The function f(x) = x2 6x 3 is transformed such that g(x) = f(x − 2). find the vertex of g(x).
Answers
the vertex of the function g(x) = f(x 2) .
A quadratic equation's vertex form is defined.If a quadratic equation is expressed as the following
[tex]y=a(x-h)^{2}+k[/tex]
It is then said to be in vertex form. Because the vertex point (peak point) occurs on the graph of this equation, it is so named (h,k)
The parabola that the quadratic equation depicts has this point (h,k) as its vertex.
How may the given equation be changed to be in vertex form?We first remove the x squared coefficient, and then inside the bracket, we strive to create a condition that resembles a perfect square.
So, this is what we have:
[tex]$f(x)=x^{2}+6 x+3$\\$g(x)=f(x-2)$[/tex]
Thus, we obtain:
[tex]\begin{aligned}&g(x)=f(x-2) \\&g(x)=(x-2)^{2}+6(x-2)+3 \\&g(x)=x^{2}-4 x+4+6 x-12+3 \\&g(x)=x^{2}+2 x-5\end{aligned}[/tex]
Vertex form transformation of g(x):
[tex]\begin{aligned}&g(x)=x^{2}+2 x-5 \\&g(x)=x^{2}+2 x+1-1-5 \\&g(x)=(x+1)^{2}-9 \\&g(x)=(x-(-1))^{2}-6 \\&g(x)=(x-(-1))^{2}+(-6)\end{aligned}[/tex]
By comparing this[tex]a(x-h)^{2}+k[/tex] to, we obtain the coordinates of the vertex of the graph of g(x) as (h,k) = (-1,-6), as shown below.
As a result, the vertex of the function g(x) = f(x 2) .
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Related Questions
Can the sides of a triangle have lengths 6, 20, and 20?
Answers
Answer:
Yes.
Step-by-step explanation:
This would be an isosceles triangle - with 2 equal sides both 20 long with a base of length 6.
A triangle can be formed from 3 line segments as long as the sum of the length of any 2 sides exceeds the length of the third side.
What is the equation of a line in slope-intercept form, of the line that passes through (0, 12) and has a slope of -5?
Answers
Answer:
y=-5x-12/5
Step-by-step explanation:
First you need to find y intercept
y=mx+b
plug in the points (0,12)
12=mx+0
now plug in -5
12=-5x+0
subtract 0 from both side
12=-5x
divide -5 from both side.
x=12/-5
Find the Diameter of the Circle with the following equation. Round to the nearest tenth.
(x - 2)2 + (y + 6)2 = 20
Answers
Answer:
11.8 units
Step-by-step explanation:
The circle equation is given as:
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2Where
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2r
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we have
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sides
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 2
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8Hence, the diameter of the circle is 11.8 units
Answer: 8,9.
Step-by-step explanation:
[tex](x-2)^2+(y+6)^2=20\\Circle \ equation\\\boxed {(x-a)^2+(y-b)^2=r^2}\\r^2=20\\r*r=\sqrt{20}*\sqrt{20}\\ r=\sqrt{20}\\ r=\sqrt{4*5}\\ r=2\sqrt{5} \\ D=2r\\D=2*2\sqrt{5}\\ D=4\sqrt{5}\\ D\approx8,9.[/tex]
Okay so this is super tricky, there is a riddle on my math quiz. Yk for extra credit and its 25% of my grade, according to Mr. Wells.
If you have 1 cow that is worth $2,500 and 2 cats worth $100. But one dog is worth $7000, what would the outcome be if there was only 1 of each animal? Hint: It could be division or multiplication.
A. 2 cats and one dog
B. 1 cow and 1 dog
C. $600 for each animal
D. If you think its none of these listed, you may write your own!
Note: this makes no sense whatsoever, so please help. Mr. Wells is a good teacher, but this question is hard
Answers
If there was just one of each animal, the outcome would be that of 1 cow and 1 dog.
Option(B) is correct.
The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function.
If you own two cats worth $100 each and a cow worth $2,500. One dog, though, is worth $7000.
Cost of 1 cow = $2500
Cost of 2 cats = $100
Thus, cost of 1 cat = $100/2 = $50
Cost of 1 dog = $7000
If there was only 1 of each animal, total cost = $(2500+50+7000) = $9550.
This outcome resembles the situation of having 1 cow and 1 dog.
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Find smallest number which on adding to 19 it is exactly divisible by 28,36 and 45 (LCM).
Answers
Answer:
1241
Step-by-step explanation:
∴
L.C.M. of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260
∴
the required number is 1260 - 19 = 1241
Hence, if we add 19 to 1241 we will get 1260 which is exactly divisible by 28, 36 and 45.
Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=0. 835, α=0. 01, n=4
Answers
Yes, the correlation coefficient is statistically significance
The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.
Given,
Sample size, n = 4
Where ρ is the population correlation.
Then the number of degrees of freedom is, df = n-2 = 4-2 = 2
The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254
Here,
The null hypothesis, [tex]H_{0}[/tex] = ρ - 0 is rejected
Suppose lr> re 0.254
Because on the sample correlation provided, we know that lrl = 0.835>=0.254.
Here, it is clear that the null hypothesis is rejected.
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A pizza has a diameter of 18 inches. If the pizza is
cut into 10 equal slices and 6 slices were eaten,
what is the area of the remaining pizza?
Answers
Answer:
25
Step-by-step explanation:
Using the same functions given above, find (h−f)(x).
Answers
The results of subtraction of functions are listed below:
x - 8m(x) = x² + 10 · x + 5m(3) = 44How to use the subtract function operatorThere three fundamental binary operators (addition, multiplication, composition) and two secondary binary operators (subtraction, division) for functions. The subtraction is operation derived from addition, defined by the following expression:
(h - f) (x) = h(x) - f(x) (1)
Now we proceed to develop each expression:
i) (h - f) (x):
h(x) = 2 · x - 3, f(x) = x + 5 Given(h - f)(x) = (2 · x - 3) - (x + 5) Definition of subtraction between functions(2 · x - x) + [(- 3) + (- 5)] Associative and commutative properties / (- 1) · a = - ax - 8 Distributive property / Definitions of addition and subtraction / Resultii) m(x) = (g - j) (x):
g(x) = x² + 6 · x + 5, j(x) = - 4 · x Givenm(x) = (x² + 6 · x + 5) - (- 4 · x) Definition of subtraction between functionsm(x) = x² + (6 · x + 4 · x) + 5 Associative, commutative and distributive property / (- a) · (- b) = a · bm(x) = x² + 10 · x + 5 Distributive property / Definition of adition / Resultiii) m(3):
m(3) = 3² + 10 · 3 + 5
m(3) = 9 + 30 + 5
m(3) = 44
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Please help me on this one I wrote it out :(
Answers
Answer:
D) 3
Step-by-step explanation:
22 * 2 = 44
To have a remainder 3, the number should be 44 + 3 = 47
47 ÷ 22 , leaves a remainder 3.
47 +22 = 69
69 ÷ 3 leaves a remainder 3.
69 +22 = 91
91 ÷ 3 leaves a remainder 3.
Answer: 47 , 69 , 91
Answer:B:1
Step-by-step explanation:
Write each number out and divide by 22 until you get one that’s answer is 3
Is the following number rational or irrational?
√64
Answers
√64 is rational.
Hope this helps :)
❄ Hi there,
let us consider this –
Is [tex]\sqrt{64}[/tex] a rational or irrational number?
Well, to answer that we need to work out [tex]\sqrt{64}[/tex].
And we know that
[tex]\sqrt{64} =8[/tex]
and 8 is a rational number.
That's it!
❄
hello please answer need help
Answers
2x + 2y = 42
2w + q = 35
2w + v = 29
x + q + y - v = ?
x = 7
y = 14
w = 3
q = 29
v = 23
7 + 29 + 14 - 23 =
The answer is 27
Answer: [tex]\Large\boxed{27}[/tex]
Step-by-step explanation:
Given information converted into a mathematical statement
[tex]a = icecream\\b=cookie\\c=brownie\\d=cake\\e=creamed cake[/tex]
[tex]1)~a+b+a+b=42[/tex]
[tex]2)~c+d+c=35[/tex]
[tex]3)~c+c+e=29[/tex]
[tex]4)~a+d+b-e=\mbox{?}[/tex]
Simplify each equation
[tex]1)~2a+2b=42[/tex]
[tex]2)~2c+d=35[/tex]
[tex]3)~2c+e=29[/tex]
[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]
Factorize 2 out of the 1) equation
[tex]2a+2b=42[/tex]
[tex]2(a+b)=42[/tex]
Divide 2 on both sides
[tex]2(a+b)\div2=42\div2[/tex]
[tex]a+b=21[/tex]
Current system
[tex]1)~a+b=21[/tex]
[tex]2)~2c+d=35[/tex]
[tex]3)~2c+e=29[/tex]
[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]
Subtract 3) equation from the 2) equation
[tex](2c +d)-(2c+e)=(35)-(29)[/tex]
Expand the parenthesis
[tex]2c+d-2c-e=35-29[/tex]
Combine like terms
[tex]2c-2c+d-e=6[/tex]
[tex]d-e=6[/tex]
Current system
[tex]1)~a+b=21[/tex]
[tex]2)~d-e=6[/tex]
[tex]3)~(a+b)+(d-e)=\mbox{?}[/tex]
Substitute values into the 3) equation to determine the final value
[tex](a+b)+(d-e)[/tex]
[tex]=(21)+(6)[/tex]
[tex]\Large\boxed{=27}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Molly is thinking of a number. twice her number take away seven is the same as her number plus five. what is her number?
Answers
Answer:
Number = 12
Step-by-step explanation:
2n-7=n+5 (+7 to both sides)
2n=n+12 (-n to both sides)
n=12
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square yards, of ΔABC.
a = 12, b = 11, c = 7
Answers
Answer:
12 sqrt (10)
Step-by-step explanation:
S = (12 + 11 + 7) / 2 = 15
A = sqrt (s(s-a)(s-b)(s-c))
= sqrt (15(15-12)(15-11)(15-7))
= sqrt (15*3*4*8)
= sqrt (1440)
= 12 sqrt (10)
Determine the factors of 5x2 29x − 6. (5x − 1)(x 6) (5x − 6)(x 1) (5x − 3)(x 2) (5x − 2)(x 3)
Answers
The correct option is option(A) (5x-1)(x+6).
The factors of the given equation are (5x-1)(x+6).
What are the factors of a quadratic equation?An algebraic expression or number that divides another expression or number equally, leaving no remainder is known as factor.
The quadratic equation [tex]ax^{2} +bx+c=0[/tex] can be expressed as the product of its linear factors as (x - k)(x - h), where h, k are the roots of the equation. This is known as factoring quadratics.
What is splitting middle term of an equation?Dividing the middle term into two factors is used in quadratic factorization in this method. In splitting of the middle term, where x is the product of two factors and last term is the sum of the two factors.
Use the splitting middle term formula
[tex]5x^{2} +29x-6[/tex]
=[tex]5x^{2} +30x-x-6[/tex]
=5x(x+6)-1(x+6)
=(5x-1)(x+6)
The factors of the given equation are (5x-1)(x+6).
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Find the A.P whose second term is 12 and 7th term exceeds the 4th by 15
Answers
The 2nd term exists 12 and 7th term exceeds the 4th by 15 exists AP : 7,12,17,....
How to estimate the arithmetic progression?
Given : The second term exists 12th and the 7th term exceeds the 4th term by 15
The formula of the nth term :
[tex]$a_{n}=a+(n-1) d[/tex]
Where d exists a common difference
n be the number of terms
a be the first term
Substitute the value of n = 2
[tex]$a_{2}=a+(2-1) d=a+d[/tex]
Let, the second term exists 12
So, a + d = 12 ..........(1)
Substitute the value of n = 7
[tex]$a_{7}=a+(7-1) d=a+6 d[/tex]
Substitute n = 4
[tex]$a_{4}=a+(4-1) d=a+3 d[/tex]
We are given that the 7th term exceeds the 4th term by 15
So, a+6d-a-3d = 15
3d = 15
d = 5
Substitute the value of d in (1)
So, a+5 = 12
a = 12-5
a = 7
AP : a,a+d,a+2d,.... = 5, 7+5, 7+2(5),....=7,12,17,....
Therefore, AP : 7,12,17,....
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cuanto da (9+4m)² cuadrado de binomio ayudaaaaa
Answers
Answer:
16m^2 + 72m + 81
Step-by-step explanation:
you expand it, by (9+4m)(9+4m), using distributive property you get
81 + 36m + 36m + 16m^2, simplifying you get the answer
The graph of y=√x is reflected in the x-axis and then translated
down 3 units. What is an equation that produces this transformation?
A. -√x-3
B. y= -3-(√x)
C. y= 3- (√x)
D. y= -(√x-3)
Answers
This is the same as y = - (√x) - 3
- 3 means the function is translated 3 units down since it is negative.
In order for the function to be reflected over the x-axis, the function (√x) has to be negative.
Note it cannot be D. because the function is being translated 3 units to the right, not down.
Beth is going to enclose a rectangular area in back of her house. the house wall will form one of the four sides of the fenced in area, so beth will only need to construct three sides of fencing. beth has 48 feet of fencing. she wants to enclose the maximum possible area. what amount of fence should beth use for the side labeled x?
Answers
The maximum possible area would have a length of 24 feet and width of 12 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the length and y represent the width, hence:
Since beth has 48 ft fencing and cover 3 sides, hence:
x + 2y = 48
x = 48 - 2y (1)
Also:
Area (A) = xy
A = (48 - 2y)y
A = 48y - 2y²
The maximum area is at A' = 0, hence:
A' = 48 - 4y
48 - 4y = 0
y = 12 feet
x = 48 - 2(12) = 24
The maximum possible area would have a length of 24 feet and width of 12 feet.
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A 3 tonne mix of gravel contains blue
metal and gravel in the ratio 2:3.
How much gravel is in the mix?
Answers
Answer:
1.8 tonne
Step-by-step explanation:
sum the parts of the ratio, 2 + 3 = 5 parts
divide the total mix by 5 to find the value of one part of the mix
3 tonne ÷ 5 = 0.6 tonne , then
3 parts = 3 × 0.6 = 1.8 tonne ← amount of gravel in the mix
What error did zacharias make? the –5 should be 5. the 52 should be –52. the 2 in the numerator should be –2. the 2 in the denominator should be –2.
Answers
The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.
Quadratic equationThere are four methods of solving quadratic equation. Namely;
Factorization methodCompleting the square methodGraphical methodFormula method0 = -2x² + 5x - 3
Using quadratic formulax = -b ± √b² - 4ac / 2a
where,
a = -2b = 5c = -3x = -b ± √b² - 4ac / 2a
x = -5 ± √5² - 4(-2)(-3) / 2(-2)
= -5 ± √25 - (24) / -2
= -5 ± √1 / -2
= -5/2 ± 1/2
= -5/2 - 1/2 or x = -5/2 + 1/2
= -5-1 / 2 or -5+1/ 2
x = -6/2 or -4/2
x = -3 or -2
Therefore, the solution to the quadratic equation is x = -3 or -2
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Which function is represented in the
graph below?
Answers
Answer:
Option 2
Step-by-step explanation:
There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.
please solve by BODMAS rule
Answers
Answer:
Step-by-step explanation:
1/3 + 1/3 x 1/3 / 1/3 - 1/3
= 1/3 + 1/3 x 1/1 -1/3
= 1/3 + 1/3 - 1/3
= 2/3 - 1/3
= 1/3
Answer:
5/9.
Step-by-step explanation:
1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3
= 1/3 + 1/3 * 1 - 1/3 * 1/3
= 1/3 + 1/3 - 1/3 * 1/3
= 2/3 - 1/9
= 5/9.
Force equals mass times acceleration.
F = ma
Solve the equation for the
acceleration, a.
-A
Answers
Answer:
m = F / a is the answer
Step-by-step explanation:
F = ma
m = F / a
Jaquelyn wants to start getting to school on time more often. She is looking at some of her habits.
On Monday, she is late twenty percent of the time.
When she is late on Monday, she is late on Tuesday 60% of the time.
When she is not late on Monday, she is late on Tuesday 20% of the time.
What is the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday?
Answers
Given that Jaquelyn was tardy on Monday, there is a 12 percent chance she will be late on Tuesday as well.
What is the Probability?
How likely it is that a stated event would occur is assessed using probability. The event would have a probability of 1 if it happened with certainty. The probability of an occurrence would be zero if it were absolutely guaranteed that it would not occur.
As getting late on Monday and Tuesday are independent events, their probabilities can be multiplied.
So the probability of getting late on Tuesday, given she was late to school on Monday = Probability of being late on Monday x Probability of she being late on Monday and she is late on Tuesday 60% of the time.
= 0.2 x 0.6
= 0.12
Thus the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday will be 0.12
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find the length of MN
Answers
Answer:
The length of MN is 5 cm
Step-by-step explanation:
Add the segment LX, parallel to QP.
Recall the properties of midsegment:
Midsegment is parallel to side,Midsegment is half the length of the parallel side.We have:
Since QL = LR, the point L is midpoint of Q,Since PN = NL, the point N is midpoint of PL,Since LX is parallel to QP, LX is midsegment of ΔPRQ.Find the length of LX:
LX = QP/2 = 20/2 = 10 cmSince QP ║ LX ║ NM, the segment NM is the midsegment of ΔPLX.
Find the length of NM:
NM = LX/2 = 10/2 = 5 cmFind the midpoint of the line segment joining the points (-1,-3) and (-11,10).
Answers
Answer: Midpoint=(−6 ,3.5)
Step-by-step explanation:
=(1+22,1+22)M=(x1+x22,y1+y22)=(−1+−112,−3+102)M=(−1+−112,−3+102)=(−122,72)M=(−122,72)=(−6,312)
Answer:
(-6,3.5)
Step-by-step explanation:
x = [tex]\frac{-1-11}{2}[/tex] = [tex]\frac{-12}{2}[/tex] = -6
y = [tex]\frac{-3+10}{2}[/tex] = [tex]\frac{7}{2}[/tex] = 3.5
I need help pls and thank you
Answers
Answer:
12 in, 7 in
Step-by-step explanation:
The area of a rectangle is the product of length and width. Here, you are given the area, and an additional relation between length and width.
SetupThe two relations between length and width described by this problem are ...
A = LW . . . . . . . dimensions are of a rectangle
L = W +5 . . . . . . length is 5 inches more than width
A = 84 . . . . . . . . area in square inches
SolutionSubstituting for L and A in the area formula, we have ...
84 = (W +5)(W)
We can solve this as a quadratic in any of several ways. One of those ways is by factoring.
Essentially, we're looking for factors of 84 that differ by 5. We can consider different factorizations of 84 to see what we get:
84 = 84×1 = 42×2 = 28×3 = 21×4 = 14×6 = 12×7
The differences between the factors in these pairs are 83, 40, 25, 17, 8, 5.
This means the last pair, with a difference of 5, is the one we're looking for.
W+5 = 12, W = 7
The rectangle is 12 inches long and 7 inches wide.
__
Additional comment
As a quadratic in standard form, we would have ...
W² +5W -84 = 0 ⇒ (W +12)(W -7) = 0 ⇒ W = {7, -12}
If you were to solve this by completing the square, you would have ...
(W +2.5)² = 90.25 ⇒ W = -2.5 ±9.5 = {7, -12}
Choose the correct simplification of 8x2(5x 2x2 − 3). 16x4 − 40x3 24x2 16x4 40x3 − 24x2 40x4 16x3 − 5x2 40x4 − 10x3 5x2
Answers
The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]
What do you mean by simplification?Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.Making anything simpler is the act or process of simplification. Everyone is in favor of streamlining court procedures.Certain "solving" issues are connected to "simplification" issues. Parentheses and even nested grouping symbols can be found in some equations, just like in some expressions. Whether we're working with equations (so we're also solving) or expressions (and only simplifying), the simplification procedure is the same in both cases.The correct simplification of 8x2(5x 2x2 − 3).
[tex]8x^{2} (5x+2x^{2+1} -3)=8*2x^{2+2} -8*3x^{2}[/tex]
[tex]=40x^{3} +16x^{4} -24x^{2}[/tex]
Rearranging the above expression in descending order of power, we get:[tex]16x^{4} +40x^{3} -24x^{2}[/tex]
The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]
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A right rectangular prism has these dimensions:
Length: Fraction 1 and 1 over 3 units
Width: Fraction 5 over 6 unit
Height: Fraction 2 over 3 unit
How many cubes of side length 1 over 6 unit are required to completely pack the prism without any gap or overlap?
Answers
160 cubes required to completely pack the prism without any gap or overlap
How to determine the number of cubes?The dimensions of the rectangular prism are given as:
Length = 1 1/3
Width = 5/6
Height = 2/3
The volume is
Volume = Length * Width * Height
This gives
Volume = 1 1/3 * 5/6 * 2/3
Evaluate the product
Volume = 20/27
The side length of the cube is
L = 1/6
The volume of the cube is
V = (1/6)^3
Evaluate
V = 1/216
The number of cubes required to completely pack the prism without any gap or overlap is
n = (20/27) / (1/216)
Evaluate
n = 160
Hence, 160 cubes required to completely pack the prism without any gap or overlap
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Answers
Answer:
We multiply by 2 and add 4
Step-by-step explanation:
To find the pattern, we find the slope
m = ( y2-y1)/(x2-x1)
m = ( 10-6)/(3-1)
m = 4/2
m =2
We are multiplying by 2
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Using the point (1,6)
6 = 2(1)+b
6 = 2+b
The y intercept is 4
y = 2x+4
We multiply by 2 and add 4
