Answer:
2, 6, 10, 14
or
14, 10, 6, 2.
Step-by-step explanation:
Let the four consecutive numbers in A.P. be a - 3d, a - d, a + d, a + 3d
According to the first condition:
a - 3d + a - d + a + d + a + 3d =32
4a = 32
a = 32/4
a = 8
According to the second condition:
[tex] \frac{(a - 3d)(a + 3d)}{(a - d)(a + d)} = \frac{7}{15} \\ \\ \frac{ {a}^{2} - (3d)^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {a}^{2} - 9d^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {8}^{2} - 9d^{2} }{ {8}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ 64 - 9d^{2} }{ 64 - {d}^{2} } = \frac{7}{15} \\ \\ 15(64 - 9 {d}^{2} ) = 7(64 - {d}^{2} ) \\ \\ 960 - 135 {d}^{2} = 448 - 7 {d}^{2} \\ \\ 960 - 448 = 135 {d}^{2} - 7 {d}^{2} \\ \\ 512 = 128 {d}^{2} \\ \\ {d}^{2} = \frac{512}{128} \\ \\ {d}^{2} = 4 \\ \\ d = \pm 2 \\ \\ when \: d = 2 \\ a - 3d = 8 - 3 \times 2 = 8 - 6 = 2 \\ a - d = 8 - 2 = 6 \\ a + d = 8 + 2 = 10 \\ a + 3d = 8 + 3 \times 2 = 8 + 6 = 14 \\\\ when \: d = - 2 \\ a - 3d = 8 - 3 \times ( -2 ) = 8 + 6 = 14 \\ a - d = 8 -( - 2 )= 8 + 2 = 10 \\ a + d = 8 + ( - 2 )= 8 - 2 = 6\\ a + 3d = 8 + 3 \times ( - 2 )= 8 - 6 = 2 \\[/tex]
Thus the four consecutive numbers of the A. P. are 2, 6, 10, 14 or 14, 10, 6, 2.
There are 75 balloons in each package. How many balloons are in 20 packages?
1,405
1,500
95
150
1,500
Step-by-step explanation:
You multiply 75 times 20
Amira is solving the equation x2 – 6x = 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
Answer:
its 9
Step-by-step explanation:
I have gotten it correct on ED
Answer:
the answer is 9
Step-by-step explanation:
I took the test edg 2020
(-12a^3b^5)/(4a^2b^7)
state any restrictions on the variable(s) if they exist.
PLEASE HELP DUE TODAYY
Restrictions are that 'a' and 'b' cannot be zero. We could write [tex]a \ne 0[/tex] and [tex]b \ne 0[/tex] as shorthand.
The restrictions are put in place to ensure that you can't divide by zero.
=========================================
Explanation:
The coefficients -12 and 4 divide to -12/4 = -3 which is the coefficient for the answer in the numerator.
The 'a' terms divide to (a^3)/(a^2) = a^(3-2) = a^1 = a. We subtract the exponents to simplify.
The b terms are handled in a similar manner to get (b^5)/(b^7) = b^(5-7) = b^(-2) = 1/(b^2)
Putting all three results together has us end up with (-3a)/(b^2) where neither 'a' nor b are zero to prevent a division by zero error. We cannot have 0 in the denominator.
describe a rule for each pattern. 35,70,105,140
Answer:
A linear sequence
Step-by-step explanation:
In this sequence, the difference between the first two terms is 70−35=35 , we can check this is correct by finding the difference between the 2nd and 3rd terms, which is 105−70=35 . This means the first difference is 35.
The first difference gives us the number we multiply n by, or the quotient of n.
This means we get the nth term as 35n+c .
To get c , we check the difference between the first term and the number we get when we multiply n by 35 , when n=1 .
This gives us:
35n+c=35
c=35−35n
c=35−35(1)
c=35−35
c=0
Once we have c , we get the nth term of 35,70,105 to be 35n .
f(0) f(0)=3(0)^2-10(0)-4
3/7 divide by 2/3 what is that answer
Answer:
9/14
Step-by-step explanation:
to divide fractions flip the second fraction and then multiply
Answer:
9/14
Step-by-step explanation:
3/7 divided by 2/3 is equal to 3/7 times 3/2 which is 9/14
11m - (6m - 5) = 25 solve for m please
Answer:
m = 4Step-by-step explanation:
[tex]11m - (6m - 5) = 25\\[/tex]
Use - to open the bracket
[tex]-(6m-5)= -6m+5[/tex]
[tex]11m-6m+5=25\\[/tex]
Collect like terms and simplify
[tex]11m-6m=25-5\\5m = 20[/tex]
Divide both sides of the equation by 5
[tex]\frac{5m}{5} = \frac{20}{5} \\\\m = 4[/tex]
describe fully the graph which has the equation x^2+y^2=16
The given equation is a circle with center = (0, 0) and radius = 4.
We compare the given equation with the standard form of a circle[tex](x-h)^2+(y-k)^2=r^2[/tex]
So, h = 0 , k = 0, [tex]r^2=16[/tex] or r = 4.
So the given equation is a circle with center = (0, 0) and radius = 4.
The graph is attached.
Learn more: https://brainly.com/question/8806877
A pole that is 3.3 meters tall casts a shadow that is 1.36 meters long. At the same time, a nearby building casts a shadow that is 47.75 long. How tall is the building?
Answer:
Height of building is 115.86 m.
Step-by-step explanation:
This is problem of proportion.
a:b = c:d
____________________________________________________________
height of pole = 3.3 m
length of shadow of pole = 1.36 m
ratio
height of pole: length of shadow of pole = 3.3 : 1.36
________________________________________________
let the height of building= x m
length of shadow of building= 47.75 m
ratio
height of building: length of shadow of building= x: 47.75
ratio in both the cases will be same
thus,
x/47.75 = 3.3 / 1.36
=> x = 3.3 / 1.36 * 47.75 = 115.86
Thus, height of building is 115.86 m.
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $1700 and her stock in Company B was worth $500. The stock in Company A has increased 20% since last year and the stock in Company B has increased 12%. What was the total percentage increase in the investor's stock account?
Answer:
All together she had a 18.1818182% raise but 18% raise rounded.
Step-by-step explanation:
First you need to find how much each stock increased.
So:
1700 to 2040
500 to 560
Add them.
1700 + 500 = 2200
2040 + 560 = 2600
Then find the raise. You can usally just find the amount for each percent or find the over all raise.
1% of 2200 is 22
400/22 = 18.18
Write a paragraph proof to prove the statement
We start with m < A + m < B = m < B + m < C as the given equation. We can rearrange the two terms on the right hand side to get m < A + m < B = m < C + m < B. From here, subtract m < B from both sides to end up with m < A = m < C. The angle B terms go away entirely. This rule I used was the subtraction property of equality. The next rule to use is the symmetric property to go from m < A = m < C to m < C = m < A. This rule is basically where we can flip the two sides of the equation and the equation is the same.
Please please help please!!
Answer:
The vertex is at (-2,-8)
Step-by-step explanation:
You go left 2, and down 8, and then it's a scale of 1
sum1 plz help me & explain it ! thank you :)
Answer:
D
Step-by-step explanation: 2 x square root of 2 is 2.8284.......
please help!! thank you
Answer: 5
Step-by-step explanation:
f(x)=3-x
f(-2)=3-(-2)
f(-2)=3+2
f(-2)=5
Hope this helps!! :)
Please let me know if you have any question
which expression is equivalent to 4/9x7?
Is there an answer key?
Answer:
3.11111111
Step-by-step explanation:
solved all the equations and simplified the original problem. The answer for the third one was the same as the original problem.
A rectangle where the ratio of the width to length is 5 : 9.
If the perimeter of the rectangle is 448 in, find the length and width.
Steps to solve please
Answer:
length=80m
breadth=144m
hope it is helpful for you
3(10 + 2) could be used to simplify which of the following problems? 130(26) 13(12) 13(20)
Answer:130(26).
Step-by-step explanation: It could basically be used to simplify 130(26) because if you multiply the number on the outside of the parentheses (13) with the numbers inside the parenthesis(10+2), you will get 130(26).
The boiling point of water is 212°F. The boiling point of helium is –452°F.
How would you compare the temperatures using an inequality?
A. –452°F < 212°F
B. –452°F > 212°F
C. 212°F < –452°F
D. 212°F > –452°F
Answer:
Option A and Option D are correct
Hey There!!
T is in the interior of angle PQR. Find each of the following. Hint: Draw each angle.
8. mPQT if mPQR=25 degrees and mRQT=11 degrees.
Answer:
13 degrees
Step-by-step explanation:
mPQR=25 degrees , mRQT=11 degrees.
mPQT=PQR-RQT
MPQT=25-11=13 degrees
.837537537 as a reapting decimal
Answer:
this is a reapeting decimal
Step-by-step explanation:
What is direct and inverse variation?
Answer:
Can you please make it more spicific or add a picture
Step-by-step explanation:
In a 200 page book, Alicia read 50 pages. What is the ratio of the number of pages Alicia read to the number of pages she has not read?
Answer:
jf
Step-by-step explanation:
f
Answer: 4
Step-by-step explanation: 4 because 200 divided by 50 is 4. The ratio is 4
22. Find three consecutive odd numbers such that the sum of five times the smaller number and twice
the larger number is 33 more than six times the median number.
Answer:
The numbers are 37, 39 and 41.
Step-by-step explanation:
Let the smallest number be [tex]x\\[/tex].
Then the other numbers will be [tex]x+2, x+4[/tex] (as they are consecutive odd numbers, their difference will be 2).
As per the given statement:
LHS(Left Hand Side) : Sum of five times the smaller number and twice the larger number.
i.e. five times the smaller number = [tex]5\times x[/tex]
twice the larger number = [tex]2 \times (x+4)[/tex]
Their sum:
The Left Hand Side becomes:
[tex]5x+2(x+4)[/tex]
RHS(Right Hand Side):
33 more than six times the median number:
i.e. [tex]6\times(x+2) +33[/tex]
Equating LHS and RHS:
[tex]5x+2(x+4) = 6x+12 +33\\\Rightarrow 7x+8=6x+47\\\Rightarrow \bold{x =37}[/tex]
Therefore, the numbers are 37, 39 and 41.
what is the fifth term of (x-2y)^7
Answer:
560x^3y^4.
Step-by-step explanation:
The (r+1)th term of (a + b)^r = nCr a^(n-r) b^r
We want the fifth term so r = 5 - 1 = 4:
(4 + 1)th term = 7C4 x^(7-4) (-2y)^4
= 35x^3 16y^4
= 560x^3y^4.
easy 10 points and brainliest :)
the line is vertical
hits the (0,0) but still on the y axis
If X = {−1, 0, 2} and Y = {1, 2, 5}, find X ∪ Y.
Answer:
(0,-1,2,5)
Step-by-step explanation:
[tex]X = (-1, 0, 2)\\Y = (1, 2, 5)\\ \\X U Y = ?\\= (-1, 0,2,5)[/tex]
find the distance between each pair of points E(-1, 0),F(12, 0)
Answer:
The answer is
[tex]13 \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
E(-1, 0) and F(12, 0)
The distance between them is
[tex] |EF| = \sqrt{ ({ - 1 - 12})^{2} + ({0 - 0})^{2} } \\ = \sqrt{ ({ - 13})^{2} } \\ = \sqrt{169} [/tex]We have the final answer as
[tex]|EF| = 13 \: \: units[/tex]Hope this helps you
Let p: the book is interesting and q: the book has pictures.
The notation p q represents the statement "The book is interesting
the book has pictures."
The notation p q represents the statement "The book is interesting
the book has pictures."
The notation qv p represents the statement "The book has pictures
the book is interesting."
The notation 9 → p represents the statement "The book is interesting
the book has pictures.
Answer:
The notation p ∧ q represents the statement “The book is interesting
✔ and <-- Answer
the book has pictures.”
The notation p ↔ q represents the statement “The book is interesting
✔ if and only if <-- Answer
the book has pictures.”
The notation q ∨ p represents the statement “The book has pictures
✔ or <-- Answer
the book is interesting.”
The notation q → p represents the statement “The book is interesting
✔ if <-- Answer
the book has pictures.”
Step-by-step explanation:
I took the test aswell.
Find P(1), if p(x)=(x-1) (x+1)
Answer:
0
Step-by-step explanation:
So we have the function:
[tex]p(x)=(x-1)(x+1)[/tex]
To find p(1), substitute x for 1:
[tex]p(1)=((1)-1)((1)+1)\\[/tex]
Simplify:
[tex]p(1)=(0)(2)\\p(1)=0[/tex]
Thus, p(1) is 0.
Three siblings are one year apart inage. If the oldest is x years old, what is the average of their ages?
Answer:
x - 1
Step-by-step explanation:
x
x - 1
x - 2
x + (x - 1) + ( x - 2)
3x - 3
3(x - 1)
Average
3(x - 1)/3
x - 1