On** simplifying **the **proportion** **18:54:12**, we get answer as **3:9:2.**

The following are crucial **proportional **characteristics:

If a: b = c: d, then a + c: b + d. **Addendum**

A - c: b - d if a: b = c: d. **Subtrahendo**

**Dividendo** states that if a: b = c: d, then a- b: b = c- d: d.

If a: b = c: d, then a Plus b: b Equals c+d: d. This is known as **combining**.

To put it another way, if **a: b = c: d,** then **a: c = b: d.**

On **simplifying**,

18:54:12

Firstly, dividing the all numbers by 3

= 6:18:4

Now **dividing** by 2

**= 3:9:2**

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50 POINTS

Does the point (1, 3) fall on the graph of the line that goes through (-2, 8) and (3, -1)? Show me how you know without graphing. Show your work algebraically (That is, don't draw me a graph... show me using numbers, variables, and/or symbols).

can someone explain please :)

**Step-by-step explanation:**

1.First work out the equation of the line.

1.1 work out gradient

[tex]y = ( \frac{ - 1 - 8}{3 - ( - 2)} )x + c[/tex]

[tex]y = - \frac{9}{5} x + c[/tex]

1.2 substitute in x and y value of one of the two given point. ill use (3;-1).

[tex] - 1 = - \frac{9}{5} (3) + c[/tex]

[tex]c = \frac{22}{5} [/tex]

therefore equation is

[tex]y = - \frac{9}{5} x + \frac{22}{5} [/tex]

2. Now sub in x value of the point you want to test and see if y value correlates.

[tex]y = - \frac{9}{5} (1) + \frac{22}{5} [/tex]

[tex]y = \frac{13}{5} [/tex]

3. We can conclude that point (3;1) does not fall on the graph

6. Match each polynomial function with its leading coefficient.

A. P(x) = (x + 2)(2x - 3)(4x + 7)

B. P(x) =

(x-2)(2x - 3)(4x + 7)

C. P(x) = 5(x-2)(2x - 3)(4x + 7)

D. P(x) = -(x-2)(2x - 3)(4x + 7)

E. P(x) = (x + 2)(2x - 3)(4x + 7)

(From Unit 2, Lesson 6.)

1.40

2.8

3.4

4.2

5.-8

The perfect match** leading coefficient **for the given **polynomial **will be as below:-

A. P(x) = (x + 2)(2x - 3)(4x + 7) => **2. 8**

B. P(x) = (x-2)(2x - 3)(4x + 7) => **3. 4**

C. P(x) = 5(x-2)(2x - 3)(4x + 7) =>** 1. 40**

D. P(x) = -(x-2)(2x - 3)(4x + 7) => **5. - 8**

E. P(x) = (x + 2)(2x - 3)(4x + 7) =>** 4. 2**

**Leading Coefficient:**

The leading coefficient of the polynomial is means the **coefficient **of the variable having the **highest **power in the **polynomial**.

Given,

Here we have the following list of polynomials,

A. P(x) = (x + 2)(2x - 3)(4x + 7)

B. P(x) = (x-2)(2x - 3)(4x + 7)

C. P(x) = 5(x-2)(2x - 3)(4x + 7)

D. P(x) = -(x-2)(2x - 3)(4x + 7)

E. P(x) = (x + 2)(2x - 3)(4x + 7)

Now, we need to find the matching leading coefficients for this polynomials.

In the given polynomials, we have to calculate the highest power variable in each **polynomial **with the coefficient. That **coefficient **is known as the leading coefficients.

First, we have to take the expression A, then we get,

A. P(x) = (x + 2) (2x - 3) (4x +7)

Here we have to multiply the x term alone to get the leading coefficient,

P(x) = (x)(2x) (4x)

Thus will results the **leading coefficient** as P(x) = 8x³

Similarly, for expression B,

P(x) = 1/2(x - 2) (2x - 3) (4x + 7)

P(x) = 1/2(x) (2x)(4x)

P(x) = 1/2 8x³

P(x) = 4x³

For expression C,

P(x)= 5(x - 2) (2x - 3) (4x + 7):

P(x) = 5(x)(2x)(4x)

P(x)= 40x³

For expression D,

P(x) = -(x - 2) (2x - 3) (4x + 7):

P(x) = -(x)(2x)(4x)

P(x) = -8x³

Finally, for the expression E,

P(x) = 1/4(X + 2) (2x - 3) (4x + 7):

P(x) = 1/4(x)(2x(4x)

P(x) = 2x³

Therefore, the corresponding leading coefficients are 8, 4, 40, -8, and 2 respectively.

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common errors for Rational Numbers.

**Answer:**

Sometimes people think negative numbers are irrational.

They aren't. They are actually rational because they can be divided and multiplied to make 0.

The fractions are often mistaken as irrational as well.

The only irrational numbers are π, terminating decimals, and non-perfect squares.

**Step-by-step explanation:**

Btw, Brainliest? Thanks!

Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y=-9x-1.

Graph the equations of the lines to check that they are perpendicular.

**Answer: **[tex]y=\frac{1}{9}x[/tex]

**Step-by-step explanation:**

Perpendicular lines have negative reciprocal slopes, so the slope of the line we want to find is 1/9.

Since the y-intercept is 0, the equation is [tex]y=\frac{1}{9}x[/tex].

You can graph the lines on a website like Desmos.

If you solve an equation by graphing each side as a separate line, which of the following corresponds to the solution of the equation? a. there is only a solution if the lines are identical c. the y–coordinate of the intersection point b. both the x–coordinate and the y–coordinate of the intersection point d. the x–coordinate of the intersection point Please select the best answer from the choices provided A B C D

**Answer:**

d. the x–coordinate of the intersection point

**Step-by-step explanation:**

The solution of the system with two lines is the **x-coordinate of their intersection point**.

a. there is only a solution if the lines are identical

b. both the x–coordinate and the y–coordinate of the intersection point,

c. the y–coordinate of the intersection point

d. the x–coordinate of the intersection point

109% as a mixed or whole number

**Answer:**

**Step-by-step explanation:**

In order to convert 109/100 to mixed number, you follow these steps :

Divide the numerator by the denominator

109 ÷ 100 = 1 with a remainder of 9

Write down the whole number 1 and then write down the remainder as new numerator (9) above the denominator (100), As below :

1

9

100

**Answer:**

109/100 or 1.09

Show whether or not each pair of triangles are similar, if possible. Justify your answer, and write a similarity statement when the triangles are similar.

If the matching sides and angles of two triangles are proportional, then the triangles are said to be **similar**.

Triangles that share the same form but differ in size are said to be **similar**.

Hence from the above properties we can find if any two triangles are **similar**.

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What is the equation of a line that passes through (8,-5) and is parallel to the graphed line? In a linear graph line diagram, A line passes through (minus 4, minus 6) and (8, 3) which intersects the x-axis at 4 units and the y-axis at minus 3 units.

The formula for the line that** intersects** at (8,-5) and is parallel to line x+y = 8 is given by the **algebraic expression** y = -x +3.

What is **Algebraic expression**?

The **Algebraic expression** in this case is:

x + y = 8

which traverses points (8,-5)

Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.

y = mx + c →(1)

x + y = 8

y = -x + 8

Comparing the aforementioned **Algebraic expression** to equation (1), we obtain

m = -1

The **slope** of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.

Let's use the point-**slope** equations of line to determine the linear equation now:

(y-y₁) = m(x-x₁)

Changing every value in the equation above to obtain the **Algebraic expression** for a line

(y-(-5)) = -1(x-8) (x-8)

(y+5) = -x+8

y + 5 = -x +8

y = -x +3

The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the **algebraic expression** y = -x +3.

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**Step-by-step explanation:**

Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y is the distance in miles and x is the time in hours to represent the motion of the faster car.

Answer:

y=30 x=22.5 =25 = 55

Step-by-step explanation:

**Answer:**

**Step-by-step explanation:**

y=30x

The function 1500x+y=35000 represents the altitude in feet, y, of a passenger airplane after x minutes of its descent.

PART A: Which graph represents the passenger airplane’s altitude?

By identifying the y and x-intercepts of the** linear equation,** we conclude that the correct **graph **is the third one

We know that the relation between altitude and time is given by the **linear equation:**

1,500x + y = 35,000

If we isolate y, we get:

y = -1,500x + 35,000

Notice that when x = 0, we have:

y = -1,500*0 + 35,000

y = 35,000

So the y-intercept is 35,000

And the plane reaches the ground when:

0 = -1,500*x + 35,000

1,500*x = 35,000

x = 35,000/1,500 = 23.3

So it intercepts the x-axis at x = 23.3

With that in mind, we can see that the correct **graph **is the third one.

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the difference of the product of 4 times a number and 2/3 is 34 / 3

**Answer: x=3**

**Step-by-step explanation:**

[tex]\displaystyle\\4x-\frac{2}{3}=\frac{34}{3}\\[/tex]

**Multiply both parts of the equation by 3:**

[tex]4x(3)-2=34\\12x-2=34\\12x-2+2=34+2\\12x=36[/tex]

**Divide both parts of the equation by 12:**

[tex]x=3[/tex]

The unknown **number** from the equation is 3.

In mathematics, an **equation** is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the **difference** of the product of 4 times a number and 2/3 is 34/3.

Let the unknown number be x.

4x-2/3 =34/3

(12x-2)/3=34/3

12x-2=34

12x=36

x=3

Therefore, the unknown **number** is 3.

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A parking garage in the city charges $2.75 for the first hour and $1.25 for each additional hour, x. Write and solve an inequality to find the maximum time of additional hours that Tony can park his car at the garage if he wants to pay less than $8. and i have another question

.The inequality is given by:

[tex]2.75+1.25t<8[/tex]Subtract 2.75 from both sides of the inequality:

[tex]\begin{gathered} 2.75-2.75+1.25t\lt8-2.75 \\ 1.25t\lt5.25 \\ \text{ Divide both sides by }1.25 \\ \frac{1.25t}{1.25}\lt\frac{5.25}{1.25} \\ t\lt4.2 \end{gathered}[/tex]Therefore, the maximum time of additional hour is **4**

**Answer:**

4 hours

**Step-by-step explanation:**

→ Write inequality

2.75 + 1.25x < 8

→ Minus 2.75 from both sides

1.25x < 5.25

→ Divide both sides by 1.25

x < 4

Do number 6 please thank you!

ANSWER: 5 Rows

EXPLANATION:

The pattern subtracts by 2, 4, 6, 8, 10

Row 5 = 10 cans (18-8)

There’s no row 6 because 10-10 is 0

That said there’s 5 rows

EXPLANATION:

The pattern subtracts by 2, 4, 6, 8, 10

Row 5 = 10 cans (18-8)

There’s no row 6 because 10-10 is 0

That said there’s 5 rows

Use the negative fractions -4/5 and -5/6

PART A

Find the decimal equivalents for each fraction.

PART B

Which is a repeating decimal? Which digit is

repeating?

**Answer:**

see below

**Step-by-step explanation:**

-4/5 using long division gives -0.8

-5/6 using long division gives -0.8333333 => repeats forever

the 3 is repeating

If x=a/b, a does not equal b, and b does not equal 0, find the value of (a+b)/(a-b) in terms of x

**Answer:**

[tex]\frac{x+1}{x-1}[/tex]

**Step-by-step explanation:**

given

x = [tex]\frac{a}{b}[/tex] ( multiply both sides by b )

bx = a

substitute a = bx into the expression

[tex]\frac{a+b}{a-b}[/tex]

= [tex]\frac{bx+b}{bx-b}[/tex] ← factor out b from each term on the numerator and denominator

= [tex]\frac{b(x+1)}{b(x-1)}[/tex] ← cancel b on numerator / denominator

= [tex]\frac{x+1}{x-1}[/tex]

consider the population p of deer in salt lake county as a function of time t, where t is the number of years after 1990. what values are in the range of this function?

The range of the function is for the** **population of the deer in the **salt lake **if found as [P, ∞).

The number of deer is proportional to t, the number of years since 1990.

As a result, time t becomes the independent variable as well as the number of deer becomes the dependent variable; the number of deer DEPENDS upon the year.

A function's range is the set of values that the dependent variable can take.

The values in the range in this example represent the number of deer throughout salt lake in specific years.

Let 'P' be the population of the deer in salt lake.

**Range**: [P, ∞)

Then, the range of the function is for the** population** of the deer in the salt lake if found as [P, ∞).

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If m/FEG is 3x - 11 and m/CBH is x + 27, what is the value of x?

**Answer:**

x= 19

**Step-by-step explanation:**

I believe you would put both expressions equal to each other. So,

3x-11= x+27

3x-x=27+11

2x=38

x= 38/2

x=19

Help please !! due at 8pm tonight

**Answer:**

y=-3x+7

**Step-by-step explanation:**

:]

**Answer:**

Y=-3x+7

**Step-by-step explanation:**

Use rise/run

Find a quadratic function to model the values in the table.

The **quadratic function** to model the **values **in the **table **will be,

y = 3x² + 3x - 3

**Option 1** is true.

**What is Quadratic equation?**

An algebraic equation of the second degree in x is called **Quadratic equation**.

Given that;

The** values** of x and y are,

x = -1, 0, 3

y = -3, -3, 33

Let a** quadratic function** is,

y = ax² + bx + c ... (i)

Then, It satisfy all the values given in table.

So, Substitute **point** (x, y) = (-1, -3) in equation (i) we get;

- 3 = a - b + c ... (ii)

And, Substitute **point **(x, y) = (0, -3) in equation (i) we get;

-3 = c .. (iii)

And, Substitute **point **(x, y) = (3, 33) in equation (i) we get;

33 = 9a + 3b + c ... (iv)

Now, Substitute c = -3 from (iii) in equations (ii) and (iv) we get;

From (ii);

- 3 = a - b - 3

a - b = 0 ... (v)

From (iv);

33 = 9a + 3b - 3

Divide by 3;

11 = 3a + b - 1

3a + b = 12 .... (vi)

Solve **equations **(v) nd (vi) we get;

a = 3 and b = 3

Thus, Substitute the values a = 3, b = 3 and c = -3 in **quadratic equation **we get;

y = ax² + bx + c

y = 3x² + 3x - 3

So, The **quadratic function** to model the **values **in the **table **will be,

y = 3x² + 3x - 3

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A small business that makes candles uses a proportional amount of essential oil and wax. For 208 ounces of wax, they use 8 ounces of essential oil.

How many ounces of essential oil is needed for 728 ounces of wax?

12.5 ounces

28 ounces

42 ounces

91 ounces

**Answer:**

B, 28.

**Step-by-step explanation:**

728 divided by 208, which is 3.5. then you multiply 3.5 & 8 to get 28.

**The answer above me has the answer.**

**Step-by-step explanation: He is 101% confident its it and I back it up because got it right (he should've been 102% confident tho)**

Valeria is a physical therapist who specializes in pediatric leg injuries. Her patients differ in age and type of injury. Knee pain Ankle pain

0-12 years old 1 4

13-19 years old 4 3

What is the probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain?

The** probability **that a randomly selected patient is 0-12 years old given that the patient suffers from **ankle pain **is 4/7.

**Probability **is used to determine the likelihood that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. The more likely it is that the event would occur, the closer to one, the probability value would be.

The** probability **that a randomly selected patient is 0-12 years old given that the patient suffers from **ankle pain** = number of 0 - 12 that suffer from **ankle pain** / total number of people that suffer from ankle pain

= 4 / (4 + 3) = 4 / 7

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please answer area only

**Answer:10**

**Step-by-step explanation:**

found area

Simply the expression below.

10-8.3

Answer: 10 - 8.3 = 1.7

in her garden pam plants the seed 2 1/4 in below the ground. After one month the tomato plant has grown a total of 10 1/2 in. How many inches is the plant above the ground.?

The plant is 8** inches** above the ground

The height of the seed below the ground is 2 1/4

9/4

After one month, the tomatoes has grown 10 1/2

10 1/2

= 21/2

The height of the plant above the ground is

21/2 - 9/4

= 8

Hence the height of the plant above the ground is 8** inches**

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Vincent earned 24$ for 3 hours worked. Later he earned 72$ for 9 hours of work. How much money does he earn per hour

Vincent earns 8 dollars per hour

how to solve a problem like this? (the bottom problem)

You have to find the angle of that corner.

If you have a garden that is 5m x 8m and there are 120 pepper plants, what is the population density of the pepper plants?

Three **pepper plants **are present per **population density.**

You must divide the **population **by the area's size to determine the population density. **Population Density **is therefore equal to the number of people divided by the land area.

Since we are working with plants here, the **formula **is as follows:

**Population Density **= Plants Per Unit Area

Given,

There are **120 plants.**

Area of Land = **5 x 8**

**= 40 m^2**

Just enter the values into the formula now.

Number of People** = 120/40**

**= 3**

Consequently, the number of pepper plants** per square foot is 3.**

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Using a map, Sasha measures the distance between the city in which she lives and her vacation destination to be 450 miles. She assumes that she may be off by 30 miles in her estimation.

What equation can Sasha use to determine the minimum and maximum distance her city is from her vacation destination?

Drag numbers or symbols to the boxes to correctly complete the equation.

The **equation**** **that** ****Sasha** can use to determine the minimum and maximum distance her city is from her **vacation** destination is 450 + 30 and 450 - 30.

It should be noted that an **equation** is simply used to illustrate the relationship between the **variables** that are illustrated or given in the data.

It should be noted that for the **minimum** distance, she has to subtract 30 miles from the vacation **destination**.

The **minimum** value will be:

= 450 - 30

= 420. miles.

For the maximum **distance**, she has to add 30 miles from the **vacation** destination.

The **maximum distance** will be:

= 450 + 30

= 480 miles.

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Select the correct answer. dudley is biking. he wants to cover 40 miles. if he travels 30 miles every 2 hours, what is the equation of a line that models y, the number of miles he has left to travel, after biking x hours? a. y = -15x â€" 40 b. y = -30x 40 c. y = -15x 40 d. y = 30x â€" 40

The **equation **will be y = -15x + 40

**Equations** help us to understand a particular problem better, they give us possible insights into the situation. **Equation Formation** is an important aspect of Mathematics. We can form equations on the basis of the information given and then analyze it.

Given:

The biker, Dudley wants to** travel **40 miles.

It is given that he **travels** 30 miles every 2 hours.

Obtaining Equation,

Distance traveled in 2 hours = 30 miles

Then, distance **traveled **in x hours = [tex]\frac{30}{2}*x = 15x[/tex]

So, the remaining distance to cover = 40 - 15x

or y = 15x - 40

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Solve for A

R= X (A+ B)

**Answer:**

**Step-by-step explanation:**

R=X(A+B)

distribute the x to get:

R=AX+BX

subtract BX from both sides

R-BX=AX

divide both sides by X

A=(R-BX)/X

A mixture of KCl and KNO3 is 44.20% potassium by mass. The percent of KCl in the mixture is closest to
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