Identify the slope and one point on the line, given the equation

Identify The Slope And One Point On The Line, Given The Equation

Answers

Answer 1

The slope of the line of the equation y - 12 = 3/4(x + 7), is: 3/4.

How to Identify the Slope of a Line in Point-Slope Form?

The point-slope form of a linear equation is given as y - y1 = m(x - x1), where m is the slope of the line, (x1, y1) is a point on the line, and y and x are the variables.

To identify the slope of a line in point-slope form, you can simply look at the coefficient of x, which is the value of m. In the equation y - y1 = m(x - x1), m is the slope of the line.

This value tells you the rate of change or steepness of the line. A positive slope value implies that the line is increasing and a negative value implies that the line is decreasing.

Given the equation of a line in point-slope form as y - 12 = 3/4(x + 7). Therefore, the slope (m) can be identified as 3/4.

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Related Questions

Problem 4.1
A tank of water breaks and begins draining at a constant rate.
Complete the table.
Time (minutes)
Change in Water
(liters)
Expression
Water in the Tank
(liters)

Answers

The table is completed as follows:

Time of 2 minutes, change of -14 liters, expression 770 + 2(-14), water is 742 liters.Time of 3 minutes, change of -14 liters, expression 770 + 3(-14), water is 728 liters.

How to model the situation?

The situation is modeled by a linear function, in slope-intercept format, as follows:

y = mx + b.

In which:

m is the slope, representing the rate of change.b is the y-intercept, representing the initial capacity.

The initial capacity is of 770 liters, decaying by 14 liters each minute, hence the parameters are given as follows:

b = 770, m = -14.

The function for this problem is defined as follows:

y = -14x + 770.

The numeric values are given as follows:

x = 2: y = -14(2) + 770 = 742 liters.x = 3: y = -14(3) + 770 = 728 liters.

Missing Information

The table is given by the image presented at the end of the answer.

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3 Select the correct answer. Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths. C. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles. D. Neither the reflection nor the dilation preserves the side lengths and angles of triangle .

Answers

The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths. Therefore, option B is the correct answer.

What is a dilation?

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

Given that, triangle is reflected across the y-axis and then dilated by a factor of centered at the origin.

The triangle ABC in a graph with vertices A (-4, -2), B (4, -2), and C (4, 4)

A reflection across the y-axis changes the coordinates of the triangle from (x, y) to (-x, y) without changing the side lengths and angles.

The dilation of the triangle by a factor an then centered at the origin increases the side length of the triangle but the angles in the triangle remain the same since the ratio of the sides before and after dilation are the same.

Therefore, option B is the correct answer.

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what is 1/5 of 99.
hwelp meh im confused

Answers

Answer:

19.8

Step-by-step explanation:

Answer:

Do 99 divided by 5

Step-by-step explanation:

Use cross multiplication

NO LINKS!!
Solve each equation. Be sure to check for extraneous solutions. Part 2
k. log₇(x + 12) + log₇(x + 1) = log₇(42)

l . log₄(x + 3) + 1 = 2log₄(x)

Answers

Answer:

k)  x = 2

l)  x = 6

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\\Equality Law:\; If $\log_ax=\log_ay$ then $x=y$\\\\Same base as number:\;\;\;$\log_aa=1$\\$\end{minipage}}[/tex]

Part k

[tex]\begin{aligned}\log_7(x + 12) + \log_7(x + 1) &= \log_7(42)\\\log_7\left[(x + 12)(x+1)\right]&= \log_7(42)\\(x + 12)(x+1)&=42\\x^2+13x+12&=42\\x^2+13x-30&=0\\x^2+15x-2x-30&=0\\x(x+15)-2(x+15)&=0\\(x-2)(x+15)&=0\\\\\implies x&=2\\\implies x&=-15\end{aligned}[/tex]

As logs of negative numbers cannot be taken, x = -15 is an extraneous solution.  Therefore, the only valid solution is x = 2.

Part l

[tex]\begin{aligned}\log_4(x + 3) + 1 &= 2\log_4(x)\\\log_4(x + 3) + \log_44 &= \log_4(x^2)\\\log_4\left[4(x + 3)\right] &= \log_4(x^2)\\4(x + 3)&=x^2\\4x+12&=x^2\\x^2-4x-12&=0\\x^2-6x+2x-12&=0\\x(x-6)+2(x-6)&=0\\(x+2)(x-6)&=0\\\\\implies x&=-2\\\implies x&=6\end{aligned}[/tex]

As logs of negative numbers cannot be taken, x = -2 is an extraneous solution.  Therefore, the only valid solution is x = 6.

A right triangle has one interior angle that measures 38% Which of these is the measure of a different interior angle of the triangle?

Answers

The measure of a different interior angle of the triangle is 52 degrees.

What is the measure of the missing interior angle ?

A right angled triangle is a triangle with one of the angles as 90 degrees.

The sum of the interior angle of a triangle is 180 degrees.

Given the data in the question;

Measure of angle a = 38 degreeMeasure of angle b = ?Measure of angle c = 90 degree

Since the sum of the interior angle of a triangle is 180 degrees.

Angle a + Angle b + Angle c = 180

38 + Angle b + 90 = 180

Angle b + 128 = 180

Angle b = 180 - 128

Angle b = 52 degrees.

Therefore, the measure of the second angle is 52 degrees.

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This is hard to do I need help

Answers

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What is the area of the shaded region below?

Answers

Step-by-step explanation:

the easiest way might be the approach to calculate the area of the whole rectangle and then subtract the area of the triangle.

the area of the whole rectangle is

18×16 = 288 m²

the area of a triangle is

baseline × height / 2

in a case like this (right-angled triangle) we can use one leg as baseline, and the other leg (90°) as height.

so, the height is the same as the width of the rectangle : 16 m.

how long is the baseline ?

it is on the 18 m length of the rectangle, and there are two 3 m "gaps", one left, and one right.

so, what's left for the baseline of the triangle itself ?

baseline = 18 - 3 - 3 = 12 m

therefore the area of the triangle is

12×16/2 = 12×8 = 96 m²

so, the total area of the shaded region is

288 - 96 = 192 m²

Indicate the equation of the given line in standard form. The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). Show calculations.

Answers

The linear function containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). is given as follows:

y = -1.67x + 6.5.

How to define the linear function?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.

The median of the trapezoid is composed by these two points:

Midpoint of RS.Midpoint of TU.

The coordinates of the midpoint of RS are given as follows:

x = (-1 + 1)/2 = 0.y = (5 + 8)/2 = 6.5.

The coordinates of the midpoint of TU are given as follows:

x = (7 + 2)/2 = 4.5.y = (-2 + 0)/2 = -1.

Hence the points of the function are:

(0, 6.5) and (4.5, -1).

When x = 0, y = 6.5, hence the intercept b is given as follows:

b = 6.5.

When x increases by 4.5, y decays by 7.5, hence the slope m is given as follows:

m = -7.5/4.5

m = -1.67.

Hence the function is:

y = -1.67x + 6.5.

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A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating, a procedure used to determine the age of an object, the researcher discovers that the fossil is 4000 years old. A. Find the percent error. B. What other estimate gives the same percent error?

Answers

A. The percent error is 25%

B. Another estimate that gives the same percent error is the Theoretical value.

How to Find the Percent Error?

A. To find the percent error, we use the following formula:

percent error = (|experimental value - theoretical value| / theoretical value) x 100

In this case, the experimental value is 4000 years (from carbon-14 dating) and the theoretical value is 3200 years (from the researcher's estimate). Plugging these values into the formula:

percent error = (|4000 - 3200| / 3200) x 100 = (800 / 3200) x 100 = 25%

B. To find an estimate that gives the same percent error, we can use the formula:

Theoretical value = experimental value / (1 + percent error / 100)

If we use the same percent error (25%) and experimental value (4000 years) as before:

Theoretical value = 4000 / (1 + 25/100) = 4000 / 1.25 = 3200

So, an estimate of 3200 years would give the same 25% percent error as the researcher's original estimate.

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a square fountain in the center of a shopping mall has an area of (4x^2+12x+9)ft^2. The dimensions of the fountain are of the form cx + d, where c and d are whole numbers. Find an expression for the perimeter of the fountain. Find the perimeter when x=2 ft.

Answers

A. An expression for the perimeter of the fountain is 8x + 12 ft.

B. The perimeter when x=2 ft. is 28 ft

How do we determine the values?

The area of the fountain is given as 4x^2 + 12x + 9 square feet. Since the fountain is a square, we know that the length and the width of the fountain are equal. This means that we can express the area of the fountain in the form of (cx + d)^2.

Expanding (cx + d)^2 gives:

(cx + d)^2 = cx^2 + 2cxd + d^2

We can equate this to the given area of the fountain:

cx^2 + 2cxd + d^2 = 4x^2 + 12x + 9

To find the expression for the perimeter of the fountain, we need to find the dimensions (length and width) of the fountain. This can be done by factoring the area expression:

4x^2 + 12x + 9 = (2x + 3)(2x + 3)

So the dimensions of the fountain are (2x + 3) ft

The perimeter of a square is the sum of all four sides, so we can find the perimeter of the fountain by multiplying the length of one side by 4:

Perimeter = 4(2x + 3) ft = 8x + 12 ft

When x = 2 ft, the perimeter of the fountain is:

8(2) + 12 = 28 ft

So when x = 2 ft, the perimeter of the fountain is 28 ft.

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(1.1) Convert 500 g to kg. (1.2) convert 1000 km to m. (1.3) Convert 1,65 ton to kg. (1.4) Convert 1,5 litre to millilitre. (1.5) Convert 50 m to cm. (1.6) if 1 inch is 2,54 cm, convert 12,5 cm to inches. (1.7) If 1 cup is 250 ml, how many cups will 1 250 ml be? (1.8) if 3 g of flour is 5 ml, how many ml will 10 g be? (1.9) Round the following number off to two decimal places: 135,2128 (1.10) Round the following number off to the nearest whole number: 250,62 (1.11) Round the following number off to the nearest ten: 123,84.
QUESTION 2 [6 MARKS] If an athlete passed the 5-km mark in a race after 19 min 58 seconds and the 10 km mark after 37 min 25 seconds, how long did it take him to complete the second 5 km?​

Answers

Answer:

(1.1)

1000g=1kg

500÷1000=0.5kg

(1.2)

1000m=1km

1000×1000= 1000000m

(1.3)

1000kg=1tonne

165×1000= 165,000kg

Karen wants to buy new shoes. There is a promotion for 3
pairs of sneakers for $450.75, how much would one pair of
sneakers cost?

Answers

Each pair of shoes will cost $150.25

Good luck hope this helps


:))))

A simple harmonic oscillator consists of a block of mass 2.00kg attached to a spring of spring constant 100N/m. When t=1.00s, the position and velocity of the block are x=0.129m and v=3.415m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t=0s?

Answers

The oscillations have an amplitude of 0.129 m. The block is positioned at 0m and moving at 0m/s at time t=0s.

The maximum deflection of a simple harmonic oscillator from its equilibrium position is its amplitude. Since this is the displacement at time t=1.00s, the oscillations in this instance have an amplitude of 0.129m. The oscillator is in equilibrium at time t=0 s, therefore the block is located at location 0 m. Additionally, since the oscillator has not yet begun to move, these values can be determined by examining the oscillator's equation of motion. According to this equation, the oscillator's position is determined by the expression x=A*cos(t), where A stands for amplitude and for angular frequency. The equation becomes simpler to x=0m for A=0.129m and t=0s. Similar to that, v=-Asin(t) gives the velocity. The equation is again simplified to v=0m/s as A=0.129m and t=0s.

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A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used.
Part 1. In January, the total cost for 100 minutes was $47 while in February, the total cost for 350 minutes
was $52. The constant charge for each minute used is:
O 0.02
O 0.04
O 0.03

Answers

The required constant charge for each minute used is $0.02.

What is linear equation of two variable?

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. ​

According to question:

Let fixed charge of monthly be x and constant rate of each minute used is y.

So,

In january

x + 100y = 47--------(1)

and in February

x + 350y = 52-----------(2)

equation(2) - equation(1)

(x + 350y) - (x + 100y) = 52 -47

250y = 5

y = 0.02

Thus, $0.02 used per minutes.

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13. Solve for x. Please help

Answers

Answer:

x = 15

Step-by-step explanation:

The sum of the four angles of a quadrilateral add up top 360°

Given:

m∠A = (5x+14)°  

m∠b = 109°        

m∠C = (3x+8)°    

m∠D = 109°°

Here we are given actual values for two angles as 109°. Their sum is: 109 + 109 = 218°

The sum of the remaining two angles which are expressions in x should be:

360 - 218 = 142°

This is the sum of m∠A an m∠C

Substituting the terms for the two angle measures we get

(5x+14)  + (3x+8) = 142

5x+14  + 3x+8 = 142

Grouping like terms:

5x + 3x + 14 + 8 = 142

8x + 22 = 142

8x = 142- 22

8x = 120

x = 120/4

x = 15

suppose you take a sample of 50 students from your school and measure their height. which one of the following is a random variable? group of answer choices

Answers

The mean of the sample is the random variable in the given problem.

The mean of any given data set can be defined as summarizing a given group of data. It is done in order to make data sets and their values easier to understand. It can be obtained by first adding all the given values and then dividing the total sum by the number of data entries.

A random variable is any quantity that depends on random events. Here, we know that the mean of the given sample depends on all of the random events or we can say random values present in the table. Hence, we can conclude that the random variable is the mean of the sample.

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two-finger morra is a game in which two players each hold up one or two fingers. the payoff, in dollars, is the total number of fingers shown. r receives the payoff if the total is even, and c receives the payoff if the total is odd. write the payoff matrix.

Answers

Payoff matrix: R (row player) receives payoff if total number of fingers shown is even, C (column player) receives payoff if total number of fingers shown is odd.

Two-finger morra is a game in which two players take turns holding up either one or two fingers. The payoff for the game is the total number of fingers shown, with the player whose total is even (R) receiving the payoff, and the player whose total is odd (C) receiving the payoff. This game can be represented in a payoff matrix, which is a table that shows the payoffs for each player in each possible situation. For two-finger morra, the payoff matrix would have two rows and two columns, representing the two players, R and C. The top row would show the payoffs for R when the total number of fingers is even, and the bottom row would show the payoffs for R when the total number of fingers is odd. Similarly, the left column would show the payoffs for C when the total number of fingers is even and the right column would show the payoffs for C when the total number of fingers is odd.

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how to find the anser to 1999+888999

Answers

890998

Step-by-step explanation:

1999+888999 = 890998

A triangle has a perimeter of 11ft. Side b is twice as long as side a. Side c is 3 more than side a.
What is the length of each side?

Answers

The length of sides a,b and c of triangle are 2, 4 and 5 respectively whereas the perimeter is 11ft.

A perimeter is defined.

A one-dimensional length, a two-dimensional shape, or both can have perimeters that are closed paths that contain, surround, or define them. A circle's or an ellipse's perimeter is measured by its circumference.

The perimeter calculation has a lot of useful applications. Calculated perimeter is the term used to describe the size of fence required to completely surround a yard or garden. How far a wheel or circle can go in one spin is determined by its circumference, which measures its perimeter. Similar to this, a spool's circumference is inversely related to the length of thread that is wound around it; if the string were exactly the same length, the circumference would be equal.

Given that

b = 2a

c = 3 +a

We know that the perimeter is equal to the sum of all the sides

Perimeter = a+b +c

11 = a +2a + a+3

8 = 4a

a = 2

Hence, sides a ,b and c are 2, 4, 5 respectively.

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56. Kotkit is the hottest new social media app. It is lowkey fire. It slays! There were no crumbs left. Users post their Tiktoks to Kotkit, but play them backwards. At the start of the year, there are 1500 users, but the number of users grows exponentially at a rate of 12% per day.

a. Write a function K(t) that expresses the number of users t days after the start of the year.

b. How many users are of the Kotkit after 30 days?

.c After how many days will the numbers of users reach one million users?

Answers

Answer:

[tex]\textsf{a)} \quad K(t)=1500(1.12)^t[/tex]

b)  44940

c)  57.4 days

Step-by-step explanation:

Exponential Growth Function

[tex]f(t)=a(1+r)^t[/tex]

where:

a is the initial value (y-intercept)r is the growth rate (in decimal form)t is the time

Given values:

a = 1500r = 12% per day = 0.12t = time in days

Part a

To create a function K(t) that expresses the number of users t days after the start of the year, substitute the given values into the exponential growth formula:

[tex]\implies K(t)=1500(1+0.12)^t[/tex]

[tex]\implies K(t)=1500(1.12)^t[/tex]

Part b

To calculate how many users there are after 30 days, substitute t = 30 into the function K(t) from part a:

[tex]\implies K(30)=1500(1.12)^{30}[/tex]

[tex]\implies K(30)=44939.8831...[/tex]

[tex]\implies K(30)=44940\; \rm users[/tex]

Part c

To calculate after how many days it takes to reach one million users, substitute K(t) = 1,000,000 into the function and solve for t:

[tex]\implies 1000000=1500(1.12)^t[/tex]

[tex]\implies \dfrac{2000}{3}=1.12^t[/tex]

[tex]\implies \ln \left(\dfrac{2000}{3}\right)=\ln 1.12^t[/tex]

[tex]\implies \ln \left(\dfrac{2000}{3}\right)=t \ln 1.12[/tex]

[tex]\implies t=\dfrac{\ln \left(\frac{2000}{3}\right)}{\ln 1.12}[/tex]

[tex]\implies t=57.3755016...[/tex]

[tex]\implies t=57.4\; \rm days[/tex]

In AQRS, m angle, then classify AQRS by its angles.
Classify:
m m m

Answers

Using Angle Sum property, the measure of 3 angles is ∠Q = 35°, ∠R = 19°, ∠S = 126°.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

As given the measure of 3 angles is -

∠Q = 4x - 17

∠R = x + 6

∠S = 10x - 4

We know that by angle - sum property,

The sum of 3 angles of triangle = 180°

⇒ 4x - 17 + x + 6 + 10x - 4 = 180

⇒ 15x -15 = 180

⇒ 15x = 180 + 15

⇒ 15x = 195

⇒ x = 13

∠Q = 4x - 17 = 4 × 13 - 17 = 35°

∠R = x + 6 = 13 + 6 = 19°

∠S = 10x - 4 = 10 × 13 - 4 = 126°

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Complete question -

If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
03
06
O 16
O 22

Answers

Answer: b is the coefficient of the x term. In the standard form f(x) = ax^2 + bx + c, b is the value of the coefficient of the x term. So the value of b is 0.

Step-by-step explanation:

The value of b in the given function is 12.

What is an equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, a table defining the function, we need to form an equation and compare with the standard form of a quadratic function,

We can use the vertex form of a quadratic function, which is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Since, we know the vertex of this parabola from the table, we can use that information to write the equation in vertex form: f(x) = a(x + 6)^2 + 8

Expanding this, we get f(x) = a(x² + 12x + 36) + 8

Comparing this with the standard form, we see that a = 1, b = 12, and c = 8.

Therefore, the value of b is 12.

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The complete question is :-

The table represents a quadratic function f(x). x f(x) −10 24 −9 17 −8 12 −7 9 −6 8 −5 9 −4 12 If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?

Which statements are true for the following expression? (11 + 7)(8 + 7) + (2 + 9) Check all that are true. All factors are the sum of two terms. 40 The solution is the sum of three terms. 40 It is not possible to find a solution. 4 The solution is the product of two factors, plus another number: 4 The solution is the difference between three terms.

Answers

Answer:

All of the following statements are true for the expression (11 + 7)(8 + 7) + (2 + 9): all factors are the sum of two terms, the solution is the sum of three terms, the solution is the product of two factors, plus another number, and the solution is the difference between three terms.

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Find the length of the arc of a circle of diameter 10
meters subtended by a central angle of π3
radians.

Round your answer to two decimal places.

Answers

The length of the arc of a circle with given radius and central angle is 5.23 meters.

What is the circle?

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Given that, a circle of diameter 10 meters subtended by a central angle of π/3 radians or 60°.

We have, radius of a circle = 5 meters

We know that, arc length of a circle is θ/360° ×2πr

Now, 60°/360° ×2×3.14×5

= 1/6×2×3.14×5

= 5.23 meters

Therefore, the length of the arc of a circle with given radius and central angle is 5.23 meters.

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If y varies inversely as x and y=9 when x=7, find y when x=6

Answers

If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.

How do you find y when y varies inversely with x?

If y fluctuates inversely of x, then y = kx, where k is a fixed value. According to the expressions "y varies inversely as x" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. For some constant k, referred to as the constant of proportionality, yx = k.

According to the expression "y varies inversely as x," y drops by the same amount that x grows. In other terms, xy = k means that the equation xy is constant.

Let the equation be x = k/y, then k be a constant

[tex]$$\begin{aligned}& x=k \times \frac{1}{y} \\& \Rightarrow k=x y=9 \times 7=63 \\& \Rightarrow x=\frac{63}{y}\end{aligned}$$[/tex]

So [tex]$y=\frac{63}{x}$[/tex]

At x = 6 we have

[tex]$y=\frac{63}{6}=10.5$$[/tex]

If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.

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Simplify the expression. Assume that the denominator does not equal zero.Write any variables in alphabetical order.



12m−3n62m−7n

Answers

The simplified expression is 14m -10n

How to simplify the expression

From the question, we have the following parameters that can be used in our computation:

12m−3n62m−7n

Express properly

So, we have the following representation

12m - 3n + 2m - 7n

Collect the like terms

This gives

12m + 2m - 3n - 7n

Evaluate the like terms

So, we have the following representation

14m - 10n

Hence, the solution is 14m - 10n

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Find the missing coordinate to complete the ordered pair for the equation 3x- 4y = 12: When the following are given (0, ?) and (?, 3)

Answers

The missing coordinates on the ordered pairs of the linear equation are:

(0, -4) and  (8, 3)

How to find the missing coordinates?

Here we have the linear equation:

3x - 4y = 12

And we want to find the missing coordinates for the given points (0, ?) and (?, 3) where these points belong to the line.

The first point is (0, ?), this means that the value of x is zero, then we can evaluate the equation in x = 0 then we will get:

3*0 - 4y = 12

-4y = 12

y = 12/-3 = -4

So the point is (0, -4)

For the other point (?, 3) we need to evaluate in y = 3.

3*x - 4*3  12

3x - 12 = 12

3x = 12 + 12

3x = 24

x = 24/3 = 8

So we have the point (8, 3)

These are the missing coordinates.

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3. Marcus makes $3,000 each month. He pays a total of 28% in taxes and 5% for *
retirement
Retirement
Net Monthly
Income
Taxes
Gross monthly
income
$3,000
оооо
$840
ооос
$150
оооо
$2,010
о

Help

Answers

The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.

What is net income?

Marcus makes $3,000 each month. He pays a total of 28% in taxes and 5% for

It's rather easy to figure out net income. Simply deduct expenses like taxes, insurance, and retirement contributions from your gross income, which is the entire amount of money you have made. Deductions from gross income equal net income.

Gross income – deductions = net income.

3000 - 840 - 150 = 2010.

The amount you make each month before taxes and other deductions is known as your monthly gross income. In other words, it is your annual income divided by 12.

monthly gross income = 3000.

The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.

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An anesthetic is given at the dosage of 15 mg per 10 lb body weight. It is packaged in vials at a concentration of 100 mg per mL.

How many mL should be given to a patient who weighs 58 kg?

Answers

0.1920 mL of the anesthetic should be given to the patient.

Calculation of Dosage

First, we need to convert the patient's weight from kilograms to pounds:

58 kg x 2.20462 lb/kg = 128.01 lbs

Next, we can calculate the total amount of anesthetic to be given to the patient:

15 mg/10 lbs x 128.01 lbs = 19.20 mg

Finally, we can divide the total amount of anesthetic by the concentration of the anesthetic in each mL:

19.20 mg / 100 mg/mL = 0.1920 mL

So, 0.1920 mL of the anesthetic should be given to the patient.

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the heptagon ($7$-sided polygon) and hexagon are drawn in plane so that they intersect at a finite number of points. let $n$ be the maximum possible number of points where two polygons can intersect. which one is correct?

Answers

The maximum possible number of points where two polygons can intersect is [tex]$n = 4$[/tex]. This is achieved when the two polygons are tangent to each other at four points.

Maximum Intersection Point Count

There are different ways to approach the problem of determining the maximum possible number of points where two polygons can intersect, but one possible method is to use geometric principles and constructive examples. Here is one possible way to do it:

Start with a heptagon and a hexagon that are both regular (i.e., all sides and angles are equal).Place the heptagon in the plane so that one of its vertices coincides with the center of the hexagon.Draw an equilateral triangle with sides of the same length as the heptagon's sides, and one of its vertices at the center of the hexagon.Connect the center of the hexagon to each vertex of the triangle, forming six congruent isosceles triangles.Draw a line segment from the center of the hexagon to the middle point of each side of the heptagon. This divides the heptagon into 14 congruent isosceles triangles.Now, it is clear that the heptagon and hexagon intersect at 4 points.

This is a constructive example for showing that the maximum possible number of intersection points between heptagon and hexagon is 4.

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