Sum of 5th & 8th terms of an AP = 37
11th term = 32
Find:A.P
Solution:We know that,
nth term of an AP – an = a + (n - 1)d
Hence,
⟹ a₅ + a₈ = 37
⟹ a + (5 - 1)d + a + (8 - 1)d = 37
⟹ 2a + 4d + 7d = 37
⟹ 2a + 11d = 37 -- equation (1)
Similarly,
⟹ a₁₁ = 32
⟹ a + (11 - 1)d = 32
⟹ a + 10d = 32
⟹ a = 32 - 10d
Substitute the value of a in equation (1).
⟹ 2(32 - 10d) + 11d = 37
⟹ 64 - 20d + 11d = 37
⟹ 64 - 37 = 20d - 11d
⟹ 27 = 9d
⟹ 27/9 = d
⟹ 3 = d
Substitute the value of d in equation (1).
⟹ 2a + 11(3) = 37
⟹ 2a + 33 = 37
⟹ 2a = 37 - 33
⟹ 2a = 4
⟹ a = 4/2
⟹ a = 2
Now,
General form of an ap = a , a + d , a + 2d...
⟶ Required AP = 2 , 2 + 3 , 2 + 2(3)...
⟶ Required AP = 2 , 5 , 2 + 6...
⟶ Required AP = 2 , 5 , 8...
I hope it will help you.
Regards.
Answer:
→ md - 2nd + 3md = 2 * [ a + (n - 1)d ]
→ 4md - 2nd = 2 * [ a + (n - 1)d ]
→ 2(2md - nd) = 2 * (a + nd - d)
→ 2md - nd - a + d = nd
→ 2md - nd - (md - 2nd) + d = nd
[ From equation (1) ]
→ 2md - nd - md + 2nd + d = nd
→ md + nd + d = nd
→ (m + n + 1)d = n * d
→ (m + n + 1) = n
Step-by-step explanation:
Kenson and Shelly are each saving money.
• Kenson has $60 in savings and will save an additional $12 every week.
• Shelly has $85 in savings and will save an additional $7 every week.
Which equation can be used to determine w, the number of weeks it will take Kenson and Shelly to save the same amount of money?
A. 720 + 60w = 595 + 85w
B. 7w + 595 = 12w + 720
C. 60 + 7w = 85 + 12w
D. 60 + 12w = 95 + 7W
Answer:
D.
Step-by-step explanation:
D. 60 + 12w = 95 + 7W
Is this equation an example of a literal equation? Why?
Answer:
yes this is...,.,.,.....
I have 4 and 11/12 . how much do i need to add to get 6 and 1/2
Answer:
= 1 7/12
Step-by-step explanation:
6 1/2 - 4 11/12 =
6 6/12 - 4 11/12 =
5 18/12 - 4 11/12 =
=1 7/12
To check if the answer is right or wrong, you can add 1 7/12 to 4 11/12
4 11/12 + 1 7/12 = 5 18/12 = 6 6/12 = 6 1/2
Hope this helps and pls do mark me brainliest if you can:)
-1/10 divided by 1/6
[tex]-0.6[/tex]
For more help, Take a look at this chart.
Answer:
-3/5
Step-by-step explanation:
-1/10 divided by 1/6
-1/10 x 6/1
-6/10 the divided by 2
-3/5
Bill can hit a bucket of 32 golf balls in 17 hours.
How much could he hit in 23 hours
17x = 32
x = 1.882
23x = 23 x 1.882 = 43.286 = 43 balls
Find the slope of AB through points A(1,7) and B(-1,4). m of AB=
Hi there & welcome to brainly !
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{ \frac{3}{2}}}}} [/tex]
Step-by-step explanation:
Given :A ( 1 , 7 ) , B ( - 1 , 4 )
To find :Slope = ?
Solution :Let A ( 1 , 7 ) ↦ ( x₁ , y₁ )
Let B ( - 1 , 4 ) ↦ ( x₂ , y₂ )
Finding the slope :
[tex] \boxed{ \tt{slope \: ( \: m)= \frac{y2 - y1}{x2 - x1} }}[/tex]
[tex] \sf{↦ \: slope = \frac{4 - 7}{ - 1 - 1}} [/tex]
[tex] \sf{↦ \: slope = \frac{ - 3}{ - 2}} [/tex]
[tex] \sf{↦ \: slope = \boxed{ \sf{ \frac{3}{2} }}}[/tex]
And we're done !
Hope I helped!
Best regards! :D
~TheAnimeGirl
Joey wants to save up enough money to buy a new baseball bat that costs $200. He already has $50. If Joey makes $40 per week, write an inequality that represents the number of weeks (w) until he will have enough money?
Answer:
50+40w=200
Step-by-step explanation:
200-50=150
150 divided by 40=3.75 so 3 1/2 weeks
Can you please answer this my homework is due ✨
If f(x) = 2x2 + 5x - 8 and f(x) = -10,
which of the following could be a
value for x?
-2
Answer:
x = -2 or x = -1/2
Step-by-step explanation:
We can just set up an equation where the quadratic is equal to -10, and then solve the equation:
[tex]2x^2+5x-8=-10\\2x^2+5x+2=0\\\\[/tex]
Now, factor:
[tex](2x+1)(x+2) = 0\\x=-2 \text{ or } x=-1/2[/tex]
OMG Help Me !Select all the correct answers. Which tables represent constant functions? Pick 2 and show your work. No guessing.
x y
2 -1
2 0
2 1
x y
2 -3
4 -7
6 -11
x y
2 3
4 3
6 3
x y
1 3
2 12
3 27
x y
1 -1
2 -1
3 -1
Tables 1 and 2 because they move at a constant rate of change and they are linear functions with a slope.
Table 3 is not a function because there is more than one input for each output.
Table 4 is an exponential equation with the equation y = 4x^2
Table 5 is not a function for the same reason as table 3.
Answer:
Yes! The answer is A and B. Or the 1st and 2nd ones.
Step-by-step explanation:
Math
Jim baked 24 cupcakes for the upcoming bake sale. He also bought drinks.
Which sets below are factor pairs of 24?
A (3,6)
B (4.6)
C (6,8)
D (1, 24)
E (38)
Click Submit below if you want to finish the test and see the results
Save and Exit
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
26 27 28
How do you write -4.50 as a mixed number
Answer:
-9/2
Step-by-step explanation:
Absolute value is DISTANCE. How many units a number is away from zero.
a.) 3
b.)4
C.) -3
d.) -4
I believe it is B) 4
The number line is going by .5 per space and there are 8 spaces in the red line segment. You can then do 8 x .5 and you will get 4.
You bought 12 red apples and 15 green apples to make a pie.
What is the ratio of the number of red apples to the total number of apples?
4 over 9
Answer:
12 over 27 = 4 over 9
Step-by-step explanation:
12 over (12 + 15) = 12 over 27 = 4 over 9
What is the measure of Angle 1 in this figure?
A. 30°
B. 80°
C. 110°
D. 130°
Answer:
A
Step-by-step explanation:
What is the speed of a car that is traveling at 75,000 meters in 5,400 seconds.
Answer:
13.9
Step-by-step explanation:
Speed=distance/time
S=75,000/5,400
S=13.8 repeating OR (rounded) 13.9 m/s
Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements: 1. As x increases infinitely, the y-values are continually doubled for each single increase in x. 2. As x decreases infinitely, the y-values are continually halved for each single decrease in x. She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine's statements and her conclusion?
Answer:
"as x increases infinitely, the y-values are continually doubled for each single increase in x".
Step-by-step explanation:
Given the exponential equation f(x) = 2x of which Geraldine is asked to explain the limits on the range, the expression that best explains the accuracy of Geraldine's statements and her conclusion is that "as x increases infinitely, the y-values are continually doubled for each single increase in x".
for example let y = f(x) so thet y = 2x
for every va;ues of x, y will be doubled as shown;
If x = 1
y = 2(1) = 2
If x = 2
y = 2(2) = 4
If x = 3
y = 2(3) = 6
I can be seen that the value of y doubles for all values of x hence making her first statement accurate.
The second statement 'As x decreases infinitely, the y-values are continually halved for each single decrease in x'. is not totally right because the y values may not be halved for some values of x as x increases.
Her conclusion is not also right because there are limits within the set of real numbers on the range of this exponential function. for every value of x, y will always tend to a real value.
What Is The Slope Of the Line
Answer:
2/2.5 or 3/4 I pretty sure that's right
I need help Type fast
An electrician charges an hourly rate of $50, but also charges a fixed fee for making house calls regardless of time spend on the job. One day, the electrician earned a total of $250 for a 2 hour job. Write an equation for C,C, in terms of t,t, representing the total cost of the electrician's services if the electrician spends tt hours at the house working.
Answer:
C=50t+150
Step-by-step explanation:
From the information given, the equation will need to show that the total cost of the electrician services would be equal to 50 that is the hourly rate for the number of hours spent working plus the fixed fee:
Fixed fee=250-(50*2)=250-100=150
According to this, the equation would be:
C=50t+150, where C is the total cost of the electrician's services and t is the number of hours spent working.
• Lawson already has $60 in his wallet but needs a total of at least $500 for his holiday. He gets
paid $30 per day for delivering newspapers. What is the least number of days he must work to
get enough money for his holiday?
Answer:
15
Step-by-step explanation:
500-60=440
440/30=14.66666667
simplify 14.66666667= 15
A company ships 26 refrigerators in a truck Each refrigerator weighs 309 pounds. What is the total weight of the refrigerators in the truck?
O 2,472 pounds
7,884 pounds
O 8,034 pounds
O 8,294 pounds
Answer:
8034
Step-by-step explanation:
C'mon!!.... easyyyy
309x26 =8034
HURRY!!!!
The value of a baseball card can be represented by the equation y = 3 x + 39, where x represents the number of years that Robert has owned the card and y represents the total value, in dollars, of the card. What was the value of the card when Robert originally purchased it?
$3
$13
$36
$39
Answer:
mark as brainliest plz... it is $39
Step-by-step explanation:
ayeeeeeeeeeeeeeee
Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
If cat and dog start running away from each other how far away from each other will they be after 30 minutes?
Answer;
They will be 0.5x miles away from each other
Explanation;
Since the dog runs twice the speed of the cat
Its speed will be 2 * x = 2x mph
Now we want to know how far they will be from each other after 30 minutes
Kindly note that 30 minutes is 1/2 hour
Mathematically;
distance = speed * time
Distance of cat = x * 1/2 = 0.5x miles
Distance of dog = 2x * 0.5 = x miles
The dog is x - 0.5x miles = 0.5x miles away from the cat
They will be 0.5x miles away from each other.
Calculation of the distance:Since Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
So here the speed of the dog should be 2x
Now we know that
[tex]Distance = speed \times time\\\\[/tex]
Here distance of cat should be x of 30 minutes or half hour = 0.5x miles
And, Distance of dog should be 2x of 0.5 = x miles
So, the difference should be
= x - 0.5
= 0.5x miles
hence, They will be 0.5x miles away from each other.
Learn more about speed here: https://brainly.com/question/1825528
can someone explain to me how to do this
Answer:
x=45
Step-by-step explanation:
We know that 2y+6 and 8y-102 are vertical angles to each other. This means that 2y+6=8y-102. [tex]6y=108[/tex], which means that y=18. [tex]2\cdot(18)+6=36+6=42[/tex]. Since one line is a straight angle, it is 180 degrees we can do [tex]3x=180-45=135[/tex], so x=45.
Answer:
y = 18
x = 46
measures of the angles:
8y - 102 = 42
2y + 6 = 42
3x = 138
Step-by-step explanation:
So first remember the verticle angles theorem, which states that, when two lines intersect there will be four angles formed; the angles that are opposite from each other will be congruent, that is, they will have the same measure.
Using this we know that opposite angles have to be congruent:
so
(2y + 6) = (8y -102)
now there is an algebra equation that can be solved by inverse operations and simplifying
2y + 6 = 8y - 102
+102 +102
2y + 108 = 8y
-2y -2y
108 = 6y
/6 /6
18 = y
Also, remember that two adjacent angles that form a line will add up to 180,
so
3x + (2y + 6) = 180
*note: I could have also used (8y - 102) but I choose to use (2y + 6)
so now substitute in the value of y that was found
y = 18
3x + (2 * 18 + 6) = 180
simplify
3x + ( 36 + 6) = 180
3x + 42 = 180
now use inverse operations
3x + 42 = 180
-42 -42
3x = 138
/3 /3
x = 46
PLEASE HELP, IM NOT SURE!!!
The scale on a map reads 2 inches = 5 miles. What is the actual distance
between two cities on the map that are 6.5 inches apart?*
O A. 2.6 miles
B. 13 miles
O C.32.5 miles
D. 16.25 miles
Answer:
Step-by-step explanation:
2 inches = 5 miles.
So if you divide both sides by 2,
1 inch = 2.5 miles
To find how many miles 6.5inches is equal to, multiply 2.5 by 6.5
6.5 inches = 2.5 x 6.5 = 16.25 miles
Can someone please help me?
Answer:
4
Step-by-step explanation:
It is 4 because there are 4 pea pods with 3 peas in each pod.
Answer:
2
Step-by-step explanation:
Solve the equation 3x + 4y = 16 for x.
O A x V 16
B. x=3(16-4)
O c. x = 16 - 4y
O D. x. 18 AV
3x-4y=16
add 4y to both sides
3x=4y+16
divide both sides by 3
x=(4y+16)/3
Megan scored 80% on a test. She got 20 questions correct. How many questions were on the test?
Answer:
25
Step-by-step explanation:
I'm writing this to get to the 20 character minimum
Answer:
26 Questions
Step-by-step explanation:
Solve for I.
-30 = 5(x + 1)
Answer:
x or I=-7
Step-by-step explanation: