Answers
The composition of transformation that maps ABCD to EHGF is "(x, y) → (x', -y') → (x' + 6, y' + 3)".
What are the transformation rules?The basic transformation rules are:
Translation: (x, y) → (x + a, y + b);Reflection: (x, y) → (x, -y) over x-axis; (x, y) → (-x, y) over y-axis;Dilation: (x, y) → (kx, ky)Rotation 90° counter-clockwise: (x, y) → (-y, x)Rotation 180°: (x, y) → (-x, -y)Calculation:The given quadrilateral ABCD has vertices,
A(-5, 2), B(-3, 4), C(-2, 4), and D(-1, 2)
The transformed quadrilateral EHGF has vertices,
E(1, 1), H(3, -1), G(4, -1), and F(5, 1)
In the map ABCD to EHGF, the transformations that took place are:
1) Reflection over x-axis
2) Translation by (x + a, y + b)
Step 1: Reflection over x-axis; (x, y) → (x, -y)
A(-5, 2) → A'(-5, (-2)) = A'(-5, -2)
B(-3, 4) → B'(-3, (-4)) = B'(-3, -4)
C(-2, 4) → C'(-2, (-4)) = C'(-2, -4)
D(-1, 2) → D'(-1, (-2)) = D'(-1, -2)
So, the reflected quadrilateral is A'B'C'D'
Step 2: Translation by (x, y) → (x + a, y + b);
The reflected quadrilateral A'B'C'D' is now translated by
A'B'C'D' → EHGF
So, (for A'(-5, -2) and E(1, 1))
x + a = 1
⇒ -5 + a = 1
⇒ a = 1 + 5
∴ a = 6
and
y + b = 1
⇒ -2 + b = 1
⇒ b = 1 + 2
∴ b = 3
Thus, the translation is (x + 6, y + 3).
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Related Questions
40 POINTS AND BRAINLIEST!! Solve for x in the following equations..
a) 6x +3 +21
b) 15(x - 5) = 75
c) 3/4 x +5 = 26
Answers
Answer:
a) x = 3
b) x = 10
c) x = 28
Explanation:
a)
[tex]\sf 6x + 3 = 21[/tex]
collect term
[tex]\sf 6x = 21-3[/tex]
simplify
[tex]\sf 6x = 18[/tex]
divide both both sides by 6
[tex]\sf x = 3[/tex]
b)
[tex]\sf 15(x - 5) = 75[/tex]
distribute
[tex]\sf 15x - 75 = 75[/tex]
collect terms
[tex]\sf 15x = 75 + 75[/tex]
combine
[tex]\sf 15x = 150[/tex]
divide both sides by 15
[tex]\sf x = 10[/tex]
c)
[tex]\sf \frac{3}{4} x +5 = 26[/tex]
collect like terms
[tex]\sf \frac{3}{4} x = 26-5[/tex]
combine
[tex]\sf \frac{3}{4} x = 21[/tex]
cross multiply
[tex]\sf x = \frac{ 21 (4)}{3}[/tex]
simplify
[tex]\sf x =28[/tex]
The equation represents a hyperbola centered at the origin with a directrix of . what is the value of b? 10 16 20 26
Answers
the value of b is = 10.
The equation of a hyperbola is x^2/24^2 - y^2/ (10)^2= 1.
What is hyperbola?The geometric characteristics of a hyperbola or the equations for which it is the solution set characterize it as a particular kind of smooth curve that lies in a plane. Mirror reflections of each other that resemble two infinite bows make up a hyperbola's two connected components or branches.
What is the general formula for hyperbola?The general formula for hyperbola = (x - h)²/a²- (y - k)²/(b)² = 1
According to the given information:x²/24 - y²/(b)² = 1
(x - 0)²/24 - (y -0)²/(b)² = 1
a=24,h=0 and k=0
Now equation of the directrix
x=a²/c...(1)
and we know x=576/26...(2)
Therefore from 1 and 2 we get
24²/c=576/26.
isolate the c so we get,
C=26
C= center of focii
c = √(a² + b³)
c² = a² + b²
b = c² - a²
b = 10
So we get the value of b is 10.
Therefore the equation of a hyperbola is x²/24² - y²/ (10)² = 1.
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Annabella wants to make the most economical decision so she chose the 3-year car loan so that after the loan is paid off to be able to invest in a structured saving account if Anabella put $200 into a saving account each month with an annual interest rate of 3.2% interest compounded monthly how much money would she have in her account after 2 years
Answers
Answer:
Annabella will save $4950.11 after 2 years.
Step-by-step explanation:
GivenPeriodic payment P = $200,Period t = 2 years,Number of compounds, monthly n = 12,Interest rate, r = 3.2% = 0.032.To findFuture value of saving, FSolutionUse periodic compound formula:
[tex]F=P\cfrac{(1+r/n)^{nt}-1}{r/n}[/tex]
Substitute the values and calculate:
[tex]F=200\cfrac{(1+0.032/12)^{12*2}-1}{0.032/12} =4950.12[/tex] rounded
Step-by-step explanation:
Given P = $200, t = 2 years, n = 12,[tex] \sf \: r = 3.2\% = \frac{3.2}{100} = 0.032[/tex]To findFuture value of savingSolutionUse periodic compound formula:
[tex] \sf \: F=P\cfrac{(1+ \frac{r}{n})^{nt}-1}{\frac{r}{n}}[/tex]
Substitute the values and calculate:
[tex]\sf \: F=200\cfrac{(1+ \frac{0.032}{12})^{12 \times 2}-1}{\frac{0.032}{12}}[/tex]
[tex]\sf \: F=200\cfrac{( \frac{ 12 + 0.032}{12})^{24}-1}{\frac{0.032}{12}}[/tex]
[tex]\sf \: F=200\cfrac{( {11.002 }{})^{24}-1}{0.002} [/tex]
[tex]\sf \: F=200 \times 24.7506[/tex]
[tex]\sf \: F=4950.12rounded[/tex]
Given: y varies directly as x squared and inversely as z cubed. If y = 12 when x = 4 and z = 2, find x when y = 1.728 and z = 5.
Select one:
a. x=6
b. x=18
c. x=27
d. x=36
Answers
Answer:
a
Step-by-step explanation:
given y varies directly as x² and inversely as z³ then the equation relating them is
y = [tex]\frac{kx^2}{z^3}[/tex] ← k is the constant of variation
to find k use the condition y = 12 when x = 4 and z = 2 , then
12 = [tex]\frac{k(4)^2}{2^3}[/tex] = [tex]\frac{16k}{8}[/tex] ( multiply both sides by 8 )
96 = 16k ( divide both sides by 16 )
6 = k
y = [tex]\frac{6x^2}{z^3}[/tex] ← equation of variation
when y = 1.728 and z = 5 , then
1.728 = [tex]\frac{6x^2}{5^3}[/tex] = [tex]\frac{6x^2}{125}[/tex] ( multiply both sides by 125 )
216 = 6x² ( divide both sides by 6 )
36 = x² ( take square root of both sides )
[tex]\sqrt{36}[/tex] = x , that is
x = 6
4. In a scale-drawing blueprint of a house, 1/4of an inch represents 1 foot. If a room in the house has
dimensions of 16.5 feet by 14 feet, what are that room's dimensions on the blueprint?
5. Henrietta and Dolores take a road trip to the beach. Henrietta drives from their hometown to the
beach, a distance of 252 miles, in 9 hours. Dolores drives the same distance on the trip back, but her
speed is 2 miles per hour faster than Henrietta's speed was. How long does it take Dolores to drive
back home?
Answers
Answer:
4. 4.125 inches by 3.5 inches.
5. 8.4 hours.
Step-by-step explanation:
4. multiply 16.5 and 14 by .25 because each foot in the house is .25 of an inch on the paper.
5. 252 miles / 9 hours = 28 mph. Add 2 so you get 30 mph. 252 miles / 30 mph = 8.4 hours.
The following duties need to be carried out: clean the board, arrange
the tables, sweep the floor and clear the waste paper basket. Find the
number of ways of assigning these duties to 4 students, given that each
student will perform only one duty?
Answers
Step-by-step explanation:
every single person will do 1/4 of each job.
divide into 2 group and each person will do half of one job and half of another.
18 times the quantity g plus 5
Answers
Comparing it to a system of equations, the expression is represented as follows:
18g + 5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, we consider g as the variable. Then:
18 times the quantity g is 18g.Adding 5 to the expression, we have that 18g + 5.More can be learned about a system of equations at https://brainly.com/question/24342899
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What is the value of x that makes AB |I CD?
Answers
In order for AB to be parallel to CD, the two labeled angles must be equivalent. If we set the two expressions equal to each other and solve for x, we can find the value of x that makes angle AEF and angle EFD equivalent and therefore the lines AB and CD parallel.
2x + 40 = 3x + 10
40 = x + 10
30 = x
If the value of x were 30, both angles would be 100°
Answer:
30°
30 is the value of x that’s makes AB//CD.
Step-by-step explanation:
the angles of measures 2x + 40 and 3x + 10 are two Alternate interior angles
If these two angle were congruent then the lines AB and CD
would be parallel .
2x + 40 = 3x + 10
⇔ 40 - 10 = 3x - 2x
⇔ 30 = x
⇔ x = 30
Find the value of x in the given figure
Answers
Answer:
x = 36
Step-by-step explanation:
3x and 2x are a linear pair and sum to 180° , that is
3x + 2x = 180
5x = 180 ( divide both sides by 5 )
x = 36
Please really need help with question d really don't understand
The answer to the question is the second image, I don't get how they got this answer and why it isn't finding x for t=0, t=1 and t=2.
Answers
Answer:
[tex]\textsf{a)} \quad v=12t^2-6t-18[/tex]
[tex]\textsf{b)} \quad a=24t-6[/tex]
c) 1.5 s
d) -19.25 m
e) 24.5 m
Step-by-step explanation:
Displacement
[tex]x=4t^3-3t^2-18t+1[/tex]
(where t ≥ 0 and x is in meters)
Part (a)To find the equation for velocity, differentiate the equation for displacement:
[tex]\implies v=\dfrac{\text{d}x}{\text{d}t}=12t^2-6t-18[/tex]
(where t ≥ 0 and v is in meters per second)
Part (b)To find the equation for acceleration, differentiate the equation for velocity:
[tex]\implies a=\dfrac{\text{d}v}{\text{d}t}=24t-6[/tex]
(where t ≥ 0 and a is in meters per second squared)
Part (c)The particle comes to rest when its velocity is zero:
[tex]\begin{aligned}v & = 0\\\implies 12t^2-6t-18 & = 0\\6(2t^2-t-3) & = 0\\2t^2-t-3 & = 0\\2t^2-3t+2t-3 & = 0\\t(2t-3)+1(2t-3) & = 0\\(t+1)(2t-3) & = 0\\\implies t & =-1, \dfrac{3}{2}\end{aligned}[/tex]
As t ≥ 0, the particle comes to rest at 1.5 s.
Part (d)Substitute the found value of t from part (c) into the equation for displacement to find where the particle comes to rest:
[tex]\implies 4(1.5)^3-3(1.5)^2-18(1.5)+1=-19.25\: \sf m[/tex]
Part (e)We have determined that the particle is at rest at 1.5 s.
Therefore, to find how far the particle traveled in the first 2 seconds, we need to divide the journey into two parts: before and after it was at rest.
The first leg of the journey is the first 1.5 s and the second leg of the journey is the next 0.5 s.
At the beginning of the journey, t = 0 s.
[tex]\textsf{when }t=0: \quad x=4(0)^3-3(0)^2-18(0)+1=1[/tex]
Therefore, when t = 0, x = 1
When t = 1.5 s, x = -19.25 m (from part (d)).
⇒ Total distance traveled in first 1.5 s = 1 + 19.25 = 20.25 m
When t = 2, x = -15 m.
Therefore, the particle has traveled 19.25 - 15 = 4.25 m in the last 0.5 s of its journey.
Total distance traveled:
1 + 19.25 + 4.25 = 24.5 m
Refer to the attached diagram
When the particle is at rest, it changes direction. If we model its journey using the x-axis, for the first leg of its journey (0 - 1.5 s) it travels in the negative direction (to the left). At 1.5 s it stops, then changes direction and travels in the positive direction (to the right), arriving at -15 at 2 seconds.
with a linear, exponential, or quadratic function.
You have to decide which of two prizes you will accept!
Prize A: $5,000 for the first month with a $100 increase every month thereafter.
Prize B: $2,000 for the first month with a 10% increase every month thereafter.
9. Create an equation for each situation (Prize A and Prize B).
Answers
The equation s for each scenario in which case, the former, Prize A is represented as a linear equation while the latter, Prize B is represented as an exponential function are;
Prize A = $5,000 + $100m (where m = no. of months).Prize B = $2,000(1.1)^m.What equations represents the given situation?It follows from the task content that in scenario which pertains to Prize A, the initial price which represents the y-intercept is; $5,000 while the slope which represents the increase per month is; $100.
Consequently, we have; Prize A = $5,000 + $100m
While, for Prize B, in which case the function via exponential, we have;
Prize B = $2,000(1.1)^m.
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Help me ASAP mark you BRAINLIEST!!!!!!!!!!!
Answers
Answer:
11÷7=[tex]\frac{11}{7}[/tex]
v= 11/7
i dont understand the math can pls help
Answers
Answer: 46.7 in/3
Step-by-step explanation:
A water skiing jump is 4.6m long. It rises 1.1m. What
of inclination to the nearest tenth of a degree?
4.6 m
0
1.1 m
Answers
The inclination to the nearest tenth of a degree exists 0.24146
What is the inclination to the nearest tenth of a degree?
The given scenario includes a right-angled triangle where the length of the ramp exists hypotenuse and the rise of ramp exists the perpendicular.
Given: H = 4.6 m and P = 1.1 m
We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse
Let x be the angle then
sin x = P/H
sin x = 1.1/4.6
sin x = 0.23913
[tex]$$sin^{-1} x[/tex] = 0.24146
The inclination to the nearest tenth of a degree exists 0.24146
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If f (x) = startroot 4 x 9 endroot 2, which inequality can be used to find the domain of f(x)?
Answers
The domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].
So long as x ≥ -9/4, the function f(x) will be defined.
How to find the domain of the function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex]?
Given: "f(x) = Startroot 4 x + 9 Endroot + 2" should be written as
[tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].
Note that [tex]$\sqrt{(4x + 9)}[/tex] exists a variation of the basic function [tex]y = \sqrt{x}[/tex], whose domain exists [0, ∞ ).
The domain of [tex]$f(x) = \sqrt{(4x + 9) }+ 2[/tex] exists seen by taking the "argument" 4x + 9 of [tex]\sqrt{(4x + 9)}[/tex]and setting it equivalent to zero:
4x + 9 ≥ 0
simplifying the equation, we get
4x ≥ -9
x ≥ -9/4
This exists the domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].
So long as x ≥ -9/4, the function f(x) will be defined.
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Answer:
B
Step-by-step explanation:
I tink old up
no its BBBBB
Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 595, α=0. 05, n=17
Answers
Answer: Yes, the correlation coefficient is statistically significant
The correlation coefficient describes how one variable actions when it comes to every other. A high-quality correlation shows that the 2 circulate within the identical path, with a +1.zero correlation once they move in tandem. A poor correlation coefficient tells you that they as a substitute flow in opposite directions. A correlation of 0 shows no correlation in any respect.
where ρ corresponds to the population correlation.
The sample size is n = 17,
so then the number of degrees of freedom is df = n-2 = 17-2 = 15
The corresponding critical correlation value re for a significance level of a 0.05, for a two-tailed test is た= 0.482
Observe that in this case,
the null hypothesis H0 : ρ-0 is rejected
if |r> re 0.482.
Based on the sample correlation provided, we have that lrl = 0.595 >=0.482,
which is concluded that the null hypothesis is rejected.
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Id like some help!!!
Answers
Answer:
50.24 ft^2.
Step-by-step explanation:
Area = pi r^2
Here the radius r = 4
Therefore the area of the circle
= pi * 4^2
= 16 pi
= 16 *3.14
= 50.24 ft^2.
Find the area of the figure
Answers
Answer:
D. 195
Step-by-step explanation:
When does the rock hit the ground? the rock hits the ground between seconds and seconds after it is dropped.
Answers
Between 2 seconds and 2.5 seconds, the rock hits the ground after it is dropped.
What are distance and time?
A distance-time graph shows how far an object has travelled in a given time. It is a simple line graph that denotes distance versus time findings on the graph. Distance is plotted on the Y-axis. Time is plotted on the X-axis.As you can see at 2s the height of the rock is 0.4m and at 2.5s it is -10.6m, which tells us that in between these values the height would have been 0m, as the movement of the rock is uniform in direction and hence, the rock will hit the ground between 2s and 2.5s.
The rock hits the ground between 2 seconds and 2.5 seconds after it is dropped.
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Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?
Answers
The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.
According to the statement
We have given that the
AB = 8 and B lies at −7, and we have to find the position of the A on the number line.
Let a be a point on number line and b be the second point on number line.
And The distance between two numbers on number line is calculate by subtracting the smaller number from larger number.
Here
AB = 8
B = -7
We have to look at the options one by one.
For A = -1
As A>B
AB = -1-(7) = -1+7 = 6
For A = 1
As A>B so
AB = 1-(-7) = 8
So with A = 1 , AB = 8
This is one of the right answers.
For A=15
As A>B
AB = 15-(-7) = 22
For A=-15
As B>A
AB = -7 -(-15) = 8
As with A=1 and A=-15, the distance between AB is 8 so these are the correct answers.
So, The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?
Select ALL that apply.
A −1
B 1
C 15
D −15
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Solve the given differential equation by undetermined coefficients. y'' 4y' 4y = 2x 3
Answers
The solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .
According to the given question.
We have a differential equation
[tex]y^{"} + 4y^{'} + 4y = 2x^{3}[/tex]
The above differerntial equation acn be written as
[tex](D^{2} +4D+ 4)= 2x^{3}[/tex]
Now, the auxillary equation for the above differential equation is given by
[tex]m^{2} + 4m + 4 = 0[/tex]
[tex]\implies m^{2} + 2m + 2m + 4 = 0[/tex]
⇒ m (m + 2) + 2(m + 2) = 0
⇒ m(m + 2)(m + 2) = 0
Therefore,
[tex]C.F = (C_{1} + C_{2}x)e^{-2x}[/tex]
Now,
[tex]PI = \frac{1}{D^{2} +4D+4} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4(1+\frac{D^{2}+4D }{4} )} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4} [1+(\frac{D^{2}+4D }{4} )]^{-1} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4} [ 1 - (\frac{D^{2} +4D}{4} )+(\frac{D^{2} +4D}{4} )^{2} -(\frac{D^{2}+4D }{4}) ^{3} ...]2x^{3}[/tex]
[tex]\implies PI =\frac{1}{2} [ x^{3} -\frac{1}{4} (6x)-3x^{2} +3x^{2} -6][/tex]
[tex]\implies PI = \frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]
Therefore, the solution of the differential equation will be
y = CI + PI
[tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]
Hence, the solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .
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Which of the following expressions can be used to find the area of a square with a side length of m?
Answers
The answer is A = m².
We know the general formula for finding the area of a square is :
Area = side²
Now, we are given the side is equal to m.
Hence, the expression which can be used to find the area is :
A = m²
Which graph shows the image of ABCD? On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (0, 3), (0, negative 1.2), (negative 2, 1). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (negative 2, 1), (0, negative 1), (0, 3). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (3, 0), (negative 1.5, 0), (0.5, 2). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (1, 2), (negative 1.5, 0), (2.8, 0).
Answers
A graph which shows the image of ABCD is: A. on a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1).
What is a transformation?A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on transformation of parallelogram ABCD, we can infer and logically deduce that a graph which shows the image of ABCD is that on a coordinate plane, with parallelogram A'B'C'D' having points (-2, 5), (0, 3), (0, -1.2), (-2, 1) as shown in the image attached below.
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What are the step to the Quadratic Formula?
Answers
The steps to solve a quadratic formula include:
Combine all of the like terms and move them to one side of the equationFactor the expressionSet each set of parenthesis equal to zero as separate equationsSolve each "zeroed" equation independentlyWhat is a quadratic equation?In algebra, a quadratic equation is a equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.
A quadratic equation is an equation that could be written as ax² + bx + c = 0
when a 0. The factoring method is illustrated:
To solve a quadratic equation by factoring, put all terms on one side of the equal sign, leaving zero on the other side.
Set each factor equal to zero.
Solve each of these equations.
Check by inserting your answer in the original equation.
Example 1
Solve x² – 6 x = 16.
Following the steps,
x² – 6 x = 16 becomes x² – 8x + 2x – 16 = 0
Factor.
( x – 8)( x + 2) = 0
Therefore, x = 8 and -2.
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Find the local maximum and minimum values of f using both the first and second derivative tests. f(x) = 6 9x2 − 6x3 local maximum value local minimum value
Answers
The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
For given question,
We have been given a function f(x) = 6 + 9x² - 6x³
We need to find the local maximum and local minimum of the function f(x)
First we find the first derivative of the function.
⇒ f'(x) = 0 + 18x - 18x²
⇒ f'(x) = - 18x² + 18x
Putting the first derivative of the function equal to zero, we get
⇒ f'(x) = 0
⇒ - 18x² + 18x = 0
⇒ 18(-x² + x) = 0
⇒ x (-x + 1) = 0
⇒ x = 0 or -x + 1 = 0
⇒ x = 0 or x = 1
Now we find the second derivative of the function.
⇒ f"(x) = - 36x + 18
At x = 0 the value of second derivative of function f(x),
⇒ f"(0) = - 36(0) + 18
⇒ f"(0) = 0 + 18
⇒ f"(0) = 18
Here, at x=0, f"(x) > 0
This means, the function f(x) has the local minimum value at x = 0, which is given by
⇒ f(0) = 6 + 9(0)² - 6(0)³
⇒ f(0) = 6 + 0 - 0
⇒ f(0) = 6
At x = 1 the value of second derivative of function f(x),
⇒ f"(1) = - 36(1) + 18
⇒ f"(1) = - 18
Here, at x = 1, f"(x) < 0
This means, the function f(x) has the local maximum value at x = 1, which is given by
⇒ f(1) = 6 + 9(1)² - 6(1)³
⇒ f(1) = 6 + 9 - 6
⇒ f(1) = 9
So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.
Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
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two remaining of a right triangle have length of 4 and 5 units. what are two possible lengths for the remaining side?
Answers
Answer:
c^2 = a^2 + b^226^2 = 10^2 + b^2 676 = 100 + b^2 576 = b^2 shortest side length = 24 units
Step-by-step explanation:
2x + 4y = 12
y = A system of equations. 2 x plus 4 y equals 12. y equals StartFraction one-fourth EndFraction x minus 3.x – 3
What is the solution to the system of equations?
Answers
Answer:
x = 4, y = 1
Step-by-step explanation:
y = (1/4)x
2x + 4y = 12
replace y with something x
2x + 4(1/4)x = 12
3x = 12
x = 4
so y = 1
PLS HELP ITS MATH PLS
Answers
Answer: x is -1/2,0 and y is 0,2
Step-by-step explanation:
Answer:
(4,0) , (0,2)
Step-by-step explanation:
Similar to the previous question.
x-intercept is where the line touches the x-axis , and y = 0.
when y = 0,
8x + 16(0) = 32
8x = 32
x = [tex]\frac{32}{8}[/tex]
x = 4
Therefore the coordinates of the x-intercept is (4,0)
y-intercept is where the line touches the y-axis, and x = 0.
when x = 0,
8(0) + 16y = 32
16y = 32
y = [tex]\frac{32}{16}[/tex]
y = 2
Therefore the coordinates of the y-intercept is (0,2)
One day, thirteen babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls?
Answers
Using the binomial distribution, there is a 0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are:
p = 0.5, n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]P(X \leq 11) = 1 - P(X > 11)[/tex]
In which
P(X > 11) = P(X = 12) + P(X = 13)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{13,12}.(0.5)^{12}.(0.5)^{1} = 0.0016[/tex]
[tex]P(X = 13) = C_{13,13}.(0.5)^{13}.(0.5)^{0} = 0.0001[/tex]
So:
P(X > 11) = P(X = 12) + P(X = 13) = 0.0016 + 0.0001 = 0.0017
[tex]P(X \leq 11) = 1 - P(X > 11) = 1 - 0.0017 = 0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
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Sketch the graphs of the equation:
y=x
The question doesn't give a number for any one of the variables, do I just create one?
Answers
Answer:
See attached image.
Step-by-step explanation:
If x=y, the (x,y) = (x,x) or (y,y). All points have the same x and y values.