The equation of the parabola is y = (x + 3)^2 - 1
What are parabolic equations?Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the equation of the parabola?The given parameters are
Vertex = (-3, -1)
X-intercept = (-4, 0)
A parabolic equation has the form y = a(x - h)^2 + k
Where the vertex is (h, k)
This means that, (h, k) is given as
(h, k) = (-3, -1)
Substitute (h, k) = (-3, -1) in the equation y = a(x - h)^2 + k
So, we have
y = a(x + 3)^2 - 1
Next, we substitute (-4, 0) for (x, y) in y = a(x + 3)^2 - 1
So, we have
0 = a(-4 + 3)^2 - 1
This gives
0 = a - 1
Solve for a
a = 1
Substitute a = 1 in y = a(x + 3)^2 - 1
y = (x + 3)^2 - 1
So, the required equation of the parabola is y = (x + 3)^2 - 1
Hence, the equation of the parabola is y = (x + 3)^2 - 1
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Solve each system using a matrix equation. Check your answer.
[x+2y=11 x+4y=17]
The values of "x" and "y" in the given matrix equation is 5 and 3 respectively.
What is matrix equation?A matrix equation is an equation in which a matrix acts as a variable.
The given system of equation;
x + 2y = 11
x + 4y = 17
Matrix form of the equation[1 2 ] = [11]
[1 4 ] = [17]
determinate of the equation, Δ
Δ = [1 2 ]
[1 4 ]
Δ = (4 x 1) - (2 x 1) = 2
x determinate of the equation, ΔxΔx = [11 2 ]
[17 4 ]
Δx = (4 x 11) - (17 x 2) = 10
y determinate of the equation, ΔyΔy = [1 11 ]
[1 17 ]
Δy = (17 x 1) - (11 x 1) = 6
Values of "x" and "y"x = Δx/Δ
x = 10/2 = 5
y = Δy/Δ
y = 6/2 = 3
Thus, the values of "x" and "y" in the given matrix equation is 5 and 3 respectively.
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A man borrows #760 at 4% and of the first year he pays back #270 after another year he repays #280. At the end of the third year he clears the debt completely. what is his final payment ?
His final payment will be $271.66464 at the end of the third year.
What is compound interest?The term "compound interest" refers to interest that is added back to the principal amount during each compounding period.
Compound interest is calculated using the formula
A = P(1+r )ⁿ, where
P = principal balance,
r = interest rate,
n = number of periods.
Given that a man borrows $760 at 4% and of the first year he pays back $270.
Amount owned by him at the end of the first year after repaying $270 = (1+4%)760 - 270
= 1.04×760 - 270
= $520.4
Amount owned by him at the end of the second year after repaying $280 = (1+4%)520.4 - 280
= 1.04×520.4 - 280
= 541.216 - 280
= $261.216
Let his final payment be x.
So, the amount owned by him at the end of the third year will be 0.
⇒ (1+4%)261.216 - x = 0
⇒ 1.04×261.216 - x = 0
⇒ 271.66464 = x
Therefore, his final payment will be $271.66464.
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what is the unit rate for 7 penguins for 188.88$
The unit rate is $26.98
How to calculate the unit rate ?Unit rate can be described as the price of a single item. From the question, we are required to find the unit rate of 1 penguin
The unit rate can be calculated as follows
7 penguins = 188.88
1 Penguin= x
Cross multiply both sides
7x= 188.88
x= 188.88/7
x= 26.98
Hence the unit rate is $26.98
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Solve. Check for extraneous solutions. √3 x+2 - √2 x+7=0
There is No Extraneous solution to the equation
The equation is
[tex]\sqrt{3x - 2}[/tex] - [tex]\sqrt{2x - 7}[/tex] = 0
We need to find the value of x,
[tex]\sqrt{3x + 2}[/tex] = [tex]\sqrt{2x + 7}[/tex]
Squaring both sides of the equation
[tex](\sqrt{3x + 2} )^{2}[/tex] = [tex](\sqrt{2x + 7} )^{2}[/tex]
3x + 2 = 2x + 7
x = 5
Now we need to put the value of x in the equation to know whether it is an extraneous solution or not.
[tex]\sqrt{(3 * 5 ) + 2}[/tex] - [tex]\sqrt{(2 * 5 ) + 7}[/tex] = 0
[tex]\sqrt{17}[/tex] - [tex]\sqrt{17}[/tex] = 0
0 = 0
Therefore we get to know that the equation has no extraneous solution.
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suppose you invested $6,000 and it grew by 8% every year for 5 years. how much would this investment be worth after 5 years?
1. $0.02
2. $8,815.96
3. $48,000
4. $8,864.73
A video cassette tape has a running time of 1 hour while at standard speed, 4 hours while at long-play
1
1
speed, and 7 hours while at super long-play speed. If of the tape is recorded at standard speed,
4
3
5
at long-play speed, and at super long-play speed, what is the total running time of the video
12
cassette tape? Write the solution as a mixed number or a fraction in lowest terms.
[tex]4\frac{6}{12}[/tex] hours play speed, what is the total running time of the video.
What does "speed" mean in mathematics?
Speed is what it means. the speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.Running time of cassettes
at standard speed = 1 hr
at standard speed = 4 hr
at standard speed = 4 hr
given the 1/4 part of tape is recorded at standard speed, 1/3 at long-play speed , 5/12 at super long-play speed,
so the running time of standard speed = 1/4 * 1 = 1/4
at long play speed
1/3 * 4 = 4/3 hours
and at super long-play speed,
5/12 * 7 = 35/12 hours
so, the total running time of the video
1/4 + 4/3 + 35/12 = 54/12 = [tex]4\frac{6}{12}[/tex] hours
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Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d(k+1).
BIUX¹ X₂ 15px
AVE
V
We have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.
Mathematical Induction : For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.
It is given that the statement is true for n = k
Explanation:
According to the principle of Mathematical Induction,
Let d(n) be a statement involving Natural Number n such that
d(1) is true
d(m) is true
d(m+1) is true
So , the statement d(n) is true for all the n natural numbers.
According to the second principle of Mathematical Induction
Let d(n) be a statement involving Natural number n such that
d(1) is true
d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .
Then the statement d(n) is true for all the values of n ( natural number)
Therefore , we have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.
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What is better when buying a $75 shirt?
a) A one time discount of 38%
b) A 14% discount followed by a 24% discount.
Which scenario gives the better buy?
How much will the shirt cost when given scenario (a) that gives a one time discount of 38%?
How much will the Shirt cost when giving scenario (b) that gives a discount of 14% followed by a 24% discount?
Answer: A. A one time discount of 38%.
How much will the shirt cost when given scenario (a) that gives a one time discount of 38%? : $46.50
How much will the Shirt cost when giving scenario (b) that gives a discount of 14% followed by a 24% discount? $49.02
Write an expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season. Let j be the number of Jets home games, d be the number of Dolphins home games, and p be the number of Patriots home games.
The expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season is 82,500 j + 65,326 d + 66829 p.
We are given that:
Team Number of seats
Jets 82,500
Dolphins 65,326
Patriots 66,829
The number of attendees at the jets home games = j
The number of attendees at the Dolphins home games = d
The number of attendees at the Patriots home games = p
So, the maximum number of attendees can be written by the expression:
82,500 j + 65,326 d + 66829 p.
Therefore, we get that, the expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season is 82,500 j + 65,326 d + 66829 p.
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Your question was incomplete. Please refer the content below:
We are given the data as:
Team Number of seats
Jets 82,500
Dolphins 65,326
Patriots 66,829
Write an expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season. Let j be the number of Jets home games, d be the number of Dolphins home games, and p be the number of Patriots home games.
Help Immediately Please
Solve ² - 5x+7=0.
Answer: D
Step-by-step explanation:
:)
Solve the system of equations using elimination: -6x - 6y = −42 and -x + 2y = 8.
The solution of given system of equations is 6 and 7.
To solve the system of equations using elimination, we will equate any one variable. In this case, we will be equating variable y.
Rewriting the equations -
-6x - 6y = −42 : equation 1
-x + 2y = 8 : equation 2
Multiplying equation 2 with 3
-3x + 6y = 24 : equation 3
Adding equation 1 and equation 3 to solve the given system of equations
-6x - 6y = −42
3x + 6y = 24
We get the answer :
-3x = -18
Negative sign will be cancelled and performing division
x = 6
Keep the value of x in equation 2
-6 + 2y = 8
2y = 8 + 6
2y = 14
y = 14 ÷ 2
y = 7
Therefore, the value of x and y is 6 and 7 in given system of equations.
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Aiza made $55 a day lifeguarding in the summer. She worked six days a week for five weeks. For two weeks of the summer she went on vacation. She spent approximately $68 a day each for two weeks. How much does Aiza have left from her lifeguarding job?
Answer: Aiza have left from her lifeguarding job = $ 700
Step-by-step explanation:
Given that,
Aiza made $55 a day lifeguarding in the summer.
She worked six days a week for five weeks.
For two weeks of the summer she went on vacation.
She spent approximately $68 a day each for two weeks.
Aiza earning per day = $55
Aiza worked for six days in a week.
Aiza worked for five weeks.
Total earning for weeks
= $ 55(6)
= $ 330 / week
Total earning for 5 weeks
= $ 330(5)
= $ 1650
Aiza spent per day for vacation = $ 68
Aiza was an vacation for two weeks.
Total expenditure for two weeks,
Number of days in each week = 7 days
= 2(7)($ 68)
= $ 952
Aiza have left with = Total earning - Total expenditure
= $ 1650 - $ 952
= $ 700
Therefore, Aiza have left from her lifeguarding job = $ 700
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For the points given below, find (a) PQ and (b) the coordinates of the midpoint of PQ. P(3,5), Q(5,-4) (a) PQ ~ (Type an integer or decimal rounded to the nearest tenth as needed.) (b) The coordinates of the midpoint of PQ are 7 (Type an ordered pair, using integers or decimals.)
a) The line segment PQ has a length of √85 (approx. 9.219).
b) The coordinates of the midpoint of the line segment PQ is (4, 0.5).
What is the length of a line segment and the coordinates of its midpoint?
Herein we find a line segment whose endpoints are known: P(x, y) = (3, 5), Q(x, y) = (5, - 4), and we are asked to determine the length of the line segment and the coordinates of the midpoint as well. a) First, we determine the vector between the points P and Q by sum of vectors:
PQ = Q(x, y) - P(x, y)
PQ = (5, - 4) - (3, 5)
PQ = (2, - 9)
And its magnitude is determined by using the Pythagorean theorem:
PQ = √[2² + (- 9)²]
PQ = √85
b) The coordinates of the midpoint is found by using the following formula:
M(x, y) = 0.5 · P(x, y) + 0.5 · Q(x, y)
M(x, y) = 0.5 · (3, 5) + 0.5 · (5, - 4)
M(x, y) = (1.5, 2.5) + (2.5, - 2)
M(x, y) = (4, 0.5)
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hyyy someone help me with this plsss (just write the equation with explanation)
Answer:
a) 10n -6
b) -5n +105
c) 7f + 1
d) -11n +48
Step-by-step explanation:
for an example let's take a) 4, 14, 24, 34
term value:
14 - 4 = 10 (coefficient)
term number:
4 = 34
4×10=40
34 - 40 = -6
coefficient and constant
therefore v = 10n -6
lol are you a Bhutanese?
50+pts to whoever can solve this correctly
Answer: Be careful. There is a slight difference in the order of the questions
2y+x/3=-6 linear or non linear?
2y+x/3=-6 is a linear equation.
An equation is written to equate two or more unknown variables and formulating a relation between them.
Equations are of various types such as:
linear equation: A equation where the highest degree of the variable is 1.quadratic equation : An equation where the highest degree of the variable is 2.logarithmic equation : An equation containing logarithmic functiontrigonometric equation : An equation containing trigonometric functionsradical equation: When the power of the variable is in a fraction it is a radical functionexponential equation: when the variable is raised to the power of another variable or constant it is an exponential function.The given equation is 2y+x/3=-6.
Here the power of both the variables is 1. Hence it can be classified as a linear equation in two variables.
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-8(b+3) what is the answer
Answer:
Either -8b - 24 or b = 3
Step-by-step explanation:
Answer: - 8b - 24
Distributive property
Two quantities,
x
and
y
, are directly proportional. If you take a third of
x
, what happens to
y
?
CLEAR CHECK
It is tripled.
It is cubed.
It depends on the starting value of
x
.
It is multiplied by 13
1
3
.
If x and y are directly proportional and we take a third of x we also have to take a third of y, which means we have to multiply y by 1/3.
What is direct and inverse proportion?Two quantities when they are in direct proportion increase or decrease by the same constant and when they are inversely proportional if one quantity increases the other quantity decreases.
We know when two quantities are directly proportional we can relate them by proportionality as x ∝ y or x = ky.
∴ if we take 1/3 of x to maintain the equality we have to multiply y also by 1/3.
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Help Which of the following could be an algebraic expression for the total cost of dinner, less a $10 coupon, divided by 4 people?
(x − 10) ÷ 4
4x − 10
10 − 4x
4x(10)
the expression that models the situation of the total cost of a diner, less a $10 coupon divided by 4 is (x - $10)÷4
Which is the correct algebraic expression?Here we have the total cost of a dinner, less a $10 coupon, divided by 4 people.
If the total cost is x, then the total cost less a $10 coupon is:
x - $10.
Now, taking the quotient (dividing the above amount by 4) we will get:
(x - $10)÷4
This is the expression that models the situation of the total cost of a dinner, less a $10 coupon divided by 4.
So the correct option is the first one.
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(2x^(4)y^(-3))
please solve
Answer:
Step-by-step explanation:
(2x^(4)y^(-3))
= 2x^4/ y^3.
A rule was used to make the pattern shown below. 51, 45, 39, 33, 27, 21 .... Which could be the rule used to make the pattern? A Divide by 7. Divide by 6. Subtract 7. Subtract 6. B C Section 2: Quantitative Reasoning PETA
Answer:
subtract 6
Step-by-step explanation:
note there is a common difference between consecutive terms, that is
45 - 51 = - 6
39 - 45 = - 6
33 - 39 = - 6
27 - 33 = - 6
21 - 27 = - 6
the rule being used to make the pattern is subtract 6
this is an arithmetic sequence for which an nth term rule can be found
Answer:
subtract 6
Step-by-step explanation:
the pattern is made by subtracting 6 from the previous number
write the equation of the line that is parallel to the graph of 3x-y=5 , and whose y intercept is (0,-7)
The formula 3x-y=5 is a linear function.
We must first examine the slope of the original function in order to determine the equation of parallel lines. We are also given the other function's intercept in this issue.
The function's slope-intercept form is y=3x-5.
In order to locate the parallel line that corresponds to the point (0,-7)
Parallel lines are those that share the same slope but have different y-intercepts, as you may have seen.
As a result, we must put in the point to solve for the y-intercept.
Thus,
y = 3x + b
-7 = 3(0) + b
-7 = b
b = -7
Thus the equation of a parallel line is y = 3x - 7
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What is the slope of this graph?
- 1/3
1/3
3
-3
Please help with problem 25, Algebra 1 question, question in the attachments
The maximum and minimum number of people will be 19700 and 17300 respectively.
How to illustrate the information?It should be noted that it was stated that the arena can hold 18500 people.
Therefore, the equation to represent the number of people that can attend the event will be:
= 18500 +/- 1200
The maximum number of people will be:
= 18500 + 1200
= 19700
The minimum number of people will be:
= 18500 - 1200
= 17300
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Fill in the blank question.
Last month, the online price of a powered ride-on car was $250. This month, the online price is $330. What is the percent of increase in the price of the car? Round the percent to the nearest tenth if necessary.
The percentage of increase in the price of the car is 32%
What is the percentage of increase?Percentage increase means adding the given percentage of value to the original value.
To calculate this percentage increase:
= 100{( final value - initial value )/initial value}
Given that last month online price of powered ride-on car was $250
and this month this cost is $330
Initial value = $250
Final value = $330
Percentage increase = 100{ ( 330 -250 )/250} =100*0.32 = 32%
This the percentage increase in the price of the powered ride-on car is 32%
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Create a
number line and plot the decimal
numbers.
0. 75, 0. 279, 1. 008, 0. 44, 0. 705
In mathematical terms, Number Line is defined:
A visual representation of numbers(whole, natural, decimal, integers, fraction) using a horizontal line drawn straight with equal spacing divisions that represent each number.
Numbers are marked at equal intervals ans it is used to illustrate basic numeric operators. There is no limit to a number line, which means that it expands to positive and negative infinity. The middle of the number line is represented by zero, and on the right side are all the positive values up to the positive infinity. The same for the left side where are all the negative values are listed up to the negative infinity.
Now what is given to us in the question statement are a bunch of decimals. We know decimal numbers are considered real numbers and thus can easily be plotted on the number line. In order to plot the decimal numbers, we need to mark the intervals with decimals values.
The image attached below gives a clear representation of how the numbers will be plotted.
Values closer to 0, like 0.75, and 0.705, will be plotted more towards the right, and those away from zero, like 0.44, 0.279 will be plotted more towards the left of zero.
1.008 will be plotted after 0 and 1 on the number line (towards the right of the zero).
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What is the simplified form of (a²/¹ b¹/⁴)²?
(A) a⁴/₅ b⁹/₁₆ (B) a⁴/₃ b³/₂ (C) a b (D) (a b)¹⁷/₆
The simplest form of the expression is a⁴ b¹/₂ which is option (B) .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by academic degree operator in between.Simplifying expressions mean rewriting an analogous math expression with no like terms and through a compact manner.To change expressions, we have a tendency to tend to combine all type terms and solve all the given brackets, if any, then inside the simplified expression, we have a tendency to are aiming to be exclusively left with not like terms that cannot be reduced any.We have given an expression (a²/¹ b¹/⁴)² .
On simplifying , we get
(a²/¹ b¹/⁴)² = [tex]a^{2\times2} \ \ b^{2/4}[/tex]
= a⁴ b¹/₂
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The complete question is given below :
What is the simplified form of (a²/¹ b¹/⁴)²?
(A) a⁴/₅ b⁹/₁₆ (B) a⁴ b¹/₂ (C) a b (D) (a b)¹⁷/₆
What is the marginal distribution of males? Weight Class vs. Gender
Underweight At Goal Weight Overweight Total
Male 93 206 81 380
Female 37 446 137 620
Total 130 652 218 1000
A. 62.0% B. 38.0% C. 13.0% D. 65.2%
The marginal distribution of males is 13 %
A two-way frequency table shows the frequencies (or "counts") of two categorical variables.
For example, the following two-way table displays the results of a study in which 100 participants were asked which sport they preferred: baseball, basketball, or football.
The rows represent the respondent's gender, while the columns show which sport they chose:
There are two variables in this example: Sports and Gender.
A marginal distribution is simply the sum of the distributions of these separate variables. The marginal distributions in a two-way table are shown in the table margins: Marginal distributions are valuable because, while we frequently collect data for two variables (such as Sports and Gender), we may have particular questions regarding only one variable.
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15 / 53
Work out the equation of the line which passes through the point (-1, 2)
and is parallel to the line y = x + 4?
The equation of the line for the point (-1, 2) is [tex]y=x+3[/tex]
The slope of a line is the ratio of how much y increases when x increases by a certain amount.The graph of the linear equation y = mx + c is a straight line with slope m and y-intercepts m and c. This form of linear equation is called the slope intercept, and the values of m and c are real numbers. The slope m represents the slope of the straight line. The y-intercept b of the line represents the y-coordinate of the point where the line graph intersects the y-axis.The equation of a line whose slope is 'm' and which passes through a point [tex](x_1,y_1)[/tex] is found using the point slope form which is given by [tex]y-y_1=m(x-x_1)[/tex] ..(1)It is given that line is parallel to the line y = x + 4 . ....(2)
On comparing equation (2) with the slope intercept form which is y = mx +c , we get m = 1 . For parallel lines slope is same .
It is given that line passes through the point (-1, 2).
Putting [tex]y_1=2,\ x_1=-1[/tex] and m = 1 in equation (1) , we get
[tex]y-2=1(x-(-1))\\y-2=x+1\\y=x+3[/tex]
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Solve for x: 4 − (x + 2) < −3(x + 4) The graph shows a number line with an open circle at negative nine and shading to the left. The graph shows a number line with an open circle at negative nine and shading to the right. The graph shows a number line with an open circle at negative seven and shading to the left. The graph shows a number line with an open circle at negative seven and shading to the right.
After solving the expression 4 − (x + 2) < −3(x + 4), we get the value of x as x < - 7.
We are given the expression:
4 − (x + 2) < −3(x + 4)
Subtract 4 from both the sides, we get that:
4 - x - 2 - 4 < - 3 x - 12 - 4
- x - 2 < - 3 x - 16
- x + 3 x < - 16 + 2
2 x < - 14
x < - 14 / 2
x < - 7
Therefore, after solving the expression 4 − (x + 2) < −3(x + 4), we get the value of x as x < - 7.
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