Answer:
the answer is on the computer
Step-by-step explanation:
At Bob's binders, a set of 3 notebooks costs $4.20. At Pam's Paper Place a set of 4 notebooks costs $5.20. What is the unit price of the notebooks at each store? Which is the better buy?
Step-by-step explanation:
At Bob's binders, the unit price = $4.20 ÷ 3
= $1.40
At Pam's Paper Place the unit price = $5.20 ÷ 4 = $1.30
the better buy is at Pam's Paper place
Find the sum Sn of the first n terms from the given sequence.
1, 1+2, 1+2+3, 1+2+3+4, ...
Please show your work and use Sigma Notation too. Thank you!
The Sequence:
1 , 1+2 , 1+2+3 , 1+2+3+4, ...
here, every term is an AP. finding the general formula for the sum of the elements of each term is:
Sₙ = [tex]\frac{x}{2}(2a + (x-1)d)[/tex] [where x = number of term, a = first term and d = common difference]
here, the first term is always 1 and so is the common difference.
Sₙ = [tex]\frac{x}{2}(2 +x-1)[/tex]
Sₙ = [tex]\frac{x}{2}(1 +x)[/tex] = [tex]\frac{1}{2}(x + x^{2})[/tex]
which is the formula for a general term in our series
now, we need to find the sum of the first n terms of this series
[tex]\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})][/tex]
[tex]\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})][/tex]
in this formula, for the first term, it's just an AP from x = 1 to x = n
for the second term, we have a general formula [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
[tex]\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
in this AP (first term), the first term and the common difference is 1 as well
[tex]\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex]\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex][\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ][/tex]
[tex]\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ][/tex]
[tex]\frac{n}{2}(n+1) [\frac{(n+2)}{3} ][/tex]
[tex]\frac{n(n+1)(n+2)}{6}[/tex]
which is the sum of n terms of the given sequence
Points A, B, and C are collinear. Point B is between A and C. Find the length indicated.
Answer:
TR = 23
Step-by-step explanation:
first we have to find TS, so we subtract 16 from 4 to get 12. then we can add 12 and 11 to get TR
[tex]\frac{\sqrt{a+b} }{\sqrt{a-b} } +\frac{\sqrt{a-b} }{\sqrt{a+b} }[/tex]
Answer:
[tex]\frac{(a+b)}{a^{2} -b^{2} }[/tex] + [tex]\frac{(a-b)}{a^{2} -b^{2} }[/tex] = [tex]\frac{2a}{a^{2} -b^{2} }[/tex]
Step-by-step explanation:
Step-by-step explanation:
[tex] \frac{ \sqrt{a + b} }{ \sqrt{a - b} } + \frac{ \sqrt{a - b} }{ \sqrt{a + b} } \\ squaring \: on \: both \: sides \\ \frac{a + b}{a - b} + \frac{a - b}{a + b} \\ \frac{(a + b) \times (a + b) + (a - b)(a - b)}{(a - b)(a + b)} \\ \frac{ {(a + b)}^{2} + {(a - b)}^{2} }{ {a}^{2} - {b}^{2} } \\ remaining \: in \: attachment[/tex]
[tex]thank \: you[/tex]
The radius of the circle below is 5 inches. What is the diameter of the circle?
Answer:
10 inches
Step-by-step explanation:
radius = 5 inches
Diameter = radius x 2 = 5 x 2 = 10 inches
Find the value of x,y and z
Answer:
hope it helps, appreciate if you can give brainliests
Can you guys help me find a flag that has at least one reflection and a translation in it? If not, then two flags that show these transformations.
This is very urgent and I need to get it done soon, whoever is willing to help me I'll mark you as brainliest. Thank you!
Answer:
The united nations flag the translation can be any of the blue triangles and the reflection if the flag itself as it is symmetrical
Step-by-step explanation:
The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.
How does reflection across axis work?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.
If we study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
If you're reflecting a point (x,y) along x axis, then its abscissa will stay same but ordinates will negate. Thus (x,y) turns to (x, -y)
Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)
Therefore, The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.
Learn more about reflection;
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18/20-4/12
Show your work
Answer:
17/30 (0.56)
Step-by-step explanation:
18/20-4/12
Reduce the fraction with 2 and 4: 9/10-1/3
Write all numerators above the least commmon denominator 30: 27-10/30
Subtract: 27-10/30 = 17/30
Please no links because they dont work :).
Answer:
semoga jawapan ini dapat membantu
A design for a banner includes a striped background. The stripes are colored in the repeating order: yellow, blue, orange, green, and purple. What calor is the 37th stripe?
Answer:
purple.orang.blue.yellow and green
purple.orang.blue.yellow and green
6x + 3y - 9 when
x = 6, y = 9
Answer:
63
Step-by-step explanation:
6x + 3y - 9
x = 6
y = 9
6(6) + 3(9)
36 + 27
= 63
A ball is thrown into the air with an upward velocity of 80 feet per second. The function
h = -16t2 + 80t models the height h, in feet, of the ball at time t, in seconds. When will the ball reach the ground?
after 3 seconds
after 4 seconds
after 5 seconds
after 6 seconds
Best explanation gets Brainliest!!
Answer:
After 5 seconds
Step-by-step explanation:
One is given the following expression to model to the flight path of a ball:
[tex]h=-16t^2+80t[/tex]
In this problem, one is asked to find the time at which the ball lands on the ground. The easiest way to do so is to factor the expression. Take out factors that both terms have in common. The one will set the equation equal to zero, as this is the height at which one wants to find the time for. Finally, use the zero product property to solve. The zero product property states that any number times zero equals zero. Apply these ideas to the given function:
[tex]h=-16t^2+80t[/tex]
Factor the expression; both terms have a common factor of (-16t):
[tex]h=-16t^2+80t[/tex]
[tex]h=-16t(t-5)[/tex]
Set the equation equal to zero to solve for when the ball has a height of zero or rather lands on the ground:
[tex]h=-16t(t-5)[/tex]
[tex]0=-16t(t-5)[/tex]
Now use the zero product property, this states that any number times zero equals zero. Set each of the factors equal to zero, and solve to find the value of (t) for which the factor will equal zero:
[tex]0=-16t(t-5)[/tex]
[tex]0=-16t[/tex] [tex]t - 5 =0[/tex]
Solve for the value (t) using inverse operations,
[tex]0=-16t[/tex] [tex]t - 5 =0[/tex]
(divide by (-16) (add (5))
[tex]0=t[/tex] [tex]t=5[/tex]
As one can see, the ball started on the ground, therefore at (0) seconds, its height was (0). Then, after (5) seconds the ball landed on the ground, therefore, after (5) seconds its height was again (0).
whats number 26.
..............................
Answer:
y = 1/3mx + b
Step-by-step explanation:
x = 3(y - b)/m
~Multiply m to both sides
mx = -3b + 3y
~Add 3b to both sides
mx + 3b = 3y
~Divide everything by 3
1/3mx + b = y
y = 1/3mx + b
Best of Luck!
[tex]\\ \rm\longmapsto x=\dfrac{3(y-b)}{m}[/tex]
[tex]\\ \rm\longmapsto mx=3(y-b)[/tex]
[tex]\\ \rm\longmapsto mx=3y-3b[/tex]
[tex]\\ \rm\longmapsto 3y=mx+3b[/tex]
[tex]\\ \rm\longmapsto y=\dfrac{1}{3}mx+b[/tex]
Write as an algebraic expression five times the sum of a number and 4
Answer:
5(x+4)
Step-by-step explanation:
It's basically asking for the sum of a number and four to be multiplied by 5. Since the sum is made up of the unknown number and four, you'd put four and the unknown number in parenthesis while putting five on the outside, making it 5(x+4).
The angle,2Θ, lies in the third quadrant such that cos2Θ=-2/5. Determine an exact value for tanΘ . Show your work including any diagrams if you plan to use them. (3 marks)
Answer:
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
Step-by-step explanation:
1. Approach
One is given the following information:
[tex]cos(2\theta)=-\frac{2}{5}[/tex]
One can rewrite this as:
[tex]cos(2\theta)=-0.4[/tex]
Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.
Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]). Substitute the given information into the ratio and simplify.
2. Solve for [tex](cos(\theta))[/tex]
Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
[tex]-0.4=2(cos^2(\theta))-1[/tex]
Inverse operations,
[tex]-0.4=2(cos^2(\theta))-1[/tex]
[tex]0.6=2(cos^2(\theta))[/tex]
[tex]0.3=cos^2(\theta)[/tex]
[tex]\sqrt{0.3}=cos(\theta)[/tex]
Since this angle is found in the third quadrant its value is actually:
[tex]cos(\theta)=-\sqrt{0.3}[/tex]
3. Solve for [tex](sin(\theta))[/tex]
Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
[tex]-0.4=1-2(sin^2(\theta))[/tex]
Inverse operations,
[tex]-0.4=1-2(sin^2(\theta))[/tex]
[tex]-1.4=-2(sin^2(\theta))[/tex]
[tex]0.7=sin^2(\theta)[/tex]
[tex]\sqrt{0.7}=sin(\theta)[/tex]
Since this angle is found in the third quadrant, its value is actually:
[tex]sin(\theta)=-\sqrt{0.7}[/tex]
4. Solve for [tex](tan(\theta))[/tex]
One can use the following identity to solve for [tex](tan(\theta))[/tex];
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute the values on just solved for and simplify,
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
Rationalize the denominator,
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
If the mine winch drum diameter is 4,5m, calculate how far the counterweight will lift each single rotation of the drum, use formula C=2πr
Answer:
i have no idea that's why I need ur help
barbara and jeff ate out for dinner the total came to &15.00. they left a 15% tip how much was the tip and the meal together?
Answer:
$17.25
Step-by-step explanation:
The tip is 15% of $15.00, or 0.15 * 15 = $2.25
We add that to the meal's cost, which is $15.00
15.00 + 2.25 = 17.25
Six times a number increased by five is fifty-three. What is the number?
Answer:
8
Step-by-step explanation:
6x+5=53
6x=48
6x/6=48/6
x=8
factorize 6(a+1)²+4(a+1)
Answer:
[tex]2(a + 1) \times (3a + 5)[/tex]
Step-by-step explanation:
[tex]6(a + 1 {)}^{2} + 4(a + 1)[/tex]
➡️ [tex]2(a + 1) \times (3(a + 1) + 2)[/tex]
➡️ [tex]2(a + 1) \times (3a + 3 + 2)[/tex]
➡️ [tex]2(a + 1) \times (3a + 5)[/tex]
Sarah ran 4 7/8miles, then walked 1 11/12 miles.
Find the total distance she traveled.
Answer:
6 19 /24
Step-by-step explanation:
find the lcd and add
all the number sets that apply to -4/5
-8/10,-12/15,-16/20,-20/25,-24/30,etc.
The number sets that apply to -4/5 is the fractions.
What is a fraction?Fractions represent the parts of a whole or collection of objects.
A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.
Now the given number is,
-4/5
-4/5 is a fraction. A fraction has two components numerator and denominator. This can positive or negative. Other example of fractions include 1/2,3/2,-5/2,-1/3.
The numbers who are not fractions are 0, 3, 6, 7.7.
Thus, the number sets that apply to -4/5 is the fractions.
To learn more about fractions:
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please help angles on a Cartesian plane
Answer:
a) 16/25
b)3/2
Step-by-step explanation:
all explaination is in picturw below
d) The shadow of a vertical tower on a level ground increases by 10m, when the altitude of sum changes from angle of elevation 45° to 30°. Find the height of the towe correct to one place of decimal. (Take root 3 = 1.732)
Help As soon as possible please with picture please
Answer:
Below.
Step-by-step explanation:
I cant draw you a picture but it will be one right triangle inside the other where the vertical tower will be one leg common to 2 triangles and the base of the 2 triangles will be x and x+10 metres.
Tan 30 = h/ (x + 10)
tan 45 = h/x where h is the height of the tower.
From the second equation x = h / tan45
Substituting in the first equation;
tan30 = h / (h/tan45 + 10
Tan 30 = 1/ √3 and tan 45 = 1 so
1/ 1.732 = h/ (h + 10)
0.5774 = h/(h + 10)
h = 0.5774h + 57.74
0.4226 h = 57.74
h = 136.6 m to nearest tenth.
Janelle is shopping around for the best cell phone plan. The best company is offering a $50 set up fee plus $60 per month. If the contract is for one year, how much will Janelle end up paying after one year?
$650
None of these choices are correct.
$770
$700
$720
Answer:
770
Step-by-step explanation:
12 month ×60 per month
Plus 50 set up fee
=770
ASAP PLS
The soda shop has 11 flavors of soda, 2 kinds of fruit syrup, and 6 sweeteners. How many different sodas can be made with one flavor of soda, one fruit syrup, and one sweetener?
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x=-3
Step-by-step explanation:
-4(-2x+5)-5x+5=-24
8x-20-5x+5=-24
3x-15=-24
3x=-9
x=-3
I hope that this helped you!
What is 1,025 divided by 68 full explanation
Answer:
15.1 (rounded to the nearest tenth decimal point)
Step-by-step explanation:
The explanation is, this is simple maths, nothing else. Let me know if it helps. Thank you
Visualize 4.385 on a number line using magnification.
Answer:
Um srry I am a hack I like this app Haha I hadked this girls brainy hehehe
(10 points) How many proportional relationships are shown in the coordinate plane
Answer:
D) 3
Step-by-step explanation:
There are 3 lines/graphs
I hope this helps!
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
6,2,2/3….
Find the 8th term.
Answer:
Just divide 2/3 by 3 (or multiply by 1/3), 6 times to get the answer.
