The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)
How to determine an element of a sequence
In mathematics, sequences are sets whose elements observe at least a condition, which is represented by a recursion formula in this question:
f(n + 1) = f(n) + 3
Thus, the following term of the sequence is:
f(2) = f(1) + 3
f(2) = - 4 + 3
f(2) = - 1
The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)
Remark
The statement is poorly formatted and reports typing mistakes. Correct statement is:
A sequence is defined recursively by the formula f(n + 1) = f(n) + 3. The first term of the sequence is - 4. What is the next term in the sequence? a) - 7, b) - 1, c) 1, d) 7
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Solve the following quadratic equation for all values of x in simplest form.
10-3x²=-2
Answer:
x = ± 2
Step-by-step explanation:
10 - 3x² = - 2 ( subtract 10 from both sides )
- 3x² = - 12 ( divide both sides by - 3 )
x² = 4 ( take square root of both sides )
x = ± [tex]\sqrt{4}[/tex] = ± 2
then x = - 2, x = 2
Answer:
x=2,-2
Step-by-step explanation:
10-3[tex]x^2\\[/tex]=-2
Can also be written as 12=3[tex]x^2[/tex]
[tex](12=3x^2)/3[/tex]
[tex]4=x^2\\\sqrt{4} =+-\sqrt{x^2} \\[/tex]
2=+-x or x=2,-2
x=2,-2
The heights of 150 oak trees are normally
distributed with a mean of 84 feet and a
standard deviation of 3 feet. about how
many trees fall within two standard
deviations of the mean?
Using the Empirical Rule, it is found that about 143 trees fall within two standard deviations of the mean.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.95% of the measures are within 2 standard deviations of the mean, hence, out of 150 trees, the amount is:
A = 0.95 x 150 = 142.5, rounded to 143.
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Solve the following equation for x.
(5/6)x + 10 = 30
x = 24
x = 20
x = 20/6
x = 25/6
Answer:
x=24
Step-by-step explanation:
6×(5/6)x +6(10)=6(30)
5x +60=180
5x +60-60=180 - 60
5x=180 -60
5x=120
5x/5 =120/5
x=24
Regress smoker on cubic polynomials of age, using a linear probability model. What is the p-value for testing the hypothesis that the probability model is linear in age? (two decimal places)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is probit regression?A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
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What is the period of f(x) = sin (8x)?
X/8
X/4
4
8
Answer: B- x/4
Step-by-step explanation:
The period is the horizontal distance needed for the values to repeat themselves.
Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x 5)(x i) f(x) = (x – 7)(x – i)(x – 5)(x i) f(x) = (x – (7 – i))(x – (5 i))(x – (7 i))(x – (5 – i)) f(x) = (x (7 – i))(x (5 i))(x (7 i))(x (5 – i))
It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.
The simplest polynomial with these characteristics would be
[tex]f(x) = (x - (7 + i)) (x - (5 - i))[/tex]
but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with
[tex]f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))[/tex]
which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:
[tex]f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48[/tex]
Answer:
C on edge 23
Step-by-step explanation:
because i said so
Based on the data in this two-way table, which statement is true?
Type of Flower/Color Red Pink Yellow Total
Rose 40 20 45 105
Hibiscus 80 40 90 210
Total 120 60 135 315
A.
A flower being pink and a flower being a rose are independent of each other.
B.
A flower being pink is dependent on a flower being a rose.
C.
A flower being a rose is dependent on a flower being pink.
D.
A flower being pink and a flower being a rose are the same.
TRUE OR FALSE
1. Standard units gives a consistent and accurate of the volume of a container.
TRUE OR FALSE ?
Answer:
True
Step-by-step explanation:
Cant really provide step by step per se.
A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm. What is the approximate density of the aluminum? Round to the nearest tenth.
If the volume of the aluminum brick will be 2218.5 cubic cm. Then the approximate density of the aluminum will be 8.9 grams per cubic cm.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
Density = mass/volume
A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm.
Then the approximate density of the aluminum will be
The volume of the aluminum brick will be
V = 29 x 15 x 5.1
V = 2218.5 cubic cm
Then the density will be
D = 19,745 / 2218.5
D = 8.900 gram per cubic cm
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If a baseball player hits 10 home runs in the first 45 game, at the same rate how many home runs can he expect to hit during the 162 game season
Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the player hits 10 home runs in 45 games, hence the proportion is:
p = 10/45.
Then, in 162 games, the amount is:
HR = 10/45 x 162 = 36.
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Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
The graphs with no solutions are the ones with no intercepts between the curves. These are the first one and the last one.
Which graphs indicate equations with no solutions?If we have an equation like:
f(x) = g(x).
One way of finding the solutions is to graph:
y = f(x) and y = g(x) and see where the two curves intercept.
From that, the graphs where the curves do not intercept are the graphs that indicate that the equations have no solutions.
The two graphs with no intercepts are the first one (top left) and the last one (bottom right), so these are the correct options.
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Answer:
kid named finger
Step-by-step explanation:
I simply just used a form of alien math solving and I got my answers but I'm not willing to share
A school sold all but 5 of ta school sold all but 5 of their old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally have
Answer:
20
Step-by-step explanation:
The proceeds from the sale can be described by an equation involving the original number of computers.
__
setupLet n represent the number of computers the school originally had. Then n-5 is "all but 5" and is the number sold. Each is sold for ₹1200, and the value of the sale is ₹18000. This can be expressed by the equation ...
(n -5)×1200 = 18000
__
solutionThis 2-step linear equation can be solved by dividing by the coefficient, and adding the opposite of the constant.
n -5 = 18000/1200 = 15 . . . . . divide by 1200
n = 15 +5 = 20 . . . . . . . . . . add the opposite of -5
The school originally had 20 computers.
which statement best describes the polynomial?
please help... Find the volume of pyramid that has a square base.
Answer:
V = 324 cm³
Step-by-step explanation:
the volume (V) of the pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the height )
here A = 9² = 81 cm² and h = 12 , then
V = [tex]\frac{1}{3}[/tex] × 81 × 12 = 27 × 12 = 324 cm³
Please help!!! answer the following questions, thanks:)
(you don't need to draw the venn diagram, I just need the questions below answered)
Answer:
hope you can understand
Question 3
the three straight paths, ab, bc, and ac meet each other at three points, a, b, and how do these points of intersection differ from each
other? explain the differences in terms of the angles that you see. also look at the length of the side opposite each angle. what pattern do you see
regarding the measurements? in what situation would all the points of intersection resemble one another modify the triangle in geogebra to
help you with your answers
b
ux
x
font sizes
aaeeen
characters used: 0 / 15000
submit
airfax county public schools
To find differences in the angles of the intersections we must know how many degrees each angle corresponds to. We must also take into account that the sum of the internal angles must equal 180°.
What is a triangle?A triangle is a polygon that is characterized by having three sides, three vertices, and three angles. An indispensable rule of the interior angles of the triangles is that they must add up to 180º.
Triangles are classified according to their characteristics as shown below:
Equilateral triangle: It is a type of triangle that is characterized by having all equal sides. Consequently, all the angles of an equilateral triangle are 60º. The equilateral triangle is a regular polygon.Isosceles triangle: It is a type of triangle that is characterized by having two equal sides and one different. Consequently, it also has two equal angles.Scalene triangle: A scalene triangle is one that is characterized by having all its sides and angles unequal, that is, different from each other.According to the above, depending on the measurements of the length of the sides and the angles of a triangle, its characteristics and classification change.
Note: This question is incomplete because the image is missing. However I can answer it based on my general prior knowledge.
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What is the slope of the line that passes through the points (-6, 8) and (-9, 7)? Write your answer in simplest form.
Answer:
m=1/3
equation y=1/3x+10
Step-by-step explanation:
Find the rise and run.
1. -6--9=run=3
2. 8-7=rise=1
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of the line that passes through (-6, 8) and (-9, 7).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex] (formula for Slope)
[tex]\longmapsto\bf{\cfrac{y2-y1}{x2-x1}}[/tex]
y2 & y1 = the y-coordinates of the two points
x2 & x1 = the x-coordinates of the two points
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{y2\;and\;y1\;are\;y-coordinates\;of\;the\;two\;points,\;and\;x2\;and\;x1\;are\;x-coordinates}}[/tex]
So we substitute the values and obtain:
[tex]\bf{\cfrac{7-8}{-9-(-6)}[/tex]
Simplifying:
[tex]\bf{\cfrac{-1}{-9+6}}[/tex]
Simplifying more:
[tex]\bf{\cfrac{-1}{-3}}[/tex]
Divide the top and bottom by -1:
[tex]\bf{\cfrac{1}{3}}[/tex]
There's the slope.
Hope it helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students
The first term in an arithmetic sequence is -3. If the sequence has a common difference of 8, what is the 30th term in the sequence?
Will give brainliest to right answer :))
Answer:
229
Step-by-step explanation:
(my work for the problem is in the photo I attached)
(I also wrote this step-by-step in the photo because I can explain things better as I do them)
This will be a little bit confusing without me writing out the numbers, so mainly this is if you can't read my handwriting
-3 + 8 = 5 ; 5 + 8 = 13
(1st term) (2nd term) (3rd term)
Instead of adding 8 repeatedly (repeated addition), we can use multiplication.
To get the 3rd term in this sequence, we had to add 8 twice, which could also be done by multiplying 8 twice (8 x 2)
13 + 8 = 21
(4th term)
to get the 4th term, we added 8 three times (or, 8 x 3)
So, if we are looking for the 30th term in a sequence, we will have to add 8, 29 times (8 x 29) to our original term.
8 x 29 = 232
-3 + 232 = 229
This means that the 30th term of the sequence will be 229.
The question is in the picture.
Answer:
x² - 22x + y² + 18y + 58 = 0
Step-by-step explanation:
Using the equation of a circle :
(x - h)² + (y - k)² = r²
Solving :
Substitute 11, -9, 12 in place of h, k and r respectively.
(x - 11)² + (y + 9)² = (12)²x² - 22x + 121 + y² + 18y + 81 = 144x² - 22x + y² + 18y + 202 = 144x² - 22x + y² + 18y + 58 = 0which of the following equations will produce the graph shown below?
A circle can be characterized by its center's location and its radius' length. The correct option is A.
What is an equation of a circle?A circle can be characterized by its center's location and its radius' length. Let the center of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units. Then, the equation of that circle would be:
(x-h)² + (y-k)² = r²
The given graph is the graph of a circle that has its origin at (0,0) and has a radius of 4 units, therefore, the equation will be,
(x-0)² + (y-0)² = 4²
x² + y² = 16
Multiply both the sides of the equation by 2,
2x² + 2y² = 32
Hence, the correct option is A.
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CORRECT ANSWER GETS BRAINLIST
Philani bough a scooter for R15 000. He paid 15% of the amount in cash and sgned a hire-purchase agreement to pay the balance in 24 equal monthly instalments. The interest rate is 10% per annum.
How much did he pay in cash?
Calculate the total amount that he must still pay.
Write the expression for the steps "12 increased by 4 and then double it." Then solve.
Expand and simplify
(5x + 2)(x + 2)
Answer:
5x²+12x+4
Step-by-step explanation:
5x²+10x+2x+4
5x²+12x+4
Answer:
[tex]5x^{2}+12x+4[/tex]
Step-by-step explanation:
Use the FOIL method to expand.
5x*x+
2*x+
5x*2+
2*2
which is
5x^2+2x+10x+2
combining the two x s we get
5x^2+12x+4
combine like terms to simplify 3x + 5 - 2x
Step-by-step explanation:
3x and 2x are like terms so,
3x + 5 - 2x
3x - 2x + 5 = x + 5
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression
[tex]\star~~\large\pmb{3x+5-2x}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Combine like terms.The like terms here are: 3x-2x; let's combine them:
[tex]\star~\large\pmb{x+5}[/tex]
We can't simplify this any further, because x and 5 are not like terms.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{Variables\:and\;numbers\;are\;not\;like\;terms}[/tex]
Hope it helps you out! :D
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~Just a smiley person helping fellow students :)
proving trigonometric identities
2(cosx sinx-sinx cos2x)/sin2x =secx
This is not an identity.
[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} \neq \sec(x)[/tex]
Check x = π/4, for which we have cos(π/4) = sin(π/4) = 1/√2. Together with sin(2•π/4) = sin(π/2) = 1 and cos(2•π/4) = cos(π/2) = 0, the left side becomes 1, while sec(π/4) = 1/cos(π/4) = √2.
Keeping the left side unchanged, the correct identity would be
[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = -2\cos(x) + 1 + \sec(x)[/tex]
To show this, recall
• sin(2x) = 2 sin(x) cos(x)
• cos(2x) = cos²(x) - sin²(x)
• cos²(x) + sin²(x) = 1
Then we have
[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = \dfrac{2\cos(x)\sin(x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = \dfrac{\sin(2x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)(\cos^2(x) - \sin^2(x))}{2 \sin(x)\cos(x)} \\\\ = 1 - \dfrac{\cos^2(x) - \sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{\sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{1 - \cos^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \sec(x) - \cos(x) \\\\ = -2\cos(x) + 1 + \sec(x)[/tex]
Tyger buys his car for $6900 he spends some Time repairing it and improving it. He sells it for $9200. What is his percentage profit?
If Tyler sold his car for $9200, then the approximate percentage profit for this product is 33.3%.
How to calculate the percentage?Final price - initial price
$9200 - $6900 = 2300Calculate the percentage $2300 is equivalent to by using the information you already have.
6900 = 1002300 = xx= 100 x 2300/ 6900x= 33.3%33.3% is the profit percentage.
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Pls solve this for me
Answer:
141/1.95 km/hr, or 72.308 km/hr
Step-by-step explanation:
To find the average speed, we need to know the total distance traveled / time (hours).
The total distance is 72 km + 69 km = 141 km.
The total time is 48 minutes / 60 (because we want this in hours, not minutes) + 69/60 = 1.95 hours
141/1.95 = 72.3 km/hr
[tex]\sqrt{8+2\sqrt{15}[/tex] Simplify this equation! Please help ASAP
[tex] \sqrt{8 \: + \: 2 \sqrt{15} } [/tex]
Factor the indicated expression:[tex] \sqrt{( \sqrt{3 } \: + \: \sqrt{5} ) ^{2} } [/tex]
Simplified the index, the root and also the exponent using the number 2.[tex] \boxed{ \bold{\sqrt{3} \: + \: \sqrt{5} }}[/tex]
MissSpanishAlex wants to cover his wall
with a circular clock that has a
diameter of 16 in. How much
space will the clock cover on
his wall?
Answer: A = π r2
r=8 and 8 squared is 64 and 64×3.14=200.96 or rounded to the nearest whole number it would be 201
Step-by-step explanation: brainliest please?
whats equlvlent to 3√6
Answer:
Important: 3
6
looks like a fraction, but it is actually an improper fraction.
There is an infinity number of equivalent fractions to 3
6
.
To find an equivalent fraction to 3
6
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 3, we get:
3 ÷ 3
6 ÷ 3
= 1
2
By multiplying the original fraction by 2, we get:
3 × 2
6 × 2
= 6
12
Step-by-step explanation: