The sequence an = -5 + (n - 1)14 is an arithmetic sequence
The value of a10 is 121
How to determine the the a10-th term?The sequence is given as:
an = -5 + (n - 1)14
To calculate the value of a10, we set n = 10
So, we have:
a10 = -5 + (10 - 1) * 14
Evaluate the difference
a10 = -5 + 9 * 14
Evaluate the product
a10 = -5 + 126
Evaluate the sum
a10 = 121
Hence, the value of a10 is 121
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Expand and simplify:
a) -1/3{6(p+q)-3[p-2(p-3q)]}
A=-3p+4q
b) y-2/3(9x-3y)
A=-6x+3y
(The answer is written at the back of our books but I am struggling with the working I mean how to achieve the answer?)
Answer:
a) -3p +4q
b) -6x +3y
Step-by-step explanation:
Use the distributive property to eliminate parentheses. Use the properties of arithmetic to combine the numbers.
__
a)The order of operations tells you to start with the inner parentheses and work outward.
[tex]-\dfrac{1}{3}(6(p+q)-3(p-2(p-3q)))=-\dfrac{1}{3}(6(p+q)-3(p+(-2)(p) +(-2)(-3q)))\\\\=-\dfrac{1}{3}(6(p+q)-3(p-2p+6q))=-\dfrac{1}{3}(6(p+q)-3(-p+6q))\\\\=-\dfrac{1}{3}((6)(p)+(6)(q)+(-3)(-p)+(-3)(6q))=-\dfrac{1}{3}(6p+6q+3p-18q)\\\\=-\dfrac{1}{3}(9p -12q)=(-\dfrac{9p}{3})+(-\dfrac{-12q}{3})=\boxed{-3p+4q}[/tex]
__
b)Same deal for the second expression: use the distributive property and combine like terms.
[tex]y-\dfrac{2}{3}(9x-3y)=y+(-\dfrac{2\cdot9x}{3})+(-\dfrac{2(-3y)}{3})\\\\=y-6x+2y=\boxed{-6x+3y}[/tex]
please help me find the slope!!
Answer:
-2/3
Step-by-step explanation:
To find the slope, you can pick two points on the graph and plug them into the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]\frac{0-2}{6-3}[/tex]
[tex]\frac{-2}{3}[/tex] is the same as [tex]-\frac{2}{3}[/tex]
hope this helps!
Given that z = 10 cis 30° and w = 5 cis 10°, find z/w. Leave your answer in polar form
Giving almost 100 pts!!
Answer:
2cis(20°)
Step-by-step explanation:
we are given that
[tex] \displaystyle \rm z = 10cis ({30}^{ \circ} )[/tex]
[tex] \displaystyle \rm w = 5cis ({10}^{ \circ} )[/tex]
We want to find z/w . To do so, divide 10cis(30°) by w = 5cis(10°) which yields:
[tex] \displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )}[/tex]
recall that,
[tex] \displaystyle \rm \frac{ r_{1} cis ({ { \theta}_{1}} )}{ r_{2}cis( { \theta}_{2})} = \frac{ r_{1} }{ r_{2} } cis({ \theta}_{1} - { \theta}_{2})[/tex]
consider,
[tex]{ r}_{1} \implies 10[/tex][tex]{ r}_{2} \implies 5[/tex][tex]{ \theta}_{1} \implies {30}^{ \circ} [/tex][tex]{ \theta}_{2} \implies {10}^{ \circ} [/tex]Therefore, utilizing the formula yields:
[tex] \displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )} \\ \implies \rm\frac{ z}{w} = \dfrac{10}{5} cis( {30}^{ \circ} - {10}^{ \circ} ) \\ \implies \rm \dfrac{z}{w} = \boxed{ \rm2cis( {20}^{ \circ} )}[/tex]
and we're done!
NB: cis(x) is also known as cos(x)+i×sin(x)
5b+ 11 = 26
Can you help me solve this equation
Answer:
b=3
Step-by-step explanation:
i subtracted 11 with the 26 and got 15 and then I divided the 5b with the 15 and got 3
Hope i helps<33
Answer:
b=3
Step-by-step explanation:
move the constant to the right-hand side and change its sign 5b = 26 - 11
subtract the numbers 5b = 15
divide both sides of the equation by 5 b = 3
A WOMAN BOUGHT A RING FOR $200.00 MANY YEARS. LATER, SHE SOLD IT FOR $375.00. WHAT IS THE PERCENT INCREASE IN VALUE OF THE RING?
Answer:87.5%
Step-by-step explanation:
(Final value - starting)/staring *100
Please HELP! I will mark BRAINLIEST. YOU ALSO GET 20 POINTS FOR HELPING ME! THANK YOU!
y=x-50
[tex]\huge\mathfrak\colorbox{white}{}[/tex][tex]\huge\mathfrak\colorbox{white}{}[/tex]
If the answer is correct I will give brainliest
Answer:
1,044cm
Step-by-step explanation:
46-21=25cm (the length of the top line)
30-14=16cm (the length of the other line on the left of the 21)
Split it into three rectangles, 25×16, 21×14 and 25×14
25×16 = 400cm
21×14 = 294cm
25×14 = 350cm
Add to together: 400+350+294= 1044cm
the other commenter is right
I need 2, 4, 7, and 3's angles pls!
Answer:
2: 125
4: 55
7: 125
3: 125
Step-by-step explanation:
Since the top and bottom lines are parallel, 2 is equal to 6.
since angles 4+2 sums up to a straight line, its 180 degrees
125+55 is 180
same with 3, 3+4 is 180
7 is same as 3
Simplify the expression.
2x³y +7x³y-xy³
Answer:
xy*(2x^2 + 7x^2 - y^2)
Step-by-step explanation:
You can get xy out of the expression since all have xy
The circumference of a globe is 16pi inches. what is the volume of the globe? show your work. use 3.14 for pi
Answer:
v=2144.66
Step-by-step explanation:
formula: 4/2 (pi) (r)³
................
Answer:
V = 2143.573333333333.... in³
Step-by-step explanation:
Formula for volume -> V = 4/3 πr³
We know the circumverence now we need to et the radius.
Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.
Divide the diameter by 2.
There you go, you found the circle's radius.
16pi/pi = 16/2 = 8
V=4/3πr³
V=4/3π8³ = 2143.5733333333333333333333333333333333333333333333333333333333333...
Louis bought a giant sub sandwich for the party. He wants to cut into 6-inch sections. If the sandwich is 18.25 feet, how many sections can he cut? Solve with steps pls<3
in your calculator, type in 18.25/6.
What was the median temperature of the pond?
Answer:
70°f is the median temperature of the pond
Mandy drove 206 miles from Newcastle to Birmingham and stayed overnight at a
hotel costing £45. She then travelled 117 miles to London and stopped in another
hotel costing £68. From London, she drove 282 miles back to Newcastle. How many
miles in total did she drive, and what was the total cost of her accommodation?
Answer:
£113 and 603 miles.
Step-by-step explanation:
206 + 117 + 282 = 605 miles
45 + 68 = £113
£113 and 605 miles.
Please Help
A triangle has a base of 13 inches and an area of 82.5 inches. What is the height of the triangle?
Answer:
Height - 12.692 in
Step-by-step explanation:
Answer:
A = 1/2 bh
Step-by-step explanation:
Replace are and base to get:
82.5 = 1/2 x 15 x height
Multiply both sides by 2:
165 = 15 x height
Divide both sides by 15:
Height = 165 / 15
Height = 11 inches.
Select each number that is between 535% and 6.01 x 10⁰.
10 poin
Answer:
5.9, 47/8, and [tex]\sqrt{35}[/tex]
Step-by-step explanation:
I did this before, Please Mark brainliest
If AB is perpendicular to radius CP at P, then is tangent to C.
Given: QRn
Prove: n is tangent to Q at R.
A. Scalene
B.Right
C.Equilateral
Answer: Right triangle
Step-by-step explanation:
QR is perpendicular to line n, so the indicated angle is a right angle. Thus, QRS is a right triangle because a triangle with a right angle is a right triangle.
Describe the pattern in the sequence. Find the next two terms of the difference. Show work
-2, -5, -8, -11, ...
Answer:
-2, -5, -8, -11, ... -14, -17
Step-by-step explanation:
-3 each time.
50 POINTS EACH!
On a 23 question test, I got 6 wrong. What is percent did I get right? (On 100 percent scale)
Answer:
26%
Step-by-step explanation:
To calculate the percentage score which you got right in your test,
Number of questions wrong/TOTAL number of questions * 100
6/23 * 100
= 26%.
Answer:
26%
Step-by-step explanation:
Hope I was able to help. Have an amazing day.
BTW- your profile pic is super adorable! :)
Please Help fast! (not rushing ya'll and, this is not high school math)
Answer:
this
Step-by-step explanation:
doesn't need any explanation
Answer:
It should be that since the -1 3/4 is negative and 4 1/2 is positive.
A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between them is 165º. To the nearest tenth, what is the length of the intercepted arc between those two cars on the Ferris wheel?
Answer: 230.4 feet
Step-by-step explanation:
arc length = circumfrance x fraction of a circle
= [tex]2\pi r[/tex] x [tex]\frac{165}{360}[/tex]
= [tex]\frac{2*\pi *80*165 }{360}[/tex]
= 230.4 feet to nearest tenth
The length of the intercepted arc between those two cars on the Ferris wheel is 230.4 feet. This is obtained by using the arc length formula in degrees.
Arc length:The distance across the curved length is said to be arc length.
The arc length is calculated by using the formula:
arc length = circumference × fraction of circle
⇒ arc length = 2πr × θ/360° when θ is given in degrees
where r is the radius.
Given data:Given that,
A Ferris wheel has a radius of r=80 feet
Two particular cars are located such that the central angle between them is 165° i.e., θ = 165°
Calculating the length of the arc:arc length = 2πr × θ/360°
⇒ 2π×80×[tex]\frac{165}{360}[/tex]
⇒ 230.38 feet
Rounding off to the nearest tenth, we get arc length = 230.4 feet.
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What is the slope of the line shown above?
Answer:
1/4
Step-by-step explanation:
we can take two points on the line: (0,2) and (4,3)
to find slope:(2-3)/(0-4)
1/4
Eddie O'Neil found a sports car advertised at a local used-car dealership for
$34,000. The car is clean and in good condition. Its average retail value is
$33,400. It has air-conditioning valued at $840 and leather seats valued at $200,
but it does not include a CD player, which is valued at $100. The used-vehicle
guide indicates that $1,690 should be deducted for excessive mileage on the car.
O'Neil plans to visit the dealership this evening. What is the average retail price
for this vehicle?
Answer:
Eddie O'Neil found a car advertised at a local used-car dealership for $34,000. The car is clean and in good condition. Its average retail value is $33,400.
Step-by-step explanation:
Solve the following system of equations and show all work.
y = x^2 + 3
y = x + 5
please help me! i know that i have to do substitution or something like that but i got really confused halfway through it and i also need to show all of the work!
An electric guitar costs $830, with a $225 full-replacement warranty. if the manufacturer sells 532,475 warranties and has to honor 12% of them, how much profit did the manufacturer gain from the warranties? a. $105,430,050 b. $66,772,365 c. $53,034,510 d. $508,726,615
The profit which the manufacturer gained from the warranties is a. $105,430,050
Calculations and Parameters:Given that count 12% of 532,475:
532,475 - 100%
x - 12%
x= 63, 897.
This means that 63, 897 guitars were sold with a full-replacement warranty and 532,475-63,897=468,578 electric guitars were sold without a full-replacement warranty.
Hence, to find the gain of the manufacturer, $225·468,578
=$105,430,050 from the warranties.
Option A is correct: $105,430,050
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Answer:
b.
$66,772,365
Step-by-step explanation:
100% on EDGE
x/(x ^ 2 + 2xy + y ^ 2) + y/(x ^ 2 - y ^ 2)
Answer:
x2 + y2
_____________
(x + y)2 • (x - y)
on the high attempts the picture was cut off and the last one is 98 in the picture
Answer:
Below in bold.
Step-by-step explanation:
Mean = (98+92+90+78+83+88+95)/7
= 89.1 to nearest tenth.
Deviations:
98 - 89.1 = 8.9
92 - 89.1 = 2.9
90 - 89.1 = 0.9
78 - 89.1 = -11.1 = 11.1 (absolute value)
83 - 89.1 = 6.1
88-89.1 = 1.1
95 - 89.1 = 5.9
So the MAD
= (8.9+2.9+0.9+11.1+6.1+1.1+5.9)/7
= 36.9/7
= 5.27
= 5.3 to nearest tenth.
help me3 i dont really understand it I try so many times but I didn't get it right
Describe a real-life situation that you can represent with an inequality.
Answer:
Think about the following situations: speed limits on the highway, minimum payments on credit card bills, number of text messages you can send each month from your cell phone, and the amount of time it will take to get from home to school. All of these can be represented as mathematical inequalities.
Step-by-step explanation: Got this online hope it helps
Multiply the complex numbers: (3 + 2i)(5 – 2i)
Answer:
19+4i
Step-by-step explanation:
Multiply using the FOIL method, then combine the real and imaginary parts of the expression.
FOIL
A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial, Outer means multiply the outermost terms in the product, Inner means multiply the innermost terms, and Last means multiply the terms which occur last in each binomial.
Result of multiplication of complex numbers will be 19 + 4i
Given,
(3 + 2i)(5 – 2i)
Here,
Complex numbers standard form : x ± iy
Here,
x = real part
y = complex part.
i = iota = [tex]\sqrt{-1}[/tex]
So,
Multiplication : (3 + 2i)(5 – 2i)
⇒15 -6i + 10i -4i²
Here,
i = √-1
i² = -1
So,
15 -6i + 10i -4i²
15 -6i + 10i - 4(-1)
⇒19 + 4i
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The ratio of the number of oranges in a fruit salad to people served is 9/40. If Lisa wants to serve 800 people, how many oranges will Lisa use?
180
Step-by-step explanation:
9:40
?:800
9×20=180
40×20=800
it is a ratio. 9 oranges to 40 people. 40 times 20 is 800 so you do the same to 9 (which gives you 180)
Answer:
180/800
Step-by-step explanation:
if you multiply the numbers by 20 you can get your answer