There are a total of 2,000 students in the school.
1.) There are 540 students in the 6th grade. 540 is only 27% of students compared to the total. To find the total students in the whole school, we divide 540 by 27%.
2.) We first change 27% into a decimal by moving the point two times to the left. (Rule to change the percent into a decimal)
27% = .27
3.) Before we divide, we remove the decimal by moving the decimal two times to the right and so do we to 540.
.27 = 27
540. = 54000.
4.) Now we have 54000 divided by 27 which give us the answer of 2,000.
Hope this Helps!!!
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Answer:
2,000 students are in school i do not know if it’s decimals because decimals are like % percentage but ok 2,000 is my answer I hope this helped
When Cedric walked into a party, two-thirds of those invited had already arrived. Six more people arrived just after Cedric, bringing the number at the party to $\frac{5}{6}$ of those invited. What was the total number of invited guests?
Answer: Hence, there are 36 total number of invited guests.
Step-by-step explanation:
Let the total number of invited guests be 'x'
Part of those invited had already arrived = [tex]\dfrac{2}{3}x[/tex]
Number of people just arrived = 6
According to question, it brings the number at the party to [tex]\dfrac{5}{6}[/tex] of those invited.
So, it becomes,
[tex]\dfrac{2}{3}x+6=\dfrac{5}{6}x\\\\6=\dfrac{5}{6}x-\dfrac{2}{3}x\\\\6=\dfrac{5x-4x}{6}\\\\6=\dfrac{x}{6}\\\\x=6\times 6\\\\x=36[/tex]
Hence, there are 36 total number of invited guests.
Answer:
42 People
Step-by-step explanation:
P is the total amount of people. Before Cedric arrived, there were (2/3)P people at the party. After Cedric and six other people arrived, there are (2/3)P+7 people at the party. Since this is the same as (5/6)P, we solve (2/3)P+7=(5/6)P to find that P=42.
Not sure how to even start this problem please help
Explanation:
DeMoivre's theorem tells you the 7th roots of unity are the 7 points evenly spaced around (on) the unit circle, including 1∠0°. They will be located at angles ...
{0, 2π/7, 4π/7, 6π/7, 8π/7, 10π/7, 12π/7} . . . in radians
Given that the circle shown is graduated in increments of π/6, you will need to do some estimating as to the actual location of the root.
___
The attached graph shows lines at increments of π/7 radians, so your graph will match every other one.
In a first -aid kit the ratio of large bandages is 3 to 2. Based on this ratio, how many large bandages are in the kit if there are a total of 80 bandages?
Answer:
48
Step-by-step explanation:
The total number of ratio units is 3+2 = 5, and the 3 ratio units representing large bandages make up 3/5 of that total. Thus, large bandages will make up 3/5 of the total number of bandages:
3/5×80 = 48 . . . . number of large bandages in the kit
What is the solution to -2(8x - 4) < 2x + 5?
Answer:
x = - 10
Step-by-step explanation:
Answer:
x > 1/6
Step-by-step explanation:
Perform the indicated multiplication. Then:
-16x + 8 < 2x + 5
Combining the x terms, we get:
8 < 18x + 5.
Simplifying further, we get:
3 < 18x, so that 3/18 < x, or x > 1/6
Figure 1 is dilated to get Figure 2.
What is the scale factor?
Enter your answer, as a fraction in simplified form, in the box.
Answer:
1/3
Step-by-step explanation:
if you multiply 24 by 1/3, you recieve 8 which is the reduced dilation
Which linear equation passes through the points (0, - 2) and (4, 10)?
y = 3x - 2
y = - 1/3x - 2
y = 1/3x - 2
y = - 3x - 2
Answer:
y = 3x - 2
Step-by-step explanation:
You can easily find the equation of a line through two points by using the point-slope form, [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is one of the points.
First, let's find the slope of the line through (0, -2) and (4, 10).
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1} = \frac{10-(-2)}{4-0}=\frac{12}{4}=3[/tex]
Next, we plug this into point-slope form. Remember that we let (0, -2) be our first point, [tex](x_1,y_1)[/tex].
[tex]y-(-2)=3(x-0)[/tex]
Finally, we rearrange this equation to get the slope-intercept form [tex]y=mx+b[/tex], where b is the y-intercept.
[tex]y+2=3x \\ y=3x-2[/tex]
We can verify using the attached graph that both points lie on this line.
Plz, answer! 34 + 2 ⋅ 5 =
[tex]3^{4}[/tex] + 2 × 5
To evaluate apply the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
Parentheses
There are none for this steps so go on to the next step
Exponent:
[tex]3^{4}[/tex]
81
so...
81 + 2 × 5
Multiplication:
81 + 2 × 5
2 × 5
10
so...
81 + 10
No division in this equation so skip this step and go to the next one
Addition:
81 + 10
91
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
44
Step-by-step explanation:
Order of operations
PEMDAS
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
Do multiply from left to right.
2*5=10
Add the numbers from left to right to find the answer.
34+10=44
44 is the correct answer.
I hope this helps you, and have a wonderful day!
PLZ HELP MARKIN BRAINEST!!!
There are 25 total Seniors.
12 of the Seniors want to see more candid pictures.
The percent would be 12/25 = 0.48 x 100 = 48%
Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile?
Answer:
about 0.81 miles
Step-by-step explanation:
Alyssa's route can be considered a right triangle with legs of length 19 and 28 (hundredths). The Pythagorean theorem tells us the hypotenuse (x) will satisfy ...
x^2 = 19^2 +28^2
x^2 = 1145
x = √1145 ≈ 34 . . . . hundredths of a mile
Then Alyssa's total route is ...
0.19 + 0.28 + 0.34 = 0.81 . . . . miles
Answer:
about 0.81 miles
Step-by-step explanation:
Alyssa's route can be considered a right triangle with legs of length 19 and 28 (hundredths). The Pythagorean theorem tells us the hypotenuse (x) will satisfy ...
x^2 = 19^2 +28^2
x^2 = 1145
x = √1145 ≈ 34 . . . . hundredths of a mile
Then Alyssa's total route is ...
0.19 + 0.28 + 0.34 = 0.81 . . . . miles
Emily, Carl and Antony altogether has 121 stamps. How many stamps does each of them have, if it is known, that Emily has 40% more than Carl, and Carl has 60% more than Antony?
In mathematics, the Nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/N. So, the first harmonic number is 1, the second is 1.5, the third is 1.83333... and so on. Assume that n is an integer variable whose value is some positive integer N. Assume also that cl is a variable whose value is the Nth harmonic number. Write an expression whose value is the (N+1)th harmonic number.
Answer:
cl + 1/(N+1)
Step-by-step explanation:
If we assume that the Nth harmonic number is cl. Then we are assuming that 1+1/2+1/3+1/4+...+1/N=cl
And we know that the (N+1)th harmonic number can be found by doing
1+1/2+1/3+1/4+...+1/N+1/(N+1)
=cl + 1/(N+1)
The (N+1)th harmonic number is cl + 1/(N+1) given that the Nth term is cl
Other way to see the answers:
Maybe you want to write it as a single fraction so you have
[cl(N+1)+1]/(N+1)=[cl*N+cl+1]/(N+1)
The expression value is [tex]hn+(\frac{1}{n+1} )[/tex].
Assume that [tex]n[/tex] is an integer variable whose value is some positive integer [tex]N[/tex].
Assume also that [tex]hn[/tex] is a variable whose value is the [tex]N_{th} [/tex] harmonic number.
An expression whose value is the [tex](N+1)th[/tex] harmonic number is [tex]hn+(\frac{1}{n+1} )[/tex].
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What is the volume of the cone with diameter 7 in. and height 9 in.? Round to the nearest cubic inch.
Answer: [tex]115in^3[/tex]
Step-by-step explanation:
The volume of a cone can be calculated with the following formula:
[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
The radius is half the diameter, then "r" is:
[tex]r=\frac{7in}{2}\\\\r=3.5in[/tex]
Since we know that radius and the height, we can substitute them into the formula.
The volume of the cone to the nearest cubic inch is:
[tex]V_{(cone)}=\frac{1}{3}\pi (3.5in)^2(9in)[/tex]
[tex]V_{(cone)}=115in^3[/tex]
Answer:
The volume of cone = 115 cubic inches
Step-by-step explanation:
Points to remember
Volume of cone = (πr²h)/3
Where r - Radius of cone and
h - Height of cone
To find the volume of cone
Here diameter = 7 in then r = 7/2 = 3.5 in and h = 9 in
Volume = (πr²h)/3
= (π * 3.5² * 9)/3
= (3.14 * 12.25 * 9)/3
= 115.395 ≈ 115 cubic inches
Therefore volume of cone = 115 cubic inches
Which expression is equivalent to ^3 √1/1000c^9d^12
1/100c^3d^4
1/100c^6d^9
1/10c^3d^4
1/10c^6d^9
Answer:
[tex]\frac{1}{10c^{3}d^{4} }[/tex]
Step-by-step explanation:
THE GIVEN EXPRESSION IS
[tex]\sqrt[3]{\frac{1}{1000c^{9}d^{12} } }[/tex]
To simplify this expression, we just have to apply the cubic root to each part of the fraction, as follows
[tex]\frac{\sqrt[3]{1} }{\sqrt[3]{1000c^{9} d^{12} } }[/tex]
Then, we solve each root. Remember that to solve roots of powers, we just need to divide the exponent of the power by the index of the root, as follows
[tex]\frac{1}{10c^{\frac{9}{3} } d^{\frac{12}{3} } }[/tex]
Therefore, the equivalent expression is
[tex]\frac{1}{10c^{3}d^{4} }[/tex]
So, the right answer is the third choice.
11. 10ac × 6ab × (–2bc) = ?
A. 14a2b2c2
B. 2a + 2b + 2c + 14
C. –120a2b2c2
D. 2a + 2b +2c – 120
Answer:
C. –120a2b2c2
Step-by-step explanation:
We'll just the multiplications one at a time...
10ac × 6ab × (–2bc) = 60a²bc * (-2bc) (multiplying 10ac × 6ab)
60a²bc * (-2bc) = -120a²b²c²
We just have to multiply the numbers together (like 10 and 6),
then all similar letters together (like ac * ab = a²bc). If a letter is already present (like a in this example), then we add up its powers a * a = a², a² * a would be a³ and so on). If the letter is not present (like 'b' in 'ac', we suppose it's there as b^0 which is equal to 1)... so we still add up its exponent (power)... so it makes b^0 * b = b
Perform the following operations s and prove closure. Show your work.
Answer:
1. [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex] = [tex]\frac{2x^2+10x+6}{(x+3)(x+5)}\\[/tex]
2. [tex]\frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}[/tex] = [tex]\frac{1}{(x+2)(x-4)}[/tex]
3. [tex]\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}[/tex] = [tex]\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}[/tex]
4. [tex]\frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}[/tex] = [tex]\frac{1}{(x-2)(x-4)}[/tex]
Step-by-step explanation:
1. [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]
Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)
[tex]=\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}\\=\frac{x^2+5x+(x)(x+3)+2(x+3)}{(x+3)(x+5)} \\=\frac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)} \\=\frac{x^2+x^2+5x+3x+2x+6}{(x+3)(x+5)} \\=\frac{2x^2+10x+6}{(x+3)(x+5)}\\[/tex]
Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.
2. [tex]\frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}[/tex]
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)
Putting factors
[tex]=\frac{x+4}{(x+3)(x+2)}*\frac{x+3}{(x-4)(x+4)}\\\\=\frac{1}{(x+2)(x-4)}[/tex]
Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.
3. [tex]\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}[/tex]
Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)
Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)
Putting factors
[tex]\frac{2}{(x+3)(x-3)}-\frac{3x}{(x+3)(x-2)}[/tex]
Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)
[tex]\frac{2(x-2)-3x(x+3)(x-3)}{(x+3)(x-3)(x-2)}[/tex]
[tex]=\frac{2(x-2)-3x(x+3)}{(x+3)(x-3)(x-2)}\\=\frac{2x-4-3x^2-9x}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-9x+2x-4}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}[/tex]
Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.
4. [tex]\frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}[/tex]
Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
[tex]\frac{x+4}{(x-2)(x+3)}\div\frac{(x-4)(x+4)}{x+3}[/tex]
Converting ÷ sign into multiplication we will take reciprocal of the second term
[tex]=\frac{x+4}{(x-2)(x+3)}*\frac{x+3}{(x-4)(x+4)}\\=\frac{1}{(x-2)(x-4)}[/tex]
Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.
The given equations are the algebric equations for obtaining solution the equation can be simplified by algebric operations.
1).
[tex]\dfrac{x}{x+3} + \dfrac{x+2}{x+5}[/tex]
Taking LCM of denomenator (x+3) and (x+5).
[tex]=\dfrac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}[/tex]
Further simplification has been done by multtiplication in the numerator.
[tex]=\dfrac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)}=\dfrac{2x^2+10x+6}{(x+3)(x+5)}[/tex]
2).
[tex]\dfrac{x+4}{x^2+5x+6}\times \dfrac{x+3}{x^2-16}[/tex]
For further simplification of above equation factorization of [tex]x^2+5x+6[/tex] and [tex]x^2-16[/tex] has been performed.
[tex]= \dfrac{x+4}{(x+3)(x+2)}\times \dfrac{x+3}{(x-4)(x+4)}[/tex]
[tex]= \dfrac{1}{(x+2)(x-4)}[/tex]
3).
[tex]\dfrac{2}{x^2-9}-\dfrac{3x}{x^2-5x+6}[/tex]
For further simplification of above equation factorization of [tex]x^2-5x+6[/tex] and [tex]x^2-9[/tex] has been performed.
[tex]=\dfrac{2}{(x-3)(x+3)}-\dfrac{3x}{(x-3)(x-2)}[/tex]
Taking LCM of denomenator (x+3)(x-3) and (x-3)(x-2).
[tex]=\dfrac{(2\times(x-2))-(3x\times(x+3))}{(x-3)(x+3)(x-2)}=\dfrac{2x-4-3x^2-9x}{(x-3)(x+3)(x-2)}[/tex]
[tex]= -\dfrac{3x^2+7x+4}{(x-3)(x+3)(x-2)}[/tex]
4).
[tex]\dfrac{\dfrac{x+4}{x^2-5x+6}}{\dfrac{x^2-16}{x+3}}[/tex]
For further simplification of above equation factorization of [tex]x^2-5x+6[/tex] and [tex]x^2-16[/tex] has been performed.
[tex]=\dfrac{\dfrac{x+4}{(x-3)(x-2)}}{\dfrac{(x-4)(x+4)}{x+3}}=\dfrac{x+3}{(x-3)(x-2)(x-4)}[/tex]
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can someone help me with this, please
Answer:
(0,4) vertex and (1,3) another pt
Step-by-step explanation:
The parabola has been shifted up 4 units from parent function (there is also a reflection)...but we only really care about the shift 4 units up from (0,0) for our vertex... Our vertex is (0,4)
Now just plug in another number to find another point...let's do x=1
Plug in you get -1^2+4=-1+4=3 so another point is (1,3)
PLS HELP. YEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEET
Answer:
The answer would be D.4.
Step-by-step explanation:
So first you would have to find the mean of the data by taking into account the amount of each type of numbers like this 1,2,2,3,3,3,4,4,4,4,5,5,5,6,6,7. Then add those all up which would give 64, since their is 16 numbers in total divide 64 by 16 which would give 4.
If A=29 and a=4.6, find c
Answer:
Step-by-step explanation:
Following your description I got
sin 29° = opp/hyp = 4.6/c
csin29 = 4.6
c = 4.6/sin29
= 9.48826.. or appr 9.5
Answer:
Option (D)
Step-by-step explanation:
Phil had made $1200 deposits in an annuity due at the beginning of each quarter in an account earning 6% interest compounded quarterly. What is the future value of the account in 2years? pay attention this is Annuity due not ordinary annuity
ractice Tests
10271.20
$5,835.12
$5,991.53
$5,902.99
Formula and set up:
A = P(1 + r/n)^(nt)
You want A.
A = 1200(1 + (0.06)/2)^(0.06)(2)
Plug right side into calculator to find A.
Which equation of a line passes through the points (3, −1) and (6, 1)?
Y = 2/3x - 3
Y = - 2/3x + 5
Y = - 2/3x + 10
Y = 3/2x - 8
Answer:
Y = 2/3x - 3
Step-by-step explanation:
Recall the general equation for a straight line is
y = mx + b
where m is the gradient and b is the y-intercept
given 2 points whose coordinates are (x1, y1) and (x2, y2), m can be found with the following formula:
m = [tex]\frac{y1-y2}{x1-x2}[/tex]
in this case, x1 = 3, y1 = -1, x2 = 6, y2=1
applying these values to the formula for m will give
m = (-1 -1) / (3-6) = 2/3
We can see immediately that only the first (top-most) answer has this value for m and we can guess that this is probably the answer.
But we can still check to confirm:
If we substitute this back into the general equation, we get:
y = (2/3)x + b
In order to find the value for b, we substitute any one of the 2 given points back into this equation. Lets choose (6,1)
1 = (2/3)(6) + b
1 = 4 + b
b = -3
Confirm Y = 2/3x - 3 is the answer.
There was a party with 50 students. They had a cylinder root beer keg that was 17 inches in height and 13 inches in diameter. They also had cylinder cups to drink the root beer out of, they were 3 inches in diameter and 4 3/4 inches tall. Would there be enough root beer for everyone to have at least one cup?
Answer:
Yes, there will be enough root beer for everyone to have at least one cup
Step-by-step explanation:
step 1
Find the volume of the cylinder root beer keg
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=13/2=6.5\ in[/tex] -----> the radius is half the diameter
[tex]h=17\ in[/tex]
substitute
[tex]V=\pi (6.5)^{2} (17)[/tex]
[tex]V=718.25\pi\ in^{3}[/tex]
step 2
Find the volume of the cylinder cups
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=3/2=1.5\ in[/tex] -----> the radius is half the diameter
[tex]h=4\frac{3}{4}\ in=4.75\ in[/tex]
substitute
[tex]V=\pi (1.5)^{2} (4.75)[/tex]
[tex]V=10.6875\pi\ in^{3}[/tex]
step 3
Multiply the volume of one cup by 50 (the total number of students) and then compare the result with the volume of the cylinder root beer keg
so
[tex]10.6875\pi*(50)=534.375\pi\ in^{3}[/tex]
[tex]534.375\pi\ in^{3}< 718.25\pi\ in^{3} [/tex]
therefore
There will be enough root beer for everyone to have at least one cup
Answer:
Yes. There is enough for everyone.
Step 1: Find the volume of the keg
Diameter : 13
Radius : 6.5
Height : 17
Formula for the area of a circle (base) is πr^2
Solve that using the above formula.
Base area = 132.73
Multiply that by the height.
Keg volume : 2,256.45 inches cubed
Step 2: Find the volume of the cups
Diameter : 3
Radius : 1.5
Height : 4 3/4
Formula for area of a circle (base) is πr^2
Solve that using the above formula.
Base area = 7.07
Multiply that by the height.
Cup volume : 33.58 inches cubed
Step 3: Multiply cup volume by 50
33.58 x 50 = 1,678.79
Step 4: Check how much root beer you have for everyone.
Root beer needed : 2,256.45
Root beer available : 1,678.79
Is there enough root beer?
Yes
a globe has a diameter of 24 inches. a smaller globe has a diameter of 18 inches. What is the surface are to volume ratio of the smaller globe? round to the nearest hundredth.
Answer:
1 pi: 3pi
Step-by-step explanation:
Step 1: Formula of surface area and volume of sphere
Surface area of sphere = 4 x pi x r^2
Volume of sphere = 4 x pi x r^3
3
Step 2: Apply values in the formula
r = radius
radius = diameter/2
r=18/2 = 9
S.A = 4 x pi x 9^2
S.A = 324pi
Volume = 4 x pi x 9^3
3
Volume = 972pi
Step 3 : Show in ratio
Surface area : Volume
324pi : 972pi
= 1 pi: 3pi
The absolute value function, f(x) = –|x| – 3, is shown. What is the range of the function? all real numbers all real numbers less than or equal to 0 all real numbers greater than or equal to –3 all real numbers less than or equal to –3
Answer:
all real numbers less than or equal to –3
Step-by-step explanation:
Look at the y-values that the graph shows. There are none greater than -3. Any value of -3 or less is possible.
Answer: D. all real numbers less than or equal to –3
A transformation T:(x,y) → (x+3, y + 1).
The image of B(4, 1) under this transformation is
(12, 1)
(7.2)
(1,0)
(-1,0)
Answer:
(7,2)
Step-by-step explanation:
If you compare (4,1) to (x,y)
You should see that in place of x you have 4
and in place of y you have 1
so just plug them in
(4+3,1+1)
(7,2)
(x – 3)³
Given: (x – y)³ = x³ – 3x²y + 3xy² – y³
ANSWER
[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]
EXPLANATION
We want to expand:
[tex] {(x - 3)}^3[/tex]
Using the identity;
[tex] {(x - y)}^{3} = {x}^{3} - 3 {x}^{2}y + 3x {y}^{2} - {y}^{3} [/tex]
We substitute y=3 into the above identity to obtain:
[tex] {(x - 3)}^{3} = {x}^{3} - 3 {x}^{2}(3) + 3x( {3}^{2} ) - {(3)}^{3} [/tex]
Let us simplify to get:
[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]
The set (3,5,___________
could not be the sides of a triangle
3,2,5,7
Answer:
(3, 5, 2)
Step-by-step explanation:
Many authors interpret the triangle inequality to mean the sum of the two short sides must exceed the length of the long side. For side measures 2, 3, 5, the sum of the two short sides is exactly equal to the long side, in violation of the triangle inequality. Hence (3, 5, 2) is not a triangle.
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Comment on the triangle inequality
Other authors allow the "or equal to" case, meaning sides of lengths 2, 3, 5 will be considered to be a triangle because 2+3=5. This interpretation of the triangle inequality will result in no solution to your question.
A (3, 5, 2) "triangle" will look like a line segment of length 5. It will have an area of zero.
Answer:
The answer to your question would be
3, 5, 2.
Please help, I'm so close to finishing all these.
Answer:
d. 43°
Step-by-step explanation:
KM is a bisector of ∠LKN, so ...
∠LKN = 2(∠4)
7q +2 = 2(4q -5)
12 = q . . . . . . . . . . . add 10-7q, simplify
Now, we can put 12 where q is in the expression for ∠4:
∠3 = ∠4 = 4·12 -5 = 43
In ΔABC, what is the value of cos B?
A) 5/13
B)12/13
C)5/12
D)13/12
Answer:
Value of cos B is B)12/13
The value of cos B in triangle ΔABC cannot be definitively determined without additional information such as side lengths. However, assuming a right triangle configuration with an adjacent side of length 12 and a hypotenuse of length 13, the cos B could be calculated as 12/13.
Explanation:In the triangle ΔABC, the value of cos B can be calculated if we know the measures of the sides of the triangle. Without the values of the sides, we can't give an exact value for cos B. However, from the given options, we would assume that the triangle is a right-triangle, and B is the angle formed by the adjacent side of length 12 and the hypotenuse of length 13. Thus, the value of cos B would be equal to the adjacent side (b) divided by the hypotenuse (c), which matches option B) 12/13.
Remember that in a right triangle:
The cosine of an angle (cos B) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. This formula, cos B = b/c is a direct application of the Pythagorean theorem.
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Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.
answers:
a) y2 = 4x
b)8y = x2
c)x = 1 divided by 8y2
d) y = 1 divided by 8x2
Answer:
[tex]y^2=\frac{1}{8}x[/tex]
Step-by-step explanation:
The focus lies on the x axis and the directrix is a vertical line through x = 2. The parabola, by nature, wraps around the focus, or "forms" its shape about the focus. That means that this is a "sideways" parabola, a "y^2" type instead of an "x^2" type. The standard form for this type is
[tex](x-h)=4p(y-k)^2[/tex]
where h and k are the coordinates of the vertex and p is the distance from the vertex to either the focus or the directrix (that distance is the same; we only need to find one). That means that the vertex has to be equidistant from the focus and the directrix. If the focus is at x = -2 y = 0 and the directrix is at x = 2, midway between them is the origin (0, 0). So h = 0 and k = 0. p is the number of units from the vertex to the focus (or directrix). That means that p=2. We fill in our equation now with the info we have:
[tex](x-0)=4(2)(y-0)^2[/tex]
Simplify that a bit:
[tex]x=8y^2[/tex]
Solving for y^2:
[tex]y^2=\frac{1}{8}x[/tex]
Answer: x = -1/8y^2
Step-by-step explanation
Focus: (-2,0)
Directrix: x=2
It meets the criteria.
1/2x + 1/3y = 7
1/4x + 2/3y = 6
What is the solution of the system shown?
A. (1/6, 14)
B. (6, 12)
C. (10 2/3, 5)
let's multiply both sides in each equation by the LCD of all fractions in it, thus doing away with the denominator.
[tex]\begin{cases} \cfrac{1}{2}x+\cfrac{1}{3}y&=7\\\\ \cfrac{1}{4}x+\cfrac{2}{3}y&=6 \end{cases}\implies \begin{cases} \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{2}x+\cfrac{1}{3}y \right)=6(7)}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}x+\cfrac{2}{3}y\right)=12(6)} \end{cases}\implies \begin{cases} 3x+2y=42\\ 3x+8y=72 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{using elimination}}{ \begin{array}{llll} 3x+2y=42&\times -1\implies &\begin{matrix} -3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2y=&-42\\ 3x+8y-72 &&~~\begin{matrix} 3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+8y=&72\\ \cline{3-4}\\ &&~\hfill 6y=&30 \end{array}} \\\\\\ y=\cfrac{30}{6}\implies \blacktriangleright y=5 \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{substituting \underline{y} on the 1st equation}~\hfill }{3x+2(5)=42\implies 3x+10=42}\implies 3x=32 \\\\\\ x=\cfrac{32}{3}\implies \blacktriangleright x=10\frac{2}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(10\frac{2}{3}~~,~~5 \right)~\hfill[/tex]