All of the following are equivalent except _____.

x - (-2)
-2 + x
x - 2
x + (-2)

Answer:  The required slpe-intercept form of the given inequality is

[tex]y\leq 0\times x+24.[/tex]

Step-by-step explanation:  We are given to write the following inequality in the slope-intercept form :

[tex]-6+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope intercept form of a straight line with slope m and y-intercept c is given by

[tex]y=mx+c.[/tex]

Writing equation (i) in slope-intercept form, we have

[tex]-6+2y\leq 42\\\\\Rightarrow 2y\leq 42+6\\\\\Rightarrow 2y\leq 48\\\\\Rightarrow y\leq 24\\\\\Rightarrow y\leq 0\times x+24,[/tex]

where slope, m = 0  and  y-intercept, c = 24.

Thus, the required slpe-intercept form of the given inequality is

[tex]y\leq 0\times x+24.[/tex]

Answer:

Step-by-step explanation:

$228

there are 10 numbers ( 0-9)

there are 26 letters ( A-Z)

10 x 26 x 26 x 10 x 10 x 10 x 10 =67,600,000 possible combinations

Area = 1039.23 square units

 Round answer as needed. See picture for equation

we have

[tex] f(x) = 2x^{2}- x -6 [/tex]

using a graph tool

see the attached figure

we know that

1) the domain of the function is all real numbers-------> interval (-∞,∞)

2) The range of the function is the interval [-6.125,∞)

3) The vertex of the function is the point (0.25,-6.125)

4) The function has two x-intercepts-----> ( -1.5,0) and (2,0)

5) The function is increasing over the interval (0.25,∞) and decreasing over the interval (-∞,0.25)

The problem involves setting up an equation based on the given situation to solve for the number of baseball cards Neil and Larry have. By solving the equation, you find that Larry has 400 cards and Neil has 320 cards. So, they have 720 baseball cards together.

This is a problem of percentages and of algebra. First, you know that the number of cards Neil has is 80% of what Larry has. This can be set up as an algebraic equation, where N represents Neil’s cards and L represents Larry’s cards: N = 0.8L. You also know that Neil has 80 fewer cards than Larry, which provides a second equation: N = L - 80.

Because both expressions equal N, you can set them equal to each other to solve for L. This leads to 0.8L = L - 80. Solve this equation for L, and you get L = 400. Substituting this into the equation N = 0.8L, you find that N = 320. Therefore, Neil and Larry have 720 baseball cards altogether.

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Answer:

The answer is rotational symmetry.

Step-by-step explanation:

The Rotational symmetry is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane. A shape is said to possess rotational symmetry when it still looks the same after we rotate it.                                            

The required solution of the expression is x = -3.

Given that,
To determine the solution of the equation  3x-15/2=4x.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Simplification of 3x-15/2=4x.
3x  - 15 = 8x
5x = -15
x = -3

Thus, the required solution of the expression is x = -3.

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The value of the motorcycle after 9 years, with a depreciation rate of 3% per year, will be approximately $9,800. This answer has been calculated using the formula for percent decrease applied to the initial value of the motorcycle.

This question revolves around the concept of percent decrease, a fundamental topic in mathematics. To estimate the value of the motorcycle after nine years, we need to apply the percent decrease continuously for these years.

The formula is: Final Value = Initial Value * (1 - rate of decrease)number of years

So in this case, the final value will be: $14,000 * (1 - 0.03)^9.

Calculating that gives us approximately $9,855, so the closest answer would be option C, $9,800.

Therefore after 9 years, the motorcycle will have depreciated to around $9,800 in value given a yearly depreciation rate of 3%.

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Final answer:

After using the Pythagorean theorem to calculate the length of the bike path as approximately 2287 feet, and multiplying by the cost of $2.20 per foot, the total comes to $5031.40. This total cost fits within the city planning budget of $5050.

Explanation:

The city planning committee needs to determine if their $5050 budget is sufficient for the bike path extension, with construction costs at $2.20 per foot. To calculate the cost of the bike path, we first must find the length of the path, which will be the hypotenuse in a right triangle formed by the height (880 ft) and the base (2112 ft). Applying the Pythagorean theorem (a² + b² = c²), where a is the height and b is the base, the length of the path (c) can be calculated as follows:

c = √(880² + 2112²) = √(774400 + 4456444) = √5230844 ≈ 2287 ft.

Now, we can determine the total cost by multiplying the length of the path by the cost per foot:

Total Cost = 2287 ft × $2.20/ft = $5031.40

Thus, the total cost for constructing the path would be $5031.40, which is within the city planning budget of $5050.

Knowing if trigonometry knowledge we can say that the distance will be 305.4 ft.

So knowing how sine and tangent work we can write the equals as:

[tex]sin (32) = CD / 960\\CD = 508.72[/tex]

[tex]tan (32) = 508.72 / AD\\AD = 814.13[/tex]

To calculate the distance, we will decrease the two values ​​found, like this:

[tex]814.13 - 508.72 = 305.4 ft[/tex]

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The variance of the five bedroom house is 864.

σ²

[tex]=\frac{X^2}{N} -u^2[/tex]

To get the value of X²

= 100²+100²+120²+120²+180²

= 81200

The number is N = 5

u = mean

[tex]u = \frac{100+100+120+120+180}{5}[/tex]

u = 124

The values in the variance formula

[tex]\frac{81200}{5} -124^2[/tex]

16240-15376

= 864

The variance is 864

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Answer:

The statement which best compares the function F(x) and G(x) is that the graph of G(x) is the graph of F(x) stretched vertically.

Step-by-step explanation:

Since the difference between the two functions is in the coefficent which multiplies the square function, 1 and 2/3 respectively in F(x) and G(x). So, as the coefficient are positive and is minor for G(x) than for F(x), the values for G(x) will be smaller and thus the graph of G(x) would be below the graph of F(x). Therefore the graph for G(x) is it compressed vertically respect to F(x). The explanation here is ore understandable by looking at the illustration attached.

Answer:

[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

We assume that the die is fair and the probability of obatin a one is 1/6.

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=12, p=1/6)[/tex]

And we want to find this probability:

[tex] P(X=12)[/tex]

And if we replace we got:

[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]

Answer:

A. 2 < x < 3

Step-by-step explanation:

The values of x which A ⋃ B = Ø is:

This refers to the grouping of data which can be graphically represented on a Venn diagram.

With this in mind, we have a set of data which makes use of a general set that contains:

Therefore, the values of x to which A ⋃ B = Ø is:

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Final answer:

A square, rectangle, and certain cases of rhombuses and trapezoids can have two consecutive right angles, while typically a parallelogram and kite do not unless they are special cases of the rectangle or square respectively.

Explanation:

In the context of quadrilaterals with two consecutive right angles, it's important to recognize that certain quadrilaterals have this property by definition. A square and a rectangle both have four right angles, which means they certainly have at least two consecutive right angles.

A parallelogram typically does not have right angles, but a rectangle is a special type of parallelogram with right angles, so it fits this description. A kite generally does not have right angles unless specifically constructed to do so, which is not typical.

A rhombus can have right angles, making it a square, so it fits the criteria too. A trapezoid can also have a pair of consecutive right angles when it is a right trapezoid.

Therefore, the list of quadrilaterals that might have two consecutive right angles is not only the square and the rectangle but extends to include the rhombus and trapezoid as well.

Given these definitions, the correct answer to the question would be:

D. i, ii, iii, v, vi

Final answer:

The quadrilaterals that can have two consecutive angles measuring 90° each are squares, rectangles, and certain parallelograms (when they are squares or rectangles). Therefore, the correct answer to the question is B. This includes a square (i), a rectangle (ii), and some parallelograms (iii).

Explanation:

If a quadrilateral has two consecutive angles measuring 90° each, it could be any of the shapes that inherently contain right angles by definition. These shapes are a square, a rectangle, and certain types of parallelograms, specifically rectangles and squares. Both a square and a rectangle always have four right angles, which makes them valid answers. A rhombus or a general parallelogram may also have right angles, but only in specific cases, such as when a rhombus is also a square. Thus, kites and trapezoids do not necessarily fit this criterion as they do not always have consecutive right angles. Therefore, the correct answer is B, which includes a square, a rectangle, and some parallelograms.