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.
If your UBER and your bill is 20$ they will ask if you want to leave a 4$ tip. what percent tip would that be?
4 out of 20 is 20% so they left a 20% percent tip
Jaida has $200 to spend on flowers for a school celebration. She decides that the only flowers that she wants to buy are roses and carnations. Roses cost $1.45 each and carnations cost $0.65 each. Jaida buys enough roses so that each of the 75 people attending the event can take home at least one rose. Write an inequality to represent the cost constraint.
Answer:
[tex]1.45x+0.65y\leq 200[/tex]
Here, [tex]x[/tex] denotes the number of roses used for a school celebration and [tex]y[/tex] denotes the number of carnations used for a school celebration.
Step-by-step explanation:
Let [tex]x[/tex] denotes the number of roses used for a school celebration and [tex]y[/tex] denotes the number of carnations used for a school celebration.
Cost of 1 rose = $1.45
Cost of [tex]x[/tex] roses = [tex]\$1.45x[/tex]
Cost of 1 carnation = $0.65
Cost of [tex]y[/tex] roses = [tex]\$0.65y[/tex]
Total cost spend on flowers = [tex]1.45x+0.65y[/tex]
Total amount with Jaida = $200
So,
the inequality to represent the cost constraint is [tex]1.45x+0.65y\leq 200[/tex]
The function g(x) = (x + 2)2 + 4 is a transformation of the parent function f(x) = x2. Select all the statements that are true about the transformation.
A. Function g is the result of f being translated right 2 units and down 4 units.
B. Function g is the result of f being translated left 2 units and up 4 units.
C. The graph of function f opens upward.
D. The graph of function g opens downward.
E. The graph of function f is compressed by a factor of 2.
Answer:
Step-by-step explanation:
B
C
Using translation and parabola concepts, it is found that the correct options are:
A. Function g is the result of f being translated right 2 units and down 4 units.
C. The graph of function f opens upward.
------------------------------
The parent function is: [tex]f(x) = x^2[/tex]Function g is given by: [tex]g(x) = (x + 2)^2 + 4[/tex]Shifting a function f(x) a units to the right is the same as finding f(x + a).Shifting a function f(x) a units up is the same as finding f(x) + a.From the last two bullet points, option A is correct and option B is incorrect.In both functions, f and g, the term that multiplies [tex]x^2[/tex] is positive, thus, both open upward, which means that option C is correct and option D is incorrect.Both are multiplied by the same factor, 1, thus none are compressed, and option E is incorrect.A similar problem is given at https://brainly.com/question/4521517
1/8 divided by 2 3/4
Answer:
2 and 1/8
Step-by-step explanation:
Reduce fractions where possible.
Then your initial equation becomes 1/8 divied by 1/17.Applying the fractions formula for division, 1 17 over 8 and 1 then multiply those. Then simplfy.
[tex]\frac{1}{8}[/tex] divided by [tex]2\frac{3}{4}[/tex] is equal to [tex]\frac{1}{22}[/tex] we get by converting the mixed fraction to improper and divide them both.
The given expression is [tex]\frac{1}{8}[/tex] divided by [tex]2\frac{3}{4}[/tex].
Convert the mixed number [tex]2\frac{3}{4}[/tex] to an improper fraction.
[tex]2\frac{3}{4} = \frac{2 \times 4 + 3}{4}[/tex]
[tex]= \frac{11}{4}[/tex]
Now, we can rewrite the expression as:
[tex]\frac{1}{8} \div \frac{11}{4}[/tex]
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
[tex]\frac{1}{8} \times \frac{4}{11}[/tex]
Next, let's simplify the multiplication:
[tex]\frac{1 \times 4}{8 \times 11} = \frac{4}{88}[/tex]
We can further simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
[tex]\frac{4}{88} = \frac{1}{22}[/tex]
Therefore,[tex]\frac{1}{8}[/tex] divided by [tex]2\frac{3}{4}[/tex] is equal to [tex]\frac{1}{22}[/tex].
To learn more on Fractions click:
https://brainly.com/question/10354322
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Which of the following is equivalent to 5(7 - p)?
5p - 35
-5p + 35
35 + 5p
-35 + 5p
Answer:
-5p+35
Step-by-step explanation:
=(5)(7+−p)
=(5)(7)+(5)(−p)
=35−5p
=−5p+35
Solve the inequality for x.
–3x – 3 < –63
Answer:
ill help:)
Step-by-step explanation:
Answer:
x < 20.
Step-by-step explanation:
-3x-3<-63
+3 +3
-3x<-60
÷-3. ÷-3
x<20
There are 15 clowns in a circus. Each clown has to act either happy or sad. Twelve of the clowns have red noses. Each of the seven happy clowns has a red nose. Five of the sad clowns have red noses. How many clowns have to act sad and do not have a red nose?
Answer:
3
Step-by-step explanation:
Each of the seven happy clowns has a red nose.This means there are (15-7) 8 sad clowns.
Five of the sad clowns have red noses.This means out of 8 sad clowns, 5 have red noses. So the clowns that have to act sad and have red noses are (8-5) 3.
√64
A. 4√2
B. 8
Which one?
Answer:
Its B.
Step-by-step explanation:
If its right plz give me Brainliest :)
Answer:
√64 = 8
Step-by-step explanation:
The Square root of 64 is 8
Square of ( +/-8) is 64. Since the negative numbers inside square root results in an imaginary number, so the square root must be positive and hence +8 is a square root of 64. The Answer is 8.
What is the simplest radical form of the square root of 64?
The "simplest radical form" of √64 is √26 if we define "simplest form" as a radical of a prime to an integer power.
Amber is making a scale drawing of a movie screen. The actual dimisions of a screen in her local theater are 60 ft wide and 20 ft tall. In her scale drawing, the screen has a width of 9 in. What will the height of the screen on her drawing be? a 2 inches b 6 inches c 3 inches d 10 inches
Answer:
c 3 inchesStep-by-step explanation:
Given the dimension in feet
Width = 60 ft
Height = 20 ft
Given the dimension in inches
Width = 9in
Height = ?
To get the height in inches, we will use the equality postulate:
60 ft = 9in
20ft = x
Cross multiply
60x = 9*20
60x =180
x = 180/60
x = 3in
Hence the height of the screen will be 3inches
I NEED HELP ASAP PLEASE!
Answer:
AB = 2
Step-by-step explanation:
Using the secant- secant theorem, that is
PA × PB = PD × PC , substitute values
10(10 + AB) = 8(8 + 7)
100 + 10AB = 8 × 15 = 120 ( subtract 100 from both sides )
10AB = 20 ( divide both sides by 10 )
AB = 2
HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!
the answer is D and i know cause i just did that and thats the answer
Answer:
d - the lines intersect,but are not perpendicular
Step-by-step explanation:
omg I know for a fact this is correct I took this test ....
your welcome!
A restaurant menu shows the price for 2 chicken wings is $2.30 and the price for 6 chicken wings is $6.90. The function below gives the price, y, for x wing
y - 2.30 = 1.15(x - 2)
If this function is graphed in the coordinate plane, what is the y-intercept?
Answer:
y - intercept = 0 [(0,0)]
Step-by-step explanation:
Given the equation y - 2.30 = 1.15(x-2), the y-intercept is when x is 0.
So to find your answer, just substitute in 0 for x, and solve for y:
y - 2.30 = 1.15(x - 2) →
x = 0
y - 2.30 = 1.15(0 - 2) →
y - 2.30 = 1.15(-2)
y - 2.30 = -2.30 →
+2.30 +2.30
y = 0
What is the 6th term of the geometric progression
12.6.3, ... ?
Answer:
a₆ = [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
The n th term of a geometric progression is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 12 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex] , thus
a₆ = 12[tex](\frac{1}{2}) ^{5}[/tex] = 12 × [tex]\frac{1}{32}[/tex] = [tex]\frac{12}{32}[/tex] = [tex]\frac{3}{8}[/tex]
An animal shelter has $2500 in its reserve fund. The shelter charges $40 per animal placement and would like to have at least $4000 in its reserve fund. Write an inequality to represent this situation.
Answer:
Step 1
Write and solve the inequality:
2,500 + 40a ≥ 4,000, or 40a ≥ 1,500
a ≥ 37.5
Step 2
If the shelter places 30 cats and 10 dogs,
or 40 animals, that will be enough to meet
its goal, because a = 40 is a solution to the
inequality a ≥ 37.5.
Help!! Anyone know how to do this?
Answer:
42.5
Step-by-step explanation:
Answer:
x = 37.5
Step-by-step explanation:
First, you'll have to find the amount between the similar triangles. This is what I mean:
42.5/17 = 2.5
20/8 = 2.5
So, that means that 15(2.5) = x.
x = 37.5
PLEASE ANSWER ASAP WILL MARK BRAINLEST
Paul and Dana both want to find the change from the 6 AM temperature to the new 12 PM temperature.
Paul says that you can use a number line and add the distance from 0 to the 6 AM temperature and from 0 to the new 12 PM temperature. Dana says that you can subtract -1.4 from the new 12 PM temperature.
Is either Paul or Dana correct> Explain your reasoning and find the change in temperature.
Answer:
Paul is correct
Step-by-step explanation:
You can add the distance of 0 to 6 AM and 0 to 12 PM, and doing so on a number line. On a number line you would add them and lets say 6 AM is 6 degrees and 12 PM is 12 degrees, you would add 6 and 12 to get 18. While doing so you would got 1 2 3 4 5 6 7 8 9 and so on. Thus, finding the difference.
I know I'm late but can I still get that brainliest
How did you find each square root?
Answer:
......
Step-by-step explanation:
join on zoom meeting now I'd 4989249097 and password MsS8pt join now for fun only girls
HELP ME PLS
GRADES ARE DUE TODAY
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Most of this exercise is looking at different ways to identify the slope of the line. The first attachment shows the corresponding "run" (horizontal change) and "rise" (vertical change) between the marked points.
In your diagram, these values (run=1, rise=-3) are filled in 3 places. At the top, the changes are described in words. On the left, they are described as "rise" and "run" with numbers. At the bottom left, these same numbers are described by ∆y and ∆x.
The calculation at the right shows the differences between y (numerator) and x (denominator) coordinates. This is how you compute the slope from the coordinates of two points.
If you draw a line through the two points, you find it intersects the y-axis at y=4. This is the y-intercept that gets filled in at the bottom. (The y-intercept here is 1 left and 3 up from the point (1, 1).)
Solve for s. 7 - 45 = -3s
Answer:
12.7=s
Step-by-step explanation:
First, write the equation and combine like terms.
7-45=-3s
-38=-3s
Next, divide both sides by 3.
-38=-3s
/-3 /-3
12.7=s (I rounded the answer.)
Hope this helps! Have a great day C:
Find the rate of change in the graph
Answer:
4/3
hope this helped :)
If a population roughly doubles in the course of 22 years, its growth rate would be close to
C) 2.0
A) 1.5
D) 3.2
B) 1.2
Answer:
hmm you need help
Step-by-step explanation:
I NEED ANSWERS!!! ASAP
The answer for the first one is 4.47945205479, if you need to round that would be 4.5.
The answer for the second one is 20.4945454545, rounding will be 20.5.
The answer for the last one is 893.84, rounding will be 893.8.
If you need to round just remember 4 or less, will be rounded to 0, and 5 or more would be rounded to 10.
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (-2,3), (5,5)
Answer: M= 2/7
Step-by-step explanation:
Find the slope of a line PERPENDICULAR TO LM:
L(3,-5), M(-4, -1)
Answer:
[tex]\frac{7}4[/tex]
Step-by-step explanation:
First, we need to find the slope, which is defined as the change in y over the change in x:
[tex]\frac{-5-(-1)}{3-(-4)} = \frac{-4}{7}[/tex]
To find a slope that's perpendicular to that, we just take the negative reciprocal of that slope, which is [tex]\frac{7}4[/tex].
I hope this helped.
Pls pls Pls pls pls helpppp meee asappppp i will give BRAINLIEST!!!!!!
Answer:
27ft
Step-by-step explanation:
Answer:
its simple you will need 5ft of carpet
Step-by-step explanation:
If 2a + 3 < 10, then which of these could be a value of a?
a. 6 b. 4 c. 2 d. 10
Answer:
it's going to be d.
Answer: c
Step-by-step explanation:
2*6=12
12+3=15
15 is not less than 10
2*4=8
8+3=11
11 is not less than 10
2*2=4
4+3=7
7 is less than 10
10*2=20
20+3=23
23 is not less than 10
Jason and Henry go to the movie theater and purchase refreshments for their friends. Jason spends a total of $66.75 on 12 drinks and 1 bag of popcorn. Henry spends a total of $82.50 on 3 drinks and 10 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of popcorn, to the nearest cent.
Answer:
The cost of one drink is $5
Step-by-step explanation:
3x-120x=82.50-667.5
120x-3x=667.50-82.50
117x=585
x=5
MAKING A PERSONAL OR HYPOTHETICAL SITUATION
1. Create or make your own situation that maybe true to your everyday life or personal experience that describe
union, intersection, and difference of two sets, and complement of a set.
Answer:
do you have answer
Step-by-step explanation:
Use the graph to find the midpoint between O and H.
(4, -1)
(-2, 8)
(8, -2)
(-1, 4)
Answer:
(-1, 4)
Step-by-step explanation:
-5+3/2 = -1
6+ 2/2 = 4
(-1, 4)
Mario simplified the expression (4 z Superscript 8 Baseline) Superscript negative 3 as shown. (4 z Superscript 8 Baseline) Superscript negative 3 = 4 z Superscript 8 times (negative 3) Baseline = 4 z Superscript negative 24 Baseline = StartFraction 4 Over z Superscript 24 Baseline EndFraction Which statement explains Mario's error?
Answer:
Step-by-step explanation:
Given the expression [tex](4z^8)^{-3}[/tex], to evaluate this, we will use one of the law of indices as shown;
[tex](a^m)^n = a^{mn}[/tex]
[tex]4^{-3} * z^{8*-3}[/tex]
[tex]= \frac{1}{4^3} * z^{-24}\\ \\= \frac{1}{64} * \frac{1}{z^{24}}\\ \\= \frac{1}{64z^{24}}[/tex]
Mario's error was that she did not raise the value of 4 to the power of -3. She only raised z^8 to the power of -3 when it is supposed to affect both 4 and z^8
Answer:
The last one
Step-by-step explanation: