Identify a horizontal or vertical stretch or compression of the function f(x) = xby observing the equation of the function g(x) = sq root 3/2x

Answer:

\(10 < {e}^{8} \)

\( ln(10) < 8\)

\( ln(10) - 8 < 0\)

Since ln(10) > 0, it follows that ln(10) + 1 > 0, and so:

\(( ln(10) + 1)( ln(10) - 8) < 0\)

\( {( ln(10)) }^{2} - 7 ln(10) - 8 < 0\)

\(( { ln(10) })^{2} - 7 ln(10) + 1 < - 9\)

\( {( ln(10)) }^{2} + 2 ln(10) + 1 < 9 ln(10) - 9\)

\( {( ln(10) )}^{2} + 2 ln(10) + 1 < 9( ln(10) - 1)\)

(ln(10) + 1)^2 < 9(ln(10 - 1)

ln(10) + 1 < 3√(ln(10) - 1)

(1 + ln(10))/3 < √(ln(10) - 1)

√(ln(10) - 1) > (1+ ln(10))/3

To graph the inequality k > 5 on a number line, mark an open circle at 5 and shade the region to the right.

To graph the solutions to the inequality k > 5 on a number line, follow these steps:

Draw a horizontal line and mark a point for the number 5 on the line.

-------------------|---|---|---|---|---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10

Since the inequality is k > 5, the solution includes all values greater than 5. Therefore, draw an open circle (○) at the number 5 to represent that 5 itself is not included in the solution.

-------------------|---|---|---|---○---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10

Shade the region to the right of the open circle. This shading represents all values that are greater than 5 and satisfy the inequality k > 5.

-------------------|---|---|---|---○===================>

0 1 2 3 4 5 6 7 8 9 10

The resulting number line graph illustrates that any value to the right of the open circle (excluding 5 itself) satisfies the inequality k > 5.

for such more question on inequality

https://brainly.com/question/17448505

#SPJ8

The store at which the apple will cost the cheapest is: Store A

The formula for the slope between two coordinates is:

Slope = (y₂ - y₁)/(x₂ - x₁)

Now, all the lines in the attached graph pass the origin and so they will all have the coordinate (0, 0)

The slope for each line will give us the cost for each apple in the store.

Thus:

Slope for store A = (3 - 0)/(4 - 0)

Cost for store A apple = $0.75

Slope for Store B = (5 - 0)/(5 - 0)

Cost for store B apple = $1

Slope for Store C = (5 - 0)/(4 - 0)

Cost for store C apple = $1.25

Slope for Store D = (6 - 0)/(3 - 0)

Cost for store C apple = $2

Thus, store A has the cheapest Apple

Read more about Slope of Linear Graph at: https://brainly.com/question/3493733

#SPJ1

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x-22.2=1.90

22.20-4x=1.90

4x + 1.90 = 22.20

The equation that represents this situation is 4.75 = 2.5x - 1.25x.

What is a linear equation in one variable?

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax + b = 0, where a and b are two integers and x is a variable. 2x + 3 = 8, for example, is a linear equation with a single variable.

Let the cost of the binder be represented with x.

The cost of the folder is x = 0.5x

The cost of the highlighter = x - $1.25

The total cost of the items = cost of binder + highlighter + folder

                      4.75 = x + 0.5x + x - 1.25

Add similar x terms together, and we get

                         4.75 = 2.5x - 1.25x

To learn more about determination of the total cost of an item visit: brainly.com/question/25879561

#SPJ1

Answer:0.8p+1 and 1+0.8p

Step-by-step explanation:

0.5p+0.3p=0.8p

7-6=+1

0.8p+1

and

Swap both numbers

(0.5p+7)+(0.3p-6)=1+0.8p

if the area is 6 that means the square is 2 x 3. 2 x 3 x 4. that equals 24.

let me know how you did !

Answer:24 cubic meters

Step-by-step explanation:

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

for more such questions on logarithmic properties

https://brainly.com/question/30226560

#SPJ8

The required graph has been attached below that represents the function f(x) = 5 cos (2x).

The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.

Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.

The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).

Thus, the graph has been attached below that represents the given function.

Learn more about Trigonometric functions here:

brainly.com/question/6904750

#SPJ1

Answer:

Sure, I'd be happy to help you with that!

To calculate Dan's earnings with simple interest, we can use the following formula:

I = P * r * t

where:

I = interest earned

P = principal amount (initial investment)

r = interest rate (as a decimal)

t = time period (in years)

We know that Dan invests £2500 and receives 5% simple interest per year, so:

P = £2500

r = 0.05

t = 2 years

Plugging these values into the formula, we get:

I = £2500 * 0.05 * 2

I = £250

This means that Dan will earn £250 in interest over the 2-year period.

To calculate Dan's total earnings, we simply add the interest earned to the initial investment:

Total earnings = £2500 + £250

Total earnings = £2750

Therefore, Dan will have £2750 in his bank account after 2 years.

Answer:

The circumference of a circle is calculated using the formula: C = πd, where C represents the circumference and d represents the diameter of the circle.

In this case, the diameter of the circle is given as 24 inches.

Using the formula, we can substitute the values:

C = πd

C = 3.14 * 24

C ≈ 75.36 inches

Therefore, the circumference of a circle with a diameter of 24 inches (and using π = 3.14) is approximately 75.36 inches.

Step-by-step explanation:

Answer:

7/10, 6/10, or 5/10

Step-by-step explanation:

So, first, we change 4/5 into tenths. That equals 8/10. 3/10 and 8/10.

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

For more such questions on vertex

https://brainly.com/question/25651698

#SPJ8

Answer:

A. Both ends go down.

General Formulas and Concepts:

Algebra II

Step-by-step explanation:

If we graph the function, we can see that when x goes to -∞, y also goes to -∞.

We also see that when x goes to ∞, y still goes to -∞.

Therefore, both ends of the graph would head towards -∞, making A. the correct answer choice.

Answer:Both ends go down

Step-by-step explanation:

The domain of (boa)(x) is [1, ∞].

In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.

Based on the information provided above, we have the following functions:

a(x) = 3x+1

\(b(x) = \sqrt{x-4}\)

Therefore, the composite function (boa)(x) is given by;

\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = [1, ∞] or {x|x ≥ 1}.

Read more on domain here: brainly.com/question/9765637

#SPJ1

Answer: (5 , 1)

Step-by-Step explanation:

hihi your problem is a system of question y = x-4 and  y = -x+6 okay so  graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!

y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right

y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left

once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!

the solution is  x = 5 and y = 1 which is also (5 , 1)

hopefully this was helpful !

The equation of the parallel line will be y = (2/3)x - 8/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y - 4 = 2/3 (x - 3)

The equation of the line that is parallel to the given line will be written as,

y = (2/3)x + c

The equation of the line that passes through (1, -2), then we have

- 2= (2/3)(1) + c

- 2 = 2 /3 + c

c = - 8 / 3

Then the equation of the parallel line will be y = (2/3)x - 8/3.

More about the equation of a parallel line link is given below.

https://brainly.com/question/402319

#SPJ1

Answer:

1.) 10: 1, 2, 5, 10.

15: 1, 3, 5, 15,

Answer would be 5.

2.) 18: 1, 2, 3, 6, 9, 18

21: 1, 3, 7, 21

Answer would be 3.

3.) 12: 1, 2, 3, 4, 6, 12.

24: 1, 2, 3, 4, 6, 8, 12, 24.

Answer would be 12.

4.) 8: 1, 2, 4, 8.

20: 1, 2, 4, 5, 10, 20.

Answer would be 4.

5.) 14: 1, 2, 7, 14.

28: 1, 2, 4, 7, 14, 28.

Answer would be 14.

Step-by-step explanation:

Using the listing method, you would first list the common factors of each number, to which that number could be multiplied by. Then, you would search for the greatest common factor.

Answer: r=2

Step-by-step explanation:

We can use the given 2 points to find slope. Since we are given the slope, we can plug it into the formula and solve for r.

\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =2\)                                        [plug in values]

\(\frac{12-r}{-6-(-11)} =2\)                                   [combine like terms]

\(\frac{12-r}{5} =2\)                                          [multiply both sides by 5]

\(12-r=10\)                                      [subtract both sides by 12]

\(-r=-2\)                                          [divide both sides by -1]

\(r=2\)

Step-by-step explanation:

We define 3 events

A = event that driver is above speed limit

B = event that driver is below limit

T = event that the gun detected him

At 95%

P(A) = 1-0.95 = 0.05

P(B) = 0.95

P(T|A) = 0.98

P(A|T) = 0.02

P(T|B) = 1-0.99 = 0.01

P(B|T) = 0.99

1. For answer a

P(TnA) = P(A) x P(T|A)

= 0.05 x 0.98

= 0.049 is the probability gun detected speeding and the driver was speeding

2. For answer b

P(TnB) = P(B) x P(T|B)

= 0.95x0.01

= 0.0095 is probability that gun deects speeding and driver was not speeding

3. For answer c

We solve this using bayes theorem

P(B|T) = P(B) x P(T|B) / (P(B)*P(T|B)) + (P(A) +P(T|A))

= 0.095x0.01 divided by (0.95x0.01)+(0.05*0.98)

= 0.0095 divided by 0.0585

= 0.16239

= 0.1624 to 4 decimal places.

Answer: B) 31.4 inches

Step-by-step explanation:

5 x 2 = diameter

10 x 3.14 (pie)

= 31.4

Answer: c) 31.4 inches

Step-by-step explanation:

5 x 2 = diameter

10 x 3.14 (pie)

= 31.4

As given by the question

There are given that the resort temperature is:

Now,

To convert Fahrenheit to Celsius, use the given formula:

Then,

Hence, -14.4444 degrees Celsius is this temperature.

a. The number of ways that this is done, if the order of the choices is relevant is 360360 ways

b. The number of ways that this can be done, if the order of the choices is irrelevant is 3003 ways

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

= n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

When the orders are relevant, this will be:

= 15P6

= 15! / (15 - 5!)

= 15! / 10!

= 360360 ways

When orders are irrelevant, this will be:

= 15C5

= 15! / (15 - 5!)5!

= 3003 ways

Learn more about combinations on:

brainly.com/question/4658834

#SPJ1

Required trapizoidal approximation is 174.

What is trapezoidal rule?

The trapezoidal rule is a numerical integration method used to approximate the definite integral of a function over a given interval. It is based on approximating the area under the curve of the function by dividing it into trapezoids and summing up their areas.

To use the trapezoidal rule, you first need to choose an interval [a,b] over which to integrate the function. Then, you divide the interval into a number of subintervals of equal width, typically denoted by h = (b-a)/n, where n is the number of subintervals.

Here,

Using the trapezoidal rule, the approximation of the integral is given by:

\(\int_{-4}^4 f(x),dx \)

\( = \frac{1}{2}[(f(-4)+f(-1))(-1-(-4))+(f(-1)+f(0))(0-(-1)) +(f(0)+f(4))(4-0)] \)

\( = \frac{1}{2}[ (4+18)(-1-(-4)) + (18+36)(0-(-1)) + (36+50)(4-0) ]\)

\(\\ = \frac{1}{2}[22(-3)+54(1)+86(4)] \\ = 174\)

Therefore, the correct answer is 174.

Learn more about trapizoidal rule here,

https://brainly.com/question/30401353

#SPJ1

Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       \(0=\frac{1}{3} x-1\)

       \(1=\frac{1}{3} x\)

       \(x=3\)

So x-intercept is the point (3,0).

Answer:

-2

Step-by-step explanation:

The coefficient of a term is literally the constant place before a variable. So in this monomial:

-2xy^2z^3

The coefficient would be -2.

Cheers.