A mouse goes from 0 m/s to 0.4 m/s in 5 seconds. What is the mouse's acceleration?

A set of steps which a student should follow to prove that the diagonals of the square are perpendicular to each other include the following: A) Step 1: Find the slope of diagonal PR and slope of diagonal QS Step 2: Show that m₁ × m₂ = -1.

In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other. Therefore, we would have to calculate the slope of each side by using this mathematical expression:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Where:

x and y represents the data points or side lengths of a quadrilateral.

For side PQ, the slope is given by:

Slope (m) = (8 - 4)/(6 - 2)

Slope (m) = (4)/(4)

Slope (m) = 1.

In Mathematics, a condition that must be met for two (2) lines or side lengths to be perpendicular is given by:

m₁ × m₂ = -1

1 × m₂ = -1

m₂ = -1

Slope (m₂) = -1

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The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.

The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;

(x²+3) (x³+4x) (x²+x-i-xi) = 0.

Hence, by further factorisation; we have;

x(x²+3) (x²+4) (x-i) (x+1) = 0.

The possible values of x are therefore;

x = 0;

x²+3 = 0; x = ±√3i

x² +4 = 0; x = ±2i

x -i = 0; x = i.

x +1 = 0; x = -1

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Answer:

t = - 0.9

Step-by-step explanation:

Given

- 1(t + 8) = - 7.1 ( divide both sides by - 1 )

t + 8 = 7.1 ( subtract 8 from both sides )

t = - 0.9

$ 1.21 * 10⁷ per minute

Movie Earning = $ 1.1 * 10⁹

Movie lasted for = 9.1 * 10¹ minutes

Money earned in 9.1 * 10¹ minutes = $ 1.1 * 10⁹

Money earned in 1 minutes =  $ 1.1 * 10⁹ / (9.1 * 10¹)

= $ 110 * 10⁷ / (9.1 * 10¹)

= $ 12.09 * 10⁶

= $ 1.209 * 10⁷

= $ 1.21 * 10⁷

Movie earning =   $ 1.21 * 10⁷ per minute

Answer:

$ 1.21 * 10⁷ per minute

Step-by-step explanation:

Answer: x is greater than or equal to 18

Step-by-step explanation:

Answer:

x ≤ - 2

Step-by-step explanation:

- x/6 ≤ 3

- x/2 ≤ 1

- x ≤ 2

x ≤ - 2

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

The journal enetry,

Debit cash is $67,000

Debit discount on payable is $670

Credit bonds payable is $66,330

(Recorded on bonds )

Debit Interest expense is $46,90

Debit discount on bonds payable is $46.9

credit cash is $4643.1..

Bonds payable

Bonds issued when the market price equals the standard rate are issued at face value. In other words, the cash received is face value.

Interest paid on the par Bond includes only the indicated. Interest rate calculated based on the number of annual payments.

We have given that

face amount, F = $67,000

Annually paid interest= $67,000

rate of bond, r = 7%

time bond, n = 10 year

market bond of interest= 7%

Coupon ammount = 7% of 67000 =$ 4690

we have to calculate bond issue and first interest payment .

bond price= C×[1 - (1 + r)⁻ⁿ] /r + F/(1+r)ⁿ

= 4690[ 1 - (8)¹⁰]/7 + 67000/(8)¹⁰

=669.99 + 0.000062 = 669.9901 ~ 670

Interest Expense = Principal * Rate * Time

=> Interest Expense = $67,000×7% ×1

= $46,90

discount or primum on bond payable

= interest expense - $66,330×7% × 1

= $46,90- $4643.1 = $46.9

date General

General journal debit credit

January, cash $67,000 $66,330

2024 Bonds

payable

Discount on

bond $670

payable

December

31, cash $4643.1

2024 interest

expense $46,90

Discount on

bond $46.9

payable

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Complete Question:.Pretzelmania, Inc., issues 7%, 10-year bonds with a face amount of $67,000 for $67,000 on January 1, 2024. The market interest rate for bonds of similarrisk and maturity is 7%. Interest is paid annually on December 31.Record the bond issue and first interest payment on December 31 . (If no entry is required for a transaction/event, select "No journal entry required" in thefirst account

Sebastian is incorrect. The correct greatest common factor of the given expression is 9mn.

The greatest common factor (GCF) of a set of numbers refers to the largest factor that all the numbers shares. The greatest common factor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For an expression, the greatest common factor is the largest expression that is a factor of all the expressions. In the given expression, 27m²n + 36m³n³ + 18mn⁴, take out the common factor out.

27m²n + 36m³n³ + 18mn⁴

Take out 3

3(9m²n + 12m³n³ + 6mn⁴)

As the expression can be divided by three again, Take out 3

3*3(3m²n + 4m³n³ + 2mn⁴)

9(3m²n + 4m³n³ + 2mn⁴)

Similarly,

Take out m

9m(3mn + 4 m²n³ + 2n⁴)

Take out n

9mn(3m + 4 m²n2 + 2n3)

Hence, the common greatest factor is 9mn and not 9m²n⁴.

Note: The question is incomplete. The complete question probably is: Sebastian wants to factor the greatest common factor out of the expression, 27m²n + 36m³n³ + 18mn⁴. Sebastian determines that the greatest common factor is 9m²n⁴. Is Sebastian correct? If he is, explain why. If he is not correct, determine the correct answer and explain your reasoning.

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Answer:

1:30pm = 13:30pm

09:12am = 09:12am

11:45 pm = 23:54pm

4:15pm = 16:15pm

Step-by-step explanation:

I'm in military school :)

The answer will be:-  x = 1

Answer:

f(2x-4)=3^2x-4+10

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Answer:

The equation would be 5000(1.02)^x with x representing the amount of years, as the values keep multiplying.

Answer:

The answer is A. And please be my friend

Step-by-step explanation:

Answer: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.)

Step-by-step explanation:  ???

The required percentage yield for the reaction when theoretical yield and actual yield are given is calculated to be 85.5 %.  

The maximum mass that can be generated when a particular reaction occurs is referred to as theoretical yield.

Theoretical yield is given as mt = 9.23 g

The actual amount of product recovered is given as ma = 7.89 g

We must comprehend that in order to calculate the reaction's percent yield, we must divide the total amount of product recovered by the utmost amount that can be recovered. If we multiply by 100%, we can represent this fraction as a percentage.

Percentage yield = ma/mt × 100 = 7.89/9.23 × 100 = 85.5 %

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At t = -6, the instantaneous rate of change of g(t) is -12. This indicates that the function is decreasing rapidly at that point.

To find the instantaneous rate of change of the function g(t) = 3 - t^2 at t = -6, we need to calculate the derivative of the function and evaluate it at t = -6.

The derivative of g(t) is given by g'(t) = -2t.

Now, let's evaluate the derivative at t = -6:

g'(-6) = -2(-6) = 12.

The instantaneous rate of change represents the rate at which the function is changing at a specific point. In this case, at t = -6, the instantaneous rate of change of g(t) is 12.

This means that for every unit increase in t, the function g(t) is changing by a rate of 12. Since the coefficient of t in the derivative is -2, which is negative, the function g(t) is decreasing at a rate of 12 at t = -6.

Therefore, at t = -6, the instantaneous rate of change of g(t) is -12. This indicates that the function is decreasing rapidly at that point.

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The expression is simplified to 10x² + 48x + 3 =0

Given the expression as;

\(5^(^4^x^+^1^)^(^x^+^2^) + 4. 5^x^(^x^+^1^5^) = 5^-^2^x^2+^2^1^x^-^1\)

We take the numerators have the same base, then we have;

(4x+1)(x+2) + 4(x(x+ 15) = -2x² + 21x - 1

expand the bracket

4x² + 8x + x + 2 + 4(x² + 15x) =  -2x² + 21x - 1

4x² + 8x + x + 2 + 4x² + 60x =  -2x² + 21x - 1

collect like terms

4x² + 4x² + 2x² + 8x + x + 60x - 21x = - 1 - 2

Add or subtract like terms

10x² + 48x = -3

Make into a quadratic equation

10x² + 48x + 3 =0

Thus, the expression is simplified to 10x² + 48x + 3 =0

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Answer:

Function with smallest zero  is:

f(x); (2, 0).

Step-by-step explanation:

f(x):

2x2 − 14x + 20 = 0

x^2 - 7x + 10 = 0

(x - 5)(x - 2) = 0

So the zeroes are (2, 0) and (5, 0)

g(x):

From the table:

when g(x) = 0, x =19 so its zero is (19, 0).

Answer: The opposite of -12 would be 12. You simply just turn the negative number, into a positive. Hope this helped you.

Step-by-step explanation:

Answer:

------------------------

The horizontal distance is 16 cm and vertical distance is 14 cm.

Therefore the perimeter is:

Given parameters:

Coordinates of the two points = (-5, 6) and (8,-4)

Unknown:

Distance between the two points.

To find the distance between two points, use the expression below;

  Distance ²  = (x₂ - x₁)² + (y₂ - y₁)²

where;

(-5, 6) and (8,-4)

         x₂ = 8 , x₁ = -5 , y₂ = -4 and y₁ = 6

Input the parameters and solve;

 Distance²  =  (8-(-5))²  +  (-4 - (6))²

                    = 169 + 100

                    = 269

Distance = \(\sqrt269}\)   = 16.4

The distance between the two points is 16.4

Answer:

72 degrees

Step-by-step explanation:

A pentagon has five lines of symmetry. For rotation symmetry, the order of any regular polygon is the number of sides. The angle of rotation would be 360 degrees divided by that order. Therefore, the answer is 72 degrees.

Answer:

It is A, B, and C

Answer:

x=18 degrees

Step-by-step explanation:

since this is a triangle, you know that the three angles added up equal 180 degrees. since it is a right triangle, 25+3x+11=90 (the right angle=90). then you just solve for x: 3x=54, x=18

Answer:

D(2.5,  7/2

Step-by-step explanation: