you would need a function to determine whether to use a formula for 1 or 2 nights or a formula for more than 2 nights
T(x)={a if x <_ 2, b if x > 2}
if it's 2 nights or less use option a, a = 75x
if its longer than 2 days use option b, b= 50x + 50
Answer:
t = 75x {x ≤ 2}
t = 150 + 50x {x > 2}
Step-by-step explanation:
A hotel chain charges $75 per night for first two nights.
If the number of nights of the stay are x then charges for x nights
= 75x where x ≤ 2
If the stay is for than 2 nights then charges for x nights
= Charges for two first 2 nights(@$75 per night) + charges for other than initial 2 nights (@$50 per night)
= (75×2) + 50x where x > 2
Therefore total cost of the hotel if represented by t then the function will be
t = 75x {x ≤ 2}
t = 150 + 50x {x > 2}
Find the equation of the quadratic function with zeros 10 and 14 and vertex at (12, -8).
Is it possible for a line segment to have more than one bisector?
Yes, it is possible to have more than one bisector in a line segment.
Bisector is a line that divides a line or an angle in to two equivalent parts. There are two types of Bisectors based on what geometrical shape it bisects.
Bisector of a Line Angle BisectorIn general 'to bisect' something means to cut it into two equal parts. The bisector is the one that doing the cutting process.
With a line bisector, we cut a line segment into two equal parts with another line - the bisector. Just imagine the line PQ is being cut into two equal lengths (PF and FQ) by the bisector line AB.
Whenever AB intersects at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types.
For obvious reasons, the point F is called the midpoint of the line PQ,
Law of sines:
Triangle ABC has measures a = 2, b = 2, and m∠A = 30°. What is the measure of angle B?
15°
30°
45°
60°
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
ΔABC has measures a=2, b=2, m∠A=30⁰
As we know the "Law of sines " i.e.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\[/tex]
so, we put the given values in above formula:
[tex]\frac{2}{\sin 30\textdegree}=\frac{2}{\sin B}\\\\\implies \sin 30\textdegree=\sin B\\\\\implies B=30\textdegreee[/tex]
Hence, Second option is correct.
What number must be added to the expression below to complete the square?
x^2+3x
A. 9
B. 9/4
C. 3/2
D. 3
I think it is c or D but it should be C
hope that help
[I don't think it did lol ]
BMK
Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks?
Final answer:
Carol practices for 8.5 hours per week, so in a 5-week period, she would practice for a total of 42.5 hours.
Explanation:
The student asked how many hours Carol practices her culinary skills in a 5-week period, if she practices for 17 hours in a 2-week period. To find the answer, we calculate how many hours Carol practices per week by dividing the total hours she practices in two weeks by two. Then we multiply the weekly hours by the number of weeks in question, which is five.
The calculation is as follows: Carol practices for 17 hours / 2 weeks = 8.5 hours per week. Then, 8.5 hours/week x 5 weeks = 42.5 hours in total for a 5-week period.
What is the area of the region completely bounded by the curve y=-x^2+x+6?
To find the area of the region completely bounded by the curve y=-x^2+x+6, you can integrate the equation with respect to x and evaluate it between the x-values where the curve intersects the x-axis. By solving the quadratic equation -x^2+x+6=0, you can determine the x-values. Then, evaluate the definite integral between these x-values to find the area.
Explanation:The area of the region completely bounded by the curve y=-x^2+x+6 can be found by integrating the equation with respect to x and evaluating it between the appropriate bounds. The integral of the given equation is ∫(-x^2+x+6) dx. To find the area, we need to find the definite integral between the x-values where the curve intersects the x-axis. First, set the equation equal to zero and solve for x:
-x^2+x+6=0
This quadratic equation can be factored as: (x-2)(x+3). Therefore, the curve intersects the x-axis at x=2 and x=-3.
By evaluating the definite integral between x=-3 and x=2, we can find the area of the region:
Area = ∫-32 (-x^2+x+6) dx
Integrating this equation will give you the area of the region bounded by the curve y=-x^2+x+6.
Linda is putting money into a savings account. She starts with $450 in the savings account, and each week she adds $70 .
Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Linda has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 19 weeks.
Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using proper notation to represent each direction of motion. Part II: What is the velocity vector of the plane? Part III: What is the ground speed of the plane?
The velocity of the plane is 200 mph due north and the velocity of the wind is 23 mph due west. The velocity vector of the plane is 200 mph due north minus 23 mph due west. The ground speed of the plane can be found using the Pythagorean theorem.
Explanation:Part I: The velocity of the plane can be represented as 200 mph due north, and the velocity of the wind can be represented as 23 mph due west.
Part II: To find the velocity vector of the plane, we subtract the velocity of the wind from the velocity of the plane. The resultant velocity vector of the plane is 200 mph due north minus 23 mph due west.
Part III: The ground speed of the plane is the magnitude of the resultant velocity vector of the plane. We can calculate it using the Pythagorean theorem: ground speed = square root of (200^2 + 23^2).
What is a rule for the total cost of the tickets ? Give the rule in words and as a algebraic expression
What is the arc length of a circle that has a 6-inch radius and a central angle that is 65 degrees? Use 3. 14 for pi and round your answer to the nearest hundredth
place a square on a coordinate graph and label each vertex with variables. prove that the diagonals of a square are congruent and perpendicular to each other.
Final answer:
To prove that the diagonals of a square are congruent and perpendicular, label the vertices of a square on a coordinate grid and calculate the slopes and lengths using the slope formula and distance formula respectively. The diagonals have slopes of +1 and -1, proving they are perpendicular, and they have equal lengths, proving they are congruent.
Explanation:
To prove that the diagonals of a square are congruent and perpendicular, we place a square with its vertices on a coordinate grid and label each vertex with variables.
Let's consider a unit square where c = 1 for simplicity, which means the length of each side is 1 unit. Place the square so that one vertex is at the origin (0,0), and label the vertices A(0,0), B(1,0), C(1,1), and D(0,1).
The diagonal AC will have endpoints at A(0,0) and C(1,1), and diagonal BD will have endpoints at B(1,0) and D(0,1). The slope of diagonal AC is (1 - 0)/(1 - 0) = 1, and the slope of diagonal BD is (1 - 0)/(0 - 1) = -1. Since the product of their slopes is -1 (1 * -1 = -1), this proves that they are perpendicular to each other.
To show they are congruent, we calculate their lengths using the distance formula: the distance between two points (x1,y1) and (x2,y2) is √[(x2 - x1)² + (y2 - y1)²]. Applying this to AC and BD reveals both lengths to be √[(1-0)² + (1-0)²] = √[1 + 1] = √2, proving the diagonals are congruent.
One bundle contains 500 $20 bills. what would be the total value of 44 bundles
which other angle must also measure 130°
opposite angles are identical so if angle 1 = 130
than angle 3 is also 130 degrees
Answer:
Angle 3
Step-by-step explanation:
we know that
[tex]m<1=m<3[/tex] -----> by vertical angles
we have
[tex]m<1=130\°[/tex]
therefore
[tex]m<3=130\°[/tex]
What is the area of the composite figure?
(6π + 4) cm2
(6π + 16) cm2
(12π + 4) cm2
(12π + 16) cm2
The area of the composite figure is 6π + 16 cm²
Composite Figure:Composite figures are composed of different dimensional figures. The area of a composite figure is the sum of the whole 2 dimensional figures that forms the composite figure.
Therefore, the figure above has 3 semi circle and 1 square.
Therefore, the area can be calculated as follows;
area = sum of the area of the 3 semi circle + area of the squarearea = 1 / 2 πr² + 1 / 2 πr² + 1 / 2 πr² + L²
area = 3 / 2 (πr²) + L²
where
r = 2 cm
L = 4 cm
Therefore,
area of the composite figure = 3 / 2(π × 4) + 4²
area of the composite figure = 3 / 2(4π) + 16
area of the composite figure = 6π + 16 cm²
learn more on composite figures here: https://brainly.com/question/1639299
Daria applied a transformation to triangle ABC to obtain triangle A′B′C′. The two triangles are not congruent. Which of the following could be the transformation Daria applied?
Help? @texaschic101
Parabola and its vertex
Multiply 3 [ 1 5 -5 6 0 0 ]
Simply multiply the number outside the brackets with each one inside it..
3 [ 1 5 -5 6 0 0 ]
3 x 1 = 3
3 x 5 = 15
3 x -5 = -15
3 x 6 = 18
3 x 0 = 0
3 x 0 = 0
[ 3 15 -15 18 0 0 ]
[ 3 15 ]
[ -15 18 ]
[ 0 0]
The answer is B and I hope I explained this well for you.
What is the equation of the line that is parallel to y=-2/3x+4 and that passes through (–2,–2)?
Answers
-
-
-
y=-2/3x-4/3
y=-2/3x-10/3
y=-2/3x-2/3
y=-2/3x-17/4
The equation of the line parallel to y=-2/3x+4 and passing through (-2, -2) is y = -2/3x - 10/3.
Explanation:To find the equation of a line parallel to y = -2/3x + 4 and passing through the point (-2, -2), we need to use the fact that parallel lines have the same slope. The given equation has a slope of -2/3, so the parallel line will also have a slope of -2/3. Using the point-slope form of a line, we can write the equation as:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Plugging in the values, we have:
y - (-2) = -2/3(x - (-2))
Simplifying the equation, we get:
y - (-2) = -2/3(x + 2)
y + 2 = -2/3x - 4/3
y = -2/3x - 4/3 - 2
y = -2/3x - 4/3 - 6/3
y = -2/3x - 10/3
Learn more about equation of a line here:https://brainly.com/question/33578579
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What equation is solved by the graphed systems of equations? Two linear equations that intersect at the point negative 1, negative 4.
To solve this problem, we have to manually solve for the value of x for each choices or equations. The correct equation will give a value of -1 since the linear equations intersects at point (-1, -4).
1st: 7x + 3 = x + 3
7x – x = 3 – 3
6x = 0
x = 0 (FALSE)
2nd: 7x − 3 = x – 3
7x – x = 3 – 3
6x = 0
x = 0 (FALSE)
3rd: 7x + 3 = x − 3
7x – x = - 3 – 3
6x = -6
x = -1 (TRUE)
4th: 7x − 3 = x + 3
7x – x = 3 + 3
6x = 6
x = 1 (FALSE)
Therefore the answer is:
7x + 3 = x − 3
In this exercise, we are going to solve using our knowledge of systems and in this way we will find that the equation that satisfies the points.
As we know that the equation that will satisfy will have to have the values of X=-1, we will solve each one of the alternatives as:
First equation is:[tex]7x + 3 = x + 3\\6x = 0\\x = 0[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
second equation is:[tex]7x - 3 = x - 3\\7x- x = 3- 3\\6x = 0\\x = 0[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
third equation is:
[tex]7x + 3 = x − 3\\6x = -6\\x = -1[/tex]
fourth equation is:[tex]7x − 3 = x + 3\\7x – x = 3 + 3\\6x = 6\\x = 1[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
See more about systems at brainly.com/question/7589753
I SERIOUSLY NEED HELP HERE!!!!!
PLEASE SOMEONE HELP ME ON THIS!!!!!
NEED MAJOR HELP HERE CALCULATOR QUIT ON ME!!!!!!!
scientific calculator of a TI83 or TI84 ( does that help?)
Use the data below to find the correlation coefficient. (Remember to choose DiagnosticOn on your calculator.)
x y
270 70
230 75
250 68
310 82
285 80
275 76
281 73
267 81
252 72
246 79
The correlation coefficient is _____. Round to the nearest thousandth.
THESE ARE MY OPTIONS:
a. 0.438
b. 0.192
c. 0.5
d. 0.720
The length and width of a rectangle are 4.9^9 cm and 5.3^3 cm, respectively. What is the approximate area of the rectangle, using only positive exponents?
A) 5^6cm^2
B) 4^6cm^2
C) 5^12cm^2
D) 4^12cm^2
The expression 4 square root of 81^3 can be rewritten as_____.
A. 81^3/4
B.81^4/3
C. 81^12
D. 81^1/12
Answer:
81^1/12
HAVE A GREAT DAY
The expression ''4 square root of 81³'' can be rewritten as,
⇒ [tex]81^{\frac{3}{4} }[/tex]
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression to write is,
⇒ 4 square root of 81³
Now, It can be written as;
⇒ 4 square root of 81³
⇒ [tex]\sqrt[4]{81^{3} }[/tex]
By rule of exponent we get;
⇒ [tex]81^{\frac{3}{4} }[/tex]
Thus, The expression ''4 square root of 81³'' can be rewritten as,
⇒ [tex]81^{\frac{3}{4} }[/tex]
Learn more about the mathematical expression visit:
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If f(x) is an odd function, which statement about the graph of f(x) must be true?
It has rotational symmetry about the origin.
It has line symmetry about the line y = –x.
It has line symmetry about the y-axis.
It has line symmetry about the x-axis.
An odd function, by definition, is a function that is symmetric about the origin.
An even function, by definition, is a function that is symmetric with respect to the y-axis.
Since the question says that f(x) is an odd function, it has rotational symmetry about the origin. First option is correct.
ANSWER: symmetric about the origin.
Answer:It has rotational symmetry about the origin.
Step-by-step explanation:
An odd function : is a function that is symmetric about the origin.
An even function : is a function that is symmetric with respect to the y-axis.
Since , f(x) is an odd function, it has rotational symmetry about the origin.
its meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
Therefore, It has rotational symmetry about the origin.
Find the equation for the tangent line of f(x)=−3x2−7x+3 at x=3.
The equation of a line is 2(y+1)=10x+3
The y-intercept of the line is ___, and the slope of the line is ___.
Answer: The answer is 0.5 and 5.
Step-by-step explanation: The given equation of the line is
[tex]2(y+1)=10x+3.[/tex]
We are to find the y-intercept and the slope of the given line.
We know that the slope-intercept form of a line is given by
y = mx + c, where, 'm' is the slope and 'c' is the y-intercept of the line.
We have
[tex]2(y+1)=10x+3\\\\\Rightarrow 2y+2=10x+3\\\\\Rightarrow 2y=10x+3-2\\\\\Rightarrow 2y=10x+1\\\\\Rightarrow y=5x+0.5.[/tex]
Therefore, c = 0.5 and m = 5.
Thus, the y-intercept of the line is 0.5 and the slope is 5.
2x-5y=-6; 2x-7y=-14
Alex has been serving 2/3 cup of lemonade to each student. If he has 1 1/3 cups of lemonade left, how many students can still get lemonade?
Question 2 options:
1
2
3
0
Expand (2x-3y)^4 using Pascal's Triangle. Show work
Answer:
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
Step-by-step explanation:
(2x - 3y)^4
Fifth line on a Pascal Triangle
1, 4, 6 4, 1
(1) 2x^4
2^4 = 16
2x^4 = 16x^4
16x^4
(4) 2x^3 (-3y)^1
2^3 = 8
-3^1 = -3
8 times -3 times 4 = -96
-96x^3y
(6) 2x^2 (-3y)^2
2^2 = 4
-3^2 = 9
4 times 9 times 6 = 216
216x^2y^2
(4) 2x^1 (-3y)^3
2^1 = 2
-3^3 = -27
2 times - 27 times 4 = -216
-216xy^3
(1) (-3y)^4
-3^4 = 81
81y^4
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
Solve by factoring and list only the positive solution: 2x2 - 5x = 88
Temperature dropped from 11 below zero to 4 below zero how much did the temperature drop