The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The figures for this problem are given as follows:
Original: abcde.Dilated: zyxwv.Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
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Find the measures of each interior angles of a regular polygon having 15 sides
The measure of each interior angle of a regular polygon having 15 sides is equal to option B: 156°.
A polygon is an enclosed figure composed of more than three straight lines. To find the measure of each interior angle of a regular polygon having n sides, we would first find the total sum of interior angles of this polygon. The formula is:
(n-2) × 180°
= (15-2) × 180°
= 13 × 180°
= 2340°
We, here, found that the sum of all interior angles of a regular polygon having 15 sides is equivalent to 2340°. Now, to find the measure of each angle, we can divide this sum by the number of sides as:
2340/15 = 156°.
Therefore, the measure of each angle of a regular polygon having 15 sides is equivalent to 156°.
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Complete question is:
Find the measures of each interior angles of a regular polygon having 15 sides.
A. 106°
B. 156°
C. 206°
D. 256°
a 5-card poker hand is dealt from a standard deck of cards (with 4 suits, and 13 kinds for each suit (2, 3, 4, 5, 6, 7, 8 , 9, 10, j, q, k, a). how many distinct ways are there to form a hand with two pairs?
A 5-card poker hand is dealt from a standard deck of cards and the number of distinct ways are there to form a hand with two pairs are 1326 ways.
To solve this problem, we got to use permutations and the combinations. Given that a 5-card poker hand is dealt from a standard deck of cards and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.
Here 4 suits with 13 different kinds for each and every suit , so number of total outcomes are 13*4 = 52
Here we use combinations, and given that a 5-card poker hand is dealt from a standard deck of cards and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.
The number of distinct ways are there to form a hand with two pairs are given by, C(52,2)
(52 * 51) / 2
(26 * 51)
1326 ways
Therefore, the number of distinct ways are there to form a hand with two pairs are 1326 ways.
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Dr. Grumman got his first job in 2020. In that year, the government took out 6.2% of a person's
income for Social Security, until a person made $137,700. If Dr. Grumman earned $141,340 in
2020, how much did he pay to Social Security?
The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
What are percentages?A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Formula for percentages: (Value/Total value) * 100
Dr. Grumman earned $141,340 in 2020.
The social security he paid is:
(141340)(6.2/100) = 8763.08
Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
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What is the inverse of a function f(x)=2x +1 ?
A•H(x)=1/2x-1/2
B•H(x)=1/2x+1/2
C•H(x)=1/2x-2
D• H(x)=1/2x+2
The inverse of a function f(x)=2x + 1 include the following: A. H(x) = 1/2x - 1/2
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = y = 2x + 1
x = 2y + 1
By rearranging the equation, we have the following:
2y = x - 1
y = (x - 1)/2
H(x) = 1/2(x) - 1/2.
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Write tan theta in terms of a and b.
Answer:ab
Step-by-step explanation:
because..........
What is 4 3/5+5/6 as a mixed number in simplest form
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
163/30
Step-by-step explanation:
4 3/5 in mixed number form would be 23/5
5/6 remains 5/6 as it is not greater than 1, therefore it cannot be simplified.
23/5 + 5/6
in order to add, we have to make the denominators alike. the least common multiple is 30. so we have to not just multiply the denominators by whatever results in 30, but also the numerators.
23 times 6 = 138
5 times 6 = 30
5 times 5 = 25
5 times 6 = 30
138/30 + 25/30
at this point, we can simply just add the numerators
163/30
i hope this helps
What are the zeros of this function?
Answer:
B
Step-by-step explanation:
the zeros are the values of x on the x- axis where the graph crosses.
the graph crosses the x- axis at x = 3 and x = 6
then
the zeros are x = 3 and x = 6
What is the formula used to calculate the surface area for a square pyramid?
The formula used to calculate the surface area of a square pyramid is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
The square pyramid is the geometric shape that has a square base and 4 lateral face. The total number of faces will be five. The base shape is square and the side shape will be triangle. Number of edges in the square pyramid is eight
The surface area is the amount space covered by the surface of the object
Here the surface area of the square pyramid is
A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
Where A is the surface area of the square pyramid
a is the base edge
h is the height of the square pyramid
Therefore, the surface area is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
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Multiply and simplify. Show work to earn full credit. (2 − 3)(7 2 − + 8
We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.
What is distributive property, and what are some examples?When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.
What is distributive property class 7?An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.
Using this property, we can expand the expression as follows:
(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)
Now we can simplify each term separately:
2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110
and
−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165
Therefore, putting the results together, we have:
(2 − 3)(7 2 − + 8) = 110 − 165 = -55
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A plumber earned AED 1,075 when he worked 3. 5 hours. He charged the customer an extra AED 200
for materials. What is his hourly rate?
A plumber worked 3. 5 hours for AED 1,075 in total. He added AED 200 for supplies to the customer's bill hourly rate of the plumber is AED 364.29.
How much is charged, paid, or earned for each hour worked?
Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.
We must first deduct the price of the materials from the plumber's overall profits in order to get his hourly rate:
Income equals AED 1,075 plus AED 200, or AED 1,275.
After that, we may split his total income by the quantity of hours he put in:
Hourly fee is calculated as follows: AED 1,275 / 3.5 hours of work.
Hourly rate is 364.29 AED.
The plumber's hourly charge is therefore AED 364.29.
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hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. what multiplicative rate of change should hal use in his function?0.020.981.021.98
If he want to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually, then the multiplicative rate will be 0.98
The initial investment = $10000
decreasing percentage = 2%
Therefore, the second term will be the 98% of the first term
The first term = 10000
The second term = 10000 × 98/100
= 10000 × 0.98
= 9800
The common ratio is the ratio of the second term to the first term
The common ratio = second term / first term
= 9800 / 10000
= 0.98
Therefore, the multiplicative rate of change should Hal use in his function is 0.98
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which of the following continuous improvement tools is often used to initiate a root cause analysis effort? group of answer choices scatter plot. cause-and-effect (fishbone) diagram. pareto chart. swim lane process map.
Among the continuous improvement tools listed in the query, the cause-and-effect (fishbone) diagram is often used to initiate a root cause analysis effort. This tool helps identify potential causes of a problem by breaking down a complex issue into smaller and more manageable components.
The diagram is shaped like a fishbone, with the problem at the head and the potential causes in the "bones" of the fish. By examining the various factors that could contribute to a problem, a team can begin to isolate the most likely root causes and develop targeted solutions to address them. Other tools like scatter plot, Pareto chart, and swim lane process map can also be useful in continuous improvement efforts, but they may not be the best choice for initiating a root cause analysis
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Which one of the following absolute value equations and inequalities have a solution set that is NOT the empty set?
O |2x-1|-7<-6
O |4x+5| -4=-5
O 3|x+2|-2=-3
O 2|x-5|-4 <-8
Help please Hurry
Based on the data, which of the following best describes the experimental probability of the arrow landing on a black or white section of the spinner? (1 point)
• a
O b
• c
• d
The spinner is equally likely to land on black or white.
The spinner is 3 times more likely to land on white.
The information cannot be concluded from the data.
The spinner is 3 times more likely to land on black.
Answer:
it's d. answer d. 57/76 is the probability of landing on black. that is roughly 3 times as much as the probability of landing in white 19/76. 19 X 3 = 60 which is roughly around the ballpark of 57.
A leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. At that
rate, how many gallons of water will the faucet leak in
48 hours?
Show your
work.
Answer:
Step-by-step explanation:
We can start by finding the amount of water the leaky faucet loses in one hour:
5 gallons / 20 hours = 0.25 gallons per hour
This means that the leaky faucet loses 0.25 gallons of water every hour.
To find how many gallons of water the faucet will leak in 48 hours, we can multiply the rate of leakage per hour by the number of hours:
0.25 gallons/hour x 48 hours = 12 gallons
Therefore, the leaky faucet will lose 12 gallons of water in 48 hours.
question 10
What is the length of segment LN?
21.93
27.57
30.36
55.14
Question 12Miple Choice Worth 4 pores)
(08.02 MC)
The expression 4x+13 represents the time it takes a commuter to travel in the morning to work. The expression 10x-2 represents the time it takes a commuter to
havel in the evening from work What is the total travel time?
Otx+18
Ox+11
06+21
Ox+15
If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.
What is meant by functions?A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.
Given f(x) = 4x + 13 and g(x) = 10x − 2
We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.
Let the equation be (f + g)(x) = f(x) + g(x)
substitute the values in the above equation, we get
= (4x + 13) + (10x − 2)
simplifying the above equation, we get
= 4x + 13 + 10x − 2
= 4x + 10x − 2 + 13
= 4x + 11
Therefore, the expression (f + g)(x) be 4x + 11.
The completed question is:
The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.
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Briana ha $3 in her piggy bank. She has all quarters and dimes. Write and equation in STANDARD FORM to represent this scenario. Use X and Y as your variables (Ax+By=C)
The equation in standard form representing the scenario where Briana has $3 in her piggy bank and has all quarters and dimes, using x for the number of quarters and y for the number of dimes, is [tex]25x + 10y = 300[/tex].
Let x be the number of quarters and y be the number of dimes Briana has in her piggy bank.
The value of each quarter is 25 cents or 0.25 dollars, and the value of each dime is 10 cents or 0.10 dollars. Therefore, the total value of the coins in Briana's piggy bank can be expressed as:
[tex]0.25x + 0.10y[/tex]
Since Briana has $3 in her piggy bank, we can set up the following equation:
[tex]0.25x + 0.10y = 3.00[/tex]
To write this equation in standard form ([tex]Ax + By = C[/tex]), we need to clear the decimals by multiplying both sides of the equation by 100:
[tex]25x + 10y = 300[/tex]
Therefore, the equation in standard form that represents this scenario is:
[tex]25x + 10y = 300[/tex]
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A.seqn T5 = 20, T₂² = T₁ T4 Find the order of the 1st term whose value is greater than 106.
The order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
How did we get the value?Using the given information, we can find the common ratio of the geometric sequence A.
First, we can use the equation T₂² = T₁ T4 to find T4. Substituting n = 4, we get:
T₂² = T₁ T4
20² = T₁ T4
T4 = 400/T₁
Next, we can use the equation T5 = 20 to find T₁r⁴:
T5 = T₁r⁴
20 = T₁r⁴
We can now substitute T4 in terms of T₁ in the equation above:
20 = T₁r⁴
20 = T₁(400/T₁)r⁴
20 = 400r⁴
r⁴ = 1/20
Therefore, the common ratio r = (1/20)^(1/4) = 0.5.
To find the order of the first term whose value is greater than 106, we can use the formula for the nth term of a geometric sequence:
Tn = T₁r^(n-1)
We want to find the smallest value of n such that Tn > 106. Substituting r = 0.5 and rearranging, we get:
T₁(0.5)^(n-1) > 106
T₁ > 212(0.5)^(1-n)
Since T₁ > 0, we can take the logarithm base 0.5 of both sides:
log(0.5)(T₁) < log(0.5)(212) + (n-1)
Solving for n, we get:
n > 1 + [log(0.5)(T₁) - log(0.5)(212)]
Therefore, the order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
Note that the exact value of this order depends on the value of T₁, which was not given in the original problem statement.
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To raise money for a charity, a Year 10 class has decided to organise a school
luncheon. Tickets will cost $6 each. The students have negotiated a special deal for
delivery of drinks and pizzas, and they have budgeted $200 for drinks and $250 for
pizzas. If they raise $1000 or more, they qualify for a special award.
a) write an equation to represent this situation.
b) solve the equation to find the number of tickets they must sell to qualify for the award. explain your answer.
The equation that represents this situation is $6t - $450 ≥ $1000.
The number of tickets that should be sold is 242.
How many tickets should be sold?The form of the equation is:
total revenue - total cost ≥ $1000
(cost of one ticket x number of tickets sold) - cost of pizza and drinks ≥ $1000
($6 x t) - ($200 + $250) ≥ $1000
$6t - $450 ≥ $1000
$6t ≥ $1000 + $450
$6t ≥ $1450
t ≥ $1450 / 6t
t ≥ 242
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Calculate the length of the legs of the triangle.
Answer: 5
Step-by-step explanation:
Select the correct answer.
Consider the equation below.
-2x
|-3 + 1| =
-2√x - 1
Use the graph to find the approximate solutions to the equation.
The approximate solutions to the equation is (0.655, -2.618)
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
-2x
|-3 + 1| =
-2√x - 1
Express the equation properly
So, we have the following representation
-2x|-3 + 1| = -2√x - 1
This gives
-4x = -2√x - 1
Next, we split the equation
y = -4x
y = -2√x - 1
To solve graphically, we plot the equation and write out the point of intersection
Hence, the solution is (0.655, -2.618)
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Sue bought a dress that normally cost $50 .00 it was on sale for 25% off How much did she save?
Answer: 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.
Let's find 25% of 50.
Explanation:
25% of 50 can be written as 25% × 50
= 25/100 × 50
= 25/2 = 12½ = 12.5
Thus, 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.
PLEASE HELP!
a. domain: all real numbers except x=0, x=2, and x=6
range: all real numbers
b. domain: all real numbers except x=0, x=2, and x=6
range: all real numbers except y=0
c. domain: all real numbers except x=6
range: all real numbers
d. domain: all real numbers except x=6
range: all real numbers except y=0
The piecewise function's domain and range are all real numbers, excluding x = 6, and all real numbers, respectively.
What does a math domain mean?The broad range of values within which we are permitted to enter into our function is known as the area of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.
The piecewise function is a function.
In the image that is attached, a function is shown.
The function's defined values are its domain, and its attainable values are its range.
With the exception of the x = 6 range, all real numbers fall inside the domain.
As a result, choice c is the right one.
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2. Choose one of the pair of starting angles in the table below::
(a = 50 degrees
y = 110 degrees)
(a= 30 degrees
b=70 degrees)
(c =30 degrees
y=120 degrees)
Please note you are only using 1 of the the selections above, and they will give different results
(a) What is the angle measurement of first unknown angle? Explain the angle relationship you used.
(b) What is the angle measurement of second unknown angle? Explain the angle relationship you used.
Hint: Remember to start with a relationship where you have one unknown.
(a) The angle measurement of first unknown angle is c = 80 degrees
(b) The angle measurement of second unknown angle is y = 110 degrees
How to find the angle measurement of first unknown angle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees
The angle measurement of first unknown angle will be:
a + b + c = 180 (sum of angles in a triangle is 180 degrees)
c = 180 - a - b
c = 180 - 30 - 70
c = 80 degrees
(b) The angle measurement of second unknown angle will be:
y = 180 - b (sum of angles on a straight line is 180 degrees)
y = 180 - 70
y = 110 degrees
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Mrs. Harris has a piece of lumber that is 11 5/8 inches wide she plans to split the width of the lumber into three equal pieces how wide will each piece be
The size of width of each lumber piece will be 3.875 inches.
What is Algebra?Logic is the arrangement of all those concepts, whereas algebra is the study of abstract concepts.
Making something a little less complicated while both making it easier to attain or understand is the concept of clarity.
Mrs. Harris intends to divide the breadth of a piece of timber that is 11 ⁵/₈ inches broad into three equal pieces.
Convert the mixed fraction number to a decimal number. Then we have
11 ⁵/₈ = 11 + ⁵/₈
11 ⁵/₈ = 11.625 inches
The width of each lumber piece is given as,
⇒ 11.625 / 3
⇒ 3.875 inches
The size of width of each lumber piece will be 3.875 inches.
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6
Find b.
5 m
4 m
M
b
10 m
The value of b is given as follows:
b = 12.5 m.
How to obtain the value of b?The value of b is obtained applying the proportions in the context of the problem.
The rule of three is given as follows:
5 m - b m.
4 m - 10 m.
Applying cross multiplication, the value of b is obtained as follows:
4b = 50
b = 50/4
b = 12.5 m.
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Find x and y if the sequence 2y, 2xy, 2, xy/2, ... is geometric.
The value of x and y in the geometric sequence are 1/r and 1
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
If the first term of the sequence is a ,second term is ar , third term = ar²
r = ar²/ar
In the sequence 2y, 2xy, 2, xy/2, ...
r = 2y/2xy
therefore r = 1/x
r = 2/2xy
r = 1/xy
therefore 1/x = 1/xy
therefore y = 1
x = 1/r
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Please solve the radical equation.
Please show work
Answer:
Step-by-step explanation:
Find common denominator.
1/x + x-1/9x = 1 => 9/9x + x-1/9x = 1 (The common denominator is 9x.)
Combine like terms.
9 + x - 1 / 9x = 1 => x + 8/ 9x = 1
Cancel out 9x from denominator. What you do to one side, you do to the other.
(9x)(x + 8/9x) = 1(9x) => x + 8 = 9x
Solve for x.
8 = 8x => x = 1 (subtract x from both sides at the beginning and then simplify.)
Change the denominator of the fraction
7/y-b to b-y
Answer:
[tex]\frac{- 7}{b - y}[/tex]
Step-by-step explanation:
Algebraic manipulation (i.e. a process involving rearranging or rewriting variables and, multiplication or division, to achieve an algebraic expression in a desired form) will be applied:
The expression in the denominator (y - b) will be algebraically manipulated by being multiplied by negative one:
[tex](y - b)[/tex]×[tex](-1)[/tex]
The parenthesis will be expanded by applying the Distributive Law. The derived variables will be rearranged to achieve the desired form of the algebraic expression:
[tex][(-1)(y)] - [(-1)(b)][/tex] = [tex]-y - (-b)[/tex]
= [tex]-y + b[/tex]
= [tex]b - y[/tex] (Desired form achieved)
∴The multiple factor of negative one will also need to be multiplied with the numerator of the fraction for balance. This is because the negative one (that is being multiplied with the denominator) was NOT present originally:
[tex](-1)[/tex]×[tex](7)[/tex] = [tex]-7[/tex]
∴The desired form of the fraction is:
[tex]\frac{-7}{b - y}[/tex]
The fraction 7/(y - b) after changing the denominator (b - y) becomes - 7/(b - y).
Fraction is a comparison between two mathematical quantities or numbers in general.
The number which is being compared is called Numerator and the with whom it is compared is called Denominator.
In mathematical words, if a fraction is look like A/B where A and B are two numbers then A is called Numerator and B is called Denominator.
Here given the fraction is, 7/(y - b)
So here numerator = 7 and denominator = y - b
We have to change the denominator that is (y - b) with (b - y).
Rearranging the fraction we get,
7/(y - b) = 7/[- (b - y)] = - 7/(b - y).
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