Tell whether x and y show direct variation, inversevariation, or neither. Explain your reasoning.X 24.68y -5 -11 -17 -23The products xy areThe ratios Y areХSo, X and y show

Answer:

They can speak in 40, 320 different orders

Explanation:

Given that 8 people have to give a presentation in class.

They can speak in many different orders:

First could be second, second could be first, third could be eight, seventh could be fifth, and so on.

This number of ways result in factorial 8.

This is written as:

Which represents the multiplications of numbers on the number line from 8 down to 1.

That is:

Here, we want to get the value of x

As we can see, we have the interior angle as 45;

The other is 90; and that means the last angle will be 45

This mean that we have an isosceles right-triangle

The sides that face the angles are equal

These sides are x and 12

That means x = 12

To get the value of y, we have to use the Pythagoras' theorem

The square of the hypotenuse (the longest side and the side that faces the right angle) is equal to the sum of the squares of the two other sides

The side facing the right angle is y

So, the sum of the squares of x and 12 will give the square of y

Mathematically, we have this as follows;

three hundred and seventeen and ninety-eight thousandths

3 = hundreds

1 = ten

7 = ones

Number after the decimal point start in ythe tenth place

0 = tenth

9 = hundredths

8 = thousandths

Naming the number:

three hundred and seventeen and ninety-eight thousandths

When converting a number from decimal to scientific notation,

The exponent is positive if the movement of the decimal point is to the left

The exponent is negative if the movement of the decimal point is to the right.

Examples :

The decimal point moves from the right of the last digit to the place between 1 and 2. It moves to the left so the exponent is positive.

The decimal point will move 3 places to the right, so the exponent will be negative.

Given relation is

Here, d is the distance in kilometers and t is the number of hours.

Since distance and time both vary, therefore, they are not constants.

The only value which is fixed is 50.

Therefore, the only constant of proportion is 50.

Since the ratio of two valus are constant, therefore, they are in direct proportional relationship.

From the given relation, we can write

Hence, another relationship between d and t is

We have an expression:

We have to evaluate it when a = 3 and x = -5. To do that we replace a and x by its values and calculate:

Answer: the expression value is -29

See graph below

We have two inequalities:

y < 6

y > x + 3

To plot the inequalities on a graph, we change the inequality sign to equal to in order to get points to plot the graph:

y = 6

This means at y = 6, there will be an horizontal line for all values of x. But due to the less than sign, it means the horizontal line will be shaded down.

y = x + 3

We assign values to x inorder to get y values:

let x = -2, 0, 2, 4

when x = -2

y = -2 + 3 = 1

when x = 0

y = 0 + 3 = 3

when x = 2

y = 2 +3 = 5

when x = 4

y = 4 + 3 = 7

When we plot this points, we get a straight line. SInce the sign is greater than, the line will be shaded towards the positive side

plotting the graph:

First inequality

Both inequalities:

Answer:

Distribution property method

We know that there are 2.54 cm in 1 inch

2.54 cm ⇔ 1 inch

We want to find what is the distance in inches of 14 cm:

14 cm ⇔ ?? inch

Then, we have the following equivalence:

14 cm ⇔ ?? inches

2.54 cm ⇔ 1 inch

If we divide both sides of the equivalence we would have the same proportion:

Solving both sides of the equation:

This means that:

14 cm ⇔ 5.51 in

We want to round our result to the nearest tenth. This is a number with one digit after the decimal point:

5.51 in ≅ 5.5 in

If a shop sells on average 250 can's of juice a day and  there are 25500 cans, these stocks last​ for 102 days

A shop sells on average 250 can's of juice a day, it has, it has 25500 cans in stock. We need to find the number of days these stocks will last.

The number of days can be found by using unitary method

1 can of juice is being sold in 1/250 day

25500 can of juice will be sold in 1/250 (25500)

25500 can of juice will be sold in 102 days

Therefore, if a shop sells on average 250 can's of juice a day and  there are 25500 cans, these stocks last​ for 102 days.

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D=35.8 °

Acute angles measure less than 90 degrees, to solve this we need to use a calculator

Step 1

a) let

, b) now, use the inverse tan function to isolate D

so, the answer is

D=35.8 °

I hope this helps you

Answer:

The sequence is given below as

Step 1:

The nth term of an arithmentic progression is given below as

To figure out the common difference, we will use the formula below

Step 2:

The first term of the sequence is given below as

Step 3:

Substitute the value of a and d in the formula below

Hence,

The final answer is

OPTION A is the right answer

The required perimeter of the scale drawing is given as 18 inches.

Given that,
The rectangular floor of a classroom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. The perimeter, in inches, of the floor in the scale drawing, is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
According to the question,

L = 30 feet, W = 24 feet,
for Scaled drawing
l = 5 inch, w = x
Now,
30/5 = 24 / x
6 = 24 / x
x = 24 {1/6}
x = 4,
So the width of the scale drawing is 4 inches,
perimeter of the scaled drawing  = 2[l + w]
                                                       = 2 [5 + 4] = 18 inches

Thus, the required perimeter of the scale drawing is given as 18 inches.

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Using the order of operation which states

Expressions in brackets/parentheses are evaluted first, followed by expressions involving orders, division, multiplication, addition and subtraction in that order.

Thus,

1)

thus, 3+(7−5)2×6 = 27

2)

thus, 25(4+4)×2 = 400

3)

thus, 8−6÷2+3×5 = 20

4)

thus, 7×3−15÷5 = 18

5)

thus, 8+2(1+12÷2)2 = 36.

We will use the next image

the angles in red are equals

The angle in blue is 30°

We need to remember that the sum of the interior angles of a triangle must be 180°

x is the red angle

2x+30=180

2x=180-30

x=150/2

x=75

the angle DBC can be calculated as a complementary angle, the complementary angle is formed with two angles that form an angle of 90°

angle DBC =90-75

angle DBC=15° the angle in green in the image

13.2 inches is. 10,730

1500 km , how far apart are

Find X= (1500/10,730) = 150/1073= 0.14

then multiply by 13.2

13.2X = 1.85

Then ,in a globe , distance between C and D cities is 1.85 inches

Answer is 1.85 inches

Given:

The radius of circle is 11 inch

The value for pi is 3

The objective is to find the area of the circle.

The area of the circle is given by the formula:

Substituting ,r = 11

We get:

Hence, the area of the circle is 363 square inches

"The square of x..." translates to x²

"...is greater than or equal to 10." translates to ≥ 10.

To determine if 3 is a solution, substitute 3 to the inequality.

The resulting number, 9 is not greater than 10. Therefore, 3 is not a solution.

Let x = the original price of the desk.

It's known that 73% of the price is $438, thus:

Multiplying by 100 and dividing by 73:

The original price of the desk was $600

Answer:

=[tex] \sqrt{85} [/tex]

Step-by-step explanation:

let, (x1,y1) = (2,-5) & (x2,y2) = (-7,-7)

now, for distance between two points,

D = [tex]\sqrt[]{(x_{1}-x_{2} )^{2} +(y_{1}-y_{2} )^{2} }[/tex]

=[tex]\sqrt[]{(2-(-7))^{2}+(-5-(-7))^2 }[/tex]

[tex]=\sqrt{(2+7)^2+(-5+7)^2}[/tex]

[tex]=\sqrt{9^2+2^2}[/tex]

[tex]=\sqrt{81+4}[/tex]

[tex]=\sqrt{85}[/tex]

Answer:

[tex] \huge{ \boxed{ \sqrt{85} \: \text{or} \: 9.219 \: \text{units}}}[/tex]

Step-by-step explanation:

The distance between two points say [tex] A(x_1,y_1) [/tex] and B(x_2,y_2) can be found by using the formula;

[tex] \bold{d = \sqrt{{x_2-x_1}^{2}+{y_2-y_1}^{2}}} [/tex]

From the question the points are (2, – 5) and ( – 7, – 7)

[tex] x_1=2 \\ y_1=-5 \\ x_2=-7 \\ y_2=-7 [/tex]

Substituting the values into the formula that is;

[tex]d = \sqrt{ {( - 7 - 2)}^{2} + {( - 5 - - 7)}^{2} } \\ d = \sqrt{ {( - 9)}^{2} + {(2)}^{2} } \\ d = \sqrt{81 + 4} \\ d = \sqrt{85} = 9.219[/tex]

We have the final answer as

PART A:

Let the number of days be represented by t. Let the total cost be represented by C.

FOR COMPANY A:

The equation to represent the total charges will be given as

FOR COMPANY B:

The equation to represent the total charges will be given as

PART B:

Company B will charge less over a 9-day rental period.

To confirm this answer, we will calculate the cost using the equations derived above:

FOR COMPANY A:

FOR COMPANY B:

Therefore, COMPANY B will charge less over 9 days.

PART C:

To know how much is saved over a 15-day period, we will first calculate the cost of both companies over the period using the equations derived from Part A.

FOR COMPANY A:

FOR COMPANY B:

We can, thus, calculate the difference as

Therefore, the amount saved will be $19 over 15 days.

x - 4 = 4 - x

4 is subtracting on the left, then it will add on the right

x is subtracting on the right, then it will add on the left.

x + x = 4 + 4

2x = 8

2 is multiplying on the left, then it will divide on the right

x = 8/2

x = 4

So, there is only one solution

Recall that the signs

helps us indicate if there is an increase or a decrease.

If the number represents a decrease from the previous one, we put a minus sign. If the number represents an increase then we put a plus sign.

Notice that Ivanna lost $40, therefore, the total money she had decreased by 40.

If the company produced 540 more cars this month than last month, then there was an increase of 540 in cars production.

Answer:

(a)

(b)

A. The function f(-2) is larger than f(2)

B. The function f(4) is smaller than f(0)

Given,

The function;  f(x) = x²- 5x + 1

We have to find;

A. The larger is f(2) or f(-2)

Here,

f(2) = 2²- 5 x 2 + 1 = 4 - 10 + 1 = - 6 + 1 = -5

f(-2) = -2²- 5 x -2 + 1 = 4 + 10 + 1 = 15

That is,

The function f(-2) is larger than f(2)

B. The smaller is  f(0) or f(4)

Here,

f(0) =  0²- 5 x 0 + 1 = 0 - 0 + 1 = 1

f(4) = 4²- 5 x 4 + 1 = 16 - 20 + 1 = - 4 + 1 = -3

That is,

The function f(4) is smaller than f(0)

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The ordered pair which makes both inequalities true are (3, 0).

Inequalities are mathematical expressions where neither side is equal.

Contrary to equations, we compare two values in inequality.

Less than, greater than, or not equal to signs are used in place of the equal to sign in between.

Let us consider the ordered pair (3, 0)

In the first inequality

y > -2x + 3

Substituting the values of x and y

0 > -2(3) + 3

0 > -6 + 3

0 > -3

In the second inequality

y < x - 2

Substituting the value of x and y

0 < 3 - 2

0 < 1

Therefore, the ordered pair which makes both inequalities true are (3, 0).

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Given the word problem:

The numerator of the expression is the product of 5 and the sum of x and y and The denominator is the product of negative 8 and x.

The numerator will be the value on top in a fraction.

Here, the numerator is the product of 5 and the sum of x and y ==> 5(x + y)

The denominator is the value below in a fraction.

Here, the denominator is the product of negative 8 and x ==> -8x

Therefore, the expression that fits this description is:

The coordinates of the vertex are:

Applying the translation rule:

G(0, 4) → (0-5, 4+2) → G'(-5, 6)

4(1 + 9x)

4 + 36x (Distributing)

The answer is 36x + 4