Lukas graphed the system of equations shown.

2x + 3y = 2
y = A system of equations. 2 x plus 3 y equals 2. y equals StartFraction one-half EndFraction x plus 3.x + 3

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

it is y = 2x + 3

Step-by-step explanation:

i just took the test

Answer:

aka c!

Step-by-step explanation:

Answer:

1.15

Step-by-step explanation:

each peach costed 1.15

Answer: Each peach was 80 cent

Step-by-step explanation: First subtract 7.05 - 2.25 = $4.80. Next divide $4.80 by 6 which gives you 80 cent each.

The correct answers from the given lists are given as follows: Relation (a) a is (strictly) older than bA. irreflexiveB. asymmetricC. antisymmetricD. reflexiveE. transitive Relation (b) a and b have a common grandparentA.

irreflexiveB. antisymmetricC. symmetricD. reflexiveE. transitiveRelation (c) a has the same first name as bA. transitiveB. irreflexiveC. antisymmetricD. symmetricE. reflexiveRelation (d) a and b were born on the same dayA. transitiveB. reflexiveC. irreflexiveD. antisymmetricE. symmetric.

The given lists include different types of relations. Let's discuss the given relations one by one.(a) a is (strictly) older than b:This relation is irreflexive because a person can't be older than oneself. This relation is asymmetric because if a is older than b then it can't be possible that b is older than a.

This relation is antisymmetric because if a is older than b and b is older than a, then it means that a and b are the same person which is not possible. This relation is not reflexive because there is no one who is older than oneself. This relation is transitive because if a is older than b and b is older than c then a is also older than c.(b) a and b have a common grandparent:This relation is irreflexive because a person can't have a common grandparent with oneself. This relation is antisymmetric because if a has a common grandparent with b then it can't be possible that b has a common grandparent with a. This relation is symmetric because if a has a common grandparent with b then b also has a common grandparent with a. This relation is not reflexive because there is no one who has a common grandparent with oneself. This relation is transitive because if a has a common grandparent with b and b has a common grandparent with c then a also has a common grandparent with c.(c) a has the same first name as b:

This relation is transitive because if a has the same first name as b and b has the same first name as c then a has the same first name as c. This relation is irreflexive because a person can't have the same name as oneself. This relation is antisymmetric because if a has the same name as b then it can't be possible that b has the same name as a. This relation is symmetric because if a has the same name as b then b also has the same name as a. This relation is not reflexive because there is no one who has the same name as oneself.

(d) a and b were born on the same day: This relation is transitive because if a was born on the same day as b and b was born on the same day as c then a was born on the same day as c. This relation is reflexive because every person is born on the same day as oneself. This relation is irreflexive because no person is born on a different day than oneself. This relation is antisymmetric because if a was born on the same day as b then it can't be possible that b was born on the same day as a. This relation is symmetric because if a was born on the same day as b then b was also born on the same day as a.

The correct answers for each given relation are listed above.

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Solution,

Given; x^3-7x^2-x+7=0

Using factor theorem,

we have,

i)x^3-7x^2-x+7=0

let's check whether 1 is the factor of given equation or not by replacing the value of x by one..

or, 1^3-7.1^2-1+7=0

or, 1-7-1+7=0(.°. Cancellation of +1&-1 and +7&-7 in equation)

.°.0=0

which proves that 1 is one of the factor of x

therefore(x-1) is a factor of x^3-7x^2-x+7=0.

Now,

Expanding the x^3-7x^2-x+7=0 to get (x-1) as a factor...

ii)x^3-7x^2-x+7=0

or,x^3-x^2-6x^2+6x-7x+7

or,x^2(x-1) - 6x(x-1) - 7(x-1) = 0

or,(x-1) (x^2-6x-7)w = 0

or,,(x-1) (x^2-(7-1)x-7) =0

or,,(x-1) (x^2-7x + x -7) =0

or,(x-1) [x(x-7)+1(x-7)] = 0

or,(x-1) (x+1) (x-7) = 0

Either,

i) x - 1=0

.°.x = 1

And,

ii)x + 1 = 0

.°. x = -1

Or,

iii) x - 7 = 0

.°.x =7

Hence, the required value of x are -1 ,+1 & 7.

Answer:

(-7, -3)

Step-by-step explanation:

The expression x³ + 3x² - 10x + 24 cannot be factorized

From the question, the polynomial is given as

x3+3x2−10x+24

Rewrite the polynomial properly

So, we have the following representation

x³ + 3x² - 10x + 24

Next, we represent the above expression on a graph

From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -5.569

This implies that the expression cannot be factored

So, we cannot further rewrite the given expression

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Answer:

--------------

Use the sum of the first n terms formula:

We are given:

First, let's find n using the nth term formula:

Now, we can find the sum using the formula:

The sum of the geometric series is 186.

Setting the discussion topic, or assisting the group in doing so, encouraging an open dialogue, including everyone, asking questions or making suggestions to enhance the conversation, summarizing or elaborating on key arguments and ideas, and concluding the meeting are among them.

Few Steps which is required during the group discussions:

1. Welcome to the audience

Try to introduce oneself before starting the group conversation before you speak about the subject.

2. Speak with clarity and ease

Try not to stutter or stammer as you introduce yourself and the subject. Present your ideas and speak with great assurance and ease.

3. Provide an intriguing viewpoint on the subject.

Make sure to start the group discussion with a traditional interpretation of the subject.

4. Keep the information current.

You must at the very least have a fundamental understanding of the subject. You can spend a moment getting familiar with the subject before beginning if necessary. Make sure you don't give unclear or extra information.

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The maximum monthly profit Mt. Nittany is  $23,100 and, for Happy Valley Rentals,  monthly profits will be approximately $23,100.

(a) To find the number of apartments Mt. Nittany should rent out each month to maximize profits, we need to find the vertex of the quadratic function P(x) = -7x^2 + 980x - 10900.

The x-coordinate of the vertex is given by -b/2a, where a = -7 and b = 980. So, x = -b/2a = -980/(2*(-7)) ≈ 70.

The maximum monthly profit is obtained by plugging this value of x into P(x), giving P(70) = -7(70)^2 + 980(70) - 10900 ≈ $23,100.

(b) Similarly, for Happy Valley Rentals, we need to find the vertex of the quadratic function P(x) = -7x^2 + 980x - 10900 when they manage 50 apartments.

The x-coordinate of the vertex is again given by

b/2a, where a = -7 and b = 980, but now we have x = -b/2a = -980/(2*(-7)) ≈ 70.

The maximum monthly profit is obtained by plugging this value of x into P(x), giving P(70) = -7(70)^2 + 980(70) - 10900 ≈ $23,100.

Therefore, both companies should rent out 70 apartments each month to maximize their profits, and their maximum monthly profits will be approximately $23,100.

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\(\Large\texttt{Answer}\)

\(\bold{n-13}\)

\(\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}\)

\(\Large\texttt{Process}\)

⇨ Again letting n be the number

\(\bold{n}\)

⇨ Subtract 13 from n

\(\bold{n-13}\)

*unlike addition, the order DOES matter, because

\(\bold{n-13\ne 13-n}\)

Hope that helped

Answer:

x=8

Step-by-step explanation:

12÷2=6

48÷6=8

hope this helps and have a greate Day ❤

Answer: x

=

2

y

=

3

Step-by-step explanation:

You can re-arrange equation

x

+

y

=

5

to get

x

=

5

−

y

and then substitute this into the equation

2

x

+

y

=

7

to get

2

(

5

−

y

)

+

y

=

7

.

This can then be simplified to

10

−

y

=

7

and so

3

−

y

=

0

which means

y

=

3

.

Substitute

y

=

3

into

x

+

y

=

5

and you get

x

+

3

=

5

, therefore:

Answer:

X=4 Y=3

Step-by-step explanation:

Step: Solvex+y=7for x:

x+y=7

x+y+−y=7+−y(Add -y to both sides)

x=−y+7

Step: Substitute−y+7forxin2x−y=5:

2x−y=5

2(−y+7)−y=5

−3y+14=5(Simplify both sides of the equation)

−3y+14+−14=5+−14(Add -14 to both sides)

−3y=−9

−3y

−3

=

−9

−3

(Divide both sides by -3)

y=3

Step: Substitute3foryinx=−y+7:

x=−y+7

x=−3+7

x=4(Simplify both sides of the equation)

Answer:

80 percent of people don't like the turkey sandwich because 80 plus 20 equals 100 so think about it as a subtraction equation

Answer: 80% of students don't like turkey sandwiches.

Answer:

Ryan swam further by 5/6

Step-by-step explanation:

34 2/3 = 104

52 5/8 = 104 5/6

104 5/6 - 104 = 5/6

Answer

A little over 16.

Step-by-step explanation:

If you convert 5 liters to milli-liters, you get 5,000. You then divide 5,000 by 300 and get 16.67.

Hope this helps!

Answer:

Explanation:

Given that:

Simplifying, we have:

Therefore, the last option is the correct answer

Answer:

B

Step-by-step explanation:

I’m smart

Answer:

Two-column, paragraph, and flowchart proofs are three of the most common geometric proofs.

Step-by-step explanation:

An example for geometry would be A triangle is a 3-sided shape, and the sum of its 3 interior angles is 180˚ A square, rectangle, or quadrilateral are 4-sided shapes, and the sum of their 4 interior angles is 360˚ Other polygons like the pentagon, hexagon, heptagon, the octagon has 5, 6, 7, 8 sides respectively and varying angles.

There is a 0.022 percent chance that a student may receive a quiz grade of 95 or above.

The z-score formula is as follows:

z = (95-85)/8.0

= 1.25

Using the z-score table, calculate the probability:

P(z >= 1.25)

= 0.022

The z-score formula can be used to determine the likelihood that a student would receive a quiz grade of 95 or higher. The data set's mean and standard deviation are considered in the formula. The mean score on the quiz in this instance is 85, and the standard deviation is 8.0. By deducting the mean from the desired score (95), the z-score can be computed by dividing the result by the standard deviation (8.0). The z-score in this instance is 1.25.  The likelihood that a student will receive a quiz grade of 95 or higher can be determined using the z-score table. The likelihood of a z-score of 1.25 or higher is 0.022, according to the table. This indicates that there is a 0.022 percent chance that a student will receive a quiz grade of 95 or above.

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Jackie would see a total of 81 clovers on the ninth day.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of letters or symbols to represent unknown values or variables, and the use of mathematical operations such as addition, subtraction, multiplication, and division to manipulate these variables and solve equations.

Algebra is used to solve a wide variety of problems in many fields, including science, engineering, economics, and finance. It is also a fundamental tool in mathematics education, providing a basis for higher-level math courses such as calculus and linear algebra.

In algebra, equations are used to represent relationships between variables, and the goal is to find the values of the variables that satisfy the equation. Algebraic expressions, which are made up of variables and mathematical operations, can be simplified using various techniques such as factoring, combining like terms, and using the distributive property.

On the fifth day, Jackie would see nine new clovers (7 + 2) for a total of 25 three-leaf clovers. On the sixth day, she would see 11 new clovers (9 + 2) for a total of 36 three-leaf clovers. On the seventh day, she would see 13 new clovers (11 + 2) for a total of 49 three-leaf clovers. On the eighth day, she would see 15 new clovers (13 + 2) for a total of 64 three-leaf clovers. On the ninth day, she would see 17 new clovers (15 + 2) for a total of 81 three-leaf clovers. Therefore, Jackie would see a total of 81 clovers on the ninth day.

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A structural break occurs when we see A. an unexpected shift in time-series data.

It is the change in a time series's data-generating mechanism, it is a phenomenon that occurs when a significant event or structural shift in the economy alters the underlying data-generating mechanism. A structural break can happen for several reasons, including natural catastrophes, changes in economic policy, new inventions, and other reasons that alter the way the data is generated.

In the presence of a structural break, we can't assume that the relationships between variables before and after the break are the same. The primary objective of identifying structural breaks in the time-series is to detect changes in the behavior of the series over time, such as changes in the variance of the series, changes in the mean of the series, and changes in the covariance of the series. So therefore the correct answer is A. an unexpected shift in time-series data, the structural break occurs.

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We first convert from degrees to radians multiplying by π/180:

θ = 1000° × π/180 = 17.45 rad

The radius is:

r = d/2 = 4 in /2 = 2 inch

So, The distance traveled is given by the product of the angle in radians and the radius. This is:

d = θr = (17.45 rad)(2 inch) = 34.9 inch

Answer: ok what do you need help with

Step-by-step explanation:

i need the material to help you

Answer:

Step-by-step explanation:

i got you step 1 step 2 step 3 step 4 answer is c

Using the given points, find the slope:

 Slope Equation: m = Δy/Δx

 m = (4 - 0)/(8 -(-8)) ⇒ Solve

 m = 4/16 ⇒ Simplify

 m = 1/4

Using the point-slope equation, solve for the line:

 Point-Slope Equation: y - y1 = m (x - x1)

 Using Point 1 (-8, 0):

 y - 0 = 1/4 (x - (-8))

 y - 0 = 1/4 (x + 8) ⇒ Distribute

 y = 1/4x + 8/4 ⇒ Simplify

 y = 1/4x + 2

Answer: y = 1/4x + 2

Answer:

First finding the slope and the y-intercept. Then we can write the equation in slope-intercept for which is

y = mx+b where m is the slope and b is the y-intercept.

Given two points (0,8) and (-8,-4). (0,8) is the y intercept which is the value of b. Since we have found the y-intercept, To find slope of these two points.

m = (y2-y1)/(x2-x1)

m = (-4-8)/(-8-0)

m = (-12)/(-8)

m = 12/8

m = 3/2

So, the equation is y = 3/2(x)+8 and has been fully reduced.

Answer:

y = x^4

Step-by-step explanation:

First, swap the variables y = x^(1/4) becomes x = y^(1/4).

Therefore, x^4 = y

Answer:

AAS

ANGLE ANGLE SIDE.........

Answer:

20 1/2

Step-by-step explanation:

because area equals length times width

Answer and Step-by-step explanation:

First, let's split the figure into two common shapes that we know the area formula for.

The top shape can become a triangle, while the bottom shape can become a rectangle.

We know the area of a triangle is

\(A = \frac{bh}{2}\)

and the area of a rectangle is

A = lw

Where:

A = Area

b = Base length (length)

h = Height

l = Longer length of a side

w = Smaller length of a side

Area of a Triangle:

b = 3

h = 3

A = \(\frac{3 * 3}{2}\)

A = 4.5

Area of a Rectangle:

w = 3

l = 8

A = 3 × 8

A = 24

Now we add together the areas to get the area of the figure.

Area of the Figure:

A = 4.5 + 24

A = 28.5

The area of the figure is 28.5 \(units^{2}\).

#teamtrees #PAW (Plant And Water)

Answer:

(a) 7.5 seconds

(b) The horizontal distance the package  travel during its descent is 1737.8 ft

Step-by-step explanation:

(a) The given function for the height of the object is s = -16·t² + v₀·t + s₀

The initial height of the object s₀ = 900 feet

The initial vertical velocity of the object v₀\(_y\) = 0 m/s

The time it takes the package to strike the ground is found as follows;

0 = -16·t² + 0×t + 900

900 = 16·t²

t² = 900/16 = 62.25

t = √62.25 = 7.5 seconds

(b) Given that the horizontal velocity of the package is given as 158 miles/hour, we have

158 miles/hour = 231.7126 ft/s

The horizontal distance the package  covers in the 7.5 second of vertical flight = 231.7126 ft/s × 7.5 s = 1737.8445 feet = 1737.8 ft to one decimal place

The horizontal distance the package  travel during its descent = 1737.8 ft.