What is the difference in
elevation between 3 feet above
sea level and 20 feet below sea
level?

Answer:10

Step-by-step explanation:

found area

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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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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Answer:

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

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

Given:

Total members in the committee = 19

Let's find the number of ways a president, vice president, secretary and treasurer can be chosen.

Here, we are to use permutation formula:

Where:

n = 19

r = 4

Thus, we have:

Solving further:

Therefore, the number of ways they can be chosen is 93024 ways.

ANSWER:

93024 ways

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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Answer:

y=30 x=22.5 =25 = 55

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=30x

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:

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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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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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.

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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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!

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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Alice spend a total of $10.50, and the 30% of total was spent on snacks.

So, if we call x the money spent on snacks we have that the ratio between x and total spent money is 30%:

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

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

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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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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The result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

What is long division method?

In mathematics, the long division method can be performed on the polynomial equations. Basically, in this big equation can be solved by making smaller group of equations to make the calculation simple. It divide the dividend with divisor.

According to the question, the given polynomial equation is 3x³ +19x² + 23x + 15. Using long division method, divide it by 25

Therefore, the expression can be written as:

Required expression: [tex]\frac{3x^{3} +19x^{2} + 23x + 15 }{25}[/tex]

Dividing it by 25, we get:

(25/3x³) +(25/19x²) + (25/23x) + (25/15)

⇒ 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

Hence, the result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

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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

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

.The inequality is given by:

Subtract 2.75 from both sides of the inequality:

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

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]

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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