Answer:
You add them together and divide it by how many number there are.
Step-by-step explanation:
For example lets say we need to find the average of 12, 15, 18, and 24.
You would do 12+15+18+24
You will get a sum of 69
Then since there are 4 numbers you do 69 divided by 4 and get a quotients of 17.25.
Therefore 17.25 is the average of all four numbers.
What is the solution to the equation?
k/6.4=8.7
2.3
5.568
15.1
55.68
[tex]\dfrac{k}{6.4}=8.7\Longrightarrow k=6.4\cdot8.7=\boxed{55.68}[/tex]
Hope this helps.
r3t40
For this case we have the following equation:
[tex]\frac {k} {6.4} = 8.7[/tex]
We must find the value of the variable "k":
Then, we must multiply by 6.4 on both sides of the equation:
[tex]6.4 * \frac {k} {6.4} = 6.4 * 8.7\\k = 55.68[/tex]
Thus, the value of the variable "k" is 55.68.
Answer:
[tex]k = 55.68[/tex]
Option D
Jacob is practicing javelin throws. He throws the javelin from a height of 6 feet. The height of the javelin, h(x), in relation to the horizontal distance that it covers, x, can be modeled by a quadratic function.
Each of the following functions is a different form of the quadratic model for this situation. Which form is most helpful in determining the horizontal distance the javelin covers?
A. h(x)= -0.01(x-150)(x+4)
B. h(x)= -0.01(x-73)^2+ 59.29
C. h(x)= -0.01x(x-146)+6
D. h(x)= -0.01x^2+1.46x+6
Answer: Option A
[tex]h(x) = -0.01 (x-150) (x + 4)[/tex]
Step-by-step explanation:
The javelin will have reached its maximum horizontal distance when it touches the ground.
Then the maximum horizontal distance occurs when the height h (x) is equal to zero.
So we must equal h(x) to zero and solve the equation for x.
Therefore the form that is most useful to determine the horizontal distance that the javelin covers is the one that is factored. Because it allows us to find the zeros of the quadratic function more easily
[tex]h(x) = -0.01 (x-150) (x + 4) = 0[/tex]
[tex]-0.01 (x-150) (x + 4) = 0[/tex]
The equation is equal to zero when [tex]x = 150[/tex] or when [tex]x = -4[/tex]
Therefore the solution is [tex]x = 150[/tex].
The horizontal distance that covers the javelin is 150 feet
Answer:
The answer is A
Step-by-step explanation:
I am 100% sure cuz I just did the test:)
Write an even square number smaller than 100.
Answer:
I believe you mean what square number that is less than 100 has the most factors.
The square numbers under 100 are 1, 4, 9, 16, 25, 36, 49, 64, and 81.
1 obviously only factors to 1*1.
4, 9, 25, and 49 are square of prime numbers. If we call the original number n and the root p (for prime) each of them can only be factored as 1*n or p*p. example: 1*4, 2*2 .We can eliminate those.
16 and 81 are not only squares, but the fourth power of a prime (2 and 3) respectively. They can be factored as 1*n, (p^3)*p, or (p^2*p^2). Example: 1*16, 8*2, or 4*4.
But 36 is 2*2*3*3 as it’s prime factoring. This allows us to find more combinations of factors: 1*36, 2*18, 4*9, 12*3, or 6*6.
Final answer:
The largest even square number smaller than 100 is 64, which is the square of 8.
Explanation:
To find an even square number smaller than 100, we can look at the squares of the even numbers less than 10, since 10² (which is 10 times 10) equals 100. Squaring each even number from 2 to 8, we get the following even square numbers: 2²=4, 4²=16, 6²=36, and 8²=64. Among these, 64 is the largest even square number that is less than 100.
Which equation and solution can be used to solve this problem?
Thirteen less than a number is sixteen.
13-n=16: Add 13 to both sides. The answer is 29.
n+13=16: Subtract 13 from both sides. The answer is 3.
n+16=13 Subtract 13 from both sides. The answer is 3.
n-13=16: Add 13 to both sides. The answer is 29.
Answer:
n = 29
Step-by-step explanation:
We need to find an equation that represents the following statement: "Thirteen less than a number is sixteen" which is the same as: "A number minus thirteen equals sixteen"
In that sense, the equation that represents that statement is: n - 13 = 16
Now, the solution is: n - 13 = 16 → n = 29
Answer:
n = 29
Step-by-step explanation:
The length and width of a rectangle are consecutive even integers. The perimeter is 68 meters. Find the length
and width
The length is
meters long while the width is
meters
Answer:
The dimensions are 16 meters by 18 meters
Step-by-step explanation:
P = 2(l+w)
is the formula for the perimeter of a rectangle.
We know the length is 2 more than the width ( consecutive even integers)
l = w+2
P = 2 (w+2+w)
P = 2(2w+2)
68 = 2 (2w+2)
Divide each side by 2
34 = 2w+2
Subtract 2
34-2 = 2w+2-2
32 = 2w
Divide by 2
32/2 = 2w/2
16 =w
l = w+2
l =16+2
l = 18
The dimensions are 16 meters by 18 meters
the width of the rectangle is 16 meters and the length is 18 meters.
To find the length and width of a rectangle when given that the length and width are consecutive even integers and the perimeter is 68 meters, we first need to express the length and width in algebraic terms. Let's call the width 'w' and since the length is the next consecutive even integer, it can be expressed as 'w + 2'. The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where 'l' is the length and 'w' is the width. In this case, since width is 'w' and length is 'w + 2', the perimeter formula becomes P = 2(w+2) + 2w.
Let's solve for 'w':
68 = 2(w + 2) + 2w
68 = 2w + 4 + 2w
68 = 4w + 4
64 = 4w
w = 16
Now that we have the width, we can easily find the length:
l = w + 2
l = 16 + 2
l = 18
Therefore, the width of the rectangle is 16 meters and the length is 18 meters.
During the spring and summer, a concession stand at a community Little League baseball game field sells soft drinks and other refreshments. To prepare for the season, the concession owner refers to the previous year's files, in which he had recorded the daily soft drinks sales (in gallons) and the average daily temperature (in degrees Fahrenheit). Using the coordinates of the two points (84,80) and (74,65), determine the slope of the line of best fit.
Answer:
1.5
Step-by-step explanation:
The slope is given by ...
(change in dependent variable)/(change in independent variable)
= (65 -80)/(74-84) = -15/-10 = 1.5
The slope of the line of best fit is 1.5.
Answer:
The slope of the line of best fit is 1.5 degrees Fahrenheit per gallon.
Step-by-step explanation:
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The given two points are (84,80) and (74,65).
The slope of the line of best fit is
[tex]m=\frac{65-80}{74-84}[/tex]
[tex]m=\frac{-15}{-10}[/tex]
[tex]m=1.5[/tex]
Therefore the slope of the line of best fit is 1.5 degrees Fahrenheit per gallon.
The sum of two consecutive integers is – 7. Find the numbers
[tex]n,n+1[/tex] - two consecutive integers
[tex]n+n+1=-7\\2n=-8\\n=-4\\n+1=-3[/tex]
-4 and -3
A bag contains 10 marbles: 4are green, 2are red, and 4 are blue. Carmen chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue?
Answer:
2/15
Step-by-step explanation:
There is a 4/10 probability that she chooses blue the first time, but the second time it is a 3/9 chance because she didn't put the marble back so there are 9 marbles in total, 3 blue ones.
4/10 x 3/9 = 2/5 x 1/3 = 2/15
I hope this helps :)
Edit: Messed up the multiplication, whoops!
[tex]|\Omega|=10\cdot9=90\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{90}=\dfrac{2}{15}[/tex]
what is the exact solution of 2e^x=14?
[tex]2e^x=14\\e^x=7\\x=\ln 7[/tex]
Determine the truth value of the given conditional statement. Given: If 3 is an even number, then 5 + 3 = 8.
Answer:
False
Step-by-step explanation:
False, because 3 can not be an even number; it's an odd number. So the condition cannot be satisfied.
regents.org/algebraone/119/algone 12019-mrsw.pdf
.
....
Question 31
31 Santina is considering a vacation and has obtained high-temperature data from the last two weeks
for Miami and Los Angeles.
Miami
76 75 83 73606676
81 83 85 83 87 8080
74
Los Angeles
Los Angeles
63
62
65
72
67 | 65 | 6565
69 64 64 61
3639
62
Which location has the least variability in temperatures? Explain how you arrived at your answer.
Answer:
Los Angeles
Step-by-step explanation:
Los Angeles has the least variability in temperatures.
To determine which location has the least variability in temperatures, we need to calculate the range or variance of the temperatures for both Miami and Los Angeles.
For Miami:
Temperatures: 76 75 83 73606676 81 83 85 83 87 8080 74
To calculate the range, we subtract the minimum temperature from the maximum temperature:
Range = Maximum temperature - Minimum temperature
Range = 87 - 73
Range = 14
For Los Angeles:
Temperatures: 63 62 65 72 67 | 65 | 6565 69 64 64 61 3639 62
Again, to calculate the range, we subtract the minimum temperature from the maximum temperature:
Range = Maximum temperature - Minimum temperature
Range = 72 - 61
Range = 11
Comparing the ranges, we see that Miami has a range of 14, while Los Angeles has a range of 11. Therefore, Los Angeles has the least variability in temperatures.
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Lilly owes $52,000 in student loans for college. If the loan will be repaid in 5.5 years and the interest rate charged is 6.75%,then how much will she pay altogether?
Answer:
55510
Step-by-step explanation:
Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.
Answer:
1.25.
Step-by-step explanation:
The common ratio r is 1/5 and the first term a1 = (1/5)^(1-1) = 1.
Sum to infinity = a1 / (1 - r)
= 1 / (1 - 1/5)
= 1 / 4/5
= 5/4
= 1.25 (answer)
Answer:
Step-by-step explanation:
1.25
Please help me! Will mark brainliest!
Answer:
x = 8
Step-by-step explanation:
The 12 on the right is 1/3 the number 36 on the segment above. The value of x will have the same proportion to the segment above it, so will be 1/3 of 24, or 8.
x = 8
On the first day of camp, 5 10 of the skaters were beginners. Of the beginners, 2 6 were girls. What fraction of the skaters were girls and beginners? Complete the explanation. of the skaters were girls and beginners
Answer:
1/6
Step-by-step explanation:
5/10(3/3)=15/30
2/6(5/5)=10/30
15/30 - 10/30= 5/30 = 1/6
Answer: 1/6
Step-by-step explanation:
A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 640t. After how many seconds does the projectile take to reach its maximum height?
Answer:
20 seconds
Step-by-step explanation:
We just need the x-coordinate of the vertex...so find -b/(2a) and we are done:
-b/(2a)=-640/(2*-16)=-640/-32=20
20 second
Answer:
[tex]\boxed{\text{20 s}}[/tex]
Step-by-step explanation:
The standard form of a quadratic function is
y = ax² + bx + c
Your function is
h(t) = -16t²+ 640t
a = -16; b = 640; c = 0
a is negative, so you have a downward-opening parabola.
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
Your parabola opens downward, so the vertex is a maximum.
Calculate h
[tex]h = \dfrac{640}{-2(-16)}} = \dfrac{640}{32} = 20\\\text{The projectile reaches maximum height }\boxed{\textbf{20 s}} \text{after it is thrown}\\[/tex]
The figure below shows the graph of h(t).
if ABCD is an isosceles trapezoid, what is the value of x
Answer:
Since we know that ABCD is an isosceles trapezoid, we can also asume that its diagonals have the same length, which means:
AC = BD
=> 7x - 21 = 5x + 13
=> 7x - 5x = 21 + 13
=> 2x = 34
=> x = 34/2 = 17
So the answer is C.
Since we know that ABCD is an isosceles trapezoid, the value of Option C. x= 17
we can also assume that its diagonals have the same length, which means:
AC = BD
=> 7x - 21 = 5x + 13
=> 7x - 5x = 21 + 13
=> 2x = 34
=> x = 34/2 = 17
So the answer is C.
An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals
Properties of Isosceles TrapezoidIt has an axis of symmetry. It has no rotational symmetry and one line of symmetry joining the midpoint of the parallel sides.One pair of sides is parallel and they are the base sides. (AB II DC in the given image)The remaining sides other than the base are non-parallel and are equal in length. (c = d in the given image)The diagonals are the same in length. (AC = BD)The base angles are the same. (∠D = ∠C, ∠A=∠B)The sum of opposite angles is 180° or supplementary. (∠A + ∠C = 180° and ∠B + ∠D = 180°)The line segment joining the midpoints of the parallel sides is perpendicular to the bases. (PQ ⊥ DC)Learn more about Isosceles Trapezoid, refer
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What number will be in the blue box
Answer: D) 5832
Step-by-step explanation:
The y values are the x values cubed. Since the x values are increasing by 3, the last x would be 18. 18 cubed is 5832.
(URGENT) Can someone help me find x, I’ve gotten it wrong twice.
Answer:
x = 24.10
Step-by-step explanation:
The given sides of the triangle are the hypotenuse (x) and a side of length 20 that is adjacent to the 34° angle and opposite the 56° angle.
The mnemonic SOH CAH TOA reminds you of relationships between the hypotenuse and adjacent or opposite sides:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
If we want to use the "adjacent" side, we would choose ...
cos(34°) = 20/x
x = 20/cos(34°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions
__
If we want to use the "opposite" side, we would choose ...
sin(56°) = 20/x
x = 20/sin(56°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions
_____
Comment on rounding
If you round correctly (only at the last step), the proper answer is 24.12.
Solve for the variable z in this equation 2y(x+z)=w
A. Z = w-2xy/2y
B. Z = 2w-2xy/2y
C. Z = w-2x/2y
D. Z = w-xy/2y
Answer:
I think is a for the answer
the simplified value of the given expression 2y (x+z) = w for z will be z = (w- 2xy)/2y.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, an expression 2y (x+z) = w
Simplifying the given expression for z
=> 2y (x+z) = w
divide by 2y into both sides
=> x + z = w/2y
subtract by x into both sides
=> z = w/2y - x
=> z = w-2xy /2y
thus,
z = (w- 2xy)/2y
therefore, the simplified value of the given expression 2y (x+z) = w for z will be z = (w- 2xy)/2y.
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please help will mark brainliest
One number to the right of the decimal will mean there are two numbers to the left of the decimal.
When rounding to 50 as the nearest ten the number needs to be between 45 and 54.
Using the 3 numbers shown that would be 48.3
PLEASE HELP ME!!! WILL GIVE BRAINLIEST!!!!,find (f+g)(x) for the following functions.
f(x)=6x^2+9x+8
g(x)=4x+6
Answer:
[tex](f+g)(x)=6x^2+13x+14[/tex]
Step-by-step explanation:
(f+g)(x) simply means that you are adding f(x) to g(x) to get a new equation that is the sum of them.
[tex]6x^2+9x+8+4x+6[/tex]
simplifies down to, by combining like terms,
[tex]6x^2+13x+14[/tex]
What is the value of log625^5
Answer:
Value of log625^5 is 13.95
Step-by-step explanation:
We need to find the value of log625^5
Using log rule log a^n = nloga
log625^5
= 5log625
=5(2.79)
=13.95
So, value of log625^5 is 13.95
Answer with explanation:
We have to find the value of :
[tex]\rightarrow\log 625^5\\\\\rightarrow 5 \log625\\\\\rightarrow 5 \log 5^4\\\\\rightarrow 4 \times 5 \log 5\\\\ \rightarrow 20 \log 5\\\\\rightarrow 20 \times 0.69897\\\\ \rightarrow 13.9794\\\\=13.98\\\\ \text{Used following properties of log}\\\\ \log a^b=b \log a[/tex]
Please help me! Will mark brainliest!
Answer:
A 2sqrt(7)
Step-by-step explanation:
Use similar triangles and ratios of lengths of corresponding sides.
2/x = x/14
x^2 = 28
x = 2sqrt(7)
If the given sequence is a geometric sequence, find the common ratio.
3/3, 3/12, 3/48, 3/192, 3/768
a. 4
b. 1/30
c. 30
d. 1/4
Answer:
d. 1/4
Step-by-step explanation:
The common ratio will be the ratio of any two adjacent terms:
(3/12)/(3/3) = (1/4)/1 = 1/4
Answer:
d
Step-by-step explanation:
If the sequence is geometric then a common ratio r will exist between consecutive terms.
[tex]\frac{3}{12}[/tex] ÷ 1 = [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{3}{48}[/tex] ÷ [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{3}{192}[/tex] ÷ [tex]\frac{3}{48}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{3}{768}[/tex] ÷ [tex]\frac{3}{192}[/tex] = [tex]\frac{1}{4}[/tex]
A common ratio of r = [tex]\frac{1}{4}[/tex]
Hence sequence is geometric
If (A, B) is the solution to the system of equations shown above, and A and B are integers, then what is the value of A+B?
A) -12
B) -6
C) 0
D) 6
Answer:
A) -12
Step-by-step explanation:
The point of intersection on the graph is (-6, -6). That is the solution to the system of equations. The sum of the solution values is ...
(-6) +(-6) = -12
Answer:
A
Step-by-step explanation:
The solution to the system of equations is at the point of intersection of the 2 lines, that is
(- 6, - 6) ⇒ A = B = - 6, thus
A + B = - 6 + (- 6) = - 6 - 6 = - 12 → A
Use the Polynomial Identity below to help you create a list of 10 Pythagorean Triples:
([tex]x^{2}[/tex]+[tex]y^{2}[/tex])[tex]^{2}[/tex]=([tex]x^{2}[/tex]-[tex]y^{2}[/tex])[tex]^{2}[/tex]+(2xy)[tex]^{2}[/tex]
Hint #1: c² = a² + b²
Hint #2: pick 2 positive integers x and y, where x > y
Answer:
See explanation
Step-by-step explanation:
You are given the equality
[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]
where x, y are two positive integers with x>y.
1. x=2,y=1, then
[tex]c=x^2+y^2=2^2+1^2=5\\ \\a=x^2-y^2=2^2-1^2=3\\ \\b=2xy=2\cdot 2\cdot 1=4[/tex]
First Pythagorean triple is (3,4,5)
2. x=3,y=1, then
[tex]c=x^2+y^2=3^2+1^2=10\\ \\a=x^2-y^2=3^2-1^2=8\\ \\b=2xy=2\cdot 3\cdot 1=6[/tex]
Second Pythagorean triple is (6,8,10)
3. x=3,y=2, then
[tex]c=x^2+y^2=3^2+2^2=13\\ \\a=x^2-y^2=3^2-2^2=5\\ \\b=2xy=2\cdot 3\cdot 2=12[/tex]
Third Pythagorean triple is (5,12,13)
4. x=4,y=1, then
[tex]c=x^2+y^2=4^2+1^2=17\\ \\a=x^2-y^2=4^2-1^2=15\\ \\b=2xy=2\cdot 4\cdot 1=8[/tex]
Fourth Pythagorean triple is (8,15,17)
5. x=4,y=2, then
[tex]c=x^2+y^2=4^2+2^2=20\\ \\a=x^2-y^2=4^2-2^2=12\\ \\b=2xy=2\cdot 4\cdot 2=16[/tex]
Fifth Pythagorean triple is (12,16,20)
6. x=4,y=3, then
[tex]c=x^2+y^2=4^2+3^2=25\\ \\a=x^2-y^2=4^2-3^2=7\\ \\b=2xy=2\cdot 4\cdot 3=24[/tex]
Sixth Pythagorean triple is (7,24,25)
7. x=5,y=1, then
[tex]c=x^2+y^2=5^2+1^2=26\\ \\a=x^2-y^2=5^2-1^2=24\\ \\b=2xy=2\cdot 5\cdot 1=10[/tex]
Seventh Pythagorean triple is (10,24,26)
8. x=5,y=2, then
[tex]c=x^2+y^2=5^2+2^2=29\\ \\a=x^2-y^2=5^2-2^2=21\\ \\b=2xy=2\cdot 5\cdot 2=20[/tex]
8th Pythagorean triple is (20,21,29)
9. x=5,y=3, then
[tex]c=x^2+y^2=5^2+3^2=34\\ \\a=x^2-y^2=5^2-3^2=16\\ \\b=2xy=2\cdot 5\cdot 3=30[/tex]
9th Pythagorean triple is (16,30,34)
10. x=5,y=4, then
[tex]c=x^2+y^2=5^2+4^2=41\\ \\a=x^2-y^2=5^2-4^2=9\\ \\b=2xy=2\cdot 5\cdot 4=40[/tex]
10th Pythagorean triple is (9,40,41)
PLS HELP ME.
A strip of metal sheet 2cm thick is wound ten times round a cylindrical rod of diameter 9cm and height 8cm such that it fits exactly .calculate the volume of the resulting object [take pi = 22/7 ]
Answer:
15092cm^3
Step-by-step explanation:
The total thickness of the strip of metal sheet would be 2*10=20cm
the new radius of the cylinder would be 9/2+20=24.5cm
Volume of a cylinder: ((pi)r^2)h
the height is 8cm
Volume : (22/7)*24.5^2*8
=15092cm^3
Can someone please explain to me how to do this?
1. Write an algebraic expression that simplified to -3x - 1. Simplify the expressions to verify your answer.
2. Write an algebraic expression that simplified to -7x - 4. Simplify the expressions to verify your answer.
Answer:
1. (-10x -5) -(-7x -4)
2. (-10x -5) -(-3x -1)
Step-by-step explanation:
The process of simplifying an expression generally involves eliminating parentheses, collecting terms, simplifying fractions, rationalizing denominators, removing appropriate factors from under radicals, and generally putting expressions into general form.
So, to accomplish what the problem is asking, you can create an expression that requires you accomplish as many or as few of these steps as you may like.
In general, you will want to both "do" and "undo" whatever operation(s) you may choose. For example, consider a couple of expressions "a" and "b". For this example, we want our final result to simplify to "a".
If we choose to add "b", we might have ...
(a+b) -b . . . . . we have both added and subtracted b, so the simplified result is "a"
If we choose to multiply by "b", we might have ...
(ab)/b . . . . . . we have both multiplied by b and divided by b, so the simplified result is again "a"
_____
We can solve both these problems at once by using ...
a = -3x -1b = -7x -4If we choose the first approach, we want an expression that is (a+b). That will be ...
a+b = (-3x -1) +(-7x -4) = -10x -5
By subtracting "b" from this expression, we get "a"--and vice versa. That is ...
(-10x -5) -(-7x -4) . . . simplifies to . . . -3x -1(-10x -5) -(-3x -1) . . . simplifies to . . . -7x -4_____
Alternate solution to 2
Suppose we choose to multiply instead. Let "b" be -3x+2. Then, using the template for multiplication above, we can write the expression
(-7x -4)(-3x +2)/(-3x +2) = (21x^2 -2x -8)/(-3x +2)
and we know this rational expression simplifies to -7x -4.
_____
Of course, we can be as elaborate as we might like in modifying the original expression. Whatever we do, we must also include the "undo" so the original expression is recovered when we simplify. To illustrate the point, we can add and subtract 2x from the above rational expression.
((21x^2 -2x -8)/(-3x +2) + 2x) - 2x = (21x^2 -2x -8 +2x(-3x +2))/(-3x +2) - 2x
= (21x^2 -2x -8 -6x^2 +4x)/(-3x +2) -2x
= (15x^2 +2x -8)/(-3x +2) -2x . . . . . . another alternate solution to #2.
If we're not careful, we can create an expression that is extremely difficult to simplify. The one we have here can be factored to be ...
(-5x -4)(-3x +2)/(-3x +2) -2x = -5x -4 -2x = -7x -4 . . . our original #2 expression
Knowing that it can be factored is a big help.
Two rectangals are similar. The ratio of their coresponding sides is 1:4what is the ratio of thier preimeters
Step-by-step answer:
Between similar figures, if the ratio between the sides is k, then
- ratio between linear measurements, such as diagonals, perimeter, width, heights, etc, are also linear.
Therefore, if the ratio of the corresponding sides is 1:4, the ratio of their perimeters is also 1:4.
Note:
the ratio of area measurements, or surface areas of similar solids, are proportional to k^2.
Similarly, the ratio of volumes of similar solids are proportional to k^3.