Using the Factor Theorem, the function factored into linear factors is given as follows:
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
-9 is a zero of f(x), hence [tex]x_1 = -9[/tex] and:
3x³ + 23x² - 35x + 9 = (x + 9)(ax² + bx + c)
ax³ + (b + 9a)x² + (9b + c)x + 9c = 3x³ + 23x² - 35x + 9
The coefficients are given as follows:
a = 3.9c = 9 -> c = 1.b + 9a = 23 -> b = -4.Hence:
3x³ + 23x² - 35x + 9 = (x + 9)(3x² - 4x + 1)
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
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Myra blended 24 oz of orange sherbet when making 5/8 of smoothie. How many ounces of orange sherbet are needed for one batch?
Answer: To find out how many ounces of orange sherbet are needed for one batch of smoothie, you can use the proportion of orange sherbet to the total amount of smoothie.
24 oz of orange sherbet / 5/8 of smoothie = x oz of orange sherbet / 1 batch of smoothie
To solve for x, you can cross-multiply and simplify:
(24 oz of orange sherbet) * (1 batch of smoothie) = (5/8 of smoothie) * x oz of orange sherbet
24 * 1 = 5/8 * x
24 = 5/8 * x
By multiplying both sides by 8/5,
x = 24 * 8/5
x = 38.4 oz
So, 38.4 ounces of orange sherbet are needed for one batch of smoothie.
Step-by-step explanation:
evaluate function expressions
If you answer first with the correct answers ill mark you brainlist:)
All the correct values are,
a)⇒ f (0) = - 1
b)⇒ f (1) = 1
c)⇒ f (-1) = - 3
d)⇒ f (a) = 2a - 1
e)⇒ g (0) = - 4
f)⇒ g (-2) = 0
g)⇒ g (3) = 5
h)⇒ g (t) = t² - 4
i)⇒ f (a+5) = 2a + 9
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The function are,
⇒ f (x) = 2x - 1
⇒ g (x) = x² - 4
Now, We can find all the values by substituting as;
a) f (0)
⇒ f (x) = 2x - 1
Put x = 0;
⇒ f (0) = 2×0 - 1
⇒ f (0) = - 1
b) f (1)
⇒ f (x) = 2x - 1
Put x = 1;
⇒ f (1) = 2×1 - 1
⇒ f (1) = 1
c) f (-1)
⇒ f (x) = 2x - 1
Put x = -1;
⇒ f (-1) = 2×-1 - 1
⇒ f (-1) = - 2 - 1
⇒ f (-1) = - 3
d) f (a)
⇒ f (x) = 2x - 1
Put x = a;
⇒ f (a) = 2×a - 1
⇒ f (a) = 2a - 1
e) g (0)
⇒ g (x) = x² - 4
Put x = 0;
⇒ g (0) = 0² - 4
⇒ g (0) = - 4
f) g (-2)
⇒ g (x) = x² - 4
Put x = -2;
⇒ g (-2) = -2² - 4
⇒ g (-2) = 4 - 4
⇒ g (-2) = 0
g) g (3)
⇒ g (x) = x² - 4
Put x = 3;
⇒ g (3) = 3² - 4
⇒ g (3) = 5
h) g (t)
⇒ g (x) = x² - 4
Put x = t;
⇒ g (t) = t² - 4
i) f (a+5)
⇒ f (x) = 2x - 1
Put x = a + 5;
⇒ f (a+5) = 2×(a + 5) - 1
⇒ f (a+5) = 2a + 10 - 1
⇒ f (a+5) = 2a + 9
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a) Write 5.1 x 10¹ as an ordinary number.
b) Work out the value of (1.7 x 10¹) × (8.5 × 10-²)
Give your answer in standard form.
On solving the provided question we can say that ordinary number the answer is 1.495 x 10^0
What is an ordinary number?An ordinary number, also known as a standard form number or a decimal number, is a number that is written in the familiar base-10 format, with a whole number part and a fractional part separated by a decimal point.
A) 5.1 x 10¹ as an ordinary number is 51.
B) To work out the value of (1.7 x 10¹) × (8.5 x 10-²), we first need to multiply the two numbers:
(1.7 x 10¹) × (8.5 x 10-²) = 1.7 x 8.5 x 10¹ x 10-² = 14.95 x 10-1
To express the answer in standard form, we need to move the decimal point to the left so that there is only one non-zero digit to the left of it. 14.95 x 10-1 is 1.495 x 10^0. So the answer is 1.495 x 10^0
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Solve for y,
-2y+9= -1
oy = -5
y = -4
O y = 4
O y = 5
Answer:
Step-by-step explanation:
-2y + 9 = -1
Adding 2y to both sides:
9 = 2y - 1
Adding 1 to both sides:
10 = 2y
Dividing both sides by 2:
y = 5
Therefore, the value of y that makes the equation true is y = 5
Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-angled triangle. Give your answer in centimetres (cm) to 1 d.p. 4.8 cm 2 cm
The length of hypotenuse = 5.2 centimeters.
What is right angle and Pythagorean theorem?The triangle that has at least one angle 90 degrees is called right angle triangle. The largest side length of a right triangle is termed as hypotenuse.
The Pythagorean theorem is applicable for right-angled triangle. The theorem stated that the square of hypotenuse is equal to the sum of the square of the remaining two side lengths. If a right-angled triangle has hypotenuse H and other two side length b and o respectively, then H² = b² + o².
What is the length of hypotenuse in this right-angled triangle?Assume this right-angled triangle is named as ABC, AC is the hypotenuse and AB and BC is the other sides.
As AB = 2 cm and BC = 4.8 cm
then according to the Pythagorean theorem AC² = AB²+ BC²
AC²= 2² + 4.8²
Hypotenuse AC = 5.2 centimeter.
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There are 16 ounces in 1 pound, so the expression z/16, where z represents the number of ounces, can be used to find the number of pounds for any given number of ounces. How many pounds are in 40 ounces?
Answer:
40 ounces is equal to 2.5 pounds------------------------
Use the given expression z/16, substitute z with 40 and calculate:
z/16 = 40/16 = 2.5 poundsThree cups of soup and two sides of rice cost $15.85. Six cups of soup and four
sides of rice cost $31.70. Find the cost of 1 cup of soup and 1 side of rice.
The cost of 1 cup of soup is, $5.28 and 1 side of rice is $7.92.
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;
Three cups of soup and two sides of rice cost $15.85.
And, Six cups of soup and four sides of rice cost $31.70.
Let cost of 1 cup of soup = x
And, The cost of 1 side of rice = y
Here, Three cups of soup and two sides of rice cost $15.85.
Hence, We can formulate;
⇒ 3x + 2y = 15.85 .. (i)
And, Six cups of soup and four sides of rice cost $31.70.
Hence, We can formulate;
⇒ 6x + 4y = 31.70 .. (ii)
By equation (i) and (ii);
⇒ x = $5.28
⇒ y = $7.92
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A month later, Mayor Bruns (from Exercise 5-23) picks up the morning edition of the city's leading newspaper, the Sun-American, and reads an exposé of unemployment fraud. In this article, the newspaper claims that out of every 15 unemployment beneficiaries, the probability that four or more have jobs is 0.9095, and the expected number of employed beneficiaries exceeds 7. You are a special assistant to Mayor Bruns, who must respond to these claims at an afternoon press conference. She asks you to find the answers to the following two questions: (a) Are the claims of the Sun-American consistent with each other? (b) Does the first claim conflict with the opinion of the mayor's assistants?
Answer:
Follow me if this helped you
Step-by-step explanation:
a)The claims of the Sun-American are not consistent with each other. The probability that four or more out of every 15 unemployment beneficiaries have jobs is 0.9095, but the expected number of employed beneficiaries exceeds 7, which is more than 4.
WHAT IS THE NUMBER BOND FOR 540 + 280 NUMBER BOND
541 + 279 = 820 is the number bond for the expression 540 + 280.
What is number bond?A number bond is a simple addition sum that has become so familiar to a child that they can recognise it and complete it almost immediately, with recall as automatic as that of an entry from a multiplication table in multiplication. Number bonds are used in the teaching of mathematics at the primary school level.
When given the other two numbers, a child who "knows" this number bond should be able to instantly fill in any one of these three numbers if it were missing, without having to "work it out." Number bonds are frequently taught in sets whose sums are common round numbers like 10 or 20.
We can find the number bond by simply adding 1 to first term and subtracting 1 from 2nd term.
540 + 280 = 820
(540 + 1) + (280 -1) = 820
541 + 279 = 820
Thus, 541 + 279 = 820 is the number bond for 540 + 280.
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Convert into symbolic form.
“Michael does not have the time or money to complete the project.” Each phrase should be declared as a symbol before you put it into symbolic form. (P, Q, R, S)
The statement can be represented symbolically as: (P) ∨ (Q) → (S)
How to represent a statement in symbolic form?
Representing a statement in symbolic form involves using logical symbols and logical operators to create a logical expression that captures the meaning of the statement. Here are some common symbols and operators used in symbolic logic:
Negation (¬ or ~): used to represent "not", e.g. ¬P means "not P"Conjunction (∧): used to represent "and", e.g. P ∧ Q means "P and Q"Disjunction (∨): used to represent "or", e.g. P ∨ Q means "P or Q"Implication (→): used to represent "if-then", e.g. P → Q means "if P, then Q"Bi-Implication (↔): used to represent "if and only if", e.g. P ↔ Q means "P if and only if Q"Parentheses: used to group symbols and indicate the order of operations, e.g. (P ∧ Q) ∨ R means "either (P and Q) or R".To put the statement "Michael does not have the time or money to complete the project" into symbolic form, we first need to identify the key phrases and declare them as symbols. Here are a few possible ways to do this:
(P) Michael does not have the time
(Q) Michael does not have the money
(R) Michael does not have the time or money
(S) Michael can not complete the project
We can put them in different ways, depending on the statement you want to make.
Then the statement can be represented symbolically as:
(P) ∨ (Q) → (S)
This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.
Alternatively, we can use the following representation
(R) → (S)
This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.
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.En el piso de una sala cuadrada
hay un total de 49 mosaicos grandes,
todos del mismo tamaño
Cuantos mosaicos ,colocado uno
a continuación del otro, completan la
longitud de una cuadrícula
de los lados
de la sala?
The number of mosaics tiles in each side of the square floor is 7 tiles.
What is a square ?Since a square has four equal sides and four equal angles, it is a regular quadrilateral. It may alternatively be explained as a rectangle with two neighboring sides that are of equal length.
A square can have many different characteristics. The following list includes some of a square's key characteristics.
A quadrilateral having four sides and four vertices is called a square.The square's four sides are equal to one another.A square's diagonals are parpendicular to one another.Each vertex of a square has a 90° internal angle.360° is the total of all interior angles.A square's diagonals are 90 degrees apart from one another.The diagonals are all the same length.A square is also referred to as a parallelogram since its sides are parallel.In a square, the diagonals are longer than the sides.The square is divided into two similar triangles by the diagonals.The total number of mosaic tiles = 49
Let the lenght of each side of the floor be x
Therefore,
x² = 49
⇒ x = 7
The number of mosaics tiles in each side of the floor is 7 tiles.
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3. Higher Order Thinking Kim makes a bar
graph to record votes for the choice of a
class pet. Each grid line represents 4 votes.
Fish got 8 votes. The bar for hamster is
3 grid lines higher than the bar for fish.
How many votes did hamster get?
Therefore , the solution to the given problem of unitary method comes out to be Hamster got 20 votes.
What does unitary method mean?The unit method is a way of problem-solving where you first calculate the amount of a single item, then multiple that value to get the answer. Simply expression, a single system value is extracted from a specified multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and inverse are equivalent. (Linear Algebra, Mathematical Interpretation, Mathematics of Matrix or Operators).
Here,
4 votes are represented by each grid line. then, four votes per grid.
Fish received 8 votes.
There are three more grids for hamsters than for fish.
votes per grid times the number of grids
So,
the number of fish grids is 4.
2 grids are needed for fish.
There are 3 more grids for hamsters than for fish. As a result, 2 + 3 = 5 grids for the hamster.
Grids times votes per grid divide the total number of ballots.
As a result, there are 20 votes or hamsters (5 x 4).
Hamster has 20 votes as a result.
Therefore , the solution to the given problem of unitary method comes out to be Hamster got 20 votes.
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A geometric sequence begins with −4, 20, −100, 405, … Which option below represents the formula for the sequence? f(n) = −5(−4)n−1 f(n) = −4(−5)n−1 f(n) = −5(−4)n f(n) = −4(−5)n
The equation that represents the formula for the sequence is f(n) = −4(−5)^n−1
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
The ratio of any term to the one that precedes it should be the same for all terms. If they are all the same, then r, the common difference, is that value
The nth term of a geometric sequence is given as
a(n) = ar^n -1
where a is the first term which is -4
r is the common ratio = 20/-4 = -5
Therefore f(n) = -4(-5)^n -1
Therefore the expression that represents the formula of the sequence is f(n) = -4(-5)^n - 1
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A contractor purchases 5 dozen pairs of padded work gloves for $70.40. She incorrectly calculates the unit price as $13.44 per pair for the expense report. What is the correct unit price? What is the error?
The unit price of the gloves is $ 1.173.
Finding the Unit price of the gloves:To find the Unit price of the gloves find 1 dozen gloves by dividing the total price by the number of dozens. From that find the unit price by dividing a dozen gloves price by 12 as 1 dozen = 12.
Here we have
A contractor purchases 5 dozen pairs of padded work gloves for $70.40.
She incorrectly calculates the unit price as $13.44 per pair for the expense report.
Cost of 1 dozen pairs of padded work gloves = $70.40/5
Cost of 1 dozen pairs of padded work gloves = $ 14.08
Here 1 dozen = 12 gloves
Let 'x' be the Unit price
=> 60x = 70.40
=> x = 70.40/60
=> x = 1.173
Therefore,
The unit price of the pair of gloves is $ 1.173.
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I HAVE AN HOUR TO DO THIS HELP
Answer:
Step-by-step explanation:
Your first answer is correct. Good job
Your second answer is correct. good job
Your last answer is correct. good work
Which of the following equations represent the graph that is shown on the coordinate plane below?
Answer:
the coordinate plane has a big example
Step-by-step explanation:
HELP PLEASE DUE IN 10 MINUTES 20 POINTS
A. AC=0.8, mLA'= 53°
B. AC = 1, mLA' = 37°
C. A'C'= 1, mLA = 7.4°
D. AC = 25, mLA' = 37°
After dilatation, the length of AC will be 20. The angle A’ will then be measured at 37°.
What exactly is dilation?Dilation is the process of expanding the size of something without changing its shape. The size of the item can be increased or decreased depending on the scale factor.
We have done so.
AABC is dilated by a factor of four to provide AA’B’C’.
The triangle A’B’C’ is formed by diluting the triangle ABC by a factor of four.
Then the length of AC after dilatation. We now have
A’C’ = scale factor multiplied by AC
A’C’ = 4 x 5
A’C’ = 20
The angle A’ will then be measured.
Dilation has no influence on the angle.
∠A = ∠A’ = 37°
As a result, the proper selection.
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jonah is playing a game with his frind rita.there using a spiner below for there game.If jonah spins the spinner twice ,which of these reprensents the possible outcomes of his spin
It all depends on how the spinner is set up, what symbols or numbers it contains and how it is marked.
What is symbol?Symbols are an important part of human communication. They are used to convey a specific meaning, feeling, or idea. Symbols can be visual, such as an object or gesture, or verbal, such as a word or phrase. Symbols are used to represent a concept or idea, often in a way that is easier or more efficient than using words.
The possible outcomes of Jonah's spin could be any of the following:
1. Two of the same numbers, e.g. both 7s or both 11s.
2. Two different numbers, e.g. 8 and 4.
3. One number and a symbol, e.g. 5 and the star.
4. Two symbols, e.g. the heart and the diamond.
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In a survey, a group of students were asked to name their favorite type of game. There were 5 students who chose “other” types of games.
The percentage of students who chose " other " types of games, from the group of students was 25 %
How to find the percentage ?The percentage of students who chose " other " types of games can be found by the formula:
= Number of students who chose " other " types of games / Total number of students x 100 %
Number of students who chose " other " types of games = 5 students
Total number of students = 20 students
The percentage is:
= 5 / 20 x 100 %
= 0. 25 x 100%
= 25 %
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The full question is:
In a survey, a group of 20 students were asked to name their favorite type of game. There were 5 students who chose “other” types of games. What is the percentage of those students who chose " other "?
A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. A = [3 7 3 3 6 4 0 -4 4 3 10 0] ~ [1 0 0 2 1 0 4 4 0 -2 -3 0] Find a basis for Col A. (Simplify your answer. Use a comma to separate answers as needed.)
The basis for Col A is linearly independent.
When are two matrices called being equal?Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.
We are given that;
A = [3 7 3 3 6 4 0 -4 4 3 10 0] ~ [1 0 0 2 1 0 4 4 0 -2 -3 0]
Now,
To find a basis for Col A, we need to find the columns of A that correspond to the pivot columns of the echelon form. The pivot columns are the columns that have a leading 1 in a row. In this case, the pivot columns are the first, second, and fourth columns. Therefore, a basis for Col A is given by the vectors in those columns of A. We can write them as:
3303,76−410,3440
These three vectors are linearly independent and span Col A, so they form a basis for Col A.
Therefore, by matrices the answer will be linearly independent.
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jon paid $200 for 8 classes at gold dawn yoga studio. the cost, y, is rorportional to the number of classes purchased, x. graph three points and find the slope
The slope of the given data is 25.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Jon paid $200 for 8 classes at gold dawn yoga studio.
the cost, y, is proportional to the number of classes purchased, x
The slope will be cost of each class
200/8=25
So the equation will be y=25x
25 is the slope.
Hence, the slope of the given data is 25.
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A woodpecker can live 27 years, a swallow 3 times less, and a crow lives 45 years longer than a swallow. How many years can a crow live?
Answer:
54 years
Step-by-step explanation:
If we want to know how to solve for the number of years a crow can live, we can use this equation:
(27 ÷ 3) + 45 =?
We can first solve for 27 divided by 3.
(27 ÷ 3) + 45 =?
9 + 45 =?
Now solve for 9 plus 45:
9 + 45 = 54
Therefore, if a woodpecker can live 27 years, a swallow 3 times less, and a crow 45 years longer than the swallow, we can say that a crow can live for 54 years.
PLEASE I NEED HELP PLS THANK U SM MATH
In the given circle graph, central angle of people like to travel by boat is 72°.
What is circle graph?Circle graphs also known as pie charts are one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information. It is used to visualize information and data.
Given that, A travel magazine surveyed 500 of its adult readers about their favorite ways to travel.
The circle graph below shows that 125 people like to travel by train, 275 people like to travel by airplane, and 100 people like to travel by boat.
In a circle graph, the whole circle which subtends a 360-degree angle at the center is broken into different.
Central angle of people like to travel by train:
125/500 ×360°
= 90°
Central angle of people like to travel by airplane:
275/500 ×360°
= 198°
Central angle of people like to travel by boat:
100/500 ×360°
= 72°
Therefore, in the given circle graph, central angle of people like to travel by boat is 72°.
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Evaluate The Following Integral If R [0, 1] X [0, 1]. 3yexy DA
Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
What is integral ?
An integral is a mathematical concept that represents the area under a curve, or the accumulation of a quantity over a given interval. Integrals are a fundamental concept in calculus, which is the branch of mathematics that deals with the study of rates of change and accumulation. In other words, an integral can be thought of as the sum of an infinite number of infinitesimal "slices" of the quantity being measured, over a given interval. Integrals can be used to solve a wide variety of problems.
The integral is evaluated as follows,
∫[0,1]∫[0,1] 3yxy dydx
= 3∫[0,1] yxy dxdy
= 3 * (1/4) * ∫[0,1] x dxdy
= 3 * (1/4) * (1/2) * x^2 dy
= 3 * (1/4) * (1/2) * (1/3) = 3/24
Hence , Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
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A depth finder shows that the water in a certain place is 620 feet deep.The difference between d,
the actual depth of the water, and the reading is |d-620] and must be less than or equal to 0.05d. Find the minimum and maximum values of d, to the nearest tenth of a foot.
Answer:
Step-by-step explanation: ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠆⠒⠒⢄⡂⠄⠀⠀⠀⠐⡓⢶⠶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠠⣔⣛⡉⠀⠬⣈⠀⢛⣬⡳⣽⣺⢿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠤⣫⢌⠳⣍⠶⣻⡵⣯⢿⣯⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⠀⠀⠀⠀⢠⡀⠀⠀⡠⢀⠰⢌⡳⣭⢓⣮⢻⣵⣻⣽⡿⣯⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣩⣙⣉⣅⣤⢶⣶⣟⣷⣧⣬⡐⣎⢳⡱⣏⡿⣼⣳⢷⣻⢾⣽⣻⣿⢾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣯⣿⣷⣯⣞⣳⢯⡷⣯⢿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢻⣭⢻⡽⢯⣟⣾⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠚⡴⣛⣮⠳⡍⣿⣞⣿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢟⠫⡝⢩⢿⣿⢿⠿⡹⠄⡀⠀⠀⠀⢳⡹⣎⡗⡨⣽⣾⣹⣿⣟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣘⠲⡌⢎⠱⣼⠇⣾⣛⣎⠳⡡⠒⠁⠀⠀⢉⠆⡵⣎⢷⡳⣝⣶⢫⣿⡾⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡞⠃⢌⣴⡿⠏⢸⡛⡴⢊⢧⡑⢌⠐⢠⡐⢠⢚⡵⣫⢞⡵⢫⠜⡻⣾⡽⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡶⠋⢀⣼⡿⣋⡞⢀⡡⢚⡕⡫⢆⠴⣨⡉⠲⢌⢲⣋⢾⣱⢫⠔⣫⢞⣵⣺⢿⣽⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣴⡿⣣⢟⡵⠂⢄⢣⢏⡼⡑⢎⡰⢆⡱⡙⣎⠳⣜⢯⣞⡱⢪⠵⣚⡷⣯⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⢜⢫⢃⠷⡡⢏⠆⡁⡌⢊⠖⠡⡙⢌⠲⢌⡲⢹⠴⣛⡼⣳⢎⡷⣡⢫⣝⡾⣽⡿⣷⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠠⠉⠀⠂⠉⠐⠡⠪⠔⡡⣜⢢⠌⡀⠀⠂⡜⢪⡱⣋⢾⣱⢫⡗⣿⣲⠱⣏⡾⣙⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠌⢣⡜⢬⣑⠢⣅⢣⢵⣩⢖⢧⡻⣼⣳⣭⢟⣼⢻⡽⣾⣯⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣐⣈⣅⣩⣝⢢⣝⣣⢞⡳⢌⡓⢮⢖⡭⣚⡵⢧⣟⡾⣝⡾⣯⣟⣷⡿⣽⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠲⣉⠓⢎⡳⡱⣞⢿⣾⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣦⡀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠰⠉⠰⠠⢍⠢⡵⡹⣬⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⣿⣷⣄⠀⠀⠀⠀
⣤⣶⣿⡿⠛⠁⠀⣾⣿⡿⠿⠿⠟⠟⠻⢛⠛⠛⠉⠉⠂⠁⠀⠀⠰⢡⠙⡬⢳⡱⢯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⣿⣧⡄⠀⠀
⣿⣿⣯⣄⡀⠀⢼⣿⣷⣶⣶⣤⣤⣤⣀⣄⣀⣀⡀⡀⢀⡀⠅⢢⣑⢪⡱⡭⢧⣻⡽⣞⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣷⣄
⠀⠉⠻⢿⣿⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⢷⣎⣧⢳⡹⡷⣭⢿⡽⣾⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣶⣾⣿⣿⣿⠟
⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣳⡾⣭⢷⣻⢽⣹⢯⣟⣿⡿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡿⠋⠉⠀⠀⠀⠀
⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣟⢷⣫⣽⢳⡝⡾⣭⣟⣾⢿⣽⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀
⠀⠙⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣛⠶⣙⢮⣓⢮⢳⡙⢴⣋⢾⡽⣿⣻⣾⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⡳⣌⠿⣱⡮⡝⣎⢧⣛⢦⣯⢿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠙⠛⠙⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⣞⣿⣟⣷⣽⣞⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣶⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣙⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Daniel takes out a 40-year $150,000 loan from his bank in 2020. The
quadratic equation that approximates the year/loan balance relationship is
y = -120x^2 - 2500x + 80,000, where x is the number of years and y is the
balance. In what year, will his loan balance be $21,480?
So on solving the provided question we can say that - the equation will be y = -120x^2 - 2500x + 80,000; x = 0 so, y = 80000
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.
y = -120x^2 - 2500x + 80,000
x = 0
so, y = 80000
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8.Gracie Lou sold 15x + 4xy in inventory at her Dance Store on Saturday. Mariella
sold -15x + 3x - 2xy on Sunday. What is their combined inventory for the weekend?
Here we are given that Gracie sold 15x + 4xy in her inventory and Mariella sold -15x +3x -2xy on weekends. We need to find combined inventory.
For that simplify add both the expressions as ,
15x + 4xy + (-15x) + 3x - 2xy
15x + 4xy - 15x + 3x - 2xy
Group like terms ,
(15x + 3x - 15x ) + (4xy - 2xy)
simplify,
3x + 2xy [ required answer]
And we are done!
Graph the linear inequality y < 3x using slope-intercept form.
Given inequality:
y < 3xTo graph it first, consider line:
y = 3xFind two points on the line.
x = 0 ⇒ y = 3*0 = 0, so the point is (0, 0)x = 1 ⇒ y = 3*1 = 3, the point is (1, 3)Now, plot the two points.
Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.
The last step, shade the area below (to the right) the line. Below the line because 'y <' means 'y-values less than' which appears below the line.
Answer:
See attachment.
Step-by-step explanation:
Given linear inequality:
[tex]y < 3x[/tex]
When graphing inequalities, temporarily replace the inequality sign for the equals sign:
[tex]\implies y=3x[/tex]
Find two points on the line by substituting two values of x into the equation:
[tex]x=0 \implies y=3(0)=0 \implies (0, 0)[/tex]
[tex]x=1 \implies y=3(1)=3 \implies (1,3)[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given linear inequality:
Plot points (0, 0) and (1, 3).Draw a dashed straight line through the points.Shade under the dashed line.When performing a hypothesis test on two dependent samples, the variable of interest is
Choose one answer.
a. the data that is the same in both samples.
b. all of the combined data.
c. the absolute value of the differences that exist between the matched-pair data.
d. the differences that exist between the matched-pair data.
When performing a hypothesis test on two dependent samples, the variable of interest is
d. the differences that exist between the matched-pair data.
In a hypothesis test on dependent samples, the variable of interest is the difference between the two samples. The test compares the means of the two samples and checks whether the difference is significant or not. The sample data are matched-pair, meaning that each data point in one sample corresponds to a specific data point in the other sample.
The variable of interest is the difference between the two matched data points, this difference is also known as the dependent variable.
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