Determine the constant of variation for the direct variation given. 2 1

The fourth term a₄ of the sequence is 15

The definition of the function is given as

a₁= 6

aₙ = aₙ₋₁ + 3

The above definitions imply that we simply add 3 to the previous term to get the current term

using the above as a guide,

so, we have the following representation

a₂ = 6 + 3

a₂ = 9

Also, we have

a₃ = 9 + 3

a₃ = 12

Lastly, we have

a₄ = 12 + 3

Evaluate the equation

a₄ = 15

Hence, the value of a₄ is 15

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Answer:  "If my bill is not expensive. I did not use my cell phone too much"

Reason:

The original statement is of the form "If P, then Q"

P = "I use my cell phone too much"

Q = "my bill will be expensive"

An equivalent form to the original condition is known as the contrapositive of the form "If not Q, then not P". We swap the positions of P and Q. We also negate each part. You can use a logical truth table to verify that the conditional and contrapositive have equivalent truth values, which means they are effectively equivalent statements.

Answer:

If my bill is not expensive. I did not use my cell phone too much

Step-by-step explanation:

Answer:

Step-by-step explanation:

tents is what place it is <3

The family of all linear equations that are parallel to y=-1/2x-2 is defined as:

y = (-1/2)*x + b

Such that b ≠ -2.

We know that a general linear equation is written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

We know that two linear equations are parallel if and only if the lines have the same slope and a different y-intercept.

So the family of lines parallel to:

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

Are of the form:

y = (-1/2)*x + b

Where b ≠ -2.

All these lines are parallel to the given ones.

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The other wall is 12 feet long can be evaluated using Pythagoras theorem.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can  find out the length of the other wall

b²=h²-p²

b²=13²-5²

b²=169-25=144

b=√144

b=12 feet

Hence the other wall is 12 feet long.

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• x(5-2)=4x-x

distributive property:

5x -2x = 4x -x

3x =3x

Infinite solutions

• 14x - 17 -8x + 2 = 12x +3 -x - 10

Combine like terms:

14x -8x -12x +x = 3 - 10 + 17 - 2

-5x= 8

x = -8/5

Unique solution

• 6(x-2)=6x-12

Apply distributive property:

6(x) + 6(-2) = 6x-12

6x - 12 = 6x - 12

Since both sides are equal:

Infinite solutions

• 2/3x - 7/4 = 4/3x - 2/3 (x+5)

Apply distributive property:

2/3x-7/4 = 4/3x - 2/3(x) - 2/3(5)

2/3x-7/4= 4/3x-2/3x - 10/3

Combine like terms

2/3x + 2/3x - 4/3x = -10/3 + 7/4

0 = -19/12

Since 0 is not equal to -19/12

No solution

This makes the correct answer to be exponential function

Answer: It would be c x=12

Step-by-step explanation:

Answer

Answer = (6.95 × 10⁻¹⁰)

Explanation

We are asked to solve (13.9 × 10⁻⁸) ÷ (2 × 10²)

To solve this, we will have

Hope this Helps!!!

Force, F = 585 N

Angle, θ = 80°

The diagram that shows the resolution of the force into its rectangular component is drawn below

The magnitude of the horizontal component is:

The magnitude of the vertical component is:

Therefore, the magnitudes of the horizontal and vertical components of the force are (576, 102)

Answer:

[tex]-4 \leq x < -2.2[/tex]

Step-by-step explanation:

-5x - 3 > 8
-5x > 11
x < -11/5
We know that -4 ≤ x ≤ 3 and x < -11/5 (-2.2)
-4 <= x < -2.2

The number of mangoes = 48

The number of grapefruit = 12

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A box of fruit has four times as many oranges as grapefruit.

And, Total number of fruit = 60 pieces

Now,

Let number of grapefruit = x

Then, Number of Mangoes = 4x

So, We can formulate;

⇒ x + 4x = 60

Solve for x as;

⇒ 5x = 60

⇒ x = 12

Thus, Number of grapefruit = x

                                          = 12

Then, Number of Mangoes = 4x

                                          = 4 × 12

                                          = 48

Therefore, The number of mangoes = 48

The number of grapefruit = 12

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The answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.

Given:

x = 3 , y = 1/3 and z = 5 and expression  12x - 3y / 4x - z.

substitute the x,y,z values in expression.

= 12(3)-3(1/3) / 4(3)-5

= 36 - 3/3 / 12 - 5

= 36 - 1 / 7

= 35/7

= 5.

Therefore the answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.

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Answer

Area = 324π ft²

Explanation

The area of a circle is given as

Area = πr²

where

π = pi

r = radius of the circle = 18 ft.

Area = πr²

Area = π (18²)

Area = 324π ft²

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The price of the online ticket after discount, including sales tax, is  $423.81.

Percentage is a measurement to find the value of a given number out of a hundred.

Given that,

The original price of the airline ticket = $473

Discount after applying coupon code = 20%

The price after applying coupon code = 473x4/5  = 378.4

Since, there is a sales tax of 12%,

So the price of airline ticket after sales tax = 378.4 x 112/100 = 423.808

The price of online ticket after discount and including sales tax is  $423.81

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The results of the transformations carried out are respectively;

1) Preserves only angles but not distance

2) Preserves both angles and distance.

3) Preserves only angles but not distance

In transformations, there are different types such as dilation, reflection, translation, rotation, e.t.c

1) Dilation of a quadrilateral by a scale factor of 2;

When we dilate by a scale factor of 2, it simply means we are enlarging the side lengths by a scale factor of 2. Thus, the side lengths will increase but angles remain the same.

2) Translation of a rhombus 3 units to the right and then a reflection across the x-axis;

When we translate an object, it means we just move it from one point to the other and this means that the length and angles do not change, Similarly, reflection is just a mirror image and it also means that the length and angles do not change.

3) Translation of a triangle 2 units to the left and then a dilation by a scale factor of 5 about the origin;

This will end up changing the side lengths but not the angles.

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Answer:

10^5

Step-by-step explanation:

10 is multiplied by itself 5 times so you use 5 as the exponent

10 is the number you're multiplying so it the bottom number

10^5

The system of equations we have is:

And we need to check if the point (3,-1) is a solution.

Step 1. Identify the values of x and y from the point.

In a point, the first number represents the x-value, and the second number represents the y-value. So in point (3,-1) 3 is the x-value, and -1 is the y-value:

Step 2. Substitute the x and y-value into the first equation and check that the result is equal to -7.

The first equation is:

Substituting x=3 and y=-1:

Solve the operations:

Since we get -7 as the result, (3,-1) is a solution for the first equation. But we still need to check if the point is a solution for the second equation.

Step 3. Substitute the x and y values into the second equation and check that the result is 1.

The second equation of the system is:

Substituting x=3 and y=-1:

Solving the operations:

The result we get is -1, not 1. Thus, since the point (3,-1) is not a solution for the second equation, it is also not a solution to the system of equation.

Answer: False

Given two quantities (number of cookies and carrot sticks), we find the greatest common divisor (gcd) to know that were 20 cast members at the party. Below is a solution algorithm written in Python.

if __name__ == '__main__':

a = int()

b = int()

x = int()

gcd = int()

# Number of cookies

a = 20

# Number of carrot sticks

b = 40

gcd = 1

x = 1

while x<=a:

 if a%x==0 and b%x==0:

  if x>gcd:

   gcd = x

 x = x+1

print("Number of cookies: ",a)

print("Number of carrot sticks: ",b)

print("Number of cast members at the party: ",gcd)

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As it is normally distributed, we can use Z to find the result.

Procedure

0. Finding the value of ,Z

1.2. Replacing the values given in the problem:

2. As it is normally distributed:

3. Using the normal standard table, we can conclude:

As it is asking for a percentage, we multiply by 100.

Answer: C) 84%

The domains of each function are classified as follows:

The domain of a function is the set composed by all the input values that are assumed by the function.

For each function in this problem, the inputs are given as follows:

Hence, the domain of function A is a discrete domain, as the number of quarters in the jar can assume countable values such as 0, 1, 2, ..., it does not assume decimal values.

For function B, the domain is a continuous domain, as measures of time can assume decimal values, for example, 10.5 minutes.

These differences discussed represent the comparison of the domains of each function.

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3/6, 1/4, 1/8

Step-by-step explanation:

All three fractions have a common denominator of 24.

1/4=6/24

3/6=12/34

1/8=3/24

Lastly, order them from greatest to least, hence 3/6, 1/4, and 1/8

Given: An objective function

with constraints-

Required: To graph the linear inequalities representing the constraints and determine the objective function's value at each corner.

Explanation: The inequalities can be graphed by considering them as equations and then determining the shaded region by less than or greater than symbol.

The equation for the first inequality is-

This represents a straight line passing through points (6,0) and (0,12).

The shaded region will be below this line as the inequality is-

Similarly, the inequality-

Represents a shaded region above the line x+y=6.

The inequalities-

Represents the positive values of x and y. Hence we need to determine the graph in the first quadrant.

The graph of the inequalities is-

The graph in blue represents the inequality-

While the graph in green represents the inequality-

The corner points of the common shaded area are A(0,6), B(0,12), and C(6,0).

Now the value of the objective function at these points is-

a) At A(0,6)

b) At B(0,12)

c) At C(6,0)

Final Answer: a) The graph is drawn.

b) 36,72,18

Answer:

x = 1 , x = 13

Step-by-step explanation:

(x - 7)² = 36 ( take square root of both sides )

x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )

x = 7 ± 6

then

x = 7 - 6 = 1

x = 7 + 6 = 13

Let x be the total amount collected at the door. Then, we can write

where the 0.02 denotes the comission of 2%. From this equation, we can find x.

Then, by moving 3000 to the right hand side, we have

which gives

Now, by moving 0.02 to the right hand side, we get

then, x is given by

Therefore, the total amount collected at the door is $ 27 000.

After making and solving an equation, we can say that the value of x is 1.

So, to find the value of x, we will solve the equation:

7(x/9) + 2 = 25/9

Now, solve this equation as follows:

7(x/9) + 2 = 25/9

7x/9 = 25/9 - 2

7x/9 = 7/9

x = 1

Therefore, after making and solving an equation, we can say that the value of x is 1.

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We have the following equation given:

If we solve in the form y=mx+b we got:

Part a

S

We are asked to determine the equation of an ellipse that has a base of 40 feet and a height of 18 feet. This can be visualized in the following diagram:

The general form of the equation of an ellipse is:

We have set the origin of the coordinate system to be in the middle of the ellipse. The value of "a" is the x-intercept of the ellipse and the value of "b" is the y-intercept of the ellipse. Therefore, the equation is:

Now, we solve the squares:

And thus we have determined the equation of the ellipse.

PART B

The probability is 1/2

STEP - BY - STEP EXPLANATION

What to find?

The probability of identical twins given that the twins consists of two boys.

Let A be the event of identical twins.

Let B be the event of having two boys as twins.

From the table given;

P(A) = 2/38

P(B)= 2/38

Recall the formula for a condititional probabibility

Note that:

P(A n B) =1/38

Therefore, the probability of identical twins given that the twins consists of two boys is 1/2