a. The value of r = 3, -1/2.
b. The 4th term of each progression;
for r = 3; AP = 14, GP = 216.for r = -1/2; AP = 7/2, GP = 1/2.What is defined by AP and GP?An Arithmetic Progression (AP) is a collection of terms with the same differences between them. In a Geometric Progression (GP), each successive term is created by multiplying the common ratio by previously acted.As, per the given question;
Let the first three terms of GP be a, ar, and ar².
The 1st, 2nd and 3rd terms of a GP equals 1st, 9th and 21st terms of an AP respectively.
First term are equal; a = a2nd term GP = 9th term of AP; ar = a + 8d. 3rd term GP = 21st term of AP; ar² = a + 20d.where, 'r' is the common ratio in GP and 'd' is the common difference in AP.
Part 1: Multiply equation 1 by 5 and 2 by 2 and subtract 1 from 2.
2ar² - 5ar - 3a = 0
Put a = 8 and solving.
16r² - 40r - 24 = 0.
Factorising the above equation;
(r - 3)(2r + 1) = 0
Thus, r = 3 and r = -1/2
Part 2:
Case 1: For r = 3; a =8;
ar = a + 8d
d = 2.
Thus, 4th term = a + 3d
= 8 + 3×2
4th term = 14.
For GP;
4th term = ar³
= 8(3)³
4th term = 216.
Case 2: For r = -1/2; a =8;
ar = a + 8d
d = -3/2
Thus, 4th term = a + 3d
= 8 + 3×(-3/2)
4th term = 7/2
For GP;
4th term = ar³
= 8(-1/2)³
4th term = -1.
Therefore, the values for the r and 4th term is estimated.
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Easy math, Just to lazy to do it.
Answer:
9 26/30 or 9 13/15
Step-by-step explanation:
20/30 6/30
Answer:
9 13/15
Step-by-step explanation:
A Question 2 (1 point) Retake question
Which variable expression represents the following word phrase?
four times the sum of five and a number, n
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Consider the provided phrase.
Four times the sum of five and a number
Let the number is n and the sum of five and a number can be written as:
[tex]n+5[/tex]
Thus, four times the sum of five and a number can be written as:
[tex]4(n+5)[/tex]
Hence, the required expression is [tex]4(n+5)[/tex].
What is phrase in math?
In mathematics, we may use a phrase to describe an expression. When we describe an expression in words that incorporates a variable, we are doing so by using an algebraic expression. An example of this may be the phrase "greater than" (an expression with a variable).
run the numbers. to conduct a rational analysis of an issue. You can do the math because I was the last person to depart yesterday night and the first person to arrive this morning, and since only the overweight security guy was present. on April 7, 2005, by Dave L. Flag.
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The base rate for workers compensation insurance for roofers in one state is $16.95 per $100 paid to employees. The total monthly payroll for Certified Roofing Contractors is $15,738. What is the monthly premium for workers compensation insurance?
Answer:
3.3972 repeating dbbdeebebbbebe
Step-by-step explanation:
wvehhww3g33gg3g33vv3hh333h33hhh3
Answer:
C. not covered by workers' compensation and could recover damages from the employer.
Step-by-step explanation:
What is 6 1/9 - 3 1/3
I’m in s2
Answer: 2 7/9
Step-by-step explanation:
6 1/9 - 3 1/3
first change so denominators are the same (times the second fraction by 3)
6 1/9 - 3 3/9
now borrow form first fraction
5 10/9 - 3 3/9
subtract whole numbers and numerators with each other
2 7/9
pls give brainiest
solve: let f(x)=2x-1 and g(x)=x^2-4. find g(f(x))
Work Shown:
g(x) = x^2 - 4
g(f(x)) = ( f(x) )^2 - 4
g(f(x)) = ( 2x-1 )^2 - 4
g(f(x)) = (2x-1)(2x-1) - 4
g(f(x)) = 4x^2-2x-2x+1 - 4
g(f(x)) = 4x^2 - 4x - 3
A startup sports public relations company is looking to grow. They currently represent 1 client and plan on representing 2 additional clients each year. The following graph can be used to
help determine the number of clients, y, the company will have after x years.
Based on the context, what is the range of the function?
The range the number of clients, y, the company will have after x years of the function will be -∞ ≤ y ≤ ∞
What is Range and Domain ?The range of a function is the complete set of possible dependent variable values. While domain is the set of all possible independent values. We can substitute domain to get range.
From the given graph, the line of the equation of the graph is a linear. We can then say that y = - ∞, y = 1 and y = ∞
Y = 1 when x = 0
Therefore, the range of the function will be -∞ to +∞ That is,
-∞ ≤ y ≤ ∞
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Answer:
1,∞ is the answer
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Solve the inequalities for x, and match each solution to its number line graph. Two less than of a number (x) is no more than . The sum of two times a number (x) and -2 is at least 8. Seven subtracted from 4 times a number (x) is more than 13. Four added to 3 times a number (x) is less than 19.
in the figure, the first number line goes with x [tex]\leq[/tex]5
the second number line goes with x [tex]\geq[/tex] 5
the third number line goes with x > 5
the fourth number line goes with x < 5
Two less than 3/2 of a number x is no more than 5/2 is shown as:
3/2 x- 2 [tex]\leq[/tex] 5 1/2
3/2 x [tex]\leq[/tex] 11/2 + 2
3/2 x [tex]\leq[/tex] 15/2
3x [tex]\leq[/tex] 15
x [tex]\leq[/tex] 5
The sum of two times a number (x) and -2 is at least 8 is shown as :
2x+(-2) [tex]\geq[/tex] 8
2x - 2 [tex]\geq[/tex] 8
2x [tex]\geq[/tex] 8+2
2x [tex]\geq[/tex] 10
x [tex]\geq[/tex] 5
Seven subtracted from 4 times a number (x) is more than 13 is shown as
4x -7 > 13
4x > 13+7
4x > 20
x > 20 ÷ 4
x > 5
Four added to 3 times a number (x) is less than 19 is shown as
3x + 4 < 19
3x < 19-4
3x < 15
x < 15 ÷ 3
x< 5
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The curve is the graph of function f. Use the graph to find the value of the function for the following values of x: -2,-.5,0,2.5, and 6.
Answer:
1, 0.75, 1.25, 3, 0
Step-by-step explanation:
To find the value of the function, we find the y coordinate of the point with the given x value.
At a school concert the total value of tickets sold was $3888. Student tickets sold for $7 and adult tickets sold for $10. The number of adult tickets sold was 6 less than 4 times the number of student tickets. Find the number of student tickets sold.
Number of student tickets sold = 84
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
Let the number student tickets sold = x
Let the number adult tickets sold = y
7x+10y = 3888 -----------i
y = 4x-6 ----------------------ii
Substituting eq ii in i
7x + 10 ( 4x -6) = 3888
7x + 40x - 60 = 3888
47x = 3888+60
x = 3948 / 47
= 84
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Does the mapping diagram represent a function? Why or why not?
x -7 -1 8
y -4 4
A. No; the input values x = -7 and x= -1 are paired with the same output value.
B. No; each input pairs with only one output. C. No; the output value y = -4 pairs with two different input values.
D. Yes; each input pairs with only one output.
Answer:
D
Step-by-step explanation:
A relation is a function is each input maps onto no more than one output.
graph the lines Slope -1 passing through point (2,2)
The graph of the equation (y = x ) is attached below and this can be determined by using the point-slope form of the line.
Given :
A line with a slope of 1 that passes through the point (2,2).
The following steps can be used in order to sketch the graph a line with a slope of 1 that passes through the point (2,2):
Step 1 - First, determine the equation of the line that passes through the point (2,2) and has a slope of 1
Step 2 - Point-slope form can be used in order to determine the equation of a line.
y-y1 = m(x- x1)
where m is the slope and (x1, y1) is the point on the line.
Step 3 - Substitute the known terms in the above formula.
y-2 = 1(x-2)
Step 4 - Simplify the above equation.
y-2=x-2
x=y
Step 5 - Now, graph the above equation. The graph of the equation
(y = x ) is attached below.
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ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST and also explain what explicit rule is..
what percent of 141963.78 is 380.16
Answer:
It is 0.2678 percent .....
Ray BD bisects angle abc. Find the m angle abd m angle cbd and m abc
m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°;
Bisector BD bisects ∠ABC.
∠ABD= (8x+35)°, ∠CBD= (11x+23)°.
As given, bisector BD bisects the angle ABC so this means, the angle ABC is divided into two halves.
So,
angle ABD= angle CBD.
and ∠ABD= (8x + 35)° (i)
∠CBD= (11x + 23)° (ii)
So,
(8x + 35)° = (11x + 23)°
On solving the above equation, we have
3x= 12
x= 4.
Putting x=4 in (i) we have,
∠ABD= 8(4) + 35
∠ABD= 67°
As ∠ABD = ∠CBD, we have
∠CBD= 67°
Now,
∠ABC= ∠ABD + ∠CBD
∠ABC= 67° + 67°
∠ABC= 134°.
Hence, m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.
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21(x + 1) - 6x = 15x + 21
Answer:
15x = 15x
or
0 = 0
Step-by-step explanation:
21(x + 1) - 6x = 15x + 21
21x + 21 -6x = 15x + 21
21x - 6x = 15x
15x = 15x
or
0 = 0
this equation is always true
whats the distance between points p1=(-3,5) P2=(4,2)
Step-by-step explanation:
First, find the vector.
= (4,2) - (-3,5)
= (4-(-3),2-5)
= (7,-3)
And then, find the distance.
= √(7² + (-3)²)
= √(49 + 9)
= √58 ✓
THIS IS IMPORTANT
Where can you find the pulse that is closest to your head?
elbow
wrist
neck
foot
Answer:
Neck
Step-by-step explanation:
Which one is closest to your head?
T-T
The distance of the segment formed by the two points
is 15. What is the number that goes in the blank?
Explain or show your reasoning.
(-3,-4) (6, _)
The missing coordinate can either be - 16 or 8.
Let the missing coordinate be x.
Now, we know that the distance between (-3, -4) and (6, x) is 15.
Using the distance formula, we get that:
Distance² = (x₂ - x₁)² + (y₂ - y₁)²
Substituting the values in the formula, we get that:
15² = (6 + 3)² + ( x + 4)²
225 = 9² + x² + 16 + 8 x
225 = 81 +x² + 16 + 8 x
225 = x² + 8 x + 97
x² + 8 x - 128 = 0
x² + 16 x - 8 x -128 = 0
x ( x + 16) - 8 ( x + 16) = 0
(x + 16)(x - 8) = 0
x = -16 or x = 8.
Therefore, the missing coordinate can either be - 16 or 8.
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Sixteen participants pre-registered for a workshop that had a total of 30 participants.
Approximately what percentage of all participants pre-registered for the workshop? A 1.9% B 5.3% C 18.8% D 53.3%
Answer: D
Step-by-step explanation:
16/30 x100= 53.3%
Select the approximate value of 9 - √7 on a number line.
The value of 9 - √7 is between 6 and 7:
4 < 7 < 9
⇒ √4 < √7 < √9
⇒ 2 < √7 < 3
⇒ -3 < -√7 < -2
⇒ 9 - 3 < 9 - √7 < 9 - 2
⇒ 6 < 9 - √7 < 7
How many quarts of pure antifreeze must be added to 6 quarts of a 20% antifreeze solution to obtain a 60%
antifreeze solution? (Hint: pure antifreeze is 100% antifreeze.)
...
Answer:
6 quarts
Step-by-step explanation:
You want to know the number of quarts of 100% antifreeze to add to 6 quarts of 20% antifreeze to make a 60% solution.
SetupLet x represent the number of quarts of 100% antifreeze added to the solution. Then the total amount of antifreeze in the mixture is ...
20%(6) +100%(x) = 60%(6 +x)
SolutionSimplifying the equation, we have ...
1.2 +x = 3.6 +0.6x
0.4x = 2.4 . . . . . . . . . subtract 0.6x+1.2 from both sides
x = 6 . . . . . . . . . . divide by 0.4
6 quarts of pure antifreeze must be added.
-x-6=-14 how to solve x
Answer:
x=8
Step-by-step explanation:
-x-6=-14
-x=6-14
x=14-6
x=8
(2 x 10⁴) + (3 x 10³) =
Answer:
23000
Step-by-step explanation:
(2 x 10⁴) + (3 x 10³)
= (2 x 10000) + (3 x 1000)
= 20000 + 3000
= 23000
Complete the final two columns in the following frequency distribution table and then find the percentiles
and percentile ranks requested:
X f cf c%
5 2
4 5
3 6
2 4
1 3
we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.
We are given the frequency distribution table as:
X f
5 2
4 5
3 6
2 4
1 3
We need to find cumulative frequency (c f) and percentiles(c %)
c % = 100 × ( c f / n )
c f means the frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.
n = 20
X f c f c %
5 2 2 10 %
4 5 7 35 %
3 6 13 65 %
2 4 17 85 %
1 3 20 100 %
Therefore, we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.
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A. Write the FF sets using the roster method:
B. Complete the FF by writing each set in three defferent ways :
The roster form of the given sets will be S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}, S = { blue, red, green } and S = { Math, Science, English, Hindi, SST, Computer }.
We are given some sets in descriptive form.
We have to write it in the roster form.
The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
1 ) The set of all counting numbers less than 10.
Roster form will be:
S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}
2) The set of primary colors.
Roster form will be:
S = { blue, red, green }
3 ) The set of all subjects in grade 7 level:
Roster form will be:
S = { Math, Science, English, Hindi, SST, Computer }
Therefore, the roster form of the given sets will be S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}, S = { blue, red, green } and S = { Math, Science, English, Hindi, SST, Computer }.
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2 + (-5) = ? I can't figure this out
Answer:
Step-by-step explanation:
2 + (-5)
just like subtracting
2-5
=-3
Answer:
-3
Step-by-step explanation:
I have had this question before, and -3 is the answer.
HELP PLEASE I WILL GIVE BRAINLYEST! ALGEBRA 1 HW
no brainlyest unless questions are fully answered
Find the value of x.
(6x - 35)°
(3x + 7)°
Answer:
x = 14
Step-by-step explanation:
These are corresponding angles, so the angles are equal to each other.
6x - 35 = 3x + 7
3x - 35 = 7
3x = 42
x = 14
A ball is thrown from an initial height of 6 feet with an initial upward velocity of 40 fVs. The ball's height h (in feet) after / seconds is given by the following.
h=6+401-16r²
Find all values off for which the ball's height is 28 feet.
Round your answer(s) to the nearest hundredth.
The value for which the ball's height is 28 feet are 0.817sec and 1.683sec using quadratic equations.
What is a quadratic equation?
In algebra, a quadratic equation( from Latin quadratus' forecourt') is any equation that can be rearranged in standard form asax^2 + bx + c = 0
where x represents an unknown, and a, b, and c represent known figures, where a ≠ 0. is still, not quadratic, as there's no ax^2 term,( If a = 0( and b ≠ 0) also the equation is direct.)
The figures a, b, and c are the portions of the equation and may be distinguished by calling them, independently, the quadratic measure, the direct measure, and the constant or free term.The values of x that satisfy the equation are called results of the equation, and the roots or bottoms of the expression on its left-hand side. A quadratic equation has at most two solutions.Given,
h(0)=6 ft (six)
v(0)=40 ft/sec (fourty)
h(t)=6+40t-16t2 (equation)
for h=28 ft(twenty eight)
28=6+40t-16t2 (equation)
or 16t2 - 40t + 22 = 0 (equation)
or 8t2 - 20t + 11= 0(equation)
on solving the quadratic equation
t=0.817sec and 1.683sec (answer)
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9. Assessment Practice Which pair of
equations show you how to find 16 – 9?
A9+1 = 10, 10+5 = 15
B 9+1=10,
10+6=16
C9+2=11,
11 + 6 = 17
D 9+1 = 10, 10+9 = 19. Answers
The pair of equations show you how to find 16 – 9 is 9+1=10, 10+6=16. Therefore, option B is the correct answer.
The given numerical expression is 16-9.
What is a numerical expression?A numerical expression in mathematics can be a combination of numbers, and integers combined using mathematical operators such as addition, subtraction, multiplication, or division.
Now, the pair of equations show you how to find 16 – 9 is 9+1=10,
10+6=16
Therefore, option B is the correct answer.
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