Answer: (1, 34) and (2, 17)
Step-by-step explanation:
Step 1: Divide 34 by the smallest prime factor.
34/2 = 17
Step 2: Since 17 itself is a prime number, therefore, it is divisible by 17 only.
17/17 = 1
Step 3: Now further division is not possible. Thus, we will consider 2 and 7 as the prime factors of 34.
Ten runners are racing. How many different ways can the runners finish first, second,
third, and fourth? (Assume there are no ties.)
There are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.
What is the permutation?The permutation is defined as considered an ordered combination.
The general formula for this is:
P(n, r) = n! (n-r)!
Ten runners are racing
There are ten runners who can win first place, hence there are ten ways.
Any of the remaining 9 runners may get up to the second position in nine different ways.
Any of the remaining 8 runners may get up to the third position in eight different ways
Any of the remaining 7 runners may get up to the fourth position in seven different ways
So total number of ways = 10 × 9 × 8 × 7 = 5040
Another way 4 Out of 10 need to select where order matters
= ¹⁰P₄
= 10!/6!
= 10 × 9 × 8 × 7
= 5040
Hence, there are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.
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Write two division problems that both have a quotient of -3.
3/4 h -12= 8 5/8 pls answer with a detailed explanation
The value of h based on the information illustrated is 24 1/2.
How to calculate the value?It should be noted that the fraction given is illustrated as:
3/4h - 12 = 8 5/8
Add 12 to both sides
3/4h - 12 + 12 = 8 5/8 + 12
3/4h = 20 5/8
Multiply both side by 4/3
3/4h × 4/3 = 20 5/8 × 4/3
h = 165/8 × 4/3
h = 27 1/2
Therefore, the value of h is 24 1/2.
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Which lines are parallel to the graph of 4x – y = 6?
Answer:
Step-by-step explanation:
-y = -4x +6
y = 4x -6
Any line with a slope of 4 and y-int other than -6 is parallel to y = 4x-6
Kate cut a 100-foot rope into two pieces.one piece was 5 feet longer than 4 times the length of the other. Find the length of each piece
Answer:
81 feet & 19 feet
Step-by-step explanation:
First person to answer gets brainliest!
Please give me a step-by-step explanation for question m).
No links are allowed, and will be blocked. ❌
Answer:
118
Step-by-step explanation:
[tex]10^{2} + 2(6-3)^{2}[/tex] To start off, we work in the Parenthesis; 6-3 = 3
[tex]10^{2} + 2(3)^{2}[/tex] Now, we must do the exponents; 10^2 = 100; 3^2 = 9
[tex]100 + 2(9)[/tex] Next, we have to distribute the 2 to the 9; 2 x 9 = 18
[tex]100 + 18[/tex] Lastly, we have to add 100 and 18; 100 + 18 = 118
So! Our final answer is 118!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Answer:
118
Step-by-step explanation:
m) [tex]10^{2} + 2(6-3)^{2} = 10^{2} + 2(3)^{2} = 10^{2} + 2(9)= 100 + 18 = 118[/tex]
How to write four hundred seven million six thousand nine hundred and sixty two?
Answer:
470,006,962
hope this helped :)
Answer:
407,006,962
you can check it on the internet ;)
Find the sum of each infinite geometric series. 1- 1/2 + 1/4- . . . .
The sum of the infinite geometric series 6+5+ 25/6 + . . is S = 36
The given geometric series is:
1 - 1/2 + 1/4 - . . ..
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 1
a(2) = -1/2
a(3) = 1/4
Hence, the common ratio is
r = a(2) / a(1) = -1/2
Since 0 < | r | < 1, the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) = 1 and r = -1/2 into the formula:
S = 1 / (1 - (-1/2))
= 1 / (3/2)
= 2/3
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The measure of one angle is 3 degrees more than 1/2 the measure of its supplement. Identify and solve an algebraic equation.
Based on the definition of supplementary angles:
Algebraic equation: A. x + (1/2x + 3) = 180
The measure of the smaller angle is: 62°
The measure of the larger angle is: 118°.
What are Supplementary Angles?The sum of the two angles that are supplement of each other is equal to 180 degrees, hence they are called supplementary angles.
One of the angles = x
The second angle = 1/2x + 3
Since they are supplementary angles, we will have the following algebraic equation:
x + (1/2x + 3) = 180
Solve for x
x + 1/2x + 3 = 180
3/2x = 180 - 3
3/2x = 177
2/3(3/2x) = 2/3(177)
x = 118°
The second angle = 180 - 118 = 62°
Therefore, based on the definition of supplementary angles, we have the following:
Algebraic equation: A. x + (1/2x + 3) = 180
The measure of the smaller angle is: 62°
The measure of the larger angle is: 118°.
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What is the index when x23
x
2
3
is rewritten as a radical expression?
When written as a radical, the index of a expression x²/³ is 2.
What are defined as the radicals?A radical is the inverse of an exponent, which is represented by the symbol "√, also known as the root. It can be a square root or even a cube root, and the number preceding the symbol and otherwise radical is known as an index number and degree.To rewrite the expression x²/³ as a radical expression, we must first understand what such a radical expression is.
A radical expression is a form expression: ⁿ√x.
As, ⁿ√x = x¹/ⁿ
Thus the given expression x²/³ can be written in the above form as;
x²/³ = (³√x)²
Now, the obtained result (³√x)² is written in the radical form where (³√x) is a radical.
As, the expression (³√x) is raised to the 2 power, the index of the expression when the expression is written as x²/³ have a radical is 2.
As a result, the index of the expression x²/³ when rewritten as a radical is 2.
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The complete question is-
What is the index when the expression x^2/3
is rewritten as a radical expression?
what is 49/200 equal to explain
Answer:
0.245
Step-by-step explanation:
Divide both the numerator and denominator by 2.
49/200 will be 24.5/100
If you divide a number by 100, you move the decimal place 2 digits to the left. 24.5/100 will become 0.245
The measure of one angle on a right triangle is 16° more than the measure of the smallest angle.
find the measures of all three angles
Answer: 37° 53° 90°
Step-by-step explanation:
Given:
ΔABC m∠C=90°
Solution:
m∠A+m∠B+m∠C=180°
m∠A+m∠B+90°=180°
m∠A+m∠B+90°-90°=180°-90°
m∠A+m∠B=90°
Let m∠A=x°
Hence,
m∠B=(x+16)°
Thus,
x°+(x+16)°=90°
(2x)°+16°=90°
(2x)°+16°-16°=90°-16°
(2)(x)°=74°
Divide both parts of the equation by 2:
x°=m∠A=37°
m∠B=37°+16°
m∠B=53°
What is the simplified answer to 5.3. √2 ? 8√2 2/2 15√2
The simplified answer to 5.3. √2 will be 7.495.
How to calculate the value?It should be noted that we are to find the simplified answer to 5.3. √2 .
This means that we have to multiply them. This will be:
= 5.3 × ✓2
= 5.3 × 1.1414
= 7.495
Note that the options given aren't complete.
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HELP MEEE!!!! Anna walks 49,879 feet from her house. She rest to get something to eat, then she walked all the way back home. Since Anna walked 49,879 feet from her house, how many miles in total did she walk from her house and walk back?
Answer:24939.5 i think
Step-by-step explanation:
80 percent of 42 is what percent of 16 ?
a. 240
b. 210
c. 150
d. 50
e. 30
The percent of 16, which is equal to the 80 percent of 42 is 210.
What is meant by percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.
Let x be the percent of 16, which is equal to the 80 percent of 42.
80% of 42 = x % of 16
80/100 [tex]*[/tex] 42 = x/100 [tex]*[/tex] 16
80(42)/100 = 16/100 [tex]*[/tex] x
Multiplying both sides of the equation by 16/100, then we get
80(42)/100 [tex]*[/tex] (16/100) = 16/100 [tex]*[/tex] x [tex]*[/tex] (16/100)
simplifying the above equation, we get
80(42)/100 [tex]*[/tex] (16/100) = x
80(42)/16 = x
210 = x
The value of x = 210.
Therefore, the correct answer is option b. 210.
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Answer:
210
Step-by-step explanation:
We can start by finding 80% of 42:
80% of 42 = (80/100) x 42 = 33.6
So, the question now becomes: what percent of 16 is 33.6?
Let's call the unknown percentage "x".
We can set up the following equation:
x/100 x 16 = 33.6
Multiplying both sides by 100/16, we get:
x = (33.6 x 100)/16
x = 210
Perform the indicated division and write your answers in the form P(x)/D(x) = Q(x) + R(x)/D(x) as shown in the following example;
Answer:
[tex]\textsf{1.} \quad 5x+3-\dfrac{3}{x-4}[/tex]
[tex]\textsf{2.} \quad 2x^2-4x+3[/tex]
[tex]\textsf{3.} \quad x^3+3x^2-2x+4+\dfrac{25}{2x-5}[/tex]
Step-by-step explanation:
Long Division Method of dividing polynomials
Dividend: The polynomial which has to be divided.Divisor: The expression by which the divisor is divided.Quotient: The result of the division.Remainder: The part left over.Divide the first term of the dividend by the first term of the divisor and put that in the answer.
Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.
Repeat until no more division is possible.
Write the solution as the quotient plus the remainder divided by the divisor.
Question 1[tex]\large \begin{array}{r}5x+3\phantom{)}\\x-4{\overline{\smash{\big)}\,5x^2-17x-15\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2-20x)\phantom{-b)..}}\\3x-15\phantom{)}\\-~\phantom{()}\underline{(3x-12)\phantom{}}\\-3\phantom{)}\\\end{array}[/tex]
Solution
[tex](5x^2-17x-15) \div (x-4)=\dfrac{5x^2-17x-15}{x-4}=5x+3-\dfrac{3}{x-4}[/tex]
Question 2[tex]\large \begin{array}{r}2x^2-4x+3\phantom{)}\\3x-2{\overline{\smash{\big)}\,6x^3-16x^2+17x-6\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-4x^2)\phantom{-bbbbbbbb.)}}\\-12x^2+17x-6\phantom{)}\\-~\phantom{()}\underline{(-12x^2+8x)\phantom{))))).}}\\9x-6\phantom{)}\\-~\phantom{()}\underline{(9x-6)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Solution
[tex](6x^3-16x^2+17x-6) \div (3x-2)=\dfrac{6x^3-16x^2+17x-6}{3x-2}=2x^2-4x+3[/tex]
Question 3[tex]\large \begin{array}{r}x^3+3x^2-2x+4\phantom{)}\\2x-5{\overline{\smash{\big)}\,2x^4+x^3-19x^2+18x+5\phantom{)}}}\\{-~\phantom{(}\underline{(2x^4-5x^3)\phantom{-bbbbbbbbbbb.bb.)}}\\6x^3-19x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(6x^3-15x^2)\phantom{))))bbbb..).}}\\-4x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(-4x^2+10x)\phantom{)))..}}\\8x+5\phantom{)}\\-~\phantom{()}\underline{(8x-20)}\\25\phantom{)}\end{array}[/tex]
Solution
[tex]\begin{aligned}(2x^4+x^3-19x^2+18x+5) \div (2x-5) & =\dfrac{2x^4+x^3-19x^2+18x+5}{2x-5}\\ & =x^3+3x^2-2x+4+\dfrac{25}{2x-5}\end{aligned}[/tex]
Find a₁ for each arithmetic series.Evaluate S₁₅ for the series 3 x+(3 x-2 y)+(3 x-4 y)+ ......
In the given arithmetic series, the first term is a(1) = 3x and the sum of the first 15 terms is S(15) = 45x - 210y
The given series is:
3x + (3 x-2 y) + (3x-4y) + ......
Notice that this is an arithmetic series with:
the first term, a(1) = 3x
the second term, a(2) = 3x - 2y
the 3rd term, a(3) = 3x - 4y
Hence, the common difference is:
d = (3x - 2y) - 3x = -2y
Recall that the nth term of an arithmetic series is given by:
a(n) = a(1) + (n -1) . d
Substitute n = 15, a(1) = 3x, and d = -2y:
a(15) = 3x + (15 - 1) . (-2y)
a(15) = 3x - 28y
The sum of the first n terms in an arithmetic series is given by:
S(n) = n/2 [a(1) + a(n)]
Substitute n = 15
S(15) = 15/2 [a(1) + a(15)]
S(15) = 15/2 . (3x + 3x - 28y)
S(15) = 15 . (3x - 14y) = 45x - 210y
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Solve each equation. 4t = 48
Every year, the number of birds in a bird sanctuary increases by 3 percent. In 1997, there were 175 birds in the sanctuary. Using this data, predict the number of birds in the sanctuary in 2020.
There are 190 more birds than expected at the refuge.
The information provided in the question indicates that there are 3 percent more birds than there were previously. The sanctuary houses 175 birds, which may be pictured as follows:
There are 175 birds in all.
According to the inquiry, it is rising by 3%.
Number of birds = (175)(3%) = 5.25 at this point.
As a result, given the data, the anticipated enhanced data is as follows:
Added birds is 175 + 5 + 5 + 5 = 190.
190 more birds are therefore expected in the refuge.
How much is a percentage?The final computed numbers should be divided by the total value and then multiplied by 100 to obtain the percentage.
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cindy was able to earn $275 in two weeks . at the same rate , how much will he earn in 6 weeks
Answer 825
Step-by-step explanation:
275/2=137.5
137.5x6=825
In ΔKLM, k = 56 inches, m = 51 inches and ∠M=28°. Find all possible values of ∠K, to the nearest degree.
The possible value of angle ∠K, to the nearest degree is 31 degrees
How to find all possible values of ∠K, to the nearest degree?The given parameters are
Triangle = ΔKLM,
Length k = 56 inches,
Length m = 51 inches
Angle ∠M =28
To calculate the possible value of angle K, we make use of the following sine rule
k/sin(K) = m/sin(M)
Substitute the known values in the above equation
So, we have
56/sin(K) = 51/sin(28)
Cross multiply in the above equation
So, we have
51 x sin(K) = 56 x sin(28)
Evaluate the product in the above equation
So, we have
51 x sin(K) = 26.29
Divide both sides of the above equation by 51
So, we have
sin(K) = 0.52
Take the arc sin of both sides
So, we have
K = 31
Hence, the possible value of angle ∠K, to the nearest degree is 31 degrees
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Which quadratic equation has solutions x=8 and x=−1? clear submit 8x2 7x−1=0 x2 7x−8=0 x2−x 8=0 x2−7x−8=0
The quadratic equation which has solutions x = 8 and x = -1 is [tex]\bold{x^2-7x-8}[/tex] = 0.
An equation of degree 2 is called a quadratic equation. That is, the highest power of x in the equation will be two. It has at most two solutions.
Given the solutions are x = 8 and x = -1.
If x = a is a solution, then (x-a) is a factor for the equation.
So here, x-8 and x+1 are factors of the required quadratic equation.
Thus, the quadratic equation will be, (x-8)(x+1) = [tex]\bold{x^2-7x-8}[/tex] = 0.
We can check if x = 8 and x = -1 are the solutions. Put x = 8 in [tex]\bold{x^2-7x-8}[/tex]
Then, 8 x 8 - 7 x 8 - 8 = 0 and -1 x -1 - 7 x -1 - 8 = 0.
So [tex]\bold{x^2-7x-8}[/tex] = 0 is the quadratic equation with solutions x = 8 and x = -1.
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Use the given rule to write the 4th, 5th, 6th, and 7th terms of each sequence. an = n²/{n+1}
The 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.
According to the given question.
We have,
A formual for finding the gereral term of the sequence i.e.
an = n²/{n+1}.
Since, we have to find the 4th, 5th, 6th, and 7th term of the sequence.
Therefore,
4th term of the sequence is given by
[tex]a_{4}[/tex] = (4)^2/{4 + 1) = 16/5
5th term of the sequence is given by
[tex]a_{5}[/tex] = (5)^2/{5 + 1} = 25/6
6th term of the sequence is given by
[tex]a_{6}[/tex] = 6^2/{6 + 1} = 36/7
7th term of the sequence is given by
[tex]a_{7}[/tex] = 7^2/{7 + 1} = 49/8
Hence, the 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.
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Look at the photo and answer the question
(first person to answer correctly gets brainlyest)
Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 6+7.4+8.8+ . . . ; n=11
The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.
The given arithmetic series is 6+7.4+8.8+ . . .
The summation notion of given series is ∑6+1.4n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=11, [tex]a_{1}[/tex] = 6
To calculate sum of arithmetic series, we need to find [tex]a_{11}[/tex] .
[tex]a_{11} = a_{1} + (n-1)d[/tex]
d = 1.4 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{11}[/tex] = 6 + (11-1)(1.4)
[tex]a_{11}[/tex] = 6 + 14 = 20
On substituting values in sum of arithmetic series formula, we get
[tex]S_{7}[/tex] = (11(6 + 20))/2 = 143
The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.
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Solve for X
Please Give explanation
Answer:
Step-by-step explanation:
[tex]\frac{x}{5} +1=\frac{1}{15}[/tex]
[tex]\frac{x}{5} = \frac{1}{15} -1[/tex]
[tex]\frac{x}{5} = \frac{1-15}{15}[/tex]
[tex]\frac{x}{5} = \frac{-14}{15}[/tex]
multiply both sides by 5
[tex]5*\frac{x}{5} = \frac{-14}{15} *5[/tex]
[tex]x=-\frac{14}{3}[/tex]
Determine whether each statement is always, sometimes, or never true. (Lesson 1-5 )
Two angles that form a linear pair are supplementary.
Two angles that form a linear pair are supplementary: Always TRUE
What do we mean by supplementary angles?Supplementary angles are 2 types whose sum totals 180°. A linear pair's two angles, always are supplementary. However, two angles do not have to be adjacent to just supplementary. The angles are supplementary if they form a linear pair.A linear pair creates a straight angle that contains 180, so you have two angles whose measurements add up to 180, indicating that they are supplementary.Therefore, the statement "two angles that form a linear pair are supplementary" is Always TRUE.
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someone help me for 100 points and brainliest pls
The decimal number with repeating digits can be written as:
0.344... = 31/90
How to write the number as a fraction?Here we have the number:
0.3444....
Where the 4 keeps repeating.
First, we need to multiply this by 10, so we get:
10*0.344... = 3.444...
Now if we subtract the original number we get:
10*0.344... - 0.344... = 3.444... - 0.344...
9*(0.344...) = 3.1
Now, isolating the original number:
0.344... = 3.1/9
Finally, we multiply and divide the fraction by 10 so we get two whole numbers:
0.344... = (10/10)*(3.1/9) = 31/90
0.344... = 31/90
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Identify the segment bisector of JK
The length of JM is
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
What is the numerical value of JK and JM?Given the data in the question;
Point M bisects segment JK.Segment JM = 7x + 5Segment MK = 8xA bisector divides a line or angle into two equal halves.
Hence
Segment JM = Segment MK
7x + 5 = 8x
Solve for x
8x - 7x = 5
x = 5
Now, numerical value of segment JM will be;
Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40
Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
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Ginger's cat gave birth to a kitten that weighed 3 3/8 ounces when it was born. On the day Ginger sold the kitten to its new owner, it weighed 5 1/2 ounces. How many ounces did the kitten gain before it went home with its new owner?
The number of ounces gained by the Kitten before it went home with its new owner is; 3 1/8 ounces.
Fraction subtractionIt follows from the task content that the it is required that the weight gained by the kitten in ounces is to be determined.
Since the kitten weighed 5 1/2 ounces on the day it was sold and weighed; 3 3/8 ounces at birth, the number of ounces gained is;
= 5 1/2 - 3 3/8
= 11/2 - 27/8
= (44 - 27)/8
= 17/8
= 2 1/8 ounces.
Ultimately, the weight gained by the kitten, in ounces following evaluation from the task content is; 2 1/8 ounces.
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