Calculating the LCM of all these, one gets 2^2. 3^2 . 5^4 .7^5. Using the factor counting formula, the answer is 3.3.5.6 = {270}
Step-by-step explanation:
Note that for all n, 149^n-2^n is divisible by 149-2=147 by difference of nth powers. That is 3.7^2, so now we can clearly see that the smallest n to make the expression divisible by 3^3 is just 3^2 Similarly, we can reason that the smallest n to make the expression divisible by 7^7 is just 7^5.
Finally, for 5^5, take (mod {5}) and ( mod {25} )of each quantity (They happen to both be -1 and 2 respectively, so you only need to compute once). One knows from Fermat's theorem that the maximum possible minimum n for divisibility by 5 is 4, and other values are factors of 4. Testing all of them(just 1,2,4 using mods-not too bad), 4 is indeed the smallest value to make the expression divisible by 5, and this clearly is NOT divisible by 25. Therefore, the smallest (n) to make this expression divisible by 5^5 is $2^2 .5^4.
Using the factor counting formula, 2^2. 3^2 . 5^4 .7^5 = 3.3.5.6 = {270}
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Blake uses 2 gallons of gas to drive 34.6 miles in his car. Find the rate of change.
Answer:
17.3 miles / gallon
Step-by-step explanation:
RatesRates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)
SolutionGiven information from the question,
2 gallons = 34.6 miles
1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon
3x-y=2 and 12x-4y=4 parellel or perpendicular line
Answer:
They are parallel line.
HELP THIS IS URGENT!!!! During a sale, a store offered a 35% discount on a camera that originally sold for $750. After the sale, the discounted price of the camera was marked up by 35%. To the nearest whole number, what percent of the original price was the price after markup?
Answer:
the percentage is 62%
Step-by-step explanation:
Rent-A-Car charges $50 to rent a car plus $0.25 per mile. Save-To-Rent charges $25 to rent a car plus $0.41 per
After how many miles will the cost be the same to rent a car?
miles
After 156.25 miles will the cost be the same to rent a car. This can be solved by the concept of cross-multiplication.
What is cross-multiplication?Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.
In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.
Let, assume miles be m.
and, Let the total cost be x.
According to the question,
0.25m + 50 = x ........(i)
0.41m + 25 = x ........ (ii)
By solving equation (ii) by (i) we get -
0.16 m - 25 = 0
or, 0.16m = 25
or, m = 25 /0.16
or, m = 156.25
Thus, number of miles = 156.25 miles.
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Use the function f(x) = 4x2 + 8x − 5 to answer the questions.
Part A: Completely factor f(x).
Part B: What are the x-intercepts of the graph of f(x)? Show your work.
Part C: Describe the end behavior of the graph of f(x). Explain.
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.
a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).
b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.
c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.
d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.
How to graph the quadratic function?The quadratic function for this problem is defined as follows:
f(x) = 4x² + 8x - 5.
Hence the coefficients are given as follows:
a = 4, b = 8, c = -5.
The discriminant is given as follows:
D = 8² - 4 x 4 x (-5)
D = 144.
Hence the x-intercepts are given as follows:
x = (-8 + square root (144))/8 = 0.5.x = (-8 - square root (144))/8 = -2.5.Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:
f(x) = 4(x - 0.5)(x + 2.5).
As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.
The y-intercept is given as follows:
f(0) = 4(0)² + 8(0) - 5
f(0) = -5.
The coordinates of the vertex are given as follows:
x = -b/2a = -8/8 = -1.y = -D/4a = -144/16 = -9.More can be learned about quadratic functions at https://brainly.com/question/24737967
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A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have
With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.
How to interpret a standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
We have given,
Mean weight of Eskimo dogs is μ = 30 pound
Standard deviation of Eskimo dogs is σ = 2 pound
The range of weights would 99.7% of the dogs have,
R = μ ± 3σ
R = 30 ± 3*2
R = 30 ± 6
R = (30 - 6) , (30 + 6 )
R = 24, 36
With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.
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Write the equation of a line that is perpendicular to y=14x - 4 and passes through the point (28, 16)
The equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the equation of the line as -
y = 14x - 4
The given equation of line is -
y = 14x - 4
Slope of the line perpendicular to the given line is -
m{p} = -1/14
The equation of this line will be -
y = -(1/14)x + c
For the point (28, 16), we can write -
16 = -(1/14) x 28 + c
c = 16 + 2
c = 18
So, the equation will be -
y = - (1/14)x + 18
Therefore, the equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.
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Does a parabola have an inverse?
An inverse does not exist for a parabola.
What is a parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.
It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
An inverse does not exist for a parabola.
One definition of a parabola includes a line and a point (the focus) (the directrix).
The directrix is not the main focus.
The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.
A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.
Therefore, an inverse does not exist for a parabola.
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will mark u brainliest
Answer:
( - 7, - 1, 1, 4 )
Step-by-step explanation:
( x, y )
where,
x is Domain
y is Range
Hence,
Domain is ( - 7, - 1, 1, 4 )
Help me. The question is giving me problems help.
D/3
The real world situation that can be modelled with the given expression can be modelled as shown below.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
D/3
A real world situation that can be modelled with this expression can be written as follows -
Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.
Therefore, the real world situation that can be modelled with the given expression can be modelled as shown above.
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What is the simplified form of this expression?
(-3x2 + 2x − 4) + (4x2 + 5x + 9)
7x2 + 7x + 5
x2 + 7x + 5
x2 + 7x + 13
x2 + 11x + 1
Answer:
x² + 7x + 5
Step-by-step explanation:
(- 3x² + 2x - 4) + (4x² + 5x + 9)
since both parenthesis are being multiplies by 1 , remove parenthesis
= - 3x² + 2x - 4 + 4x² + 5x + 9 ← collect like terms
= (- 3x² + 4x²) + (2x + 5x) + (- 4 + 9)
= x² + 7x + 5
Help needed! ASAP please!
Answer:
x = - 1 or x = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
3x² + 5x + 2 = 0 ← in standard form
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × 2 = 6 and sum = + 5
the factors are 3 and 2
use these factors to split the x- term
3x² + 3x + 2x + 2 = 0 ( factor the first/second and third/fourth terms )
3x(x + 1) + 2(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(3x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]
In Lewis County , there were 2 , 277 student athletes competing in spring sports in 2014 . That was 110% of the number from 2013, which was 90% of the number from the year before. How many student athletes signed up for a spring sport in 2012
In the spring of 2012, 2300 student athletes participated in a sport.
How do I calculate a percentage?The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
In 2014, there were 2277 student athletes participating in spring sports.
Suppose there were x contestants in 2013.
The answer was 2277, which was 110 percent more pupils competing in 2014 than in 2013. So,
[tex]$110 \%$ of $\mathrm{x}=2277$$\frac{110}{100} \times \mathrm{x}=2277$$\mathrm{x}=\frac{2277 \times 100}{110}$$\mathrm{x}=2070$[/tex]
2070 pupils therefore competed in 2013.
Let y be the student who will be vying in 2012.
Now, the number of pupils competing in 2070 was 90% that of the year 2012's.
So,
[tex]$90 \%$ of $y=2070$$$\begin{aligned}& \frac{90}{100} \times y=2070 \\& y=\frac{2070 \times 100}{90} \\& y=2300\end{aligned}$$[/tex]
As a result, 2300 students competed in the 2012 competition.
Therefore, the answer is 2300.
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Lenny paid $13 for 4 1/3 pounds of apples.
How many pounds of apples can he buy
for $29?
Answer: 9 2/3
Step-by-step explanation:
you take 29 and divide by 13 to get 2.23076923077 and you then take that times the 4 1/3 to get 9 2/3
Answer:
Step-by-step explanation:
13(X-4 1/3)=29
13X-56.3=29
+56.3 = +56.3
13X=85.3
X=6.56
You are running a concession stand at a football game. You are selling snacks and sodas. Each order of nachos costs $2 and each soda costs $1.50. At the end of the night, you made a total of $125. You sold a total of 76 nachos and sodas combined. You must report the number of nachos sold and the number of sodas sold. What equations did you use to solve this
The equations are n + s = 76 and 2n + 1.50 s = 125.
let n = number of Nachos sold
let s = number of sodas sold
Two equations are presented to us, and we can use them together to solve one variable at a time.
Eq. 1: n + s = 76
Eq. 2: 2n + 1.50 s = 125
So, s = 76 - n
Put (76 - n) for s in the second equation
2n + 1.50 (76 - n) = 125
2n + 114 - 1.50 n = 125
2n - 1.50 n + 114 = 125
0.5n + 114 = 125
0.5n = 125 - 114
0.5n = 11
n = 22
s = 76 - 22
s = 54
22 nachos sold and 54 sodas sold.
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HELP ASAP PLS 50!!!!
Identify or mark the missing side or angle that would make triangle ABC a congruent to triangle PDF by SAS
Answer:
AC = PF
Step-by-step explanation:
Given the following set of numbers, use the measures of central tendency to
identify the type of distribution. Defend your answer.
70 67 75 60 67 65
The measure of the central tendency is 67 as the data in the set are integers.
What is a central tendency?A single number that seeks to characterize a set of data by pinpointing the center position within that set of data is referred to as a measure of central tendency.
As a result, measures of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.
Given, A data set 70, 67, 75, 60, 67, 65.
Arranging the data set in ascending order,
60, 65, 67, 67, 70, 75.
Now, The mean of the set is (60 + 65 + 67 + 67 + 70 + 75)/6.
= 67.33.
Mode of the data set 67.
So, The central tendency of the data set is 67 as the data in the set are all integers.
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From midnight to 2:00 am, the temperature dropped 1.4 °c each hour. If the temperature at 2:00am was 11.2 °c, what was the temperature at midnight
The temperature at midnight as required to ve determined in the task content is; 14°C.
What is the temperature at midnight as required to be determined from the given information.According to the task content; the temperature was 11.2°C at 2 : 00am.
However, since the temperature dropped 1.4 °c each hour; we have that;
In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.
On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.
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How do you read FG stats?
Field goal stats include number of made/attempted, percentage made, average points scored per made, total points scored/attempted, and possibly rebounds, assists, turnovers.
FG (field goal) stats are a way of measuring an individual or team's performance in the sport of basketball. Generally, the stats will include the number of field goals made, the number of field goals attempted, the percentage of field goals made, the average number of points scored per field goal made, the total number of points scored, and the total number of points attempted. This data can be used to compare different players or teams, or to track a player or team's performance over time. Depending on the context, other stats such as rebounds, assists, and turnovers may also be included. This data can help coaches, scouts, and analysts make decisions and evaluate performance. Ultimately, it is important to use field goal stats in combination with other data and context to create an accurate picture of a player or team's performance.
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expand the polynomial (x+1)(x+2)(y-3)
Answer: X^2y + 3xy + 2y -3x^2 -9x -6
explanation
1. Foil (x+2)(x+1)
X^2 +2x + x + 2
2. Simplify
X^2 + 3x + 2
3. Distribute x^2 + 3x +2 (y-3)
X^2y + 3xy + 2y -3x^2 -9x -6
Q14
How can I prove (a)
AE is congruent to CE.We can prove by assuming two triangle in the given diagram and by using SAS rule.
How do you find congruent triangles?If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.
What is an alternate angle in a triangle?Alternate angles are angles that occur on opposite sides of the transversal line. If two parallel lines are cut by a transversal then the alternate angles are equal.The pair of angles formed on the inner side of the parallel lines but on the opposite sides of the transversal are called alternate interior angles.
Now we have
Given a triangle ABC.Where E is the midpoint of AC. We have to prove that AE is congruent to CE.
In ΔAED and ΔCED
ED=ED (∵Common side are equal)
∠AED=∠CED (∵Alternate angles)
∠A=∠C (∵Alternate angles)
By ASA rule, ΔAED≅ΔCED
By Corresponding Parts of Congruent triangles
AE=EC
Hence, AE is conruent to CE.
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what is the area of the shaded part, in square meters, below?
Check the picture below.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(4)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{5})(\underset{h}{20})}}\implies 80+50\implies \text{\LARGE 130}~m^2[/tex]
How do you find the 3 side of a triangle?
Answer:
by using sine rule and cosine rule.
Exercise: Use the method of mathematical induction to prove that if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1)
if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1) IS 1
What is meant by integer?An integer, which is pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Examples of integers include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are examples. The set of whole numbers and their antipodes is known as the integers. The set of integers excludes fractions and decimals. For instance, 2,5,0,12,244,15, and 8 are all numbers. Any positive or negative number that does not contain fractions or decimal places is known as an integer, often known as a "round number" or "whole number." For instance, the numbers 3, -10, and 1,025 are all integers, whereas the numbers 2.76 (decimal), 1.5 (decimal), and 3 12 (fraction) are not.P(n) :
1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)
P(1) :
[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]
[tex]1=\frac{6}{6}=1[/tex]
∴ LHS = RHS
Assume P(k) is true
P(k):
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What happens when a function tries to assign or change a value of a variable that has been defined at the module level
When Python constructs a function, it also generates a temporary variable with the same name, and only the function can access the value of that variable.
What is Using a temporary variable?Using a temp variable is the quickest and easiest way to switch the values of two variables. Using the formula temp = a, the first variable's value is stored in the temp variables. By doing this, you can change the values of the two variables so that a = b before assigning the value of temp to the second variable.Tuple packing and sequence unpacking are two additional methods for changing the values of two variables without the usage of a temporary variable. Using commas to divide up the pieces in a tuple is one method of creating a tuple. Additionally, Python examines a task's right side before its left. As a result, the variables are packed into a tuple on the right side of the statement by using commas to separate them, and they are unpacked on the left side using the same number of target variables separated by commas.As long as the statement has the same number of variables on both sides as there are variables, this approach of variable swapping and permutation can be applied to more than two variables.To Learn more About temporary variable Refer To:
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answer fast need in 10 min
10 equally sized slices of the spinner's 250 results. 25 times were made by Diane's dial. 12 spins are for 208.33333333333334 .
What is the probability of spinner?12 spins are for 208.33333333333334, 5 spins are worth 500, and 8 spins are worth 312.5. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. In this case, the probability is 18.
If you spin three times and fall on red (or any other colour), the likelihood is 3/30. The likelihood that the spinner will land on an even number is 5/10. The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it.
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18. Solve for b:
3 (23-2b) + 3b = 48
A. 10
B. 13
C. 7
D. -10
Answer:
Step-by-step explanation:
3(23-2b) + 3b = 48
1. Use the distributive property and distribute the 3 before the parenthesis
3(23-2b) (make sure you read the (-) as part of the 2b so it's -2b
69 - 6b
2. 69 - 6b +3b = 48 (combine like terms...the bs: -6b + 3b)
69 -3b=48
3. 69 - 3b = 48 (subtract 69 from both sides)
-69 -69
4. -3b = -21 (divide both sides by negative three...we want the b to be +
/-3 /-3
Answer: b = 7
So, C is your answer
Can you help me do this exercice that I don't know how to do it, can you help me for this homework ?
After simplifying each expression, we get (2+5a - 10 b), (8a² - 15ca +2c),
(11- 2a+b) and (a+ b) respectively.
What is simplification?
The word simplify means to write an expression, equation or problems
in the simplest form so as to easy to evaluate it. we simplify an expression by removing the parenthesis and collecting like terms.
How can we simplify the expression given in question?
exercise 1.
given, A = 7 - 4a + 7a - 3b -5 -7b +2a
We collect the like term and get
A= 7 - 5 -4a +7a +2a -3b- 7b
A = 2 + 5a -10b
next, given B = 4a × 2a -5c - c +8c -3c × 5a
B = 8a² -6c +8c - 15ca
B = 8a² -15ca +2c
exercise 2.
given, A = 7 + [(2- a) -( 2+a) +9] + (b-5)
at first, we remove the parenthesis and get
A= 7 + [2-a - 2 -a+ 9] +b- 5
A = 7 + 9- 2a +b- 5
after collecting the like term
A = 11- 2a + b
given, B = 15 - [(7-b) - 9- (a-17)]
B = 15 - [7- b- 9 - a+17]
B = 15 - [15 - b -a]
after removing the parenthesis
B = b +a
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In ΔDEF, f = 5 cm, m∠E=79° and m∠F=75°. Find the length of d, to the nearest 10th of a centimeter.
Using sine and cosine rule, the length of d in the triangle is equal to 4.5cm
What is Sine RuleThe sine rule is a mathematical formula used to calculate the lengths of the sides and angles of any triangle when given two angles and one side or two sides and one angle. It is also known as the law of sines.
To find the length of d, we have to find the length of E.
Using sine rule;
f / sin F = e / sin E
5 / sin 75 = e / sin 79
e = 5sin79 / sin 75
e = 5.7cm
To find the length of d, we have to find the angle D by using the sum of angle theorem.
m∠ E + m∠ F + m∠ D = 180°
79 + 75 + m∠ D = 180
m∠ D = 180 - 154
m∠ D = 26°
Using cosine rule
d² = e² + f² - 2efCosD
d² = 5.7² + 5² - 2(5.7)(5)cos26
d² = 20.615598
d = √20.615598
d = 4.5cm
The length of side d is 4.5cm
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AOC and BOD are diameter of a circle, centre O, prove that ABD and DCA are congruent by RHS
It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.
RHS congruency criteria:Triangles must have equal corresponding sides and equal corresponding angles in order to be congruent.
According to the RHS congruence theorem, two right-angled triangles are congruent if their respective hypotenuses and sides are the same as those of another right-angled triangle.
Here we have
AOC and BOD are diameters of a circle and have a center O.
It is given that AOC and BOD are diameters of a circle.
From the triangles Δ AOC and ΔBOD
⇒ BD = CA [ Diameters of the circle i.e Hypotenuse of triangles ]
⇒ ∠BAD = ∠CDA [ Right angles in a semicircle is 90°]
⇒ AD = AD [ Common in both triangles i.e sides of triangles ]
Thus, Using RHS congruence criteria
⇒ ΔABD ≅ ΔDCA
Hence,
It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.
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