Answers
The answers are subtraction, subtraction, and addition property of equality
There are 9 properties of equality, which are addition, subtraction, multiplication, division, distributive, substitution, reflexive, symmetric, and transitive. In this case, we are using the first 2. In algebra, whatever you do to one side has to be done to the other, in the case of the first problem x is being subtracted on both sides, which represents the definition of the subtraction property (If a = b, then a – c = b – c, a is the one side of the equation, b is the other side, and c is the subtraction done on both sides). The first one is the subtraction property of equality, then, and if we look at problem 2, the same thing is done (apart from that it is done with a number, which doesn't affect the property), so it is also the subtraction property.
Now the last problem seems to do the opposite, it seems to be adding instead, in this case, adding 1 on both sides. This follows the definition of the addition property of equality (If a = b, then a + c = b + c) since it is adding c (1) on both sides. So the last problem is the addition property of equality.
Related Questions
y = 3x + 2 is reflected in the line y=-1. What is the equation of the image?
Answers
The equation of the image is y = 3x - 4
In this question, we have been given a line y = 3x + 2 is reflected in the line y = -1.
We need to find the equation of the image.
The reflected line must be parallel to the line y = 3x + 2
So, the slope of the image must be equal to the slope of the line y = 3x + 2
The y-intercept of the line y = 3x + 2 is (0, 2)
The distance between point (0, 2) and the line y = -1 is 3 units.
So, the y-intercept of the reflected line must be (0, -4)
With slope m = 3 and y-intercept (0, -4) the equation of the line would be,
y = 3x - 4
Therefore, the equation of the image is y = 3x - 4
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3. Find the number of volunteers in the group if each volunteer cleans up a section of the following lengths. Be prepared to explain or show your reasoning.
a. 0.4 mile
b. 2/7 mile
c. 0.125 mile
d. 6/45 mile
Answers
The number of volunteers needed for each case is given as follows:
a. 0.4 miles: 5.
b. 2/7 miles: 7.
c. 0.125 miles: 16.
d. 6/45 miles: 15.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates of the context of the problem along with basic arithmetic operations, especially multiplication and division.
In this problem, a two mile section will be cleaned, hence the number of volunteers needed is calculated as follows:
n = 2/s.
In which s is the section cleaned by each volunteer.
In item a, the section is of 0.4 miles, hence the number of volunteers is given as follows:
n = 2/0.4 = 5 volunteers.
In item b, the section is of 2/7 miles, hence the number of volunteers is given as follows:
n = 2/(2/7) = 2 x 7/2 = 7 volunteers.
In item c, the section is of 0.125 miles, hence the number of volunteers is given as follows:
n = 2/0.125 = 2/(1/8) = 2 x 8 = 16 volunteers.
In item d, the section is of 6/45 miles, hence the number of volunteers is given as follows:
n = 2/(6/45) = 2 x 45/6 = 90/6 = 15 volunteers.
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find the value of x please
Answers
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{x}{7}~~ = ~~\cfrac{10}{x}\implies x^2=70\implies x=\sqrt{70}[/tex]
Fill in the missing number.
20% of
= 3
Answers
Answer:0.6
Step-by-step explanation:
20/3 is 6
HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT
Answers
Answer:
y=x/4
Step-by-step explanation:
if the line is perpendicular (m2)=-1/(m1)
m2=1/4
y=x/4+c
sub in 8,2
2=8/4+c
c=0
equation is therefore y=x/4
If a space rover has a mass of 3900 kg, then what is its weight on Earth?
N=?
Use g-9.81m/s? and do not include units in your answer.
Answers
If a space rover has a mass of 3900 kg, then its weight on Earth N will be 38220 N.
What is a weight?Weight can be described as the body's relative mass which can be regarded as the quantity of matter that can be found in the particles of the object and the unit can be written as Newton.
To calculate the weight of a particular particles, we can use the formular (mg) which is that product of the mass of the object to that of the gravity.
from the question, the gravity is been given as g-9.81m/s
Then the weight = (3900 kg* 9.8) = 38220 N
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HELP
25 POINTS!!!!!!!!!!!!!!!!!!!!!!11
Answers
Answer:
8/9 cups is the correct answer
Graph a line with a slope of 1/4 that contains the point (6,3) khan academy
Answers
4y = x + 6 is the equation of the line using the slope value.
What is a line's slope?The steepness of a line segment is explained by the slope of the line. It is a ratio of the vertical x-axis coordinates and the y-axis coordinates. The classification of whether two lines are parallel or perpendicular depends on the slope value.
The parameters for the line segment are as follows, in accordance with the question:
The coordinate points (6, 3) and the slope of a line (1/4) are as follows: (x = 6; y = 3)
Using the line segment's standard equation now: y = mx + c
If (x, y) are coordinates, "m" is the slope, "c" is the y-intercept,
The following results are obtained by replacing the slope and y-intercept values in the formula:
y = mx + c
⇒ 3 = (1/4)(6) + c
⇒ c = 3 - 3/2 = 3/2
Consequently, c = (3/2) is the y-value. intercept's
by changing the slope value and y-intercept value in the line's equation:
y = (1/4)x + (3/2) = 4y = x +6
Consequently, 4y = x + 6 is the equation of the line using the slope value.
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Rewrite 0.00518 in scientific notation.
Answers
Answer: 5.18 x 10^-3
Step-by-step explanation:
0.00518
**Move the decimal 3 spaces to the right**
5.18
**Since it goes like 0.00, you want to make sure the exponent is negative**
5.18 x 10^-3
Hope this helped <3
Need help on this geometry problem, solving for x.
Answers
Answer:
A.) 30 degrees
Step-by-step explanation:
Brainly pls :)
Making a equation with the slope: 2/3 and the y intersept:2
Answers
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Equation of line is y = 2/3x + 2
The perimeter of a rectangular parking lot is 370 m.
If the width of the parking lot is 86 m, what is its length?
Answers
Explanation: 370 divided by 86 is 4.30232 then just round
Answer:
the length is 99m
Step-by-step explanation:
you have to add 86 to 86 to get 172, subtract 172 from 370 then you have 198 then divide to have 99m the length.
What is the opposite of 6?
Answers
Answer:
1
Step-by-step explanation:
The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.
A lawnmower with a 3-gallon gas tank uses an average of 0.6 gallons per hour.
A function modeling this situation, where x represents the amount of gas in the tank, has a domain described by which inequality?
A. 0 ≤ x ≤ 5
B. 0 < x < 5
C. 0 < x < 3
D. 0 ≤ x ≤ 3
Answers
The inequality that describes the domain is 0 ≤ x ≤ 5
How to determine the domain of the situation?The given parameters are
Size of tank = 3 gallons
Rate = 0.6 gallons per hour
The highest number of time is calculated as
Time = Size of tank/Rate
Substitute the known values in the above equation
So, we have the following equation
Time = 3/0.6
Evaluate
Time = 5
The domain is then represented as
0 ≤ x ≤ Time
This gives
0 ≤ x ≤ 5
Hence, the domain of the situation is 0 ≤ x ≤ 5
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Ivanna makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answers
Answer:
9h=p
9 times the number of hours worked equals the total pay.
I need help fast please. I also need explanation on an easy way to do it.
Answers
The correct equation that is balanced using the given numbers once is;
5(-1 + (-3)) = (7 * -4) + 8
How to carry out Algebra Properties?There are different properties of Algebra such as;
Commutative Property of Addition or multiplication
Associative Property of Addition or multiplication
Distributive Property
Now, from the given numbers, it will be best to use only a positive digit outside the bracket on the left hand side to make it easy to balance on the right hand side. Thus, for the left hand side we will try;
5(-1 + (-3))
When that is solved we will get -20
Now, to balance that on the right hand side , we will have;
(7 * -4) + 8
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write a algebraic expression 4 less than the sum of a number and 7
Answers
The representation of the expression is 4 < x + 7
How to translate the algebraic expression?The mathematical statement is given as
"4 less than the sum of a number and 7"
Sum means Plus
So, we have the following representation
"4 less than the sum of a number and 7" ⇒ 4 less than a number + 7"
Let the number be x
So, we have
"4 less than the sum of a number and 7" ⇒ 4 less than x + 7"
Less than as used here means <
So, we have
"4 less than the sum of a number and 7" ⇒ 4 < x + 7"
Hence, the expression represented by "4 less than the sum of a number and 7" is 4 < x + 7
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Johanna bought 17 items at the college bookstore. The items cost a total of $41.50. The pens cost $0.50 each, the notebooks were $4.00 each, and the highlighters cost $1.50 each. She bought 3 more notebooks than highlighters. How many of each item did she buy?
Answers
The answer to the given word problem is as follows. From the calculations: Johanna purchased
4 pens, 8 notebooks, and 5 highlighters.What is a word problem?A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation.
The calculations is given as follows:
Step 1 - First, let's define the variables to represent the unknowns.
Let p = number of pens
Let n = number of notebooks
Let h = number of highlighters
p + n + h = 17 ......................... 1 (purchased 17 items)
.5p + 4n + 1.5h = 41.5 ...................2 (total cost $41.50)
n = h+3 ................................3 (3 more notebooks than highlighters)
Step 2...............Solve for P in equation 1
P = 17 - n - h..................4
Recall that in equation 3,
n = h + 2
If we make n the subject of the expression, we have:
n = h+ 3
Substituting that into equation 4, we have
p = 17 - (h+3) - h
p = 17 -2h - 3 ..................5
Going back to equation 2, let's substitute n with h+3 and replace p with 17 -2h - 3
.5(17 -2h - 3) + 4 (h+3) + 1.5h = 41.5
To remove all decimals, we can multiply all with 10 to get:
5(170-20h -30) + 40(10h +30) + 15h = 415
Expand all brackets and we have:
850 - 100h - 150 + 400h + 1200 + 15h = 415
Collect like terms
-100h + 400h + 15h = 415-850+150-1200
315h = -1485
h = -1485/315
h = -4.71
Since a physical item cannot be negative, we utilize the absolute value which is:
h = 4.71
h [tex]\approx[/tex] 5 highlighter
Recall that
n = h + 3
Hence
n = 5 +3 = 8 notebooks
Recall that
p + n + h = 17
Hence we have
p + 8 + 5 = 17
p = 17 -8 - 5
p = 17 - 13
P = 4 pens.
Hence Johanna purchased
4 pens, 8 notebooks and 5 highlighters.
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A certain illness is spreading
at a rate of 10% per hour.
How long will it take to
spread to 1,200 people if 3
people are initially exposed?
Round to the nearest hour.
Answers
The illness is spreading at a rate of 10% per hour -> it is spreading 1.1x faster per hour as 10% more people are infected each time.
Therefore, we can write the amount of people infected as 3 x [tex]1.1^{n}[/tex], where n is the hour. So, if n equals 1, the amount of people infected is 3 x 1.1 = 3.3 (so when this mark surpasses the 1200 limit, we round up to the nearest whole number)
It will take 1200 : 3 : 1.1 = 363.636364.. (hours)
If it's only 363 hours, the number of people infected will not have reached 1200, as we have .636364 hours left. So, it will take 364 hours.
Hey there! I am having trouble on a quiz so I'll be asking some questions. Look at my profile if you are looking to earn points and help someone out! ( 25 Points For Each Question Answered Correctly - Do Not Comment Silly Stuff Or Your Points Will Be Removed.)
1st Question:
Answers
The simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18
The given the expression is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)
To solve this problem first we have to use the distributive property
The distributive property states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together
The distributive property of addition
A(B+C) = AB + AC
The distributive property of subtraction
A(B-C) = AB - AC
The given equation is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)
Apply distributive property
4(4y-[tex]7y^{2}[/tex])-9(5y+2) = 16y -28[tex]y^{2}[/tex]-45y-18
Rearrange the terms
-28[tex]y^{2}[/tex]-45y+16y-18 = -28[tex]y^{2}[/tex]-29y-18
Hence, the simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18
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A case of 24 pairs of the same kind of switches cost a little more than $800 explain whether $28 per pair with tax included is a good estimate of the price
Answers
If a case of 24 pairs of the same kind of switches cost a little more than $800. $28 per pair with tax included is not good estimate of the price but $33.33 is the good estimate for the price .
Estimated priceAssuming that the cost per pair is the amount of $28. Hence, cost of 24 pairs is calculated as:
Cost= $28x24
Cost = $672.
Based on the above calculation for the cost of 25 pairs we can see that that the 24 pairs of the same kind of switches does not cost more than $800 which implies that $28 is not good estimate for the price.
Now let determine the best estimate of the price with tax included :
Cost = $800/24
Cost = $33.33
Therefore the good estimate for the price with the tax included is $33.33.
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the mean is 115 the other numbers that make the mean are 110 and 90 i cant figure out what the third number is
Answers
Answer: 145
Step-by-step explanation:
To find the total of the three numbers: 115 x 3 = 345
So the 3rd number must be 345 - 110 -90 = 145
Check the answer= 110 + 90 +145
3
= 115
Please look at photo for further clarification, the length of a conduit is needed for sections and be shown in the picture. you may round the final answer to the nearest hundred if needed as well as all the intermediate values rounded to the nearest hundred if needed.
Answers
Using trigonometric functions :
From the problem, we have a hypotenuse of 22.25 cm and an angle of 31°28'
To find A, we will use the sine function :
[tex]\begin{gathered} \sin 31^{\circ}28^{\prime}=\frac{A}{22.25} \\ A=22.25\sin 31^{\circ}28^{\prime} \\ A=11.615 \end{gathered}[/tex]To find B, we will use the cosine function :
[tex]\begin{gathered} \cos 31^{\circ}28^{\prime}=\frac{B}{22.25} \\ B=22.25\cos 31^{\circ}28^{\prime} \\ B=18.978 \end{gathered}[/tex]The total length is the sum of A and B :
A + B = 11.615 + 18.978 = 30.59
The answer is 30.59 cm
Please put all the numbers above your phone on the number line
Answers
1.
(a) 2π - 9
= 2 x 3.142 - 9 = 6.284 - 9
= -2.716
This will be closest to the letter C on the number line.
(b) [tex]\sqrt{3}[/tex]
= 1.732
This will be closest to the letter T on the number line.
(c) [tex]\sqrt[3]{9}[/tex] - 8
= 3-8
= -5
This will be closest to the letter S on the number line.
What are Real numbers?In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line. Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Real numbers include things like 23, -12, 6.99, 5/2, and so on.Most physical constants, like the universal gravitational constant, and physical variables, including position, mass, speed, and electric charge, are represented using real numbers in the physical sciences.Although the Zermelo-Fraenkel axiomatization of set theory is the method most frequently used to formalize the real numbers, other mathematicians also explore the real numbers using other logical mathematical foundations. Electronic calculators and computers, with a few notable exceptions, do not work with real numbers. Instead, they frequently use floating-point numbers, which are finite-precision approximations that resemble scientific notation.To learn more about Real numbers, refer to:
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Determine the x-coordinate that would yield a y-coordinate of 30, assuming the pair follows the same trend that currently exists in the data set below. {(45, 18), (38, 21), (26, 31), (64, 13), (29, 28), (33, 25), (49, 17)}
Answers
Based on the trend found in the data set, the x-coordinate that would yield a y-coordinate of 30 is 28
What is the trend in the data set?Pick two points from the data set:
(26, 31) and (64, 13)
The slope is:
= Change in y / Change in x
= ( 13 - 31) / (64 - 26)
= -18 / 38
= -9/19
The y-intercept is:
y = mx + b
13 = -9/19(64) + b
b = 43.3
The x-coordinate that gives a y-coordinate of 30 is:
30 = -9/19x + 43.3
x = 28
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help pass due asap!!!
Add (7x³ - 2x² - 5x+6) and (2x³ + 3x² − x − 1)
a) 9x³ + x² - 6x +5
b) 9x6 + x4 + 5x² − 6
c) 9x³x² - 6x + 5
d) 14x³ - 6x² – 5x - 6
Answers
Solve the following inequality. 3x - 4 > 11
A. (∞ ,5)
B. (15, ∞)
C. (5, ∞)
D. [5, ∞)
Answers
15 it’s not that hard
explanation:
first u need to solve for x:
3x - 4 > 11
3x > 15
x > 5
so if x is greater than 5, then the domain is above 5 to infinity, written as (5, ♾) instead of [5, ♾) because the bracket means greater than or equal to, but > is just greater than
Name a plane parallel to plane ABCD.
A. plane ADHE
B. plane DCGH
C. plane ABFE
D. plane EFGH
Answers
Answer:
Plane EFGH
Step-by-step explanation:
we can see that plane ABCD is on the bottom
and that plane EFGH is on the top
so if the go left and right, they will never touch that is what parallel is
any other plane will intersect or touch eventually
Adriana mows lawns. She charges an initial fee and a constant fee for each hour of work.
Answers
Answer: It's $12 an hour.
Step-by-step explanation:
is each pair of lines parallel, perpendicular, or neither?
Answers
Answer:
1. perpendicular
2. parallel
3. neither
Step-by-step explanation:
The first set of lines are perpendicular because they intersect each other at a right angle.
The second set of lines are parallel because they never cross.
The first pair forms a 90° angle therefore the lines are perpendicular.
The second lines are straight that it's obviously clear they will never meet meaning they are parallel
the third lines are neither perpendicular nor parallel.