The quadratic function is f(x) = x² -6x + 16.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Let the standard form of quadratic function polynomial is ax² + bx + c = 0
And the zeros of the equation is (x +2) and (x-8)
Now to find the polynomial,
we multiply both zeros
(x +2)(x -8)
= x² + 2x -8x + 16
= x² -6x + 16
And the function in the standard form.
Therefore, the quadratic function is f(x) = x² -6x + 16.
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A nickle has a mass of 5 grams while a penny has a mass of 2. 5 grams. What is the mass in kilograms of a bag of coins containing 186 nickles and 72 pennies?.
Answer: 1.11 kg
Step-by-step explanation:
1 kg = 1000 grams
Nickle has a mass of 5 grams = 0.005 kg
Penny has a mass of 2.5 grams = 0.0025 kg
Now take 0.005 times 186 = 0.93 kg for 186 nickles
Next, take 0.0025 times 72 = 0.18 kg for 72 pennies
0.93 kg + 0.18 kg = 1.11 kg
So the bag is 1.11 kg
A right triangle has one side that measures 4 in. The angle opposite that side measures 80o. What is the length of the hypotenuse of the triangle? round to the nearest tenth. 3. 9 in. 4. 1 in. 22. 7 in. 23. 0 in.
The length of the hypotenuse of the triangle is 4.1.
Here we have to find the length of the hypotenuse of the triangle.
Data given:
A right triangle has one side that measures 4 in and the angle opposite that side measures 80°
To determine the length of the hypotenuse of the triangle, the trigonometry function can be used.
sinФ = perpendicular/ hypotenuse
sin80° = 4/ hypotenuse
0.98 = 4/ hypotenuse
hypotenuse = 4/ 0.98
Hypotenuse = 4.0617 inch.
Therefore the length of the hypotenuse of the triangle to the nearest tenth is 4.1
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A contractor bought 7.6 to the power of 2 ft of sheet metal. she has used 2.3 to the power of 2 ft so far and has $159 worth of sheet metal remaining. The equation 7.6x-2.3x=159 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
what does the sheet metal cost per foot?
Answer:
Step-by-step explanation:
he bought 7.6 ft2 of sheet metal He used 2.3 ft2 7.6x−2.3x= $95.40 simplify 5.3x = $95.40 divide by 5.3 to get x by itself x = 18 so each sheet of metal costs $18.00 per square foot.
PLEEASE I NEED THIS RN
Cars lose value the farther they are driven. A random sample of 11 cars for sale was taken. All 11 cars were the same make and model. A line was fit to the data to model the relationship between how far each car had been driven and its selling price.
Based on this equation, estimate The price of a car that had been driven 56000 km.
Based on this equation, estimate the price of a car that had been driven 56 thousand kilometers.
Step-by-step explanation:
A hula hoop ha a radiu of 18 inche. Madion i going to roll it down her 15 foot driveway. How many rotation will it take to get to the end?
Working on the perimeter of the hoop, The rotation by the hoop to reach the end of 15 foot is about 1.59.
What do you perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
What is the formula for the perimeter of circle?The required formula is:
[tex]P = 2\pi r[/tex]
radius = 18 inches = 1.5 foot
Perimeter = 2 * 3.14 * 1.5
=9.42
Number of rotations = 15 / 9.42
=1.59
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tommy is buying used books for school. the price of the book is 180. he uses the 30% off student discount and there is a 4% sales tax. what is the total price ?
Using percentages we know that the total price of the book that Tommy will pay is $131.04.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A% is a number that has neither dimensions nor a defined unit of measurement.
For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, we know that the price of the book is 180.
Sales tax is 4%. So, the total price:
180/100 * 4 = 7.2$ ⇒ $187.2
Now, there is a 30% discount:
187.2/100 * 30 = $56.16
⇒ 187.2 - 56.16 = $131.04
Therefore, using percentages we know that the total price of the book that Tommy will pay is $131.04.
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Solve the following linear equation for x.
5\{x}-2+\{x}=9+3\{x}+105x−2+x=9+3x+10
Answer:
x=21.
Step-by-step explanation:
x=21.
Describe the relationship between and when the two lines are perpendicular to . Also describe the relationship between and when is not perpendicular to ?
Perpendicular lines have slopes that are negative reciprocal of each other.
Parallel line have same slope.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
When two lines are perpendicular their slopes are negative reciprocal of each other and they also intersect at a point.
When two lines are parallel they have the same slope and they do not intersect.
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Sophia uses 334 cups of flour for each cake she makes. She has a 10-pound bag of flour that costs $8.79 and contains 152 quarter-cup servings.
Question 1
Part A
How many cakes can Sophia make with this flour?
Answer:
The number of cakes Sophia can make is 10.
Step-by-step explanation:
The bag of flour contains 152 quarter-cup servings. So, the quantity in t he bag has to be divided by four.
Number of cups = 152 / 4 = 38 cups
In order to determine the number of cakes she can make, divide the number of cups in the bag by the cups needed to make one cake.
38 ÷ 3 3/4
38 ÷ 15/4
38 × 4/15 = 10.1 cakes
In ΔUVW,
U
W
‾
UW
is extended through point W to point X,
m
∠
U
V
W
=
(
3
x
+
4
)
∘
m∠UVW=(3x+4)
∘
,
m
∠
V
W
X
=
(
8
x
−
12
)
∘
m∠VWX=(8x−12)
∘
, and
m
∠
W
U
V
=
(
x
+
20
)
∘
m∠WUV=(x+20)
∘
. What is the value of
x
?
x?
The value of x is 9°
What do you mean by degree?
A unit of measure is used to measure the magnitude of an angle.
1 degree equals 1/360 of a complete revolution in magnitude.
Given that:
ΔUVW with side UW extended to X
m ∠UVW = (3x + 4)°
m ∠VWX = (8x -12)°
m ∠WUV = (x + 20)°
We know that ,
Sum of angles of triangle = 180°
m ∠UVW + m ∠WUV + m ∠VWU = 180°
m ∠VWU = 180° - (m ∠UVW + m ∠WUV)
Also we know that sum of angles on a straight line
m ∠VWX and m ∠VWU are supplementary angles
m ∠VWX + m ∠VWU = 180°
m ∠VWU = 180° - m ∠VWX
m ∠VWX = (m ∠UVW + m ∠WUV)
Substituting the given values , we get
(8x -12)° = (3x + 4)° + (x + 20)°
8x - 3x - x = 4 + 20 + 12
4x = 36
x = 36/4 = 9
x = 9°.
Therefore , The value of x is 9°
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the p-value is less than the significance level. (a) we have a type i error (b) we have a type ii error (c) we may have a type i error (d) we may have a type ii error
If the p-value less than the significance level then we have a type i error.
We know that if your P-value is less than the chosen significance level then you reject the null hypothesis i,e. accept that your sample gives reasonable evidence to support the alternative hypothesis.
Im statistics, a type i error means rejecting the null hypothesis when it's actually true, while type ii error means failing to reject the null hypothesis when it's actually false.
The chance that you commit type i errors is known as the type i error rate or significance level (p-value). This number is conventionally and arbitrarily set to o.o5 or 5%. Type ii errors are like "false negatives", an incorrect rejection that a variation in a test has made no statistically significant difference.
The probability of making a type i error is represented by alpha level, which is the p-value below which you reject the null hypothesis.
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help please i need help
How do you calculate modus?
Modus is a statistical measure that is used to identify the most frequently occurring number in a set of numbers.
To calculate modus, first arrange the numbers in numerical order. Then count the number of times each number occurs in the set. The number that occurs most often is the modus. To calculate modus, first list all the numbers in the set in numerical order. The number that appears most frequently is the modus. For example, if the set of numbers is [1, 2, 3, 3, 3, 4], the modus is 3 because it appears three times, which is more than any other number in the set.
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Your uncle wants to create a dog small enough to fit into a purse. Of the hundreds of dogs on his farm, he breeds only the smallest 10% of them. He then breeds only the smallest 10% of their offspring, and continues to breed only the smallest 10% of each generation. Over 20 years, he observes that his group of dogs did become smaller (though not small enough to fit into a purse). Which line of support does he have that his dogs have evolved?.
A kind of evolution through artificial selection is the practice of choosing creatures with desired features over several generations.
The mix of alleles found in an organism is known as its genotype. A phenotype is also the culmination of all the organism's discernible traits. In artificial selection, people choose animals or plants with favored phenotypic features for reproduction.
Since the phenotype is impacted by the genotype, the process of artificial selection alters allele frequencies throughout generations, resulting in the evolution of desirable features in offspring.
In conclusion, a kind of evolution through artificial selection is the practice of selecting creatures with desired qualities over several generations.
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Two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure.
Circle O has diameter A D and radii B O and C O. Angle A O B is adjacent to angle B O C. Angle B O C is adjacent to angle C O D.
If m∠AOB = (3x − 6)° and m∠BOD = (5x + 14)°, what is the value of x?
10.0
21.5
58.5
121.5
If m∠AOB = (3x − 6)° and m∠BOD = (5x + 14)° in this pizza, the value of x is equal to: B. 21.5.
What is a supplementary angle?In Mathematics, a supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees.
Mathematically, a supplementary angle can be calculated by using this formula:
X + Y = 180
Where:
X and Y are measure of the angles subtended.
Generally speaking, we know that an entire pizza is circular in shape with an angular measure of 360°. This ultimately implies that, one-half of an entire pizza is equal to 180°, which means m∠AOB and m∠BOD are supplementary angles.
Substituting the given parameters into the formula, we have;
m∠AOB + m∠BOD = 180
3x − 6 + 5x + 14 = 180
8x + 8 = 180
8x = 180 - 8
8x = 172
x = 172/8
x = 21.5.
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Answer:
Step-by-step explanation:
B) 21.5
Find the equation of all horizontal asymptotes of the following function.
x → -∝ , f(x) → -∝ and x → ∝ , f(x) → ∝
What is a Function ?The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
What is the limit of a function ?The limit of a function in mathematics is a key idea in calculus and analysis regarding the behaviour of that function close to a specific input. Below are formal definitions that were initially developed in the early 19th century. Informally, a function f gives each input x an output f(x).
According to the given information
We are given with the function
[tex]f(x)=x^{6}+12x^{5} +26x^{4}-116x^{3}-363x^{2} +104x[/tex]
When
limit( x → ∝ ) = f(x) = ∝
limit( x → -∝ ) = f(x) = -∝
So
as x → -∝ , f(x) → -∝ and as x → ∝ , f(x) → ∝
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calculate the volume of the pyramid below. V=blank cm3. 6,4,5,6
Which One Doesn't Belong? Identify the linear expression that does not belong with the other three. Multiple choice question. A) (−5x+3)−(−7x−1) B) (−3x+3)−(−5x−2) C) (x−6)−(−x−10) D) (−7x+2)−(−9x−2)
Answer:
Step-by-step explanation:
a d c
please help!!!!!!!!!!!!!
Answer:-3
Step-by-step explanation: -3 because when you do it I really don't know how to explain it srry
you have a deck of 52 cards, and you keep taking pairs of cards out of the deck. if a pair of cards are both red, then you win that pair; if a pair of cards are both black, then i win that pair; if a pair of cards has one red and one black, then it's discarded. if, after going through the whole deck, you have more pairs than i do, then you win $1, and if i have more pairs than you do, i win $1. what is the value of this game in the long run?
The required value of this game in the long run has no value, as game will discarded because both players identical pairs.
Explain deck of 52 cards.A standard 52-card deck contains 13 positions in every one of the four French suits: clubs (♣), precious stones (♦), hearts (♥) and spades (♠). Each suit incorporates three court cards (face cards), Lord, Sovereign and Jack, with reversible (twofold headed) pictures. Each suit additionally incorporates ten numeral cards or pip cards, from one to ten.
According o question:After the blended matches are disposed of, there are an equivalent number of dark red still in the deck, so the two players will have similar number of pairs.
So, No one will win the game.
Thus, the game will discarded.
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What is the length of DE?
The value of the length of side DE is 6.3 units
How to determine the length of DE?From the question, we have the following parameters that can be used in our computation:
The triangles ABC and DBE
From the question, we can see that the following corresponding sides on the triangles:
Sides AD and DB
Sides CE and EB
This implies that these sides are congruent sides
This is evident by the marks on these sides
Also from the figure, we have that:
The endpoints of the line DE is at the midpoint of lines AB and BC
This means that we have the following equation
DE = 1/2 * AB
Substitute the known values in the above equation, so, we have the following representation
DE = 1/2 * 12.6
Evaluate the products
DE = 6.3
Hence, the length DE is 6.3 units
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suppose the exam instructions specify that at most one of questions 1 and 2 may be included among the nine. how many different choices of nine questions are there?
The number of different choices for nine questions is 384, when at most one of questions 1 and 2 may be included among the nine.
Given, the exam instructions specify that at most one of questions 1 and 2 may be included among the nine.
We have to find the number of different choices for nine questions.
Now, using the concept of Permutation and Combinations we get
There will be three cases,
Case 1 : we include question 1
Case 2 : we include question 2
Case 3 : we neither include question 1 nor question 2
Case 1 :
question 1 is included, so question 2 can not be included and remaining 7 questions have 2 choices.
Case 2 :
question 2 is included, so question 1 can not be included and remaining 7 questions have 2 choices.
Case 3 :
neither question 1 nor question 2 is included and also remaining 7 questions have 2 choices.
Total choices = 2^7 + 2^7 + 2^7
So, the number of different choices of nine questions are 384.
Hence, the number of different choices of nine questions are 384, when at most one of questions 1 and 2 may be included among the nine.
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a rock dropped into a pond causes a circular wave of ripples whose radius increases at 3 inches per second. how fast is the area of the circle of ripples expanding at the instant that the radius of the circle is 21 inches?
The area of the circle is increasing at a rate of 126π sq. inches per second
What are Derivatives?
The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
Solution:
Area of Circle = πr²
To find the rate of change we need to use Derivatives
dA/dt = 2πr * dr/dt
we know that the radius is increasing at a rate of 3 inches per second so,
dr/dt = 3 inches per second
Rate of Change = 2π*21*3 inches per second
The area of the circle is increasing at a rate of 126π sq. inches per second
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HELP PLEASE
3. Julia makes apple juice for 3 people by adding 5 cans of water to 1 cans of frozen
concentrate. If Julia needs to make apple juice for 8 people, how many cans of frozen apple
juice concentrate does she need?
0 3
0 3 1/
04
041/
For making apple juice for 8 people she needs 2.67 cans of frozen concentration
What is Proportion?
A proportion is a component, share, or quantity compared to the total. A proportion is a comparison of two integers, each representing a piece of a larger whole.
Solution:
Since, Julia needs 1 can of frozen concentration for making apple juice for 3 people
We can say for 6 people she needs 2 cans
Similarly for 8 people she needs 8/3 cans = 2.67 cans
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[extra credit] how many ways are there to create an injective function from a set of 5 elements to a set of 7 elements?
There is a total of 2520 ways to create an injective function.
What is an injective function?
A function f called an injective function (sometimes called an injection, or one-to-one function) translates different elements of its domain into different elements.
Now, we can create an injective function from a set of 5 elements to a set of 7 elements
Based on the definition of an injective function,
For 1st element, we have a total of 7 choices
For 2nd element, we have a total of 6 choices and so on.
So, total ways = 7*6*5*4*3 = 2520
Hence, 2520 ways are there to create an injective function.
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What does splitting a verb mean?
Splitting a verb represents the meaning to divide lengthwise basically by layers or along a grain.
Explanation:
Splitting a verb represents the meaning as follow :
Word split defines to divide any group into small groups or subgroups.Splitting a verb explains to divide lengthwise basically in layer form or along a grain.Splitting a large group into small groups as per the category defined .For example : Students participates in discussion divided into different groups.It makes the work easy .It represent any number or group apart forcibly.Therefore, splitting a verb represents to divide lengthwise basically layer wise or along a grain.
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Solve the inequality and graph the solution. Just say the points (x, y).
1/2x < 6
No links or I will report. Please help.
The solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
The relationship between two values that are not equal is described by inequalities. Equal does not necessarily mean unequal. The "not equal symbol" is typically used to denote that two values are not equal.
Given:
1 / 2x < 6
x < 6 × 2
x < 12
Therefore, the solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.
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George and Ringo are building frames for the backdrop in the school play. The frames include braces made by two by fours to stabilize the backdrop. The height of the backdrop and the side of the brace on the floor are the same length. What is the angle the long, slanted part of the brace makes with the side of the brace?
Answer: i need the answer
Step-by-step explanation:
HE LP
3m-8n/13
show work !
The verbal description of the algebraic expression 3m-8n/13 is; Three m minus eight n divided by thirteen
How to write algebra word problems?Algebraic word problems are defined as questions that need translation of sentences to equations and thereafter solving those equations usually having a single variable. Now, the single variable usually denotes an unknown quantity in a real-life scenario.
To solve an algebraic word problem, the following steps are taken;:
Define a variable.Write an equation using the variable.Solve the equation.If the variable is not the answer to the word problem, then use the variable to calculate the answer.Now, we want to write the verbal description of the algebraic expression given as 3m-8n/13.
This is expressed as Three m minus eight n divided by thirteen
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Complete question is;
Write a verbal expression for 3m-8n/13
A cylinder has height of 17 centimeters it volume 1921.68 cubic centimeters what is the radius cylinder
The radius of the cylinder is found to be 6 cm.
What is a right circular cylinder?A right circular cylinder is a three dimensional figure having its base and top as a circle and the height is perpendicular to circular base. The volume is given as V = πr²h.
Given that,
The height of the cylinder is 17 cm.
And, the volume is 1921.68 cm³.
Suppose the radius be r cm.
Substitute the corresponding values in the expression of volume V = πr²h as follows,
V = πr²h
=> 1921.68 = π × r² × 17
=> π × r² = 1921.68/17
=> r² = 1921.68/17π
=> r = 6
Hence, the radius of the cylinder is obtained as 6 cm.
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