In the following graph we observe line segment AB being mapped by translation to line segment A'B'.
A. In two or more sentences, explain what test you could perform to check the validity of this translation.
B. Prove mathematically that the translation is valid using the test you mentioned above.
The translation of line AB to line A'B' is valid and the translation rule is (x,y) ⇒ (x - 7, y - 3)
How to validate the translation?The graph that completes the question is added as an attachment
From the graph, we have:
A = (3,9) and B = (5,6)
A' = (-4,6) and B' = (-2,3)
Subtract the x and y coordinates of A' from A and B' from B.
So, we have:
AA' = (3 + 4, 9 - 6)
AA' = (7, 3)
BB' = (5 + 2, 6 - 3)
BB' = (7, 3)
See that:
AA' = BB' = (7, 3)
This means that the line AB is translated 7 units left and 3 units down
How to prove the translation mathematicallyThe translation above means:
(x,y) ⇒ (x - 7, y - 3)
Recall that:
A = (3,9) and B = (5,6)
So, we have:
A' = (3 - 7, 9 - 3)
A' = (-4, 6)
Also, we have:
B' = (5 - 7, 6 - 3)
B' = (-2, 3)
Hence, the translation is valid
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PLEASE HELP!!! I WiLL GIVE BRAINLIEST!!!!!
Identify the coefficients of x, y and z
5z - 2 + 6x + 3y
Answer:
x=5 y=3 z=5
Step-by-step explanation:
The coefficient is the number in front of the variable
Answer:
coefficient of x: 6coefficient of y: 3coefficient of z: 5Step-by-step explanation:
The coefficient in an expression is the multiplier of a designated part of a term of the expression.
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coefficients hereThe given expression is
5z -2 +6x +3y
It consists of four (4) terms, added together. One term is a constant, -2. The others each have a single variable that is multiplied by a constant. When we ask for the coefficient of the variable, we are asking for the value of that constant multiplier.
The term containing x is 6x. The multiplier of x in that term is 6, so we say ...
the coefficient of x is 6.
The term containing y is 3y. The multiplier of y in that term is 3, so we say ...
the coefficient of y is 3.
The term containing z is 5z. The multiplier of z in that term is 5, so we say ...
the coefficient of z is 5.
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other coefficientsIn an expression such as πr²h, different parts of the expression will have different coefficients. If we ask for the coefficient of the expression, we are generally asking for the constant: π. (The Greek letter pi is the symbol used to represent the irrational constant ratio between the circumference and diameter of a circle. Is is about 3.1415926535....)
If we ask for the coefficient of h, we are asking for the product (πr²) that multiplies h in this expression. Similarly, the coefficient of r² is (πh). Note that we have specified a "designated part" of the expression for which we want the coefficient. This is important when we are solving equations.
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The commutative property of multiplication means that parts of a product can be written in any order. That is, 5·z is the same product as z·5. When the constant and variable parts of the expression can be unambiguously identified, the order does not matter. In some cases, a constant coefficient may come in several parts: 3z·5·2 has a z-coefficient of 30, for example.
See below for a case where there may be some ambiguity.
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exponentsIn the expression r², the constant 2 that comes after the variable, written as a superscript, is called an "exponent," not a coefficient. Often on Brainly, and sometimes in curriculum materials, you will see this written as r2, because superscripts do not get properly rendered. If you're writing this in plain text, the form r^2 is preferred.
find the prime factorization of 420
Answer:
2,3,7,2,5
Step-by-step explanation:
When you factorize a number you divide them until the outcome numbers are prime. 420 is equal to 42 and 10.
42 is equal to 6 and 7 and 6 is 2 times 3
2,3,7 is prime
10 is 2 times 5
2 and 5 is prime
Answer:
420 = 2² × 3 × 5 × 7
Step-by-step explanation:
The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, ...
To find which prime numbers multiply together to make 420, start by dividing 420 by the first prime number, 2:
⇒ 420 ÷ 2 = 210
As 210 is not a prime number, we need to divide again. Let's try dividing by 2 again:
⇒ 210 ÷ 2 = 105
As 105 is not a prime number, we need to divide again. 105 is not divisible by 2, so let's try dividing it by the next prime number, 3:
⇒ 105 ÷ 3 = 35
As 35 is not a prime number, we need to divide again. 35 is not divisible by 2 or 3, so let's try dividing it by the next prime number, 5:
⇒ 35 ÷ 5 = 7
As 7 is a prime number, we can stop.
Therefore, 420 is the product of all the prime numbers we found together with the final one:
⇒ 420 = 2 × 2 × 3 × 5 × 7
As 2 appears twice, we can write this using exponents:
⇒ 420 = 2² × 3 × 5 × 7
A class of 30 students plans to collect at least $500 in donations for a rehabilitation camp. They have collected $270. How much more should each student collect?
Credit card A has an APR of 22% and an annual fee. All else being equal, at about what balance will the cards offer the same deal over the course of a year? (Assume all interest is compounded monthly)
All else being equal, at a $1,333.33 balance, the two credit cards will offer the same deal (finance charge) over a year.
What is a credit card finance charge?A credit card finance charge is the fee associated with using credit.
Credit card issuers use the finance charges to minimize non-payment risks and earn some profits for extending credit to cardholders.
Data and Calculations:Card A Credit B
APR 22% 25%
Annual fee $40 $0
To calculate the balance required, the required equation is
= 22%x + $40 = 25%x
Where x = required balance
Thus,
= 0.22x + $40 = 0.25x
= $40 = 0.03x (0.25x - 0.22x)
= 0.03x = $40
x = $40/0.03
x = $1,333.33
Question Completion:Credit card A has an APR of 22% and an annual fee of $40, while credit card B has an APR of 25% and no annual fee.
Thus, all else being equal, at a $1,333.33 balance, the two credit cards will offer the same deal over the course of a year.
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please help i need the answer ASAP
Answer:
I believe what you would have to do is add each number so the top left box would be two and the bottom right would be 11
Step-by-step explanation:
Solve the following inequality using both the graphical and algebraic approach: 8 minus x greater-than-or-equal-to 5 (8 minus x) Graph A On a coordinate plane, a line goes through (0, 8) and (8, 0). Another line goes through (8, 0) and (7, 10). Graph B On a coordinate plane, a horizontal line is at y = 5 and another line goes through (8, 0) and (0, negative 8). a. x greater-than-or-equal-to 8 Graph A b. x less-than-or-equal-to 8 Graph A c. x greater-than-or-equal-to 8 Graph B d. x less-than-or-equal-to 8 Graph B
The given inequality (8 - X ≥ 5(8 - x)) is solved using graphs method and the result is (Option A); that is x ≥ 8 Graph A.
The inequality is given as: 8-x≥5(8-x)
The next step algebraically is to open the brackets. Hence,
8-x ≥ 40 -5x
Next, we collect like terms
= -x+5x ≥ 40-8
= 4x ≥ 32
Make x the subject of the statement by dividing both sides with 4
= x ≥ 8
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Argelis had þhe following containers of paint leftover, 1/2 gallon, 3/4 quarts and 1/4 gallon. How many quarts of paint does argelis have left
3.75 quarts of paint does Argelis have left with her.
What is Gallons?A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces.
Here, we know that,
1 gallons = 4 quarts
so, 1/2 gallons = 1/2 X 4 = 2 quarts.
and 1/4 gallons = 1/4 X 4 = 1 quarts.
Now, total paint left with Argelis = 1/2 gallons + 3/4 quarts + 1/4 gallons
= 2 quarts + 3/4 quarts + 1 quarts
= 3 quarts + 3/4 quarts
= 15/4 quarts or 3.75 quarts
Thus, 3.75 quarts of paint does Argelis have left with her.
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Which polygon is a convex heptagon?
A polygon has 7 sides. No angles go inside of the shape.
A polygon has 8 sides. No angles go inside of the shape.
A polygon has 8 sides. One angle goes inside of the shape.
A polygon has 7 sides. One angle goes inside of the shape.
Option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
As we know, a convex heptagon is a polygon with seven sides, seven internal angles, and seven vertices, which means that a convex heptagon has seven sides.
A convex heptagon is a polygon that has 7 sides. No angles go inside of the shape.
Thus, option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.
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Answer: the first option
Step-by-step explanation:
Pls help me with number
Answer:
Total people = 240
Step-by-step explanation:
Let the total number of people by 'x'.
[tex]\sf \text{Number of men =$ \dfrac{1}{4}*x$} \\[/tex]
[tex]\sf \text{Number of women =$\dfrac{1}{3}x$}[/tex]
Number of children = 100
When we subtract the total number of men and women from the total people 'x', we get the number of children.
[tex]\sf x - \left(\dfrac{1}{4}x+\dfrac{1}{3}x\right)= 100\\\\x - \left(\dfrac{1*3}{4*3}x+\dfrac{1*4}{3*4}x\right)=100\\\\[/tex]
[tex]x- \dfrac{4+3}{12}x=100\\\\x - \dfrac{7}{12}x = 100\\\\ \dfrac{12}{12}x-\dfrac{7}{12}x = 100\\\\ \dfrac{5}{12}x=100\\[/tex]
[tex]\sf x = 100*\dfrac{12}{5}\\[/tex]
x = 20 * 12
x = 240
Total number of people = 240(Need help answering these questions… please don’t give me links in the comments, because it doesn’t help me. Answer it in comments please. )
A bucket holds 5 gallons of water and a barrel holds 8.4 buckets of water.
a. What is the conversion factor to change gallons to buckets?
b. What is the conversion factor to change buckets to barrels?
c. A gallon (gal) of water is equivalent to 128 fluid ounces (fl oz). How many fl oz of water are in 1 barrel?
Answer:
a) 1/5 bucket = 1 gallon
b) 8.4 buckets = 1 barrel
c) 5376 fl oz per barrel
Step-by-step explanation:
a) From the given information, 1 bucket = 5 gallons. This means 1/5 of a bucket is 1 gallon.
b) From the given information, 8.4 buckets = 1 barrel. This seems to be in the form that the question is asking for. If the question was asking how many barrels were in a bucket the answer would be 1/8.4 barrels = 1 bucket.
c) From the previously determined conversion factors, we can take ounces to barrels by converting barrels down to gallons.
1/8.4 barrels = 1 bucket; 1/5 bucket = 1 gallon; 1 gallon = 128 fluid ounces
We need to set up a series of fractions that use these factors:
[tex]\frac{128 fl oz}{1 gallon}*\frac{1 gallon}{1/5 buckets}*\frac{1 bucket}{1/8.4 barrels}[/tex]
These fractions can be simplified to [tex]\frac{128 fl oz}{1 gallon}*\frac{5 gallon}{1 bucket}*\frac{8.4 buckets}{1 barrel}[/tex]
Multiply the fractions: 5376 fl oz per barrel
(Note that the units cancel out in the fractions so that only fluid ounces per barrel are left.)
A rectangle patio has a perimeter of 38 feet. If the length of the patio is 5 feet less than twice the width, find the dimensions of the patio
Answer:
The length is 11ft.
The width is 8ft.
Step-by-step explanation:
Hello!
Perimeter of a rectangle: [tex]P = 2(l + w)[/tex]
P = perimeterl = lengthw = widthWe know that the length is 5 ft less than twice the width, which can be expressed by the equation: l = 2w - 5. We can plug in 38 for "P".
We can substitute the equation for l, and solve for the width.
Solve for W[tex]P = 2(l + w)[/tex][tex]38 = 2((2w - 5) + w)[/tex][tex]38 = 2(3w - 5)[/tex][tex]38 = 6w - 10[/tex][tex]48 = 6w[/tex][tex]8 = w[/tex]The width is 8. We can solve for the length by plugging it back into the equation l = 2w - 5
Solve for Ll = 2w - 5l = 2(8) - 5l = 16 - 5l = 11The length is 11.
The dimensions are 11 ft and 8 ft.
the number of keys on the keyring minus 2
Translating the given phrase into a variable expression is equal to k - 2.
What is a variable expression?A variable expression refers to a mathematical equation which can be used to show the relationship that exist between a numerical quantity and a variable.
Next, we would translate the given phrase into a variable expression as follows:
Let the number of keys on the keyring be k.
Therefore, the variable expression is equal to k - 2.
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Complete Question:
Translate the phrase into a variable expression. Use the letter k to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.
The number of keys on the keyring minus 2?
Write the equation in standard form for the circle with center (9,0) and radius 3
15.
Bailey went out to dinner. It cost $ 45.00. He wanted to leave a 20% tip for his waitress. Find the tip.
Answer:
The tip should be $9.00
Step-by-step explanation:
What is true of the function g(x) = -2x² + 5?
O g(x) is the multiplication of g and x.
O-212 +5 is the input of the function.
The variable x represents the independent variable.
The variable g represents the input of the function.
Answer:
C.) The variable x represents the independent variable
Step-by-step explanation:
The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.
A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.
B.) is incorrect because "x" is the input.
D.) is incorrect because "x" is the input.
17.
select the correct answer
what is the equation of the problem shown with its focus on this graph?
Options are in photo!
Answer:
B
Step-by-step explanation:
ADEF is translated 5 units straight up so that point F lands on the x-axis. where does point D land?
Point D would be translated to the point (0, 5).
What is translation?Translation is an aspect of geometry that moves plane shapes from one point to another along the cartesian coordinates without changing the form in which the shape exists.
Analysis:
Point D is at (0,0) if it is translated up from 0,0 the point D moves 5 units along the y-axis while x axis remain same. So that the new point of D becomes (0,5)
In conclusion, the point D will land at point (0,5)
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The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2+4x-60. The cost, in dollars, of producing the toy cars can be modeled by 3X2-x+ 200. The number of toy cars sold is represented by X
The equation that represents the profit function is P(x) = 5x - 260
How to determine the profit function?The given parameters are:
C(x) = 3x^2 - x + 200 --- cost function
R(x) = 3x^2 + 4x - 60 --- revenue function
The profit function is calculated as:
P(x) =R(x) - C(x)
This gives
P(x) = 3x^2 + 4x - 60 - 3x^2 + x - 200
Evaluate the like terms
P(x) = 5x - 260
Hence, the equation that represents the profit function is P(x) = 5x - 260
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Select the correct answer.
Over which interval of the domain is function h decreasing?
25?
Answer:
the function is only increasing.
Step-by-step explanation:
Gray can ride his bike 6miles in 20 minutes at this rate how many miles can he ride in 100 minutes
( PLEASE HELP WITH THIS QUESTION)
You are studying a single-celled organism under a microscope. Is it possible for this organism to be classified as fungi?
Answer: Yes it is possible
Example: Yeast is a single-celled fungus.
There are probably other types of fungus that are single-celled. However, some other fungi are multi-celled. You will likely need more information about the organism under the microscrope before you can classify it properly.
Find the volume of the prism.
8in. 5in. 5in
The regular hexagon has a radius of 4 in.
A regular hexagon has a radius of 4 inches.
What is the approximate area of the hexagon?
24 in.2
42 in.2
48 in.2
84 in.2
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
What is the approximate area of the hexagon?Given that;
Radius of the regular hexagon = 4inArea A = ?Since a regular hexagon can be divided into six equal triangle, we will determine the area of a single triangle and then multiply the area by 6 to get the area of the regular hexagon.
Angle of one triangle in the regular hexagon = 360°/6 = 60°.
To determine the height, we divide the triangle into two equal half, making a right angled triangle with hypotenuse 4in, Base 4in/2 = 2in.
We find the perpendicular height using Pythagoras theorem
h = √( (4)² - (2)² )
h = √( 16 - 4 )
h = √( 12 )
h = √( 2² × 3 )
h = 2√3
Now, we determine the area of a single triangle.
Area = (1/2) × base × height
Area = 0.5 × 4 × 2√3
Area = (4√3)in²
Now, to get the area of the regular hexagon, we multiply the area of the triangle by 6
Area of regular hexagon = 6 × (4√3)in²
Area of regular hexagon = 24(√3)in²
Area of regular hexagon = 41.57in² ≈ 42in²
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
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Answer: b
Step-by-step explanation:
4^2/5 / 4^x/5 = 4^0
Can you help me please
Find the area A and circumference C of a circle of diameter 12 cm. Use 3.14 for . Round the result to the nearest tenth.
Answer:
Area: 113cm²
Circumference: 37.7cm
Step-by-step explanation:
to find area use the formula πr², π being Pi (3.14) and r being radius
radius = 6cm (half the diameter)
3.14 × 6² = 113.04cm²
to find the circumference use the formula πd
diameter = 12cm
3.14 × 12 = 37.68
sally has 10 pounds she wants to buy 28 cans of soda which cost 26p each. how much money does she spend and does she have enough
Answer:
she will need 728 pounds to buy 28 cans but she only has 10 pounds so she doesn't even have enough for 1 can of soda
Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars. Which table of values matches this equation?
Answer:
Table D
Step-by-step explanation:
I have all of the tables listed below and the correct one circled! I used to tutor my cousin about this topic!
I hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!
Have a great day!
:)
The 4th table in the option is the correct one.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars.
The given equation is y = 6x + 50
Put x = 0
y = 50
Put x = 5
y = 80
Put x = 10
y = 110
Put x = 15
y = 140
Creating the table,
x y
0 50
5 80
10 110
15 140
Hence, we get the table.
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Ted needs 2500 metres for job. What length is this in kilometres
Answer:
2.5 kilometers
Step-by-step explanation:
One kilometer is 1000 meters
To convert from metres to kilometers, we divide by 1000
2500 ÷ 1000 = 2.5km
Which newspaper is actually closest to the percentage of voters who support the governor reelection?
No Links Please
The newspaper that is actually the closest to the percentage of voters who support the governor's reelection is the tribune at 71%.
What is the sample size of a population?The sample size (n) is the total number of completed responses gathered from a survey sampling process.
From the given information, using the formula for standard error of a sample proportion:
= √ [p (1-p) / n)]
71% of 1100 of the tribune = 0.0136867% of 900 of the herald = 0.0148381% of 700 of the times = 0.01567Therefore, the sample size of the tribune has the greatest and closest estimate to the actual percentage of voters that supports the governor for reelection,
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