Answers
Part (i)
We start with five dots to make the pattern in figure 1.
In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.
In figure 3, there are 9+4 = 13 dots
So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.
The first three terms of this arithmetic sequence are: 5, 9, 13
Your teacher wants to know what the general nth term is
We start with a = 5 and the common difference is d = 4
T(n) = nth term
T(n) = a + d(n-1)
T(n) = 5 + 4(n-1)
T(n) = 5 + 4n - 4
T(n) = 4n + 1
Let's try it out. Say we want to plug in n = 2
T(n) = 4n + 1
T(2) = 4(2) + 1
T(2) = 8 + 1
T(2) = 9
This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.
Answer: 4n + 1============================================================
Part (ii)
Your teacher wants to know how many dots occur when n = 50
T(n) = 4n + 1
T(50) = 4(50)+1
T(50) = 200 + 1
T(50) = 201
Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.
Answer: 201Related Questions
1 21.1.1 Study: Characteristics of Ecosystems
A population of Clark's nutcrackers like this one lives in a forest on a mountainside in
Colorado. Which two characteristics of this group of birds make it a population?
A. They live in the same area.
B. They have the exact same genes.
C. They are offspring of the same parents.
D. They belong to the same species.
Answers
Answer:
The two populations living habitats are different. Also they are only similar not the same. Although the physical features may look the same, the actual species may be totally different. :)
Step-by-step explanation:
I think of a number, double it and the result is 9. Evaluate the number that I first thought of
Answers
Answer:
4.5
Step-by-step explanation:
9/2 = 4.5
Resolve the expression [tex]\frac{(x-2)}{(x^{2} +1)(x-1)^{2} }[/tex] into the simplest partial fractions
Answers
The partial fraction expansion will look like
(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²
Get everything in terms of a common denominator, and compare the numerators on both sides:
x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)
Expand the right side:
x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)
x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d
Match up the coefficients and solve the resulting system of equations:
a + c = 0
-2a + b - c + d = 0
a - 2b + c = 1
b - c + d = -2
==> a = -1, b = -1/2, c = 1, d = -1/2
So the expansion into partial fractions is
(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)
… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)
a shipping boox has the dimentsions what is the volume of the box in cubic yards
Answers
Answer: 1/32
Step-by-step explanation:
plz give me this ans by explaining
Answers
Answer:
I don't know what to do so I just answered the volume of this tell me if I am wrong
Step-by-step explanation:
radius : 3.5 cm
volume : ?
now,
volume (v) : π × r (2)
: 22/7 × 3.5(2)
:22×3.5×3.5 by 7
therefore,
the volume is 38.5
Find the value of x that will make L||M.
2x - 3
M
X + 4
x = [?]
Answers
find the area of the right triangle
Answers
Answer:
the area of right angle is 1.5×2.5=3.75
Answer:
1.5 units^2
Step-by-step explanation:
If we say that the missing side is x, we can use the pythatgorean theorem to find it.
1.5^2 + x^2 = 2.5^2 => 2.25 + x^2 = 6.25 => x^2 = 4 => x=2
The area of a triangle is hieght * base * 1/2 => 1.5 * 2 * 1/2 = 1.5
cho f(t)=(t-4)u(t-2)phep bien doi laplace la
F(s)=e^-2s/s^2-2e^-2s/s62
Answers
Step-by-step explanation:
cho f(t)=(t-4)u(t-2)phep bien doi laplace la
F(s)=e^-2s/s^2-2e^-2s/s62
Explain how to solve the equation
.
b – 7 = 12
Answers
Answer:
19
Step-by-step explanation:
Add 7 onto 12 to find answer.
Answer:
b = 19
Step-by-step explanation:
b = 12 + 7
Simplify 12+7 to 19.
Rewrite the expression (x2 – 3x – 18)/(x – 9) using the long division method.
Answers
Answer:
x + 3
Step-by-step explanation:
Image below
find the third proportional of 3 5 7
Answers
Answer: Third proportion is 21/5.
Step-by-step explanation:
Let the proportion be x
so,
3:5:x:7
so
3:5 = x:7
or, 3/5 = x/7
or, 21 = 5x
or, x = 21/5
Find the missing side. Round to the nearest tenth
Answers
We know
[tex]\boxed{\sf cos\theta=\dfrac{Base}{Hypotenuse}}[/tex]
[tex]\\ \sf\longmapsto cos59=\dfrac{x}{28}[/tex]
[tex]\\ \sf\longmapsto 0.5=\dfrac{x}{28}[/tex]
[tex]\\ \sf\longmapsto x=28\times 0.5[/tex]
[tex]\\ \sf\longmapsto x\approx 14[/tex]
Answer:
[tex]x = 14[/tex]
Step-by-step explanation:
[tex] \cos( \theta) = \frac{a}{h} \\ \cos(59) = \frac{x}{28} \\ 0.5 \times 28 = x \\ 14 = x[/tex]
which are partcial products
for 34 x 28
Answers
Answer:
952
Step-by-step explanation:
34 = (30 + 4)
28 = (20 + 8)
34 x 28 = (30 + 4) x (20 + 8)
34 x 28 = 30 x 20 + 30 x 8 + 4 x 20 + 4 x 8
34 x 28 = 600 + 240 + 80 + 32
34 x 28 = 952
952 = 952
. A research study about test anxiety will measure the change in heartrate of the test-taker. The researcher randomly assigns participants into one of two groups, either the Test group or the No-test group (where the first group takes a timed test and the second group reads for the same amount of time). What is the operational definition of the independent variable
Answers
Answer:
Timed test.
Step-by-step explanation:
An operational definition gives exactly what the independent variable means and its mode of measurement. The Independent variable is the variable in a research or experimental study which causes a change in the the measured variable. Hence, the independent variable is the predictor variable. In the study above, the independent variable is the timed test which is used to observe changes in the heart rate of the test taker (test anxiety). The change innheartrate of the test taker is the dependent variable.
Pls help me with this pls
Answers
To find where a coordinate is on a graph you need to start with the first number (x) (let’s say the coordinate is (2, -3), so 2) and find where it is ( you always find where the first number is on the x-axis and the second number on the y, remember that by x, y and x comes first.) Then, you need to find the second number (-3) then you need to find where they meet. So 2, -3 is on the letter I.
To find what coordinates a point that’s already been plotted is to see, for example, L, the two numbers that meet where L is are -4, -3, remember whatever was on the x axis comes first, -3, -4 is not the same.
Hopefully this makes sense, I don’t normally answer stuff.
AXYZ has side lengths that measure 20 centimeters each. Which of the
following best describes this type of triangle?
A. Scalene triangle
B. Right triangle
C. Obtuse triangle
D. Equilateral triangle
Answers
Step-by-step explanation:
The triangle is equilateral (OPTION D) because any triangle that has 3 equal side lengths is an equilateral triangle.
The polygons in each pair are similar. find the missing side length
Answers
If both are similar ratio of sides will be same
[tex]\\ \sf\longmapsto \frac{x}{25} = \frac{7}{5} \\ \\ \sf\longmapsto 5x = 7 \times 25 \\ \\ \sf\longmapsto 5x = 175 \\ \\ \sf\longmapsto x = \frac{175}{5} \\ \\ \sf\longmapsto x = 35[/tex]
Questions
Steve played a car race game. He gained some points, lost 27 points, and
finished with less than 400 points. Which of the following inequality
represents the given situation?
A.)X - 400 < 27
B.)x + 27 < 400
C.)X - 27 > 400
D.) X - 27 < 400
Answers
Can I have brainliest ?
According to the information we can infer that the correct inequality that represents the given situation is D.) X - 27 < 400.
Which inequality does represent the given situation?Let's break down the information provided: Steve gained some points, lost 27 points, and finished with less than 400 points. To represent the number of points Steve had initially, let's use 'X'.
After gaining some points, his total would be X + G, where G represents the gained points.After losing 27 points, his total would be X + G - 27.Since he finished with less than 400 points, we can express this as X + G - 27 < 400.
Simplifying the equation, we get X - 27 < 400.According to the above we can conclude that the correct inequality that represents the given situation is D.) X - 27 < 400.
Learn more about inequality in: https://brainly.com/question/20383699
#SPJ2
a two-digit number is 5 times as large as the sum of its digits. What number is it?
Answers
Answer:
45
Step-by-step explanation:
CHECK ANSWER:
45 *5 = 225
45+5 = 50
50 < 225
sum < times
I hope this helped !
What is the domain of the given function? {x | x = -6, -1,0,3}, { y | y = -7,-2,1,9}, {x | x = -7, -6, -2, -1, 0, 1, 3 , 9}, { y | y = -7, -6 , -2 , -1 , 0 , 1 , 3 , 9}
Answers
Answer:
domain = {-6,-7,-7,-7}
SEE QUESTION IN IMAGE
Answers
Answer:
See belowStep-by-step explanation:
(b)
The table is attached(i)
The graph is attached(ii)
(a) Cumulative frequency is 500, median is at 249, 250, the horizontal line from point 250 on y-axis intersecting the graph at approximately 52%, this is the median
(b) Vertical line from the 45% mark intersects the graph at approximately 177th point. The number of candidates passed the test:
500 - 177 = 323(iii) P(pass) = 323/500 = 0.626 or 62.6%
Amazon hires you as their data analysist. You have to make a presentation
to their board of directors about which shipping method they should invest
an additional $10 million in. The data they provide you is below.
Please help due today
Answers
Answer:
standard= 21.333%
prime= 42.666%
expedited= 6.666%
locker= 29.333%
classmate DAN sual For madenaldy asymmetrical distribution, the arithmetic mean 28 and the median = 25. Find modo of this dish button Sekulin
Answers
We know
[tex]\boxed{\sf M_o=3M_d-2M}[/tex]
[tex]\\ \sf\longmapsto M_o=3(25)-2(28)[/tex]
[tex]\\ \sf\longmapsto M_o=75-56[/tex]
[tex]\\ \sf\longmapsto M_o=19[/tex]
WILL MARK BRAINLIEST!! Multiply. −1/2⋅3/4 a)−2/3 b) −3/8 c) 3/8 d)2/3
Answers
Explanation:
When multiplying fractions, we multiply the numerators together, and the denominators are handled separately.
The numerators in this case are -1 and 3. They multiply to -3
The denominators multiply to 2*4 = 8
So that's how we end up with -3/8 as the final answer
This fraction cannot be reduced any further, because 3 and have 8 no factors (other than 1) in common.
How much of salt would you get if you evaporate all water from:
375g of a 12% salt solution

Answers
Answer:
45g
Step-by-step explanation:
The amount of salt left once the whole water is evaporated can be calculated as follows
= 12% × 375
= 12/100 × 375
= 0.12×375
= 45
Hence 45g of salt is left after the evaporation of water
Answer:
45g
Step-by-step explanation:
Convert this rational number to its decimal form and found to the nearest thousands?
Answers
Answer:
7 and 1 respectively
Step-by-step explanation:
1/7= 7 ) 1 (, the basic definition of division
Ervin sells vintage cars. Every three months, he manages to sell 13 cars. Assuming he sells cars at a constant rate, what is the slope of the line that represents this relationship if time in months is along the x-axis and the number of cars sold is along the y-axis?
A. 3/13
B. 3
C. 13/3
D. 13
Answers
Answer: C. 13/3
Step-by-step explanation:
Time (in months) = xNumber of sold cars = y[tex]slope=\frac{rise}{run} =\frac{y}{x} =\frac{13}{3}[/tex]
PLEASE HELP DUE IN 15 MNUTES MARKING BRAINLIEST AND 15 POINTS YOU DONT HAVE TO EXPLAIN MUCH
Answers
Answer:
see below
Step-by-step explanation:
11a -2(x^2 -3)
Distribute
-2*x^2 -2(-3)
-2x^2 +6
11b 2x(x+4)
Distribute
2x*x +2x*4
2x^2 +8x
12 The perimeter is the sum of all sides
The top is equal to the bottom and the left side is equal to the right
x-10 + x+20+x-10+x+20
Combine like terms
4x +20
Please help me with this question I would really appreciate it!!!
Answers
Answer:
0, 1.32
Step-by-step explanation:
16cos(t)*sin(t)=4sin(t)
cos(t)=1/4 or sin(t)=0
t=1.32 or 0
the ratio of corresponding side of similar triangles is 5:2, then find the ratio of their areas
Answers
Answer:
25:4
Step-by-step explanation:
The ratio of the sides is 5:2
The ratio of the areas is the scale factor squares
5^2 : 2^2
25:4
