Answer:
64
Step-by-step explanation:
using the rule of exponents
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](2^{3}) ^{2}[/tex]
= [tex]2^{3(2)}[/tex]
= [tex]2^{6}[/tex]
= 64
Penelope determined the solutions of the quadratic function by completing the square.
f(x) = 4x2 + 8x + 1
–1 = 4x2 + 8x
–1 = 4(x2 + 2x)
–1 + 1 = 4(x2 + 2x + 1)
0 = 4(x + 2)2
0 = (x + 2)2
0 = x + 2
–2 = x
What error did Penelope make in her work?
Penelope should have subtracted 1 from both sides instead of adding 1.
Penelope should have subtracted 4 from both sides instead of adding 1.
Penelope should have added 4 to both sides instead of adding 1.
Penelope should have subtracted 8 from both sides instead of adding 1.
Penelope should have added 4 to both sides instead of adding 1.
And the solution is x = (√3 - 4)/2.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
Penelope determined the solutions of the quadratic function by completing the square.
For that,
f(x) = 4x² + 8x + 1
–1 = 4x² + 8x
–1 = 4(x² + 2x)
Add 4 to both sides,
–1 + 4 = 4(x² + 2x + 1)
3 = 4(x + 2)²
3/4= (x + 2)²
x + 2 = √3/2
x = √3/2 - 2
x = (√3 - 4)/2
Therefore, Penelope should have added 4 to both sides.
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Find the length of the diameter if the area is 40.3units 2
The diameter of the circle is 7.16 units.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
We are assuming that the area is given for a circle.
Now,
Area of a circle = πr².
Area of a circle = 40.3 units²
Now,
πr² = 40.3
r² = 40.3/3.14
r² = 12.83
r = √12.83
r = 3.58
The diameter of the circle.
= 2r
= 2 x 3.58
= 7.16 units.
Thus,
The diameter is 7.16 units.
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if you're given a true equation and you multiply each side by the same number the resulting equation is also a true equation if you're given a false equation and you multiply each side by the same number will the resulting equation be a true equation or a false equation?
Multiplying each side of a false equation by the same number will result to a false equation
What is a false equation?A false equation refers to equation where the left hand side of the equation is not equal to the right hand side of the equation.
False equations are not useful and hence in math, converted effort are made towards getting a true equation.
A true equation refers to an equation where each side of the equation are same hence the equality sign is truly represented.
Example of true equation say 2x = 10 for x = 5
2 * 5 = 10 correct
multiplying the two sides by 3 results to
6x = 30
plugging in x = 5
6 * 5 = 30
for false equation, say 2x = 10 for x = 6
2 * 6 = 10 incorrect
multiplying the two sides by 3 results to
6x = 30
plugging in x = 6
6 * 6 = 30 incorrect hence false equation remains false
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use tables to evaluate 13.81×14.28 in logarithmic
Answer:
197.2
Step-by-step explanation:
You want to use a table of logarithms to evaluate the product 13.81×14.28.
LogarithmsLogarithms turn a multiplication problem into an addition problem, along with some table look-ups. The basic idea is ...
log(ab) = log(a) +log(b)
Finding the logTo find the logarithm of a number, it can help to write it in scientific notation. This puts one non-zero digit to the left of the decimal point and expresses the multiplier as a power of 10. The first attachment shows a number in scientific notation.
A log table is used to find the logarithm of the mantissa of the number in scientific notation. The result will be a decimal fraction between 0 and 1.
You start by locating the first digits of the mantissa in the left column of the table, and additional digits across the top. The second attachment shows a portion of a table of logarithms with the relevant table entries identified.
The log of 13.81 = 1.381×10¹ is found by locating 13 in the left column, and the next digit, 8, at the top of the table. The final digit, 1, is located at the top of the portion of the table labeled Mean Difference. The number in the Mean Difference column is added to the number found in row 13, column 8: 1399 +3 = 1402. This sum is the mantissa of the logarithm of 13.81. (See the third attachment for the naming we're using.)
Similarly, the log of 14.28 is found in row 14, column 2, and the value in Mean Difference column 8 is added to that: 1523 +24 = 1547.
The characteristic of each logarithm is the corresponding characteristic of the number in scientific notation. For each of these numbers, it is 1.
log(1.381×10¹) = 1.1402log(1.428×10¹) = 1.1547Log of productThe logarithm of the product is the sum of these logarithms:
log(1.381×10¹ · 1.428×10¹) = 1.1402 +1.1547 = 2.2949
Finding the antilogThe value corresponding to this logarithm is found by a procedure that is the reverse of the lookup procedure.
Our logarithm has a characteristic of 2, and a mantissa of 0.2949.
First, we locate the highest number in the table that is less than or equal to the mantissa. Here, that value is 2945, located in row 19, column 7 of the table. The value we want, 2949, is 4 more than this, so we look in the Mean Difference table on row 19 for a value of 4. That is found in column 2.
The mantissa of the antilog of 2949 is the row number (19) with the column numbers appended: 1972. The decimal point for this is located to the right of the leading digit: 1.972.
The characteristic of the antilog is the characteristic of the logarithm: 2.
Then the antilog in scientific notation is ...
10^2.2949 = 1.972×10²
In standard form, this is ...
1.972×10² = 197.2
ProductThe desired product is found to be 13.81×14.28 ≈ 197.2.
__
Additional comment
Different tables of logs may show the interpolation values (Mean Difference) differently. These values are intended to aid in interpolating between table values so that you can find logs and antilogs of numbers with 4 significant digits. (Larger tables let you work with more significant digits.)
In general, the number of significant digits in the values you work with will be less than or equal to the number of significant digits in the logs in the table. Here, the table has 4-digit logs, so our result, 197.2, can have at most 4 significant digits. (The actual product is 197.2068.)
When the characteristic of a number is negative, care must be taken to use correct values for the mantissa and characteristic of the logarithm. Table values are logs of numbers between 1 and 10, and are positive. The log of 0.003949 would be the sum of the negative characteristic -3 and the positive logarithm mantissa 0.5965. That sum would be -2.4035 = (-2) + (-0.4035). Since we want to keep the fractional part positive, we sometimes add and subtract a large positive number. The logarithm of 0.003949 might be expressed in this way as 7.5965-10, effectively the log of 3.949×10⁷×10⁻¹⁰.
Math on the Spot Garrett is 8 years old. He and his family are going to the county fair. What is the price of admission for Garrett , his 2 parents , his grandmother, and his baby sister?
The cost of admission for Garrett, his 2 parents, his grandmother, and his baby sister would vary depending on the county fair and their individual ages.
What is cost?Cost is the monetary value of goods, services, or resources in exchange for money. It is the amount of money paid for goods or services, which includes all expenses incurred in the purchase or production of goods or services. Cost is determined by the sum of the total expenses involved in producing or acquiring a good or service. Cost is a major factor in decision-making, as it affects both the cost of production and the price of goods and services.
Generally, most county fairs charge a reasonable rate for children and seniors, and a slightly higher rate for adults.
For Garrett, he would likely qualify for the children's rate, which could range from free to around $10. For the 2 parents and the grandmother, the adult rate would likely apply, which is usually around $15. For the baby sister, some county fairs offer free admission for children under a certain age, while others offer a discounted rate.
Therefore, the total cost of admission for Garrett, his 2 parents, his grandmother, and his baby sister could range from free to around $50, depending on the county fair and the individual ages.
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7/8- 1/4 ÷ 4/3
A.11/16
B.15/32
C.13/24
D.5/6
Use technology to find points and then graph the function y=(x-2)^2, following the instructions below
The five points on the graph are (0, 4), (2, 0), (4, 4) (- 2, 16) and (6, 16).
And, The graph of function y = (x - 2)² is shown in figure.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The function is,
⇒ f (x) = (x - 2)²
Now, We have to find the value of points on the graph of function.
Here, The function is,
⇒ f (x) = (x - 2)²
Substitute f (x) = 0;
⇒ 0 = (x - 2)²
⇒ 0 = (x - 2)
⇒ x = 2
Hence, Point is, (2, 0)
Put x = 0;
⇒ f (x) = (x - 2)²
⇒ f (x) = (0 - 2)²
⇒ f (x) = 4
Hence, The point is, (0, 4)
Put x = 4;
⇒ f (x) = (x - 2)²
⇒ f (x) = (4 - 2)²
⇒ f (x) = 4
Hence, The points is, (4 4)
Put x = - 2;
⇒ f (x) = (x - 2)²
⇒ f (x) = (-2 - 2)²
⇒ f (x) = 16
Hence, The points is, (- 2, 16)
Put x = 6;
⇒ f (x) = (x - 2)²
⇒ f (x) = (6 - 2)²
⇒ f (x) = 16
Hence, The point is, (6, 16)
Thus, The five points on the graph are (0, 4), (2, 0), (4, 4) (- 2, 16) and
(6, 16).
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What is the value of the lower quartile?
Answer:
not sure
Step-by-step explanation:
lolshjshebshuzhsbbsjxhgdpsizhgxe
Can somebody help I give 10 points
Answer:
B
Step-by-step explanation:
We need to find the radio between earth weight and venus weight, which is:
120 ÷ 106 = 1.1320754717
This number means 1 pound of venus weight is equal to 1.1320754717 of earth weight.
if there's a 180 pound earth weight and we need to find the venus weight, the calculation might loooks like this:
180 ÷ 1.1320754717 = 159 pounds
Anne has $2 less than half
of what James has.
Together, they have $97
saved. Find how much
each person has saved.
The amount Anne has is $31.
The amount James has is $66.
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,
James amount = x
Anne amount = y
x + y = 97
x = y/2 - 2
Now,
y/2 - 2 + y = 97
y/2 + y = 97 + 2
y + 2y = 99 x 2
3y = 198
y = 66
Now,
x = y/2 - 2
x = 66/2 - 2
x = 33 - 2
x =31
Thus,
Anne has $31.
James has $66.
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Please answer qiuckly
Question 2 (1 point)
The two rectangles are similar. Which is the correct proportion for corresponding sides?
The solution is Option D.
The proportion for the similar rectangles is given by the equation
12/4 = 24/8
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the equation will be
Let the length of the first rectangle be = L₁
Let the width of the first rectangle be = W₁
Let the length of the second rectangle be = L₂
Let the width of the second rectangle be = W₂
The two rectangles are similar ,
So , the proportion is given by
Length of the first rectangle : width of the first rectangle : : length of the second rectangle : width of the second rectangle
Substituting the values in the equation , we get
L₁ / W₁ = L₂ / W₂
12 / 4 = 24 / 8
On simplifying the equation , we get
3 = 3
Therefore , the value of A is 12 / 4 = 24 / 8
Hence , the proportion is 12 / 4 = 24 / 8
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A stack of nested paper cups is 8 inches tall. The first cup is 4 inches tall and each of the rest of the cups in the stack adds of an inch to the height of the stack. How many cups are in this 1 4 stack?
Answer: answer is 20
Step-by-step explanation: 4+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=20
Eve has $16.00 in gift money and earns $7.00 per hour as a lifeguard. Nisha has a job painting houses. The following table shows the number of dollars d that Nisha earns working h hours.
h d
1 8.60
2 17.20
3 25.80
While discussing their jobs, Eve and Nisha realize that they have the same amount of money and have worked the same number of hours.
How many hours have they worked:
How much money do they have? Enter your answer as a decimal showing dollars and cents:
The number of hours they have worked would be = 3hours
The quantity of money each individual has would be = Eve = $48.8, While Nisha = 25.80.
Who is a lifeguard?A lifeguard is a trained individual who is specialised in swimming skills and whose job is to rescue drowning victims from a swimming pool or beach.
The number of hours both Eve and Nisha worked is the same = 3 hours.
The total amount earned by both at the end of the third hour = $25.80
But for Eve, the total amount of money ;
Eve has $16.00 as gift money and earns $7.00 per hour
16 + 7+ 25.80 = $48.8, While Nisha = 25.80.
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Select all the expressions that are equivalent to 312 • 79. 33 • 34 • 49 (33)9 • (73)6 73 • (3–4)–3 • 76 (33 39) • (76 73) 320 • (73)3 • (34)–2
Answer:
73 x 8 =678
Step-by-step explanation:
Robert went shopping for a new pair of sneakers. The listed price of the pair of sneakers was $48, but the price with tax came to $50.40. Find the percent sales tax.
The percent sales tax of the initial price of the sneakers would be = 5%
What is sales tax?Sales tax is defined as the amount of money that a particular good is being sold after the addition of its consumption tax funds imposed by the government.
The initial amount of the sneakers = $48
The price after tax = $50.40
The increased difference from the former price = 50.40 - 48 = $2.4
The percentage increase would be;
= 2.4/48 × 100
= 240/48
= 5%.
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2. Use the list below to write the correct term for each definition on the line provided.
axes (of a graph) coordinates coordinate grid intersection number line ordered pair
origin quadrant x-axis
x-coordinate y-axis y-coordinate
a.) the first number of an ordered pair
b.) the second number of an ordered pair
c.) any of four regions formed by the axes in a rectangular coordinate system
d.) the point at which two lines meet
e.) numbers that correspond to points on a graph in the form (x, y)
f.) the intersection of the x-axis and y-axis in a coordinate plane, described by (0,0)
g.) the horizontal and vertical number lines used in a rectangular graph or coordinate grid system as a fixed reference for determining the position of a point
h.) the vertical ( ) axis on a coordinate plane
i.) the horizontal ( ) axis on a coordinate plane
j.) a line on which numbers can be written or visualized
k.) the location of a single point on a rectangular coordinate system where the digits represent the position relative to the x-axis and y-axis Example: (x, y) or (3, 4)
l.) network of evenly spaced, parallel horizontal and vertical lines especially designed for locating points, displaying data, or drawing maps
a. x-coordinate
b. y-coordinate
c. quadrant
d. intersection
e. ordered pair
f. origin
g. coordinate grid
h. y-axis
i. x-axis
j. number line
k. coordinates
l. axes (of a graph)
What is the axes of a graph?The axes of a graph are the two lines that define the coordinate system and divide the plane into four quadrants. These lines are called the x-axis and the y-axis. The x-axis is the horizontal line and the y-axis is the vertical line. The point where the two axes intersect is called the origin and is identified by the coordinates (0,0). The x-axis is typically used for the independent variable and the y-axis is used for the dependent variable. When plotting data on a graph, the x-axis is often labeled with the independent variable and the y-axis is labeled with the dependent variable. The axes of a graph provide a reference for determining the position of a point and are used for displaying data and drawing maps.
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Which is the graph of y=-x+2 answer and solution please
Answer:
Step-by-step explanation:
Parabolas in Standard Form Please Help
Also please include work.
Find the vertex: y=x²+2x+1
Answer:
vertex = (- 1, 0 )
Step-by-step explanation:
given a parabola in standard form
ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² + 2x + 1 ← is in standard form
with a = 1 and b = 2 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{2}[/tex] = - 1
substitute x = - 1 into y for corresponding y- coordinate
y = (- 1)² + 2(- 1) + 1 = 1 - 2 + 1 = 0
vertex = (- 1, 0 )
What is the end behavior of:
1. [tex]\sqrt[3]{6x}[/tex]
2. [tex]\sqrt[3]{x-5}-6[/tex]
3. [tex]-3\sqrt[3]{x+3}+7[/tex]
The end behavior is
[tex]\sqrt[3]{6x}[/tex] has an end behavior of as x approaches positive infinity,[tex]$\sqrt[3]{x-5}-6$[/tex] has an end behavior of as x approaches positive infinity[tex]$-3 \sqrt[3]{x+3}+7$[/tex] has an end behavior of as x approaches positive infinityWhat is end behavior?Generally, End behavior refers to the long-term behavior or trend of a function as the input values (x-values) approach positive or negative infinity. It is often determined by the leading term of the function, which is the term with the highest degree of x. For example, the end behavior of a function like f(x) = x^2 is that it increases without bound as x approaches positive infinity, and similarly it decreases without bound as x approaches negative infinity.
[tex]\sqrt[3]{6x}[/tex] has an end behavior of as x approaches positive infinity, it approaches positive infinity and as x approaches negative infinity it approaches negative infinity.
[tex]$\sqrt[3]{x-5}-6$[/tex] has an end behavior of as x approaches positive infinity, it approaches negative infinity and as x approaches negative infinity it approaches negative infinity.
[tex]$-3 \sqrt[3]{x+3}+7$[/tex] has an end behavior of as x approaches positive infinity, it approaches positive infinity and as x approaches negative infinity it approaches positive infinity.
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What is the measure of angle bcd? 25º 40º 140º 155º
After solving, the measure of angle BCD is 25 degree.
In the given question, we have to find the measure of angle BCD.
As we know that the angle of line is 180 degree.
From the graph we can see that angle yAD = 25 degree
So, the value of angle DAB = 180 - 25
The value of angle DAB = 155
As we know that in the quadrilateral the sum of opposite angle is equal to 180 degree.
So ∠DAB + ∠BCD = 180
155 + ∠BCD = 180
Subtract 155 on both side, we get
∠BCD = 25 degree
Hence, the measure of angle BCD is 25 degree.
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The measure of angle BCD is 45 degrees.
To solve for the measure of angle BCD, we need to use the Triangle Angle Sum Theorem which states that the measure of the angles of a triangle add up to 180 degrees.
Let us use the following figure to illustrate the calculation:
We have angle BCD with unknown measure, angle ABC with measure 45 degrees, and angle ACD with measure 90 degrees.
We can now use the Triangle Angle Sum Theorem to find the measure of angle BCD.
180 degrees = 45 degrees + 90 degrees + x
x = 180 degrees - 135 degrees
x = 45 degrees
Therefore, the measure of angle BCD is 45 degrees.
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Help with math I’ll pay u <3 please :,(
Answer:
0^5 = x^ 2 + 18
Step-by-step explanation:
I hope am not too late
A student investigating study habits asks a simple random sample of 16 student at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are mu = 45 minutes and sigma = 15 minutes. Which of the following best describes what we know about the sampling distribution of means for the student's sample? O mu x = 45; sigma x unknown; shape of distribution unknown O mu x = 45; sigma x = 15; distribution approximately Normal O mu x = 45; sigma x = 15; shape of distribution unknown O mu x = 45; sigma x = 3.75; distribution approximately Normal O mu x = 45; sigma x = 3.75; shape of distribution unknown
The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.
What is Sampling Distribution?Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.
Given that,
μ = 45 minutes and σ = 15 minutes
Sampling distribution of means for the student's sample is :
μₓ = μ = 45
σₓ = σ / √n, where n is the sample size.
σₓ = 15 / √(16) = 15 / 4 = 3.75
Now since the sample size 16 which is less than 30, shape of the distribution is unknown.
Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.
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Find the value of x. Round to the
nearest tenth.
12
x= [?]
Step-by-step explanation:
We use soh,cah,toa
since we where giving the hypotenuse and we are looking for adjacent we use CAH.
cos35=x\12
0.852×12=x
10.23
so therefore to d nearest tenth is 10.2
Drag the tiles to the correct boxes to complete the pairs. Match each cross section to its area. a cross section passing through the diagonals of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches a cross section parallel to the base of a cube whose edges are 8 inches long a cross section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base a cross section parallel to the base of a right rectangular prism that is 3 inches long, 7 inches wide, and 11 inches tall Area Cross section 21 square inches arrowBoth 64 square inches arrowBoth 70 square inches arrowBoth 300 square inches arrowBoth Reset
a) A cross-section passing through the diagonals of opposite faces of a cube = 21 square inches.
b) A cross-section parallel to the base of a cube = 64 square inches.
c) A cross-section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism = 70 square inches.
d) A cross-section parallel to the base of a right rectangular prism = 300 square inches.
What is a cross-section?
A cross-section is a representation of a three-dimensional object as it would appear if it were sliced by a plane, revealing the internal structure of the object. The resulting shape that is formed is known as the cross-section.
a cross-section passing through the diagonals of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches = 21 square inches (since it will be a right triangle with legs of 7 inches and hypotenuse of 10 inches)
a cross-section parallel to the base of a cube whose edges are 8 inches long = 64 square inches (since the base will be a square with sides of 8 inches)
a cross-section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base = 70 square inches (since it will be a right triangle with legs of 12 inches and 24 inches and hypotenuse of 25 inches)
a cross-section parallel to the base of a right rectangular prism that is 3 inches long, 7 inches wide, and 11 inches tall = 300 square inches (since the base will be a rectangle with length of 3 inches and width of 7 inches)
Hence,
a) A cross-section passing through the diagonals of opposite faces of a cube = 21 square inches.
b) A cross-section parallel to the base of a cube = 64 square inches.
c) A cross-section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism = 70 square inches.
d) A cross-section parallel to the base of a right rectangular prism = 300 square inches.
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Evaluate the coordinate points (x,y) for the function y = f(x) = -1.25x -0.25 where x=-1 then y=?
Substituting the value of x and solving the function we get the value of y as y = 1
To evaluate the co-ordinate point (x, y) for the function
y = f(x) = -1.25x -0.25,
you need to substitute the value of x into the function and solve for y.
If x = -1,
then y = f(-1) = -1.25×(-1) - 0.25 = 1.25 - 0.25 = 1.
Therefore, the coordinate point (x, y) for the function:
y = f(x) = -1.25x - 0.25 when x = -1 is (-1, 1).
A function in mathematics is a collection of values connected by a predetermined rule or formula. The output value (also known as the dependent variable) is represented by a letter or a symbol that depends on the input value, whereas the input value (also known as the independent variable) is represented by a letter (such as x or y). Functions are frequently used to represent relationships between several numbers or to simulate real-world occurrences.
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A plane veered off its course at an angle of 14°. If the plane ends up 23 miles due west of its planned destination, how far did it fly? Estimate your answer to 2 decimal places.
The plane flew 95.08 miles.
What is trigonometric ratio?The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Given,
A plane veered off its course at an angle of 14°.
Plane ends up 23 miles due west of its planned destination.
By the figure,
Sin 14° = AB/AC
= 23/AC
AC = 23/Sin 14°
AC = 23/0.2419
AC = 95.08 miles
Hence, 95.08 miles, the aero plane flew.
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Triangle
J
K
L
was dilated with the origin as the center of dilation to create triangle ′′′.
J
′
K
′
L
′
.
The triangle was dilated using a scale factor of 12
1
2
.
Which rule represents the dilation applied to triangle
J
K
L
to create its image, triangle ′′′
J
′
K
′
L
′
?
On a coordinate plane, triangle J K L has points (negative 4, 5), (2, 5), (2, negative 5.5). Triangle J prime K prime L prime has points around (negative 2, 2.5), (1, 2.5), (1, negative 3).
CLEAR CHECK
(, )→(12, 12)
x
,
y
→
1
2
x
,
1
2
y
(, )→(−12, −12)
x
,
y
→
x
-
1
2
,
y
-
1
2
(, )→(2, 2)
x
,
y
→
2
x
,
2
y
(, )→(+12, +12)
The required rule is (x, y) → ( (1/2)x, (1/2)y) represents the dilation applied to the given triangle.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The triangle is given in the question, as shown.
When it comes to transformations, dilation might imply growing or contracting the triangle by a scale factor.
As per the given transformation, the required rule would be
(x, y) → ( (1/2)x, (1/2)y)
Hence, the correct answer would be an option (A).
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Why should I cross out 9\12 when trying to add 1/12 + 2/3
Both numerator and the denominator both are the multiples of 3, so these can be divided by three. So we cross out 9/12 and we get 3/4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 1/12 + 2/3
The LCM of 12 and 3 is 12
1+8/12
9/12
Cross-cancellation can be used to make math easier when fractions are divided.
The numerator and the denominator both are the multiples of 3, so these can be divided by three. So we cross out 9/12 and we get 3/4
Hence, numerator and the denominator both are the multiples of 3, so these can be divided by three. So we cross out 9/12 and we get 3/4
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divide (x^2+1)/(x+4)
this question is on khanacademy in divide quadratics by lineare expressions with remainders
The result of the polynomial division in which case the numerator is quadratic while the denominators equal is linear is; ( x - 3 ) remainder 13.
What is the result of the polynomial division as required?As evident in the task content; the result of the polynomial division which is as given in the task content is required to be determined.
Since the given polynomial division is; ( x² + 1 ) / ( x + 4 ).
The division can be carried out by long division method as in the attached image.
Hence, the result of the polynomial division is; ( x - 3 ) remainder 13.
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