A town's population went from 40,000 to 50,000. What was the percent of change in the population?
1. Prove that the product of the second and third numbers out of four consecutive whole numbers is two greater than the product of the first and the fourth numbers.
2. Prove that the square of the second number out of three consecutive odd numbers is four greater than the product of the first and third numbers.
Answer:
1.
(x+1)(x+2)>x(x+3)
x^2+2x+x+2>x^2+3x
x^2+3x+2>x+3x
2>0
2.
(x+2)^2>x(x+4)
x^2+4x+4>x^2+4x
4>0
Step-by-step explanation:
1.
Suppose x is the lowest number in the set of 4 consecutive numbers, then x+1, x+2, and x+3 are then the next numbers in the sequence since they are the next whole numbers.
Then, to follow the conditions of the problem, we make the equation:
(x+1)(x+2)>x(x+3)
Using the formula of (a+b)(c+d)=ac+ad+bc+bd, we can expand both sides of the equation into this:
x^2+2x+x+2>x^2+3x
=x^2+3x+2>x^2+3x
We can then cancel x^2+2x from both sides and we are left with 2>0.
2.
Again, suppose x is the lowest value in the set of consecutive numbers. In this case, odd numbers increase by 2 each time so the series of numbers are:
x, x+2, x+4
Therefore, to follow the conditions of the problem, we make the equation:
(x+2)^2>x(x+4)=
(x+2)(x+2)>x(x+4)
Using the same formula of (a+b)(c+d)=ac+ad+bc+bd, we get:
x^2+4x+4>x^2+4x
Cancel x^2+4x from both sides and we are left with 4>0
Hope this helps!
I need help on 12 please 14 points
Step-by-step explanation:
P = 6+6+5x-3 + 5x -3 = 10x+6
A = 6(5x-3) = 30x -18
Answer:
30x-18 is the area
the perimeter is 10x+6
Step-by-step explanation:
not enough info to solve for x, but we can still have a variable
6(5x-3)
distribute
6(5x)-6(3)
30x-18 is the area
the perimeter is 10x+6
I NEED HELP ASAP!!!!!!!!
Quick answer please!
Avante walked 1 and 1/2 miles in 22.5 minutes. Avante walked at a constant rate. How long did it take him to walk 1 mile?
I don't know how to do these 3 circled problems. can you do it step by step?
Find the GCF. Show work
Answer:The greatest common factors
Step-by-step explanation:
GCF of 18 : 27 , 9
GCF of 36 : 36 GCF of 27 : 9
GCF of 54 : 18
GCF of 12 : 3
GCF of 24 : 3
GCF of 40 : 40
Which expressions are equivalent to 4m + 12? Choose all that apply. Whoever answers fastest, I’ll mark the Brainliest!
Answer: 1st and 3rd
Step-by-step explanation:
Answer:
third one
Step-by-step explanation:
6m-2m =4m
Hence 4m+12
Car survey in a survey of 1200 people who owned a certain type of car,600 said they would buy that type of car again.What percent of people surveyed were satisfied with the car?
Answer:
50 percent
Step-by-step explanation:
Total number of people in this car survey = 1200
Total number of people who they would still buy same car type = 600 (these are the satisfied people)
The percentage = 600/1200 x 100
= 0.5 x 100
= 50 percent
So the percentage of satisfied people who would buy this type of car again is 50%
Which set of three numbers can be used to make a right triangle?
Group of answer choices
4, 5, 6
3, 4, 5
5, 6, 7
Answer:
3, 4, 5
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]3^{2} + 4^{2} = 5^{2}[/tex]
9+16=25
25=25
Solve for h.
-4h - 10 = 10 - 9h
h = |
What is the least common denominator of
1/7 and 2/3
Answer:
Step-by-step explanation:
The LCD here is the smallest integer evenly divisible by both 7 and 3. That number would be 21. Then:
1/7 and 2/3 become 3/21 and 14/21.
is 0.24 greater than 0.42?
Answer:
yes it is greater
Step-by-step explanation:
help please what is the domain and range of S
S={(0,-2), (5,3), (-3,5), (1,1)}
Answer:
Domain: {0,5,−3,1}
Range: {2,3,5,1}
Step-by-step explanation:
Do not factor by grouping. Solve 2(x-2)^1/3=x+2
Step-by-step explanation:
2(x-2)⅓=x+2
so we first cube each side,such that...
(2(x-2))⅓•³=(x+2)³
we get...
2(x-2)=(x+2)³
expanding...
2x-4=x³+6x²+12x+8
grouping....
x³+6x²+12x+8-2x+4=0
solving...
x³+6x²+10x+12=0
now you can use you calculator to solve for the possible values of x
I hope this will help
who uses y=mx+b in School
please help!!!! will mark brainlest
Answer:
16.59
Step-by-step explanation:
πr^2/2
radius is 6.5/2 = 3.25
πx3.25x3.25/2= 16.59
Find the arc length of the partial circle.
Answer:
12.42 units
Step by step explanation:
Given,
length of the radius = 2 units
Therefore, arc length of the complete circle = 2 × 3.14 × 2 units = 12.56 units
Therefore, arc length of the partial circle = 3/4 × 12.56 units
= 12.42 units
Determine whether the following sequences are arithmetic. If so, identify the common
difference.
9, 15, 21, 27, ...
Answer:
Yes the sequence is arithmetic
The common difference is 6
Step-by-step explanation:
Determine whether the following sequences are arithmetic. If so, identify the common difference.
9, 15, 21, 27, ...
The sequence given in the above question is arithmetic because it follows the formula
Un = a + (n -1)d
Where
a= First term
n = Number of terms
d = Common difference
The common difference is calculated as the
Second term - First term
15 - 9
= 6
or the Third term - Second term
21 - 15
= 6
or the Fourth term - Third term
= 27 - 21
= 6
Therefore, the Common difference = 6
What is the Mean of the data below 2,4,5,6,8,2,5, 6
the answer is 4.75
Step-by-step explanation:
The mean of a set of numbers, sometimes simply called the average , is the sum of the data divided by the total number of data. Example 1 : ... There are 8 numbers in the set. Add them all, and then divide by 8 . so just add all you numbers and divide it by 8. simple
Solve the following quadratic equation using the quadratic formula.
Write the solutions in the following form, where r, s, and t are integers, and the fractions are in simplest form.
Answer:
x = (8-6i)/10
x = (8+6i)/10
Step-by-step explanation:
what is the surface area of a rectangular prism that has a height of 47 a length of 19 and a width of 6 IF U AREN'T SYDNEETEAL I WILL REPORT U
answer:
2578
step-by-step explanation:
A=2(wl+hl+hw)=2·(47·19+6·19+6·47)=2578
good luck
hopefully this helps
have a nice day :)
is it a function? and explain briefly why
Answer:
No
Step-by-step explanation:
Each output can only have one input
The equation below can be used to find how much Julie took to the mall (d), in dollars.
d - $44.00 = $22.00
How much did Julie take to the mall?
$968.00
$2.00
$66.00
$22.00
Answer:
$22.00
Step-by-step explanation:
the reason it's 22 dollars is because you take away 44 - 22 and it's 22
please help me ill mark you brainliest and please show your work :)
Answer:
12
Step-by-step explanation:
Multiply both sides of the equation by 8/5.
4x-16=32
Move 16 to the other side
4x=32+16
add numbers on the right side
4x=48
divide both sides by 4
x=12
PLEASE HELP! :) IMAGE IS BELOW!! QUESTION: Describe a series of transformations that will transform ∆ABC to ∆A'B'C'.
Answer:
Dilation and translation.
Hope that helps!
Step-by-step explanation:
The value of x for the system is 1. What is the value of y?*
1 point
3x + y = 9
y = -4x + 10
1. Substitute the value of y in the first equation:
2. Combine like terms:
3. Apply the subtraction property of equality:
4. Apply the division property of equality:
3x + (-4x + 10) = 9
-x+ 10 = 9
-X = -1
x = 1
O y = 14
O y = 12
O y = 6
O y=3
When loesolved
system lisin
bstitution bet7
TA
Solve for x- round to the nearest tenth- Trigonometry
Answer:
sin26=11/X
0.438371146789×x=11
X. = 11/0.438371146789
X=25.09289235975
Write an equation in slope-intercept form (y = mx + b) , that perpendicular to y = 2x - 4 that passes through the point (3, - 3) .
Answer:
Step-by-step explanation:
perp. -1/2
y + 3 = -1/2(x - 3)
y + 6/2 = -1/2x + 3/2
y = -1/2x - 3/2
