Answers
Answer:
r = 2Step-by-step explanation:
[tex]a_n-\text{geometric sequence}\\\\a_1,\ a_2,\ a_3,\ ...,\ a_n-\text{terms of a geometric sequence}\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\hdots=\dfrac{a_n}{a_{n-1}}-\text{common ratio}\\\\\text{We have:}\ a_1=2,\ a_2=4,\ a_3=8,\ a_4=16,\ ...\\\\\text{The common ratio:}\\\\r=\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=2[/tex]
Related Questions
solve 2x^2 + 8 = 0 by graphing the related function
Answers
The solutions to the equation [tex]\( 2x^2 + 8 = 0 \)[/tex] are complex numbers [tex]\( x = 2i \) and \( x = -2i \), where \( i \)[/tex] is the imaginary unit.
The statement that the graph of [tex]\( 2x^2 + 8 = 0 \)[/tex] does not cross the x-axis is correct, as the graph of this equation represents a parabola that opens upwards and is centered above the x-axis, meaning it has no real roots.
To find the solutions for the equation [tex]\( 2x^2 + 8 = 0 \)[/tex], we can start by isolating [tex]\( x^2 \):[/tex]
[tex]\[ 2x^2 = -8 \][/tex]
Dividing both sides by 2:
[tex]\[ x^2 = -4 \][/tex]
Now, to solve for ( x ), we take the square root of both sides:
[tex]\[ x = \pm \sqrt{-4} \][/tex]
[tex]\[ x = \pm 2i \][/tex]
So, the solutions to the equation [tex]\( 2x^2 + 8 = 0 \)[/tex] are complex numbers [tex]\( x = 2i \) and \( x = -2i \), where \( i \)[/tex] is the imaginary unit.
These are the roots of the equation, even though they do not lie on the real number line.
Hence, while there are no real solutions, there are indeed complex solutions for the given function.
The function whose graph is shown below has the following characteristics.
•Two relative minima
•Two relative maxima
○True
○False
Answers
Answer with explanation:
A function is said to attain maximum in the interval , if you consider any two points on the curve suppose (a,b) and (c,d)
if , c>a
Then , f(d) > f(a).
A function is said to attain minimum in the interval,
if ,c>a
Then,f(d)< f(a).
A function can have more than one relative Maximum and more than one relative Minimum.
The function whose graph is given here has following Characteristics
•Two relative minima
•Two relative maxima
is True .
convert -3 degree to farenheit
Answers
Answer:
26.6 degrees
Step-by-step explanation:
Use the converting formula:
(-3°C × 9/5) + 32 = 26.6°F
-3 degrees to Fahrenheit would be 26.6
The formula is attached in the image below
-3 × 1.8 = -5.4
-5.4 + 32 = 26.6
The student council is selling sweatshirts with the school name and enim...
shirts come in three different colors, two different styles and three different sizes.
How many different types of sweatshirts are available?
Answers
In order to find all the types of sweatshirts, we simply have to multiply all the numbers by all the factors.
3 colors * 2 different styles * 3 different sizes = 18 different types of sweatshirts
The total of 18 different types of sweatshirts are available if shirts come in three different colours, two different styles and three different sizes.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
The student council is selling sweatshirts with the school name and shirts come in three different colours, two different styles and three different sizes.
Total number of different sweatshirts = 3×2×3
= 18
Thus, the total of 18 different types of sweatshirts are available if shirts come in three different colours, two different styles and three different sizes.
Learn more about permutation and combination here:
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What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)}
{x|x = -5, -4,-2, 0, 2)
{yly = -9, -3, 0,5,7)
{x|x= -9,-5, 4, -3, -2, 0,2 5,7}
{yly = -9, -5, -4 -3 -2,0, 2, 5, 7}
Answers
Step-by-step explanation:
range is all the y values
{y|y=-9, -3, 0, 5, 7}
The range of a function are all the ys included in the graph. In this case that would be:
(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)
Remember to order it from least to greatest:
{yly = -9, -3, 0,5,7}
Hope this helped!
~Just a girl in love with Shawn Mendes
On Monday there were 92 fish in the
fish tank. On Tuesday 4 fish were
sold, on Wednesday 1 fish was sold,
on Thursday 4 fish were added to the
tank, and on Friday 3 fish were sold.
How many fish were in the fish tank
at the end of the week?
Answers
Answer:
35
Step-by-step explanation:
92-5+4-3=35
Match the expression with its name.
10x2 – 5x + 10
quadratic trinomial
cubic monomial
not a polynomial
fourth-degree binomial
Answers
Answer:
[tex]\large\boxed{10x^2-5x+10\ -\ \bold{quadratic\ trinomial}}[/tex]
Step-by-step explanation:
[tex]\text{quadratic trinomial}\ -\ ax^2+bx+c\\\\\text{cubic monomial}\ -\ ax^3\\\\\text{not a polynomial}\ -\ \dfrac{a}{x}\\\\\text{fourth-degree binomial}\ -\ ax^4+bx[/tex]
[tex]10x^2-5x+10\\\\\text{the highest power of variable (x) is 2}\to \boxed{x^2}\ \to\ \bold{quadratic}\\\\\text{polynomial has 3 terms}\ \to\ \boxed{10x^2,\ -5x,\ 10}\ \to\ \bold{trinomial}[/tex]
Which product is equivalent to 25x2 – 16?
Answers
Answer:
The correct answer would be 34
Step-by-step explanation:
When solving an expression, we would first solve the operator with the highest precedence. In mathematics, there are four basic operators. Addition, subtraction, multiplication and division. The precedence of Division and multiplication is higher than the precedence of Addition and subtraction. So by solving this with the precedence, we would first solve the multiplication operator which is 25 * 2, it will give 50, then we will subtract 16 from it like 50-16, which will give us 34.
Answer:
(5x+4)(5x-4)
Step-by-step explanation:
The product expression can be obtained by factorizing the expression 25x²-16 provided in the question.
The expression is a difference of two squares whose factors are generally
(a-b)(a+b)
√25x² is 5x
√16 is 4
Therefore the product required is (5x+4)(5x-4)
25x²-16 is equivalent to (5x+4)(5x-4)
19. x² + x = 6
the graf
Factors:
Solution(s):
Answers
For this case we must factor the following equation:
[tex]x ^ 2 + x-6 = 0[/tex]
We must find two numbers that, when multiplied, obtain -6 and when summed, obtain +1. These numbers are: +3 and -2
So, we have to:
[tex](x + 3) (x-2) = 0[/tex]
The roots are:
[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]
ANswer:
[tex](x + 3) (x-2) = 0[/tex]
Which expression is equivalent to (5x^5)(4x)^3
Answers
Answer:
5x. 5x. 5x. 5x. 5x. 4x. 4x. 4x
Step-by-step explanation:
Just seperate all of the numbers out. Because 5x is raised to the fifth it is being multiplied by itself 5 times, the same goes for 4.
write three equivalent fractions for 60.1% with denominators of 1,000, 100, and 10
Answers
Final answer:
Three equivalent fractions for 60.1% with different denominators are found by converting the percent to a decimal and then to the requested fractions. The fractions are 601/1,000 (simplest form), 60.1/100 simplifies to 601/1,000, and 6.01/10 simplifies to 601/1,000.
Explanation:
To write three equivalent fractions for 60.1% with denominators of 1,000, 100, and 10, we first convert the percent to a decimal by dividing by 100. So, 60.1% becomes 0.601. This decimal can then be written as a fraction with the various denominators.
With a denominator of 1,000: 0.601 × 1,000/1,000 = 601/1,000
With a denominator of 100: 0.601 × 100/100 = 60.1/100 which simplifies to 601/1,000
With a denominator of 10: 0.601 × 10/10 = 6.01/10 which simplifies to 601/1,000
Note that 601/1,000 is the simplest form for the fraction equivalent of 60.1%. When we adjust for the different denominators, we always arrive back at the equivalent fraction of 601/1,000 because it is the simplest form.
How many x-intercepts does the graph of y = 2x2 + 5x + 9 have?
Answers
Answer:
The graph of y = 2x² + 5x + 9 has zero x-intercepts.Step-by-step explanation:
x-intercepts are for y = 0.
Put y = 0 to the equation y = 2x² + 5x + 9:
2x² + 5x + 9 = 0
Calculate the discriminant of quadratic equation ax² + bx + c = 0:
Δ = b² - 4ac
if Δ < 0, then an equation has no solution
if Δ = 0, then an equation has one solution
if Δ > 0, then an equation has two solution.
2x² + 5x + 9 = 0
a = 2, b = 5, c = 9
Δ = 5² - 4(2)(9) = 25 - 72 = -47 < 0 - no solution
There are zero x- intercepts of given function.
X- Intercepts:To find x- intercepts, substitute [tex]y=0[/tex] in the function.
Given function is, [tex]y=2x^{2} +5x+9[/tex]
Substitute [tex]y=0[/tex] in above equation.
[tex]2x^{2} +5x+9=0\\\\[/tex]
The graph of function where crosses the x- axis that point is known as x- intercepts of function.
Graph of given function attached below, It is observed that graph will not crosses the x axis at any point.
Thus, There are zero x- intercepts of given function.
Learn more about the intercepts of function here:
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Complete the table for the given rule y=6x-4
Answers
Answer:
1 = 2
3 = 14
10 = 56
Step-by-step explanation:
y = 6x - 4
y = 6 - 4
y = 18 - 4
y = 60 - 4
Step-by-step explanation:
In first there is 2
ln second there is 14
ln third there is 56
I hope this is right answer!
Event v occurs 28% of the time on Tuesdays.
and event v and event w occur together 19%
of the time on Tuesdays. Given that event v
occurs on a Tuesday, what is the probability
that event w occurs with event v?
A. 47%
B. 58%
C. 68%
D. 75%
Answers
Answer:
68%
Step-by-step explanation:
Probability of occurrence of Event v = P(v) = 28% = 0.28
Probability of occurrence of both Events v and Event w together = P(v and w) = 19% = 0.19
We have to find what is the probability that event w occurs with event v given that event v occurs on a Tuesday. This is a conditional probability. In other words we have to find what is the probability of event w given that event v occurs of Tuesday. i.e we have to find P(w|v)
The formula to calculate this conditional probability is:
[tex]P(w|v) = \frac{P(v \cap w)}{P(v)}[/tex]
Using the given values, we get:
[tex]P(w|v) = \frac{0.19}{0.28}\\\\ P(w|v) = 0.68\\\\ P(w|v) = 68\%[/tex]
Therefore, the probability that even w will occur with event v given that event v occurs on Tuesday is 68%
Given the following coordinates complete the reflection transformation. A(−5,0) B(−3,3) C(−3,0) Transformation: Complete the double reflection over the lines x=−2 followed by x=1. A"( , ) B"( , ) C"( , )
Answers
Answer:
A''(1,-1) B''(3,2) C''(3,2)
Step-by-step explanation:
A(−5,0) B(−3,3) C(−3,0)
reflection over x=-2
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 3,1 and 1
after reflections, the perpendicular distance will be 6,2,2, and the points will be at
A'(1,0) B'(−1,3) C'(−1,0)
again reflection over x=1
Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 0,2,2
after reflections, the perpendicular distance will be 0,4,4 and the points will be at
A''(1,-1) B''(3,2) C''(3,2)!
plz help me plz plz plz
Answers
Answer:
195
Step-by-step explanation:
9 times 10 is 90 and 7 times 15 is 105
so 105+90=195
Answer:
195 cm
Step-by-step explanation:
The area of ABCD is 195 cm.
Multiply the sides together:
9 ⋅ 10 = 90
7 ⋅ 15 = 105
Add them together:
105 + 90 = 195
Therefore, the area of ABCD is 195 cm.
The following table shows a portion of a three-year amortization schedule.
Use the information in the table to decide which of the following statements is true.
a.
The payment amount changes each month.
b.
The amount applied to the principal is decreasing each month.
c.
The amount applied to the principal is increasing each month.
d.
The amount applied to interest is increasing each month.
Answers
Answer:
Option C is correct.
Step-by-step explanation:
If we look at the table,
The amount of Principal of Month 13 is $325.82
The amount of Principal of Month 14 is $328.19
The amount of Principal of Month 15 is $330.57
So, the amount of principal is increasing every month.
Rest of the options seems incorrect.
So, Option C The amount applied to the principal is increasing each month.
is correct.
Answer:
The answer is C
Step-by-step explanation:
I got the right answer on the test in e2020
A box can hold 24 crayons. How many boxes must be used to put all of Mr.Syed's 98 crayons into boxes?
Answers
Answer:
5 boxes
Step-by-step explanation:
Given:
Total crayons : 98
Capacity of each box : 24
Number of boxes of 24 crayons needed to hold 98 crayons,
= 98 ÷ 24
= 4.08 boxes.
However since we cannot have 0.08 of a box, we must round this up to the next larger whole number of boxes.
4.08 rounded up to next whole number = 5
Hence he will need 5 boxes to hold all 98 crayons
98/24= 4 r2
So it’s be four full boxes and one with two and four plus one is five
What equation is the inverse of y=x^2+16
Answers
Answer:
[tex]y = \sqrt{x - 16} [/tex]
Step-by-step explanation:
[tex]y = {x}^{2} + 16[/tex]
[tex]x = {y}^{2} + 16[/tex]
[tex]x - 16 = {y}^{2} [/tex]
[tex] \sqrt{x - 16} = y[/tex]
Answer:
f^-1 (x) = ±sqrt(x-16)
Step-by-step explanation:
To find the inverse of a function, exchange x and y and solve for y
y=x^2+16
Exchange x and y
x = y^2 +16
Then solve for y
Subtract 16 from each side
x-16 = y^2 +16-16
x-16 = y^2
Take the square root of each side
±sqrt(x-16) = sqrt(y^2)
±sqrt(x-16) = y
The inverse
f^-1 (x) = ±sqrt(x-16)
If AB = 8, BC = 5, and CA = 7. list the angles of
AABC in order from smallest to largest measure.
Answers
Answer:
∠A, ∠B, ∠C
Step-by-step explanation:
In a triangle the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side, therefore:
∠A < ∠B < ∠C
Answer:
a,b,c
Step-by-step explanation:
The angle opposite the longest side has the largest angle measure, the angle opposite the shortest side has the most small angle measure etc.
Since BC is the shortest line, the angle opposite will have the smallest measure, this is ∠a.
CA is in the middle with length this means that the angle opposite of it will have an angle measure in between that of the other angle measures. This is ∠b
AB has the longest length, therefore, the angle opposite it will have the largest measure, this is ∠c
Complete the table for the given rule. Rule: y=X/4(fraction)
Table
X Y
4
2
9
What would X be i am really confused here does the fraction mean divide the numbers or something else
Answers
The complete table of values for the equation y = x/4 is
x 4 2 9
y 1 1/2 9/4
Completing the table of values for the equationFrom the question, we have the following parameters that can be used in our computation:
y = x/4
The missing y values are at x = 4, 2 and x = 9
Substitute the known values in the above equation, so, we have the following representation
y = 1/4 * 4 = 1
y = 1/4 * 2 = 1/2
y = 1/4 * 9 = 9/4
So, the missing values are 1, 1/2 and 9/4
Read more about linear relation at
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Final answer:
The rule 'y = X/4' describes division of X by 4 to find Y. The student completes the table by dividing each X value by 4 to find the corresponding Y values, providing an organized data set.
Explanation:
The student is asking about the operation indicated by the rule y = X/4, which involves division. The fraction bar signifies division. Given this rule, we can complete the table for y when x-values are provided.
For x = 4: y = 4/4 = 1
For x = 2: y = 2/4 = 0.5
For x = 9: y = 9/4 = 2.25
To organize the data in the table, you simply divide the x-value by 4 to find the corresponding y-value.
Which numbers are real numbers ?
Select ALL correct answers.
Answers
Answer:
A, e, F
Step-by-step explanation:
Evaluate the following expression when x = 5 and z = 3.
z
-
3x=
Answers
Answer:-12
Step-by-step explanation:
Z-3x=
=3-3(5)
=3-15
=-12
Answer:
-12
Step-by-step explanation:
3 - 3(5)
3 -15 = -12
the answer to the question
PLEASE
The three sides of a triangle measure 6, 15, and n. What is the range of possible lengths of n?
6 < n < 15
6 < n < 21
9 < n < 21
9 < n < 15
Answers
Answer:
9 < n < 21
Step-by-step explanation:
15-6 < n < 15+6
9 < n<21
We are limited by the other two sides of the triangle
It can be no smaller than the other two sides subtracted and no larger than the other two sides added
Factor completely x3 + 4x2 + 8x + 32. (x + 4)(x2 + 8) (x − 4)(x2 − 8) (x − 4)(x2 + 8) (x + 4)(x2 − 8)
Answers
[tex]\tt x^3+4x^2+8x+32\\\\=x^2(x+4)+8(x+4)\\\\=\boxed{\tt(x+4)(x^2+8)}[/tex]
Answer:
(x+4)(x^2+8)
Step-by-step explanation:
x^3 + 4x^2 + 8x + 32
We will factor by grouping
Factor out an x^2 from the first two terms and an 8 from the last two terms
x^2 (x+4) + 8(x+4)
Now we can factor out an (x+4)
(x+4)(x^2+8)
Solve (x + 2<5) n (x-7>-6).
{x11
{x1x < 3 or x> 1)
{all real numbers)
Answers
For this case we must solve [tex]x + 2 <5[/tex]intersected with [tex]x-7> -6[/tex]
So, we have:
[tex]x + 2 <5\\x <5-2\\x <3[/tex]
The solutions are given by all strict minor numbers to 3.
[tex]x-7> -6\\x> -6 + 7\\x> 1[/tex]
The solutions are given by all the major strict numbers to 1.
If we intersect the solutions of both equations we have [tex]x <3[/tex] ∩ [tex]x> 1[/tex].
The intersection is given by [tex]1 <x <3[/tex]
Answer:
The solution interval is (1,3)
Solve the following literal equation for x then for y
8x+5y=10
Answers
Answer:
see explanation
Step-by-step explanation:
Given
8x + 5y = 10 ← solve for x by subtracting 5y from both sides
8x = 10 - 5y ( divide both sides by 8 )
x = [tex]\frac{10-5y}{8}[/tex]
------------------------------------------------------------
Solve for y by subtracting 8x from both sides
5y = 10 - 8x ( divide both sides by 5 )
y = [tex]\frac{10-8x}{5}[/tex]
Evaluate x^2+3.5when x=1/2
Answers
Answer:
3.75.
Step-by-step explanation:
Substitute x = 1/2 into x^2 + 3.5:
(1/2)^2 + 3.5
= 1/4 + 3.5
= 3.75.
Answer:
3.75Step-by-step explanation:
[tex]\text{Put the value of}\ x=\dfrac{1}{2}=0.5\ \text{to the expression}\ x^2+3.5:\\\\0.5^2+3.5=0.25+3.5=3.75[/tex]
Liliana wants to start a seventh-grade computer club at Hamden Middle School. She surveyed 20 seventh-grade students at the town park. She asked each student how many hours they spend on their computers each week. She obtained the following results.
8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21
What is the ratio of the total number of students who used their computers to the total number of students surveyed?
2/18 or 1/9
18/2 or 9/1
2/20 or 1/10
18/20 or 9/10
Answers
Answer:
18/20 or 9/10
Step-by-step explanation:
The list shows the amount of hours each student USED the computer.
Wherever we see a "0", that means he/she DID NOT USE computer.
There are 2 "zeroes", so 2 didnt use out of 20, so number of student who DID USE is 20 - 2 = 18
To find ratio of total number of students who used to the total number surveyed, it is going to be:
18/20 or 9/10
Answer:
Ratio would be 9 : 10
Step-by-step explanation:
Liliana surveyed 20 students that how many hours they spend on their computers each week.
The results are as follows
8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21
In the above results 2 students did not use computers out of 20 students.
Therefore, The total number of students who used their computers = 20 - 2 = 18
So the ratio would be 18 : 20 or 9 : 10
What value of b will cause the system to have an infinite
number of solutions?
у= 6x –b
—3х + 1/2y=-3
a) 2
b) 4
c)6
d)8
Answers
Answer:
Option C) b=6
Step-by-step explanation:
we know that
If two linear equations of a system of equations have an infinite of solutions, then both equations are identical
we have
[tex]y=6x-b[/tex] -----> equation A
[tex]-3x+(1/2)y=-3[/tex]
Multiply by 2 both sides
[tex]-6x+y=-6[/tex]
Adds 6x both sides
[tex]y=6x-6[/tex] ------> equation B
equate equation A and equation B
[tex]6x-b=6x-6[/tex]
solve for b
[tex]b=6[/tex]