1. What is the constant rate of change between x and y in the table below?
A. 3/2
B.2/3
C.-2/3
D.-3/2

Answer:

see explanation

Step-by-step explanation:

1

1 + \(\frac{x-5}{2}\) - \(\frac{x+3}{5}\) ≤ 0

multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10 + 5(x - 5) - 2(x + 3) ≤ 0 ← distribute parenthesis on left side and simplify

10 + 5x - 25 - 2x - 6 ≤ 0

3x - 21 ≤ 0 ( add 21 to both sides )

3x ≤ 21 ( divide both sides by 3 )

x ≤ 7

2

\(\frac{6x}{5}\) - \(\frac{2}{3}\) ≥ 4

multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

18x - 10 ≥ 60 ( add 10 to both sides )

18x ≥ 70 ( divide both sides by 18 )

x ≥ \(\frac{70}{18}\) , that is

x ≥ \(\frac{35}{9}\)

3

\(\frac{x}{10}\) - \(\frac{2}{8}\) ≥ 1

multiply through by 40 ( the LCM of 10 and 8 ) to clear the fractions

4x - 10 ≥ 40 ( add 10 to both sides )

4x ≥ 50 ( divide both sides by 4 )

x ≥ \(\frac{50}{4}\) , that is

x ≥ \(\frac{25}{2}\)

Answer:

\(\textsf{1.} \quad x \leq 7\)

\(\textsf{2.} \quad x \geq \dfrac{35}{9}\)

\(\textsf{3.} \quad x \geq \dfrac{25}{2}\)

Step-by-step explanation:

Given inequality:

\(1+\dfrac{x-5}{2}-\dfrac{x+3}{5} \leq 0\)

\(\textsf{Add \; $\dfrac{x+3}{5}$ \; to both sides}:\)

\(\implies 1+\dfrac{x-5}{2}-\dfrac{x+3}{5} +\dfrac{x+3}{5}\leq 0+\dfrac{x+3}{5}\)

\(\implies 1+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}\)

\(\textsf{Rewrite $1$ as $\dfrac{2}{2}$}:\)

\(\implies \dfrac{2}{2}+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}\)

\(\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:\)

\(\implies \dfrac{2+x-5}{2}\leq \dfrac{x+3}{5}\)

\(\implies \dfrac{x-3}{2}\leq \dfrac{x+3}{5}\)

Cross multiply:

\(\implies 5(x-3)\leq 2(x+3)\)

\(\implies 5x-15\leq 2x+6\)

Subtract 2x from both sides:

\(\implies 5x-15-2x\leq 2x+6-2x\)

\(\implies 3x-15\leq 6\)

Add 15 to both sides:

\(\implies 3x-15+15\leq 6+15\)

\(\implies 3x\leq 21\)

Divide both sides by 3:

\(\implies \dfrac{3x}{3}\leq \dfrac{21}{3}\)

\(\implies x \leq 7\)

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

Given inequality:

\(\dfrac{6x}{5}-\dfrac{2}{3} \geq 4\)

\(\textsf{Add \; $\dfrac{2}{3}$ \; to both sides}:\)

\(\implies \dfrac{6x}{5}-\dfrac{2}{3} +\dfrac{2}{3}\geq 4+\dfrac{2}{3}\)

\(\implies \dfrac{6x}{5}\geq \dfrac{12}{3}+\dfrac{2}{3}\)

\(\implies \dfrac{6x}{5}\geq \dfrac{12+2}{3}\)

\(\implies \dfrac{6x}{5}\geq \dfrac{14}{3}\)

Cross multiply:

\(\implies 3(6x) \geq 14(5)\)

\(\implies 18x \geq 70\)

Divide both sides by 18:

\(\implies \dfrac{18x}{18} \geq \dfrac{70}{18}\)

\(\implies x \geq \dfrac{70}{18}\)

Reduce the fraction by dividing the numerator and the denominator by 2:

\(\implies x \geq \dfrac{70 \div 2}{18 \div 2}\)

\(\implies x \geq \dfrac{35}{9}\)

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

Given inequality:

\(\dfrac{x}{10}-\dfrac{2}{8} \geq 1\)

\(\textsf{Add \; $\dfrac{2}{8}$ \; to both sides}:\)

\(\implies \dfrac{x}{10}-\dfrac{2}{8} +\dfrac{2}{8}\geq 1+\dfrac{2}{8}\)

\(\implies \dfrac{x}{10}\geq \dfrac{8}{8}+\dfrac{2}{8}\)

\(\implies \dfrac{x}{10}\geq \dfrac{8+2}{8}\)

\(\implies \dfrac{x}{10}\geq \dfrac{10}{8}\)

Cross multiply:

\(\implies 8(x) \geq 10(10)\)

\(\implies 8x \geq 100\)

Divide both sides by 8:

\(\implies \dfrac{8x}{8} \geq \dfrac{100}{8}\)

\(\implies x \geq \dfrac{100}{8}\)

Reduce the fraction by dividing the numerator and the denominator by 4:

\(\implies x \geq \dfrac{100 \div 4}{8 \div 4}\)

\(\implies x \geq \dfrac{25}{2}\)

Answer:

C

Step-by-step explanation:

Answer:

angle QPR and angle RPQ

Step-by-step explanation:

hope this helps!

Answer:

m

Step-by-step explanation:

the slope or growth rate of the function is the coefficient of the variable x, which is m in this case

The Airy differential equation is a second-order linear ordinary differential equation given by Fourier Transform:

-d^2u/dx^2 = x*u

To find a bounded solution to this equation, we can use the Fourier transform. The Fourier transform of a function f(x) is given by:

F(ω) = ∫ f(x) e^(-iωx) dx

Using the Fourier transform, we can convert the differential equation into an algebraic equation in terms of the Fourier transform F(ω):

-ω^2 F(ω) = ∫ x*u(x) e^(-iωx) dx

We can rewrite the integral on the right-hand side using integration by parts:

∫ x*u(x) e^(-iωx) dx = -∫ u(x) d/dx(e^(-iωx) dx)

= -iω∫ u(x) e^(-iωx) dx + [u(x) e^(-iωx)]^∞_0

Since we are looking for a bounded solution, the term [u(x) e^(-iωx)]^∞_0 must be equal to zero. Therefore, we have:

ω^2 F(ω) = iω∫ u(x) e^(-iωx) dx

We can then solve for the Fourier transform F(ω):

F(ω) = i/ω ∫ u(x) e^(-iωx) dx

Finally, we can take the inverse Fourier transform to find the solution u(x):

u(x) = (1/2π) ∫ F(ω) e^(iωx) dω

Substituting the expression for F(ω), we have:

u(x) = i/(2πω) ∫ ∫ u(y) e^(-iω(y-x)) dy dω

This gives us an integral formula for a bounded solution to the Airy differential equation in terms of the Fourier transform.

More related to Fourier Transform: https://brainly.com/question/28984681

#SPJ11

a) x b) 1 c) 0 d) x , x ⊕ x ⊕ 0 → Since 0 is the neutral element of the XOR operator, it will not affect the result of the expression. Therefore, the expression simplifies to just x.

a) x ⊕ 0 → Since 0 is the neutral element of the XOR operator, it will not affect the value of x. Therefore, the expression simplifies to just x.

b) x ⊕ 1 → Since 1 is the identity element of the XOR operator, it will return the opposite of x. Therefore, the expression simplifies to just 1.

c) x ⊕ x → Since x ⊕ x is equivalent to x XORing itself, the result will be 0. Therefore, the expression simplifies to just 0.

d) x ⊕ x ⊕ 0 → Since 0 is the neutral element of the XOR operator, it will not affect the result of the expression. Therefore, the expression simplifies to just x.

a) x ⊕ 0 simplifies to just x.

b) x ⊕ 1 simplifies to just 1.

c) x ⊕ x simplifies to just 0.

d) x ⊕ x ⊕ 0 simplifies to just x.

Learn more about expression here

https://brainly.com/question/14083225

#SPJ4

The rectangular coordinate for the polar coordinate (4, 210°) is  (-3.46, -2).

The rectangular coordinate for the polar coordinate (4, 210°) is calculated by applying the following formula as shown below;

x = r cos(θ)

y = r sin(θ)

where;

From the given  polar coordinate (4, 210°);

r = 4

θ = 210⁰

The rectangular coordinate is calculated as follows;

x = 4 x cos(210°)

y = 4 x sin(210°)

x = -3.46

y = -2

Learn more about rectangular coordinate here: https://brainly.com/question/1402079

#SPJ1

The polynomial representing the area of the is 49n² - 25

The formula for area of a square is expressed as;

Area = a²

Where a is the side length

From the image shown, we can see that the side length takes the value (7n - 5)

Substitute the value into the formula

Area = a²

Area = (7n - 5)²

Area = (7n - 5) ( 7n + 5); this is so because of the difference of two squares

Expand the bracket

Area = 49n² + 35n - 35n - 25

collect like terms

Area = 49n² - 25

Thus, the polynomial representing the area of the cube is 49n² - 25

Learn more about a square here:

https://brainly.com/question/24487155

#SPJ1

Complete question is;

The function ​f(x) = (25000 + 280x)/x models the average cost per unit, f(x), for Electrostuff to manufacture x units of Electrogadget IV. How many units must the company produce to have an average cost per unit of $390?

Answer:

227 units

Step-by-step explanation:

We are given the function;

​f(x) = (25000 + 280x)/x

Where;

f(x) is the average cost per unit

x is the number of units

Now, we want to find out how many units the company must produce to have an average cost per unit of $390.

Thus, plugging $390 for f(x), we have;

390 = (25000 + 280x)/x

When we cross multiply, we get;

390x = 25000 + 280x

390x - 280x = 25000

110x = 25000

x = 25000/110

x ≈ 227

the general formula of a parabola is

we can replace the the points to find a,b and c

First (0,4)

Then (-5,1.5) and c=4

Answer:

It was D I took the test

Step-by-step explanation:

Answer:

it is d

Step-by-step explanation:

Answer:

4th quadrant is the red point..

Answer:

\(=\pm i\sqrt{66}\)

Step-by-step explanation:

So we have:

\(\pm\sqrt{-66}\)

This is the same as:

\(=\pm\sqrt{66\cdot-1}\)

Separate:

\(=\pm\sqrt{66}\cdot\sqrt{-1}\)

Replace the second term with i:

\(=\pm i\sqrt{66}\)

The square root of 66 cannot be simplified.

So, this is our answer :)

Answer:

36.5

Step-by-step explanation:

The pattern was the difference of one day and the next doubled

The correct option is option C: 0.06.

Given that a couple has an Education Level = 4, the probability that it has SC Index = 10 is 0.06.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number that ranges from 0 to 1.

When an event is certain to occur, its probability is 1, while when an event is impossible to occur, its probability is 0.

The probability of an event A is denoted by P(A). It can be calculated using the following formula: P(A) = (number of favorable outcomes)/(total number of outcomes)

In this question, we need to calculate the probability of the event that a couple has an Education Level = 4 and SC Index = 10.

Given that a couple has an Education Level = 4, there are a total of 50 such couples. Of these, 3 have SC Index = 10.

Therefore, the probability that a couple has an Education Level = 4 and SC Index = 10 is: P(Education Level = 4 and SC Index = 10) = 3/50 = 0.06Hence, the correct option is option C: 0.06.

To know more about the SC Index  visit:

https://brainly.in/question/17634908

#SPJ11

Answer:

1.true

2.false

3.false

4.true

5.true

6.false

Step-by-step explanation:

just graph it and look at it

The measure of each of the acute angles of the right triangle is 32° and 58°.

A right triangle is a kind of triangle which has a right angle (90°) and two acute angles (less than 90°).

Let x = measure of one of the acute angles

If the measure of one acute angle of a right triangle is 6 less than twice the measure of the other acute angle, then

measure of the other acute angle = 2x - 6

The sum of all the angles of any triangle is equal to 180°. Hence,

90° + x + 2x - 6 = 180°

Solve for the value of x.

3x = 96

x = 32

Solve for the measure of the other acute angle.

2x - 6 = 2(32) - 6 = 58

Hence, the two angles are 32° and 58°.

Learn more about right triangles here: https://brainly.com/question/1635412

#SPJ4

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 4700\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &11 \end{cases} \\\\\\ 4700=Pe^{0.04\cdot 11} \implies 4700=Pe^{0.44}\implies \cfrac{4700}{e^{0.44}}=P\implies 3027\approx P\)

Answer:

D

Step-by-step explanation:

Properties used in the given equation is Commutative property, Associative property, Additive inverse, Identity property.

In a commutative property multiplication and addition which posses commutative property takes place without considering the order of arrangement of data.

12.2 + 18.6 + -4.3 + (-18.6)

12.2 + -4.3 _ 18.6 + (-18.6)

The second step results into the presence of a commutative property.

12.2 + -4.3 + [18.6 + (-18.6)] is an associative property because here, regrouping of numbers which gives the same result.

[18.6 + (-18.6)] is an additive inverse since the result is zero. Additive inverse occurs when the addition of a number to another number results into zero.

12.2 + -4.3 + (0) is an identity property.

This property occurs when the addition of any number with zero eventually resulted into that number.

So here we used 4 properties which are

Commutative property,

Associative property,

Additive inverse,

Identity property.

Given question is written in wrong language.

Here is the given question 12.2 + 18.6 + -4.3 + (-18.6)12.2 + -4.3 + 18.6 + (-18.6)12.2 + -4.3 + [18.6 + (-18.6)]12.2 + (-4.3) + (0)12.2 + -4.3 7.9

To know more about property here

https://brainly.com/question/17271811

#SPJ4

Answer:

Not right triangle

Step-by-step explanation:

Answer:

q=7

Step-by-step explanation:

3(q +4/3)+2=23

3q+4+2=23

3q+2=23

3q=23-2

q=21/3=7

Answer:

- 2/3

Step-by-step explanation:

on khan academy

Answer:

5 : 7

Step-by-step explanation:

Assuming simplest form means in whole numbers, to find the ratio in simplest form, just multiply both sides by the same value until they are both whole numbers. So 2.5 : 3.5 = 2.5 * 2 : 3.5 * 2 = 5 : 7

Answer:

5:7

Step-by-step explanation:

The simplest form of 2.5 : 3.5 is 5:7 because 2.5 x 2 = 5 and 3.5 x 2 = 7

Answer:

Step-by-step explanation:

Answer:

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Step-by-step explanation:

C = 2P  .....equation 1

4C + 2P = 20  .....equation 2

Substituting eqn 1 into eqn 2, we have;

4(2P) + 2P = 20

8P + 2P = 20

10P = 20

P = 20/10

Pie, P = $2

Next, we would determine the cost of a cake;

From equation 1;

C = 2P

Substituting the value of "P" we have;

C = 2 * 2

Cake, C = $4

Therefore, we would have the following answers;

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Check:

From equation 2;

4C + 2P = 20

4(4) + 2(2) = 20

16 + 4 = 20

20 = 20

Answer:

yes it relates to a function

Therefore, the rate of the boat in still water is 70 mph, and the rate of the current is 30 mph.

Let's denote the rate of the boat in still water as "b" and the rate of the current as "c."

When the boat is traveling upstream, it is going against the current, so the effective speed is reduced. The speed of the boat relative to the ground can be calculated as (b - c).

Given that it takes 5 hours to travel 200 miles upstream, we can set up the equation:

Distance = Speed * Time

200 = (b - c) * 5

Dividing both sides by 5, we get:

40 = b - c (Equation 1)

When the boat is traveling downstream, it is aided by the current, so the effective speed is increased. The speed of the boat relative to the ground can be calculated as (b + c).

Given that it takes 2 hours to travel 200 miles downstream, we can set up the equation:

200 = (b + c) * 2

Dividing both sides by 2, we get:

100 = b + c (Equation 2)

Now we have a system of equations consisting of Equation 1 and Equation 2:

40 = b - c

100 = b + c

We can solve this system of equations using any method of solving simultaneous equations, such as substitution or elimination.

Adding Equation 1 and Equation 2:

40 + 100 = (b - c) + (b + c)

140 = 2b

Dividing both sides by 2, we get:

b = 70

Substituting the value of b back into Equation 1 or Equation 2:

40 = 70 - c

Subtracting 70 from both sides:

-30 = -c

Multiplying both sides by -1, we get:

30 = c

To know more about rate,

https://brainly.com/question/29270113

#SPJ11