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.
sum1 plz help me & explain it ! thank you :)
Answer:
D
Step-by-step explanation: 2 x square root of 2 is 2.8284.......
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
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.
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
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
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
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
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]
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.
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!!
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.
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
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
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
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
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.
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 .
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.
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
What is direct and inverse variation?
Answer:
Can you please make it more spicific or add a picture
Step-by-step explanation:
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.
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).
.837537537 as a reapting decimal
Answer:
this is a reapeting decimal
Step-by-step explanation:
(-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.
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.
f(0) f(0)=3(0)^2-10(0)-4
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]
easy 10 points and brainliest :)
the line is vertical
hits the (0,0) but still on the y axis
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
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