19th term of an AP = 52
38th term = 128
Find:the sum of the first 56 terms
Solution:We know that,
nth term of an AP – a(n) = a + (n - 1)d
Hence,
→ a + (19 - 1)d = 52
→ a + 18d = 52 -- equation (1)
Similarly,
→ a + (38 - 1)d = 128
→ a + 37d = 128 -- equation (2)
Subtract equation (1) from (2).
→ a + 37d - (a + 18d) = 128 - 52
→ a + 37d - a - 18d = 76
→ 19d = 76
→ d = 76/19
→ d = 4
Substitute the value of d in equation (1).
→ a + 18 * 4 = 52
→ a = 52 - 72
→ a = - 20
We know,
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
Hence,
→ S(56) = 56/2 * [ 2 (- 20) + (56 - 1) * (4) ]
→ S(56) = 28 * [ - 40 + 55 * 4 ]
→ S(56) = 28 * [ - 40 + 220 ]
→ S(56) = 28 * (180)
→ S(56) = 5040
Hence, the sum of first 56 terms of the given AP is 5040.
I hope it will help you.
Regards.
The sum of the first 56 terms of the given AP is 5040.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression. A number series is a number-based sequence. In the number series questions, we must identify the rules that lead to the formation of a number series.
Given that in an AP. 19th term is 52 and 38th term is 128.
nth term of an AP – a(n) = a + (n - 1)d
a + (19 - 1)d = 52
a + 18d = 52 -- equation (1)
Similarly,
a + (38 - 1)d = 128
a + 37d = 128 -- equation (2)
Subtract equation (1) from (2).
a + 37d - (a + 18d) = 128 - 52
a + 37d - a - 18d = 76
19d = 76
d = 76/19
d = 4
Substitute the value of d in equation (1).
a + 18 * 4 = 52
a = 52 - 72
a = - 20
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
S(56) = 56/2 * [ 2 (- 20) + (56 - 1) * (4) ]
S(56) = 28 * [ - 40 + 55 * 4 ]
S(56) = 28 * [ - 40 + 220 ]
S(56) = 28 * (180)
\S(56) = 5040
Hence, the sum of the first 56 terms of the given AP is 5040.
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3/4+?=9/8
what does ? equal
A line is drawn along the top side of a square
Rewrite the equation B - 3,368 = 2t as a function of t.
Answer:
Step-by-step explanation:
b-3368/2 = t
A choir director at your school wants to divide the choir into smaller groups. There are 24 sopranos, 60 altos, and 36 tenors. Each group will have the same number of each type of voice. What is the greatest number of groups that can be formed?
GCF or LCM?
GCF
GCF
LCM
LCM
Answer:
gcf
Step-by-step explanation:because it say greatest number of groups
express 3 4/5 as a percent rounding to the nearest tenth of a per
Answer:
3.8%
Step-by-step explanation:
if what you meant was percent, then thats your answer
A triangle has angles of 124, 28° and 28º. Using the given angle measures, how many triangles can be formed?
Answer: 340
Step-by-step explanation:
i need help asap can anyone do this?
Step-by-step explanation:
since they are similar...
DF= 2.68
EF= 2.01
How many hours does it take to clean all the windows on the burj Khalifa
Answer:
It takes three months to clean all the windows.
Step-by-step explanation:
The building is cleaned four times a year.
The ratio of butterflies to bees in Juan's insect collection is 3 to 4. If there are 32 bees, how many butterflies would there be? Group of answer choices
Answer: There would be 24 butterflies.
Step-by-step explanation:
Given: The ratio of butterflies to bees in Juan's insect collection is 3 :4.
Let 3x = Number of butterflies
4x = Number of bees
As per given, 4x = 32 (number of bees)
x= 8 [Divide both sides by 4]
Number of butterflies = 3x = 3 (8)=24
Hence, there would be 24 butterflies.
Simplify: 11y - 17y
Enter the original expression if it cannot be
simplified.
Answer:
-6y
Step-by-step explanation: 11-17=-6 which means that the answer would be -6y
A town has 15 acres of farmland. The town plans to increase the amount of farmland about 6% every 8 years. If the town continues to follow their plan, how much farmland will be there after 64 years?
Answer:
Approximately 23.91 acres of farmland after 64 years.
Step-by-step explanation:
A town has 15 acres of farmland.
It plans to increase 6% every 8 years.
We can set up equation for the increase.
A=P[tex](1+r)^{\frac{t}{8} }[/tex]
From the given information
P= 15
r=0.06
t=64
Plug in these values into the formula
A=15[tex](1+0.06)^{\frac{64}{8} }[/tex]
Simplify it
A=15[tex](1.06)^{8}[/tex]
Simplify further
A=23.90772...
Approximately 23.91 acres of farmland after 64 years.
please someone help me
use slope two point formula ans is 3/4
Answer: 3/4
Step-by-step explanation:M=5-2/1 - -3
A restaurant customer left $1.95 as a tip. The tax was 7% and the tip was 15% of the after-tax cost. What was the total bill?
Answer:
The tax was 5% and 14.95
Step-by-step explanation:
Answer:
$14.95
Step-by-step explanation:
550 + 13 < 750 + 39
Answer:
True
Step-by-step explanation:
550 + 13 = 563750 + 39 = 789Re-write: 563 < 789Because 563 IS less than 789, the answer is true.I hope this helps!
okay smart amazing humans , help ? :((
Answer:
m angle 1 = 14 degrees
m angle 2 = 76 degrees
Step-by-step explanation:
I honestly have no clue
Answer:
I really dont know
Step-by-step explanation:
2+2????
Answer:
fourth option
Step-by-step explanation:
If f(x) and g(x) are inverse functions , then
(f ￮ g(x) = (g ￮ f)(x) = x for all real numbers
Please help me solve this
Answer:
the answer to both is y approaches infinity
A prime polynomial cannot be written as a product of lower-degree polynomials. Which polynomial is prime?
8x2 – 10x – 3
8x2 + 2x – 3
8x2 – 6x – 3
8x2 + 23x – 3
Answer: C. 8x2 - 6x - 3
Step-by-step explanation:
I took the test. Hope this helps
The prime polynomial is 8x^2 - 6x - 3
What are polynomials?Polynomials are expressions that are represents using terms and coefficients
For a polynomial to be prime, then the polynomial cannot be factored into smaller expressions
From the given options, 8x^2 - 6x - 3 cannot be factorized.
Hence, the prime polynomial is 8x^2 - 6x - 3
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At a school store, pencils are sold in packages of 8 pencils each. One package costs $1.92. What is the unit cost per pencil?
Answer:
Step-by-step explanation:
So to solve this problem, you need to divide 1.92 by 8.
1.92 divided by 8 is .24
So the unit price per pencil is .24 or 24 cents
The unit cost per pencil is $0.24.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
Given that, at a school store, pencils are sold in packages of 8 pencils each. One package costs $1.92.
Cost of each pencil = Cost of pack of pencils ÷ Number of pencils in each pack
= 1.92/8
= $0.24
Therefore, the cost of each pencil is $0.24.
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The scale factor for the reduction is
The length of A=204) = 4 feet
What is the length of B?
B =
feet
Answer:
Step-by-step explanation:
The scale factor is 1/5
B = 5 feet
Jon ate too many holiday cookies and gaines 2.2 kilograms in December. Then he went on a diet and lost 1.5 kilograms in January. Then he lost another 3.7 kilograms in February. Jon wants to know what the total change in his weight was over these three months.
WICH OF THE FOLLOWING EQUATIONS MATCHES THE SITUATION ABOVE?
A.) 2.2+(-1.5)+(-3.7)=?
B.) 2.2+1.5-3.7=?
c.) None of the above
Answer:
A
Step-by-step explanation:
Solve: (-8) (2) (-1) (1) =
A -16
B -18
C 16
D 18
Answer:
16 (C)
Step-by-step explanation:
-16*-1 is 16*1 is 16
A monthly budget is shown. Which equation can be used to determine y, the minimum amount of money a family must earn to meet the requirements of this budget for one year?
Answer:
$3600 * 12
Step-by-step explanation:
To get the minimum amount of money the family must earn to meet the requirements of their budgets for one year, first you have to get their total budget for a month and then multiply it by the number of months in a year.
The monthly budget = Rent + food + child care + transportation + utilities + insurance + savings + taxes
Monthly budget = $870 + $550 + $375 + $480 + $400 + $235 + $400 + $290 = $3600
Minimum requirements for one year = $3600 * 12 months
[tex]2 \sqrt{ - 49} [/tex]
please simplify
Answer:
14i
Step-by-step explanation:
Write the equation in standard form of the line that passes through (-1,-4) parallel to 9x -y = 4
Answer:
9x-y=-5
Step-by-step explanation:
First, put this equation into slope intercept form (makes it easier)
9x-y=4
subtract 9x from both sides
-y=-9x+4
multiply by -1 on both sides
y=9x-4
Parallel lines have the same slopes, so the second line is y=9x+b (b is a placeholder for the y intercept)
now, find the y intercept
since the line has to go through (-1,-4), plug it into the equation
-4=9(-1)+b
-4=-9+b
5=b
so now the line would be y=9x+5... in slope intercept form. The question asks for the answer to be in standard form.
5 from both sides
y-5=9x
subtract y from both sides
-5=-y+9x
or
9x-y=-5
I am totally confused about this
[tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]
______________________________
[tex]\bold{Solution~Steps:}[/tex]
1.) Input [tex]a=4[/tex], [tex]b=3[/tex], and [tex]c=9[/tex] into the equation.
[tex]\frac{4^2-2*3*9}{7}[/tex]2.) Calculate 4 to the power of 2.
[tex]4^2=16[/tex]Equation at the end of this step: [tex]\frac{16-2*3*9}{7}[/tex]3.) Multiply 2 and 3.
[tex]2[/tex] × [tex]3=6[/tex]Equation at the end of this step: [tex]\frac{16-6*9}{7}[/tex]4.) Multiply 6 and 9.
[tex]6[/tex] × [tex]9=54[/tex]Equation at the end of this step: [tex]\frac{16-54}{7}[/tex]5.) Subtract 54 from 16.
[tex]16-54=-38[/tex]Equation at the end of this step: [tex]\frac{-38}{7}[/tex]6.) Fraction [tex]\frac{-38}{7}[/tex] can be rewritten as a decimal by dividing:
[tex]-38[/tex] ÷ [tex]7=-5.42857143[/tex]______________________________
[tex]\bold{Answer:}[/tex]
[tex]-5.42857143[/tex]______________________________
[tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~~-TotallyNotTrillex}[/tex]
Solve the question.
A company’s stock begins the week with a price of $43.85 per share.
The price changes by $2.70 each day for 2 days. Then the price changes by −$1.10 each day for 2 days. On the last day, the price changes by −$4.45.
What is the price per share of the company’s stock after those five days?
Answer:
$42.60 per share
Step-by-step explanation:
1. 2(2.7) + 2(-1.1) + (-4.45) = -1.25
2. 43.85 + -1.25 = 42.6
Write an equation of the parabola with vertex (0, 0) and directrix x=2.
Answer:
y² = -8xStep-by-step explanation:
directrix x=2 and vertex (0, 0) means focus: (-2, 0)
also means the distance from the origin to the focus: a=2
y² = -4ax
y² = -4×2x
y² = -8x
A department store is offering the same percentage discount on all of their shoes. Suppose one pair of shoes is marked down from $70 to 549. Based on that percentage discount, what would the new price
for a pair of shoes that originally cost $110?
A89.00
B.77.00
C.73.33
D.33.00
O
Answer:
B.77.00Step-by-step explanation:
Note: there is typo- 549 should read $49
Discount is:
$70 - $49 = $21Discount % is:
21/70*100% = 30%Applying same discount to pair of shoes for $110:
$110 - 30% =$110*(100 - 30)/100 = $110*0.7 =$77Correct option is B