an agle formed outside a polygon by extending one of it sides.

The equation equivalent to the formula d = rt is t = d/r

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16.

Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

The equation is d = rt

As we need the value of t we take t to the left hand side

∴ t = d/r

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Answer: 50%

Step-by-step explanation: math

if the matrix is invertible.22. \(\left( {\begin{aligned}{*{20}{c}}5&1&{ - 1}\\1&{ - 3}&{ - 2}\\0&5&3\end{aligned}} \right)\) then,  the determinant of the matrix A is -3 (non-zero), the matrix is invertible.

To determine if a matrix is invertible, we need to find its determinant. If the determinant is non-zero, the matrix is invertible. Let's calculate the determinant for the given matrix:

Matrix A = \(\begin{pmatrix} 5 & 1 & -1 \\ 1 & -3 & -2 \\ 0 & 5 & 3 \end{pmatrix}\)

Step 1: Use the first row for cofactor expansion:

Determinant(A) = 5 × Cofactor(1,1) - 1 × Cofactor(1,2) + (-1) × Cofactor(1,3)

Step 2: Calculate the cofactors:

Cofactor(1,1) = Determinant of the 2x2 matrix obtained by removing the first row and first column:

\(\begin{pmatrix} -3 & -2 \\ 5 & 3 \end{pmatrix}\)

Cofactor(1,1) = (-3)(3) - (-2)(5) = -9 + 10 = 1

Cofactor(1,2) = Determinant of the 2x2 matrix obtained by removing the first row and second column:

\(\begin{pmatrix} 1 & -2 \\ 0 & 3 \end{pmatrix}\)

Cofactor(1,2) = (1)(3) - (-2)(0) = 3

Cofactor(1,3) = Determinant of the 2x2 matrix obtained by removing the first row and third column:

\(\begin{pmatrix} 1 & -3 \\ 0 & 5 \end{pmatrix}\)

Cofactor(1,3) = (1)(5) - (-3)(0) = 5

Step 3: Substitute the cofactors back into the formula for Determinant(A):

Determinant(A) = 5 × 1 - 1 × 3 + (-1) × 5 = 5 - 3 - 5 = -3

Since the determinant of the matrix A is -3 (non-zero), the matrix is invertible.

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7.051 can be written as the fraction 7051/1000.

To express 7.051 as a fraction in the form of p/q, we need to identify the decimal places and convert them to the corresponding fractional parts.

Since 7.051 has three decimal places, we multiply it by 1000 to move the decimal point three places to the right, which gives us 7051.

Now, the numerator (p) of the fraction will be 7051, and the denominator (q) will be the corresponding power of 10, which is 1000.

Therefore, 7.051 can be expressed as 7051/1000.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

In this case, the GCD of 7051 and 1000 is 1, so the fraction is already in its simplest form.

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Answer:

\(m=4\) or \(m=\frac{4}{1}\)

Step-by-step explanation:

To find slope we use the slope formula

\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

Two points on the line we can classify are (3,4) and (4,8)

Step-by-step explanation:

I don't know what the equations are, but I'll do my best to help

ax² + bx + c

"a" is multiplied by (-4) and (c), as well as 2 in the denominator

"b" is put in front of the equation so, hypothetically speaking, b = -1

-b = -(-1) = 1 so it would turn a positive into a negative and a negative into a positive number.

b is also squared so no matter what it will be positive in √b² - 4ac

"c" is multiplied by (-4) and (a)

If I knew the equations I could help more but this is probably the best I can do.

I hope this helps!

The compound interest formula is

In the exercise, we have:

A=2800

P=2200

t=7

Answer: 3.51%

The plane flies approximately 13,773 meters through the air before reaching its cruising altitude.

To calculate the distance that the plane flies through the air before reaching its cruising altitude, we need to find the horizontal component of the distance traveled during the initial climb.

Speed of the plane = 300 km/h

Angle of climb = 36°49′

Time of climb = 3 minutes.

First, let's convert the angle of climb from degrees and minutes to decimal degrees for ease of calculations.

36°49′ = 36 + (49/60) ≈ 36.817°

Now, we can calculate the horizontal component of the distance traveled during the climb using trigonometry

The horizontal distance (d) can be found using the formula:

\(d = v \times t \times cos(\theta)\)

Where:

v is the speed of the plane,

t is the time of climb, and

theta is the angle of climb in radians.

Converting the speed from km/h to m/s:

\(300 km/h = (300 \times 1000) / (60 \times 60) m/s \approx 83.33 m/s\)

Converting the time of climb from minutes to seconds:

\(3 $ minutes = 3 \times 60 $ seconds = 180 seconds\).

Converting the angle of climb from degrees to radians:

\(36.817= (36.817 \times \pi ) / 180 $ radians \approx 0.642 $ radians\)

Now, we can calculate the horizontal distance:

\(d = 83.33 m/s \times 180 s \times cos(0.642 radians) \approx 13,773 meters\)

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To determine the speed of the car at the bottom of the hill, we can use the principle of conservation of energy. As the car rolls down the hill, it will convert its potential energy at the top into kinetic energy at the bottom, neglecting any energy losses due to friction or air resistance.

The potential energy of the car at the top of the hill is given by the formula:

Potential Energy = mass × gravity × height

Since the mass of the car is not provided, we can assume it to be a constant value for the purpose of this calculation. Gravity is approximately 9.8 m/s².

The kinetic energy of the car at the bottom of the hill is given by the formula:

Kinetic Energy = (1/2) × mass × velocity²

Since the potential energy at the top is equal to the kinetic energy at the bottom, we can equate the two equations and solve for velocity.

mass × gravity × height = (1/2) × mass × velocity²

Simplifying the equation, we find:

velocity² = 2 × gravity × height

Taking the square root of both sides, we get:

velocity = √(2 × gravity × height)

Substituting the given values, with gravity as 9.8 m/s² and height as 50 m, we can calculate the velocity. Plugging the values into the equation, we find: velocity = √(2 × 9.8 m/s² × 50 m) ≈ 31.3 m/s

Therefore, the car will be going at approximately 31.3 meters per second (m/s) at the bottom of the hill.

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To express the integrand as a rational function, we can make the substitution u = 1 + x^2. Then, du/dx = 2x, so dx = du/(2x).

You are asked to evaluate the integral of a function that can be expressed as a rational function using substitution. The given integrand is:

∫((Tc-4)^(-1/3) dTc)

Step 1: Make a substitution to express the integrand as a rational function
Let's perform a substitution:
u = Tc - 4

Then, differentiate both sides with respect to Tc:
du/dTc = d(Tc - 4)/dTc = 1

Now, solve for dTc:
dTc = du

Now, substitute the expressions for u and dTc into the original integrand:
∫(u^(-1/3) du)

Step 2: Evaluate the integral
Now, integrate the new expression:
∫(u^(-1/3) du) = (3/2)u^(2/3) + C

Step 3: Substitute back to the original variable, Tc
Now, substitute back the original variable, Tc, using u = Tc - 4:
(3/2)(Tc - 4)^(2/3) + C

Therefore, the integral of the given expression is:
(3/2)(Tc - 4)^(2/3) + C

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\(q(x) = {x}^{2} - 3x - 4\)

\(q(10) = ( {10})^{2} - (3 \times 10) - 4 \)

\(q(10) = 100 - 30 - 4\)

\(q(10) = 70 - 4\)

\(q(10) = 66\)

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Thus the correct answer is (( C )) .

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Answer:

1560.38

Step-by-step explanation:

As far as I know, a sales tax is never calculated until money changes hands. So the rebate is the first amount to take place.

1560 - 100 = 1460

Now if the purchaser agrees to this amount and does anything to pay partially or in full, the tax is added.

Total Cost = 1460 * (1.06875)

Total Cost = 1560.38

Edit

You have to be very careful when you use a term like rebate. Rebate is a very special kind of discount. Your purchase has to qualify for a rebate. Apparently this one does. If you are willing to spend 1560 on something, the merchant selling the product offers you a rebate to help you decide.

If the TV cost is 1200 you may not get the rebate.

a. The solution for x - 3 ≥ 0  is x ≥ 3

b. The solution for 2x + 11 < 3  is x < -4

c. The solution for the quadratic equation is  -1  ≥ x ≥ 2

d. The solution is x < -4/3 or x > 1

a. x - 3 ≥ 0

isolating the variable x

x - 3 ≥ 0

x ≥ 3

b. 2x + 11 < 3

isolating variable x

2x + 11 < 3

2x < 3 - 11

2x < -8

x < -4

c. x² ≥ x + 2

rearranging the quadratic equation

x² - x - 2 ≥ 0

factorizing

(x - 2)(x + 1) ≥ 0

d. x + 4 > 3x²

rearranging the quadratic equation

3x² - x - 4 < 0

factorizing

(x - 1)(3x + 4) < 0

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Answer:

The dimensions are 5 and 7

Step-by-step explanation:

Answer:

y = 5/2x + b

3= 5/2(-2) + b

3= -5 + b

3 + 5 = b

b = 8

y = 5/2x + 8

The equation in slope-intercept form is y= 5/2x + 8.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Slope = 5/2

and, point (-2, 3).

Using Slope- intercept form

y = mx + b

y= 5/2x + b

As, the line passes through (-2, 3)

3 = 5/2(-2) + b

3 = -5 + b

b= 8

So, the Equation of line is y= 5/2x + 8.

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Answer:

5/4+5/9

45/36 +20/36

65/36

1 30/36

The Answer is 2.557 when 17.9 is divided by 7

The solutions to the equation x^2 = -8x - 7x are x = 0 and x = -15.

To solve the equation x^2 = -8x - 7x, we first need to simplify the right side:

x^2 = -15x

Now we can rearrange the terms and factor out x:

x^2 + 15x = 0

x(x + 15) = 0

By the zero product property, we know that this equation is true when either x = 0 or x + 15 = 0. Solving for x in each case, we get:

x = 0 or x = -15

Therefore, the solutions to the equation x^2 = -8x - 7x are x = 0 and x = -15.

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Answer:

Hmmmm

Step-by-step explanation:

Answer:

To show that 3 divided by 1/4 is equal to 3x4 on a number line:

1. Draw a number line starting from 0 and mark every 1/4 division.

2. Label 3 divisions with the corresponding value '3'.

3. Move 4 divisions in the same direction as that of 3 divisions.

4. Mark the point at 4 divisions and label it as ’12’.

5. From the starting point to the point labelled ‘12’, there are 7 divisions.

6. Since each division represents a quantity of 1/4, dividing 3 by 1/4 (or multiplying by 4) will result in a total of 12, or 3x4.

Answer:

The answer is 600

Step-by-step explanation:

Multiply 6 by 1000, and 10 by x.

The equation would be 6000=10x.

Now, just solve for x by dividing by 10 which equals to 600.

Answer:

B: \(y=-\frac{1}{3}x+7\)

Step-by-step explanation:

Straight lines are set out in the format of \(y = mx+c\), where \(m\) is the gradient, and \(c\) is the y-intercept.

The gradient between parallel lines remains the same, and this means the gradient of the new line will also be \(-\frac{1}{3}\).

This rules out options C and D.

Going back to the format, so far, we have filled in \(y=-\frac{1}{3}x+c\). We are still looking for the y-intercept.

We can find that using the coordinate you've been given, \((6,5)\).

This coordinate tells us that when \(x=6\), \(y=5\). Therefore we can substitute those in the places of \(x\) and \(y\) in the original equation.

This leaves us with \(5 = -\frac{1}{3}(6)+c\).

We can now rearrange for \(c\).

\(5 = -2 + c\\c=7\)

Now we have all the values we need, we can form the final equation.

\(y=-\frac{1}{3}x+7\)

This indicates the answer is option B. Hope this helps.

A male passenger has a 0.9983 chance of squeezing through the doorway without bending.

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes, when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

The likelihood that a randomly chosen male passenger is under or equal to 78 inches tall must be determined. By standardizing the height, we can achieve this using the standard normal distribution:

z = (78 - 69) / 2.8 = 3.214

The probability of a z-score less than or equal to 3.214 can be calculated using the standard normal distribution table or calculator as follows: 0.9992.

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Answer:

it's a 1/6 chance because it's a 6 faced dice

The 87% confidence interval for the population proportion of drivers who claim to always buckle up is approximately 0.73 to 0.81.

To determine the Z-score for an 87% confidence level, we need to find the critical value associated with that confidence level. We can consult a Z-table or use a statistical calculator to find that the Z-score for an 87% confidence level is approximately 1.563.

Now, we can substitute the values into the formula to calculate the confidence interval:

CI = 0.768 ± 1.563 * √(0.768 * (1 - 0.768) / 382)

Calculating the expression inside the square root:

√(0.768 * (1 - 0.768) / 382) ≈ 0.024 (rounded to three decimal places)

Substituting the values:

CI = 0.768 ± 1.563 * 0.024

Calculating the multiplication:

1.563 * 0.024 ≈ 0.038 (rounded to three decimal places)

Substituting the result:

CI = 0.768 ± 0.038

Simplifying:

CI ≈ (0.73, 0.81)

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Answer:

16

Step-by-step explanation:

no image, but 6 + 2 + 2 + 6 = 16

in the formula, =1+(2-3)+5/6-6^2,  The final result of the formula is -35.1667.

In the formula =1+(2-3)+5/6-6^2, the order of operations dictates that the exponentiation operator (^) is evaluated first, followed by multiplication and division from left to right, and then addition and subtraction from left to right.

So, access will evaluate 6^2 first, which equals 36. Then, it will evaluate the division 5/6, which equals 0.8333 (rounded to four decimal places).

Next, it will evaluate the subtraction (2-3), which equals -1. Then, it will evaluate the addition (1+(-1)), which equals 0. Finally, it will evaluate the multiplication (-6 * 6), which equals -36.

Putting it all together, we get:

=1 + (2-3) + 5/6 - 6^2

= 1 + (-1) + 0.8333 - 36

= -35.1667

Therefore, the final result of the formula is -35.1667.

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Answer: 13%

Step-by-step explanation:

Step 1:

5000

10% of 5000=500

5% of 5000=250

25%=500+500+250= 1250 rupees

so...

5000-1250= 3750 INR, which is the original price, BEFORE THE 25% WAS ADDED

but..

They only want a 10% discount of the price which is 25% above the cost (5000). So essentially we want to find  15%, because 25%-10%=15%

so if...

10%=500

5%=250

15%=750 INR

this means the price with the 10% discount off 25%= 4250 INR (5000-750)

now we need to find the percentage change. For this we need to subtract the price with the 15% discount with the price BEFORE THE 25% was added

e.g 4250-3750= 500INR

Then.. divide this price with the original price before the 25% was added

e.g 500/3750= 2/15=0.13

So...

Convert 0.13 into a percentage=13%

The PERCENTAGE PROFIT of the owner is 13%

P.S Please could someone double check this answer as I am only 15 years old and may have gotten some working out wrong! Thank you