The vertex of the given function g(x) = -3x² + 18x + 2 is (3, 29)
Function in math is defined as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.
Here we have given the function called g(x) has the expression -3x² + 18x + 2.
And here we need to find the vertex for the function that can be calculated as,
As we all know that vertex form of a parabola is written as,
=> y = a (x - h)² + k
Here we know that (h, k) is the vertex
Then the given expression is written as,
=> g(x) = -3x² + 18x + 2
When we can be written by completing the square as follows,
=> y = -3x² + 18x + 2
Here we have to take 3 as common term, then we get
=> -3(x² + 6x)+ 2
now, we have to expand the expression within the brackets, then we get,
=> -3(x² + 6x+ 9)+ 2 + 27
Then the resulting vertex form o the equation is written as
=> y = - 3(x - 3)2 + 29
While we comparing this with the standard form then we get the value of vertex is (3, 29).
Complete Question:
What is the vertex of the function g(x) = -3x² + 18x + 2?
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At the beginning of the year, Gabriel had $25 in savings and saved an additional $14
each week thereafter. Adrian started the year with $80 and saved $9 every week. Let
G represent the amount of money Gabriel has saved t weeks after the beginning of
the year and let A represent the amount of money Adrian has saved t weeks after the
beginning of the year. Write an equation for each situation, in terms of t, and
determine the number of weeks after the beginning of the year until Gabriel and
Adrian have the same amount of money saved.
Answer: 11 weeks
Step-by-step explanation:
G(t) = 25 + 14t
A(t) = 80 + 9t
set G equal to A and find t
25 + 14t = 80 + 9t
5t = 55
t = 11
the cost of chesse increased by 25%. how much is the new price of the cheese that originally cost $4.20. PLEASE HELP WILL GIVE BRAINLIST FOR SOLULTIONS
Answer:
Step-by-step explanation: The answer is $48.15 hopes this helps :)
What is the latest estimate for the likelihood of one or more M 6. 7 earthquakes in the Bay Area region before the year 2043?.
A 72 percent is the latest estimate for the likelihood of one or more M 6.7 earthquakes in the Bay Area region before the year 2043.
To estimate the likelihood of future earthquakes, scientists rely on a variety of techniques that help us understand the velocities and magnitudes of past earthquakes. Using the Global Positioning System (GPS) and other land surveys and geological techniques,scientists have determined how much current plate movement, totaling inches per year across the San Francisco Bay region, stresses these individuals. We were able to more accurately measure how well it disperses. Small earthquakes occur more frequently than large ones. There is a 98% chance that an earthquake of magnitude 6.0 or greater will occur before 2043. There is a 72% chance that at least one earthquake of magnitude 6.7 or greater will occur in the San Francisco Bay Area, and a 51% chance that at least one magnitude earthquake will occur. Therefore they concluded that there is a 72% chance (or probability) of at least one earthquake of magnitude 6.7 or greater occurring somewhere in the San Francisco Bay Area before 2043.
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The lengths of the sides of a triangle are x, x + 11, and 2x + 5. a. Write a formula for the perimeter, simplifying your answer. b. If the perimeter is 72 cm, find the value of x.
There were 200 members at a skating club. Membership dropped by 30%. How many members are there now?
Answer:
140 members
Step-by-step explanation:
find 70% of 200
Circle X has a diameter of 5 inches. Circle Y has a diameter of 3 inches. Which measurement is the closest to the difference between the circumference of circle X and the circumference of Circle Y
The difference between the circumference of circle X and the circumference of Circle Y will be 6.28 inches.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference. Let d be the diameter of the circle.
The circumference of the circle will be
C = πd units
Circle X has a diameter of 5 inches. Then the circumference is given as,
⇒ π x 5
⇒ 3.14 x 5
⇒ 15.7 inches
Circle Y has a diameter of 3 inches. Then the circumference is given as,
⇒ π x 3
⇒ 3.14 x 3
⇒ 9.42 inches
The difference is calculated as,
⇒ 15.70 - 9.42 inches
⇒ 6.28 inches
The difference between the circumference of circle X and the circumference of Circle Y will be 6.28 inches.
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Why do parallel lines require the undefined terms of line and plane?.
Parallel lines require the terms line and plane because line and plane that are parallel cannot cross each other. Thus, they will never create a point of intersection. The characteristics of that parallel lines consist of lines and planes.
The characteristics of parallel lines are;
The shortest distance between parallel lines is the same at all points along the lines.
The lines are on the same plane.
As the plane is prolonged indefinitely, the lines do not intersect.
The characteristic of these geometric figures that create the different requirements would be how these undefined terms are situated. In the case of parallel lines, these are lines that would not intersect no matter how long the line is extended or whether it goes infinitely; thus, the lines lie on the same plane.
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Please help this question is on my test and if u help me and it’s right I will memorize the answer u gave me. Btw 20 points
Answer: a. w=3x+8 in b. P=24+6x in, c. P=27 in
Look at the Image Below for work.
Step-by-step explanation:
Which is the equation of the axis of symmetry of the graph of y = –3(x – 6)2 + 5?
x = –6
x = –5
x = 5
x = 6
The equation that represents the axis of symmetry of the graph of the quadratic function is the line; x = 6
What is a quadratic function?A quadratic function is a function that has 2 as the highest exponent. The shape of the graph of a quadratic function is a parabola, which is U shaped.
The equation of the axis of symmetry of the graph of y = -3·(x - 6)² + 5 is obtained as follows.
The specified equation is in the vertex form of a quadratic function, which is; f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinate of the vertex
The equation of the axis of symmetry is x = h
Comparison of the equation, y = -3·(x - 6)² + 5 and the vertex form of a quadratic equation, we get.
The vertex, (h, k) = (6, 5)
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What i the difference between 4 x 3 and 43? Prove your anwer and explain your thinking
The difference between 4 x 3 and 43 is that 4 x 3 is the mathematical operation of multiplying 4 and 3, which equals 12, while 43 is just a number.
The Mathematical OperationsThe difference between the expression "4 times 3" and the number 43 is that the former indicates the mathematical action of multiplying "4 times 3," which results in the value 12, while the latter simply represents the number itself.
To prove this, you can perform the mathematical operation of 4 x 3 = 12 and compare it to the number 43. As 12 is not equal to 43, it is clear that these are two different values.
In general, when we see a number with multiple digits, like 43, it is generally not thought of as the result of a mathematical operation. However, when we see an expression like 4 x 3, we know that it is the result of a multiplication operation and it is not just a number.
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2.Find the GCF(224,264) using Euclid division algorithm.
Answer:
GCF = 8.
Step-by-step explanation:
First, we divide 264 by 224 and we get the identity:
264 = 1*224 + 40 ( That is 264 divided by 224 goes once and the remainder is 40)
Now we divide 224 by 40 to get:
224 = 5*40 + 24
Repeating this process, we get:
40 = 1*24 + 16
24 = 1*16 + 8
16 = 2*8 + 0 <------ we stop because the remainder is 0.
So, The GCF is 8.
halp i need this asap
Answer: 126 mm^2 - C
Step-by-step explanation: Hello! The formula for area of a triangle is 1/2(b)(h). b = base and h = height. You would multiply the base and height by 1/2 because a triangle is 1/2 the size of a square. The formula for the area of a square is (b)(h), and you would have to multiply (b)(h) to find the area of a triangle with the same base and height. The base of this triangle is 28 mm, and the height of this triangle is 9 mm. Substitute 28 mm in for the base, and 9 mm in for the height. (28)x(9) = 252. Now you have to multiply 252 x 1/2. 252 x 1/2 = 126. The answer is C, 126.
railroad crew can lay 5 miles of track each day. They need to lay 140 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function.
Answer:
L = 140 - 5d
Step-by-step explanation:
To get the length left to lay you're going to have to multiply 5 and the number of days and further subtract it from 140
please help me !!! i need answers asap and i’ll give brainlist
You would need to know the values of each letter in the alphabet to prove AMNO~ATUV.
What other piece of information would you need to prove MNO~TUV?In order to prove that MNO~TUV, we would need to know the values of M,N,T,U,V,O. We would need to know the relationship between these variables in order to determine if MNO~TUV is true. For example, if MNO is equal to TUV, then MNO~TUV would be true.We would also need to know the type of relationship between the variables. For example, if the variables are related by addition, then if M + N = T + U, then MNO~TUV would be true.Additionally, we would need to know the context of the equation. For example, if the equation is related to a geometric problem, then we would need to know the type of shape and the number of sides in order to prove if MNO~TUV is true.Finally, we would need to know any other constraints or conditions that would be affecting the equation. For example, if there is a time limit, then the equation would need to be solved within that time limit in order to prove if MNO~TUV is true.To learn more about to prove MNO~TUV refer to:
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How many square inches of cloth are cut from the square (n = 3.14) if it’s 38inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The radius is given as,
r = 36 / 2
r = 18 inches
The area of the circle is given as,
A = π x (18)²
A = 3.14 x 324
A = 1,017.36 square inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
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The complete question is given below.
A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth is cut from the square?
(π = 3.14)
1,017.36 in2
1,489.24 in2
1,182.96 in2
1,276.00 in2
Solve for m.D:
D (9x-44)
X =
(6x+7)
Answer:
m∠D = 109
Step-by-step explanation:
This is a parallelogram.
In parallelograms, the opposite interior angles are congruent, so we can write the following equation to find, first value x the measure of m∠D:
9x - 44 = 6x + 7
Transfer like terms to the same side of the equation.9x - 6x = 7 + 44
Add/subtract.3x = 51
Divide both sides by 3x = 17
Now we can calculate measure of m∠D:
m∠D = 9x - 44
Rewrite equation using the value we found for x.9×17 + 44 = 109
Reason What can you conclude about the domain and the range of a relation if a vertical line at =x equals 5 passes through 2 points? 1 point? No points? Explain.
The required domain of the vertical line is {5} and the range is all real numbers.
Given that,
Domain and range of the vertical line x = 5 is to be determined.
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
Here,
We can infer that the domain of this relation can only be constrained if a vertical line at x = 5 passes through 0 locations. This function's range can only be a collection of real numbers or a constraint.
Thus, the required domain of the vertical line is {5} and the range is all real numbers.
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make a the subject of the relation S(a+b) =t
Answer:
a = [tex]\frac{t-sb}{s}[/tex]
Step-by-step explanation:
s(a + b) = t Distribute the s
sa + sb = t Subtract sb from both sides
sa + sb - sb = t - sb Simplify
sa = t - sb Divide both sides by s
a = [tex]\frac{t-sb}{s}[/tex]
How to solve triangles?.
There are several methods to solve a triangle such as SSS, SAS, ASA, and HL, using the Pythagorean theorem, the Law of Sines, and the Law of Cosines.
SSS (Side-Side-Side) Congruence: If the lengths of all three sides of one triangle are equal to the lengths of all three sides of another triangle, the two triangles are congruent.SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the two triangles are congruent.ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the two triangles are congruent.HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the two triangles are congruent.Using the Pythagorean theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.Law of Sines: states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.Law of Cosines: states that the square of the length of the hypotenuse of a triangle is equal to the sum of the squares of the lengths of the legs, minus twice the product of the lengths of the legs and the cosine of the angle between them.To learn more about the triangle, visit:
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Question
Name the included angle between JK¯¯¯¯¯¯¯¯
and KL¯¯¯¯¯¯¯¯
.
Answer:
K is the angle between JK and KL. It is called the included angle of sides JK and KL.
arthur benjamin says that the current top of the pyramid of mathematics curriculum is
What are characteristics of perpendicular lines?.
The characteristics of perpendicular lines:
1) Perpendicular lines are intersecting lines.
2) The perpendicular lines are coplanar.
3) The perpendicular intersect at a 90° angle.
4) The product of slopes of perpendicular lines is -1.
We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°
Since these lines are inclined at 90° to each other, hence they create right angles.
Perpendicular lines are intersecting lines.
Also, the perpendicular lines are coplanar.
Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.
If two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.
The product of slopes of perpendicular lines is always -1.
Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.
If line l₁ and l₂ are perpendicular to each other then m₁ × m2₂ = -1
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What kind of line is Y =- 6?.
y = -6 is a horizontal line and perpendicular to y-axis.
A horizontal line is perpendicular to the y-axis and parallel to the x-axis.
The equation for a horizontal line is y = c.
where c is constant and c constant is the y-coordinate of every point on the line.
In the equation y = -6, the constant is -6.
This means that every point on this line has an y-coordinate of -6.
Every point on the line (x, y) will have a y-coordinate of -6, while the
x-coordinate can be anything.
Therefore, y = -6 represent a horizontal straight line with perpendicular to the y-axis and parallel to the x-axis.
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Please Help. The picture of the question is below. My teacher is going to fail me if I do not get this question so please make it snappy.
The roots of a function are the points at which the graph of the function crosses the x-axis.
What are the roots of the function?The definite solutions to the equation are x = -2 and x = 1.The equation for the function whose graph is shown is y = (x+2)(x-1).The roots of the function are x = -2 and x = 1.The definite solutions to the equation are x = -1 and x = 3.The equation for the function whose graph is shown is y = (x + 1)^2 - 4.The roots of the function are x = -1 and x = 3.These are the x-coordinates of the points where the graph crosses the x-axis.They are also the solutions to the equation y = 0.The roots are also known as the zeros of the function. In other words, the roots of a function are the values of x that make the function equal to zero.For example, the equation x^2 + 3x + 2 = 0 has roots at x = -1 and x = -2. This means that when x is equal to -1 or -2, the equation's left-hand side (x2 + 3x + 2) is equal to zero.To learn more about the roots of the function refer to:
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if (-1)^n+(-1)^4n =0 then n is?
a) any positive number b) any negative number c)any odd number d)any even number
The correct statement regarding the value of n is given as follows:
c) any odd number.
How to obtain the value of n?The expression for this problem is given as follows:
(-1)^n+(-1)^4n.
The numeric value for the expression is given as follows:
0.
The n powers of -1 are given as follows:
Negative 1 if n is odd.Positive 1 if n is even.(-1)^4n will always be an even power due to the multiplication by the even number 4, hence it is positive.
As (-1)^4n is always positive and the numeric value of the expression is of zero, we have that (-1)^n is always negative one, meaning that the value of n is an odd number.
This means that option c is correct.
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How do you find the mean median and mode in class 9?.
To find the mean, median and mode add up the values and divide, the value of set in middle of the list and identify the most number of times a number is repeated.
The sum of all observations divided by the total number of observations yields the arithmetic mean of a set of data. For illustration, a cricketer's five ODI scores are as follows: 12, 34, 45, 50, 24. We compute the arithmetic mean of the data using the mean formula in order to get his typical score in a game:
Mean = Sum of all observations/Number of observations
Mean = (12 + 34 + 45 + 50 + 24)/5
Mean = 165/5 = 33
The median of the data is the value of the middle observation after the data have been arranged in either ascending or descending order.
Take these numbers as an example: 4, 4, 6, 3, 2. Let's organize these numbers ascending: 2, 3, 4, 4, 6.
Median = (n + 1)/2th observation
A data mode is the value that appears the most frequently in the provided data, or the observation with the highest frequency.
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A pizza delivery man makes $50.00 a shift. If he makes $3.00 on each shift he makes, how much money will he make if he makes 22 deliveries in one shift?
The total money to make 22 deliveries in one shift is, $116.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
A pizza delivery man makes $50.00 a shift.
And, He makes $3.00 on each shift.
Now, For the total money to make 22 deliveries in one shift is,
⇒ $50 + $3 × 22
⇒ $50 + $66
⇒ $116
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The perimeter of a rectangular garden is 4.8 meters. Its length is twice its width. How wide is the garden? (Full Answer)
Answer:
0.8 meters is the width.
Step-by-step explanation:
Answer: 0.8
Step-by-step explanation: All you have to do is set the equation up so you're looking at the length being twice the width (which in equation form would be l=2w) then you say there is two lengths, so you have 4w. Then you add the original width to the lengths (2w) so you have 6w= 0.8
Use the graph to write a linear function that relates y to x
The linear function of the graph is written as: y = 4/3x + 2.
How to Write a Linear Function that Relates y to x of a Graph?The most common form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept.
To write a linear function in this form, you will need to find the slope and y-intercept of the line.
The slope is the ratio of the change in y to the change in x, and the y-intercept is the point at which the line crosses the y-axis. Once you have these two values, you can substitute them into the equation and write the linear function.
Using the given graph:
Slope (m) = rise/run = 8/6
Slope (m) = 4/3
The y-intercept (b) = 2.
To write the linear function, substitute m = 4/3 and b = 2 into y = mx + b:
y = 4/3x + 2
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B is the midpoint of AC. AB - 6x + 1 and BC - 2x + 9. Find the length of AC
The length of AC in the line segment is 26 units.
How to find the length of a line segment?B is the midpoint of AC.
AB = 6x + 1
BC = 2x + 9
A midpoint is a point lying between two points and is in the middle of the line joining the two points.
Hence,
AB = BC
6x + 1 = 2x + 9
6x - 2x = 9 - 1
4x = 8
divide both sides by 4
x = 8 / 4
x = 2
Therefore,
AC = 2AB
AC = 2(6x + 1)
AC = 2(6(2) + 1)
AC = 2(12 + 1)
AC = 26 units
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