The coordinates of the point H are (−2,2) and the coordinates of point I are (6,2). What is the distance, in units, between the point H and point I?

The inequality representing the shaded region is given by 2y - x < 4.

For the given question, the graph is shown,

Consider two coordinates from the graph and find the slope using them.

(x₁, y₁) = (0, 2)

(x₂, y₂) = (4, 4)

slope m = (y₂ - y₁)/(x₂ - x₁)

Put the values.

m = (4 - 2)/(4 - 0)

m = 1/2

Put the value of slope in the equation of line in slope intercept form.

y - y₁ = m(x - x₁)

Put the values;

y - 2 = 1/2(x - 0)

Simplifying;

2y - 4 = x

2y - x = 4

Now, from the graph, as the origin of the coordinate axis and the shaded region region of the graph lies on the same side, the inequality is less than.

2y - x < 4, only less than as the graph is made with dotted lines.

Thus, the inequality representing the shaded region is given by 2y - x < 4.

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Using mathematical operations, the maximum whole number of gigabytes of data Genesis can use while staying within her budget is 2GB.

Mathematical operations are used in mathematical functions to produce a defined output.

Some of the mathematical operations include addition, subtraction, multiplication, division, exponentiation, and modulus operations.

In this situation, we used the mathematical operations of subtraction, division, addition, and multiplication to determine Genesis's data maximum usage that does not exceed her budget.

Fixed cost per month = $40.50

Usage rate per gigabyte or part thereof = $5

Budgeted bill = $55 per month

Maximum gigabyte usage per month = 2.9 {($55 - $40.50) ÷ $5}

But Genesis cannot use 3GB but only 2GB because 3GB will make her total bill exceed her budget.

Check:

Cost of using 3GB = $55.50 ($40.50 + $5 x 3)

Cost of using 2GB = $50.50 ($40.50 + $5 x 2)

Thus, for Genesis to maintain her data plan within budget, the maximum she can spend is 2GB.

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Answer: The arrow is pointing to 76.5.

Step-by-step explanation: It's pointing to 76.5 because there are 10 spaces between 75 and 80 so in that case, each line is .5, and since it's on the third line that means it is 1.5 more than 75 so 76.5.

Answer:

C) The arrow points to 76.5.

Step-by-step explanation:

The number line is divided into 10 parts equally.

We can find out the distance between each point by taking the difference between the largest and smallest number on the number line and dividing the difference by 10.

80 - 75 = 5

5/10 = .5

So, the distance between each number/mark on the line is .5

Now, we can label each point by adding .5 to each mark as we go. Then, we'd get this.

*see attachment below

Since the number line constructed here has all the values, we can now tell which value the arrow is pointing to.

The answer is therefore 76.5.

The statements which best describes the value of the expression 18x – 35, when x = 2 is that the result is a whole number that is neither prime nor composite and is denoted as option D.

This is referred to as the number which is divided by one and itself and there must be exactly two numbers involved.

18x – 35 =  18(2) – 35

                = 36 - 35 = 1

In the case of 1, the numbers involved is just one which 1 which is why it isn't regarded as a prime number. A composite number can be formed with two small integers and the formation of 1 is 1 × 1 which is why 1 isn't.

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Answer:

The Answer Is: D.! The Results is A Whole Number That is Neither Prime nor Composite

Step-by-step explanation:

Hope This Helped! You Have a Great Day!

The number of terms of the second arithmetic progression is 46.

The two arithmetic progression have the same first and last terms.

The first arithmetic progression has 21 terms with a common difference of 9.

The second arithmetic progression have common difference of 4.

Therefore,

using the first arithmetic progression,

a + (n - 1)d = nth term

a + 20(9) = last term

last term = a + 180

using the second arithmetic progression,

a + (n - 1)d = nth term

They have the same last and first term,

Hence,

a + 180 = a + (n - 1)4

a + 180 = a + 4n - 4

180 + 4 = 4n

184 = 4n

n = 184 / 4

n = 46

Therefore, the number of terms is 46

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The value of d i.e. the diameter will be 8 inches when the circumference is 25.12 inches.

The distance a circle's circumference extends from one end to the other is known as the diameter.

The circumference of a circle is the distance of its outer length.

According to the formula, c = πd, c is the circumference of the circle and d is the diameter of the circle.

Value of π is 3.14

When c = 25.12 inches, the value of d will be

d = c/π

d = 25.12/3.14

d = 8 inches

The diameter will be 8 inches when circumference is 25.12 inches.

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The error Julius made in his explanation is using the area of a rectangle as the longest side instead of area of a square.

Pythagorean theorem is the sum of the square of opposite and adjacent sides which result in the sum of the square of the hypotenuse of a triangle.

c² = a² + b²

Where,

The error Julius made in his explanation is using the area of a square as the hypotenuse. The figure he used to represent the longest side (hypotenuse) is a rectangle.

The correct working should be:

c² = area of square a + area of square b

c² = 25 + 16

c² = 41

c = √41

c = 6.40312423743

Approximately,

c = 6.4

In conclusion, Julius made the mistake of representing the longest side with area of a rectangle instead of a triangle.

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Answer:

1/4

Step-by-step explanation:

17/20, 14/20, 11/20, 8/20, 5/20

5/20 = 1/4

This is a Metric conversion problem. Note that it will take 38.4 minutes to create a 2-foot by 4-foot pattern drive. See the explanation below.

There are several ways to do this. Let's use the area of the times and that of the pattern drive.

Note that the area of the 3inch by 5-inch tile =

Area of a rectangle

L x B =

3 x 5

= 15inches

Applying the same rule to the pattern drive, we have
2 x 4

= 8 foot

Note that 1 foot = 12 inches

For convenience, thus, we convert the area of the pattern drives into inches. This gives us:
8 x 12

= 96 inches

To get how many minutes it will take to create a 2 by 4-foot pattern drive, we have

Recall that it takes 6 minutes to lay a 3x5 which is 12 inches in area.
Hence,

96/15
= 6.4
6.4 x 6
= 38.4 minutes.
Hence, it will take Rachel 38.4 minutes to lay a 2 by 4-foot pattern drive given the parameters above.

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Answer: 60.96 pi or just 60 pi rounded to the nearest whole and the base is a circle , the shape is a cylinder

Step-by-step explanation:

Answer: [tex]y=\frac{1}{7}x+19[/tex]

Step-by-step explanation:

Perpendicular lines have slope that are negative reciprocals, so the slope of the line we want to find is 1/7.

The equation in point-slope form is [tex]y-21=\frac{1}{7}(x-14)[/tex].

Rearranging into slope-intercept form,

[tex]y-21=\frac{1}{7}x-2 \\ \\ y=\frac{1}{7}x+19[/tex]

the length of the rectangle is 10 cm and the width of the rectangle is 11 cm.

We are given that the length and the width of a rectangle are consecutive integers.

Let the length be x

Width = x + 1

Now, we are also given that perimeter is:

P = 42 cm

We know the formula for perimeter of a rectangle is:

P = 2( l + w)

Substituting the values in the formula, we get that:

42 = 2( x + x + 1)

42 = 2 (2 x + 1)

42 = 4 x + 2

4 x = 40

x = 40 / 4

x = 10

length = 10 cm

width = 10 + 1 = 11 cm

Therefore, we get that, the length of the rectangle is 10 cm and the width of the rectangle is 11 cm.

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The layer of dirt would be between 3 and 4 yards and precisely 3.6458 yards.

Given the volume of the lot is 7000 cubic yards.

After spreading to an even layer

The dimension is 30 yards and 64 yards

The volume of the lot can be given as Length x Width x Depth

Let us say the depth of the lot is x

Which means

30 x 64 x X = 7000

1920 x X = 7000

X = 3.6458

Hence the depth of the lot is 3.6458 which is between 3 and 4.

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The experimental probability of an odd number other than 9 being generated is 0.38.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes.

Given Data

A random number generator is used to create a list of 150 single-digit numbers. Of those 150 numbers, 72 are odd and 78 are even. The number 9 was generated 15 times.

Total numbers generated = 150

Odd numbers = 72

Even numbers = 78

Generation of number 9 = 15

Number of odd numbers except 9 itself

= 72 -15

= 57

Probability = [tex]\frac{Odd numbers except 9 itself}{total munbers}[/tex]

Probability = [tex]\frac{57}{150}[/tex]

Probability = 0.38

The experimental probability of an odd number other than 9 being generated is 0.38.

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Answer:

Step-by-step explanation:a-t457 =e36_0uh

Answer:

B) To make a right triangle in the center, the area of the smaller two square must add to equal the area of the largest square

Step-by-step explanation:

1) add the area of the two smaller squares together

f^2= 9

g^2 = 16

9+16=25

2) compare the sum of the two squares to the larger square (the hypotonus)

h^2= 25 so, f^2 + g^2 = h^2

3) The area of the smaller squares is equal to the area of the larger square, therefore b is the correct answer.

Using combinations, the probability that a randomly selected jury of 12 people is all male is 0.00781.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given,

Jury pool consists of 27 people, 20 men and 7 women

the probability that a randomly selected jury of 12 people is all male =

[tex]\frac{^{20}C_{12} }{^{27}C_{12} }[/tex] = [tex]\frac{20!}{12! 18!}[/tex] × [tex]\frac{12! 15!}{27!}[/tex]

On solving,

⇒ 1/128

= 0.00781

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Step-by-step explanation:

0 20 40 60 80 100.................

Answer:

a) 0.25% b) 99.75%

Step-by-step explanation:

the chance that one bulb is defective is 0.05, so two bulbs being defective has a chance of 0.05 * 0.05 which equals 0.25%

For at least 1 bulb to work, both bulbs can't be broken. We already know that the chance for both bulbs being broke is 0.25%, so 100%-0.25% would equal the chance that at least one light bulb works, which is 99.75%

Answer:

m= 3

Step-by-step explanation:

In the slope-intercept form (y= mx +c), the coefficient of x (when the coefficient of y is 1) is the slope.

y= x +5

Slope of line= 1

Parallel lines have the same slope, hence the slope of 3y -mx +3= 0 is also equal to 1.

Let's rewrite the equation into slope-intercept form.

Keep the y term on the left-hand side, bring the others to the right.

3y= mx -3

Divide both sides by 3:

[tex]y = \frac{m}{3} x - 1[/tex]

Given that the slope is 1,

[tex] \frac{m}{3} = 1[/tex]

Multiply both sides by 3:

m= 1(3)

m= 3

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Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient so equation of line is y = -3x + c.

Substitute (1,7) into the equation to find c.

7 = -3(1) + c

c = 10

Hence equation of line is y = -3x + 10

The polynomial that represents the volume of the rectangular box is 3x² - x - 24 = 0

The dimension of the rectangular box are 9 inches, 8 inches and 3 inches.

The volume of the rectangular box can be expressed as follows:

volume of the rectangular box = l w h

where

Therefore,

w = x inches

l = 3x

h = 3x - 1

volume of the rectangular box = 72x

Therefore, the polynomial that represents the volume of the rectangular box is as follows:

72x = 3x × x × (3x - 1)

72x = 3x²(3x - 1)

72x = 9x³ - 3x²

9x³ - 3x² - 72x = 0

3x(3x²- x - 24) = 0

3x² - x - 24 = 0

Therefore,

x = 3 or - 8 / 3

we can only use positive values.

Hence, the dimension of the rectangular box is as follows:

w = 3 inches

l = 3(3) = 9 inches

h = 3(3) - 1 = 8 inches

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if an organization wants to test whether a minority of its employees are dissatisfied with their bonuses, the null hypothesis would be that the true population proportion would be equal to 0.5

This is further explained below.

Generally, The null hypothesis is a common kind of statistical theory that proposes there is no statistical link and significance between two sets of observed data and measurable phenomena in a set of provided single observable variables.

In conclusion, In the event that a company is interested in determining whether or not a subset of its workers are unsatisfied with the incentives they get, the null hypothesis would state that the actual population percentage would be equal to fifty percent.

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CQ

If an organization wants to test whether a minority of its employees are dissatisfied with their bonuses, the nult hypothesis would be that the true population proportion would be: less than 5 OOOO greater than 5 not equal to 5 .5

The correct answer is:  " 1 * 2 <  1 + 2 ".

____________

Step-by-step explanation:
The following text provides a detailed explanation of how one can reach the answer.
______
We are given:  "{Use digits and symbols to write ''the product of one and two is less than the sum of one and two'' pls help}."
______
Okay;  First, relax.  Then:
Second:  Note the following parts of the Actual Brainly Question:                                                                                          
1) "Use digits and symbols" to..  (represent this word problem/inequality).
2) Write down the following—including the "blanks" :
      {The product of _____ is less than the
sum of ____ " ;

3)  Then, Refer to:  "{The product of 1 and 2 is less than...}" ;

Note: The "{product of 1 and 2}" ; indicates multiplying " 1" by " 2" ;
    →  {e.g. to get the product; that is; to get the value when multiple numbers [i.e. "two or more numbers"] are multiplied.}.
      When one multiplies " 1 " by "2", the product is "2" ;

       [since:  " 1 * 2 = 2 "] ;  yet, for our purposes, we shall write:
     →  "  1 * 2  " ;
______
Then:  Note that this ^[product of 1 and 2) is "less than...{something}..." ;
  Let's start by writing a "less than symbol { < }" ;
            →    " 1 * 2 <   ? " ;
  Then, go back to the problem and note:
      " {...is less than "the sum of one and two"} " ;
Take note of the phrase: "[the sum of one and two]" ;
We can write this as:  " 1 + 2 " ;  
      ⇒ " the sum [of]..." indicates addition; that is, adding values [together] .

So; we can write this inequality by using digits and symbols; as follows:
     →  " 1 * 2 <  1 + 2 " ;  which is our answer.
______
{ For potential interest:  
One could simplify each side of the equation:
1 *2 =2  ;   1 + 2 = 3 ;   2 < 3  ;  which does hold true!
However, the actual question never specifically states to simplify}.
 As aforementioned:
     →  " 1 * 2 <  1 + 2 " ;  is  our answer!
 ______
   Hope this lengthy explanation is helpful!
    Wishing you the best!

 ______

answer

The correct answer is:  " 1 * 2 <  1 + 2 ".

____________

Step-by-step explanation:

The following text provides a detailed explanation of how one can reach the answer.

______

We are given:  "{Use digits and symbols to write ''the product of one and two is less than the sum of one and two'' pls help}."

______

Okay;  First, relax.  Then:

Second:  Note the following parts of the Actual Brainly Question:                                                                                          

1) "Use digits and symbols" to..  (represent this word problem/inequality).

2) Write down the following—including the "blanks" :

     {The product of _____ is less than the

sum of ____ " ;

3)  Then, Refer to:  "{The product of 1 and 2 is less than...}" ;

Note: The "{product of 1 and 2}" ; indicates multiplying " 1" by " 2" ;

   →  {e.g. to get the product; that is; to get the value when multiple numbers [i.e. "two or more numbers"] are multiplied.}.

     When one multiplies " 1 " by "2", the product is "2" ;

      [since:  " 1 * 2 = 2 "] ;  yet, for our purposes, we shall write:

    →  "  1 * 2  " ;

______

Then:  Note that this ^[product of 1 and 2) is "less than...{something}..." ;

 Let's start by writing a "less than symbol { < }" ;

           →    " 1 * 2 <   ? " ;

 Then, go back to the problem and note:

     " {...is less than "the sum of one and two"} " ;

Take note of the phrase: "[the sum of one and two]" ;

We can write this as:  " 1 + 2 " ;  

     ⇒ " the sum [of]..." indicates addition; that is, adding values [together] .

So; we can write this inequality by using digits and symbols; as follows:

    →  " 1 * 2 <  1 + 2 " ;  which is our answer.

______

{ For potential interest:  

One could simplify each side of the equation:

1 *2 =2  ;   1 + 2 = 3 ;   2 < 3  ;  which does hold true!

However, the actual question never specifically states to simplify}.

As aforementioned:

    →  " 1 * 2 <  1 + 2 " ;  is  our answer!

______

  Hope this lengthy explanation is helpful!

   Wishing you the best!

______

Step-by-step explanation:

1 f(x) = ax (x − a)² + 1

Take the derivative

f'(x) = d/dx ( a x( x -a) ²+1

Use differentiation rules

f' x = ax2 x-a +0

Simplify

= f'(x)=2ax-2a²

answer

The value of k that will make the quadratic equation kx² - 4x + 1 = 0 to have two equal roots is; k = 4

The general form of representing a quadratic equation is;

ax² + bx + c = 0

Now, we are given the quadratic equation which is;

kx² - 4x + 1 = 0

Now, for a quadratic equation to have 2 equal roots, it means that;

b²  = 4ac

Thus, applying that to our given quadratic equation gives us;

(-4)² = 4(k * 1)

4k = 16

k = 4

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Answer: The value of f/5 is 4.

Step-by-step explanation:  This question can be solved by using substituting the value of f( which is 20) in the earlier given expression ( which is f/5).

Here are the steps to solve this question:-

Step 1. Expression = f/5 ( according to the question)

Step 2. Value of f=20 ( according to the question)

Step 3. Using the value of f in step 2 in the equation given in step 1,

                        f/5=20/5

                         f/5=4

Thus, the value of expression f/5 is 4.

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Graph is plotted below.

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x, y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line. A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Coordinates are:

(-6,-8)

(1,--8)

(10,-8)

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