Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.
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Mamas bakery just opened and is currently selling only two types of pastry. Each month mamas bakery will add two more types of pastry to their menu. Suppose this pattern continues. What algebraic expression can be used to find the number of pastries offered after any given number of months? How many pastries will be offered in one year?
The number of pastries will be offered in one year could be 26 and the algebraic expression could be x = 2 + 2y
What is Arithmetic progression ?
Arithmetic progression could be defined as the sequence of number where the difference between two consecutive number is same.
Given,
Mamas bakery just opened and is currently selling only two types of pastry.
Each month mamas bakery will add two more types of pastry to their menu.
let the number of pastries be x.
let y be the given number of pastries.
Hence the algebraic expression could be
x = 2 + 2y
Number of pastries will be offered in one year could be
x = 2 + 2 * 12
x = 26
Hence, the number of pastries will be offered in one year could be 26 .
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Write the phrase as an expression.
7 fewer than a number s
An expression is
Answer:
u just do a variable minus 7
s-7=
Find the point(s) on the surface at which the tangent plane is horizontal.
z = xy + 1 x + 1 y
The point(s) on the surface at which the tangent plane is horizontal are (0, 0, 1).
To find the point(s) on the surface at which the tangent plane is horizontal, we need to find the points at which the partial derivatives of z with respect to x and y are both equal to 0. This means we need to solve the system of equations:
∂z/∂x = 0 ∂z/∂y = 0Solving this system of equations yields x = 0, y = 0, and z = 1. Therefore, the point(s) on the surface at which the tangent plane is horizontal is (0, 0, 1).
To understand why solving the system of equations yields the points for which the tangent plane is horizontal, it is important to understand what the partial derivatives represent. The partial derivative of z with respect to x is the rate of change of z with respect to x, and similarly for y.
When the partial derivatives are both equal to 0, it means that the rate of change of z with respect to x and y is 0, which implies that the tangent plane is horizontal.
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Please Answer This For Me<33
Answer:
a) 4.2 - 2.8 = 1.4
b) 72.1 - 45.6 = 26.5
c) 82.2 - 41.3 - 29.2 = 11.7
d) 17.1 - 11.7 - 0.8 = 4.6
e) 29.2 - 12.5 - 0.9 = 15.8
f) 21 - 14 = 7
g) 71 - 37 - 18 = 16
h) 50 - 19 - 8 = 23
i) 92 - 57 - 16 = 19
j) 44 - 18 - 9 = 17
Lesson 1. 12
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth.
Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point.
Assume at x= O the buoy is at normal ocean depth.
Find the following:
Period =
Equation of the mideline:
Amplitude =
Maximum =
Minimum =
For the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
What is the sine function?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Asin(Bx)+C is the usual sine function formula.
A buoy bobs 6 meters up and down.
That is, the amplitude of the buoy shifts by 6 meters both vertically and horizontally.
A=6 Amplitude
The x-axis distance that constitutes one complete oscillation is known as the period.
We are aware that it takes a buoy 10 seconds to go from its greatest position to its lowest point (half oscillation).
20 seconds make up the complete oscillation period.
⇒ 20 (B) = 2π
B=2π /20
= π/ 10
Given that the buoy is 10 meters under the ocean's surface, C equals –10.
Using the formula's whole range of values:
⇒y = 6sin ( (π/ 10) x ) - 10
The midline is the initial point.
x=0 is the first point.
⇒y=6sin(0)-10
y= -10
The line is drawn from the origin at y = -10.
Either the highest or smallest value is at the second point.
Therefore, (5,-4) and (15, -16.)
Therefore, for the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
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Complete question:
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
PLEASE HELP!!! I need these answers for Geometry.
Answer: x=(y+9)5−32 simplified
Step-by-step explanation:
What does Scrooge see out of the window when Marely leaves?
(A Christmas Carol) (it was an English question)
Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.
What is the ghost?Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.
Here, we have,
Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.
Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.
Therefore, option B is the correct option.
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N plus 75 used in a real world sentence.
Answer:
Laura has "n" amount of nickels. She receives 75 more from her grandmother.
Explanation:
(If this is not what the question meant, please let me know!)
Because the question is asking us to write a sentence for an addition problem, we need to write a sentence that involves two amounts of one thing being combined, in this case nickels.
Need this question quick 20 points
On solving the provided question we can say that the rectangular form of the equation is y = -1
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Ф = [tex]\pi[/tex]/2
y = - 1
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which statement correctly compares the function shown on this graph with
the function y = 4x + 2?
A. The function shown on the graph has a smaller rate of change, but
a higher starting point.
O B. The function shown on the graph has a greater rate of change, but
a lower starting point.
C. The function shown on the graph has a greater rate of change and
a higher starting point.
D. The function shown on the graph has.a omaller rate of change and
a lower starting point.
B. The function shown on the graph has a smaller rate of change, but a higher starting point.
What is rate of change in linear graph?Rate of change = slope of a linear graph.
Given the linear function, [tex]y=4x+2[/tex] , the rate of change here is represented by the slope of the line, which is 4.
Let's find the rate change of the function represented on the graph using slope formula:
Rate of change = [tex]\frac{y2-y1}{x2-x1}[/tex]
Use coordinates of any two points on the line. Let's take,
[tex](0,4)= (x1,y1)\\(1,7)=(x2,y2)[/tex]
Rate of change = [tex]\frac{7-4}{1-0} = 3[/tex]
Rate of change of the linear function of the graph = 3.
Thus the function on the graph has a smaller rate of change, than the function, y = 4x + 2.
The starting value of a function is the y-intercept, that is, the value of y, when x = 0. It is the point at which the line intercepts the y-axis.
The starting value of the linear function, y = 4x + 2 is 2.
The starting value of the function on the graph is 4. At this point, x = 0.
Thus, the function on the graph has a higher starting point.
The statement that correctly compares the function shown on this graph with the function y= 4x+2 is:
B. The function shown on the graph has a smaller rate of change, but a higher starting point.
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Thirty people are waiting in line at the cinema. Alex counts 13 people in front of him. Gina counts 21 people between her and Dana. What is the least possible number of people between Dana and Alex
Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are:
20.
What is the number line called?In advanced mathematics, the number line can be called as a real line or real number line, formally defined as the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one.
Why is number line important?A number line is useful because it acts as a visual math aid. It can support teachers and parents as they teach children how to count and write numbers. It's also a tool that can help build understanding behind adding, subtracting, multiplying, and dividing numbers.
Let's assume that Gina is standing on first number while Dana on the last. Hence the total number of people in the line are: n= 23.Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are: (n-2) = 20.
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Find the 66th term of the arithmetic sequence 25, 10, -5, ...
On solving the provided question, we can say that - The provided arithmetic sequence's 66th term is -950.
Arithmetic sequence is what?An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word.An ordered group of integers with a shared difference between each word is known as an arithmetic sequence.
The given arithmetic sequence is,
25, 10, -5, .....
The sequence's initial word, a, equals 25, while the common difference, d, equals -15.
Use the formula nth term of arithmetic series = a+ (n-1)d to determine the 66th term of the sequence.
66th term =
[tex]25 + (66-1)(-15)\\ = 25 + 65× (-15)\\ = 25 - 975\\ = -950\\[/tex]
The 66th term of the arithmetic sequence is -950.
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__________ are designed so that the objective of the test is not apparent to the test taker. A. Projective tests B. Source errors C. MMPI tests D. 16PF tests Please select the best answer from the choices provided A B C D
Projective tests are created so that the test taker cannot tell what they are testing for.
What is Projective tests?Projective tests are created so that the test taker cannot tell what they are testing for.A personality test used in psychology is called a projective test. This kind of test provides answers to confusing situations, phrases, or visuals. Unconscious motivations or attitudes are disclosed by asking the person a question or giving them a stimulus that is unclear. Projective exams are designed to enlighten individuals about sentiments, wants, and conflicts that are not readily apparent to them. Psychoanalysts try to find unconscious feelings that might be behind a person's troubles in life by evaluating responses to ambiguous stimuli. Projective testing is mostly used to evaluate personality functioning.To learn more about Projective tests refer to:
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Approximately 297 million guests visit the 400 American amusement parks annually, and take 1.7 billion safe rides. The National Safety Council publishes a report titled "Fixed-Site Amusement Ride Injury Survey" for the International Association of Amusement Parks and Attractions. The number of injuries per million patron-rides, X, has a Poisson distribution with parameter 0.8. In one million patron-rides, what is the probability that there are
a) No injuries?
b). More than TWO injuries?
The probabilities are given as follows:
a) No injuries: 0.4493 = 44.93%.
b) More than two injuries: 0.0474 = 4.74%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.The mean for this problem is of:
[tex]\mu = 0.8[/tex]
The probability of no injuries is of P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
The probability of more than two injuries is of:
P(X > 2) = 1 - P(X <= 2)
In which:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)
Hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]
[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]
Then:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4493 + 0.3595 + 0.1438 = 0.9526.P(X > 2) = 1 - P(X <= 2) = 1 - 0.9526 = 0.0474.More can be learned about the Poisson distribution at https://brainly.com/question/7879375
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A box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. Assume the plain donuts are identical, and the chocolate donuts are identical. How many visually distinct arrangements of the donuts are there?
If a box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. The number of visually distinct arrangements of the donuts that are there is: 60.
How to find the number of visually distinct arrangements?Using this formula to find the number of visually distinct arrangements of the donut that are there.
Number visually distinct arrangements = Box of donuts!/ Plain donuts! × Chocolate donuts! × Blueberry donut!
Let plug in the formula
Number visually distinct arrangements = 6!/ 3! × 2! × 1!
Number visually distinct arrangements = 720/ 6 ×2 × 1
Number visually distinct arrangements = 720 /12
Number visually distinct arrangements = 60
Therefore the number of Number visually distinct arrangements is 12.
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c=⟨–5,8⟩ and d=⟨7,4⟩, find –4c–4d.–4c–4d=
A cube with volume 8 cubic centimeters is cut in half by a plane which contains two edges of the cube. What is the area of the rectangle formed by the intersection of the plane and cube ? express your answer in simplest radical form.
In simplest radical form as A = 22 = 4 cm2
The formula for the volume of a cube is V = a3, where a is the length of each of the cube's sides. In this case, we know that the volume of the cube is 8 cm3, so a3 = 8. When we take the cube root of 8, we get that a = 2 cm.
Therefore, the area of the rectangle formed by the intersection of the plane and cube is A = 2*2 = 4 cm2. This can also be expressed in simplest radical form as A = 22 = 4 cm2.
To calculate this step by step, we first use the formula V = a3 to find the length of each side of the cube. We plug in 8 cm3 for V and solve for a.
V = a3
8 cm3 = a3
Taking the cube root of both sides gives us:
a = ∛8
a = 2 cm
Next, we use the formula for the area of a rectangle, A = l*w, where l is the length and w is the width. We know that the length and width of our rectangle are both equal to 2 cm.
A = l*w
A = 2*2
A = 4 cm2
This can also be expressed in simplest radical form as A = 22 = 4 cm2.
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Find all the real and complex solutions of the polynomial equation. Be sure to show ALL work (4 points):
The real and complex solutions of the polynomial equation are 2,-3i and 3i
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is x³-2x²+9x-18
Factor out x² from x³-2x² which becomes x²(x-2)
Factor out 9 from 9x-18 which becomes 9(x-2)
x³-2x²+9x-18
x²(x-2)+9(x-2)
Factor out common term x-2
( x²+9)(x-2)=0
x²+9=0
x=-3i and 3i
x-2=0
x=2
Hence, the real and complex solutions of the polynomial equation are 2,-3i and 3i
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Question 1
Solve for x.
x(x + 6) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
X =
|
X =
Answer:
[tex]x=-6, 0[/tex]
Step-by-step explanation:
Using the zero-product property, we know that [tex]x=0[/tex] or [tex]x+6=0[/tex].
This means [tex]x=-6, 0[/tex].
What type of triangle is a 50/50 80?
50-50-80 is a Isosceles acute triangle.
An isosceles acute triangle is a triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement. One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.
Properties of Isosceles Acute Triangle
It is easy to point to an isosceles acute triangle if we know its properties. The properties of the isosceles acute triangle are noted below:
Two angles and two sides opposite those angles are equal.All three angles are less than 90° (acute angles).The summation of all the interior angles is 180°.Read more about the Isosceles acute triangle.:
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Jo ha three metal block. The weight of each block i the ame. When he weighed one block againt 8 gram, thi i what happened
The block weighed 8 grams. The other two blocks average have weighed the same amount as the first block, so they also weighed 8 grams each.
1. Joe has three metal blocks.
2. The weight of each block is the same.
3. Joe weighed one of the blocks against 8 grams.
4. The block weighed 8 grams.
5. The other two blocks must have weighed the same amount as the first block, so they also weighed 8 grams each.
Joe had three metal blocks that all weighed the same. He weighed one of the blocks against 8 grams, and it weighed exactly 8 grams. This meant that the other two blocks must also have weighed 8 grams each, since the weight of all three was the same. Joe was able to determine the weight of all three blocks with just one measurement.
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A sphere is inscribed in a cone with height 4 and base radius 3. What is the ratio of the volume of the sphere to the volume of the cone
The radius of the sphere 1.5 units
The volume of the cone is pi (3)^2 *4 / 3 units^3 = 12pi units^3
The volume of the sphere is (4/3)pi (1.5)^3 units^3 = 4.5 units^3
So ratio of the volume of the sphere to the cone is :
4.5 pi / 12 pi = 4.5 / 12 = (9/2) / (24/2) = 9 / 24 = 3 / 8
What is radius?In geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere. Look at the image of a circle given below showing the relationship between radius and diameter.To learn more about diameter refer to:
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Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting a green marble.
0.27
0.33
0.40
0.73
0.27 is the experimental probability of selecting a green marble.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Michael has a bag of marbles.
The frequency of selecting each color is recorded
Outcome Frequency
Green 4
Black 6
Orange 5
The total number of marbles are 4+6+5=15 marbles.
We need to find the experimental probability of selecting a green marble.
We need to select green marbles (4) from total marbles (15).
Probability=4/15=0.266=0.27
Hence, 0.27 is the experimental probability of selecting a green marble.
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Enter your answer and show all the steps that you use to solve this problem in the space provided in the triangle there is a 72° c113° write a list of steps that are needed to find the measure of b
The steps for measuring the angle b is shown below, <b= 41.
What is Exterior angle Property?If a triangle side is created, the outside angle that results is equal to the sum of the two opposite internal angles.
If an equivalent angle is measured at each triangle vertex, the exterior angles always add up to 360 degrees.
Given:
exterior angle = 113
and, opposite interior angle =72
Using Exterior angle property we have
72 + b = 113
Subtract 72 from both side
72 + b -72 = 113 -72
b = 113- 72
b = 41
Hence, the measure of b is 41 degree.
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50% of 188 is equal to what number?
Answer:
Step-by-step explanation:
a.50%=[tex]\frac{1}{2}[/tex]
b.so 50% of 188 means 188·[tex]\frac{1}{2}[/tex]=94
answer is 94
Mason has 2 1/2 cups of peanut
butter. He is making peanut butter
sandwiches. If he uses 1/8cup of
peanut butter in each sandwich,
how many sandwiches can he
make?
Help
Answer:
Mason can make 20 sandwiches.
Step-by-step explanation:
2 1/2 ÷ 1/8 = 20Which expression has a coefficient of 4?
The required expression that has the coefficient 4 is 4x⁵. Option B is correct.
What is the expression?The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.
here,
Since the question seems to be incomplete,
A standard question can be given as,
Among the following option find the expression that has a coefficient of 4.
(a) 2x + 1
(b) 4x⁵
(c) ax⁶
(d) 7x²
Since the coefficient is the value present at the prefix of the variable term,
So the variable term that holds the coefficient 4 is 4x⁵.
Thus, the required expression is 4x⁵. Option B is correct.
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Someone please answer... In 2010, the population of a city was 59,000. From 2010 to 2015, the population grew by 7.3%. From 2015 to 2020, it fell by 5.3%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
what is the quotient of 6x^3+2x-x/x where x≠0
Answer:
6[tex]x^{2}[/tex] + 1
Step-by-step explanation:
[tex]\frac{6x^{3}+ 2x-x }{x}[/tex] combine 2x -x = x
[tex]\frac{6x^{3} + x}{x}[/tex]
[tex]\frac{x(6x^{2} + 1) }{x}[/tex] the x's cancel out
6[tex]x^{2}[/tex] + 1
A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use. In Plan B, the customer pays a monthly fee of $26.30 and then an additional 4 cents per minute of use. For what amounts of monthly phone use will Plan A cost no more than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.
34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
In Plan A, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use
20+7m
In Plan B, the customer pays a monthly fee of $26.30 and then an additional 4 cents per minute of use
26.3+4m
We need to find the amounts of monthly phone use will Plan A cost no more than Plan B
20+7m<26.3+4m
7m-4m<26.3-20
3m<6.3
m<2.1
Hence, 34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.
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