I think it's 84 I'm not good with math though I multipled 7 and 12
Please help…. The table below shows the amount of money Linda spends for a craft demonstration
to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{53}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{53}-\stackrel{y1}{32}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{8}}} \implies \cfrac{ 21 }{ 7 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{ 3}(x-\stackrel{x_1}{8}) \\\\\\ y-32=3x-24\implies {\Large \begin{array}{llll} y=3x+8 \end{array}}[/tex]
I need help on this question it’s due tomorrow.
The transformation in the graph is 1 units vertically downwards.
The correct option is A: The graph of g(x) is the graph of f(x) shifted down 1 unit.
What is transformation on the graphs?Let the function f(x) and g(x) are two real functions.
And g (x) = f (x) + k, where k is real numbers.
Function can be sketched by shifting f (x), k units vertically.
The direction of shift can be found by the value of k:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
Given:
The function f(x) = eˣ,
and the function g(x):
g(x) = f(x)-1= eˣ-1.
The graph of both the functions are given in the attached images.
For the base function f (x) and a constant k, the function given by
The transformations in the graph is defined by:
g (x) = f (x) + k, where k is real numbers.
Function can be sketched by shifting f (x), k units vertically.
The value of k determines the direction of the shift. Specifically,
if k > 0, the base graph shifts k units upward, and
if k < 0, the base graph shifts k units downward.
Here, k = -1
And the graph of g(x) is the graph of f(x) is shifted down 1 unit.
Therefore, the f(x) is shifted to 1 unit downward.
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Complete this table so it shows a relation that is not a function.
X
2
-4
-3
y
3
1
7
-5
If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.
what is function ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.
given
Table 1:
x 0 -4 3 -2 9 3
y 5 8 7 8 5 -2
No, Table 1 is not a function.
Since there are two images of element '3'.
i.e. 3 is mapped to 7 and -2.
Table 2:
x 2 -7 5 1 -6 3
y 5 8 -6 8 5 7
Yes, this relation is a function.
Because corresponding to each x there is a single image.
If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.
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Parallelogram ABCD has vertices at A (-3, 6.5), B (-1, -1.5), and C (4.5, 0). What are the coordinates of Point D?
The coordinates of Point D are (2.5, 8).
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.
Given:
Parallelogram ABCD has vertices at A (-3, 6.5), B (-1, -1.5), and C (4.5, 0).
We have to find the coordinates of Point D.
Let its fourth vertex be D(a, b).
Join AC and BD. Let AC and BD intersect at point O.
We know that the diagonals of a parallelogram bisect each other.
So, O is the midpoint of AC as well as that of BD.
Using the midpoint formula,
Midpoint = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
Here, ([tex](x_1, y_1) = (-3, 6.5), (x_2, y_2) = (4.5, 0)[/tex]
⇒ Midpoint of AC = [tex](\frac{-3 + 4.5}{2}, \frac{6.5 +0}{2}) = (\frac{1.5}{2}, \frac{6.5}{2}) = (0.75, 3.25)[/tex]
Now,
Midpoint of BD is = [tex](\frac{-1+a)}{2}, \frac{-1.5+b}{2})[/tex]
⇒
[tex]\frac{-1+a}{2} = 0.75, \frac{-1.5+b}{2} = 3.25 \\ -1 + a = 1.5, -1.5 + b = 6.50\\a = 2.5, b = 8[/tex]
Hence, the coordinates of Point D are (2.5, 8).
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Need with this … substitution method..
Answer:
The solution is the point (-3,2)
Step-by-step explanation:
x + 2y = 1 Subtract 2y from both sides
x + 2y - 2y = 1 - 2y
x = 1 - 2y Substitute 1 - 2y in for x in the second equation and solve for y.
5x -4y = -23
5(1 - 2y) -4y = -23 Distribute the 5
5(1) - 5(2y) - 4y = -23
5 -10y - 4y = -23 Combine like terms
5 -14y = -23 Subtract 5 from both sides
5 -5 - 14y = -23 -5
-14y = -28 Divide both sides by -14
[tex]\frac{-14y}{-14}[/tex] = [tex]\frac{-28}{-14}[/tex]
y = 2
Solve for y
x + 2y = 1 Substitute in 2 for y and solve for x
x + 2(2) = 1
x + 4 = 1 Subtract 4 from both sides
x + 4 - 4 = 1 - 4
x = -3
The solution is the point (-3,2)
Check:
2 + 2y = 1
-3 + 2(2) = 1
-3 + 4 = 1
1 - 1 checks
5x - 4y = -23
5(-3) - 4(2) -23
-15 - 8 = -23
-23 = -23
Bethany and Samuel are buying a new house. They have $25,000 saved for a down payment and know that they can afford a monthly payment of $1,500 or less. They also know that the best interest rate they can get is 5.1% annually and they want to sign a 30-year mortgage.
1. This equation is used to find the monthly payment, m, given the monthly interest rate, i, the principal, P, and the number of interest periods, n, in months:
Using the equation, find the largest possible principal P for their situation. In other words, what is the largest amount of money they can borrow? (Hint: To answer the question, you must rearrange the equation.)
The largest amount of money they can borrow is $$276.268.65
How to calculate the largest amount?The main formula used in this problem is the Present Value of an annuity Formula:
P = R[1-(1+i)⁻ⁿ]/i
Where;
P: present value (the mortgage value)R: periodic paymentt: time (in years)r: annual interest ratem: number of compounding per yeari=r/m (rate per period)n=mt the total number of paymentsThe maximal monthly payment that Bethany and Samuel can afford is $1,500.
The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.
This implies that
R=1,500
t=30
r=%5.1 = 5.1 /100 = 0.051
m=12, because they make the payments monthly
i=r/m=0.051/12=0.00425
n=mt = 12*30=360
That is,
i) they will make 360 monthly payments,
ii) the largest amount of money they can borrow can be found using the formula:
P = R[1-(1+i)⁻ⁿ]/i
Substituting the known values:
P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425
Therefore, $276.268.65 is the largest possible principal for the situation
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Find the distance between the points.
(-6,5),(-6,-3.5)
The distance is
Answer:
8.5
Step-by-step explanation:
there's a rule to get the distance between 2 points
√((1st x- 2nd x)²+(1st y- 2nd y)²)
√((-6-(-6))²+(5-(-3.5))²)
=√((-6+6))²+(5+3.5))²)
you can just type that on your calculator and you'll get the result
√((-6+6))²+(5+3.5))²)
=√((5+3.5))²)
= √((8.5))²)
the root goes away with the power (exponent)
so it equals 8.5
please help asap
will give brainliest
Answer:
15
Step-by-step explanation:
Opposite angles in a parallelogram are equal. (this is a parallelogram because it has 2 pairs of parallel sides.)
So
3x+2=47
3x=45
x=45/3
x= 15
The length of a rectangle is four times its width. If the area of the rectangle is 196 yd², finds its perimeter.
Answer:
perimeter = 70 yards
Step-by-step explanation:
⭐What is the area of a rectangle?
area = length * width⭐What is the perimeter of a rectangle?
perimeter = 2(length) + 2(width)Strategy1. Make the equation for the area of the given rectangle and solve for x
2. Substitute x into the expressions of the length and width and solve for the perimeter
Working1. Define the expressions of the length and width of the rectangle
width: x
length: 4x
2. Make the equation for the area of the rectangle
[tex]196yd^2 = 4x * x\\196yd^2 = 4x^2[/tex]
3. Solve for x
[tex]\frac{196}{4} = x^2[/tex] . . . . . . . . . . divide both sides by 4
[tex]49 = x^2[/tex]
[tex]\sqrt{49} = \sqrt{x^2}[/tex] . . . . . . . . square root both sides to isolate x
∴ [tex]7 = x[/tex]
4. Substitute x into the expressions of the length and the width
width: x
width = 7
height: 4x
height = 4(7) = 28
5. Solve for the perimeter
[tex]perimeter = 2(length) + 2(width)[/tex]
[tex]perimeter = 2(28) + 2(7)\\perimeter = 56 + 14\\perimeter = 70[/tex]
IF THIS RESPONSE HELPED YOU, PLEASE MARK IT THE "BRAINLIEST"! :)
Emily is single and has earned both qualified and nonqualified dividends this year. Her taxable income is $125,000. Using this
information and the tables provided, determine how much tax Emily will pay on each type of dividend.
Type the correct answer in each box. Use numerals instead of words.
Single Taxpayers: Income Brackets
Tax Rate
10%
12%
22%
24%
32%
35%
37%
Income Bracket
O to 9,525
9,526 to 38,700
38,701 to 82.500
82,501 to 157.500
157.501 to 200.000
200,001 to 500.000
> 500,000
Single Taxpayers: Qualified Dividends
and Long-Term Capital Gains
Tax Rate
Income Bracket
0%
15%
20%
The tax rate on Emily's nonqualified dividends is
The tax rate on Emily's qualified dividends is
0 to 38.600
38,601 to 425,800
> 425,800
96. Her taxes on $500 in ordinary dividends will equal
96. Her taxes on $2,000 in qualified dividends will equal
On solving the provided question, we can say that - the value of the percentage = 1/10; 12/100
What is percentage?
A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
10%; 12%; 22% and 24%
1/10; 12/100; 11/50 and 6/25
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Give an example of Limit of a Polynomial Function.
Note; With explanation po sana.
Pa help po pls.. I'll mark as brainliest for the one who can answer.
An example of limit in polynomial will be the polynomial function f(x) = x³ + 2x² - 5. As x approaches 2, the value of the function approaches 11. So, the limit of f(x) as x approaches 2 is 11.
What is a polynomial?A polynomial simply means an expression which is composed of variables, constants and exponents, which are combined using mathematical operations such as addition, subtraction, multiplication and division
In mathematical notation, we can write it as: Here, lim x->2 (x³ + 2x² - 5)
= x³ + 2x² - 5
= 2³ + 2(2²) - 5
= 8 + 8 - 5
= 11
This means that as x gets arbitrarily close to 2, the values of the function gets arbitrarily close to 11.
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Which property is illustrated by the statement below? 4(3+2)=4(3)+4(2)
Distributive property is illustrated by the statement given as 4[3+2]=4[3]+4[2]
What is distributive property?The distributive property is defined as an expression of the form A(B + C). This property is known by distributive law and applies to subtraction also. This can be solved by a multiplication over addition operation that is written as:
A(B + C) = AB + AC
Distributive property is the sum of two numbers times a third number is equal to the sum of each add end times the third number.
Since the general rule is that:
a(b + c) = ab + ac
Then, 4[3+2]=4[3]+4[2]
Therefore, the given statement elaborates the Distributive property.
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Question 1 of 10
Which choices are equivalent to the expression below? Check all that apply.
√5. √20
☐
A. 100
B. 5.2
C. 10
D. √5 √√5√4
E. √5 20
F. √25
.
SUBMIT
Choices that is equivalent to the expression √5. √20 is 5.2
Define equivalence.In mathematics, the word "equivalent" designates two quantities, numbers, or meanings that are the same. A bar across an equivalent sign or Equivalent Sign shall be used to indicate the equivalence of two such quantities. Additionally, it denotes the logical equivalent of two values or a group of quantities.
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
x= (5)^1/2*(20)^1/2
x= (5)^1/2*(2.2.5)^1/2
x=5.2
So B is the correct option.
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Part B
Next, rewrite the exponential expression using factors of 8 so that the base of the equation is a product of two factors, with one factor being a perfect square.
The exponential expression is (√4×√2)².
What is radical form?Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.
The given number is √8.
Now, 8=(√4×√2)²
=(2×√2)²
= 4×2
= 8
Therefore, the exponential expression is (√4×√2)².
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"Your question is incomplete, probably the complete question/missing part is:"
Rewrite the exponential expression using factors of √8 so that the base of the equation is a product of two factors, with one factor being a perfect square.
ccording to the Australian Bureau of Agricultural and Resource Economics, Queensland egg farmers produce millions of eggs every year. Suppose egg production per year in Queensland is normally distributed, with a standard deviation of 83 million eggs. If during only 3% of the years Queensland egg farmers produce more than 2,655 million eggs, what is the mean egg production by Queensland farmers (in million)?
Round your answer to 1 decimal place.
The standard deviation of 83 million eggs and 2,655 millions eggs represent that of 3% of the farmers, of the production that is normally distributed, indicates that the mean egg production by Queensland farmers is about 2498.1 million eggs.
What is a normal distribution?A normal distribution is a probability distribution such that the values of the distribution are symmetrical around the mean value of the distribution.
The standard deviation, σ = 83 million eggs
The percentage of farmers that produce more than 2,655 million eggs, x = 3%
The formula for the z-score is; [tex]Z = \dfrac{x - \mu}{\sigma}[/tex]
Therefore, we get;
[tex]Z = \dfrac{2655 - \mu}{83}[/tex]
From the z-score table for P(Z > Z₁), where Z₁ is the z-score corresponding to Φ(1 - 0.03) = Φ(0.97)
The z-value corresponding to Φ(0.97) is about 1.89
Therefore;
[tex]Z = \dfrac{2655 - \mu}{83} \approx 1.89[/tex]
83 × 1.89 ≈ 2655 - μ
μ ≈ 2655 - 83 × 1.89 = 2498.1
The mean egg production by Queensland farmers is about 2498.1 million eggs per year
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If QR = 8, RS = x + 2, and QS = 6x, what is QS?
Answer:
QS = 12
Step-by-step explanation:
Hello!
We can see that QS is the sum of QR and RS, which is equal to 6x.
We can substitute the given values to solve for x, and then use that to find QS.
Solve for xQS = QR + RS6x = 8 + x + 2 Substitute values6x = 10 + x Combine like terms5x = 10 Subtract xx = 2 Divide by 2The value of x is 2. We can now find QS by substituting 2 for x in 6x.
QS = 12.
The cross-section of a wall is 7/16 of an inch thick. If the drywall is 1/4 inches thick, how thick is the texturing on wall? A. 3/16, b. 6/12, C 1/4, D 6/16
When the cross-section of a wall is 7/16 of an inch thick and the drywall is 1/4 inches thick, the thickness of the texturing on wall is A. 3/16
How to calculate the Fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
From the information, the cross-section of a wall is 7/16 of an inch thick. If the drywall is 1/4 inches thick. The thickness of the texturing on the wall is the total thickness of the wall minus the thickness of the drywall. The total thickness of the wall is 7/16 inches, and the thickness of the drywall is 1/4 inches, so the thickness of the texturing is:
= 7/16 inches - 1/4 inches
= 3/16 inches.
Therefore, the answer is A. 3/16 inches.
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A science teacher makes two mixtures of red dye and water. Mixture A has 3 mL of red dye every 20 mL of water. Mixture B has 4mL of red dye fr every 30 mL of water. Which mixture is redder?
The decimal value of the ratio for A is greater than for B. Then mixture A is redder.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Two red dye and water combinations are created by a science teacher. For every 20 mL of water in Mixture A, 3 mL of red dye is present. For every 30 mL of water in Mixture B, 4 mL of red dye is present.
The ratio of the red dye to water for A is given as,
⇒ 3 / 20
⇒ 0.15
The ratio of the red dye to water for B is given as,
⇒ 4 / 30
⇒ 0.133
The decimal value of the ratio for A is greater than for B. Then mixture A is redder.
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Given that a square root of a number N is a value, that when multiplied by itself, results in N. What's the square root of 49? a. 9, b. 5, c. 7, d. 8
Answer:
Step-by-step explanation:
[tex]N^{2} =49[/tex]
To solve take the square root of 49.
[tex]\sqrt{49}[/tex] = 7
Option c which is 7
FOR BRAINIEST PLEASE ANSWER ASAP
Please help me with this question
Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.
Trigonometry is what?The study of relationships among triangle angles and angles is known as trigonometry. Mathematical modeling is a fundamental idea in all of geometry because it can be used to reduce any straight-sided form to a collection of triangles. Amazingly complex connections exist between trigonometry and other areas of mathematics, particularly mathematics, real or complicated, infinite series, logarithms, and infinite series.
Here,
Given : Cosx = 9/26 (First quadrant)
To find : Cos2x
We use the formula:
=>Cos2x = 2Cos²x -1
=> Cos2x = 2(9/26)² - 1
=> Cos 2x = -0.760355
Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.
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Determine whether the relation is a function.
How do you write 0.00000000090 in scientific notation?
Answer:
Step-by-step explanation:
9.0 × 10-10 I think.....
Predict a ranking for the speed of sound in four different substances: steel, 25°C air, 50°C air, and water. Use the kinetic theory of matter to defend your predictions.
Based on the principles of kinetic theory, the speed of sound in matter is determined by the mean free paths of the molecules that make up the matter and the properties of the material itself.
What is speed?Velocity is the speed at which an object moves or changes position over a period of time. It is usually measured in units such as meters/second, miles/hour, kilometers/hour. It is an important factor in the movement of objects and the movement of sound, light and other forms of energy. Speed is also an important factor in transport safety, as it affects how long it takes a vehicle to stop and how far it must travel to stop safely.
Predict the ranking of sound speeds for four different materials.
Steel, 25°C air, 50°C air and water. Use the theory of motion of matter to protect your predictions.
Therefore, the speed of sound varies greatly depending on the material. Below is the ranking of the speed of sound for the four substances listed. From fastest to slowest:
1. 25°C Air: The speed of sound in warm air at 25°C is the fastest of the four substances, and because air is made up of both light and heavy molecules, it can travel quickly. The speed of sound in warm air at 25 °C is about 343 m/s.
2. 50°C air: The speed of sound in air at 50°C is slower than in air at 25°C. This is because molecules in warm air spread out more and move more slowly. The speed of sound in air at 50 °C is approximately 331 m/s.
3. Water: Water molecules are denser and move slower, so the speed of sound in water is slower than in air. The speed of sound in water is approximately 1,482 m/s.
4. Steel: The speed of sound in steel is the slowest of the four substances. This is because steel is composed of heavier molecules that move slower than those in air and water.
Overall, the order of sound velocities for the four materials is air at 25°C, air at 50°C, water, and steel. This classification is based on the principle of kinetics that the speed of sound in a material is determined by the mean free paths of the molecules that make up the material and the properties of the material itself.
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You can sand 4 over 9 yd.² of wood and one over two hour how many square yards can you send in 3.2 hours?
You can sand 14.4 yd² of wood in 3.2 hours.
What is Ratio?A ratio is used to compare two or more like quantities or numbers with the same units. It is often written with a colon, and when used in words, we say the ratio of one quantity "to" the second quantity. A rate is a ratio that compares two different quantities which have different units.
9:2
x:3.2
therefore;
x = (3.2 x 9)/2
x = 28.8/2
x = 14.4 yd² of wood
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help yall please!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Well it would be funchen because as you see it just makes sence
Answer:
not a function
Step-by-step explanation:
In a function, an input gives only one output. As you can see from the graph, the input which is 4 produces 3 different outputs which are 2, 3 and 4, thus it cannot be a function.
New York City is 2.727272.% of the United States' population. NYC's population is 9 million people. What is the population of the United Sates?
The population of US is 330 million approx.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.
Given
population of new york = 2.727272% population of US
population of new york = 9 million
population of US = 1/2.727272% of new york
population of US = 36.6666 x 90,00,000
population of US = 33,00,00,087.9 = 330 million approx
Hence population of US is approx 330 million.
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You cut a loaf of plantain bread into 20 equal slices . you and friends eat 3/10 of the bread . you want to put each leftover slice into its own bag. How many bags do you need
Answer:
14 bags.
Step-by-step explanation:
20 equal slices, so 20/20.
You eat 3/10 of it. 3/10 is equivalent to 6/20.
20/20 - 6/20 is 14/20.
You need 14 bags.
NEED HELP ASAP DUE TMR
1. The length of the altitude is 15 units.
2. The perimeter of trapezoid ABCD is 132 units.
Perimeter of a trapezoid.An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.
The perimeter of a trapezoid is the sum of all its sides.
From the question;
1. To determine AE,
DE = (DG - EF)/ 2
= (22 - 6)/ 2 (since AB = EF = 6)
= 8
DE = 8 units
The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;
/hyp/^2 = /opp/^2 + /adj/^2
AD^2 = DE^" + AE^2
17^2 = 8^2 + AE^2
289 = 64 + AE^2
AE^2 = 225
AE = 15
Thus the length of the altitude is 15 units.
2. To determine the perimeter of the trapezoid, we have;
AE = (AD - EF)/ 2
= (58 - 16)/ 2 (since BC = EF = 16)
= 21
AE = 21 units
So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;
/hyp/^2 = /opp/^2 + /adj/^2
AB^2 = BE^2 + AE^2
= 20^2 + 21^2
AB = 841^1/2
AB = 29
Perimeter of the trapezoid = 29 + 16 + 29 + 58
= 132 units
Thus, the perimeter of the trapezoid is 132 units.
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Help!! Like what even is this
The new transformation coordinates are B""(6, 15), C""(-3, 12), and Dilate k=3 by multiplying both x and y by 3.
what is coordinates ?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
given
For point B,
B(1,2) → B'(1 , -2) → B"( 2, -5) → B""( 6 ,-15)
For point C,
C(-2,1) → C'( -2 , -1) → C"( -1 , -4 )→ C"" ( -3 , -12)
In order to reflect a point across the x-axis, keep the x coordinate constant while changing the y coordinate to its opposite.
<1, -3> the following translations: Add 1 to x, take 3 away from y.
Add 3 to both x and y to dilate k=3.
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