Find two sets of parametric equations for the rectangular equation. y=(x-6)^2-7x.
If x=t+6 then y=
If x=7t then y=
Show all work !
The two sets of parametric equations for the rectangular equation are;
If x=t+6 then y= t²-7t-42.If x=7t then y= 49t² - 133t +36.What are the parametric equations from the rectangular equation?It follows from the task content that the parametric equations can be determined as follows;
By substituting the x= t+6 into the rectangular equation; we have;
y = (t+6-6)²-7(t+6)
y = t²-7t-42.
By substituting the x= 7t into the rectangular equation; we have;
y = (7t-6)² -7(7t)
y = 49t² - 84t +36 - 49t
y = 49t² - 133t +36.
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Which of the following terms completes the sentence below?
A sign chart helps you record data about a function's values around its
and
asymptotes.
The terms that completes the sentence are zeros; vertical. Option A
Function of a sign chart
The functions of a sign chart include;
It helps in the record of information about the functions values around its zeros and vertical asymptotesA sign chart indicates the sign of the result any mathematical operation between unknowns.From the mentioned functions, we can se that the terms that completes the sentence are zeros and vertical asymptotes.
Thus, the terms that completes the sentence are zeros; vertical. Option A
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Type the correct answer in each box. Use numerals instead of words.
Consider function g.
6,
0,
-4,
-8<-2
-2 ≤ x < 4
4 x < 10
What are the values of the function when = -2and when = 4?
g(x)
=
g (-2) =
g (4) =
Reset
Next
When x = -2, we use the second part of the function, so g(-2)=0.
Similarly, g(4) = -4.
copy the problems onto your paper, mark the given and prove the statements asked. if PO is congruent to PR and UO is congruent to UR prove angle O is congruent to angle R
The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.
What is the Side-side-side Congruence Theorem (SSS)?The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.
What is the CPCTC Theorem?The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.
We are asked to prove that ∠O ≅ ∠R.
With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).
We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.
This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.
Applying the CPCTC theorem, ∠O ≅ ∠R.
The two-column proof is attached in the image below.
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If f(x) = 4x, which statements are true of g(x)? Select two options.
The two statements that are true for g(x ) are:
g(x) = [tex]4^{x}[/tex] - 1
g(x) is translated both vertically and horizontally.
What is a function?A function is a relation showing the relationship between two or more variables.
A function produces a unique output when a unique input is given to it. The input is called the domain and the output is called the Range.
Analysis:
If we use the values of x as 0,1,2,3
for x = 0
g(0) = [tex]4^{0}[/tex] -1 = 1 -1 = 0
for x = 1
g(1) = [tex]4^{1}[/tex] -1 = 4 - 1 = 3
for x = 2
g(2) = [tex]4^{2}[/tex] - 1 = 16 - 1 = 15
for x = 3
g(3) = [tex]4^{3}[/tex] - 1 = 64 - 1 = 63
Therefore g(x) = [tex]4^{x}[/tex] - 1
Also since the values of g(x) changes along the y - axis and x-axis also changes, therefore, g(x) is translated along both axes.
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Solve for x if sqrt (3x-8) + 1 = sqrt (x+5)
The solution of x in the given expression [tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex] is 4. However, if it is [tex]\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}[/tex], it is 6.
What is the solution to algebraic expression?The solution to the given algebra expression involving surds can be seen in the steps below.
Given that:
[tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex]
Remove the square roots, we have:
12x - 32 = 4x² - 48x + 144
Solving the quadratic equation at the RHS and equating it to LHS, we have:
x = 11, x = 4
Verifying the solutions by replacing the value of x with the given equation:
x = 11 Falsex = 4 TrueTherefore, we can conclude that the value of x = 4
NOTE:
Given that:
[tex]\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}[/tex]
Square both sides
3x - 7 = x +5
Solve for x
3x - x = 5 + 7
2x = 12
x = 6
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HELP PLSSSSSSSSSSSS!!!!!
Answer:
6 x 2 x 2 x 1
Step-by-step explanation:
6 x 2 = 12
12 x 2 = 24
24 x 1 = 24
Simplify the following fractions.
Answer:
The solution for the above fraction is
[tex] \frac{146}{167} [/tex]
Step-by-step explanation:
Greetings!
look at the attachment above for the explanation.
Vrite the equation of a line in the slope-intercept form that has a slope of 4
and contains the point (4, 12).
Answer:
y= 4x -4
Step-by-step explanation:
Slope-intercept form is given by y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is 4, m= 4.
Substitute the value of the slope into the equation:
y= 4x +c
The value of c can be found by substituting any point in which the line passes through into the equation above.
When x= 4, y= 12,
12= 4(4) +c
12= 16 +c
Subtract 16 from both sides:
c= 12 -16
c= -4
Thus, the equation of the line is y= 4x -4.
Additional:
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https://brainly.com/question/27941697Round to 4 significant figures 2.3581x10^3
Answer:
2358.1
Step-by-step explanation:
2.3581 x 10^3
= 2.3581 x 10000
=2358.1
How large an equilateral triangle can you fit inside a 2-by-2 square?
Answer:
An equilateral triangle with a length of 2
Step-by-step explanation:
A 2-by-2 square implies that the square has a length and width of 2. Since equilateral triangles have the same length for all sides, it tells you that if one side is a certain length, all the other sides must have the same length. The largest length we can fit into this square would be 2 because any larger, the sides of the triangles would not fit into the square. Under the assumption that the length needs to be a whole number, the answer would be 2.
Can anyone help with this?
The logarithmic function expresses the output variable, y, as a function of the logarithm of the input variable, x, as a function of a base b. The true statements are therefore;
I, II, and III onlyWhich statements are true based on the definition of a logarithm?The given logarithmic equation is presented as follows;
[tex]y = log_{b}(x) [/tex]
Therefore, we have;
[tex]x = {b}^{y} [/tex]
Where b = 1, we have that x will always be 1, therefore;
b ≠ 1Option III is true[tex]b = \sqrt[y]{x} [/tex]
Therefore;
x > 0Option I is trueWhich gives;
b > 0Option II is trueThe statements that are true is therefore;
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help!
Nora and Annie are raising money to purchase books for their school's library. The number of books they will be able to purchase for the library depends on the amount of money they raise.
b = the number of books Nora and Annie will be able to purchase
m = the amount of money Nora and Annie raise
Which of the variables is independent and which is dependent?
Answer: B is dependent and M is independent
Step-by-step explanation:
This is because the question says that they are raising money to buy books. In order to buy the books, they must raise money. So they raise money than buy the books which makes buying the books dependent on how much they raise.
A city has a population of 350,000 people. Suppose that each year the population grows by 4.75%. What will the population be after 13 years? Use the calculator provided and round your answer to the nearest whole number.
Answer: 4766125
//////////
Answer:
Step-by-step explanation:
first you we need to times 350,000 4.75 and you got 1662500 then subtract 1662500 - 13 years you got 1662487.
022 A. Find the unit vector in the direction of F 2+3j+4k B. Find the distance between F1 = 3i+2j+ 5k and F2 = 3i +4j +5k C Find the component of each directed line segment whose initial point contains p, and the terminal point P₂ i.) P, (3,2,2), P₂(3,-2,-3) ii.) P₂(2,-3,-6), P3(-3,3,2)
By definition of vectors exist as quantities that contain magnitude (positive or negative) and direction.
A) The unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]
B) The distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.
C) i.) Required vector = −4j − 5k
ii.) Required vector = 5i − 6j − 8k
How to estimate unit vector?To estimate the unit vector in the direction of V = 2i+3j+4k
|V| [tex]$= \sqrt{2^2+3^2+4^2}[/tex]
[tex]$= \sqrt{29}[/tex]
A) Unit vector
[tex]$F= \frac{V}{ |V|}[/tex]
[tex]$F= \frac{2i+3j +4k}{2}[/tex]
[tex]$F = \frac{2i}{2} + \frac{3j}{2} +\frac{4k}{2}[/tex]
[tex]$F= i + \frac{3j}{2} +2k.[/tex]
Therefore, unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]
B) To estimate the distance between [tex]F_{1}[/tex] = 3i+2j+ 5k and [tex]F_{2}[/tex] = 3i +4j +5k
[tex]$d = \sqrt{(3-3)^{2}+(4-2)^{2}+(5-5)^{2}}[/tex]
= 2
Therefore, the distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.
C) i.) P, (3,2,2), P₂(3,-2,-3)
Required vector =|[tex]P_{1}[/tex]P₂|=(3−3)i + ((−2)-2)j + ((-3)-2)k
= −4j − 5k
ii.) P₂ (2,-3,-6), [tex]P_{3}[/tex] (-3,3,2)
Required vector =|P₂[tex]P_{3}[/tex]|=(-3-2)i + (3-(-3))j + (2-(-6))k
= 5i − 6j − 8k
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(02.03 MC)
Choose the equation that represents the graph.
graph of a line passing through points negative 2 comma 0 and 0 comma negative 4
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
y = - 2x - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, - 4) ← 2 points on the line
m = [tex]\frac{-4-0}{0-(-2)}[/tex] = [tex]\frac{-4}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4
y = - 2x - 4 ← equation of line
Amy and Vince want to save $7,000 so that they can take a trip to Europe in four years. How much must they save each month to have the money they need if they can get 3% per year, compounded monthly, on their savings?
Answer:
10
9
0
Step-by-step explanation:
you subtract the number of all your answers
Sketch the function of f(x)=x^(3)-5x^(2)
The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
How to estimate the function of [tex]$f(x)=x^{3}-5x^{2}[/tex]?Put x = 0.
Replace the variable x with 0 in the expression.
[tex]f(0)=(0)^3-5(0)^2[/tex]
Raising 0 to any positive power yields 0.
f(0) = 0 − 5⋅0
f(0) = 0
y = 0
Put x = 1.
Replace the variable x with 1 in the expression.
[tex]f(1)=(1)^3-5(1)^2[/tex]
f(1) = 1− 5⋅1
f(1) = −4
y = −4
Put x = 2.
Replace the variable x with 2 in the expression.
[tex]f(2)=(2)^3-5(2)^2[/tex]
[tex]f(2)=8-5(2)^2[/tex]
f(2) = 8 − 5⋅4
f(2) = −12
y = −12
Put x = 3.
Replace the variable x with 3 in the expression.
[tex]f(3)=(3)^3-5(3)^2[/tex]
f(3) = 27 − 45
f(3) = −18
y = −18
Put x = 4.
Replace the variable x with 4 in the expression.
[tex]f(4)=(4)^3-5(4)^2[/tex]
[tex]f(4)=64-5(4)^2[/tex]
f(4) = 64 − 5 ⋅16
f(4) = 64 − 80
f(4) = −16
y = −16
The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
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An auction website charges $1 for a bid. The bidding starts at 1¢ and goes up 1c at a time. A television that is worth
$2000 is won, on average, with a bid of $160. You make one bid at random.
Find the expected value of the outcome of the bid. (Write as an exact decimal, with a negative sign, if necessary.)
Expected Value: $
The expected value of the outcome of the bid is $0.18
So let's start by counting how many bids are placed up to a total of 160.
100*160 = 16000.
What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)
Your odds of winning are 1/16000 (1 bid out of 16000).
If you win, your profit is 1920 ($2000 minus $80.00).
1920/16000 is $0.12
Your cost to enter the auction is $1, and your average winning offer is $0.12.
The result is $0.18 (0.12-1=-0.88).
Thus the expected value of the outcome of the bid is $0.18
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A college currently has 600 students enrolled
full time. Of these students, 400 are science
majors while 200 are liberal arts majors. If
350 of the students are male, and 250 of the
males are science majors, how many female
students are liberal arts majors?
(A) 200
(B) 150
(C) 100
(D) 50
Answer:
C) 100
Step-by-step explanation:
250+600-350-400
850-350-400
500-400=100
Find the solution to m^2+9m=0
Work Shown:
m^2+9m=0
m(m+9)=0
m = 0 or m+9 = 0
m = 0 or m = -9
For more information, check out the topics about factoring and the zero product property.
Emma throws an object upwards from a hill
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A non linear function is a function whose graph is not linear or can be represented by a straight line.
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
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A recent tax bill proposed raising the income-tax rate on families earning at least $200,000 a year by 25%, to 25%. What was the previous tax rate ?
The previous tax rate was 20%
What is tax rate?
Tax rate is the percentage of the earnings tax payers would pay to the government from their earnings as taxes.
It should be borne in mind that the new tax rate is 25% which has increased by 25% compared to the previous tax rate, which is the unknown.
The mathematical relationship between the current and prior tax rates is as shown below:
Current tax rate=previous tax rate*(1+% increase in tax rate)
Current tax rate=25%
previous tax rate=X
% increase in tax rate=25%
25%=X*(1+25%)
25%=X*1.25
X=25%/1.25
X=previous tax rate=20%
Technically speaking, an increase of 25% in 20% is 5%(i.e. 20%*25%=5%), which when added to the original 20% would give a tax rate of 25%.That the shortcut to affirming that the new tax rate of 25% is correct
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Joey is twenty years younger than Becky in two years time Becky will be twice as old as Joey
Answer:Joey is 18 hope that helped you
A card is drawn at random from a deck of cards. What is the probability that
a. it is a heart, given that it is red?
b. it is higher than a 10, given that it is a heart? (Interpret J, Q, K, A as 11, 12, 13, 14)
c. it is a jack, given that it is red?
Answer:
a. 13/26 = 1/2
b. 3/13
c. 2/26 = 1/13
Step-by-step explanation:
A. 26 red cards and 13 of them are hearts so 13/26 which can be simplified to 1/2
B. 13 hearts but only jack, queen king are higher than 10 so 3/13
C. 26 red cards altogether and we have a total of 2 red jacks so 2/26 which can be simplified to 1/13
is this what you wanted?
Easy points because I got points to blow,
Answer:
Did you know that the first person convicted of speeding was going eight mph.
Step-by-step explanation:
a2 + ab -2b2 factorise
[tex]a {}^{2} + ab - 2 {b}^{2} [/tex]
[tex] = (a - b) {}^{2} [/tex]
triangle mno is equilateral. find x and y.
Answer:
x = 7.5 and y = 75
==============
GivenEquilateral triangle MNO.We know each interior angle of an equilateral triangle is 60°, since each of three angles are of same value.
180°/3 = 60°We can see:m∠MNO = 2x + 4x + 2x Sum of interior angles60 = 8x Substitute the value of ∠MNOx = 60/8 Solve for xx = 7.5The middle triangle with two interior angles 4x and y has the missing angle also y, since it is isosceles, because both adjacent angles are equal at vertex N.
It gives us:4x + y + y = 180 Sum of interior angles4*7.5 + 2y = 180 Substitute the value of x30 + 2y = 180 Solve for y2y = 150y = 75First
Measure of any angle in an equilateral triangle is 60°
So
2x+4x+2x=60°8x=602x=15x=15/2x=7.5And
4x=4(7.5)=30Apply angle sum property
2y+30=1802y=150y=75The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
Using the normal distribution, it is found that the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is of 3.7 minutes.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 4.5, \sigma = 1[/tex]
The cut-off time is the 100 - 75.8 = 24.2th percentile, which is X when Z = -0.7, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.7 = \frac{X - 4.5}{1}[/tex]
X - 4.5 = -0.7
X = 3.7.
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10yy'=x y(10)=4
Find the solution of the differential equation that satisfies the given initial condition.
Answer:
Step-by-step explanation:
10yy'=x
[tex]10y\frac{dy}{dx} =x\\separating~the~variables\\10 ydy=xdx\\integrating\\\int 10ydy=\int xdx+c\\\frac{10y^2}{2} =\frac{x^2}{2} +c\\10y^2=x^2+2c\\when~x=10\\y=4\\10(4)^2=10^2+2c\\160=100+2c\\2c=160-100=60\\c=\frac{60}{2} =30\\10y^2=x^2+60\\10y^2-x^2=60[/tex]