Answer:
131
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₁₂ = 38 and a₈₅ = 257 , then
a₁ +11d = 38 → (1)
a₁ + 84d = 257 → (2)
Subtract (1) from (2) term by term
73d = 219 ( divide both sides by 73 )
d = 3
Substitute d = 3 into (1)
a₁ + 11(3) = 38
a₁ + 33 = 38 ( subtract 33 from both sides )
a₁ = 5
Thus
5 + 3(n - 1) = 395 ( subtract 5 from both sides )
3(n - 1) = 390 ( divide both sides by 3 )
n - 1 = 130 ( add 1 to both sides )
n = 131
Thus there are 131 terms in the sequence
Please help Quickly
Answer:
2x+1= 8
2x= 8-1
2x= 7
x= 7/2
x= 3.5
hope this helps uh
How do I do 123°15’-40°26’ ?
Answer: 82° 49'
Step-by-step explanation: A degree is subdivided
into minutes and seconds.
1° = 60' and 1' = 60"
One degree = 60 minutes
123° 15' - 40° 26'
= 7395' - 2426'
= 4969'
= 82° 49'
please someone help me to prove this.
We know that,
[tex]\dag\bf\:sin^2A=\dfrac{1-cos2A}{2}[/tex]
[tex]\dag\bf\:sin2A=2sinA\:cosA[/tex]
___________________________________
Now, Let's solve !
[tex]\leadsto\:\bf\dfrac{sin^2A-sin^2B}{sinA\:cosA-sinB\:cosB}[/tex]
[tex]\leadsto\:\sf\dfrac{\frac{1-cos2A}{2}-\frac{1-cos2B}{2}}{\frac{2sinA\:cosA}{2}-\frac{2sinB\:cosB}{2}}[/tex]
[tex]\leadsto\:\sf\dfrac{1-cos2A-1+cos2B}{sin2A-sin2B}[/tex]
[tex]\leadsto\:\sf\dfrac{2sin\frac{2A+2B}{2}\:sin\frac{2A-2B}{2}}{2sin\frac{2A-2B}{2}\:cos\frac{2A+2B}{2}}[/tex]
[tex]\leadsto\:\sf\dfrac{sin(A+B)}{cos(A+B)}[/tex]
[tex]\leadsto\:\bf{tan(A+B)}[/tex]
Answer: see proof below
Step-by-step explanation:
Use the Power Reducing Identity: sin² Ф = (1 - cos 2Ф)/2
Use the Double Angle Identity: sin 2Ф = 2 sin Ф · cos Ф
Use the following Sum to Product Identities:
[tex]\sin x - \sin y = 2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x - \cos y = -2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \dfrac{\sin^2A-\sin^2B}{\sin A\cos A-\sin B \cos B}[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\sin A \cos A-\sin B\cos B}[/tex]
[tex]\text{Half-Angle:}\qquad \qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\dfrac{1}{2}\bigg(\sin 2A-\sin 2B\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{1-\cos 2A-1+\cos 2B}{\sin 2A-\sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{-\cos 2A+\cos 2B}{\sin 2A - \sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 2B-\cos 2A}{\sin 2A-\sin 2B}[/tex]
[tex]\text{Sum to Product:}\qquad \qquad \dfrac{-2\sin \bigg(\dfrac{2B+2A}{2}\bigg)\sin \bigg(\dfrac{2B-2A}{2}\bigg)}{2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\sin \bigg(\dfrac{2A-2B}{2}\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{-2\sin (A + B)\cdot \sin (-[A - B])}{2\cos (A + B) \cdot \sin (A - B)}[/tex]
[tex]\text{Co-function:}\qquad \qquad \dfrac{2\sin (A + B)\cdot \sin (A - B)}{2\cos (A + B) \cdot \sin (A - B)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{\cos (A+B)}{\sin (A+B)}\\\\\\.\qquad \qquad \qquad \quad =\tan (A+B)[/tex]
LHS = RHS: tan (A + B) = tan (A + B) [tex]\checkmark[/tex]
Carly withdraws $18 from her bank account. Which number line represents this amount? A number line going from negative 20 to positive 20. A point is at 18. A number line going from negative 20 to positive 20. A point is at 12. A number line going from negative 20 to positive 20. A point is at negative 12. A number line going from negative 20 to positive 20. A point is at negative 18.PLEASE HELP QUICKLY!!!
A withdrawal is taking money out which is a negative value.
She took $18 out so it would be written as -18.
The answer is:
A number line going from negative 20 to positive 20. A point is at negative 18.
Answer:
Carly withdraws $18 from her bank account.
We assume that Carly has $x in her account. She withdraws $18 from her bank account.
So we have to subtract $18 from $x amount.
Which is $x - 18.
So we are subtracting $18 from her account.
It should be represented by an integer -18.
Now we have to identify the which number line represents -18.
It is D)
Step-by-step explanation:
what is the sum of a rational number and an irrational number
Answer:
Irrational Number
Step-by-step explanation:
Answer:
"The sum of a rational number and an irrational number is irrational."
Step-by-step explanation:
By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.
The temperature rose from -4 F to 45 F in spearfish, South Dakota and only two minutes. By how many degrees does the temperature change?
Answer: 49 degrees
Step-by-step explanation:
One foot is equal to 1 3 of a yard. What is the decimal equivalent to 1 3 ?
answer is C 0.3
I just took the test
M is the midpoint of segment VW. Find the value of n.
Answer
x=4
Step-by-step explanation:
4x-1=3x+3 because both sides are equal, since M is a midpoint.
Subtract 3x to both sides to get x-1=3.
Add 1 to both sides to get x=4.
Answer:
[tex]\huge\boxed{\sf x = 4}[/tex]
Step-by-step explanation:
If M is the midpoint of VW.
Then,
WM = MW
Given that WM = 4x - 1 and MW = 3x + 3
So,
4x - 1 = 3x + 3
Combining like terms
4x - 3x = 3 + 1
x = 4
6v-6v how would I solve that?
[tex]\huge\boxed{0}[/tex]
Any value minus itself will always be [tex]0[/tex]. This means that no matter what the value of [tex]v[/tex] is, [tex]6v-6v=\boxed{0}[/tex].
you tape two pieces of paper together that each measure 34.85 cm. you then cut off 14.91 cm . how long is the paper.
Answer:
the paper is 54.79 cm .
Step-by-step explanation:
34.85 * 2 = 69.7 ( two pieces of paper altogether )
69.7 - 14.91 = 54.79 ( when got cut )
Let $a$, $b$, $c$, $d$, and $e$ be positive integers. The sum of the four numbers on each of the five segments connecting "points" of the star is 28. What is the value of the sum $a + b + c + d + e$?
Answer:
i dunno
Step-by-step explanation:
somebody help
Answer:
Step-by-step explanation:
[tex]a+c=23\\a+d=20\\e+c=21\\b+e=24\\d+b=22\\[/tex]
...
In the figure shown, AB = 8 and AD = 5. What is BC?
Answer: 5
Step-by-step explanation:
Since we know that equal number of dashes will always be equal to another we can easily solve the question. They said AB=8 and as you can see 8 is represented by two dashes here and if we take in what i said earlier,, that means DC= 8 too. They also said AD= 5. Since 5 is represented by one dash we can easily see that since BC also has one dash,, it is going to be equal to AD which concluded to the answer of 5.
Identify the type of transformation in the following graphic and describe the change.
Answer:
Translation of MATH to M'A'T'H' by 5 units to the left.
Step-by-step explanation:
From the figure attached,
Quadrilateral MATH has been transformed to the image M'A'T'H'.
Shape and size of MATH is not altered in this transformation, only translation has been done.
We take a point A(4, 3) which has been translated to A'(-1, 3).
Rule followed for the translation,
(x, y) → (x-5, y)
Translation by 5 units to the left.
Answer:
lol the number of comments got maxed out
Step-by-step explanation:
Help me with this math problem please
Answer:
[tex]y=8[/tex]
[tex]RS=77, ST=31[/tex]
Step-by-step explanation:
Note that the entire segment RT is the combined lengths of RS and ST. So:
[tex]RT=RS+ST[/tex]
We know that RT is 108, RS is (9y+5), and ST is (3y+7). Substitute:
[tex]108=(9y+5)+(3y+7)[/tex]
On the right, combine like terms:
[tex]108=(9y+3y)+(5+7)[/tex]
Add:
[tex]108=12y+12[/tex]
Subtract 12 from both sides. The right cancels:
[tex]96=12y[/tex]
Divide both sides by 12:
[tex]y=8[/tex]
So, the value of y is 8.
To find RS and ST, substitute 8 for y. So:
[tex]RS=9y+5[/tex]
Substitute 8 for y:
[tex]RS=9(8)+5[/tex]
Multiply:
[tex]RS=72+5[/tex]
Add:
[tex]RS=77[/tex]
Do the same for ST:
[tex]ST=3y+7[/tex]
Substitute 8 for y:
[tex]ST=3(8)+7[/tex]
Multiply:
[tex]ST=24+7[/tex]
Add:
[tex]ST=31[/tex]
The diameter of a circle is 13 cm. Find its area to the nearest tenth.
Area=[tex]\pi[/tex] [tex]r^{2}[/tex]
divide diameter with 2 to get radius 13/2= 6.5
area= pi 6.5x6.5
=[tex]\pi[/tex]42.25
answer= 42.25[tex]\pi[/tex]
Area of a circle is equal to [tex]\boldsymbol{132.8}[/tex] square inches.
Area of a circleA circle is a collection of all the points that are at the fixed distance (radius) from a fixed point (center).
Diameter of a circle [tex]=\boldsymbol{13}[/tex] centimeter
Radius of a circle is half of the diameter.
So,
Radius of a circle [tex]=\frac{13}{2}[/tex] centimeter
Area of a circle [tex]=\boldsymbol{\pi r^2}[/tex] where [tex]r[/tex] denotes radius of a circle.
[tex]=\frac{22}{7}\times \left ( \frac{13}{2} \right )^{2}\\=132.7857[/tex]
[tex]\boldsymbol{\approx 132.8}[/tex] square inches
So, area of a circle is equal to [tex]\boldsymbol{132.8}[/tex] square inches.
Find out more information about circle here:
https://brainly.com/question/11833983?referrer=searchResults
What is 3x + 2 + 4x - 1 after combining like terms
3x and 4x are like terms. Add them together and you get 7x.
2 and -1 are like terms. Add them together and you get 1.
3x+2+4x-1
7x+1 is your final answer
Sam is flying from Columbus, Ohio, to Kralendijk, Bonaire, a distance of 2,488 miles. First, he flies 995 miles to Miami, Florida. He then flies from Miami to San Juan, Puerto Rico, a distance of 1,033 miles. How many miles will he travel flying from Columbus to San Juan? How many more miles does he have to fly to Kralendijk? Enter your answers in the boxes. From Columbus to San Juan, Sam flies miles. He will have more miles to fly.
Answer:
1) From Columbus to San Juan, Sam flies 2,028 miles
2)Sam will have 460 miles more miles to fly to Kralendijk
Step-by-step explanation:
The given information are;
The total (flight) distance from Columbus, Ohio to Kralendijk, Bonaire = 2,488 miles
The distance Sam flies from Columbus to Miami, Florida = 995 miles
The distance Sam flies from Miami to San Juan = 1,033 miles
1) Therefore, the number of miles Sam travels flying from Columbus to San Juan is given as follows;
The number of miles Sam will have to travel flying from Columbus to San Juan = (The distance Sam flies from Columbus to Miami, Florida) + (The distance Sam flies from Miami to San Juan)
The number of miles Sam will have to travel flying from Columbus to San Juan = 995 miles + 1,033 miles = 2028 miles
The number of miles Sam will have to travel flying from Columbus to San Juan = 2,028 miles
Therefore, from Columbus to San Juan, Sam flies 2,028 miles
2) The number of more miles Sam has to fly to Kralendijk from Sam Juan is therefore;
The number of more miles Sam has to fly to Kralendijk from Sam Juan = (The total (flight) distance from Columbus, Ohio to Kralendijk, Bonaire) - (The number of miles Sam will have to travel flying from Columbus to San Juan)
The number of more miles Sam has to fly to Kralendijk from Sam Juan = 2,488 miles - 2,028 miles = 460 miles.
The number of more miles Sam has to fly to Kralendijk from Sam Juan = 460 miles.
Therefore, Sam will have 460 miles more miles to fly to Kralendijk
From the division of the trip into parts, it is found that:
From Columbus to San Juan, Sam flies 2028 miles.He will have more 460 miles to fly.--------------------
The total distance of Columbus -> Kralendijk is 2488 miles.The first part, Columbus -> Miami, is 995 miles.The second part, Miami -> San Juan, is 1033 miles.The final part, San Juan -> Kralendijk, is x miles.--------------------
Since Columbus to Miami is 995 miles and Miami to San Juan is 1033 miles, we have that the distance from Columbus to San Juan, in miles, is of:
[tex]995 + 1033 = 2028[/tex]
Thus:
From Columbus to San Juan, Sam flies 2028 miles.
--------------------
The total distance is 2488 miles.Until San Juan, it is 2028 miles. The final part is San Juan to Kralendijk, x miles, thus:[tex]2028 + x = 2488[/tex]
[tex]x = 2488 - 2028[/tex]
[tex]x = 460[/tex]
Thus:
He will have more 460 miles to fly.
A similar problem is given at https://brainly.com/question/24352869
The following lists the weight (in pounds) of dogs at a kennel.
16, 34, 44, 20, 50, 19, 30, 54
Two more dogs weighing 25 pounds and 45 pounds come to the kennel. If these dogs' weights are
added to the data set, which statement describes the change in the data set?
Answer:
The mean increased, but the median stayed the same
Step-by-step explanation:
hope it help luvs
The mean increased, but the median remained constant If new dogs' weights are added to the data set.
What is the mean of a data set?The mean of a data set is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
Given the set of observations as :
16, 34, 44, 20, 50, 19, 30, 54
Arrange the data in ascending order, we get
16, 19, 20, 30, 34, 44, 50, 54
The median of the given data would be (30+34)/2 = 32.
Here, n = 8
⇒ ∑x = Sum of Observations
⇒ ∑x = 267
Mean = ∑x/n
Mean = 267/8
Mean = 33.375
If two more dogs weighing 25 pounds and 45 pounds come to the kennel.
Arrange the given data in ascending order, we get
16, 19, 20, 25, 30, 34, 44, 45, 50, 54
The new median of the data would be (30+34)/2 = 32.
New mean = 337/10 = 33.7
Therefore, the mean increased, but the median remained constant If new dogs' weights are added to the data set.
Learn more about the mean of the data set here:
brainly.com/question/13000783
#SPJ2
-(5+-6)*(2-7^2)
Show all work, will give brainliest
100 points
Answer:
-47
Step-by-step explanation:
[tex]-(5-6) x (2-7^{2})\\[/tex]
[tex]-(-1) x (2-49)[/tex]
1 x (-47)
= -47
Complete the pattern. 14, 22, 30, _, _, _
Answer:
14, 22, 30, 38, 46, 54
Step-by-step explanation:
the pattern has a difference of 8, so if you want to get the remaining answers you are to add 8 to it. thanks mark as brainlest
Dave is currently scuba diving at an elevation of -24 meters. What integer is used to represent the elevation?
Answer:
-24
Step-by-step explanation:
The integer in "elevation of -24 meters" is -24.
Simon has a poster with a margin of 1 inch on all sides. The printed area is 25 square inches. He wants to determine the area of the entire poster including the margin. His work is shown. in2= 5 in 5 (side) + 1 (margin) = 6 inches Poster area = 62 = 36 in2 Which of the follow statements about Simon’s calculations are true? Check all that apply. Simon did not calculate the correct area of the poster. Simon calculated the correct area of the poster. Simon needed to find the perfect square of 7 to find the poster’s area. Simon needed to multiply 7 by itself to find the correct area. Simon needed to multiply 6 by itself to find the correct area. help me fast
Answer:
the Answer is the 1,3,and 4
Chloe drives from her house to her grandma's house 64 miles away in an hour and 35 minutes. How fast was she driving on average? About 47 mph About 53 mph About 40 mph About 30 mph
Answer:
She was driving at 40.42 mph on averageStep-by-step explanation:
In this exercise, for us to find the speed that Chloe drives with we need to first convert the time she spent driving to hours completely since the time given is in hours and minute
Data
distance= 64 mile
time= 1hr 35min
to covert 1 hr 35 min to hours we have
= 1 + 35/60 (we are converting 35 min to hrs)
= 1+0.583
= 1.583
hence speed= 64/ 1.583
speed= 40.42 mph
She was driving at 40.42 mph on average
About 40 miles per hour
when it comes to finding the common denominator, do I add or subtract it to the denominator
Answer: Subtract
Step-by-step explanation: Make your denominator equal using the concept of LCM, then subtract the numerators accordingly. Rewrite each fraction to its equivilent fraction with a denominator equal to the LCM=30, then you need to subtract the numberators, but make sure to reduce your answer to the lowest possible term. I hope this helps.
Answer:
when you find the common denominators you find the LCM.
Step-by-step explanation:
Isabel has scored 22, 20, and 20 points in her three basketball games so far. How many points does she need to score in her next game so that her average is 20 points per game?
Answer: 18
Step-by-step explanation:
To average 20 in 4 games, she would need 80 points in total. In her 3 games, she gets 62 points.
80 - 62 = 18
What is the length, in dekameters, of 1073.4 centimeters?
1073.4 centimeters = 1.073 decameters
Answer:
107.34 decimeter
Step-by-step explanation:
7+(a+b)=(7+a)+b please help asap
Answer:
We are using the Associate property of addition
Step-by-step explanation:
7+(a+b)=(7+a)+b
We are using the Associate property of addition
Point Mis on line segment LN. Given LN = 9, MN. = 4x, and
LM = 5x, determine the numerical length of MN.
Answer: 4
Step-by-step explanation:
If a number added to five is divided by the difference of the number and two, the result is three-fourths. Find the number.
Answer:
x = - 26
Step-by-step explanation:
Let the number be x.
According to the question,
[tex]\frac{x+5}{x-2} = \frac{3}{4}\\[/tex]
Cross multiplying 4 & 3 gives :-
[tex]4(x+5)=3(x-2)[/tex]
And solving this eqn. gives :-
[tex]4(x+5)=3(x-2)\\=> 4x+20=3x-6\\=>4x-3x=-20-6\\=>x=-26[/tex]
Verification :-
(putting the value of x = -26 )
[tex]\frac{x+5}{x-2} \\\\=>\frac{-26+5}{-26-2} \\\\=> \frac{-21}{-28} \\\\=>\frac{21}{28}[/tex]
Reducing [tex]\frac{21}{28}[/tex] by 7 gives [tex]\frac{3}{4}[/tex] .
3.456x(2.05x10^5) = ?
Answer:
708480
Step-by-step explanation:
You follow the order of BEDMAS. There are brackets in this equation, meaning we have to focus on what is inside the brackets first. The next step is Exponents. So you multiply 2.05 by 10^5.
This would give you 205000.
You then multiply this number by the number on the outside of the brackets which is 3.456.
This would give you 708480. (You can get these answers by using a calculator).
Don't forgot to follow the order of BEDMAS or whatever law of operations you were taught (BIDMAS/BIMDAS etc)