The preimage of the point C'(x, y) = (- 3, - 10) is the point C(x, y) = (5, - 14).
What is the preimage of a point according to the translation formula?
In this question we find the coordinates of a point that is result of a translation. Translations are examples of rigid transformations, whose vector formula is shown below:
C'(x, y) = C(x, y) + T(x, y)
Where:
C(x, y) - Original pointC'(x, y) - Resulting point T(x, y) - Translation vectorPlease notice that the original point C(x, y) is the preimage of C'(x, y).
If we know that C'(x, y) = (- 3, - 10) and T(x, y) = (- 8, 4), then the preimage of the point C is:
(- 3, - 10) = C(x, y) + (- 8, 4)
C(x, y) = (- 3, - 10) - (- 8, 4)
C(x, y) = (- 3, - 10) + (8, - 4)
C(x, y) = (5, - 14)
The preimage is the point C(x, y) = (5, - 14).
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What are the solutions of the equation 6x²-x-1-0?
A.1/2
B.1/3
C.-1/2
D.-1/3
Answer:
A. 1/2
D. -1/3
Step-by-step explanation:
You want to know the solutions to 6x² -x -1 = 0.
FactorsWe can factor the equation as ...
6x² -3x +2x -1 = 0
3x(2x -1) +1(2x -1) = 0
(3x +1)(2x -1) = 0
SolutionsThe solutions will make the factors zero:
3x +1 = 0 ⇒ x = -1/3
2x -1 = 0 ⇒ x = 1/2
The solutions are 1/2 and -1/3.
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a circle has radius 12 milimeters. what it its area
Answer:
[tex]\huge\boxed{\sf Area = 454.4\ mm\²}[/tex]
Step-by-step explanation:
Given that,
Radius = r = 12 mm
We know that,
Area = πr²So,
Area = (3.14)(12)²
Area = (3.14)(144)
Area = 454.4 mm²
[tex]\rule[225]{225}{2}[/tex]
3) Hugh has a goal of exercising 12/4 hours a day. He plans to go on several runs
today. His runs take him 4/6 of an hour. How many runs will Hugh need to go on?
Answer:
Hugh will go on 3 runs !
Step-by-step explanation:
12/4=4/6
I need working out for the questions because I don’t understand it that much.
Factor completely: 49x² - 4
Answer:
Factor 49x^2-4 49x2 − 4 49 x 2 - 4 Rewrite 49x2 49 x 2 as (7x)2 (7 x) 2. (7x)2 − 4 (7 x) 2 - 4 Rewrite 4 4 as 22 2 2.
Step-by-step explanation:
Hoped it helped
Answer:
(7x-2)(7x+2)
Step-by-step explanation:
This was the easiest thing I had in Analytic Geometry!!
system of equations?
Answer:
Equation 1: 3x + 4y = 31
Equation 2: 3x - 4y = -1
Add Equation 1 to Equation 2 gets you:
6x = 30
6x/6 = 30/6
x = 5
The answer is x = 5.
on june 1, grey co. borrows $15,000 cash from national bank by signing a 120-day, 10% interest-bearing note. grey will record interest during the year totaling $ ____
Grey will record interest during the year totaling $500.
Define the term interest-bearing note?An interest-bearing note is a sum of money that a lender lends to a borrower, with interest accruing in line with the conditions of the contract.Notes with an interest component have a defined rate of interest that must be paid on top of the principal amount. There is no specified interest rate on zero-bearing and non-interest bearing notes.For the stated question-
Borrowed money from national bank = $15,000.
Time 120 days.
10% interest-bearing note
Thus, interest during the year;
interest = 15000 x 120 x 0.10 / 360 (days)
interest = 500
Thus, Grey will record interest during the year totaling $500.
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you are asked to size the diameter of a bolt loaded in shear to the nearest 1/8 inch with a factor of safety of 1.5. you find that bolt diameter that yields this factor of safety is 2.4183 inches. what is the diameter of the bolt you should use (in units of inches to 3 decimal places).
Answer:
2.375 inches
Step-by-step explanation:
Main Steps
1. Identifying important parts of the question
2. Solving the problem
Step 1. - Identifying important parts of the question
In the question, there is some extraneous information. For instance, the question introduces the terms "diameter" and "loaded in shear" and "with a safety factor of 1.5". However, given the information in the problem, and the question asked, it isn't necessary to know that it is "loaded in shear" means, or to know what a diameter is (since everything stays with diameters, and doesn't involve another dimension), and the problem gives the result that will satisfy "a safety factor of 1.5".
Sifting through the problem/question, these are the important parts:
- "to the nearest 1/8 inch" (meaning round to the nearest 1/8th of a unit)
- with "units of inches to 3 decimal places"
- The number to round is "2.4183 inches
Step 2. - Solving the Problem
To round to the nearest 1/8 inch, we can divide the number 2.4183 by 1/8.
[tex]2.4183 \div(1/8)[/tex]
Recall that dividing by a fraction is the same as multiplying by the reciprocal
[tex]2.4183 * 8[/tex]
19.3464
So, there are approximately 19, one-eighth-inches in the measurement. (Note that 19.3464 is closer to 19 than it is to 20). To find the final rounded measurement, multiply 19 by 1/8
[tex]19 * (1/8)[/tex]
2.375 inches
So, the diameter of the bolt that should be used (if rounded to the nearest 1/8 inch, to allow for a factor of safety of 1.5) is 2.375 inches
4. After 4 hours of work, a worker has made 12 cars, and after 8 hours he has made 24 total cars. Is this an
example of a proportional relationship? What is the expression of the proportional relationship?
a. Yes
b. No
1 Pt
A
B
Expression:
Answer:
lmfa you answer my questions i recently posted ill answer yours...
Step-by-step explanation:
okay?
in a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. if we randomly select three bolts from this process: what is the standard deviation of the sampling distribution of the sample mean?
The standard deviation of the sampling distribution of the sample mean is 0.1 when a machine produces bolts that have an average length of 3 inches with a variance of .03.
What is standard deviation?The positive square root of the variance is the standard deviation. One of the fundamental techniques used in statistical analysis is standard deviation. Standard deviation, also known as SD or denoted by the symbol "σ" indicates how far a value deviates from the mean value.
Here,
σx = σ/√n
= √.03/√3
= .1732/1.732
= 0.1
When a machine creates bolts with an average length of 3 inches and a variance of.03, the standard deviation of the sampling distribution of the sample mean is 0.1.
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Solve one fifth times quantity x plus 15 end quantity equals negative 5.
x = −10
x = −40
x = 8
x = 15
The value of x is -40.
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
One fifth times quantity x plus 15=(1/5)(x+15)
So, one fifth times quantity x plus 15 end quantity equals negative 5 shows"
(1/5)(x+15)= -5
0.2(x+15)= -5
0.2x+3= -5
0.2x=-5-3
0.2x=-8
x=-8/0.2 = -40
So, the value of x is -40.
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A cla i made up of 6 boy and 14 girl. Half of the boy wear glae. A tudent i elected at random from the cla. What i the probability that the tudent i a boy with glae?
Write your anwer a a fraction in implet form
The probability that the student is a boy with glass is 3/20
Number of boys in the class = 6 boys
Number of girls in the class = 14 girls
Half of the boys wear glass
The number of boys that wear glass = 6 / 2
= 3 boys
Total number of students in the class = 6 + 14
= 20 students
Probability = Number of favorable outcomes / Total outcomes
= The number of students that wear glass / Total number of students
Substitute the values in the equation
= 3/20
Hence, the probability that the student is a boy with glass is 3/20
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Your class is learning to tie knots. Each student needs a piece of rope that is 3/8 yards long. How many yards of rope are needed for the 16 students in your class
The length of the rope that is needed for the 16 students of the class is 6 yards .
In the question ,
it is given that
the class is learning to tie knots .
the length of rope required by 1 student to tie the knot = 3/8 yards ,
the length of rope for 16 students can be calculated using the formula
length of rope for 16 students = 16 × (length of rope required by 1 student)
Substituting the values
we get ,
length of rope for 16 students = 16 × 3/8
= 2 × 3
= 6
Therefore , 16 students will require 6 yards of rope .
The given question is incomplete , the complete question is
Your class is learning to tie knots. Each student needs a piece of rope that is 3/8 yards long. How many yards of rope are needed for the 16 students in your class ?
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Jae makes a playlist of 24 songs for a party. Since he prefers reggaeton and hip-hop music, he builds the playlist from those two types of songs.
Determine two different combinations of reggaeton and hip-hop songs that Jae could use for his playlist.
The different combinations of reggaeton and hip-hop songs that Jae could use for his playlist include:
10 reggaeton and 14 hip hop music 18 reggaeton and 6 hip hop musicHow to calculate the combination?In this scenario, Jae makes a playlist of 24 songs for a party and he prefers reggaeton and hip-hop music and then builds the playlist from the two music types.
In this case, the combination will be gotten by the addition of two values that can give 24.
The combination can include:
10 reggaeton + 14 hip hop music = 24 songs
18 reggaeton + 6 hip hop music = 24 songs.
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A mean ogre stole 9 of your muffins. That 3 was of all of them! With how many did 8 you start?
We started with 11 muffins in total.
What is Addition?
Addition is a method of merging items and counting them as a single large group. In mathematics, addition is the process of joining two or more integers. The numbers added are referred to as addends, while the result or final response obtained after the procedure is referred to as the total.
Solution:
Since the orge stole 9 muffins and still we have 3 muffins left.
This implies that we started with 9+3 = 11 muffins
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The linear model c= 2.20 + 2m describes the cost of the cab ride, c, as a function of the
number of miles traveled, m. How much will it cost Jules to travel 16 miles in a cab?
the u.s.post office will accept a box for shipment only if the sum of height and girth(distance around of bottom) is at most 108 in. find the dimensions of the largest volume of acceptable box with square bottom.
The dimensions of the box of height 36in and the side of the square is 18in.
A topological measure of the size of an object's covering properties is its dimension. It is roughly the number of coordinates required to specify a point on the object.
Given that the u.s.post office will accept a box for shipment only if the sum of height and girth(the distance around of bottom) is at most 108 in.
We must first determine the box's dimensions.
Let s be the side of the square base and h be the height of the box
So , h + 4s = 108
H = 108 – 4s -----(1)
Volume = s^2 h
V = s^2(108-4s)
= 108s2 – 4s3
V’ = 216s – 12s2
Let v’ = 0
S[216-12s] = 0
216 – 12s = 0
12s = 216
S = 216/12
S = 18
V” = 216 – 24s for s =18
V” = 216 – 432
= -216(-ve)
Volume is maximum when s =18
So h= 108-72
=36 in
Therefore the dimensions of the box of height 36in and the side of the square is 18in.
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PEASE HELP ASAP ALSO PLEASE SHOW YOUR WORK!
ACB~ EFD
What is x equal to?
Enter your answer in decimal form.
Answer:11.4
Step-by-step explanation: Set up a proportion: [tex]\frac{15}{x}[/tex]=[tex]\frac{5}{3.8}[/tex]
To solve a proportion, multiply the numbers diagonal from each other, then divide by the last number. In this problem, we would multiply 15 and 3.8, which equals 57, then we would divide by 5. That is why the answer is 11.4.
hope this helps!
please give brainliest!
suppose the height of children age 2 years has a probability of 0.54 to be 34 inches or taller. a random sample of 31 children age 2 years is collected.a) Calculate the mean of the sampling distribution of the sample proportion(b) Calculate the standard deviation of the sampling distribution of the sample proportion. (Round your answer to three decimal places.)
Rounded to three decimal places, the standard deviation of the sampling distribution of the sample proportion is 0.024.
What is the standard deviation?The degree of variance or dispersion of a collection of numbers from the mean is measured by standard deviation. It is calculated as the square root of variance, which is the average of the squared deviations from the mean. A low standard deviation suggests that the values are close to the mean, whereas a high standard deviation suggests that the values are dispersed over a wider range. In many other disciplines, including finance and economics, standard deviation is frequently used to assess the risk or volatility of a particular dataset. It is also frequently used in statistics and probability theory. Due to its ability to objectively compare and contrast various values, it is a crucial statistic for comprehending and analyzing data.
How to solve?
sqrt( (population proportion * (1 - population proportion)) / sample size)
sqrt( (0.54 * (1 - 0.54)) / 31) = 0.024
Rounded to three decimal places, the standard deviation of the sampling distribution of the sample proportion is 0.024.
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When 6x = 2y - 18 is graphed in the standard (x,y)
coordinate plane, what is the y-intercept?
A. 2
B. 3
C. 4
D. 6
E. 9
The co-ordinate of y intercept is 9 i.e. option (E)
What is Co-ordinate Geometry?
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Solution:
Given the equation 6x = 2y - 18
See the attached graph below
So we can observe that on x = 0
The y intercept is equal to 9
So, the co-ordinates of the point of intercept is (0,9)
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Simplify your answer and write it as a proper fraction, mixed number, or integer.
The length of RT is 12 units.
What is length?
Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. When there is a basis from which vertical measurements may be made, height is employed. When length is the greatest dimension, width or breadth generally relate to a lesser dimension.
given, RS+ST=RT
or, 9 + x - 1 = 3x
or, 8 + x = 3x
or, 3x - x = 8
or, 2x = 8
or, x = 8/2
or, x=4
Then, the length of RT = 3x = 3.4 = 12 units
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3 of 4
A, B & C lie on a straight line.
BD = CD.
BCD = 70° and / BAD = 5°.
Work out x, explaining each stage of your
working in the comment box.
The value of x is 65°
From the question, we have
BD = CD.
As the sides are equal
∠BCD=∠CBD= 70°
70° = x + 5°
x = 70°-5°
x = 65°
Subtraction:
Subtraction symbolizes the activity of deleting elements from a collection. A negative symbol is used to denote subtraction. The stack will include nine oranges less four oranges, or five oranges, for example, if there are nine oranges stacked together (as seen in the above figure) and four of those oranges are later moved to a basket. As a result, the difference between 9 and 4 is equal to 5, or 9. In addition to being used with natural numbers, subtraction can also be incorporated into other sorts of numbers. The letter "-" stands in for subtraction. The difference, the minuend, and the subtrahend are the three numerical components that make up the subtraction operation.
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pls help me its due tomarow!!!!
Answer:
A: 1
Step-by-step explanation:
the lines only intersect once and will never intersect again so only 1 solutions
Hopes this helps please mark brainliest
4x - 3y = 8
5x - 2y = -11
Answer:
Step-by-step explanation:
4x - 3y = 8
5x - 2y = -11
8x - 6y = 16
-15x + 6y = 33
-7x = 49
x = -7
4(-7) - 3y = 8
-28 - 3y = 8
-3y = 36
y = -12
What is the solution to the equation D 10 2d 7 8 D 10 3d?.
The value of d i s 1 .
ie. d=1
Define linear equation .
An equation between two variables that gives a straight line when plotted on a graph.
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables .
Given:
d - 10 - 2d + 7 = 8 + d - 10 - 3d
On rearranging the given equation ,we get
In other words on taking the like terms to on one side ,so
⇒(d-2d-d+3d)=(8-10+10-7)
⇒d=1
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A local charity is running a fundraiser selling cookies. Each box contains 15 cookies. The ratio of chocolate : vanilla is 2:1.
If the charity sells 2210 boxes of
cookies, how many chocolate
cookies were sold?
The number of chocolate cookies that were sold is 22100.
What is a ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Since the ratio of chocolate : vanilla is 2:1 and the charity sells 2210 boxes of cookies, the number of chocolate will be:
= 2/(2+1) × 2210 × 15
= 2/3 × 2210 × 15
= 22100
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7/10 × 1/3 × 5/11 Write your answer in simplest form
Answer:
7/66
Step-by-step explanation:
Given problem,
→ (7/10) × (1/3) × (5/11)
Let's solve the given problem,
→ (7/10) × (1/3) × (5/11)
→ (7 × 1 × 5)/(10 × 3 × 11)
→ 35/330
→ 7/66
Hence, the answer is 7/66.
Your job pays you 10% commission on every sale you make. If your base pay is
$20,000 per year and you sell $50,000 of merchandise, what is your total earnings
for the year.
$20,000
$25,000
$30,000
$35,000
Answer: 30,000
Step-by-step explanation: 50,000 - 20,000 = 30,000
When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude f = ax+bx2, where a and b are constants. The work done in stretching this rubber band from x = 0 to x = l is:.
This rubber band's work in stretching from x = 0 to x = l is:
[tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]
Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of displacement .
We say that work has been done whenever a force moves an object. When a ball rolls down a hill due to gravity, when you pick up your backpack from the ground, or when your car's internal engine applies a force to move your wheels, all of these events involve a force moving an object over a distance and thus involve some work. No work is done when a force is applied to an object but it does not move.
Given,
force , [tex]f=ax+bx^2[/tex]
work done can be determined by formula,
[tex]W=\int\limits^a_b F\, dx \\\\W=\int\limits^L_0(ax+bx^2)dx\\\\W=(\frac{ax^2}{2}+\frac{bx^3}{3}})|\limits^L_0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})-0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]
Thus, the work done is [tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex].
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The length of a rectangle is 3 yd longer than its width.
If the perimeter of the rectangle is 50 yd, find its length and width.
Answer:
Length is 14 yd width is 11 yd
Step-by-step explanation:
The equation to find the perimeter is ( 2 x Length ) + ( 2 x Width ), so first you divide the perimeter by 2 so we only have to add length + width, you get 25 yds. Since the length is 3 yds longer than width, you can mentally assume Length is going to be 14 yds and width is 11 yd, since Length is 3 yd longer, and finally if you add them together, 14 + 11 = 25. (Apologies if you don't understand I'm not good at explaining)
