Answer:
Step-by-step explanation:
350x2x5=3500
write absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that has the following solution set: x is less than or equal to 5
The absolute value equations in the form of |x-b|= c(where b is a number and c can be either a number or an expression) that has the following solution set
all numbers such that x ≤ 5 and all numbers such that x ≥ -1.3 will be x -5 ≤ 0 and x + 1.3 ≥ 0.
Isolate the absolute number on one side of the equation to solve an equation containing the absolute value.
Then, resolve both equations by changing their respective contents to the positive and negative values of the variable on the other side of the equation.
In another word, the absolute value equation is the equation that has a real absolute value not imaginary and not binary.
In the mode function, it could be two values if the mode is going negative or positive.
Given that the equation |x-b| = c and the constraint is
all numbers such that x ≤ 5
all numbers such that x ≥ -1.3
so by substituting we will get x -5 ≤ 0 and x + 1.3 ≥ 0.
The complete question is-
Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that has the following solution set
all numbers such that x ≤ 5
all numbers such that x ≥ -1.3
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Please Help Solve This Geometry Problem
So ΔOAP≅ΔOBQ(by AAS) so OA ≅ OB(CPCTC) and PO ≅ OQ(CPCTC)
What do you mean by AAS Theorem ?The AAS theorem, also known as the angle-angle-side theorem, is a theorem in Euclidean geometry that states: "If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent."
Given that,
AP ≅ BQ
AP ⊥ AB and BQ ⊥ AB
so ∠A = 90° and ∠B = 90°
To prove that
AO ≅ BO and PO ≅ OQ
In ΔOAP AND ΔOBQ
AB ≅ BQ (given)
∠A = ∠B = 90°
∠AOP = ∠BOQ (vertically opposite angle theorem)
Therefore,Δ OAP ≅ Δ OBQ
∴ OA ≅ OB (CPCT)
PO ≅ OQ (CPCT)
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81x 1 please help !!!!!!1
Answer:
The answer would 81, LOLOLOLOL
Step-by-step explanation:
7.
Kermit solved the equation below and got x = 5, but he isn't sure he solved correctly.
Show Kermit how he can check his equation using his solution. Let him know if he
solved the equation correctly or not, explaining how you know.
5(x - 4) + 20 = 14
The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To check if Kermit's solution is correct, we can substitute x = 5 back into the original equation and see if it makes a true statement:
5(x - 4) + 20 = 14
5(5 - 4) + 20 = 14
5(1) + 20 = 14
25 ≠ 14
Hence, The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.
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what signs are sin(100°) and tan(100°)?
A)sin(100°) >0 and tan (100°) < 0
B) they both positive
c) sin(100°) < 0 and tan (100°) > 0
d) they both negative
Answer:
A)sin(100°) >0 and tan (100°) < 0
Step-by-step explanation:
You want to know the signs of sin(100°) and tan(100°).
Quadrant100° is an angle in the 2nd quadrant, where angles between 90° and 180° lie.
In that quadrant, the sine function is positive, and the cosine function is negative. The tangent is the ratio of sine to cosine, so the tangent is negative in the 2nd quadrant.
sin(100°) > 0tan(100°) < 0__
Additional comment
Of course, your calculator can help you figure this out. Be sure it is in degrees mode.
The second attachment shows you sine is positive above the x-axis; cosine is positive to the right of the y-axis. Everything else derives from this.
Find the volume of this sphere use 3 for pi 2ft
The volume of the sphere is 32/3 cubic feet.
What is Volume ?
Volume is a measure of the amount of space that a three-dimensional object takes up. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.
To find the volume of a sphere, we use the formula:
V = (4/3) * pi * [tex]r^{3}[/tex]
where V is the volume of the sphere, pi is the constant pi (3.14...), and r is the radius of the sphere.
In this case, the radius of the sphere is given as 2ft. So, substituting this value into the formula, we get:
V = (4/3) * 3 * [tex](2ft)^3[/tex]
= (4/3) * 3 * 8[tex]ft ^ 3[/tex]
= 32/3 [tex]ft ^ 3[/tex]
Therefore, the volume of the sphere is 32/3 cubic feet.
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A baker uses food coloring to color cake batter he needs 4 1/8 ounces of green food coloring the baker only has 2 1/2 ounces how much more green food coloring does he need is the baker only find one ounce of food coloring at the store how many more ounces does the baker need
The baker needs 13/8 more ounces of green food color.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
The process of subtraction can also be termed as finding difference.
Given that,
A baker uses food coloring to color cake batter.
He needs 4 1/8 ounces of green food coloring.
Total amount of food color needed for the batter = 4 1/8 ounces
= (4 × 8 + 1) / 8
= 33/8 ounces
The baker only has 2 1/2 ounces.
Amount of food color he has = 2 1/2 ounces
= (2 × 2 + 1) / 2
= 5/2 ounces
Amount of color he need = 33/8 ounces - 5/2 ounces
= 13/8 ounces
= 13/8 ounces
Hence the baker needs 13/8 more ounces of color.
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i needed help finding x y and z
The value of the given relation of the parallelogram to justified the relation of the given part is x = 7, y = 9 and z = 17.
What about the property of parallelogram?
A parallelogram is a four-sided flat shape that has two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are also equal. The parallel sides of a parallelogram are usually denoted by "a" and "b", while the height or perpendicular distance between the parallel sides is denoted by "h"
Define relation:
A relation is a set of ordered pairs that describe the relationship between two or more variables. Specifically, a relation is a set of ordered pairs (x, y) where x and y belong to some sets of objects, called the domain and range, respectively.
For example, consider the relation R between the set of all real numbers and itself defined by:
R = {(x, y) | y = x²}
This relation is a set of ordered pairs where the second element (y) is equal to the square of the first element (x). In this case, the domain and range of the relation R are both the set of all real numbers.
According to the given information:
As, we know opposite side of parallelogram are equal so,
10x + 14 = x + 77
9x = 63
x = 7
In the same way we also know that in case of parallelogram diagonal bisect equally to each other so,
4y-19 = y + 8
3y = 8 + 19
y = 9
And,
2z + 3 = 37
2z = 34
z = 17
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What is the surface area, in square centimeters, of the toy box?
The surface area of the toy box is 846 [tex]cm^2[/tex].
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here the given toy is form of rectangular prism.
Length = 15 cm , width w = 9 cm and height h = 12 cm
Surface area of the rectangular prism is,
=> A = 2( lw+ wh+ lh) square unit.
=> A = 2( 15*9+9*12+12*15)
=> A = 2(135+108+180)
=> A = 2(423)
=> A= 846 [tex]cm^2[/tex].
Hence surface area of the rectangular prism is 846 [tex]cm^2[/tex].
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A quick quiz consists of a multiple-choice question with 5 possible answers followed by a multiple-choice question with 6 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.
The probability that the submitted responses to the questions were correct will be 2/11.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective.
So, the probability formula is as follows:
Probability = Favourable events/Total events
Now, insert values as follows:
Probability = Favourable events/Total events
Probability = 1+1/5+6
Probability = 2/11
Therefore, the probability that the submitted responses to the questions were correct will be 2/11.
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Explain why domain restrictions are necessary to create inverse trigonometric functions rather than relations.
This would make the inverse function a relation rather than a function, and it would fail the vertical line test.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of trigonometric functions, which are functions that relate the angles of a triangle to the ratios of the lengths of its sides.
Inverse trigonometric functions are used to find the angle whose trigonometric ratio is given. For example, if we know that sin θ = 1/2, we can use the inverse sine function to find the angle θ, which is sin^-1(1/2) = 30°.
However, inverse functions must be functions, meaning that they must pass the vertical line test, where each input (x) produces exactly one output (y). To ensure that inverse trigonometric functions meet this criteria, we need to restrict the domain of the original trigonometric functions.
Trigonometric functions are not one-to-one functions, which means that multiple angles can produce the same value of a trigonometric ratio. For example, sin 30° = sin 150° = 1/2. If we were to define the inverse sine function as the inverse of the sin function without a domain restriction, we would have multiple possible outputs for the same input.
Therefore, this would make the inverse function a relation rather than a function, and it would fail the vertical line test.
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What is the cost price if the selling price = $980 and the loss = 12%?
Therefore, the cost price is $1113.64 if the selling price is $980 and the loss is 12%.
What is cost price?Cost price (also known as CP) is the amount of money that is required to produce or purchase a particular product or service. It includes all the expenses incurred in the production or purchase of a product, such as the cost of raw materials, labor, transportation, rent, and other overhead expenses. The cost price is an important factor in determining the profit margin of a business, as it is used to calculate the selling price of a product or service. In general, the cost price is the amount that a seller pays to acquire a product, while the selling price is the amount that a buyer pays to purchase the same product.
Let's assume that the cost price is "C".
We know that the selling price (S) is $980, and the loss percentage is 12%.
We can use the formula for calculating the cost price:
C = S / (1 - Loss%)
where Loss% is expressed as a decimal (i.e., 12% = 0.12).
Substituting the values, we have:
C = $980 / (1 - 0.12)
C = $980 / 0.88
C = $1113.64
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Jerry and his friends are celebrating Jerry's birthday at Adventure Zone, which has trampolines, mini golf, laser tag, and an arcade. Jerry's mom gives 14 arcade tokens to each kid at the party. In all, she gives out 126 tokens.
Express answer in exact form. Show all work for full credit.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3 .)
The area of the segment formed by a side of the hexagon and the circle is (3π - 9 √(3)) / 4 square inches.
How to calculate area of segment formed?A regular hexagon ABCDEF inscribed in a circle with center O. Let's consider the segment bounded by side AB and the arc ACB. We want to find the area of this segment.
First, find the central angle of the sector AOC. Since the hexagon is regular, the central angle of each sector is 60 degrees. Therefore, the central angle of AOC is 120 degrees.
Next, find the area of sector AOC by using the formula for the area of a sector:
Area of sector AOC = (central angle / 360) × π × radius²
= (120 / 360) × π × (3 / 2)²
= (1 / 3) × π × 9 / 4
= (3 / 4) × π
Now, find the area of triangle AOB. Since the hexagon is regular, triangle AOB is equilateral with side length 3". Therefore, use the formula for the area of an equilateral triangle:
Area of triangle AOB = (1 / 4) × (3)² × √(3)
= (9 / 4) × √(3)
Finally, find the area of the segment by subtracting the area of triangle AOB from the area of sector AOC:
Area of segment AB = Area of sector AOC - Area of triangle AOB
= (3 / 4) × π - (9 / 4) × √(3)
= (3 π - 9 √(3)) / 4
Therefore, the area of the segment formed by side AB and the circle is (3 π - 9 × √(3)) / 4 square inches.
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Think of letters A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z. if BAD=10,DAC=,11andCGI=22 what is PAD?
A rectangular park measuring 200m by 100m has a 2m flower border constructed around the two longer sides and one shorter side. Also a circular fish pond of diameter 20m is in the center of the park and the remainder of the park is grassland. Calculate the following areas correct to the nearest square meters. a) the fish pond. b) the flower borders. c) the grassland. d) the perimeter of the park.
Step-by-step explanation:
a) The area of the fish pond is given by the formula:
Area = πr^2
where r is the radius of the pond (which is half of the diameter). So, in this case, r = 10m.
Area = π(10m)^2
Area = 100π m^2
Area ≈ 314 m^2 (rounded to the nearest square meter)
b) The flower border has a width of 2m on the two longer sides and one shorter side of the rectangular park. So, we need to find the area of three strips of land, each of which is 2m wide and has a different length.
The length of the two longer sides is 200m, so the total length of the two strips along these sides is:
2 × 200m = 400m
The length of the shorter side is 100m, but we need to subtract the width of the fish pond (which is 20m) from it, since the flower border does not extend around the pond. So, the length of the strip along this side is:
100m - 20m = 80m
Therefore, the total area of the flower border is:
2m × 400m + 2m × 80m = 960m^2
c) The grassland is the remaining area of the rectangular park after we subtract the area of the fish pond and the flower border from the total area of the park.
The total area of the park is:
200m × 100m = 20,000m^2
The area of the fish pond is:
π(10m)^2 ≈ 314m^2
The area of the flower border is:
960m^2
So, the area of the grassland is:
20,000m^2 - 314m^2 - 960m^2 = 18,726m^2
d) The perimeter of the park is the sum of the lengths of all its sides.
The two longer sides have a length of 200m each, but we need to add the lengths of the two flower borders (each of which is 2m wide), so the total length of the two longer sides is:
200m + 2m + 2m = 204m
The shorter side has a length of 100m, but we need to add the length of the flower border (which is 2m wide), so the total length of the shorter side is:
100m + 2m = 102m
The perimeter of the park is:
204m + 204m + 102m = 510m
Therefore, the perimeter of the park is 510 meters.
Using the properties of integer exponents, match each expression with its equivalent expression.
125
1
-1
-125
5-3
-5-3
(-5-3)-¹
(-5-3)0
125
→
→
→
Answer:
c
Step-by-step explanation:
Answer question no.3
The diagonal of the Rhombus intersect at point M and thus, m<IMJ is 90 degrees
How to prove the angleIt is important to note the properties of a Rhombus, they are;
All sides of the rhombus are equal.Opposite sides of a rhombus are parallel.Opposite angles of a rhombus are equal.Diagonals bisect each other at right angles, that is 90 degrees in a Rhombus.Diagonals bisect the angles of a rhombus.The sum of two adjacent angles is equal to 180 degrees.From the diagram shown, we can see that the diagonals are;
Diagonal 1: JL
Diagonal 2: IK
These diagonals intersect at point M and since diagonals in a Rhombus intersect at right angles, that is , 90 degrees.
Then, m< IMJ is 90 degrees
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The following data have been gathered for Syncronics, Inc.:
a. The July 31 bank balance was $4,000,
b. The bank statement included $65 in service charges.
c. There was an EFT deposit of $900 on the bank statement for the monthly rent from
the tenant.
d. Checks #541 and #543 for $205 and $320, respectively, were not among the canceled
checks returned with the statement, therefore the checks are outstanding.
e. The July 31 deposit of $350 did not appear on the bank statement
f. The bookkeeper had erroneously recorded a $50 check as $500. The check was
written to a vendor to pay- off an accounts payable.
g. Included with the canceled checks was a check written by Syncronize
Corporation for $200 which was deducted from Syncronics' account. .
h. The bank statement also included an NSF check written by Multimedia, Inc for a $460
payment on accounts receivable
i. The cash account showed a balance of $3,200 on July 31.
REQUIRED:
1. Prepare the July 31 bank reconciliation for Syncronics Inc.
2. Adjust the Cash Balance (using Journal Entries, T accounts, or the Accounting Equation)
·
After answering the provided question, we can conclude that Following expression the completion of the necessary journal entries, the T-account for Cash would show an adjusted balance of $2,575.
What is expression ?An expression in mathematics is a collection of representations, octal, and huge corporations that resemble a clear association or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include inclusion, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
Starting Balance: $4,000
Addition: $900 EFT deposit from tenant
Less: ($65) service charges
Less: ($460) NSF check
$4,375 in adjusted bank balance
Book Balance according to Company Records:
Starting Balance: $3,200
Addition: $350 deposit not yet recorded
($525) in outstanding checks [$205 + $320]
Less: Erroneous $500 check recorded: ($450) [$500 - $50]
$2,575 in Adjusted Book Balance
Bank Reconciliation: Modified $4,375 in bank balance
$2,575 in Adjusted Book Balance
The difference is $1,800. (overdraft)
a. Not yet recorded deposit:
Debit: $350 in cash
Credit: $350 in earnings
b. Uncollected checks:
Debit: $525 Accounts Payable
Credit: $525 in cash
c. Incorrectly recorded $500 check:
Debit: $450 Accounts Payable
Credit: $450 in cash
Following the completion of the necessary journal entries, the T-account for Cash would show an adjusted balance of $2,575.
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complete question
the following data gathered the latest details for Synchronic, Inc.:
A. The bank amount as of July 31 was $4,000.
a. There have been $65 in service fees on the bank statement.
c. The bank statement showed an EFT deposit of $900 for the tenant's monthly rent.
d. The cancelled checks that were included with the statement were not checks #541 and #543, which were for amounts of $205 and $320, respectively.
g. The $350 deposit made on July 31 did not show up on the bank statement.
f. A $50 cheque was mistakenly reported as $500 by the bookkeeper. A seller received the check as payment for a debt.
g. A check from Synchronize Corporation for $200 that was taken out of Synchronic' account was included with the cancelled checks.
h . An NSF check for a $460 payment to an account that was written by Multimedia, Inc. was also included in the bank statement.
i. As of July 31, the bank had a $3,200 balance in the cash account.
1. Complete the bank reconciliation for Synchronic, Inc. on July 31.
2. Modify the company's cash position.
Simplify (3x²-2) + (2x² - 6x + 3).
O 5x² - 6x +1
O 5x² - 6x-1
Ox² - 6x +1
O 5x²-8x +3
Answer:
5x²-6x+1 this is the answer
उजन 441.13 6406 17 Area and Perimeter
Answer: I just want points
Step-by-step explanation:
This is not understandable math.
Carson bought a cost for 40% of the original price, then another 15% off the discounted price. If the cost originally coast $149, what was the final sale sale price Carson paid.
The final price Carson paid was $75.99.
The original cost of the item is $149.
Carson bought the item for 40% off the original price, which means he paid:
$149 x 0.6 = $89.40
Carson paid only $89.40 after he got a 40% discount.
Now, Carson receives an additional discount of 15% off the discounted price. This means he pays:
$89.40 x 0.85 = $75.99
After getting an additional discount of 15% Carson paid $75.99 only.
Therefore, Carson's final sale price for the item was $75.99 after getting 40% and additional 15% discount.
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Find the measure of X
Answer:
X=18.88
Step-by-step explanation:
This is a 90 degree triangle which means that you can use Sin, Cos, Or Tan. In this case you have to use Tan as you don't know the hypotenuse length. Which means you would set up an equation that looks like Tan(42°)=17/x as tangent is opposite over adjacent. Then if you were to solve for X eventually you'll get X= 17/Tan(42°) and if you plug it in a calculator you would get that X= 18.88 or 19 if you round to a whole number.
The vertex of a parabola is (0, 0) and the focus is(1/8,0).What is the equation of the parabola?
The equation of the parabola is
[tex]y = \frac{1}{32} {x}^{2} [/tex]
What is the vertex form of the equation of a parabola?
[tex]y = a {(x - h)}^{2} + k[/tex]
where (h, k) is the vertex and 'a' is a constant that determines the shape of the parabola. For a parabola with a horizontal axis of symmetry (opening to the right or left), the focus is (h + c, k), where c is the distance from the vertex to the focus, and the directrix is the line x = h - c.
Given,the vertex of a parabola is (0, 0) and the focus is(1/8,0).
We want to find equation of the parabola.
Given by In this problem, the vertex is at (0,0) which means h=0 and k=0. Also, the focus is at (1/8,0) which means c=1/8. So, the directrix is the line x = -1/8.
Since the parabola opens to the right, the equation of the parabola can be written as:[tex]y = {(x - 0)}^{2} + 0[/tex]
or simply: [tex]y = a {x}^{2} [/tex]
To find the value of 'a', we need to use the distances formula between the vertex and the focus:
[tex]c = \frac{1}{8} = \sqrt{ \frac{4a}{2} } \\ a = \frac{1}{32} [/tex]
Therefore, the equation of the parabola is:
[tex]y = \frac{1}{32} {x}^{2} [/tex]
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what is the domain of the function?
Answer:
(-infinity, -11) U (-11, 9) U (9, infinity)
Step-by-step explanation:
we have to restrict this so that the denominator isn't 0
to find this, we can factor the denominator to (x+11)(x-9). the zeroes, then, are x=-11 and x=9.
so, the domain must exclude these values, and we get (-infinity, -11) U (-11, 9) U (9, infinity)
Which graph shows a proportional relationship? (Check Screenshot)
Also I need answers ASAP, I’m already behind in this subject :(
Which expression is equivalent to the given expression? - 2 x 2 + 8 x − 9 + 4 x + 7 x 2 + 2 A. - 9 x 2 − 12 x + 11 B. - 5 x 2 + 4 x + 11 C. 5 x 2 + 12 x − 7 D. - 9 x 2 + 4 x − 7
Answer: Option C = 5x^2 + 12x - 7
Step-by-step explanation: First, we need to combine like terms.
-2x^2 + 8x - 9 + 4x + 7x^2 + 2 = (7x^2 - 2x^2) + (4x + 8x) + (-9 + 2) = 5x^2 + 12x - 7
So the expression is equivalent to option C, which is 5x^2 + 12x - 7.
Answer:
ITS THE FIRST ONE
Step-by-step explanation:
-2X2+8
HOPE THIS HELPS
Challenge Question: 146.794/0.643 I bet u 100 bucks to do it!!!!!!
The answer would be 228.295489891
Rounded to the nearest tenth it would 228.3
Wolf packs in the Northern Yukon Territory have territories of various sizes. Pack A has a territory of 900km^2 and of that 600km^2 are mountainous. Pack B has a territory of 700km^2 with 500km^2 being mountainous. Do both territories have the same ratio of mountains to the total range? Write each ratio in the simplest form and compare.
The ratio of pack A is 3 : 2 [tex]km^{2}[/tex] and for pack B is 7 : 5 [tex]km^{2}[/tex] . Pack A has more of mountainous territory.
What is ratio?
One can calculate how much of one quantity is included in the other by comparing two amounts of the same unit and obtaining the ratio.
We are given two packs.
Pack A has a territory of 900 [tex]km^{2}[/tex] and of that 600 [tex]km^{2}[/tex] are mountainous.
So, the ratio in the simplest form is 3 : 2 [tex]km^{2}[/tex] .
Similarly, Pack B has a territory of 700 [tex]km^{2}[/tex] with 500 [tex]km^{2}[/tex] being mountainous.
So, the ratio in the simplest form is 7 : 5 [tex]km^{2}[/tex] .
On comparing the ratios, we get that Pack A has more of mountainous territory than Pack B.
Hence, both territories do not have the same ratio of mountains to the total range.
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Circle M has radius MN, and Circle P has radius PQ.
Points M and P are distinct points.
Choose a translation and a dilation below that
prove Circle M and Circle N are similar.
O
Translate the circled onto point Q and dilate the image with scale factor
Translate the circle M onto point P and dilate the image with scale factor
Translate the circle M onto point P and dilate the image with scale factor
AB
BC
MM
PP
PQ
MN
The answer of the given question based on proofing Circle M and Circle N are similar the correct option is (c) Translate the circle M onto point P and dilate the image with scale factor PQ/MN.
What is Scale factor?A scale factor is a mathematical ratio that describes how the size of an object or a figure changes between two similar shapes. In geometry, two figures are considered similar if they have the same shape, but not necessarily the same size.
The scale factor is defined as ratio of any two corresponding lengths in two similar figures. It is usually denoted by letter "k", and can be calculated as:
k = length of corresponding side in the larger figure / length of corresponding side in the smaller figure
The correct answer is (c):
Translate the circle M onto point P and dilate the image with scale factor PQ/MN.
To prove that Circle M and Circle P are similar, we need to show that they have the same shape, which means that corresponding angles are congruent and corresponding sides are proportional.
Translation is a transformation that preserves shape, so we can translate Circle M onto Circle P to make them coincide. Then, we can dilate the image with a scale factor that preserves the ratio of the radii of the circles.
The scale factor that preserves the ratio of the radii is PQ/MN, because PQ is the corresponding radius of Circle P, and MN is the corresponding radius of Circle M. Therefore, dilating the image of Circle M with a scale factor of PQ/MN will result in a circle that is similar to Circle P, with corresponding angles congruent and corresponding sides proportional.
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