Describe any 3 of the 4 features listed below for the function g(x) = log₂ (x + 4) - 1. Include a description of how you found those answers using complete sentences. HELP​

Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.

Answer:7

Step-by-step explanation: 21/3 = 7

Answer:

1/7 km/min

Step-by-step explanation:

Divide/simplify the two values, 3/21 = 1/7

The process of converting a quadratic function to vertex form.

In math quadratic function is defined as a polynomial where the highest degree of any variable is 2.

Here we have to write the steps to convert the a quadratic function to vertex form.

Here we have to convert quadratic equation from standard form to vertex form

Let us consider that the given quadratic equation is given as,

=> y = ax² + bx + c { a, b, c € R, a ≠ 0}.

Here from the above equation we have to take a as common from the terms containing x.

then the equation is rewritten as,

=> y = a(x² + bx/a) + c

In order to Complete the square inside the bracket by adding and subtracting (b/2a)², then we get,

[tex]y=a[x^2+\frac{bx}{a} +(\frac{b}{2a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]

When we factorize it, then we get,

[tex]y=a[(x+\frac{bx}{a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]

Rewrite it as follows:

[tex]y=a[x+\frac{bx}{a}]^2 - (\frac{b}{2a})^2+ c[/tex]

Let us consider that the value of

=> h = -b/2a and k = c - b²/4a

Then we get the vertex form of the expression as,

=> y = a(x - h)² + k.

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Answer: hope this helps

The food truck operator should park her truck on the perpendicular bisector of the line connecting the two streets.

A perpendicular bisector is a line that bisects a line segment and is perpendicular to it. In this case, it would be a line that is equidistant from both streets and also perpendicular to the line connecting them. This is the best option for the food truck operator because it ensures that she is equidistant from both streets.

An angle bisector is a line that bisects an angle and divides it into two congruent angles. It is not appropriate in this case as it would not guarantee that the food truck is equidistant from both streets.

A median is a line that connects a vertex of a triangle to the midpoint of the opposite side. It is not appropriate in this case as the streets are not a triangle and it would not guarantee that the food truck is equidistant from both streets.

An altitude is a line that is perpendicular to the base of a triangle and goes from a vertex to the opposite side. It is not appropriate in this case as the streets are not a triangle and it would not guarantee that the food truck is equidistant from both streets.

Step-by-step explanation:

The height of the cylinder is h = 11 yards.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed figure determines how much space it can occupy in three dimensions.

Given:

A cylinder with a diameter of 8 yards has a volume of 552.64 yd3.

We have to find the height of the cylinder.

Consider, the volume formula for cylinder

[tex]V = \pi r^2h[/tex]

Here diameter = 8 yards

⇒ Radius = 4 yards

Plug V = 552.64,  r = 4,  π = 3.14 in the above formula.

⇒

[tex]552.64 = (3.14)(4^2)h\\h = \frac{552.64}{(3.14)(16)} \\h = 11[/tex]

Hence, the height of the cylinder is h = 11 yards.

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The original price of the shiny key chain that Zachary wants to buy, can be found to be $ 1.33

The question notes that there is a sale going on where the items on sale are being discounted by 25 %. This means that the current sale price of the shiny key chain as $ 1, is actually 25 % less than the original price.

The original price of the shiny key chain can then be found by the formula :

= Sale price / ( 1 - sales discount percentage )

= 1 / ( 1 - 25 %)

= 1 / 0. 75

= $ 1.33

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The full question is:
A sale says that all items are 25% off. Zachary wants to buy a shiny key chain. The sale price is $1. What was the original price?

Answer:

d) 0.1a

e) -5.2m^2 + 7.8m + 4.5k

f)[tex]4g^{2}[/tex]

g)-3t^2 +4.29t+9

h)4n

i)2.6g^2 -5.4g

Step-by-step explanation:

Hope this helps!

Answer:

Price after discount: $33.75

You saved: $11.25

Step-by-step explanation:

The surface area of a square pyramid with base length of 3 ft. and height of 6 ft. is 45 square ft. (option A)

The formula for the surface area of a square pyramid is given by:

A = a² + a  √(a² + 4h²)

Where:

A = surface area

a = base length

h = height of the pyramid

In the given problem, the side length of the base = W = L = 3 ft.

Hence,

a = 3 ft.

h = 6 ft.

Plug these parameters into the formula:

A = 3² + 3 x √(3² + 4x6²)

A = 9 + 3 x √153

A = 45 ft². (option (A)

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Answer:

О   XY

Step-by-step explanation:

The chord is a segment that joins two points of a circumference and differs from the diameter because it passes through the central point of the circle.  

To add two mixed numbers, you can separate the whole number and fraction parts. Add the whole numbers together as you normally would, and then find a common denominator to add the fractions. Once you have your sum, you may need to simplify the fraction for your final answer.

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Minutes it will take the tank to drain completely is 3.88

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

To find out the rate divide the amount of water leaving the tank by the time the water takes to leave the tank.

Jada notices 9 gallons of water leave the tank in five minutes.  ( The two gallons was obtained from 16-7 = 9)

The rate at which the tank is being emptied is  9 gallons/5 minutes = 1.8 gallons per minute;

For the tank to be empty, it has to lose all 7 gallons of water it has;

1 minute 1.8 gallons are lost

x minutes 7 gallons are lost

By cross multiplying;

x = 7/1.8 = 3.88 minutes

Therefore, the time taken at the rate will be 3.88 minutes

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Multiply the total acceleration by the sine of the acceleration angle to determine the vertical acceleration. The formula for vertical acceleration is: [tex]A_y=A_t\times\sin(a)[/tex].

Any object on which gravity is the only force is referred to as a projectile. Gravity causes projectiles to move in a parabolic trajectory. Projectiles are not subject to any horizontal forces, and as a result, they are not accelerated horizontally.

A projectile's horizontal velocity is constant. Gravity causes a downward vertical acceleration with a magnitude of 9.8 m/s/s. A projectile's vertical velocity varies by 9.8 m/s each second. A projectile's vertical motion is unrelated to its horizontal motion.

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We can see from the graph that the temperature decreases with increasing time. As a result, the two quantities temperature and time are inversely proportional to one another. The necessary relationship between these quantities is  x ∝ 1/y or x = k(1/y)

The two are said to be inversely proportional when one quantity's value increases relative to another's decline or vice versa. It suggests that in nature, the two quantities behave in opposite ways. Taking time and speed as an example, they are inversely related. Speed increases result in a shorter amount of time.

Other names for this type of proportion that are also used in this context are reciprocal proportion, inverse proportion, varying inversely, inverse variation, and inverse variation. Let's use the example of x and y to illustrate the relationship between the two variables.

x ∝ 1/y or  x ∝ y⁻¹

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Answer:

x = 2

Step-by-step explanation:

у = 12 - 4x

5x - Зу = -2

Solve the system algebraically.

Substitute the first equation into the second equation.

5x - 3( 12 - 4x) =-2

Distribute.

5x - 36 + 12x = -2

Combine like terms.

17x -36 = -2

Add 36 to each side

17x -36+26 = -2+36

17x = 24

Divide by 17

17x/17 = 34/17

x = 2

Answer:

x = 2

y = 4

Step-by-step explanation:

y = 12 - 4x  ⇒  ( 1 )

5x - 3y = -2  ⇒  ( 2 )

Let us find the value of x.

For that, take equation (2) and replace y with ( 12 - 4x ).

5x - 3y = -2

5x - 3 ( 12 - 4x ) = -2

5x - 36 + 12x = -2

Combine like terms.

17x - 36 = -2

Add 36 to both sides.

17x = -2 + 36

17x = 34

Divide both sides by 17.

x = 2

Let us find the value of y.

To find the value of y let us take equation ( 1 ) and replace x with 2.

y = 12 - 4 × 2

y = 12 - 8

y = 4

The Production Possibility Frontier (PPF) is often called the "Opportunity Cost Curve" because it illustrates the concept of opportunity cost.

Opportunity cost is the cost of one alternative in terms of the benefits forgone of the best alternative. In other words, it's the cost of one choice in terms of the best alternative choice.

As we move along the PPF, we can see that as we produce more of one good, we must give up some production of the other good. This trade-off is represented by the slope of the PPF, which is the opportunity cost of producing one good in terms of the other good. The PPF illustrates the relationship between production and opportunity cost by showing the trade-offs that must be made and the opportunity costs associated with different production choices.

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Answer:

6.3

Step-by-step explanation:

70+7x=114.1

7x=44.1

x=6.3

mark brainliest

Answer:64π cm2

Step-by-step explanation:your welcome

The radical function that has a domain of (x ∈ R such that x <= -3) and range of (y ∈ R such that y >= 4) is y = √(-x - 3) + 4.

The domain of this function is (x ∈ R such that x <= -3) because the inside of the square root must be non-negative, and x + 3 is negative when x <= -3. The range of this function is (y ∈ R such that y >= 4) because the square root of a non-negative number plus 4 is always greater than or equal to 4.

Answer:

(x+8)^2=40

Step-by-step explanation:

x^2+16x+24=0.

Well, to solve for this, you do:

1. (16/2)^2 to find what number should be in place of 24.

That, by the way, is 64.

2. There's no 64! We have to add 64-24 on both sides, which makes the equation

x^2+16x+64=40.

3. Since we know that (16/2)=8, using the completing the square formula, you know that it's going to be a variation of (x+8)^2 or (x-8)^2.

As we are adding for the middle term, it must be (x+8)^2.

4. Answer: (x+8)^2=40.

Sorry if this is too late :)

Answer:

it should be eight

Step-by-step explanation:

if i am correct

In a direct relationship, Y increases when X increases. On a graph, a direct relationship always has a positive slope. Inverse relationship: An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.

Now, According to the question:

Direct relationship:

A direct relationship means that both variables increase together or both decrease together.

In a direct relationship, Y increases when X increases.

On a graph, a direct relationship always has a positive slope.

Inverse relationship:

An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.

In an inverse relationship, Y decreases when X increases.

On a graph, an inverse relationship always has a negative slope.

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Answer: 24%

Step-by-step explanation: 48 out of 200 is 24%, meaning that 48 is 24% of 200. To find our answer, we follow two simple steps before we add the percentage symbol, though there can be three steps if we have to round a decimal in a percentage to two digits after the decimal point.

Answer:24%

Step-by-step explanation:

To plot the graph of the given quadratic function y = 2x², evaluation the value of the function for several values of x  at the left and right side of the origin, then plot the data.

The standard form of a quadratic function is:

y = f(x) = ax² + bc + c

Steps to plot the graph of a quadratic function includes:

However, in the given function y = 2x²,  x-intercept, y-intercept, and the extreme point are all (0,0) or the origin. Hence, we need to use auxiliary points.

Evaluate the value of y for several values of x in the left and right of the extreme value, (0,0). The results are given in the following table.

x  y

-5  50

-4  32

-3  18

-2  8

-1  2

0  0

1  2

2  8

3  18

4  32

5  50

Plot the data and we get the graph of y = 2x² ( as in the attached picture)

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Answer:  (x*4) - 3= 11.   X = 3.5

Step-by-step explanation

(4x) - 3 = 11 or (x*4) - 3 = 11.

11 + 3 = 14

So then,

14 = x * 4 (or 4x)

14 / 4 = 3.5

so,

X = 3.5

As a result, 3.90 represents the top's angle to Jada.

Trigonometric identities are equations involving trigonometric functions that hold true for each possible value of the variables.

The area of mathematics known as trigonometry deals with particular angles' mathematical functions and how to use them. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms (csc).

Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation. The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities.

The height of the Empire State building exists 1466.85 ft.

Let the given information be

She is 100 feet away when she spots it.

The top, she has to look up at an angle of 86.1 degrees.

[tex]$$\begin{aligned}& =(\sin (86.10) \times 100) \div(\sin (3.90)) \\& =1466.85 \mathrm{ft} .\end{aligned}$$[/tex]

Therefore, 3.90 represent the angle of the top to Jada.

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The units that is appropriate for the time the number of bacteria is 300 is seconds.

The population of bacteria in a petri dish doubles every 40 seconds. The population of the bacteria is initially 400 organisms.

Therefore, the units that is most appropriate for the time at which the number of bacteria is 300 can be calculated as follows:

The bacteria population doubles every 40 seconds. Therefore, the units appropriate for when the population of the bacteria is 300 is second.

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Answer: can you help me i cant put a q     i have to points

Step-by-step explanation: plssssssssssssssss      

A customer wanted to purchase a video game and realized that they were short $4.28 to be able to pay. Which value is the opposite of being short $4.28

A number line showing the solution of -8 - (-6) is :  A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

Given expression is -8 - (-6).

That is the number -6 is subtracted from the number -8.

So we have to first draw an arrow to the number -8.

Then we have to draw an arrow of length -6 units from the number -8.

Then the arrow will stop at -2, which is the solution.

Hence the solution of the expression is -2.

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Inconsistent Pair of Linear Equations is the type of system of linear equation which has no solution notice that the two lines are parallel and will never intersect.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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