Describe the transformation and identify the domain and range.

f (x) = -(x - 2)^2



f (x) = √x + 1 - 3

Answer:

Step-by-step explanation:

The inequality that represents Jenny's situation is:

600 - 20w > 300

To solve for w, we can start by subtracting 600 from both sides of the inequality:

-20w > 300 - 600

-20w > -300

Next, we can divide both sides by -20, remembering to reverse the direction of the inequality because we are dividing by a negative number:

w < (-300) / (-20)

w < 15

Therefore, the number of weeks that Jenny can continue to withdraw $20 from her account is less than 15. Since Jenny cannot withdraw a fractional number of weeks, the largest whole number of weeks that satisfies the inequality is 14.

Therefore, Jenny can continue to withdraw $20 from her account for 14 weeks while still keeping more than $300 in her account for college.

Answer:

Area = 4x^2 + 12x + 9

Perimeter = 8x + 12

Step-by-step explanation:

Answer:

\(y = \sqrt{x^2+4}\)

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the solution of the differential equation that satisfies the given initial condition. dy/dx = x/y, y(0) = -2

Using the variable separable method.

Step 1: Separate the variables

dy/dx = x/y

x dx = y dy

Step 2: Integrate both sides of the resulting equation

\(\int\limits {x} \, dx = \int\limits{y} \, dy\\\frac{x^2}{2} = \frac{y^2}{2} \\ \frac{y^2}{2} = \frac{x^2}{2} + C\\y^2 = x^2 + 2C\\y^2 = x^2 + K; K = 2C\)

Note that the constant of integration added to the side containing x

Step 3: Apply the initial condition y(0) = -2

This means when x = 0, y = -2. From step 2:

\(y^2+x^2 = K\\(-2)^2+0^2 = K\\4 = K\)

Step 4: Substitute K = 4 into the resulting differential equation above

\(y^2=x^2+4\\y = \sqrt{x^2+4}\)

This gives the solution to the differential equation.

Answer:

yes

Step-by-step explanation:

Answer:

(1 , -1)

Step-by-step explanation:

7( 1 ) - 3( -1 ) = 10

7 - - 3 = 10

7 + 3 = 10

10 = 10

true

Answer:

Step-by-step explanation:

p = 8

Answer:1,208 square centimeters

Step-by-step explanation:

==========================================

Explanation:

The equation should be h(t) = -16t^2 + (initial height). If you subtract off the initial height, then you'll have a negative starting height, which is not correct. Try plugging t = 0 into h(t) = -16t^2 - (initial height) and you'll see what I mean.

The initial height is 5184. We want to find the t value when h(t) = 0. So we want to find the time value when the height is 0.

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

h(t) = -16t^2 + (initial height)

h(t) = -16t^2 + 5184

0 = -16t^2 + 5184

16t^2 = 5184

t^2 = 5184/16

t^2 = 324

t = sqrt(324)

t = 18

It takes 18 seconds for the rope to hit the ground.

The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

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Answer:

Step-by-step explanation:

4/mx

Answer:

38.5 is your answer of this questions

Answer:

58

Step-by-step explanation:

5x5= 25

33+25

=58

use BODMAS

Bracket of division, multiplication; addition, subtraction

Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

Given that x is equal to 1 and S is the centroid of the triangle NLQ, NS will have a length of 4 units.

The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition. The centroid of a triangle is the location where the triangle's three medians connect. It may alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Here,

We may infer from the centroid's features that it divides each median in a ratio of 2:1.

NS=2SR

7x-3=2(5x-3)

7x-3=10x-6

3x=3

x=1

NS=7x-3

=7*1-3

=4 units

The length of NS will be 4 units as the value of x is 1 and S is the centroid of triangle NLQ.

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Answer:

\(v=46\\\)

Step-by-step explanation:

Simply:

\(-v=-46\)

Number of ways to select five city commissioners from a group of eighteen candidates is equal to 8568.

As given in the question,

Total number of candidates = 18

An election ballot asks voters to select five city commissioners from 18 candidates

Number of ways to select 5 city commissioners from a group of 18 candidates

= ¹⁸C₅

= ( 18!) ) / (5!)(18 - 5)!

= (18!) / (5!)(13!)

= ( 18 ×17×16×15×14×13! ) / ( 5×4×3×2×1 )( 13! )

= 8568

Therefore, number of ways to select five city commissioners from a group of eighteen candidates is equal to 8568.

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66. For equation -1.48 = (x - 30)/4,  the value of  x is 24.08. 68. For equation 0.88 = 22,000.44/σ, the value of σ is 25,000.5.

An equation is a mathematical statement that shows the equality between two expressions, using symbols and mathematical operations. An equation typically contains variables, which are symbols representing unknown values, and constants, which are known values. The variables can be solved for using algebraic methods to find their specific value(s) that make the equation true.

Equations can take many forms, depending on the mathematical context. For example, a linear equation has the form y = mx + b, where y and x are variables, m is the slope of the line, and b is the y-intercept. Quadratic equations have the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. There are many other types of equations, such as trigonometric equations, logarithmic equations, and differential equations, each with their own specific form and properties.

66. -1.48 = (x - 30)/4

To solve for x, we can begin by multiplying both sides by 4:

-1.48 * 4 = x - 30

-5.92 = x - 30

Next, we add 30 to both sides to isolate x:

-5.92 + 30 = x

x = 24.08

Therefore, the solution is x = 24.08.

68. 0.88 = 22,000.44/σ

To solve for σ, we can begin by multiplying both sides by σ:

0.88σ = 22,000.44

Next, we divide both sides by 0.88 to isolate σ:

σ = 22,000.44/0.88

σ = 25,000.5

Therefore, the solution is σ = 25,000.5.

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Answer: the answer is 21

Step-by-step explanation:

first, u divide the odd and positive numbers last u divide the both answers and it should be the answer

The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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A test point which is in the solution set for the linear inequality is: C. (-2, 4).

In order to determine which ordered pairs is a true solution based on the given linear inequality, we would have to test each of the ordered pairs by substituting their values into the linear inequality as follows;

For ordered pair (-2, -4), we have:

2x - 9y < 0

2(-2) - 9(-4) < 0

-4 + 36 < 0

32 < 0 (False).

For ordered pair (-1, -5), we have:

2x - 9y < 0

2(-1) - 9(-5) < 0

-2 + 45 < 0

43 < 0 (False).

For ordered pair (-2, 4), we have:

2x - 9y < 0

2(-2) - 9(4) < 0

-4 - 36 < 0

-40 < 0 (True).

For ordered pair (-1, -1), we have:

2x - 9y < 0

2(-1) - 9(-1) < 0

-2 + 9 < 0

7 < 0 (False).

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Answer:

6(y-2) would be 6y-12

Step-by-step explanation:

Answer:

\( 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}\)

If we simplify we got:

\( 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368\)

And the best option would be:

4368

Step-by-step explanation:

For this case we have a total of 16 IT specialists and we want to select 5 IT specialists from the total of 16 so we can use the combination formula given by:

\( nC x= \frac{n!}{x! (n-x)!}\)

And replacing we got:

\( 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}\)

If we simplify we got:

\( 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368\)

And the best option would be:

4368

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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The net force on the cart is 62N

and the vertical component =36.64 N

the horizontal component= 50N

What is revolution of vector?

The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component

30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.

40N tension isN 30° E which means

the vertical component= 40 sin60=36.64N

Horizontal component= 40 cos 60= 20N

sum of vertical = 36.64N +0= 36.64N

sum of horizontal= 30N+20N= 50N

60° was used for tension 40N because the angle of vector must always lie on the horizontal axis

therefore the net force F is obtained by using Pythagoras theorem

F= √(50^2+36.64^2)

= 62N to the nearest whole number.

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Answer:

The length of XY is 22.5

Step-by-step explanation:

Since you need to hurry I will not write an explanation

Hope this helps! :)

૮ ・ﻌ・ა

Answer/Step-by-step explanation:

Based on the factor theorem, a polynomial, x - a, is said to be a factor of another polynomial, f(x), if an only if f(a) = 0.

Using this theorem, let's determine whether each of the given first polynomial, is a factor of the second polynomial.

1. x - 1; x² + 2x + 5

By the factor theorem, x - 1 will be a factor of f(x) = x² + 2x + 5, if and only if f(1) = 0.

f(1) = 1² + 2(1) + 5

= 1 + 2 + 5

= 8

Since f(1) ≠ 0, therefore the first polynomial, x - 1, is NOT a factor of the second polynomial, x² + 2x + 5.

2. x + 1; x³ - x - 2

By the factor theorem, x + 1 will be a factor of f(x) = x³ - x - 2, if and only if f(-1) = 0.

f(1) = -1³ - (-1) - 2

= -1 + 1 - 2

= -2

Since f(-1) ≠ 0, therefore the first polynomial, x + 1, is NOT a factor of the second polynomial, x³ - x - 2.

3. x - 4; 2x³ - 9x² + 9x - 20

By the factor theorem, x - 4 will be a factor of f(x) = 2x³ - 9x² + 9x - 20, if and only if f(4) = 0.

f(4) = 2(4)³ - 9(4)² + 9(4) - 20

= 128 - 144 + 36 - 20

= 0

Since f(4) = 0, therefore the first polynomial, x + 4, is a factor of the second polynomial, 2x³ - 9x² + 9x - 20.

4. a - 1; a³ - 2a² + a - 2

By the factor theorem, a - 1 will be a factor of f(a) = a³ - 2a² + a - 2, if and only if f(1) = 0.

f(1) = 1³ - 2(1)² + 1 - 2

= 1 - 2 + 1 - 2

= -2

Since f(1) ≠ 0, therefore the first polynomial, a - 1, is NOT a factor of the second polynomial, a³ - 2a² + a - 2.

5. y + 3; 2y³ + y² - 13y + 6

By the factor theorem, y + 3 will be a factor of f(y) = 2y³ + y² - 13y + 6, if and only if f(-3) = 0.

f(-3) = 2(-3)³ + (-3)² - 13(-3) + 6

= -54 + 9 + 39 + 6

= 0

Since f(-3) = 0, therefore the first polynomial, y + 3, is a factor of the second polynomial, 2y³ + y² - 13y + 6.

Answer:

it's simple, put the values in the equation.

5 + d( 3b-2d) = 5 + 4( 3×-3 - 2× 4)

= 5 + 4( -9-8)

= 5+ 4 × -17

= 5-68 = -63 ans.

Answer:

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to \(0.6155\) radian

Step-by-step explanation:

Please see the attached image for better understanding

Length of OB is equal to

\(\sqrt{19^2 + 19^2 }\)

\(19\sqrt{2}\)

Now the length of OE is equal to

\(\sqrt{19^2 + 19^2 + 19^2 } = 19 \sqrt{3}\)

Now Angle BOE is equal to

\(cos^{-1} (\frac{722}{19\sqrt{2}* 19\sqrt{3} }) = 0.6155\) radians

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to \(0.6155\) radian

The rewritten statements are 1. ∀x∃y¬P(x, y), 2. ∃y∃x¬(P(x, y)∨Q(x, y)), 3. (∃x∃yP(x, y)∨∃x∃y¬Q(x, y)), and 4. ∃x(∀y∀z¬P(x, y, z)∧∀z∀y¬P(x, y, z)).

1. ∀x∃y¬P(x, y) - This statement states that for all x, there exists a y such that P(x, y) is not true. This rejects the statement "there exists x such that for all values of y, P(x, y) is true."

2. ∃y∃x(¬P(x, y)∧¬Q(x, y)) - This statement states that there exists a y and x such that both P(x, y) and Q(x, y) are not true. This rejects the statement, "for all the values of y and x, either P(x, y) or Q(x, y) will be true."

3. ∃x∀y¬P(x, y)∨∃x∀y¬Q(x, y) - This statement states that either there exists x such that for all y, P(x, y) is not true or there exists x such that for all y, Q(x, y) is not true. This rejects the statement, "for all the values of x, there exists y such that both P(x, y) and Q(x, y) will be true."

4. ∀x(¬∃y∃zP(x, y, z)∧¬∃z∀yP(x, y, z)) - This statement states that for all x, it is not the case that there exists y and z such that P(x, y, z) is true, and it is also not the case that there exists z such that for all y, P(x, y, z) is true. This rejects the statement "for all x, either there exists y and z such that P(x, y, z) is true, or there exists z such that for all y, P(x, y, z) is true."

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--The given question is incomplete; the complete question is

"Rewrite each of these statements so that negations appear only applied to predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives).

1. ¬∃x∀yP(x, y)

2. ¬∀y∀x(P(x, y)∨Q(x, y))

3. ¬(∃x∀y¬P(x, y)∧∀x∀yQ(x, y))

4. ¬∀x(∃y∃zP(x, y, z)∨∃z∀yP(x, y, z))"--