The sum of 8th term of an A.P is 160 while to sum of the 20th term is 880. Find the 43rd term
The value of the 43rd term of the arithmetic sequence will be 482.
What is the sum of an arithmetic sequence?Let a be the first term, L be the last term, n be the number of terms, and d be a common difference.
Then the sum of the arithmetic sequence will be
Sₙ = (n / 2)[a + L]
Sₙ = (n/2) [2a + (n − 1) d]
An A.P.'s eighth term is worth 160 while their twentieth term is worth 880.
160 = (8/2)(2a + 7d)
2a + 7d = 40 ...1
880 = (20/2)(2a + 19d)
2a + 19d = 88 ...2
From equations 1 and 2,
40 - 7d + 19d = 88
12d = 48
d = 4
Then the value of 'a' is given as,
2a + 7(12) = 40
2a = 40 - 84
2a = -44
a = -22
The value of the 43rd term is given as,
aₙ = a + (n - 1)d
a₄₃ = - 22 + (43 - 1)(12)
a₄₃ = - 22 + 42 x 12
a₄₃ = - 22 + 504
a₄₃ = 482
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A tablespoon is equivalent to about 4 teaspoons. A recipe calls for 2/3 cup of sugar for every 1/2 teaspoon vanilla. What is the unit rate in tablespoons
per cup?
Answer:
I understand the exercise is about unit rates, but why go out of the way to state false information? A tablespoon is exactly 3 teaspoons!
Anyway,
(1/2 tsp)/(2/3 cup) * (1tbsp)/(4tsp) = 1/2 * 3/2 * 1/4 = 3/16 tbsp/cup
Step-by-step explanation:
Ok
Choose the appropriate condition for the following pairs of triangles to be congruent.
Which division sentence is represented by the model?
Number Line
6÷69=9
19÷6=23
19÷23=6
The modal represent the division is 6 ÷ 6/9 = 9.
What is division?One of the most fundamental operations in arithmetic is division, in which a larger number is divided into smaller groups with the same number of items. Dividing a large group into smaller groups so that each group has the same number of items is called division. In math, it is an operation that equalizes sharing and grouping.
Given the number line in figure,
shows the number is divided in 9 equal parts
1/9, 2/9, 3/9, ..........9/9
and from 0 to 6/9 parts are marked,
there are 6 parts in 0 to 6/9
the division model for equation is
6 ÷ 6/9
and division is 6 ÷ 6/9 = 9
Hence the division sentence is represented by the model is 6 ÷ 6/9 = 9.
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The question is incomplete, complete question is attested in image
Someone please help me!
Answer:
Look when angle 3= angle B
It would make AD parallel to BC
Step-by-step explanation:
So go with
AD//BC
#BeBrainly
You can substitute a number for a variable and then find the value of the expression. This is called _________________ the expression.
A variable is a letter, for example x, y or z, that represents an unspecified number.
6+x=12
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.Step-by-step explanation:
What is the circumference of this circle?
A.
3π
B.
(
3π
⁄
4
)
C.
4π
D.
(
3π
⁄
2
)
E.
None of the above
Answer:
the circumference of circle is 2 πr
What is the equation of the line passing through the points (1, 5) and (0, -3)
Answer:
The equation of this line is y=8x-3, I hope this helps you! :D
Answer:
y = 8x - 3
Step-by-step explanation:
The point (0, -3) is the y-intercept. You can take this and calculate the slope using the other point. Then you can form the formula y = mx+b.
A contractor bought 12.6 ft? of sheet metal. He has used 2.1 ft? so far and has $210 worth of sheet metal remaining. The equation 12.6x-2.1x = 210 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:
$20
Step-by-step explanation:
12.6x-2.1x=210
10.5x=210
x=210/10.5
x=20
The heights of Karina, Miya and Clint were 155cm, 158cm, and 161cm respectively. What is the height of Roger if the mean of all of them is 158cm?
Answer:
The height of Roger is 158cm
Step-by-step explanation:
All of them=158cm
They are 4.So,158^4=632cm
Height of 3 persons=155cm+158cm+161cm=474cm
Therefore the height of Roger is 632cm-474cm=158cm
The height of Roger with the mean of all of them is given is 158 cm.
Given that, the heights of Karina, Miya and Clint were 155cm, 158cm, and 161cm respectively.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
Let the height of Roger be R.
Mean= 158 cm
We know that, mean =Sum of all the observations/Number of observations
⇒ (155+158+161+R)/4 =158
⇒ 474+R=632
⇒ R=632-474
⇒ R=158 cm
Hence, the height of Roger with the mean of all of them is given is 158 cm.
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His new employer has offered Malcom Davis a choice of profit-sharing plans. For Plan A, he can receive 1/90 of the company’s gross income. For Plan B, he can receive 1/60 of the company’s profit. Gross income is the total amount the company takes in. Profit is the difference of the gross income and expenses. The company’s expenses for one month are $100,000.
A) Write an equation for finding the gross income that would give Malcom Davis the same amount of money with either plan.
B) Solve the equation from Exercise A and interpret the solution.
C) How much would Malcom Davis receive when the two plans are the same?
D) If the gross income of the company is less than the amount from Part B, which plan would be better for Malcom Davis? Show work to support your answer.
Malcom Davis earnings is an illustration of equations and proportions.
The equation is: [tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]The gross income must be $300000, for Dave to earn the same amount with either plan.His earning is $3333.33 when the plans are the same.Let the profit be P, and the gross income be G.
So, we have:
[tex]\mathbf{P= G - 100000}[/tex]
(a) The equations
For plan A, we have:
[tex]\mathbf{A = \frac{1}{90}G}[/tex] ----1/90 of the company's gross income
For plan B, we have:
[tex]\mathbf{B = \frac{1}{60}P}[/tex] ----1/90 of the company's profit
When both are the same, we have:
[tex]\mathbf{A= B}[/tex]
This gives
[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}P}[/tex]
Substitute [tex]\mathbf{P= G - 100000}[/tex]
[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]
Hence, the equation is: [tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]
(b) Solve the equation in (a), and intepret
[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]
Cross multiply
[tex]\mathbf{60G = 90G - 9000 000}[/tex]
Collect like terms
[tex]\mathbf{90G - 60G = 9000 000}[/tex]
[tex]\mathbf{30G = 9000 000}[/tex]
Divide both sides by 30
[tex]\mathbf{G = 3000 00}[/tex]
The gross income must be $300000, for Dave to earn the same amount with either plan.
(c) His earnings based on (c)
We have:
[tex]\mathbf{A = \frac{1}{90}G}[/tex]
Substitute [tex]\mathbf{G = 3000 00}[/tex]
[tex]\mathbf{A = \frac{1}{90} \times 300000}[/tex]
[tex]\mathbf{A = 3333.33}[/tex]
His earning is $3333.33 when the plans are the same
(d) If the gross income in less than (b)
If the gross income is less than $300,000, then plan A would better for Malcom Davis, because his earnings in plan A would be greater than plan B
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factorizar de ambas formas a cada número.
(por favor, ayudaa llevó más de dos horas con esto ....)
25
48
52
33
46
Here's a question ~
p1 and p2 are points on either of the two lines
[tex]y - \sqrt{3} |x| = 2[/tex]
at a distance of 5 units from their point of point of intersection. Find the coordinates of the foot of perpendiculars drawn from p1 , p2 on the bisector of the Angle between the given lines.
Answer:
(0, 5√3/2 + 2)Step-by-step explanation:
Given is the absolute value function.
Observations:
It has a slope of ±√3 and the y- intercept of 2.There is no horizontal shift, so the the y-axis is the line of symmetry.The y-axis is also an angle bisector of the two lines.The foot P₁P₂ is parallel to the x-axis since it's perpendicular to the y- axis.We need to find the coordinates of intersection of the line P₁P₂ with the y- axis (the point Y in the picture).
Consider the triangle AYP₂.
We know AP₂ = 5.
The angle YAP₂ is:
arctan (1/√3) = 30°The distance AY is:
AY = AP₂ cos 30° = 5*√3/2The distance from the x-axis to the point Y is:
5√3/2 + 2, added the y- intercept of the graphed linesThe coordinates of the point Y:
(0, 5√3/2 + 2)If l is parallel to m find the value of X (x+72)=(3x)
Answer:
x = 27°
Step-by-step explanation:
Given the lines are parallel you have a pair of same-side interior angles and these angles = 180°
x + 72 + 3x = 180
4x + 72 = 180
4x = 108
x = 108/4
x = 27°
The value of x will be 27 degree
The solution to the above problemGiven the lines are parallel you have a pair of same-side interior angles and these angles = 180°
x + 72 + 3x = 180
4x + 72 = 180
4x = 108
x = 108/4
x = 27°
The value of x will be 27 degree
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Solve the equation. 2p + 15 − 11p = 3(5 − 3p)
0=0
For the full explanation simply copy and paste your equation to your device browser.
Answer:
2p+15-11p=3(5-3p)
2p-11p+15=15-9p
-9p+9p=15-15
p£R
suppose that 11 inches of wire costs 55 cents how many inches of wire can be bought for 25 cents
Answer:
5 inches of wire costs 25 cents.
Step-by-step explanation:
To answer this question, we want to find the unit price per inch of wire. Therefore, we need to divide the cost of the 11 inches (55) by the length of the wire (11):
55 / 11 = 5
So, 1 inch of wire costs 5 cents.
Now, to see how many inches can be bought with 25 cents, multiply 5 times both the 1 inch and 5 cents, which are the unit price to get:
5 inches of wire costs 25 cents.
Hope this helps :)
can someone help me?
Step-by-step explanation:
a)
a whole circle represents always 360 degrees.
we see the angle J is 72 degrees. the angle K is 90 degrees.
that leaves us for M and L together :
360 - 72 - 90 = 198 degrees.
we now know that twice as many people voted for L as for M. that means the angle L is twice as big as the angle M
on other words : L = 2M
and when we now say
198 = L + M
this means
198 = 2M + M = 3M
M = 66 degrees
and L is then 2M = 2×66 = 132 degrees
b)
again, the whole circle is 360 degrees.
J covers 72 of these 360 degrees.
that is 72/360 of all voting people.
72/360 = 1/5
the total of all voting people was 15840.
so, 1/5 of 15840 is
15840/5 = 3168
that means 3168 people voted for J.
What is the missing statement in the proof?
Evaluate for b:
50 = -1/3b + 20
Answer:
=3000/53
Step-by-step explanation:
At a local fitness, members pay a $6 membership fee and $3 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Answer:
4 classes
Step-by-step explanation:
1. Write an equation for the cost for both members and nonmembers, in which x is the number of aerobics classes.
Cost = 3x + 6 for members
Cost = 4x for nonmembers
2. Set the equations to equal each other and solve.
3x + 6 = 4x
-3x -3x
6 = x
3. Check your answer
4*6 = 24
(3*6) + 6 = 24
For 4 aerobics classes, the cost for members and nonmembers is the same.
What is the slope of a line perpendicular to the line represented by the equation 2y=-6x+8
Answer:
First we need to solve the linear equation for y because we need to get the slope. Once we have the slope we need to convert it to its negative reciprocal, this means to just change the sign of the slope and flip it. The negative reciprocal is always perpendicular to the original slope.
2y = - 6x + 8
y = (-6x/2) + 8/2
y = - 3x + 4
The current slope is -3 or -3/1
The negative reciprocal is 1/3
Nick is making a fruit salad. He buys apples for $1,29 per pound and oranges for $1.35 per pound. He spends no more than $12.
Let x represent the number of pounds of apples that Nick buys. Let y represent the number of pounds of oranges that Nick buys.
Which inequality represents this situation?
a.) 1.29x + 1.35y > 12 b.) 1.29x + 1.35y≥ 12 c.) 1.29x + 1.35 < 12 d.) 1.29x + 1.35y ≤ 12
Answer:
D 1.29x+1.35y≤12
Step-by-step explanation:
Nick is making a fruit salad. He buys apples for $1.29 per pound and oranges for $1.35 per pound. He spends no more than $12.
Let x represent the number of pounds of apples that Nick buys. Let y represent the number of pounds of oranges that Nick buys.
1.29x+1.35y≥121.29x+1.35y≥12
1.29x+1.35y>121.29x+1.35y>12
1.29x+1.35y<121.29x+1.35y<12
1.29x+1.35y≤12
I really need help i need this ASPA
Answer:
Vertical angles
Actually the correct answer should be Vertically opposite angles
step by step explanation of
((3^-1)^-2 -2^3)^-1
Answer:
SEARCH MO PARA MALAMAN MO HEHE
mike wants to buy the same number of balloons for 2 of his friends. her has $59, and each balloon costs $7. What is the largest number of balloons that mike buys for each friend
Answer:
4
Step-by-step explanation:
7x8=56 wich is the highest number it can go to
so 8/2=4
What are the outputs for an input If x= 5 and the output is y= 3x -4
Answer:
11
Step-by-step explanation:
y=3 × 5 -4
=15-4
11
this is your answer
Step-by-step explanation:
yyuejekkgebbehekkejwjuehhehjeklwmsb
bdbjejejejjej
please do this for me
The table below shows the amount of money
needed to buy different number of paint
buckets. What number should replace x?
Bucket Price
($)
5
25
6
30
7
X
8
40
II
Your answer
Explain how you got the answer you entered for #1. *
Your answer
Answer:
35
Step-by-step explanation:
if you multiply all of the numbers in the first boxes by five, those numbers would be correct. So if you multiply 7 by 5, your answer would be 35
7. David needed to keep the weight of his
luggage below 50 pounds. After removing
12 lb. 8 oz. of items, his luggage weighed
47 lb. 10 oz. How much did his luggage
weigh before he removed items?
A number increased by 331 is equal to 761. Find the number.
Answer:
430
Step-by-step explanation:
761-331=430
Answer:
the answer would be 430 because you subtract 761-331=430