What is the square root of 144?

If the Area= Length × Width

Then, The width of the rectangle is (x -1).

We know that area of rectangle is the number of unit square within the boundary of the rectangle.

The formula of area of rectangle is:

    Area = Length × width

⇒ Width = Length / Area

Given that,  

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = Width   ----------------- (1)

Let's simply the expression :

Note that: x=1 is a zero of the numerator since the sum of the coefficient is zero.

So, (x-1) is a factor:

Putting the values in equation (1)

(x⁴ +4x³ + 3x² -4x -4) = (x-1)  (x³ + 5x² + 8x + 4 )

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = (x-1)

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Answer:

D on Edge 23

Step-by-step explanation:

because i said so

The amount that Vince will be able to spend on the bike, given the amount deposited in the savings account, is $410. 29

The amount that Vince would have to spend on the bike is the future value of the amount he deposited in the savings account.

This future value is found by the formula:

= Amount deposited x ( 1 + rate) ^ number of years

= 300 x ( 1 + 11%) ³

= 300 x 1. 11 ³

= 300 x 1. 367631

= $410. 2893

= $410. 29

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Answer:

Step-by-step explanation:

As we see the two expressions are equal in value

Answer:

log3 1/3 = logb 1/b

(Both expressions are equal)

Step-by-step explanation:

Now we have to,

→ find the expression with greater value.

Then the greatest value is,

→ log3 1/3 = logb 1/b

→ log3 3^(-1) = logb b^(-1)

→ -1 = -1

→ [ LHS = RHS ]

Hence, both have same value.

5725 is the height of the mountain prior to construction, represented by the variable h.

Two or more expressions with an Equal sign is called as Equation.

Given,

The mountain that contains Mount Rushmore is approximately 5,675 feet high.

The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.

1.1h – 622.5 = 5,675 is the equation to find the height of the mountain prior to construction, represented by the variable h

1.1h – 622.5 = 5,675

We need to find the value of h

Add 622.5 on both the sides

1.1h=5675+622.5

1.1h=6297.5

Divide both sides by 1.1

h=6297.5/1.1

h=5725

Hence 5725 is the height of the mountain prior to construction, represented by the variable h.

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Answer:

No

Step-by-step explanation:

listen to guy above he opened my eyes

Answer:

Rs. 4000

Step-by-step explanation:

Profit = 80% = 180% of original price

Therefore, [tex]\frac{180}{100}x=7200\\ 180x=720000\\x=4000[/tex]

Answer:

9000

Step-by-step explanation:

80 percent *9000 =

(80:100)*9000 =

(80*9000):100 =

720000:100 = 7200

The probability that the number generated contains the digit 3 at least once is 0.7458.

Probability that there is digit 3 at least once =  1- P(no 3s in the number)

Total probability is, 10^13.

Here the digits are 0 to 9. we have 10 choices and the digits can be repeated hence the total probability is 10^13.

Now, if there is no 3, the choices will 9, hence the probability is 9^13.

Further, the probability of an event happening, is equal to the

favourable outcomes/total outcomes.

Hence, we get the probability of no 3's is 9^13/10^13

=0.2542

Probability that there is digit 3 at least once =  1- 0.2542

=0.7458

Therefore, the probability of at least one 3 is 0.7458.

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The probability that every even number appears at least once before the first occurrence of an odd is 1/20.

Given:

A fair 6-sided die is repeatedly rolled until an odd number appears.

There are 6! ways to order the 6 numbers and 3!(3!) ways to order the evens in the first three spots and the odds in the next three spots.

so the probability = 3!*3! / 6!

= 3!*3! / 6*5*4*3!

= 3*2*1 / 6*5*4

= 6*1 / 30*4

= 6/120

= 1/20

Therefore the probability that every even number appears at least once before the first occurrence of an odd is 1/20.

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Answer:

$6.30

Step-by-step explanation:

The state sales tax rate in North Carolina is 4.5% estimate the state sales tax on a model of the wright brothers’ airplane that costs $139.99.

You are asked to estimate meaning $139.99 should be rounded to $140. Because 4.5% = 0.045

sales tax (estimated):

0.045 * $140 = $6.30

CHECK:

Exact amount is:

0.045 * 139.99 = $6.29955

The value of the expression -15x+14y as calculated from the given equations is 12.

The pair of simultaneous equations are given as

-9x+8y=3............................1

6x-6y=-3

Now we will solve these equation by elimination method.

6x-6y=-3

or, 2x-2y=-3.......................2

Now multiplying equation 2 by 4 and adding to equation 1 we get:

-9x+8y=3

8x - 8y = -12

or, -x = -9

or, x = 9

Now we use this value of x to find the value of y

-9x + 8y = 3

or , -81 -3 = -8y

or, y = 10.5  

Hence the value of the expression -15x+14y is

=-15(9) + (14)(10.5)

=12

The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics. Computing techniques for obtaining the solutions, which are essential to the disciplines of engineering, physics, chemistry, computer science, and economics are included in numerical linear algebra.

It is useful to approximate a system of nonlinear equations by a linear system when developing a mathematical model or computer simulation of a relatively complex system.

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Using the substitution method, the solution is: x = 31, y = -5.

To solve a system of equations by substitution, rewrite one of the equations in terms of one of the variables, then substitute its value into the other equation and solve.

Given the system:

x - 3y = 16 --> eqn. 1

4x - y = 9 ---> eqn. 2

Rewrite equation 1:

x = 16 + 3y

Substitute the value of x into eqn. 2:

4(16 + 3y) - y = 9

64 + 12y - y = 9

64 + 11y = 9

11y = 9 - 64

11y = -55

y = -5

Substitute the value of y into eqn. 1:

x - 3(-5) = 16

x + 15 = 16

x = 16 - 15

x = 1

The solution is: x = 1, y = -5

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The height of the school is 8.5 m.

For a project in his Geometry class, Jacob uses a mirror on the ground to measure the height of his school building.

To find out how tall is the school:

An image is always formed at the back of a mirror. Thus, the appropriate option is -8.75 m. The flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

         = [tex]\frac{1.65}{1.7}[/tex]

Tan θ = 0.9706

θ = [tex]Tan^{-1} 0.9706[/tex]

 = [tex]44.2^{o}[/tex]

θ = [tex]44.2^{o}[/tex]

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

        = [tex]\frac{h}{8.75}[/tex]

0.9706 = [tex]\frac{h}{8.75}[/tex]

h = 0.9706 x 8.75

 = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m.

Hence the answer is the height of the school is 8.5 m.

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Answer:

d) {(-2,0), (-1,0), (1,0), (2,0)}

Step-by-step explanation:

We know that,

→ A set function has different x values.

Then the set function will be,

a) {(1,0), (1,1), (2,2), (2,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

b) {(0,0), (1,1), (1,1), (3,3)}

→ The x values underlined are repeated.

Hence, it is not a set function.

c) {(0,-2), (0,-1), (0,1), (0,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

d) {(-2,0), (-1,0), (1,0), (2,0)}

→ There are no repeated values for x.

Hence, it is a set function.

Answer:

See below

Step-by-step explanation:

I hope this is what you're looking for!

Some examples include:

Answer: b

Step-by-step explanation:

It's a line, so the formula will be y = mx + b.

        [tex]-3=1(-7)+b\\7-3=b\\b=4[/tex]

So, the function would be y = x + 4. Plug the values of the coordinate in to find the missing value:

[tex]y=x+4=-1+4=3[/tex]

Answer: x≤12

Step-by-step explanation: the room holds a max of 12 people, so the number of people will be less than or equal to 12

The possible values of k that forms a triangle with an area of 1.5 square units are 1 and 2/3

A triangle is a three sided polygon.

The equation of the parabola is; y = 0.5•(x - 3)•(x + k)

The area of the triangle = 1.5 square units

A x-intercept of the equation, y = 0.5•(x - 3)•(x + k) is x = 3.

The area of a triangle, A, is found from the equation

A = 0.5 × Base length × Height

When x = 3, the height of the triangle is therefore;

A = 1.5 = 0.5 × 3 × Height

Height = 1.5 ÷ (0.5 × 3) = 1

Similarly, when the height is 3, the base length is 1

The y-intercept has a value of y = 0.5•(0 - 3)•(0 + k) = -1.5•k

Area of triangle = 0.5 × 1.5•k × k = 1.5

k = 1

When the x-intercept is 3, we have;

0.5 × 1.5•k × 3 = 1.5

k = 1/(1.5) = 2/3

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The The temperature at midnight is -5.6°C.

What is the short definition of temperature?

It should be noted that there are 8 hours between midnight and 6 am.

Therefore, the equation will be:

x + (0.65 × 8) = -0.1

x + 5.5 = - 0.1

x = -0.1 - 5.5

x = - 5.6

The temperature at midnight is -5.6°C.

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Answer:12 1/2

Step-by-step explanation:

Answer:

That is a line. Here's two points that pass through the line:

Literally just graph a line that passes through those two points.

The inequality can be simplified to:

-7 < x < 3

And the graph can be seen in the image at the end.

Here we have the inequality:

|x + 2| + 1 > 6

To solve this, we need to isolate the variable x, so if we first subtract 1 we get:

|x + 2| +1 - 1 > 6 - 1

|x + 2| > 5

The absolute value part can be decomposed into two.

-5 < x + 2 < 5

Now we can subtract 2 in all the inequality, so we get:

-5 - 2 < x + 2 - 2 < 5 - 2

-7 < x < 3

The graph of this can be seen below

Answer:

the C(X) pattern is +4? i need more context but i can give u that much

Step-by-step explanation:

Answer:

240?

Step-by-step explanation:

The correct option regarding the end behavior of p(x)=-9x^9+6x^6-3x^3+1 is given as follows:

B. As x -> -∞, f(x) -> ∞ and as x -> ∞, f(x) -> -∞.

The end behavior of a polynomial function is obtained by the limits of the function as x approaches infinity, meaning that only the term with the highest exponent is considered.

These limits are divided into two tails, as follows:

The function for this problem is defined as follows:

p(x)=-9x^9+6x^6-3x^3+1.

Hence the term with the highest exponent is:

-9x^9.

At the left tail of the graph, the end behavior is given as follows:

lim x -> -∞ f(x) =lim x -> -∞ -9x^9 = -9(-∞)^9 = -9 x (-∞) = ∞.

At the right tail of the graph, the end behavior is given as follows:

lim x -> ∞ f(x) =lim x -> ∞ -9x^9 = -9(∞)^9 = -9 x (∞) = -∞.

Hence option B is correct.

The problem is given by the image shown at the end of the answer.

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Answer:

24√2

Step-by-step explanation:

[tex]2 \sqrt{50} + 3 \sqrt{72} - \sqrt{32} [/tex]

[tex]2 \sqrt{25 \times 2} + 3 \sqrt{36 \times 2} - \sqrt{16 \times 2} [/tex]

[tex]2 \sqrt{25} \sqrt{2} + 3 \sqrt{36} \sqrt{2} - \sqrt{16} \sqrt{2} [/tex]

[tex]2(5 \sqrt{2} ) + 3(6 \sqrt{2} ) - 4 \sqrt{2} [/tex]

[tex]10 \sqrt{2} + 1 8\sqrt{2} - 4 \sqrt{2} [/tex]

[tex]24 \sqrt{2} [/tex]

Answer: \frac{2x^3-3x^2+5}{x-4}

Step-by-step explanation:

If the system of equations, A·x + B·y = C and P·x + Q·y = R has infinitely many solutions, then the relationship between the values, A, B, C, P, Q, and R is; A/P = B/Q = C/R

A system of linear equations can have no solutions, only one solution or infinitely many solutions.

Part of the question that appear missing is presented as follows;

The system of equations in the question is;

If the system has infinitely many solutions, then the equations (1) and (2) represent the same equation, such that equation (1) can be obtained directly from equation (2) and vice versa

This indicates that equation (1) is a multiple of equation (2)

Let the common factor be c, we have;

A = c·P

B = c·Q

C = c·R

Which gives;

A/P = B/Q = C/R = c

The relationship between the coefficient is that; A/P = B/Q = C/R

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