The 12th term of the arithmetic sequence is 10.5. The 18th term of this sequence is 13.5. Find the common difference and the first term.
let the n'th term be called x, and the value of the term y,
then there is a function y=a*x + b
that will give us all term we want.
this formula is also used for straight lines.
we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula
10.5 = a*12 + b
13.5 = a*18 + b
now lets manipulate these lines.
multiply the first line by 3 and the second line by 2
31.5 = a*36 + 3b
27 = a*36 + 2b
subtract the second line from the first line
4.5 = b
yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.
10.5 = a*12 + 4.5
6 = a*12
0.5 = a
now y=a*x + b can be filled with a and b
y = 0.5 * x + 4.5
for x=1 (the first term) it's f(1)=5
each step is 0.5, hence the common difference.
2and way:(13.5-10.5)/(18-12)
= 3 / 6
= 0.5
we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.
from step 12 to step one it's 11 steps down
10.5 - 0.5*11
= 10.5 - 5.5
= 5
okay I admit... 2and way to do it might be faster and more intuitive... :DFind a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1
The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'
To prove, we will look at some situations:
If we add up the two digits of 18. We get,
[tex]1 + 8 = 9[/tex]
And we multiply 18 by 2 which is greater than 1. We get,
[tex]18[/tex] × [tex]2 = 36[/tex]
The sum remains the same i.e. [tex]3 + 6 = 9[/tex]
Similarly,
If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;
[tex]18[/tex] × [tex]3 = 54[/tex]
where (5 + 4 = 9)
Once more,
Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.
[tex]18[/tex] × [tex]4 = 72[/tex]
[tex](7 + 2 = 9)[/tex]
[tex]18[/tex] × [tex]5 = 90[/tex]
[tex](9 + 0 = 9)[/tex]
Thus, 18 is the answer.
Learn more about 'numbers' here: brainly.com/question/1624562
In the PQRS triangle PQ=QR, QR side extended to S Show that PQ+RS=QS. -S Q R
pls explain too
Answer:
Step-by-step explanation:
from the picture:
QP = QR
and
QR = RS
so
PQ + RS = QS
indentify the explicit function for the sequence in the table
Answer:
Option B
a(n) = 8 + (n-1) • 6
Answered by GAUTHMATH
working alone, aliyah can dig a 10ft by 10 ft hole is 6 hours. one day her friend eugene helped her and it only took 3.75 hours. how long would it take eugene to do it alone? disclaimer: the answer is 11.95 hours, but i keep getting 10. please use the 1/x+1/y=1/z strategy
Answer:
I think the answer is 10 hours
the 11.95 seems wrong
Step-by-step explanation:
[tex]\frac{1}{6} + \frac{1}{y} = \frac{1}{3.75}[/tex]
multiply by 22.5 y
3.75 y + 22.5 = 6y
y = 10
please help, will give brainliest!!!
Answer:
≈ 0.19
Step-by-step explanation:
So first, we find the probability of getting 1 yellow marble (the formula is the number of amount of type over the total number of items), which is:
10/(6+10+5+1)
= 10/22
= 5/11.
So getting a yellow marble on the first try is 5/11 likeliness.
Now, for the second one, we do the same except that you are NOT putting it back into the bag, which means we have to subtract the yellow marble you already took AND ALSO ONE FROM THE TOTAL AMOUNT OF YELLOW MARBLES.
To find the probability of getting the second marble, our equation is:
9/(6+9+5+1)
= 9/21
= 3/7.
Lastly, to find the probability of getting them both consecutively, we multiply the two results.
5/11 * 3/7
= 15/77
≈ 0.19
I hope this helped! :D
given m||n, find the value of x
Answer:
x = 155º
Step-by-step explanation:
y = 25° {Vertically opposite angles}
x + y = 180 {Co-interior angles are supplementary}
x + 25 = 180
Subtract 25 from both sides
x = 180 - 25
x = 155°
Write down at least five number pairs to solve the equation vw = 50
Answer:
1, 50
2, 25
5, 10
10, 5
25, 2
Answer:
Step-by-step explanation:
V W
1 x 50 = 50
1.5 x 33 1/3 = 50
2 x 25 = 50
2.5 x 20 = 50
3 x 16 2/3 = 50
3.5 x 14 2/7 = 50
4 x 12 1/2 = 50
4.5 x 11 1/9 = 50
5 x 10 = 50
5.5 x 9 = 50
6 x 8 1/3 = 50
6.5 x 7 2/3 = 50
7 x 7 1/7 = 50
7.5 x 6 2/3 = 50
8 x 6 1/4 = 50
8.5 x 5 8/9 = 50
9 x 5 5/9 = 50
9.5 x 5 1/4 = 50
10 x 5 = 50
10.5 x 4 3/4 = 50
11 x 4 5/9 = 50
11.5 x 4 1/3 = 50
12 x 4 1/6 = 50
12.5 x 4 = 50
13 x 3 6/7 = 50
13.5 x 3 5/7 = 50
14 x 3 4/7 = 50
3 different problems.
solve b - 4 = 3.
solve -32 = 8w
solve n
— = -4
7
Answer:
see below
Step-by-step explanation:
b - 4 = 3
Add 4 to each side
b - 4+4 = 3+4
b = 7
-32 = 8w
Divide by 8
-32/8 = 8w/8
-4 = w
n/7 = -4
Multiply by 7 to each side
n/7 *7 = -4*7
n = -28
A chef mix his salt and pepper. If he put 2/3 cup of salt and 1/2 cup of pepper in his shaker, what is the ratio of salt to pepper ?
Answer:
4 to 3
Step-by-step explanation:
The ratio of salt to pepper is
2/3 to 1/2
Multiply both fractions by 6
6 * 2/3 to 6 * 1/2
4 to 3
Use the Diagram to find BC.
Answer:
Step-by-step explanation: you have to ask your parents for help
solve A = 1/2bh, for b
Answer:
b=2A/h
Step-by-step explanation:
First I throw everything else to another side with A by dividing them
(A = b)/2h
then I get
b=2A/h
Step-by-step explanation:
A = 1/2 bh
divide by 1/2
2A = bh
divide by h
2A/h = b
The bar graph shows the median income for families in the United States from 1993 through 2000.
Which two consecutive years saw the largest increase in median income?
A. 1994–1995
B. 1997–1998
C. 1998–1999
D. 1999–2000
The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.
Given that
In 1994-1995, the median income is 37,500 and 38,500.In 1997-1998, the median income is 39,700 and 41,000.In 1998-1999, the median income is 41,000 and 42,200.In 1999-2000, the median income is 42,500 and its less.So after analysis, we can conclude that The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.
Learn more about the bar graph here: brainly.com/question/14894834
help me please !! find the domain and range of the function represented by the graph. determine wether the domain is discrete or continuous.
Answer:
Domain is the whole R and the range is R+. The domain is continuous
Please help i do not understand this question!
Answer:
Distributive property
Step-by-step explanation:
The rule being shown here is the distributive property, because the first binomial is taken apart and separately multiplied with the other binomial.
if f(x) = 2x²+2x-1, g(x) = x²+5x+2 f(x)=g(x), find the value of x
Answer:
Possible Answers: –5. –21. 7. –1
Answer:
just put the values and simpilyfy it untill you get the value of X
hence, the value of X is either 3 or, -1
the train regularly travels 135 miles in 60 minutes.
What is the speed, in miles per minute, on this portion of the route?
Answer:
2.25 miles per minute
Step-by-step explanation:
Speed = Distance/Time
135/60
2.25 miles per minute
Answer from Gauthmath
A spherical ball has a radius of 4 inches. What is the volume of this sphere, to the
nearest cubic inch.
Answer:
V = 267.9 in^3
Step-by-step explanation:
V = 4/3 * (pi) * r^3
V = 4/3 * 3.14 * 4^3
V = 4/3 * 3.14 * 64
V = 256/3 * 3.14
V = 803.84/3
91. Jack can read 45 pages of his book in one and a
half hours. At that rate, how long will it take him to
read the entire 300-page book?
Answer:
10 hours
Step-by-step explanation:
45 pages per 1 hour and 30 minutes, or 60 min +30 min =90 min
90 minutes / 45 pages has to be equal to an equivalent fraction where we have 300 pages
90 minutes /45 pages = ? minutes / 300 pages , multiply both sides by 300
? minutes = 90*300/45 = 600 minutes
to read 300-page book will take 600 minutes = 10 hours
if measure of three angles of a quadrilateral are 65 degree 95 degree and 45 degree then find the measure of the fourth angle?
Answer:
155 degrees
Step-by-step explanation:
Hi there!
The sum of the interior angles of a quadrilateral is always 360 degrees. To find the measure of the fourth angle, subtract 65, 95 and 45 from 360:
360-65-95-45
= 155
Therefore, the measure of the fourth angle is 155 degrees.
I hope this helps!
Answer:
155 degrees
Step-by-step explanation:
A quadrilateral has a total internal angle sum of 360 so we can set up an equation where x is the fourth angle
360=65+95+45+x
360=205+x
x=155
on the number line, which of the following numbers below can be found on the right of 2.26??
A.2.30
B.-2.25
C.2.25
D.1.26
Answer:
2.25
Step-by-step explanation:
The lower number will always be on the right side unless its negative numbers , So the lower number is 2.25 , Why it isn't 1.26 is because its much far from 2.26 and so cannot be counted . Thanks
Look at this cube
If the side lengths are halved, then which of the following statements about its surface area will be true?
Answer:
the new surface Will be 1/4 pf the old surface
Step-by-step explanation:
because the surface with 7 in Is about 294 and with 3.5 (1/2 of 7) Is 73.5.
so 294:4 Is 73.5
excuse me for my bad English but I'm italian
will mark brainliest help!
In parallelogram ABCD, m∠B = 105°.
What is the value of x. (Round your answer to the nearest tenth, if necessary.)
Answer:
52.5
Step-by-step explanation:
Since ED ≈ AD, ∆AED is a isosceles triangle where <EAD and <AED has same angle measurement
Now, m<B = 105°, since ABCD is a parallelogram, <B = <D
so, m<ADC = 105° so, m<ADE = 180°-105° = 75°
Now, m<EAD+m<AED+m<ADE = 180°
or, m<AED+m<AED+m<ADE = 180°
or, x+x+75°=180°
or, 2x=180+75°
or, 2x=105°
or, x=52.5°
Someone please help me find y if you don’t mind Thankyouu so much
Answer:
Step-by-step explanation:
Decreasing rate = 12% = 0.12
y = 2400 * (1- 0.12)^x = 2400*(0.88)^x
x = 8 years
[tex]y = 2400 *(0.88)^{8}\\\\= 2400*0.36\\\\= 863[/tex]
Find the cross product (7,9, 6)x 44, 1, 5). Is the resulting vector perpendicular to the given vectors?
a. (-57, 43, 33); yes
c. (33. – 59, - 57); no
b. (39, – 59,43), yes
d. (33, - 57, 49); no
Answer:
Option B, (39, -59, 43)
Answered by GAUTHMATH
The difference of a number and 11
Answer:
x - 11
Step-by-step explanation:
"A number" is the same thing as a variable.
Answer:
x-11
Step-by-step explanation:
42 deliveries in 3 hours = deliveries per hour
Answer:
14 deliveries per hour
Step-by-step explanation:
42/3
14
The person makes 14 deliveries per hour
Answer:
14
Step-by-step explanation:
42 / 3 = 14
If 1 angle is four time of another angle in linear pair find the angles. Please do it fast as you can
Answer:
let the angle be x then other angle is 4x
so,
x + 4x = 180
5x = 180
x = 36
so other angle I.e 4x = 4 × 36 = 144
Let one angle be x
Other angle=4xBoth are linear pair hence their sum will be 180
[tex]\\ \sf \longmapsto x+4x=180[/tex]
[tex]\\ \sf \longmapsto 5x=180[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{180}{5}[/tex]
[tex]\\ \sf \longmapsto x=30[/tex]
[tex]\\ \sf \longmapsto 5x=5(30)=150[/tex]
Four times an angle is equal to half of its supplement. Find the measures of both angles.
Answer:
The bigger angle is 144 degrees and the smaller one is 36 degrees
Find the place value of 8 in 2456.1387.
Tenths
Hundredths
Thousandths
Thousands
Answer: Third Choice. Thousandths
Step-by-step explanation:
Concept:
Here, we need to know the order and name of each place value.
Please refer to the attachment below for the specified names.
Solve:
STEP ONE: Orde and name each place
2 ⇒ One Thousands
4 ⇒ Hundreds
5 ⇒ Tens
6 ⇒ Ones
.
1 ⇒ Tenths
3 ⇒ Hundredths
8 ⇒ One Thousandths
7 ⇒ Ten Thousandths
STEP TWO: Find the number [8] in the number
As we can see from the list above, 8 is at the right of the decimal point, thus, the place value is Thousandths.
Hope this helps!! :)
Please let me know if you have any questions
