Problem 1
Calculate the slope of each line. Click on the
appropriate cell in the table to highlight the
line you are interested in.

(-5, 7) (1, 1)

(2, 6) (8, 4)

(-6, -3) (-2,-8)

Answer:

Have a great rest of your day :)

Step-by-step explanation:

Answer:

1.1 : C - x^2 + x - 2

1.2 : A - 4a^2 - 6b^2 + 12

Step-by-step explanation:

When we have the expression p(x) - q(x), we can substitute those functions in:

(x^2 + 2x - 5) - (x - 3)

We can distribute:

x^2 + 2x - 5 - x + 3

and then combine like terms(2x & -x, -5 & 3)

x^2 + x - 2

This is the same as C.

We can start by distributing:

a^2 - 2b^2 + 3 - 4b^2 + 5 + 3a^2 + 4

Now, we can combine all the a^2 terms(a^2 & 3a^2):

4a^2 - 2b^2 + 3 - 4b^2 + 5 + 4

Then, we can combine the b^2 terms(-2b^2 & -4b^2):

4a^2 - 6b^2 + 3 + 4 + 5

and lastly, all the constants:

4a^2 - 6b^2 + 12

This aligns with option A

Lateral area of cylinder is,

⇒ A = 80π cm²

We have to given that;

A figure for a cylinder is shown.

Since, We know that;

Lateral area of cylinder is,

A = 2πrh

Here, We have;

Radius of cylinder = 16 /2 cm

Radius of cylinder = 8 cm

And, Height of cylinder = 5 cm

Hence, Substitute given values, we get;

⇒ A = 2πrh

⇒ A = 2π × 8 × 5

⇒ A = 80π cm²

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Answer:

f(0) = 0.25 = 1/4

f(x) = f(x-1) × 2/3

Step-by-step explanation:

a0 = 0.25×(2/3)⁰ = 0.25×1 = 0.25 = 1/4

a1 = 0.25×(2/3)¹ = 0.25×(2/3) = 1/4 × 2/3 = 2/12 = 1/6 =

= a0 × 2/3

a2 = 0.25×(2/3)² = 0.25×(4/9) = 1/4 × 4/9 = 4/36 = 1/9 =

= a1 × 2/3

=>

an = an-1 × 2/3, n >= 1

but what about negative x ?

is a0 = a-1 × 2/3 ?

\(a - 1 = 0.25 \times {(2 \div 3)}^{ - 1} \)

so, yes, a0 = a-1 × (2/3)

and a-1 = a-2 × (2/3)

...

Answer:

The correct answer is B

Step-by-step explanation:

.

Answer:

2 hr

Step-by-step explanation:

Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer:

3:4

Step-by-step explanation:

That ratio would be 12:16, or 3:4.

The aspect ratio of a computer screen will be 4: 3.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The computer screen measures 12 inches by 16 inches.

Then the aspect ratio will be given by the number 16 inches divided by 12 inches.

We know that the aspect ratio will be greater than 1. Then the aspect ratio will be

Aspect ratio = 16 / 9

Aspect ratio = 4/3

Aspect ratio = 4: 3

The aspect ratio of a computer screen will be 4: 3.

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It takes approximately 19.26 hours for the size of the sample to double.

N(t) = N0 * \(e^(rt)\)

2N0 = N0 * \(e^(rt)\)

Dividing both sides by N0, we get:

2 = \(e^(rt)\)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2) / r

Substituting r = 0.036 (since the growth rate parameter is 3.6% per hour), we get:

t =  \(\frac{ln(2)}{0.036}\)

t ≈ 19.26 hours

A logarithm is a mathematical function that represents the relationship between two quantities that are related by a constant ratio. In other words, it is the inverse operation of exponentiation. The logarithm of a number is the power to which another fixed number (called the base) must be raised to produce that number. For example, if the base is 10, the logarithm of 100 is 2 because 10 raised to the power of 2 equals 100.

Logarithms are useful in many areas of mathematics, science, and engineering because they allow for the simplification of complex mathematical expressions and the comparison of quantities that vary over a wide range of magnitudes. They are also used in the study of growth and decay processes, such as population growth and radioactive decay.

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The number of distinct arrangements are there of these six people if the two coaches sit opposite each other is 420.

The arrangement can be represented as : M M C M M C

here,

M = mathletes

C = coach

The number in which they can be seated can be represented as a permutation,

There, the number of possible arrangements can be given as ,

6 !

= 6 . 5 . 4 . 3 . 2 . 1

= 420

Permutation is a concept in mathematics using which we can calculate the possible number of arrangements for a given set of collection.

The objects are generally arranged in a specific set or a definite set.

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The search direction that is both improving and feasible while providing the most rapid objective function improvement is to increase the value of y₁.

To determine the search direction that improves the objective function most rapidly while remaining feasible, we need to calculate the reduced costs for each variable and choose the variable with the most negative reduced cost.

The reduced cost of a variable represents the amount by which its coefficient in the objective function can be decreased before it becomes profitable to include it in the solution.

In this case, the objective function is minimized, so we want to identify the variable with the most negative reduced cost. The reduced cost of a variable is calculated as the difference between its coefficient in the objective function and the dual price (shadow price) of the corresponding constraint.

For y₁: reduced cost = 2 - 1 = 1

For y₂: reduced cost = 3 - 0 = 3

For y₃: reduced cost = 5 - 1 = 4

Among the variables, y₁ has the lowest reduced cost of 1. By increasing the value of y₁, the objective function will improve by 1 unit for every unit increase in y₁, while keeping all the constraints satisfied.

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Measure of angle 4 + measure of angle 5 + measure of angle 6 = 360°

The correct answer is an option (d)

Here, the exterior angle to angle 1 is 4.

We can observe that angle 1 and angle 4 are linear angles.

So, ∠1 + ∠4 = 180°           .......(1)          

Similarly angle 5 is an exterior angle to 5,

⇒ ∠2 + ∠5 = 180°       ..............(2)

And the exterior angle to angle 3 is 6.

⇒ ∠3 + ∠5 = 180°        ...........(3)

Consider the sum  Measure of angle 4 + measure of angle 5 + measure of angle 6:

= m∠4 + m∠5 + m∠6

= 180° -  m∠1 + 180° -  m∠2 +  180° - m∠3            .....(from (1), (2) and (3))

= 540° - ( m∠1 +  m∠2 +  m∠3)

= 540° - 180°                                   ........(sum of all angles of triangle is 180°)

= 360°

Therefore, the required sum = 360°

The correct answer is an option (d)

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The complete question is:

What is Measure of angle 4 + measure of angle 5 + measure of angle 6?A triangle has angles 1, 2, 3. The exterior angle to angle 1 is 4, to angle 2 is 5, to angle 3 is 6.

a) 180°

b) 270°

c) 300°

d) 360°

Answer:

1.1666 (repeating) is the correct answer

Answer:

Divide 7 by 16, and the result is 0.4375.

Step-by-step explanation:

The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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Answer:

2r

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{-1}{12}\)

Answer:

a

Step-by-step explanation:

- \(\frac{1}{4}\) × \(\frac{2}{3}\) × \(\frac{1}{2}\) ( cancel the 2 on the numerator/ denominator of last 2 fractions )

= - \(\frac{1}{4}\) × \(\frac{1}{3}\) × 1

multiply values on numerators and values on denominators )

= - \(\frac{1(1)}{4(3)}\) × 1

= - \(\frac{1}{12}\)

Answer:

Step-by-step explanation:

The answer would be A because the hypothesis of a conditional statement is the statement after the "if", but before the "then".

Answer:

Hello,

Step-by-step explanation:

\(A=(1,2)\\B=(0,-1)\\\overrightarrow{AB}=((0,-1)-(1,2)=(-1,-3)\ ||\overrightarrow{AB}||^2=1+9=10\\\overrightarrow{BC}=((3,-2)-(0,-1)=(3,-1)\ ||\overrightarrow{BC}||^2=9+1=10\\\\Triangle\ is\ isosceles.\\\\\overrightarrow{AB}.\overrightarrow{BC}=(-1,-3)*\left[\begin{array}{c}3\\-1\end{array}\right] =-3+3=0\\\\Triangle \ is\ right.\\\\\)

Answer:

(Work below)

BRAINLIEST, PLEASE!

Step-by-step explanation:

A(1, 2) B(0, -1) C(3, -2)

The distance between A and B is:

3^2 + 1^2 = c^2

9 + 1 = c^2

c = 10^1/2

The distance between B and C is:

1^2 + 3^2 = c^2

1 + 9 = c^2

c = 10^1/2

The distance between C and A is:

4^2 + 2^2 = c^2

16 + 4 = c^2

c= 20^1/2

Since AB and BC are the same, but AC isn't, the triangle is isosceles.

The open intervals on which the function P(x) = x² - 10 is increasing, decreasing, or constant are:- P(x) is decreasing on the open interval (-∞, 0).- P(x) is increasing on the open interval (0, +∞).

To determine the intervals on which the function P(x) = x² - 10 is increasing, decreasing, or constant, we need to find the derivative of the function and examine its sign.

First, let's find the derivative of P(x) with respect to x:

P'(x) = 2x

To determine the intervals of increase or decrease, we need to find where the derivative is positive (increasing) or negative (decreasing). In this case, P'(x) = 2x is positive for x > 0 and negative for x < 0.

Now, let's consider the intervals:

1. For x < 0: Since P'(x) = 2x is negative, the function P(x) is decreasing in this interval.

2. For x > 0: Since P'(x) = 2x is positive, the function P(x) is increasing in this interval.

To summarize:

- P(x) is decreasing on the interval (-∞, 0).
- P(x) is increasing on the interval (0, +∞).

Therefore, the open intervals on which the function P(x) = x² - 10 is increasing, decreasing, or constant are:
- P(x) is decreasing on the open interval (-∞, 0).
- P(x) is increasing on the open interval (0, +∞).

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The probability that both will be married before the age of 18 is 0.0036. The probability that both will be married by the age of 25 is 0.25. Finally, the probability that both will be married by the age of 30 is 0.5476.

According to the brief report by NCHS, approximately 6% of women in the United States married for the first time before their 18th birthday, and 50% of women married by their 25th birthday. 74% of women married by their 30th birthday.The probability of a family with two daughters marrying at different ages is asked in the question. The probability that both daughters will be married by the ages of 18, 25, and 30 will be determined

The question requires finding the probability that both daughters of a family will be married by the ages of 18, 25, and 30 respectively. Since each daughter's wedding is a separate event, the individual probability of a daughter marrying at a given age will be determined separately and then multiplied together to get the probability of both daughters being married at the given age. So, let's find the probabilities of each daughter marrying at a given age:

Probability of one daughter getting married by 18 years:

As per the brief report, 6% of women in the United States married before the age of 18.

Therefore, the probability of one daughter getting married before the age of 18 is 0.06

Probability of one daughter getting married by 25 years:

As per the brief report, 50% of women in the United States get married by the age of 25. Therefore, the probability of one daughter getting married by 25 years is 0.5.

Probability of one daughter getting married by 30 years:

As per the brief report, 74% of women in the United States get married by the age of 30. Therefore, the probability of one daughter getting married by 30 years is 0.74.

The probability of both daughters getting married at the same age is the product of each daughter's probability of getting married at that age.

The probability that both daughters will get married before the age of 18 is:

P(both daughters married at 18 years) = P(daughter1 married at 18) × P(daughter2 married at 18)= 0.06 × 0.06= 0.0036

The probability that both daughters will get married by the age of 25 is:

P(both daughters married at 25 years) = P(daughter1 married at 25) × P(daughter2 married at 25)= 0.5 × 0.5= 0.25

The probability that both daughters will get married by the age of 30 is:

P(both daughters married at 30 years) = P(daughter1 married at 30) × P(daughter2 married at 30)= 0.74 × 0.74= 0.5476

The probability that in a family with two daughters, both will be married before the age of 18 is 0.0036. The probability that both daughters will be married by the age of 25 is 0.25. Finally, the probability that both daughters will be married by the age of 30 is 0.5476.

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The statement "The point (9, 3π/2) in the spherical coordinate system represents the point (3, 50) in the cylindrical coordinate system" is False.

In the spherical coordinate system, a point is represented by three coordinates: (ρ, θ, φ), where ρ represents the distance from the origin, θ represents the angle in the xy-plane, and φ represents the angle from the positive z-axis. In the cylindrical coordinate system, a point is represented by three coordinates: (ρ, θ, z), where ρ represents the distance from the z-axis, θ represents the angle in the xy-plane, and z represents the height.

The given points, (9, 3π/2) in the spherical coordinate system and (3, 50) in the cylindrical coordinate system, have different values for the distance coordinate (ρ) and the angle coordinate (θ). Therefore, the statement is false as the two points do not correspond to each other in the different coordinate systems.

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Answer:

$92.43

Step-by-step explanation:

Original value of money paid is $79

Tip is 17% of $79 = $13.43

Total is the original value + the tip

79 x 0.17(this is because 17% is the same as 17/100 If you turn this to a decimal you get 0.17) = $13.43

Total = $13.43 + $79

$92.43 the 43 cents are whole so there is no need to round off.

Answer:

+ or - $9

Step-by-step explanation:

Answer: Jazz and heavy Metal

Step-by-step explanation:

Answer:

The immediate roots of rock and roll lay in the rhythm and blues, then called "race music", and country music of the 1940s and 1950s. Particularly significant influences were jazz, blues, gospel, country, and folk.

True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.

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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.

the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.


The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.

Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.

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Probability that the senator will either be a republican or will have voted against the bill = \(\frac{53}{100}\)

What is Probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Number of republicans = 21  + 22 = 43

Number of voters who voted against the bill = 22  + 9  +1 = 32

Number of republicans who voted against the bill = 22

Total number of voters = 21 + 22  + 42 + 9 + 5 + 1 = 100

Probability that the senator will either be a republican or will have voted against the bill =

                         \(\frac{43 + 32 - 22}{100}\\\frac{53}{100}\)

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Complete Question

The table has been attached here

Answer:

c

Step-by-step explanation:

the answer is c becuase i know this que

Answer:

All

Step-by-step explanation:

We can check it by using the Pythagorean theorem.

\(a {}^{2} + b {}^{2} = c {}^{2} = {3}^{2} + { \sqrt{27} }^{2} = 6 {}^{2} = 9 + 27 = 36 = 36 = 36 \)

\( {a}^{2} + {b}^{2} = c {}^{2} = {8}^{2} + {15}^{2} = {17}^{2} = 64 + 225 = 289 = 289 = 289\)

\(a {}^{2} + b {}^{2} = c {}^{2} = 5 {}^{2} + {5}^{2} = { \sqrt{50} }^{2} = 25 + 25 = 50 = 50 = 50 = \)

Hope this helps ;) ❤❤❤

Answer:

the second, and fourth one's are triangles, and the 1st and 2nd are not

Step-by-step explanation:

We know that the angles in a triangle add up to 180 degrees. So we need to find which angles add up to 180 degrees. We have:

56+34+42=132

That means the first one can't be a measures of a triangle.

75+55+50=180

Second one is a triangle.

35+32+23=90

Third isn't a triangle

124+64+16=180

So all in all, the second, and fourth one's are triangles, and the 1st and 2nd are not

The average temperature decrease of -6.5 degrees/km Celsius is known as Normal lapse rate.

Normal lapse rate is defined as the decrease in the temperature while moving upwards in the atmosphere. Normally, the rate of decrease is 1 degree Celsius for every 165 meter rise in altitude or we can say that it is 6.5 degree Celsius for every 1 km rise in altitude.

This lapse rate is known as normal lapse rate or environmental lapse rate.

This is why when we move higher in the atmosphere, we experience low temperatures. On average this decrease is equal to the amount of temperature as discussed in the normal lapse rate.

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Answer:

It's a right angle, so 90 degrees

Step-by-step explanation:

The tangent line is always perpendicular to the radius that goes to the tangental point.

Answer:

y = 90°

Step-by-step explanation:

because when a line is tangent to a circle, a radius to that point forms a 90° angle.