Answer:
3rd option
Step-by-step explanation:
Under a rotation about the origin of 270°
a point (x, y ) → (y, - x ) , then
A (- 3, 4 ) → (4, - 3 )
B (4, - 5 ) → (- 5, - 4 )
C (1, 6 ) → (6, - 1 )
The center of rotation is therefore (h, k) = (1/2, 7/2), and the rule for the rotation is R90 (a 90-degree counterclockwise rotation about the point (1/2, 7/2)).
What is coordinate plane?The coordinate plane is a two-dimensional plane formed by the intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis.
The given information suggests that each point has been rotated 90 degrees counterclockwise around some point (h, k) on the coordinate plane.
To find this point, we can use the fact that the midpoint of the line segment joining each point to its image must be the center of rotation.
Midpoint of segment AA'/4: ((-3 + 4)/2, (4 + 3)/2) = (1/2, 7/2)
Midpoint of segment BB'/5: ((4 - 5)/2, (-5 - 4)/2) = (-1/2, -9/2)
Midpoint of segment CC'/6: ((1 + 6)/2, (6 - 1)/2) = (7/2, 5/2)
Thus, the center of rotation is therefore (h, k) = (1/2, 7/2), and the rule for the rotation is R90 (a 90-degree counterclockwise rotation about the point (1/2, 7/2)).
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Find the equation of a line that passes through the point (-4,1) and has a gradient of 2.
Leave your answer in the form
y=mx+c
Answer:
y = 2x + 9.
Step-by-step explanation:
Using the point-slope form:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
So here we have:
y - 1 = 2(x - (-4))
y - 1 = 2(x + 4)
y - 1 = 2x + 8
y = 2x + 9.
00
3 A total of 30 shirts were recently sold at Friday night's football game. Each adult shirt cost
$11.50 and each youth shirt cost $9.45. The total revenue was $324.50.
of two equations that can be used to solve for the number of A (adult) shirts
Answer:
number of adult shirts sold (a) = 20
number of youth shirts sold (b) = 10
Step-by-step explanation:
a = number of adult shirts sold
y = number of youth shirts sold
30 = a + y
$324.50 = 11.50a + 9.45y
This is the resulting system of equations from the given information in the problem.
Solve for y in the first equation and then substitute the equation for y into the second equation :
a+y=30 --> y=30-a
324.50 = 11.50a + 9.45(30-a)
Solve for a.
324.50 = 11.50a + 283.5 - 9.45a
41 = 2.05a
a = 20
Now that we have solved for a, we can back substitute into our equation for y and solve.
y=30-(20)
y = 10
CHECK:
(20)+(10) = 30 True
(11.50)(20) + (9.45)(10) = 324.5 True
Let $F,$ $G,$ and $H$ be collinear points on the Cartesian plane such that $\frac{FG}{GH} = 1.$ If $F = (a, b)$ and $H = (7a, c)$, then what is the $x$-coordinate of $G$?
F, G, and H all lie on the same line. If FG/GH = 1, then FG = GH, which is to say the distance between F and G is equal to the distance between G and H. This means either F and H are the same point, or G is the midpoint of F and H.
They're not the same point, because the x-coordinate of H is 7 times that of F. So G must be halfway between F and H.
Then the x-coordinate of G is
(a + 7a)/2 = 8a/2 = 4a
help me answer please
Answer:
Sorry
Step-by-step explanation:
Leo solved the equation b = 12 a−1−−−−−√3 for a, but made an error. His work is shown. Complete the sentences that follow.
The value of a in terms of b is given as [tex]a = 8b^3[/tex]
Given the equation solved by Leo expressed as [tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]
We are to solve the equation for the variable "a"
Given;
[tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]
Cross multiply
[tex]2b=\sqrt[3]{a-1}[/tex]
Cube both sides of the equation:
[tex](2b)^3=(\sqrt[3]{a-1})^3 \\8b^3=a-1[/tex]
Add 1 to both sides of the equation:
[tex]8b^3+1=a-1+1\\8b^3=a\\Swap\\a=8b^3[/tex]
Hence the value of a in terms of b is given as [tex]a = 8b^3[/tex]
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Need help SOS l don’t understand
Answer:
−5<n≤2 I think, I don't really understand the question either I'm sorry!!!!
What is the LCD of 11/6 and 5/9
if you multiply a number by 3 an then subtract 5,you will get 40.what is the number?
Answer:
The answer is 15
Step-by-step explanation:
15*3=45-5=40
Which inequality represents this statement?
A number is no more than 5.
n<5
n≥5
n>5
n≤5
Answer: the last one!! [tex]n\leq 5[/tex]
Step-by-step explanation:
When there is a line under it means no more than!
Which expression is equivalent lo the following complex fraction?
Answer:
[tex] \frac{ - 1}{2} [/tex]
Hope this helps you !!2(2c+12)=68
Using the opposite steps, inverse operations, solve for the value of the variable
[tex]\huge\boxed{Good\:evening!:)}[/tex]
2(2c+12)=68
4c+24=68
4c=68-24
4c=44
Divide both sides by 4:
c=11
[tex]\huge\boxed{Hence,\:the\:answer\:is\:11.:)}[/tex]
[tex]\huge\underline{Hope\:it\:helps!}[/tex]
[tex]\huge\sf{Good\:luck.}[/tex]
[tex]\boxed{DreamyTeenager\:here\:to\:help}[/tex]
9) Jamar drove 228 miles and used 6 gallons of gas.
a) How many miles/gallon did he get on the trip?
b) On another trip, he used 9 gallons of gas. How far did he travel?
Answer: 38 miles per gallon ; 342 miles.
Step-by-step explanation:
The miles/gallon that he got on the trip will be:
= 228/6
= 38 miles per gallon.
When he used 9 gallons of gas, the distance travelled will be:
= 38 × 9
= 342 miles
Answer:
Question :
Jamar drove 228 miles and used 6 gallons of gas.
a) How many miles/gallon did he get on the trip?b) On another trip, he used 9 gallons of gas. How far did he travel?Solution :
a) How many miles/gallon did he get on the trip?
[tex]{\implies{\sf{\dfrac{228}{6}}}}[/tex]
[tex]{\implies{\sf{ \cancel{\dfrac{228}{6}}}}}[/tex]
[tex]{\implies{\sf{\underline{\underline{\red{36 \: miles/gallon}}}}}}[/tex]
Hence, he get 38 miles/gallon for his trip.
[tex]\rule{200}2[/tex]
b) On another trip, he used 9 gallons of gas. How far did he travel?
[tex]{\implies{\sf{38 \times 9}}}[/tex]
[tex]{\implies{\sf{\underline{\underline{\red{342 \: miles}}}}}}[/tex]
Hence, he traveled 342 miles by using o gallon og gas.
[tex]\underline{\rule{220pt}{3pt}}[/tex]
Based on the Rational Zero Test, which of the following is
NOT a possible zero of f(x) given below after the reciprocal
of LCD is factored out?
f(x)=x^3 -5x + (2/5)
(A) 1/2
(B) 1/5
(C) 1
(D) -1
The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.
(a) 1/2 is not a possible zero of the function
The function is given as:
[tex]f(x) =x^3 - 5x + \frac 25[/tex]
For a function,
[tex]f(x) = px^n +......q[/tex]
The list of possible roots is:
[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5
[tex]5f(x) = 5x^3 - 25x + 2[/tex]
So, we have:
[tex]p= 5[/tex]
[tex]q = 2[/tex]
The factors are:
[tex]p =\pm 1, \pm 5[/tex]
[tex]q =\pm 1, \pm 2[/tex]
So, the possible roots are:
[tex]Roots = \pm\frac{1,2}{1,5}[/tex]
Split
[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]
Hence, 1/2 is not a possible zero of the function
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Graph the line with the equation
y = -1/3x + 4.
Answer:
Answer in the image
Step-by-step explanation:
Find 34−13.95 . Express your answer in decimal form.
Answer:
34-13.95 = 20.05
Step-by-step explanation:
Answer:
20.05
Step-by-step explanation:
34 - 13.95 = 20.05
number 4 plssss!!!!!!!!!!
Answer:
AB = 21
Step-by-step explanation:
Tales' theorem
[tex]\frac{12}{14} =\frac{18}{AB}[/tex]
[tex]AB=\frac{(14)(18)}{12}[/tex]
[tex]AB=21[/tex]
Hope this helps
(i)Given that:
AE || BD
AB = ? [Let AB be x]
BC = 3
ED = 12
DC = 4
We know that
By Basic Proportionality Theorem,
AB/BC = ED/DC
On substituting these values in the above formula
⇛ AB / 3 = 12 / 4
On applying cross multiplication then
⇛ x(4) = (12)3
⇛ 4x = 36
Shift the number 4 from LHS to RHS.
⇛ x = 36÷4
⇛ x = 36/4
Therefore, AB = 9
Answer: The value of AB for the given problem is 9.
Similarly,
(ii) Given that:
EB || DC
AE = 14
ED = 12
AB = ? [Let AB be X]
BC = 18
We know that
By Basic Proportionality Theorem,
AE / ED = AB / BC
On substituting these values in the above formula
⇛ 14 / 12 = x / 18
On applying cross multiplication then
⇛ 14(18) = (12)x
⇛ 252 = 12x
Shift the number 252 from LHS to RHS.
⇛ X = 256÷12
⇛ X = 21
Therefore, AB = 21
Answer: The value of AB for the given problem is 21
Additional comment:
Basic Proportionality Theorem
" A line drawn parallel to the one side of a triangle intersecting other two sides at two different points, then the line divides the other two sides in the same ratio".also read similar questions: In the given figure QR ∥AB, RP∥ BD,CQ=x+2,QA=x,CP=5x+4,PD=3x.The value of x is..
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solve for x
2x +2 <14
solve similar triangles (advanced)
Answer:
12 =x
Step-by-step explanation:
We can use proportions to solve
6 x
---- = -------
10 10+10
Using cross products
6 ( 10+10) = x*10
6*20 = 10x
120 = 10x
Divide by 10
120/10 = x
12 =x
Answer:
x = 12
Step-by-step explanation:
ABC ~ ADE
AB/AD = BC/DE
10/20 = 6/x
x = 20 x 6 ÷ 10
x = 12
given a isotope with a 3 charge, a mass number of 28, and an atomic number of 13, what are:
Answer: The element described is aluminum.
The relationship between y and x is 9/3 which table represents this relationship and why?
Answer:
First one
Step-by-step explanation:
For every 1 in x the y goes up by 3
The square of a number minus twice the number is 48. Find the number.
Answer: 8 or -6
Step-by-step explanation:
x^2 - 2x = 48
x^2 - 2x - 48 = 0
(x-8)(x+6) = 0
x = 8 or -6
Lin is playing hand ball and wants the ball
to bounce off wall CB and land at D.
Where on the wall should she aim if she's
standing at point A?
Lin should aim the ball at 7.8 feet away from point B
From the question (see attachment), we have the following equivalent ratios:
[tex]AB : BE = DC :CE[/tex]
This is so because triangles ABE and DCE are similar triangles.
Such that:
[tex]BE + CE = 20[/tex]
[tex]AB = 16[/tex]
[tex]DC = 16 + 9 = 25[/tex]
So, we have:
[tex]AB : BE = DC :CE[/tex]
[tex]16 : BE = 25: CE[/tex]
Make CE the subject in [tex]BE + CE = 20[/tex]
[tex]CE=20 - BE[/tex]
Substitute 20 - BE for CE in [tex]16 : BE = 25: CE[/tex]
[tex]16 : BE = 25: 20 - BE[/tex]
Express as ratio
[tex]\frac{16 }{ BE} = \frac{25}{ 20 - BE}[/tex]
Cross multiply
[tex]16(20 - BE) = 25BE[/tex]
Open bracket
[tex]320 - 16BE = 25BE[/tex]
Collect like terms
[tex]25BE + 16BE = 320[/tex]
[tex]41BE = 320[/tex]
Divide both sides by 41
[tex]BE = 7.8[/tex]
Hence, she should aim at 7.8 feet away from point B
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Answer:You want to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the yellow stripe 9 ball into the top middle pocket.
Step-by-step explanation:
i really need your help on this
Answer:
That is an improper fraction
Step-by-step explanation:
When the numerator (the top) is greater than the denominator (The bottom) then the fraction is improper
Hope this helps!
Answer:
Improper fraction
Step-by-step explanation:
Find the term indecent of x in the expansion of (x^2-1/x)^6
By the binomial theorem,
[tex]\displaystyle \left(x^2-\frac1x\right)^6 = \sum_{k=0}^6 \binom 6k (x^2)^{6-k} \left(-\frac1x\right)^k = \sum_{k=0}^6 \binom 6k (-1)^k x^{12-3k}[/tex]
I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that
12 - 3k = 0 ===> 3k = 12 ===> k = 4
which corresponds to the constant coefficient
[tex]\dbinom 64 (-1)^4 = \dfrac{6!}{4!(6-4)!} = \boxed{15}[/tex]
Which equation matches the given points? (0, 7.6), (1, 6.2), (2, 4.8), (3, 3.4), (4,2)
The equation that matches the given points is g(x) = -1.4x + 7.6
The standard form of a linear equation is expressed as [tex]g(x)=mx + b[/tex]
m is the slope of the lineb is the y-intercept:Using the coordinate points (3, 3.4), (4,2)
[tex]m=\frac{2-3.4}{4-3}\\m=\frac{-1.4}{1}\\m=-1.4[/tex]
Substitute m = -1.4 and the coordinate (4, 2) into the formula:
[tex]2=4(-1.4)+b\\2=-5.6+b\\b=2+5.6\\b=7.6[/tex]
Get the required equation:
[tex]g(x)=mx+b\\g(x)=-1.4x+7.6[/tex]
Hence the equation that matches the given points is g(x) = -1.4x + 7.6
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One smartphone plan costs $52 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone plan costs $82 per month for talk and messaging and $3 per gigabyte of data used each month. Let c represent the total cost in dollars and d represent the amount of data used in gigabytes.
The system of equations
c=52+8d
c−3d=82
can be used to represent this situation.
How many gigabytes would have to be used for the plans to cost the same? What would that cost be?
Answer:
Both plans would cost $100 if 6 gigabytes of data are used.
Explanation:
From the question, the system of equation are correctly represented by using small letter c to represent the total cost in dollars for both equations as already assumed in the question as follows:
c = 52 + 8d ........................... (1)
c = 82 + 3d ........................... (2)
Since c is common to both, equations (1) and (2) can therefore be equated and d solved for as follows:
52 + 8d = 82 + 3d
8d - 3d = 82 - 52
5d = 30
d = 30 / 5
d = 6
Substituting d = 6 into equation (1), we have:
c = 52 + (8 * 6)
c = 52 + 48
c = 100
Since d = 6 and c = 100, it therefore implies that both plans would cost $100 if 6 gigabytes of data are used.
Write
48
:
132
:
84
in its simplest form.
Answer:
4:11:7
Step-by-step explanation:
Find the GCF, or greatest common factor of the 3 numbers. In this case it is 12. To simplify, divide each number by 12
Answer:
4:11:7
Step-by-step explanation:
please mark me as brainlest
9. Determine whether the parallelogram is a rectangle, square, or rhombus. G(-4,3), D(2,1) F(-5, 0) and E(1, -2)
Answer:
rectangle
Step-by-step explanation:
Answer:
Rectangle
Step-by-step explanation:
FG's slope is the opposite reciprocal of GD's, so they are perpendicular. The same with the other sides.
The opposite sides have the same length.
pls help!!!!!!! its applications in pre calc
The total weight W of such a plane is equal to
W = w + gf
where
w = weight of plane without fuel
g = number of gallons of fuel
f = weight of 1 gallon of fuel.
When carrying g = 10 gallons, the total weight is W = 1955, so
1955 = w + 10f
When carrying g = 42 gallons, the weight is W = 2131, so
2131 = w + 42f
We want to find W when g = 52, and to do this we first need to find the weight of the plane w and the weight of 1 gallon of fuel f.
Solve the system of equations,
w + 10f = 1955
w + 42f = 2131
We can combine the equations like so to eliminate w and solve for f :
(w + 42f) - (w + 10f) = 2131 - 1955
32f = 176
f = 11/2 = 5.5
Then solving for w, we get
w + 10 (5.5) = 1955
w + 55 = 1955
w = 1900
So, when the plane carries g = 52 gallons of fuel, the total weight is
W = 1900 + 52 (5.5) = 2186
larry needs to change a lightbulb in the ceiling Larry liens a 16 foot ladder against a wall with its base 5 feet away from the wall which is closest to the distance of the height of the wall to the top of the ladder
A 3 feet
B 11 feet
C 15 feet
D 17 feet
The solution is Option C.
The height of the wall to the top of the ladder is 15 feet
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Let the height of the wall be represented as h = AB
Now , Larry liens a 16 foot ladder against a wall
So , the hypotenuse of the triangle AC = 16 feet
And , the base is 5 feet away from the wall
So , the base of the triangle BC = 5 feet
The height of the wall h is given by the Pythagoras theorem ,
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
16² = AB² + 5²
On simplifying the equation , we get
Subtracting 5² on both sides of the equation , we get
AB² = 16² - 5²
AB² = 256 - 25
AB² = 231
Taking square root on both sides of the equation , we get
AB = 15.19
AB ≈ 15 feet
Therefore , the value of h is 15 feet
Hence , the height of the wall is 15 feet
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