Recall that
[tex]1-x^n=(1-x)(1+x+x^2+\cdots+x^{n-1})[/tex]
So we have
[tex]x^2+x+1=0\implies\dfrac{1-x^3}{1-x}=0\implies x^3=1[/tex]
Then for any [tex]n[/tex], we have
[tex]x^{3n}=(x^3)^n=1^n=1[/tex]
A system of equations has no solution. If y=8x +7 is one of the equations,which could be the other equation
Answer:
Step-by-step explanation:
Two lines that are parallel have the same slope but different y intercepts.
So you could have any equation that satisfies y = 8x + b. The only value that b cannot have is 7. All other values including 0 are fine.
So here are a couple of examples.
y = 8x b = 0
y = 8x + 92
y = 8x + 1/2
y = 8x + pi
y = 8x - 13
7 = 8x - pi
Write a proportion to find how many points x a student needs to score on a test worth 50 points to get a test score of 40%.
Answer:
20 pts
Step-by-step explanation:
50 points corresponds to a 100% grade. How many points (x) correspond to a 40% grade?
x 40%
------------ = ---------
50 pts 100%
Then 100x = 2000, and so x = 20.
A score of 20 points would correspond with a test score of 40%.
Answer:
A score of 20 points would correspond with a test score of 40%.
Step-by-step explanation:
x 40% How many points (x) correspond to a 40% grade?
------------ = ---------
50 pts 100% 50 points corresponds to a 100% grade.
100x = 2000 divide both sides by 100
x = 20
In the system of equations, which variable would it be easiest to solve for?
2x+4y=26
3x+y=9
The easiest to solve for is x in the first equation.
The easiest to solve for is y in the first equation.
The easiest to solve for is x in the second equation.
The easiest to solve for is y in the second equation.
Answer:
Step-by-step explanation:
The easiest to solve for is y in the second equation. Just subtract 3x from both sides, obtaining y = -3x + 9.
The value of x = 1 and y = 6. The easiest to solve for is y in the second equation.
How to estimate the value of the system of equations?
Let the equations be
2x + 4y = 26 ......(1)
3x + y = 9 ........(2)
From (2), we get
3x + y = 9
y = -3x + 9 .......(3)
then substitute the value of y in (1), then we get
2x + 4y = 26
2x + 4(-3x + 9) = 26
Simplifying the above equation, we get
2x - 12x + 36 = 26
-10x + 36 = 26
-10x = 26 - 36
-10x = -10
Then the value of x = 1
Substitute the value of x in (3), then we get
y = -3x + 9
Simplifying the equation, we get
y = -3(1) + 9
y = -3 + 9
y = 6
The value of x = 1 and y = 6.
Therefore, the correct answer is option (d) The easiest to solve for is y in the second equation.
To learn more about algebraic equations
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if f(x)=3x + 10 and g(x)= 2x - 4 find (f-g)( x)
[tex](f-g)(x)=3x+10-(2x-4)=3x+10-2x+4=x+14[/tex]
FIRST GETS BRAINLIEST
Use roots or exponents to solve the each equation. Write fractions in the simplest form
Answer:
8, 36, 81, 11, 7, 1000
Step-by-step explanation:
A
Lets start with number one.
x^2 = 64.
That means that x times x equals 64.
To find x's value, simply find the square root of 64, which is 8.
So x = 8.
For the second one, the square root of x is 6.
That means that 6 x 6 = x
6 x 6 = 36.
So, x = 36.
B
For the third one, the square root of x is 9.
That means that 9 x 9 = x
9 x 9 = 81
So, x = 81.
For the fourth one, x^2 = 121
That means x times x = 121
To find x's value, simply find the square root of 121, which is 11
So, x = 11.
C
For the fifth one, x^3 = 343.
That means that x times x times x = 343
To find x's value, simply find the square root of 343, which is 7.
So, x = 7.
For the sixth and last one, the cube root of x is 10.
That means 10 x 10 x 10 = x.
10 x 10 x 10 = 1,000
So, x = 1,000
I hope this helps! :)
what is the value of x?
14
15
16
17
Answer:
X = 14
Step-by-step explanation:
The given figure is a quadrilateral .In a Quadrilateral sum of angles is 360 degrees.
The given four angles in the quadrilateral are 70°,110°,110° and 5x °.
Applying angle sum property of quadrilateral:
70+110+110+5x=360°
Adding ,
290+5x=360
Subtracting both sides by 290 so that x term can be isolated,
290-290+5x=360-290.
5x=70
Dividing both sides by 5
x=14.
Value of x is 1
Answer:
x=14
Step-by-step explanation:
At a competition with 5 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answer:
a
Step-by-step explanation:
thanks
Answer:
B: Permutation; Number of ways are 60
Step-by-step explanation:
At a competition with 5 runners, medals are awarded for first, second, and third places.
Each of the 3 medals is different.
This is a case of Permutation and the Number of ways are 60.
We have to award 3 medals among 5 runners.
This can be done in 5P3 ways.
= [tex]\frac{5!}{(5-3)!}[/tex]
= [tex]\frac{5\times4\times3\times2\times1}{2\times1}[/tex]
= [tex]5\times4\times3=60[/tex]
Therefore, the answer is option A.
Find the circumference of a circle with a radius of 6. Leave your answer in terms of 3 6 12 36
Answer:
C≈37.7 or 36
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
2x3.14x6=36
Step-by-step explanation:
Ali has a 64 gram bar of chocolate. on day 1 he eats half of his chocolate. on day 2 he eats half of what is left. he does the same each day.
a. when will he have only 1 gram left?
b. how much would a bar of chocolate need to weigh to last All 14 days?
Answer:
A: Day 6
B: 8196 grams (He will become obese for sure)
Step-by-step explanation:
Part A:
As you can infer from the problem, Ali halves his bar everyday, regardless of how the bar is.
Day 1= 32 grams left
Day 2= 16 grams left
Day 3= 8 grams left
Dat 4= 4 grams left
Day 5= 2 grams left
Day 6=1 gram left
He will have one gram left on Day 6
Part B:
This part is basically vice versa. Instead on halving, we need to be doubling. I will do Part a in reverse until Day 14 comes
Day 1= 1
Day 2= 2
Day 3= 4
Day 4= 8
Day 5= 16
Day 6= 32
Day 7 = 64
Day 8= 128
Day 9= 256
Day 10= 512
Day 11= 1024
Day 12= 2048
Day 13= 4096
Day 14= 8192
He will need 8192 grams of chocolate!!!
The number of days when he has only 1 gram left will be 6. And the chocolate needs to weigh to last All 14 days will be 1/256 grams.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
Ali has a 64 grams bar of chocolate.
On day 1 he eats half of his chocolate.
And on day 2 he eats half of what is left.
He does the same each day.
Then the value of a is 64 grams and b is 1/2.
y = 64 · (1/2)ⁿ
Where n is the number of days.
The number of days when he has only 1 gram left will be
1 = 64 · (1/2)ⁿ
1/64 = (1/2)ⁿ
(1/2)⁶ = (1/2)ⁿ
n = 6
The number of days when he has only 1 gram left will be 6.
The chocolate needs to weigh to last All 14 days will be
y = 64 · (1/2)¹⁴
y = 64 · (1/16384)
y = 1/256 grams
The chocolate needs to weigh to last All 14 days will be 1/256 grams.
More about the exponent link is given below.
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HELPPPPPPPPPPPPPPPPPPP
Answer:
C
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x)
= - 4x² - 6x - 1 + (- x² - 5x + 3) ← remove parenthesis
= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms
= - 5x² - 11x + 2 → C
Select the coordinates of two points that are on the line x = 5
(5,0) and (0,5)
15, 0) and (5,-2)
5,0) and (0, 2)
0, 5) and (0, 2)
Answer:
(5,0) and (5,-2)
Step-by-step explanation:
we know that
If two points are on the line x=5, then the x-coordinates of the points must be equal to 5
therefore
The coordinates of two points that are on the line x=5 are
(5,0) and (5,-2)
If `f(x) = 2x^2 - 4x - 3` and `g(x) = (x - 4)(x + 4)`, find `f(x) - g(x).`
Answer:
[tex]\large\boxed{f(x)-g(x)=x^2-4x+13}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-4x-3\\\\g(x)=(x-4)(x+4)=x^2-4^2=x^2-16\qquad\text{used}\ a^2-b^2=(a-b)(a+b)\\\\f(x)-g(x)=(2x^2-4x-3)-(x^2-16)\\\\=2x^2-4x-3-x^2-(-16)\\\\=2x^2-4x-3-x^2+16\qquad\text{combine like terms}\\\\=(2x^2-x^2)-4x+(-3+16)\\\\=x^2-4x+13[/tex]
Which of the following describe an angle with a vertex at E?
Check all that apply.
Answer: The correct options are
(A) DEF.
(C) FED.
Choices:
A. DEF B. DFE C. FED D. EFD
Answer:
FED and DEF
Step-by-step explanation:
vertex is the middle letter
Earth revolves on its axis once every 24 hours. Which statements are true? Check all that apply.
The angular velocity of Earth is π/12 radians per hour.
The angular velocity of Earth is π/12 radians per day.
The angular velocity of Earth is 2π radians per hour.
The angular velocity of Earth is 2π radians per day.
The angular velocity of Earth is 12π radians per day.
Answer:
The angular velocity of Earth is π/12 radians per hour.
The angular velocity of Earth is 2π radians per day.
Step-by-step explanation:
A full circumference of a circle (as the Equator line on Earth) is 2π radians.
Since the planet does a full revolution in 24 hours... that means it makes a full turn in a day.
So, we can see that in a day, the planet rotates 360 degrees... or 2π radians per day!
Now, if you want to find the angular velocity per HOUR... you divide that by 24... so 2π/24 = π/12 radians
So, we can also say it does π/12 radians per hour.
Answer:
a and d on ed
Step-by-step explanation:
what is the ratio of 200 to 350
Answer:
Simply Put:
Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 200 and 350 is 50
Divide both terms by the GCF, 50:
200 ÷ 50 = 4
350 ÷ 50 = 7
The ratio 200 : 350 can be reduced to lowest terms by dividing both terms by the GCF = 50 :
200 : 350 = 4 : 7
Therefore:
200 : 350 = 4 : 7
Step-by-step explanation:
What is the perimeter of a rectangle if the length is 5 and the width is x?
Answer:
The perimeter of the rectangle is 10 + 2x.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2(l + w) where l = length and w = width because you add up the length of all the sides.
So we can plug in our givens into the formula and simplify:
2(5 + x)
So the perimeter is: 10 + 2x
Notice that we cannot simplify the expression further because there is an unknown (the length).
Answer:
2x + 10
Step-by-step explanation:
A rectangle has opposite sides equal
2(5 + x)
2x + 10
Calculate the sale price on a pair of blue jeans if the original price is $45.50 and the markdown is 15%.
Answer:
38.68
Step-by-step explanation:
First we need to find the markdown
markdown = original price * markdown rate
= 45.50 * 15%
= 45.50 * .15
= 6.825
Then we need to find the sale price
sale price = original price- markdown
= 45.50 - 6.825
=38.675
Rounding to the nearest cent
= 38.68
The sale price is 38.68
please help ASAP! i will mark brainliest
Use two pints on the graph to find the slope:
(0,0) and (5,1)
Slope = Change in Y over the change in x.
Slope = (1-0) / (5-0) = 1/5 = 0.20
The slope of the given equation is 0.25 which is greater than 0.20.
The unit rate is greater in the equation.
Please help with this question
Answer:
Many possible answers, including
Major Arc: JKM
Minor Arc: JM
Step-by-step explanation:
The answers you selected in this photo are correct. But let's see why.
A major arc is an arc that is bigger than a minor arc.
They are defined using a starting point and an ending point. In this case, you have many reference points (J, K, L and M), and none is identified in the question. However, the answers shown indicate they're using point J as starting point and M as ending point.
If you look at the positions of J and M on the diagram, you see you can take two routes to join them... the shortest route is the minor arc (going counter-clockwise direction from J to M). While the other route, going clockwise passes through the points K and L is much longer.... and forms the major arc.
That major arc could be identified as JKM, JLM or JKLM, since it starts at J, ends in M, but passes through points K and L, in that order.
What is the solution to x – 10 > – 12?
Answer:
x>-18
Step-by-step explanation:
What is the solution to the system of equations below? y = -2x - 6 and 2y = -4x - 12
no solution
infinitely many solutions
(–3, 0)
(3, –12)
Answer: Infinitely Many Solutions
Step-by-step explanation:
Substitute y into the second equation:
2(-2x-6)=-4x-12
Then you get -4x-12=-4x=-12. Since this is 0=0 it would make it infinitely many solutions.
There are infinitely many solutions to the given system. The equations in the system are y = -2x - 6 and 2y = -4x - 12.
What are the solutions to a system?For a system of linear equations, there are three types of solutions. They are,
Unique solutionNo solutionInfinitely many solutionsInfinitely many solutions are there for a system if they both are equal on both sides while solving. (their graphs intersect at all the points)
Finding the solutions for the given system:Given the system of equations as
y = -2x - 6
2y = -4x - 12
Using substitution method, substituting first equation into the second equation,
2( -2x -6) = -4x - 12
⇒ -4x -12 = -4x - 12
Thus, both sides are equal, and the given system has infinitely many solutions.
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The chart shows how the Lewis family spends their money. Make a circle graph to display the data.
Lewis Family spending:
Housing $10,500
Food $ 7,500
Clothing $3,000
Investments $3,000
Miscellaneous $6,000
Write an equation of a line with the given slope and y-intercept. m = –5, b = –7 y = –5x + 7 y = –7x – 5 y = –5x – 7 y = 5x – 7
Answer:
y = - 5x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
here m = - 5 and b = - 7, hence
y = - 5x - 7 ← equation of line
Since b equals the y-intercept, we automatically know that the answer will be in slope-intercept form which is y = mx + b where m equals slope and b equals the y-intercept.
Given.
m = –5, b = –7
Slope intercept formula.
y = mx + b
Plug in m = -5 and b = -7.
y = -5x - 7 ← Choice C
Clara is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Clara's body after time t:
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41
Heidi was administered 300 mg of the same medicine. The amount of medicine in her body f(t) after time t is shown by the equation below:
f(t) = 300(0.946)t
Which statement best describes the rate at which Clara's and Heidi's bodies eliminated the medicine?
Clara's body eliminated the antibiotic faster than Heidi's body.
Clara's body eliminated the antibiotic at the same rate as Heidi's body.
Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.
Clara's body eliminated the antibiotic at one-fourth of the rate at which Heidi's body eliminated the antibiotic.
Answer:
Clara's body eliminated the antibiotic at the same rate as Heidi's body.
Answer:
Option. B is the answer.
Step-by-step explanation:
Clara is taking a medicine for a common cold. Table that shows the amount f(t) that was present in Clara's body after time t is
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41
Now we will find the explicit formula of geometric sequence.
f(1) = 236.5
and f(2) = 223.73
Therefore, common ratio of the sequence = [tex]\frac{f(2)}{f(1)}=\frac{223.73}{236.5}[/tex]=0.946
So the equation will be f(t) = [tex]236.5(0.946)^{t}[/tex]------(1)
At the same time Heidi was administered 300 mg of same medicine of the same sample.
Amount of medicine in her body f(t) after time t is shown by the equation
f(t) = [tex]300(0.946)^{t}[/tex]----(2)
By comparing these equations 1 and 2, we find common ratio is same as (0.946), which reflects the rate of elimination of the antibiotic was same for both Clara and Heidi.
Option B is correct.
What is the value of x in the equation 1.5(х + 4) — 3 = 4.5(х – 2)?
A 3
B 4
C 5
D 9
Answer:
B.4
Step-by-step explanation:
1.5(x+4) - 3 = 4.5( x-2)-----------------------open brackets on both sides
1.5 x +6 -3= 4.5x- 9.................................collect like terms
3+9 = 4.5 x- 1.5x
12=3x..................................divide by 3 both sides to get x
12/3=x
x=4
ANSWER
x=4
EXPLANATION
The given equation is
[tex]1.5(x + 4) - 3= 4.5(x - 2)[/tex]
Multiply through by 10
[tex]15(x + 4) - 30= 45(x - 2)[/tex]
We expand to get:
[tex]15x + 60 - 30= 45x - 90[/tex]
Group similar terms to get;
[tex]15x - 45x = - 90 - 60+ 30[/tex]
[tex] - 30x = - 120[/tex]
[tex] x= 4[/tex]
What are the 3 different forms of a quadratic function and what do the variables in each represent?
Answer:
general, factored, and vertex form.
general: y=ax^2+b^2+c
Factored: y=(x+a)(x+b)
Vertex: y=a(x-h)^2+k
Step-by-step explanation:
Which description from the list below accuratley describe the relationship between ABC and DEF check all that apply.
Answer:
B. Similar
D. Same Shape
Step-by-step explanation:
In the given triangles:
∠A ≅ ∠D = 22°
∠B ≅ ∠E = 120°
∠C ≅ ∠F = 38°
Hence using the AAA axiom of geometry
Triangle ABC and DEF are similar.
More over due to the similarity of angles the triangles also have same shape.
One more thing, that can be observed is that
DE = 2* AB
EF = 2*BC
DF = 2*AC
The sides of triangle ABC are scaled with a factor of 2 which makes it similar to DEF ..
Hence,
Option B and Option D are correct ..
Answer with explanation:
Given two triangles ΔABC and ΔDEF
⇒Ratio of Sides
[tex]\rightarrow \frac{AB}{DE}(\frac{5}{10})=\frac{BC}{EF}(\frac{3}{6})=\frac{AC}{DF}(\frac{7}{14})=\frac{1}{2}[/tex]
⇒Comparison of Angles
→∠A=∠D=22°
→∠B=∠E=120°
→∠C=∠F=36°
⇒As length of corresponding sides are Proportional ,as well as corresponding Angles of two triangles are same.So Two Triangles are similar either by SSS Similarity or AA Similarity or S AS Similarity.
→If Triangles are similar then they are congruent also.
→The description which accurately describe the relationship between ΔABC and ΔDEF is:
→ Option B: Similar
A bag contains 3 red marbles 4 white marbles and 5 blue marbles if one marble is drawn from the bag what is the probability that the marble will be blue
Follow below steps;
The probability of drawing a blue marble from the bag:
Calculate the total number of marbles in the bag: 3 red + 4 white + 5 blue = 12 marbles.
Calculate the probability of drawing a blue marble: Number of blue marbles / Total number of marbles = 5 / 12 = 5/12.
convert 2000 Swiss francs to Dutch guilders
The conversion from 2000 Swiss francs to Dutch guilders requires a historical exchange rate which is not provided. The Dutch guilder is obsolete since 2002, and precise conversions cannot be made without the rate from the time period when both currencies were in use.
To convert 2000 Swiss francs to Dutch guilders, you would need to know the specific exchange rate between the Swiss franc and the Dutch guilder at the time of the conversion. Unfortunately, as of today, the Dutch guilder is no longer in use, as the Netherlands adopted the euro as its currency in 2002. However, if you were to convert currencies similar to how holders of dollars are willing to exchange $2,500 for euros or vice versa, you would need the specific exchange rate from Swiss francs (CHF) to Dutch guilders (NLG) during the time when both currencies were in use.
Without historical exchange rate data, it is impossible to provide an exact number of Dutch guilders you would receive for 2000 Swiss francs. If you have a specific date in mind, you could find the historical exchange rate for that date and then calculate the conversion using this formula:
Amount in Swiss francs * Exchange rate (CHF to NLG) = Amount in Dutch guilders
Remember, when performing historical currency conversions, it's essential to use the correct exchange rate from the time period in question.
12x+15y=34
-6x+5y=3
Answer:
x = 5/6 , y = 8/5
Step-by-step explanation:
Solve the following system:
{12 x + 15 y = 34 | (equation 1)
{5 y - 6 x = 3 | (equation 2)
Add 1/2 × (equation 1) to equation 2:
{12 x + 15 y = 34 | (equation 1)
{0 x+(25 y)/2 = 20 | (equation 2)
Multiply equation 2 by 2/5:
{12 x + 15 y = 34 | (equation 1)
{0 x+5 y = 8 | (equation 2)
Divide equation 2 by 5:
{12 x + 15 y = 34 | (equation 1)
{0 x+y = 8/5 | (equation 2)
Subtract 15 × (equation 2) from equation 1:
{12 x+0 y = 10 | (equation 1)
{0 x+y = 8/5 | (equation 2)
Divide equation 1 by 12:
{x+0 y = 5/6 | (equation 1)
{0 x+y = 8/5 | (equation 2)
Collect results:
Answer: {x = 5/6 , y = 8/5