Sum of 8th & 4th terms of an AP = 24
Sum of 6th & 10th terms = 44
Find:A.P.
Solution:We know that,
nth term of an AP = a + (n - 1)d
Hence,
⟹ a + (8 - 1)d + a + (4 - 1)d = 24
⟹ a + 7d + a + 3d = 24
⟹ 2a + 10d = 24 -- equation (1)
Similarly,
⟹ a + 5d + a + 9d = 44
⟹ 2a + 14d = 44 -- equation (2)
Subtract equation (1) from (2).
⟹ 2a + 14d - (2a + 10d) = 44 - 24
⟹ 2a + 14d - 2a - 10d = 20
⟹ 4d = 20
⟹ d = 20/4
⟹ d = 5
Substitute the value of d in equation (1).
⟹ 2a + 10(5) = 24
⟹ 2a = 24 - 50
⟹ 2a = 24 - 50
⟹ 2a = - 26
⟹ a = - 26/2
⟹ a = - 13
We know,
General form of an AP is a , a + d , a + 2d...
Hence,
⟹ required AP = - 13 , - 13 + 5 , - 13 + 2(5)...
⟹ required AP = - 13 , - 8 , - 3....
I hope it will help you.
Regards.
A store sells new video games for $45 each. Used video games sell for $18 each. Alex is buying 2 new video games and x used video games. Which equation can be used to find y, the total price Alex must pay in dollars?
Answer:
u = t/18 - 5
Step-by-step explanation:
45n + 18u = t where t is the total price, n is the number of new video games, and u is the number of used video games
plug in two:
90 + 18u = t
solve in terms of u:
18u = t - 90
u = t/18 - 5
can i get a thanks and brainliest please?
b) Simplify 2-(3-a) = -4
Answer:
-1+a
Step-by-step explanation:
2-(3-a) = (2-3-(-a)) = -1+a
Answer:
a=-3
Step-by-step explanation:
First off subtract 2 from both sides:
-(3-a)=-6
Then distribute the negative:
-3+a=-6
Finally add 3 to both sides:
a=-3
tadah!!
Hope that helps.
PLEASE ANSWER QUICK leggings are 54.95 they are 30% off how much are they?
Answer:
$38.47
Step-by-step explanation:
i did the math on it
kala needs to make a total of 80 deliveries this week. So far she has completed 28 of them. What percentage of her total deliveries has kala completed?
Answer:
35 %
Step-by-step explanation:
50 % of 80 is 40 so 28% of 80 is 35%
if you just divide 80 by 28 you will get 35.
54/x = 9/7
What does X=
Answer:
the answer is 42.
Step-by-step explanation:
9 times 6 is 54.
7 times 6 is 42.
Answer:
It'd be 486/7 or 69 and 3/7
Step-by-step explanation:
please help asap, the question is
Do you see a pattern? If so, explain your reasoning. and What predictions can you make about future rectangles in the set if your pattern continues?
Answer: the pattern is that the rectangles width and length get timed 2.
Step-by-step explanation: that pattern will continue until the rectangle will get bigger than the unobservant universe...
4c = d for c
Solve for indicated variable.
Answer:
c=1/4d
Step-by-step explanation:
Answer:
c = d/4
Step-by-step explanation:
solve this literal equation using inverse operations:
4c = d
/4 /4
c = d/4
A patient is placed in an elliptical tank that is 178 centimeters long and 102 centimeters wide to undergo sound wave lithotripsy treatment for kidney stones. Determine where the sound emitter and the stone should be positioned relative to the center of the tank
Complete Question
The diagram for this question is shown on the first uploaded image
Answer:
The position of the emitter is [tex]E = + 72.9 \ cm\ from\ the\ center [/tex]
The position of the stone is [tex]S = - 72.9 \ cm\ from\ the\ center [/tex]
Step-by-step explanation:
From the question we are told that
The length is l = 178 cm
The width is w = 102 cm
Generally the position of the stone along the horizontal axis is mathematically evaluated as
[tex]h = \frac{178}{2}[/tex]
=> [tex]h = 89 \ cm [/tex]
Generally the position of the emitter along the vertical axis is mathematically evaluated as
[tex]k = \frac{102}{2}[/tex]
=> [tex]k = 51 \ cm [/tex]
Generally the resultant position of both stone and the emitter is
[tex]R = \pm \sqrt{h^ 2 - k^2}[/tex]
=> [tex]R = \pm \sqrt{89^ 2 - 51^2}[/tex]
=> [tex]R = \pm 72.9 \ cm [/tex]
Hence the position of the emitter is [tex]E = + 72.9 \ cm[/tex]
the position of the stone is [tex]S = - 72.9 \ cm[/tex]
PLEASE HELP I AM BEING TIMED.
A frame designer is making a triangular frame. she has two sides of length 20 inches and 28 inches. What are the possible lengths for the third side?
help show work
42,44,46,48,50
assig 9
Answer: see below
Step-by-step explanation:
42) 11 < 3y + 2 < 20
-2 -2 -2
9 < 3y < 18
÷3 ÷3 ÷3
3 < y < 6
Graph: o----------o
3 6
44) 36 ≥ 1 - 5z > -21
-1 -1 -1
35 ≥ -5z > -22
÷ -5 ↓ ÷ -5 ↓ ÷ -5
7 ≤ z < 4.4
Graph: o------------ ·
4.4 7
46) 6b + 3 < 15 or 4b - 2 > 18
-3 -3 +2 +2
6b < 12 4b > 20
÷6 ÷6 ÷4 ÷4
b < 2 or b > 5
Graph: ←--------o o---------→
2 5
48) 8d < -64 and 5d > 25
÷8 ÷8 ÷5 ÷5
d < -8 and d > 5
there is no number that is both less than - 8 and greater than 5
No Solution
Graph: (empty)
50) 15x > 30 and 18x < -36
÷15 ÷15 ÷18 ÷18
x > 2 and x < -2
there is no number that is both less than - 2 and greater than 2
No Solution
Graph: (empty)
Write 45 as a product of primes.
Use index notation where appropriate.
Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24. Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18. They set up the situation with the equation below, where x is the number of pairs of pants. Is there a situation in which they pay the same amount for their purchases? Which statements are true? Select all that apply.Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24. Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18. They set up the situation with the equation below, where x is the number of pairs of pants. Is there a situation in which they pay the same amount for their purchases? Which statements are true? Select all that apply.
Answer:
If both Kelsey and Jeana purchase 6 pairs of uniform pants then they would pay the same amount for their purchases.
Step-by-step explanation:
The information provided is as follows:
Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24. Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.The variable x is the number of pairs of pants.
The total cost function for Kelsey will be:
[tex]TC_{K}=17.95\cdot x+24[/tex]
The total cost function for Jeana will be:
[tex]TC_{J}=18.95\cdot x+18[/tex]
Consider that both pay the same total cost for their purchases.
Compute the value of x as follows:
[tex]TC_{K}=TC_{J}[/tex]
[tex]17.95\cdot x+24=18.95\cdot x+18\\\\18.95\cdot x-17.95\cdot x=24-18\\\\x=6[/tex]
Thus, if both Kelsey and Jeana purchase 6 pairs of uniform pants then they would pay the same amount for their purchases.
A label printer prints 7 labels in 3.4 seconds. How long will it take to print 56 pages of labels?
Answer:
27.20seconds
Step-by-step explanation:
hope this helped,brainliest?
A recipe calls for 4 cups of flour to 6 tablespoons of shortening. How many tablespoons of shortening are needed for 6 cups of flour?
Answer:
8 tablespoons of shortening
Step-by-step explanation:
mathhhh
Which list shows the numbers below in order from least to greatest? −5.9, −234, 5.78, 58%−5.9, −234, 5.78, 58% −234, −5.9, 58%, 5.78−234, −5.9, 58%, 5.78 −5.9, −234, 58%, 5.78−5.9, −234, 58%, 5.78 58%, −234, 5.78, −5.958%, −234, 5.78, −5.9
A ball is thrown upward from the top of a 192-foot-high building. The ball is 240 feet above ground level after 1 second, and it reaches ground level in 6 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.
Answer:
The equation of this function is [tex]h = -16\cdot t^{2}+64\cdot t+192[/tex].
Step-by-step explanation:
From Mechanical Physics we must remember that height reached by the ball as a function of time is a quadratic function if and only if ball is uniformly accelerated by gravity and viscous forces and Earth's rotation effects can be neglected. After assuming those considerations as true, the standard form of the quadratic function is:
[tex]h = a\cdot t^{2}+b\cdot t + c[/tex] (Eq. 1)
Where:
[tex]t[/tex] - Time, measured in seconds.
[tex]h[/tex] - Height of the ball, measured in feet.
[tex]a[/tex] - Second order coefficient, measured in feet per square second.
[tex]b[/tex] - First order coefficient, measured in feet per second.
[tex]c[/tex] - Zero order coefficient, measured in feet.
From Algebra, we can obtain a quadratic function by know three distinct points and solving the resulting system of linear equations:
[tex]A(t, h)= (0\,s,192\,ft)[/tex]
[tex]c = 192\,ft[/tex] (Eq. 2)
[tex]B(t,h) = (1\,s,240\,ft)[/tex]
[tex]a+b+c = 240\,ft[/tex] (Eq. 3)
[tex]C(t,h) =(6\,s,0\,ft)[/tex]
[tex]36\cdot a + 6\cdot b + c = 0[/tex] (Eq. 4)
By Algebraic methods, we get this unique solution:
[tex]a = -16\,\frac{ft}{s^{2}}[/tex], [tex]b = 64\,\frac{ft}{s}[/tex], [tex]c = 192\,ft[/tex]
The equation of this function is [tex]h = -16\cdot t^{2}+64\cdot t+192[/tex].
Just the picture, Geometry. Thanks.
Angle 1 is congruent to ∠5 as they are corresponding angles on a transversal .
Option (d) Angle 4Angle 4 is congruent to ∠5 as they are alternate interior angles .
I need some help with geometry!
Answer:
vertical
Step-by-step explanation:
Select True or False for each statement.
A.16.302 rounded to the nearest whole number is 16 feet per second.
Select True or False for each statement.
16.302 rounded to the nearest whole number is 16 feet per second.
16.302 rounded to the nearest tenth is 16.3.
16.302 rounded to the nearest hundredth is 16.31.
16.302 rounded to the nearest tenth is 16.3.
C.16.302 rounded to the nearest hundredth is 16.31.
Answer:
True
True
False
What’s the value of X ?
Answer:
x=25
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
(2x+2)+(5x+3)=180
Write an algebraic expression for the statement.
The cost of m pounds of meat when the cost per pound is $3.54.
Answer:
y=3.54m
Step-by-step explanation:
it is pretty self explanatory
An algebraic expression for the statement could be as; y = 3.54m
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.
Thus which can also be used to indicate the logical syntax's order of operations and other features.
We need to write an algebraic expression for the statement.
Given that The cost of m pounds of meat when the cost per pound is $3.54.
Therefore, the expression could be as;
y = 3.54m
hence, An algebraic expression for the statement could be as; y = 3.54m
To know more about an expression follow;
brainly.com/question/19876186
#SPJ2
There were 5 boys for every 7 girls at Rayville High School last year. If there were 420 students at the school, how many were girls?
Answer:
240
Step-by-step explanation:
Lucia wishes to advertise her business, so she gives packs of 6 red flyers to each restaurant owner and sets of 4 blue flyers to each clothing store owner. At the end of the day, Lucia realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color? Flyers
Answer:
12
Step-by-step explanation:
No. of red flyers = 6
No. of blue flyers = 4
We need to find the minimum number of flyers of each color if she gave out the same number of red and blue flyers. For this we must find the LCM of 6 and 4.
Prime factorization of 6 = 2×3
Prime factorization of 4 = 2×2
Lowest common multiple of 6 and 4 = 12
Hence, there are 12 minimum number of flyers of each color
Write the inequality. Lawyers work up to 80 hours a week. (Use x for your variable)
For art class, each student
is going to make a piñata using pound of
paste. The art teacher bought 20 pounds of
paste. Which equation can be used to determine
the number of students that can make piñatas?
A. (n = 20
20
B. 4 = 20
D. 2n = 20
n =
Answer:
s=25
Step-by-step explanation:
Which one of the following words is a pronoun A) Two B) Him C) Boys D) Go
Answer:
I believe it is Him.
Step-by-step explanation:
Answer:
B) Him
Step-by-step explanation:
Him refers to someone else, and that is exactly what a pronoun does!
The area of the triangle below is 2/5 square foot.
What is the length, in feet, of the base of the
triangle?
Answer:
B. 2/3
Step-by-step explanation:
The equation for area of a triangle is A=1/2bh
so we can plug in what were given
2/5 =1/2(6/5)b now we solve for b
2/5=6/10 b
2/5 divided by 6/10 =b
2/5 x 10/6 =b
4/6=b
2/3=b
(2x−6)+4(x−3) i need this answer
Answer:
(2x-6)+4(x-3)
2x-6+4x-12
6x-18
6(x-3)
Which relation is also a function?
{(-1, 3), (0, 2), (3, -1), (3, 2)} {(2,-4), (2,-2), (2, 1), (2, 3)}
{(0, 3), (1, 2), (1, 4), (2.1)}
{(-4,-3), (0.-3). (1, -3), (4, -3)}
Answer:
{(-4,-3), (0, -3,) (1, -3), and (4,-3)}
Step-by-step explanation:
There can only be one y- output for each x-input. Every other answer is a relation because there are multiple y-values for an x-value.
Answer:
The second one.
Step-by-step explanation:
A function can have two of the same inputs, but not two of the same outputs.
In the first one, the output 2 is found more than once.
In the third one, the output -3, is also found more than once.
The second one has completely unique numbers for both the input and output.
What is the volume of the cylinder below
Answer:
I think d or b
Step-by-step explanation:
Answer:
c
Step-by-step explanation: