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We will have the following:

*Initially, as x increases, y decreases.

*The slope of the graph is equal to -1 for all x between x = 0 & x = 3.

*Starting at x = 3, the function value y increases as x increases.

*The slope of the graph is equal to 3 for x between x = 3 & x = 5.

*For x between x = 0 & x = 4, the function value y ≤ 0.

*For x between x = 4 & x = 8, the function value y ≥ 0.

SOLUTION

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Write the formula for total surface area of cuboid

STEP 2: Get the dimension of the sides

STEP 3: Substitute the dimensions into the formula to get the value of x

STEP 4: Get the other dimensions

Hence, the dimensions are:

The value of x in the angles is 19.

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, let's find the value of x in the intersecting lines.

Hence,

7x - 8 = 6x + 11 (vertically opposite angles)

Vertically opposite angles are congruent and they share the same vertex point.

Hence,

7x - 8 = 6x + 11

subtract 6x from both sides of the equation

7x - 8 = 6x + 11

7x - 6x - 8 = 6x - 6x + 11

x - 8 = 11

add 8 to both sides of the equation

x - 8 + 8 = 11 + 8

x = 19

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Explanation:

Area of the rectangular rug = length × width

dimension of rug = 9'×12'

length = 12', width = 9'

Area = 12 × 9

Area = 18

We will use the following formula:

First, we compute the probability that we get a blue marble:

Now, we compute the probability of getting an odd-numbered marble:

Finally, the probability that we draw a blue and odd-numbered marble is:

Answer: The probability that the marble is blue or odd-numbered is:

Given:

The given expression is,

Required:

Write the product using exponent.

Answer:

Let us compute the product using exponents.

Final Answer:

The product using exponents is given by,

Any two lines must have a point of intersection, with ONLY ONE exception : when the lines are parallel. That means they have exactly the same inclination or Slope.

As an example of two lines that hasnt point of intersection they are

y = 5x + 16

y = 5x + 11

We know both lines have no point of intersection because

both have the same slope or inclination m. By comparation with slope intercept equation

y = mx + b

then we see both have same inclination, and b is 11 in one line and 16 in the other line. This means both lines are parallel with one line going over the other line, without touching it in any point.

If B is the midpoint of AC, this means that point B divides the line AC exactly into 2 equal parts AB and BC, therefore,

Answer A

Thus, if AB = 28, BC = 28 too.

Answer B: Therefore, AC = 56

a) You have to find the greatest common factor for the values 45 and 54

To do so you have to determine the factors for each value and determine the highest value both numbers are divisible for.

Factors of 45 are

1, 3, 5, 9, 15, 45

Factors of 54 are

1, 2, 3, 6, 9, 18, 27, 54

The greatest common factor is 9, this means that you can divide both numbers by 9 and the result will be an integer:

b) Given the addition

You have to factorize the adition using the common factor.

That is to "take out" the 9 of the addition, i.e. divide 45 and 54 by 9 and you get the result (5+6) but for this result to be equvalent to the original calculation, you have to multiply it by 9

we have that

44/13=3.38

rounded to the nearest tenths

3.38=3.4

The equation 2(4-2x)-5=-2(x+5)+8x has a value of  1.3 for x

From the question, the equation to solve is given as

2(4-2x)-5=-2(x+5)+8x

Rewrite the equation properly

This is represented by the following representation

2(4 - 2x) - 5=-2(x + 5) + 8x

Start by opening the brackets in the equation

So, we have the following equation

8 - 4x - 5 =-2x - 10 + 8x

Collect the like terms in the equation

So, we have the following equation

8x - 2x + 4x = 10 +8 - 5

Evaluate the like terms in the equation

So, we have the following equation

10x = 13

Divide both sides of the equation by 10

So, we have the following equation

x = 1.3

Hence, the solution to the equation for x is 1.3

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Answer:

• (a)g[f(x)]=5(-3x+5)+5

• (b)No

Explanation:

Given f(x) and g(x):

(a)First, we find the composition, g[f(x)].

(b)Next, we simplify g[f(x)] obtained from part (a) above.

Given two functions, f(x) and g(x), in order for the functions to be inverses of one another, the following must hold: f[g(x)]=g[f(x)]=x.

Since g[f(x)] is not equal to x, the functions are not inverses of one another.

The end behavior of the polynomial is:

y →  −∞ as x → ∞

y →  −∞ as x → −∞

Here we have the polynomial:

Q(x) = -x²*(x² - 9)

Remember that polynomials with even degrees have the same behavior for the negative values of x than for the positive, in this case if we expand the polynomial we get:

Q(x) = -x⁴ + 9x²

The leading coefficient is negative, then the end behavior will tend to negative infinity in both ends, then we get:

y →  −∞ as x → ∞

y →  −∞ as x → −∞

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The third option that is the distance is the absolute value of the difference describes the relationship between distance and difference.

We know that the distance between two points is the difference of those two values.

But as the distance between two points can never be negative,  we will write the absolute value of the difference as the distance between the two points.

Here we can see that,

a - b = -1  when distance = 1

a - b = 5  when distance = 5

a - b = 3  when distance = 3

Hence, the relationship between difference and distance is described by the third option.

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Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Knowing that [tex]{-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1[/tex],

so x can be positive or negative 4/5,

and we know that x coordinate of any point in quadrant IV is positive,

so x = 4/5.

The area of the triangle given as in the attached image to the task content is; 1 ft².

It follows from the task comtent that the area of the triangle given be determined.

Since the area of a triangle is given by the formula; Area = (1/2) × base × height.

Since the base of the triangle in discuss is 3 ft and it's height (altitude) as given in the task content is; (2/3) feet.

It follows that the area is;

Area = (1/2) × 3 × (2/3).

Area = 1 ft².

Ultimately, the area of the triangle is; 1 ft².

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The original data is:

405, 1108, 84, 315, 495, 609, 362, 428, 224, 338, 700, 790, 814, 767, 633

To find the required percentiles, we need to sort the dataset from lowest to highest.

84, 224, 315, 338, 362, 405, 428, 495, 609, 633, 700, 767, 790, 814, 1108

The total number of data is 15.

a) The 25th percentile is the element located at the position:

25/100 * 15 = 3.75

Rounding down, the position is 3, so the 25th perc

The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).

Given: c = 20, a = 8, and b = x. Find x.

Option A

The graph shows an inverse proportion.

As x increases, y decreases in value.

Finding the slope of the graph:

dy / dx = (y₂ - y₁) / (x₂ - x₁)

x₁ = 5, x₂ = 9, y₁ = 40, y₂ = 30

dy / dx = (30 - 40) / (9 - 5)

dy / dx = -10 / 4

dy / dx = -2.5

This means that as x increases by 1, decreases by 2.5

A is the only correct option.

Inverse proportionality is when the value of one quantity increases with respect to a decrease in another, they behave opposite in nature.

It is represented by the following expression:

Since P=24 when Q=3, we can substitute and solve for the constant k:

Then, the equation that represents the inverse variation would be:

Point B is the midpoint if it divides line segment AC into two congruent segmentsIf point B is not the midpoint, then point B does not divide the line segment AC into two congruent segments, which is the statement opposite to the one that has been made.

Which statement is the converse of the conditional statement ?

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Let:

where:

k = scale factor

If the scale factor is 4, then:

Ok let's take the information given and make an equations system with it.

I'm gonna use H for Hoang present working years and B for those of Bill. We know that right now Hoang has worked for 6 years longer than Bill, with this we can create the following equation:

We also have information from two years ago, at that time Hoang's working years doubled Bill's working years. One would feel tempted to write the equation H=2*B but you have to remember that this information is from the past and H and B stand for working years in the present. The correct way to approach this is change H and B by H-2 and B-2 so we consider that this information is from 2 years ago:

So now we have constructed our equations system:

Let's take the outcome of the first equation and use it in the second one:

And going back to the first equation:

So Hoang has been working at the hospital for 14 years and Bill for 8 years.

The scatter plot is given and objective is to find the best line of fit for given scatter plot.

Let's take the few points of scatter plot,

(0,8) ,( -1,8) , (-4,10) ,( -8,12),(-10,14) (-12,14)

Take the line and check which graph contains most of the points of scatter plot.

The graph is ,

now take ,

The graph is,

This graph contains only one point of scatter plot.

Take,

Now the take the last equation,

this graph contains no point of the scatter plot.

From all the four graph of the lines it is observed that option 1) is the best line of fit for given scatter plot. because it contains 3 points of scatter plotes . which is more than the other graph of line.

Answer: Option 1)

we have the quotient

8/15

remember that

8=2^3

15=3*5

8/15------> its irreducible

we have that

1 nickel=0.5 dimes

so

8 nickels=4 dimes

the ratio is

We know that a function has a unique value of y for each value in x so the correct statement is:

c. it is not a function because there are multiple y values for a given x value

From the given picture, we can see that the figure is a right triangle, so we can apply Pythagorean theorem, that is,

where x denotes the missing length. Then, our equation give us

By taking square root to both side, we have

Therefore, by rounding this result to the nearest tenth, the answer is 9.4 ft

From the question

We are given the equation

We are to find r given that

When x = 2, y = 14

When x = 6, y = 42

When x = 11, y = 77

Substituting the first value, x = 2, y = 14 into the equation we get

Solving for r we get

This is true for all values of x and y

Hence, r

Answer

62% of the number = 806

Explanation

We are told that that the difference between 58% of a number and 39% of the same number is 247.

We are then asked to compute 62% of the number.

Let the number be x.

From the first statement,

58% of x = 0.58 × x = 0.58x

39% of x = 0.39 × x = 0.39x

The difference between them is 247

0.58x - 0.39x = 247

0.19x = 247

Divide both sides by 0.19

(0.19x/0.19) = (247/0.19)

x = 1300

So, we can now calculate 62% of the number

62% of x = 0.62 × x = 0.62 × 1300 = 806

Hope this Helps!!!

ExplanatIon

Step 1

let x represents the number

hence,

four times a number =4*x=4x

the difference of four times a number and seven=4x-7

is can be written as equal or "="",so

the difference of four times a number and seven is 13​

Step 2

solve for x

so, the number is 5.

I hope this helps you