The equation f(x) = x² + 2x - 3 is an illustration of a quadratic function
Calculate the left termThe equation is f(x) = x² + 2x - 3
The left term is calculated using:
\(x = -\frac{b}{2a}\)
This gives
\(x = -\frac{2}{2*1}\)
x = -1
Hence, the left term is -1
Compare the vertex and the axis of symmetryThe result above represents the axis of symmetry.
Substitute x = -1 in f(x) = x² + 2x - 3 to calculate the y-coordinate of the vertex
f(-1) = (-1)² + 2(-1) - 3
f(-1) = -4
This means that the vertex is (-1,-4)
So, we can conclude that the axis of symmetry passes through the x-coordinate of the vertex and it divides the graph into two equal segments.
Calculate the right termThe formula is given as:
\(x = \pm \frac{\sqrt{b^2 - 4ac}}{2a}\)
So, we have:
\(x = \pm \frac{\sqrt{2^2 - 4 * 1 * -3}}{2 * 1}\)
\(x = \pm \frac{\sqrt{16}}{2}\)
Evaluate
\(x = \pm 2\)
Hence, the right term is ±2
The horizontal distance along the axisFrom the graph of the function (see attachment), we have the horizontal distance of the vertex between each x-intercept to be 2
Compare (d) and (e)In (d), we have:
\(x = \pm 2\)
In (e), we have:
horizontal distance = 2
This means that the horizontal distance is the absolute value of the right term.
Summary of the findingsThe findings are:
The left term represents the axis of symmetry.The right term represents the horizontal distance of the vertex between each x-intercept.The axis of symmetry divides the graph into two equal segments.Read more about quadratic functions at:
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A train travels 360 km at a uniform speed, if speed has been increased it will take one hour less for the same journey then find the speed of the train.
Answer:
Given distance=360 km.
Let the speed of the train be x km/hr.
Speed when increased by 5 km/hr =(x+5) km/hr
x
360
−
(x+5)
360
=1
x(x+5)
[360x+1800−360x]
=1
x
2
+5x−1800=0
x
2
+45x−40x−1800=0
x(x+45)−40(x+45)=0
(x−40)(x+45)=0
x=40,−45
The speed of the train is 40 km/hr.
Step-by-step explanation:
thanks... ☺️
(m^(6)n^(3))/(m^(2)n^(6))
Answer:
\((m^4)/(n^3)\)
Step-by-step explanation:
See attachment
for every 10 yards on a football field, there is a boldly marked line labeled with the amount of yards. each of those lines is perpendicular to both sidelines. what can be said about the relationship of the sidelines? justify your answer.
The relationship between these sidelines is such that are parallel to each other and they will never meet.
Because they are both perpendicular to each designated line, it is accurate to say that the sidelines are parallel.
The plainly indicated lines cannot be perpendicular to both sidelines if the sidelines are parallel to each other.
All of the bolded lines must be perpendicular to both sidelines in order for there to be a perpendicular line between them.
The sidelines would therefore be parallel because they are perpendicular to the same set of lines.
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If you are not a goofy ah please answer this
Answer:
72
Explanation:
First, we can find the top and bottom smaller squares of the rectangular prism. Since we are working with a variety of rectangles, we only need to use the equation L×W.
To start with, let's multiply 2×3, which gives us 6, the surface area of both the bottom and top rectangles, so now we need to multiply it by 2 to account for both of them. 6×2=12
Now, we'll find the surface area of the bigger rectangles in the middle, which are 6 by 3, so again we will need to multiply length times width, then by 2 to count both rectangles. 6×3=18×2=36
Finally, we can find the surface area of the smaller rectangles in the middle, which are 6 by 2. 6×2=12, then multiply by 2 since there are 2 of those rectangles, 12×2=24
Now to find the total surface area, we need to add the gathered surface area from each shape, 12+36+24=72
The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t – 16t2. How long after launch does the projectile return to the ground?
2 seconds
4 seconds
14 seconds
16 seconds
Answer:
2
Step-by-step explanation:
when it returns to the ground , h = 0
32t -16t2 = 0 and solve for t
t = 0, 2 ....0 is the start, 2 is when it returns
Answer:
2
Step-by-step explanation:
A bear cub walks
5/6 miles in 5/12
age
hours. What is its
speed in terms of miles per hour?
Answer:use math(way
Step-by-step explanation
It help
Answer: 2 miles per hour
Step-by-step explanation: Reduce the common factor which would be 5 and then you divide and you get 2
Help me with my math pleasee!!
If the transformation is written in the form y = a(x - p)² + q, the values of a, p, and q include the following: a = 2, p = -4, q = 3.
How to determine the equation of a parabola?Mathematically, the standard equation of the directrix lines for any parabola is given by this mathematical expression:
y = a(x - h)² + k.
Where:
h and k are the vertex.a represents the leading coefficient.Based on the information provided about the parabola, we have the following:
Scale factor, a = 2.
Vertical translation upward, q = 3.
Horizontal translation to the left, p = -4.
Therefore, the equation becomes;
y = a(x - h)² + k.
y = a(x - (-4))² + 3.
y = a(x + 4)² + 3.
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Given that s(x)=−1x+8+9x−4, what is the antiderivative of s(x)? (Do not include the constant C in your answer.)
Note: When entering natural log in your answer, enter lowercase LN as "ln". There is no "natural log" button on the Alta keyboard.
The required answer is the antiderivative of s(x) is: 4x^2 + 4x
Given that s(x) = -1x + 8 + 9x - 4, we want to find the antiderivative of s(x) without including the constant C.
Antiderivatives are also called general integrals, and sometimes integrals. The latter term is generic, and refers not only to indefinite integrals but also to definite integrals. If the word integral is used without additional specification, the reader is supposed to deduce from the context whether it refers to a definite or indefinite integral. Define the indefinite integral of a function as the set of its infinitely many possible antiderivatives.
First, simplify s(x):
s(x) = -1x + 9x + 8 - 4
s(x) = 8x + 4
A antiderivative is a function reverses, they are taken the form of a function is an arbitrary constant. By second fundamental theorem of calculus , the antiderivative is related to the definite integral . Definite integral of a new function over a band interval.
Now, find the antiderivative of s(x):
Antiderivative of 8x + 4 = (8/2)x^2 + 4x
The natural logarithm function, if a positive real variable. This is a inverse function. Logarithm is useful for solving equations. Decayed constant or unknown time in problems.
So, the antiderivative of s(x) is:
4x^2 + 4x
where the function is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.
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how many driving lessons do you need to do with a professioanl instructor before my parents could teach me
The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.
In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.
The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.
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ASAP
What is the horizontal asymptote of this graph?
and
What is the y-intercept? What does this mean in terms of the snake population?
9514 1404 393
Answer:
horizontal asymptote: y = 0y-intercept: (0, 5)the snake population was 5 in year 0Step-by-step explanation:
The initial value of this function is the y-intercept, marked as (0, 5). The label on the graph tells you this is the snake population in year 0.
__
We note that the snake population goes up by a factor of 2 for each increase of 1 in the number of years. This indicates the function is an exponential function with a base of 2.
y = 5·2^t
Any exponential function will have a horizontal asymptote of y = 0.
Need it for grade: What is X???
Answer:
x=6
Step-by-step explanation:
FG + GH = FH
4+x-3 = 2x-5
Combine terms
x+1 = 2x-5
Subtract x from each side
x+1-x = 2x-5-x
1 = x-5
Add 5 to each side
1+5 = x-5+5
6 =x
Answer:
x=6
Step-by-step explanation:
F G + G H = F H
4+x-3 = 2x-5
I NEED THIS NOW!!
triangle abc has angle measures as shown (look at image).
(a) using the triangle sum theorem, write the equation and solve for x.
(b) what is the value of < b? show your work.
Answer:
a) x = 6° b) m∠B = 50°
Explanation:
(a) total angle measure of a triangle is 180°
8x + 2 + 70° + 60° = 180°
8x + 132° = 180°
8x = 180° - 132°
8x = 48°
x = 6°
(b)
m∠B = 8x + 2
m∠B = 8(6) + 2°
m∠B = 48° + 2°
m∠B = 50°
Answer:
A. X is 6 and B. Angle is 50
Step-by-step explanation:
PART A
Triangle sum theorem explains that all angles in a triangle add up to 180
(8x + 2) + 70 + 60 = 180
8x= 180-70-60-2
8x= 48
X= 48/8 =6
PART B
Using the formula provided, replace the x with 6
So it'll be 8(6)+2 = 48+2 = 50
Helppp!!!!!!!!!!!!!!!!!!!!!
The value of x is equal to 15°
How to determine the value of x?In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
By substituting the given parameters, we have the following:
3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.
3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.
23x + 15 = 360°.
23x = 360 - 15
23x = 345
x = 345/23
x = 15°.
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Find the first, fifth, and tenth terms of the sequence that has the rule:
A(n)=-8+(n-1)(4)
Step-by-step explanation:
A(n)=-8+(n-1)(4)
A(1)=-8
A(5)=-8+16
=8
A(10)=-8+36
=18
in utah, if not directly involved in diving activity, motorized vessels and personal watercraft (pwcs) must remain what distance from diver down flags?
In Utah, if not directly involved in diving activity, motorized vessels and personal watercraft (PWCs) must remain 150 feet from the diver down flags.
The diver down flag is a banner that is used by vessels to indicate that divers are in the water. It is typically a red flag with a white diagonal stripe that is used to indicate the presence of divers in the water. The flag must be at least 12 x 12 inches in size and must be clearly visible from all directions. When the flag is raised, boaters are expected to keep a safe distance from the divers and to take extra precautions to ensure that they do not pose a hazard to the divers.The diver down flag should be used whenever there are divers in the water. This includes scuba divers, free divers, and anyone else who is swimming or diving underwater. The flag should be raised before the divers enter the water and should be lowered when they exit the water. In addition to the flag, divers are required to use other means of indicating their presence in the water, such as lights and audible signals, to ensure that boaters can see and hear them. Motorized vessels and personal watercraft (PWCs) must remain at least 150 feet from the diver-down flag. This means that they must keep a safe distance from the divers and take extra precautions to ensure that they do not pose a hazard to the divers. If a motorized vessel or PWC is directly involved in the diving activity, such as transporting divers to and from the dive site, they may operate closer to the flag, but they must still maintain a safe distance from the divers at all times.
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Please help
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
An equation of the line in point-slope form is
(Simplify your answer. Type an equation. Type your answer in point-slope form. Use integers or fractions for any numbers in the equation)
The equation of the line in slope-intercept form is y = 6x + 55.
Describe Equation?Equations can involve variables, which are placeholders for unknown values that we wish to find. For example, the equation x + 3 = 7 asserts that the value of x plus 3 is equal to 7. We can solve for x by subtracting 3 from both sides of the equation, obtaining x = 4.
Equations can be linear or nonlinear, and they can involve one or more variables. They can be represented in various forms, such as standard form, slope-intercept form, or quadratic form.
To find the equation of the line in point-slope form, we need to first find the slope of the line. We can use any two points from the table to find the slope using the formula:
slope = (change in y)/(change in x)
Let's use the first and last points in the table:
slope = (295 - 175)/(40 - 20) = 120/20 = 6
Now we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is any point on the line. Let's use the first point (20, 175):
y - 175 = 6(x - 20)
To write this equation in slope-intercept form, we need to isolate y:
y - 175 = 6x - 120
y = 6x + 55
So the equation of the line in slope-intercept form is y = 6x + 55.
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Which of the following is a characteristic of a deferred payment plan? (2 points)
There is an introductory period where no interest is accrued.
The item purchased is used as collateral until the balance is paid in full.
A down payment is always required.
A certain number of payments must be made before the product is owned.
A characteristic of a deferred payment plan is that the item purchased is used as collateral until the balance is paid in full.
A deferred payment plan is a form of credit purchase, a way to pay for an item in arrears. The payment is usually divided into several installments, which are distributed over a certain period of time. Interest and fees are often added, which in the end makes the purchase considerably more expensive than if you had paid in cash.
Thus, through this payment system, the asset is delivered to the buyer before the payment is completed, thereby constituting the asset itself as an enforceable guarantee of payment compliance.
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Which of the following statements is false ?
Answer:
The bases of an isosceles trapezoid are congruent is false.
Step-by-step explanation:
Let's analyse each option.
In a Rhombus, the diagonals are perpendicular at the point of intersection and bisect each other is true.
In isosceles trapezoid, the sides are congruent but not the bases. So, this incorrect!
The rectangle is an Equi-angular because all the angles are equal. So, this is true.
The base angles are congruent in isosceles trapezoid. So, this is true too.
write an equation for a degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and has a y-int at 5..
The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
How to define the polynomial?The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function, along with their multiplicities, are given as follows:
Zero at x = 3 with a multiplicity of 1.Zero at x = 2 with a multiplicity of 2.Zero at x = -1 with a multiplicity of 3.Then the linear factors of the function are given as follows:
(x - 3).(x - 2)².(x + 1)³.The function is then defined as:
y = a(x - 3)(x - 2)²(x + 1)³.
In which a is the leading coefficient.
When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:
5 = -12a
a = -5/12
Hence the polynomial is:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
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2. Construct Arguments Triangle L'M'N' is the
image of triangle LMN after a translation. How
are the side lengths and angle measures of the
triangles related? Explain. MP3
We can conclude that -
In translation of a triangle without dilation, the side lengths and the angles would remain the same. In translation of a triangle with dilation of scale factor {K}, the side lengths of the triangles will change by the factor of {1/K} but the angles would remain the same.What is translation in geometry?Translation of graph is the movement of image across the 2 - Dimensional plane.
Given is Triangle L'M'N' is the image of triangle LMN after a translation.
In translation of a triangle without dilation, the side lengths and the angles would remain the same. In translation of a triangle with dilation of scale factor {K}, the side lengths of the triangles will change by the factor of {1/K} but the angles would remain the same.Therefore, we can conclude that -
In translation of a triangle without dilation, the side lengths and the angles would remain the same. In translation of a triangle with dilation of scale factor {K}, the side lengths of the triangles will change by the factor of {1/K} but the angles would remain the same.To solve more questions on translation, visit the link below -
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Given the function g(x)=2x and the domain {0, 2, 4), what is the range? {0, 1, 2} {2, 4, 8) {1, 2, 3) {0, 4, 8}
According to the question we get the following outputs For x = 0, g(0) = 0 , For x = 2, g(2) = 4 , For x = 4, g(4) = 8. the range of the function g(x) = 2x, with the given domain {0, 2, 4}, is {0, 4, 8}.
The range of the function g(x) = 2x, with the given domain {0, 2, 4}, can be determined by evaluating the function for each value in the domain.
For x = 0: g(0) = 2(0) = 0
For x = 2: g(2) = 2(2) = 4
For x = 4: g(4) = 2(4) = 8
Therefore, the range of the function is {0, 4, 8}.
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what is X?
-7x+4=-32
Answer:
The answer would be 36/7 and that would be 5.14285714286
Step-by-step explanation:
Answer:
Step-by-step explanation:
x=36/7
2(4x+5)=9(3x+2)? I need help
Answer:
\(x=-\frac{8}{19}\)
Step-by-step explanation:
2(4x + 5) = 9(3x + 2)
Solve for x
___________________
We have an alrebaric expressio and are asked to solve for x, which to do this, we need to isolate x.
2(4x + 5) = 9(3x + 2)
Distribute :
(2(4x) + 2(5)) = (9(3x) + 9(2))
8x + 10 = 27x + 18
Subtract 10 from both sides :
8x = 27x + 8
Subtract 27x from both sides :
-19x = 8
8 = -19x
Divide both sides by -19 :
\(x=-\frac{8}{19}\)
What would be the degree of financial leverage for Foggy Futures Weather Forecasters if the company has earnings before interest and taxes of $750,000, has a 4. 5% loan on $1,000,000, and is in the 38% tax bracket? The firm does not have any preferred stock outstanding. A. 1. 22 b. 0. 97 c. 1. 06 d. 1. 78
The degree of financial leverage for Foggy Futures Weather Forecasters
is 1.06
Degree of Financial leverage (DFL) = (EBIT) / (EBT)
Earnings Before Interest and Taxes (EBIT) = $750,000
Amount to be given as loan on $1000000
$1,000,000 x 4.5% = $1,000,000 x 4.5/100
= $45000
To find EBT ( Earnings Before Tax),
EBT = EBIT - 45000
= 750000 - 45000
EBT = 705000
∴ DFL = (EBIT) / (EBT)
= 750000/705000
DFL = 1.06
The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).
Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve
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which expression is equivalent to (x4)^9
Answer:
Step-by-step explanation:
\((a^{m})^{n}=a^{m*n}\\\\(x^{4})^{9}=x^{4*9}=x^{36}\)
Can someone help me with this? Its due in 30 minutes and I need help
Answer:
Quadrants I and II.
O: (-2, 2)
N: (-2, 4)
M: (1, 4)
P: (1, 2)
Step-by-step explanation:
When rotating about the origin 90 degrees in a counterclockwise direction, focus on the coordinates of one point on the preimage at a time. So, the x-coordinate on the image will be the opposite of the y-coordinate of the preimage, and the y coordinate of the image will be the x-coordinate of the preimage. That sounds complicated so here is an example from the problem.
O is a point on the preimage. Its coordinates are (2, 2). To find the x-coordinate, take the opposite of the image's y-coordinate. The y-coordinate is 2, so it will be a -2 x-coordinate on the image. To find the y-coordinate on the image, take the x-coordinate of the preimage (O). The x-coordinate of O is 2, so the y-coordinate of the image will be 2. Combine those together and after a 90 degree counterclockwise rotation, you get a point of (-2, 2)
Answer:
Step-by-step explanation:
when rotate counterclock wise 90 degrees:
(x,y)⇒(-y,x)
points (2,2) (4,2) (2,-1) (4,-1)
CCW90 degrees (-2,2) (-2,4) (1,2) (1,4)
CCW 270 degrees (2,-2) (2,-4) (-1,-2) (-1,-4)
(x,y)⇒(y,-x) the shape will be in quadrant 3 and 4
How many solutions does the equation
-2(x + 3) = 2x - (5 – x) have?
Step-by-step explanation:
-2(x + 3) = 2x - (5 – x)
-2x+6= 2x-5+x
-2x+6=3x-5
-2x-3x=-5-6
-5x=-11
x= 11/5
( 1 solution)
Answer:
Solution given:
-2(x + 3) = 2x - (5 – x)
-2x-6=2x-5+x
-6+5=2x+2x+x
5x=-1
x=\( \frac{-1}{5} \)
It has one Solution.
SOLVE ASAP WILL GIVE BRAINLIEST 100 POINTS
Answer:
I believe thats 8 to the power of 7
Step-by-step explanation:
Answer:
i clicked your link adn it looks like 8^7 or 8 to the 7th power which would be 2,097,152
Step-by-step explanation:
John goes to a restaurant and has a bill of $ 32. 57. He uses a 10% off coupon on the cost of his meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied. How much does he spend?
Answer: $36.97
Step-by-step explanation:
The cost of the meal was $32.57 and he used a 10% off coupon. You can make 10% equal to 0.1 because \(\frac{10}{100}=0.1\). Now do \(0.1 *32.57=$3.26\). This is the discount, so you want to subtract this from the original to get the actual price of the meal, \(32.57-3.26=29.31dollars\).
The tax was 8% so this means he is adding it to his total cost instead of subtracting it. Do 0.08 of $29.31 to get $2.34. Add $2.34 to the now $29.31 to get $31.69.
The tip is also adding to the total cost, so do 0.18 of $29.31 to get $5.28. Add $5.28 to $31.69 to get $36.97
Answer:
$37.51
Step-by-step explanation:
Original cost of meal is $32.57.
Since he has a coupon for 10% off, he pays for 90% of the cost of the meal.
90% of $32.57 = 0.9 * $32.57 = $29.31
Now he pays tax on the new discounted total. Let the new total be called 100%. Since he pays 8% tax, he needs to pay 108% of the new total.
108% of $29.31 = 1.08 * $29.31 = $31.65
He adds a tip of 18% of $32.57.
The tip amount is
18% of $32.57 = 0.18 * $32.57 = $5.86
The total is: $31.65 + $5.86 = $37.51
a student answers 75% of the questions on a math exam correctly. if he answers 30 questions correctly. how many questions are on the exam?