true
Hence, If the solution set S ={3}, then the equation 1 is false
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T is the midpoint of KL¯¯¯¯¯. K has coordinates (2,−6), and T has coordinates (−4,2). Identify the coordinates of L.
Using the midpoint formula, the coordinates of L is determined as: (-10, 10).
How to Determine the Coordinates of a Midpoint of a Segment?To find the coordinates of the midpoint of a segment, we have to apply the midpoint formula, which is: (x, y) = [(x2 + x1)/2, (y2 + y1)/2].
Given the following:
K(2,−6) = (x1, y1)L(?, ?) = (x2, y2)T(−4,2) = (x, y) [midpoint]Substitute the given values into the midpoint formula:
(-4, 2) = [(x2 + 2)/2, (y2 + (-6))/2]
(-4, 2) = [(x2 + 2)/2, (y2 - 6)/2]
Solve for x2:
-4 = (x2 + 2)/2
2(-4) = x2 + 2
-8 = x2 + 2
-8 - 2 = x2
x2 = -10
Solve for y2:
2 = (y2 - 6)/2
2(2) = y2 - 6
4 = y2 - 6
4 + 6 = y2
10 = y2
y2 = 10
Therefore, L has the coordinates, (-10, 10).
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Graph the equation.
y=5|x|-5
Morgan chewed 3 1/2 sticks of gum every day for 5 consecutive days. How many sticks of gum did he chew in that time?
The table represents an absolute value function f(x).
x f(x)
−5 1
−4 0
−3 1
−2 2
−1 3
0 4
1 5
2 6
3 7
What are the vertex and range of the function?
The vertex of the function is (4, 0) and the range of the function is [0, 7]
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the vertex of the function?The table of values represents the given parameter
As a general rule, the vertex of a function is the smallest or the largest value of the function
On the table of values, we have the smallest function value is 0
The corresponding x value is -4
When these values are paired, we have
(x, y) = (4, 0)
This means that the vertex of the function is (4, 0)
How to determine the range of the function?The table of values represents the given parameter
Using the definition of range stated above, we have
Smallest function value = 0
Largest function value = 7
This means that the range of the function is [0, 7]
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What is 29 divided by 5123
Ryan has $16 in a savings account. The interest rate is 15% per year and is not compounded. How much will she have in 1 year? Use formula i=p*r*t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years
Answer:
$18.4
Explanation:
At the end of the year, Ryan will have the initial saving plus the interest earned.
So, to calculate the interest earned we will use the given equation:
i = p*r*t
So, replacing p by 16, r by 0.15, and t by 1, we get:
i = 16 x 0.15 x 1
i = 2.4
Then, after 1 year, she will have:
$16 + $2.4 = $18.4
Therefore, the answer is $18.4
Find the additive inverse of each number.
1. 15
2.-27
3. 7/9
4. -9/16
5. 0
Answer:
what level math is this I am not too familiar with it
4 - 1 1/2 please help I’ll put a lot of points
cook-it food processor has a mean time before failure of 32 months with a standard deviation of 4 months, and the failure times are normally distributed. what should be the warranty period, in months, so that the manufacturer will not have more than 8% of the food processors returned? round your answer down to the nearest whole number.
The warranty period should be 26 months so that the manufacturer will not have more than 8% of the food returned.
In a set with mean μ and standard deviation σ, the z-score of a measure X is given as:
Z = ( X - μ ) / σ
The Z-score calculates the deviation of the measure from the mean in standard deviations. We glance at the z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.
Cook-Easy blender has a mean time before failure of 32 months with a standard deviation of 4 months
Therefore,
σ = 4 and μ = 32
The warranty period should be in the 8th percentile.
Therefore, the value of X when Z has a p-value of 0.08, so X when Z = - 1.405.
So,
- 1.405 = ( X - 32 ) / 4
- 1.405 × 4 = X - 32
- 5.62 = X - 32
X = 26.38
X ≈ 26
The warranty period should be of 26 months.
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Select the expression that is equivalent to (3d¹)²
6d6
A
9d8
B
9d6
C
3d8
D
The equivalent expression of (3d^4)² is 9d^8. Option B
What are algebraic expressions?Algebraic expressions are defined as expressions made up of terms, constants, factors, coefficients and variables.
They also consist of some mathematical operations, such as;
AdditionSubtractionMultiplicationParenthesesBracketDivision, etcWhat are equivalent expressions?Equivalent expressions are defined as expressions that have the same solution but usually differ in the arrangement of the values.
Given the expression;
(3d^4)²
Now, let's expand the bracket, we have
(3)²(d)^4×2
Find the squares
9d^8
Thus, the expression is 9d^8
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The complete question:
Select the expression that is equivalent to (3d^4)²
The price of a phone is AED 600. It is discounted by 18%. You also have a 7% discount voucher on the
sale price.
How much will you pay for this phone?
Answer:
You will pay $457.56.
Step-by-step explanation:
600 x .18 = 108 This is the amount taken off
600 - 108 = 492 Now we will take 7% off of 492
492 x .07 = 34.44
492 - 34.44 = 457.56
I need help with this question
Let's solve figure by figure
Figure A
This figure has a total of 5 sides, therefore it is a pentagon.
Figure B
This figure has a total of 8 sides, therefore it is an octagon.
Figure C
This figure has a total of 3 sides, therefore it is a triangle.
According to the answer table, it would be
Pentagon: Figure A
Octagon: Figure B
Hexagon: None
Which function has a domain of (-1, ∞) and a range of (-∞, ∞)?
O A. f(x) = log₂x - 1
OB. f(x) = log₂ (x-1)
C. f(x) = log₂(x + 1
D f(x) = log₂ x+ 1
The two essential characteristics of functions are domain and range. Function has a domain of (-1, ∞) and a range of (-∞, ∞), f(x) = log₂x - 1.
What is domain and range?Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money. Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range.
A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavor will be provided. As a result, domain depicts the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a Coke machine won't give you a cheeseburger. As a result, range refers to potential outputs, or in this case, soda tastes in machine. Let's discover how to graph and determine domain and range of a given function.
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In the morning, the temperature in Westfield City was
–
2°F. By afternoon, a north wind caused the temperature to drop another 8°F. What was the afternoon temperature in Westfield City?
To solve the problem, Martin subtracted
–
2–(
–
8) and came up with an answer of 6°F. Is Martin correct? Why or why not?
Martin's answer is wrong. The afternoon temperature in Westfield city is -10°F.
Given,
The temperature in Westfield city in morning = -2°F
The drop down temperature by afternoon = 8°F
We have to find the temperature in afternoon:
Temperature in afternoon = Temperature in morning - Drop down temperature
= -2 - 8 = -10
The afternoon temperature in Westfield city is -10°F
Martin subtracted like:
-2 - (-8) = -2 + 8 = 6
This is wrong.
That is,
We can conclude like:
Martin's answer is wrong. The temperature in Westfield city in afternoon is -10°F
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wich of the following numbers in the datta set is an outlier? data set: 21,23,19,25,83,23, or 21
Answer:
83.
Step-by-step explanation:
An outlier is a number in a data set that stands out from the rest.
Example: 1,2,3,89.
That was a little extreme but in the example you can see that the number isn’t even close to the others, it stands out.
Which is why I came to the conclusion that in the data set, the outlier is 83.
20% tip on a bill of $60.53
Answer:
12.106$
Step-by-step explanation:
20/100×60.53
1210.6/100
=12.106
Find the equation of the line that is perpendicular to the line y = 5x+6 and passes through the point (-3 , 3). Write the equation in point slope form.
Please help
(College Algebra)
Equation of the line in slope form that is perpendicular to the line y =5x +6 and passes through the point (-3, 3) is equal to y = -5x -12.
As given in the question,
Equation of the given line :
y = 5x + 6
Slope of the given line m₁ = 5
Required line is perpendicular to the given line
Slope of the required line is m₂ = -5
Required line is passing through the point (x₁ , y₁) = (-3, 3)
Equation of the required line in slope form
y -y₁ = m₂( x -x₁ )
⇒ y - 3 = -5(x - (-3))
⇒ y -3 = -5x -15
⇒ y = -5x -12
Therefore, equation of the line in slope form that is perpendicular to the line y =5x +6 and passes through the point (-3, 3) is equal to y = -5x -12.
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Using the formula r=d/t, where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 227.5 miles in 3.5 hours?
Answer: 35 mile/hour
Step-by-step explanation:
[tex]r=\frac{d}{t}[/tex]
∴ [tex]r=\frac{227.5}{3.5}=65[/tex]
= 65 mile/hour
solve the following equation 18x-3=4x+11
Answer:
Hope this helps
fist add three to both sides
then subtract 4x from both sides
then divide both side with the same factor
A store sells 213 bottles of water every day in the month of march. march has 31 days. how many bottles of water does the store sell in the month of march?
Using multiplication, we know that 6,603 bottles of water were sold in march by the store.
What is Multiplication?When you take a single number and multiply it by several, you are multiplying.213×31=6,603The simplest way to start teaching multiplication is to establish the relationship between the concept and addition, which your pupils should already be familiar with. Make sure your students understand the first principle of multiplication—that it is just repeated addition—before continuing on.Multiplication's characteristics. Commutative Multiplication Property.
Associative Multiplication Property.Multiple's distributive properties.Multiplication's identity property.So, bottles of water the store sells in march:
213 × 31 = 6,603Therefore, using multiplication, we know that 6,603 bottles of water were sold in march by the store.
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Translate this sentence into an equation: "The difference between three-fifths of a number a 7 is –36."
The expression represented by the mathematical sentence is 3/5a - 7 = –36
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to translate the algebraic expression?The expression is given as
"The difference between three-fifths of a number and 7 is –36."
Three-fifths of a number a means multiply 3/5 and the number i.e. 3/5 * a
So, we have
The difference between three-fifths of a number and 7 is –36 ⇒ The difference between 3/5a and 7 is –36
difference means subtraction
So, we have
The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 is –36
"is" means =
So, we have
The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 = –36
Hence, the expression represented by the difference between three-fifths of a number and 7 is –36 is 3/5a - 7 = –36
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Determine Angles of a rotation
A) 90º clockwise
B) 90º counterclockwise
C) 180º
D) 270º clockwise
E) 270º counterclockwise
Answer:
C) 180°
Step-by-step explanation:
You want the angle of rotation between triangle ABC and triangle A'B'C' given that the center of rotation is point P.
AngleThe angle of rotation will be the measure of the angle APA'. We see that this angle is a straight angle with a measure of 180°.
The angle of rotation is 180°.
__
Additional comment
Another clue regarding the answer is that 90° CW is equivalent to (and indistinguishable from) 270° CCW, and vice versa. This means each of the other answer choices is repeated, so one is as good as the other. The only possible single answer choice is 180°.
The angle of rotation can always be found this way. Form an angle between a preimage point, the center of rotation, and the corresponding image point. The measure of that angle is the angle of rotation.
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Aaliyah is preheating her oven before using it to bake. The initial temperature of the
oven is 70° and the temperature will increase at a rate of 20° per minute after being
turned on. What is the temperature of the oven 14 minutes after being turned on?
What is the temperature of the oven t minutes after being turned on?
Answer:
It is 350°
Step-by-step explanation:
14*20°=280
280° x 70°= 350°
Answers:
What is the temperature of the oven 14 minutes after being turned on?
70 = initial temp
20 = degrees per minute
70 + 20t = ??
70 + 20(14) = 350
What is the temperature of the oven t minutes after being turned on?
The temperature of the over per minute is represented by the expression 70 + 20t, when t = the minutes after being turned on
find the sum of the first 16 terms of the arithmetic sequence: 8,11,14,17,20,...
Answer:
S₁₆ = 488
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 8 and d = a₂ - a₁ = 11 - 8 = 3 , then
S₁₆ = [tex]\frac{16}{2}[/tex] [ (2 × 8) + (15 × 3) ]
= 8(16 + 45)
= 8 × 61
= 488