What is the slope of the line that passes through the points (10, 6) and (9, 5) ? Write your answer in simplest form .

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Step-by-step explanation:

to find f(5)   in f(x) , just put in '5' where 'x' is in the equation

f(5) = 3 (5) + 2 = 17

Answer:

f(5) = 17

Step-by-step explanation:

Let's evaluate the function for f(5)

Insert 5 everywhere x appears:

Therefore f(5) = 17

Answer:

Yo, the answer would be 37 which is A. Cheers

Step-by-step explanation:

The sides are equal to one another

This means   4x+2=180

4x+2=180      

    -2     -2

4x=148

/4

x=37

Answer:

Hello! answer: x = 37

These are vertical angles so they will both equal the same so we just have to figure out what multiplied by 4 + 2 = 150 and 4 × 37 = 148 and 148 + 2 = 150 so x = 37 Hope that helps!

-1 because y-intercept is where y meets zero, therefore the y intercept of this graph would be -1<3

Answer:-5

Step-by-step explanation:

you just minus it bruh

When matched, the prompts on asymptotes would be:

The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.

This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.

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Answer: C) 44

Step-by-step explanation: EDGE 2022 CORRECT

Answer:

x^2 + y^2 - 8x + 18y + 48 = 0

Step-by-step explanation:

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the centre of circle and r is the radius of circle. hence the standard form of equation can be obtained by expanding

(x-4)^2 + {y-(-9)}^2 = 7^2

The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

We have,

To determine the maximum number of miles Chenelle can travel without exceeding her spending limit of $300, we need to subtract the flat rate from her budget and divide the remaining amount by the cost per mile.

So,

Subtract the flat rate from Chenelle's budget:

Budget after subtracting the flat rate.

= $300 - $19.95

= $280.05

Divide the remaining budget by the cost per mile to find the maximum number of miles:

Maximum miles = Budget after subtracting the flat rate / Cost per mile

= $280.05 / $1.75

Using division.

Maximum miles = 160.028571

Therefore,

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

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The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Answer:

its D

bc 3 is grater

Answer:

12/20

Step-by-step explanation:

Answer:

According to the graph, there are 6 pumpkins with the mass of 9kg to 12kg and 4 pumpkins with the mass of 0kg to 3kg.

In order to find how many pumpkins more, you have to subtract it so it will be 6 pumpkins - 4 pumpkins = 2 pumpkins.

Therefore, there are 2 more pumpkins with the mass of 9 to 12kg compared to the pumpkins with the mass of 0 to 3kg.

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

The piano was in the air for 18.34 seconds.

Step-by-step explanation:

The height of the piano after t seconds is given by the following equation:

\(f(t) = -16t^{2} + 320t - 256\)

Initially, the piano is below the ground level. At the first root of the equation, it will go into the air, and then some time after that it will fall down again, which is at the second root of the equation.

Roots of a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

\(f(t) = -16t^{2} + 320t - 256\)

So

\(a = -16, b = 320, c = -256\)

\(\bigtriangleup = (320)^{2} - 4*(-16)*(-256) = 86016\)

\(t_{1} = \frac{-320 + \sqrt{86016}}{2*(-16)} = 0.8348\)

\(t_{2} = \frac{-320 - \sqrt{86016}}{2*(-16)} = 19.17\)

Subtracting:

19.17 - 0.8348 = 18.34

The piano was in the air for 18.34 seconds.

Answer:

-8 29/20

Step-by-step explanation:

Answer: -8  29/40

Step-by-step explanation:

Answer:

x + 57i

Step-by-step explanation:

x - 7² – 8=0

x -49-8

x - 57 = x + 57(-1) ; i = -1( complex number notation)

x + 57i

Answer:

There is 166.1 grams of sugar in 5.5 yards of licoroce

Step-by-step explanation:

If 1.5 yards of licorice = 45.3 grams of sugar

5.5 yards of licorice = x

Cross multiply:

45.3grams * 5.5yards / 1.5yards

= 249.15 grams/yards / 1.5yards

= 166.1 grams of sugar

Answer:

$5,250

Step-by-step explanation:

2/7x - [4/5(2/7x)] = 300

2/7x - 8/35x = 300

10/35x = 8/35x = 300

2/35x = 300

2x = 10500

x = 5250

The total cups of water the pitcher can hold is 72

A fraction is the ratio of two integers.

It is divided into two parts by a division line and the part above the line is called the numerator and the part below the line is called the denominator.

Fraction are of three types: proper, improper and mixed fractions.

Let the total number of cups to fill the pitcher be x.

The pitcher is 3-fourths full of water, that is 3/4 of x = \(\frac{3x}{4}\)

when 6 cups were taken away from the Pitcher it became 2/3 of x = \(\frac{2x}{3}\)

So that,

\(\frac{3x}{4}\) -  \(\frac{2x}{3}\) = 6

multiply  \(\frac{2x}{3}\) by 4/4 and  \(\frac{3x}{4}\) by 3/3

it becomes

\(\frac{9x}{12}\) - \(\frac{8x}{12}\) = 6

simplifying the numerator

x/12 = 6

cross multiplying

x = 12 x 6

x = 72

In conclusion, the total number of cups to fill the pitcher is 72

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3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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The sampling method used in this case is random sampling and the sample is representative.

A sample is a small proportion of individuals taken from the general population to be studied. For a sample to be representative it is expected that all the individuals represent the population, for example, if the population includes people of different ages the sample should include this too.

The random sample selected is representative because the seats of the students selected are distributed within the class rather than in only one row or line.

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The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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A: (f ÷ g)(x) = (3.6)⁻²ˣ⁺¹ is the solution of the function.

Functions are relationships that exist between a set of inputs and outputs. A function is an association of inputs, where each input is directly linked to one or more outputs. Range, codomain, and domain are all attributes of each function.

The given functions are:

f(x) = (3.6)ˣ⁺²

And g(x) = (3.6)³ˣ⁺¹

To find (f ÷ g)(x):

We take division of f(x) by g(x).

(f ÷ g)(x) = f(x) ÷ g(x)

(f ÷ g)(x) = (3.6)ˣ⁺² ÷  (3.6)³ˣ⁺¹

(f ÷ g)(x) = (3.6)ˣ⁺² ÷  (3.6)³ˣ⁺¹

(f ÷ g)(x) = (3.6)ˣ⁺² / (3.6)³ˣ⁺¹

Simplifying,

(f ÷ g)(x) = (3.6)ˣ (3.6)² / (3.6)³ˣ (3.6)¹

(f ÷ g)(x) = (3.6)ˣ⁻³ˣ (3.6)

(f ÷ g)(x) = (3.6)⁻²ˣ (3.6)

(f ÷ g)(x) = (3.6)⁻²ˣ⁺¹

Therefore, the answer is A:  (f ÷ g)(x) = (3.6)⁻²ˣ⁺¹

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We have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.

Matrices are a type of mathematical structure used to store and analyze data. They are represented as a series of rows and columns, with each cell in the matrix containing a number or other value. Matrices are used to solve systems of equations, perform matrix multiplication and determine the inverse of a matrix. They are also used in linear programming, cryptography, and other areas of mathematics.

Row equivalence is defined as a pair of matrices A and B being row equivalent if there is a sequence of row operations that can transform A into B, or vice versa. This means that if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations.

A reduced row echelon form is defined as a matrix in which all non-zero rows are above any rows of all zeroes and the leading coefficient of each non-zero row is 1. In other words, all of the non-zero rows have a leading coefficient of 1, and any rows of all zeroes are below the non-zero rows.

Therefore, if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations. This means that we can use the same series of row operations to transform A and B into the same reduced row echelon form. This proves that if A and B are row equivalent, then A and B have the same reduced row echelon form.

On the other hand, if A and B have the same reduced row echelon form, then they must have been transformed into the same form by a series of row operations. This means that the same series of row operations must have been used to transform A and B into the same reduced row echelon form, which means that A and B are row equivalent. This proves that if A and B have the same reduced row echelon form, then A and B are row equivalent.
To prove that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form, we can use the definition of row equivalence and the definition of a reduced row echelon form.


Therefore, we have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.

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Answer:

B (48)

Step-by-step explanation:

One particular property of medians is the 2/3 ratio. Basically, the centroid separates the median into two line segments, and the longer line segment is 2/3 of the median length. So, 72 x 2/3 is 48.

The equation of the curve that intersects at right angles to every curve of the family y=(1/x)+k is y=lnx

y=-x+k is the equation of a curve that meets at right angles every curve in the family y=(1/x)+k (where k can take any real value). This is known as the 'orthogonal curve' of the y=(1/x)+k family. It is calculated by obtaining the reciprocal of the original equation and then removing k from the y-axis.

A straight line with a negative slope is given by the equation y=-x+k. Every point on the line has an x-value that is the inverse of its y-value. At the point where x=1/k and y=k, the equation will always meet the curve of the family y=(1/x)+k at a right angle. This point is the same for all values of k and is known as the 'origin' of the function.

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