If these are terms of a geometric sequence, they have a common ratio. That is, ...
... (k -1)/(2(1 -k)) = (k +8)/(k -1)
... (k -1)² = 2(1 -k)(k +8) . . . . . multiply by the product of the denominators.
... k² -2k +1 = -2k² -14k +16 . . . eliminate parentheses
... 3k² +12k -15 = 0 . . . . . . . . put in standard form (subtract the right side)
... 3(k +5)(k -1) = 0 . . . . . . . . . factor
Possible values of k are ... -5, +1. The solution k=1 is extraneous, as it makes the first two terms 0 and the third term 8. (It doesn't work.)
The value of k is -5.
_____
The three terms are 12, -6, 3. The common ratio is -1/2.
If f is a polynomial function and xminus−5 is a factor of f, then f(5)equals=_______.
if (x - 5 ) is a factor of f(x ) then x = 5 is a root of f(x) and f(5) = 0
Answer:
[tex]f(5) = 0[/tex]
Step-by-step explanation:
A function [tex]f[/tex] can be simplified by it's roots.
For example, a second order function expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0.[/tex]
Can be expressed in function of it's roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex].
Is [tex]x-5[/tex] is a factor of f, this means that f can be expressed in function of [tex]x - 5[/tex], that is, x = 5 is a root of the equation.
This means that:
[tex]f(5) = 0[/tex]
The solution to w/-7=-21 is 3 true or false
false , w = 147
multiply both sides by - 7 to eliminate the fraction
w = - 7 × - 21 = 147
The solution to the equation w/-7=-21 is not 3 but 147. Therefore, the original statement is false.
Explanation:The equation in question is w/-7 = -21. To solve this equation, we multiply both sides by -7.
When we do this, the equation simplifies to w = -(-21)*7. As -(-21) turns to 21, and 21*7 is equal to 147, we find that the solution to the equation w/-7=-21 is w=147, and not w=3.
Therefore, the statement 'The solution to w/-7=-21 is 3' is false.
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It was -8 degrees in the morning, but by 5pm the temperature decreased 10 degrees. What was the temperature then?
someone anyone help me???!!!!
Try this option (note, this is not the shortest way!), the additional elements are shown by green colour.
Answers: ∠1=∠2=50°; ∠3=82°
1/2divide by 5 =1 blank of 1/2
Answer:
i am pretty sure that it is .2,
Step-by-step explanation:
first, you would do .5 divided by 5 which is 0.1. Then you would do 0.1 divided by 0.5 and you would get 0.2
Find the linearization L(x) of the function at a. f(x) = x^4 + 2x^2, a = 1
The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
9y + 3 > 4y - 7
thats it
Select all the proper fractions
5/3
6/7
12/17
9/5
11/4
6/25
6/7 and 12/17 all the other have to be reduced
These are the proper fractions
6/7
12/17
6/25
These are improper fraction
5/3
9/5
11/4
Need help on this please
If y varies directly with x, write an equation for the direct variation. Then find the value.
If y=3 when x=2, find y when x=1
Plz show work
since y varies directly with y then
y = kx ( k is the constant of variation )
to find k use y = 3 when x = 2
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{3}{2}[/tex]
equation is : y = [tex]\frac{3}{2}[/tex] x
When x = 1 then y = [tex]\frac{3}{2}[/tex] × 1 = [tex]\frac{3}{2}[/tex]
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that}~~ \begin{cases} y=3\\ x=2 \end{cases}\implies 3=k2\implies \cfrac{3}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{3}{2}x} \\\\\\ \textit{when x = 1, what is \underline{y}?}\qquad y=\cfrac{3}{2}(1)\implies y=\cfrac{3}{2}[/tex]
Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?
There are 16 cups in a gallon.
× ×
× ×
× ×
× ×
Answer:
Expression Katrina drinks of water in 7 day = 8 *7 cups .
Step-by-step explanation:
Given : Katrina drinks 0.5 gallons of water per day and There are 16 cups in a gallon.
To find : Which expression shows how to find the number of cups of water she drinks in a week.
Solution : We have given that
Katrina drinks of water per day = 0.5 galoons.
1 gallon = 16 cup .
So, Katrina drinks of water per day = 0.5 * 16 cups.
Katrina drinks of water per day = 8 cups.
1 week = 7 days .
Katrina drinks of water in 7 day = 8 *7 cups.
Katrina drinks of water in 7 day = 56 cups.
Therefore, Expression Katrina drinks of water in 7 day = 8 *7 cups .
choose the best response to explain why 3 (x+12)=3 (x+5)
3(x + 12) does not, and never will, equal 3(x + 5)
We can solve the equation to verify.
3(x + 12) = 3(x + 5)
Distributive property.
3x + 36 = 3x + 15
Subtract 15 from both sides.
3x + 21 = 3x
Cancel like terms.
21 = 0 × this is incorrect.
How do you write 300450390 in expanded form
300000000+400000+50000+300+90= 300450390
Hope this helped! :)
How do you write 300450390 in expanded form ?
300000000+ 400000+ 50000+ 300+ 90= 300450390
Hope this helps. If it does, please mark me brainiest! <3
solve 0.7cos(x)-sin(x)=r for x
where r is a real number
show all steps (if you don't show steps, I'll report the answer)
Try this solution (see the attachment), note:
1. the word 'ctgx' means 'cotangens x'; 2. this equation has roots not for all the real number 'r', it is shown in the 2-d line of the answer; 3. the answer is marked with red colour.
Answer "and" Explanation:
You know that [tex]sin^{2} + cos^{2} x = 1[/tex], so with the given information, you can write
[tex](\frac{7}{10} cos/x-r)^{2} + cos^{2} x= 1[/tex]
that becomes
[tex]\frac{149}{100} cos^{2} / x- \frac{7}{5} r / cos /x + r^{2} - 1 = 0[/tex]
or as well
[tex]149cos^{2} / x -140r / cos / x + 100(r^{2} - 1) = 0[/tex]
The condition for this equation to have real roots is
[tex]70^{2} r^{2} - 149 x 100^{2} (r^{2} - 1) \geq 0[/tex]
hence [tex]r^{2} \leq 149/ 100[/tex]
The roots of the quadratic equation [tex]149t^{2} - 140rt + 100(r^{2} - 1) = 0[/tex] are in the interval [- 1, 1], because with the limitation [tex]|r| \leq \sqrt{149/100}[/tex], the point of a minimum of the polynomial lies between - 1 and 1. Moreover, the polynomial evaluated at - 1 and 1 is > 0 for every r.
Solve for cos x and find the value of sin x.
For the following system of inequalities, which point lies in the solution set?
4x + 2y > 12
x − y > 5
Select one:
A. (1,1)
B. (8,4)
C. (3,9)
D. (9,1)
D
Substitute the coordinates of the given points into the inequalities and if both are true then the point is a solution to the system.
A(1, 1 ) : 4 + 2 = 6 and 1 - 1 = 0 not a solution
B(8, 4 ) : 32 + 8 = 40 and 8 - 4 = - 4 not a solution
C(3, 9 ) : 12 + 18 = 30 and 3 - 9 = - 6 not a solution
D(9, 1 ) : 36 + 2 = 38 and 9 - 1 = 8 is a solution
the point (9, 1 ) is the only point that makes both inequalities true
PLEASE HELP QUICK
Mike was in charge of collecting contributions for the Food Bank. He received contributions of $13, $34, $26, $31, and $28 from five co-workers. Find the median value of these contributions.
median = $28
the median is the middle value of the data arranged in ascending order
rearrange the data in ascending order
13 26 28 31 34
the middle entry is 28
hence median = $28
The median is the middle value so put the numbers in order from smallest to largest.
13,26,28,31,34
The middle value is 28, so the median value is 28
Use substitution to solve the linear system of equations
x = 4.
-y = 1/2x
(4, -2)
(-2, 4)
(4, 2)
(2, -4)
solution = (4, - 2 )
substitute x = 4 into - y = [tex]\frac{1}{2}[/tex] x
- y = [tex]\frac{1}{2}[/tex] × 4 = 2 ( multiply both sides by - 1 )
y = - 2
solution is ( 4, - 2 )
Answer:
I think it is (4,-2)
In figure, MN : NP = 9:1. If MP = 2. Find the distance from M to point K that is 1/4 the distance from M to N?
(A) 1 (B) 1 1/3 (C) 9/20 (D) 1 8/10
The distance MN is 9/(9+1) = 9/10 of the distance MP, so is
... MN = (9/10)×MP = (9/10)×2 = 9/5
The distance MK is 1/4 that, so is ...
... MK = (1/4)×(9/5) = 9/20 . . . . . matches selection (C)
Answer:
C
Step-by-step explanation:
the answer is C. give the person the brainly :) ignore this answer
Show how you could set up and find the exact value of cos(5π/4) in two different ways.
note that 5π /4 is in the third quadrant where the cos is negative
the related acute angle to 5π /4 is π/4, thus
cos( 5π /4 ) = - cos (π/4 ) = - √2/2
We can also evaluate using the addition formula for cosine
• cos (x + y ) = cosxcosy - sinxsiny
note that 5π /4 = (π + π/4 )
cos(5π /4 ) = cos (π + π/4 )
= cos(π)cos(π/4) - sin(π)sin(π/4)
= - 1 √2/2 - 0 = - √2/2
Which expression is equivalent to the expression -2 4/5+6/7: 2 4/5-6/7: -2 4/5-6/7: -(2 4/5+6/7): -(2 4/5 - 6/7)
When you factor out -1, you get ...
... -(2 4/5 - 6/7)
Ruben said that 96.52 ÷ 12.7 equals 7.6.
Is Ruben's answer reasonable?
A.
No, Ruben's answer should be closer to 0.8.
B.
No, Ruben's answer should be closer to 80.
C.
No, Ruben's answer should be closer to 800.
D.
Yes, Ruben's answer is reasonable.
By rounding to the nearest whole numbers and estimating, it is confirmed that Ruben's answer of 96.52 ÷ 12.7 equals 7.6 is indeed reasonable.
Explanation:To assess if Ruben's answer that 96.52 ÷ 12.7 equals 7.6 is reasonable, let's consider the magnitude of the numbers involved. Firstly, we can simplify our estimation by rounding the numbers to the nearest whole digits, which gives us approximately 97 ÷ 13. By using division, we see that 13 goes into 97 about 7 times with some remainder, since 13 x 7 is 91, which is close to 97.
Now, 7.6 is indeed close to our estimation, so we can determine that Ruben's answer is within a reasonable range. Thus, the correct response to whether Ruben's calculation is reasonable would be:
D. Yes, Ruben's answer is reasonable.
Please Answer The Following Questions.
Answer:
4. 73
5. 40°
Step-by-step explanation:
The sum of the angles in a triangle is 180°. The sum of angles in a linear pair is 180°.
4. 45° +62° + k° = 180°
... 107 +k = 180 . . . . . collect terms, divide by °
... k = 180 -107 = 73 . . . . . subtract 107
_____
5. ∠STR = ∠SRT = 20°
... ∠STR +∠STU = 180°
... 20° + 4x = 180°
... 4x = 160° . . . . . . . . subtract 20°
... x = 40° . . . . . . . . . . divide by the coefficient of x
If f(x) = 5x - 2 and g(x) = 2x + 1, find (f - g)(x)
(5x - 2 - g(x))(x)
(5x - 2 -(2x + 1)
(5x - 2 - (2x + 1) : 3x - 3
= 3x - 3
it takes Jupiter 11.9 years to orbit,or go around the sun. Saturn takes 17.6 more years than Jupiter to orbit the sun. About how long does it take Saturn to orbit the sun?
Saturn takes 17.6 more years than Jupiter, so 17.6 + 11.9 will get you how long Saturn will take to orbit the sun, which would give you 29.5 years.
The time it takes Saturn to orbit the sun can be calculated by adding Jupiter's orbit time to the additional time Saturn takes after Jupiter. Saturn takes approximately 29.5 years to complete one orbit around the sun.
To find out how long it takes Saturn to orbit the sun, we know that Jupiter takes 11.9 years and Saturn takes 17.6 more years than Jupiter. So, Saturn takes 11.9 + 17.6 = 29.5 years to orbit the sun.
Dad, Anna, and Todd are walking in a city park together. While dad made 3 steps, Anna made 5 steps. For every 3 of Anna's steps, Todd made 5 steps. Anna and Todd calculated that they did 400 steps together. How many steps did dad make during that period?
Answer:
Dad made 90 steps during that period.
Step-by-step explanation:
Let x,y,z be the steps made by dad,Anna and Todd.
Given that while dad made 3 steps, Anna made 5 steps.
That is [tex]\frac{x}{y}= \frac{3}{5}[/tex]
[tex]y=\frac{5x}{3}[/tex]
And for every 3 steps Anna made, Todd made 5 steps.
That is [tex]\frac{y}{z}= \frac{3}{5}[/tex]
[tex]z=\frac{5y}{3} =\frac{5(\frac{5x}{3}) }{3} =\frac{25x}{9}[/tex]
It is also given that total number of steps made by Anna and Todd is 400.
That is y+z=400
let us plugin y and z in terms of x.
[tex]\frac{5x}{3} +\frac{25x}{9} =400[/tex]
[tex]\frac{15x}{9} +\frac{25x}{9}=400[/tex]
[tex]\frac{40x}{9}=400[/tex]
[tex]x=400X\frac{9}{40} =90steps[/tex]
Hence Dad made 90 steps during that period.
An Uber fare in Columbus is $3.50 for the first ½ mile and additional mileage charged at a rate of $0.30 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $15? Please show or explain your calculations.
If we consider the first half mile to be charged at $0.30 per tenth also, that half-mile costs $1.50 and the charges amount to a fixed fee of $2.00 and a variable fee of $0.30 per tenth mile.
After you subtract the $2 tip and the fixed $2 fee from the trip budget amount, you have $11.00 you can spend on mileage charges. At 0.30 per tenth mile, you can travel
... $11.00/$0.30 = 36 2/3 . . . . tenth-miles
The trip is measured in whole tenths, so you can ride ...
... 36 × 1/10 = 3.6 miles
_____
If you want to see this in the form of an equation, you can let x represent the miles you can travel. Then your budget amount gives rise to the inequality ...
... 3.50 + 0.30((x -.50)/0.10) + 2.00 ≤ 15.00
... 3.50 + 3x -1.50 +2.00 ≤15.00 . . . . . . . eliminate parentheses
... 3x ≤ 11.00 . . . . . . . . . . . . . . . . . . . . . . . . collect terms, subtract 4
... x ≤ 11/3 . . . . . . . . . . . . . . . . . . . . . . . . . . divide by 3
... x ≤ 3.6 . . . . . rounded down to the tenth
City A and city B each have 10 parks. The table shows the number of acres for each park in the two cities. City A 6 9 10 7 10 10 2 5 8 8 City B 5 10 8 11 7 12 6 5 4 5 Select from the drop-down menus to correctly complete each statement. The mean number of acres for each park for the two cities is . The range for the number of acres for parks for the two cities is .
Answer:
The mean number of acres for each park for the two cities is:
City A: 7.5
City B: 7.3
The range for the number of acres for parks for the two cities is : 8
Step-by-step explanation:
The table shows the number of acres for each park in the two cities.
City A: 6 9 10 7 10 10 2 5 8 8
City B : 5 10 8 11 7 12 6 5 4 5
City A:
Minimum acre of park=2
Maximum acre of park=10
Range=Maximum-Minimum
Range=10-2
Range=8
Now mean is calculated as:
[tex]Mean=\dfrac{6+9+10+7+10+10+2+5+8+8}{10}\\\\\\Mean=\dfrac{75}{10}\\\\Mean=7.5[/tex]
City B:
Minimum acre of park=4
Maximum acre of park=12
Range=Maximum-Minimum
Range=12-4
Range=8
Now mean is calculated as:
[tex]Mean=\dfrac{5+10+8+11+7+12+6+5+4+5}{10}\\\\\\Mean=\dfrac{73}{10}\\\\Mean=7.3[/tex]
Answer:
1. about the same
2. the same
Step-by-step explanation:
Need help with this please
X(x+3)-x=5 is a quadratic equation?
True
False
The given equation can be simplified to ...
... x² +2x = 5
This is a quadratic equation. The highest-degree term has degree 2. (TRUE)
Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs. This situation can be represented with a linear equation written in point-slope form, where x represents the number of minutes and y represents the number of paragraphs. Use this information to complete each statement about the linear equation.
Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs.
This situation can be represented with a linear equation written in point-slope form,
Let 'x' represents the number of minutes and,
y represents the number of paragraphs.
In one minute Mila reads 2 paragraphs .
So, y=2x
Let x=1 then y=2
x=2 then y =4
Here slope of equation is 2
Let( x1, y1) and (x2,y2) be the two point the equation y=2x the ,
we can write, (y2 - y1) = m(x2 - x1)
or (y2 - y1) = 2(x2 - x1)
Answer:
(3,6)
Step-by-step explanation:
Given that Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs.
This situation can be represented with a linear equation written in slope-intercept form, as
[tex]y=2x[/tex]
where 'x' represents the number of minutes and,
y represents the number of paragraphs.
Since y intercept is 0 i.e. 0 paras in 0 minutes we have the equation as
[tex]y=2x[/tex]
Since no of minutes or paragraphs cannot take negative values this line is defined only in the I quadrant where both x and y are positive
Out of the points given as follows:
(3,6) (2,3) (-3,6) or (-2,6) ,
we can remove last two since they have negative x which is impossible.
Consider (3,6) (2,3)
Out of these only I point (3,6) satisfies [tex]y=2x[/tex] and second point (2,3) does not satisfy
[tex]y=2x[/tex]
Hence answer is (3,6)