We want to determine if [u, v, w is linearly independent. To do that we write the vectors as columns of a matrix A and row reduce that matrix To check this we add We then add We then add We conclude that times the first row to the second. times the first row to the third. times the new second row to the new third row. OA. The set [u, v, w} is linearly dependent. O B. The set {u, v, w] is linearly independent. C. We cannot tell if the set [u, v, w] is linearly independent or not.

The given division will give the result as (x-3) + [2/(x+3)].

Polynomial are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

The given division of the two of the polynomial can be carried out as shown below,

[tex]\dfrac{x^2-7}{x+3}\\\\=x+\dfrac{-3x-7}{x+3}\\\\=x-3+\dfrac{2}{x+3}\\\\=(x-3)+\dfrac{2}{x+3}[/tex]

Hence, [tex]\dfrac{x^2-7}{x+3}=(x-3)+\dfrac{2}{x+3}[/tex].

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The profit function is 250x  and the profit earned is 375000.

What is cost?

In production, research, retail, and accounting, a cost is that the value of cash that has been spent to provide one thing or deliver a service, and thence isn't obtainable to be used any longer.

Main body:

A) Profit function = R() – TC()

                        = 750 – (300+200)x

                        = 750 – 500x

                        = 250 x

b) total profit = 250 x

                     = 250 *1500

                     = 375000

c) The zero-profit condition is that the condition that happens once AN business or kind of business has a very low (near-zero) value of entry to or exit from the business. during this scenario, some companies not already within the business tend to hitch the business if they calculate that they're going to create a positive economic profit (profit in more than the price of effort investible funds). a lot of and a lot of companies can enter till the economic profit per firm has been driven all the way down to zero by competition.

hence the profit function is 250x

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A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

6. x = 28 degrees

7.  z = 1.6 cm

6.  Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:

50 + 69 + (2 x +5) = 180

combine like terms:

119 + 2 x + 5 = 180

124 + 2 x = 180

subtract 124 from both sides:

2 x = 56

divide by 2 both sides:

x = 56 / 2

x = 28 degrees

Problem 7.

If the two triangles are congruent, then the side MN must equal side RS.

Since MN  measure 1,8 cm, then RS must also measure 1.8 cm

and we can write the equation:

1.8 = 3 z - 3

adding 3 to both sides:

1.8 + 3 = 3 z

4.8 = 3 z

dividing both sides by 3:

z = 4.8 / 3

z = 1.6 cm

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It takes 11.55 years for money to double if invested at 6% compound interest.

What is compound interest?

Calculating the answer exactly:  P⁰°⁰⁶ⁿ=A .

We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.

P⁰°⁰⁶ⁿ = 2P

We divide both sides by  P

e⁰°⁰⁶ⁿ = 2

Using natural logarithm:

0.06 n = ln(2)

n = ln(2)/0.06

n = 11.55 years

Hence, It takes 11.55 years for money to double if invested at 6% compound interest.

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Applying the triangle midsegment theorem, the length of CD is: 8 units.

If the midpoints of two sides of a triangle are joined together by a line segment, that line segment is called the midsegment of the triangle. Every triangle has three of these.

According to the triangle midsegment theorem, the third side of a triangle is parallel to its midsegment, and also has a length that is twice of the length of the midsegment.

Given the image above, where points G, E, and F are the midpoints of the sides of the given triangle, thus:

EG is a midsegment that is parallel to a third side CD.

Therefore:

Length of CD = 2(EG)

Substitute

CD = 2(4)

CD = 8 units.

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Adam have 4 / 9  fraction of the 18 counters. A fraction is a number that is stated as a quotient by dividing the numerator and the denominator.

Fraction a number that is stated as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. A fractional equation is one that contains one or more terms that are fractions. The first step in solving a fractional equation is to eliminate the fractions by multiplying both sides of the equation by the LCD of each term.

Adam has 18 counters

Lesley get 10 counters

Adam have 18 - 10 = 8

8 / 18 = 4 /9

Adam have 4 /9 fraction of the counters.

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Answer:

Yes

Step-by-step explanation:

The required quotient is 34.2 ÷ 3.8 = 9.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given 3.8 divided by 34.2

According to the given question, we can write the quotient as:

⇒ 34.2 ÷ 3.8

⇒ 34.2 / 3.8

⇒ 342 / 38

Apply the division operation, and we get

⇒ 9

Therefore, the required quotient is 34.2 ÷ 3.8 = 9.

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the answer will be "all steps are correct"

Answer:

Step-by-step explanation:

Therefore, C is the correct option.

Step-by-step explanation:

We have been given the equation

The GCF of the right hand side of the equation is t. Hence, factored out the GCF.

Now,  is in multiplication with 't'. So in order to isolate t, we can divide both sides by

Therefore, C is the correct option.

Answer:

£15 and £22

Step-by-step explanation:

let,the cost of one shirt be X and one jumper be y.Then according to question,

5x+4y=163-----(1)

also,

3x+2y=89------(2)

Now, multiplying eqn (2) by 2 and then subtracting from (1),we get

5x+4y=163

6x+4y=178

- - -

_________

-x=-15

:.x=15

Putting value of X in eqn (1),

5×15+4y=163

or,4y=163-75

or,y=88/4

:.y=22

Hence cost of one shirt is £15 and one jumper is £22.

On solving the question as said we get to know that the maximum possible length of the repeating section of the decimal representation of the given number is 10.

As 941 and 1549 are already in whole number lets assume that the question says to find the decimal repetition is 941 and 15  divided by 41 and 59 respectively.

9 divided by 41 is equal to 0.2195121951

15 divided by 49 is equal to 0.306122449.

Therefore, the maximum possible length for their repeating section is 10.

The preferred method for representing both integer and non-integer numbers is the decimal numeral system, often known as the base-ten positional numeral system and denary.

It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers using the decimal system.

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Answer

150000 after 4 years

Step-by-step explanation:

An inequality that expresses the mean number of steps that Diego needs to walk during the last 3 days of this week to more than 70,000 steps is  32076+3x>70000.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Diego's goal is to walk more than 70,000 steps this week.

a) The mean number of steps that Diego walked during the first 4 days of this week is 8019.

So, the number of steps =4×8019

= 32076

Let x be the mean number of steps that Diego needs to walk during the last 3 days of this week to walk more than 70,000 steps.

Now, the inequality is 32076+3x>70000

b) The mean number of steps that Diego needs to walk during the last 3 days of this week is 12642

Substitute x=12642 in the inequality 32076+3x>70000, we get

32076+37926>70000

70002>70000

Yes, Diego will reach his goal of walking more than 70,000 steps this week.

Therefore, the inequality to represent the given situation is 32076+3x>70000.

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Answer: hope it helps

Step-by-step explanation:

2^6=64≡ -1 ( mod 13)

So 2^70=16*(2^6)^11=16*(-)^11(mod 13)

2^70 ≡-16 ( mod 13)

2^70 ≡10 ( mod 13)

Now 3^3=27≡1 ( mod 13)

So 3^70= 3*(3^3)^23≡ 3*(1)^23 ( mod 13)

≡ 3 ( mod 13)

Thus 2^70+3^70 ≡ 10+3 (mod 13)

≡ 0 ( mod 13)

The equivalent fraction with a denominator of 100 will be;

⇒ 90 / 100

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 9 / 10

Now,

Since, The fraction is,

⇒ 9 / 10

Hence, The fraction with denominator 100 is;

⇒ 9 / 10 = 9×10 / 10×10

             = 90/100

Thus, The equivalent fraction with a denominator of 100 will be;

⇒ 90 / 100

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Answer:

HL

Step-by-step explanation:

to solve this we first must see what is congruent

we see that both triangles are right triangles

that means that we can use HL (hypotenuse length) to solve

we must first see if HL works though

we see that the hypotenuses are both equal

that means that we can use HL

that is your answer

The solutions to the quadratic linear system equations are (11, 41) and (3, 9).

The given equations are y=x²-10x+30 and y=4x-3.

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

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, y=x²-10x+30 -------(I) and y=4x-3 -------(II)

Substitute equation (II) in the equation (I), we get

4x-3=x²-10x+30

⇒ x²-10x+30-4x+3=0

⇒ x²-14x+33=0

⇒ x²-11x-3x+33=0

⇒ x(x-11)-3(x-11)=0

⇒ (x-11)(x-3)=0

⇒ x=11 and x=3

So, y=4(11)-3=41 and y=4(3)-3=9

Therefore, the solutions to the quadratic linear system equations are (11, 41) and (3, 9).

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If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Here in the figure attached below,

Given two triangles ΔABC and ΔDEF

Also given that,

ΔABC and ΔDEF are congruent to each other.

Given AC = 4cm

Since both triangles are congruent ,

Side AC is congruent to DF

Therefore DF = 4cm (based on SSS theorem).

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Answer: about 4:30

Step-by-step explanation:

he used the restroom starting at 4:15, he sat on the toilet and watched tt for exactly 14 minutes, He then whiped himself which took about 50 seconds. Flushing the toilet took 10 seconds and when he flushed it was 4:30.

Answer:

perimeter of a triangle is the total

Step-by-step explanation:

p=48cm

Length=3x

width=x

Now P= 2(L+W)

48 =2(3x+x)

48=2(4x)

48=8x

dividing both sides by 8

we have x=6

and so length=18 and width =6

Answer: $1000 = 12x + 112

Step-by-step explanation:

let x be the amount of hours worked

The constant of proportionality of the image of actual height and height on set of the items is 20 / 11

Table

Stool

window

Bucket

Constant of proportionality are used to increase or decrease image. The situation of increment is usually called magnifying.

solving for the constant of proportionality, assuming the factor is k

height on set * k = actual height

44 * k = 80

k = 80 / 44

k = 20/11

Height on set for other items

Table

= 28 ÷ 20/11

= 15.4 inches

Stool

= 18 ÷ 20/11

=  9.9 inches

window

= 80/11 ÷ 20/11

= 4 inches

Bucket

= 40/11 ÷ 20/11

= 2 inches

The Constant of proportionality is calculated to be 20/11

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(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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Let the dimensions of the pen be L for the length and W for the width. The area of the pen is L*W.

We are given that the width of the pen is 80 meters and that the length of the pen is greater than the width. Therefore, the length of the pen must be greater than 80 meters.

Since the area of the pen is L*W, the area will be greatest when L is as large as possible and W is as large as possible. Therefore, we can set L equal to 80 and W equal to 80 to find the dimensions of the pen that give the greatest area:

L = 80

W = 80

The dimensions of the pen that give the greatest area are 80 meters by 80 meters. Therefore, the answer is 80m x 80m.

The dimensions of the pen are 20 m × 40 m and the area will be 600 m².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given data in the question,

Let the length of the rectangle is x and,

Let the width of the rectangle is y.

So, the equation will be,

2x + y = 80              (1)

y = 80 - 2x              (2)

Use the formula of the area of a rectangle,

A = x × y

Substitute y = 80 - 2x in the above formula,

A = x × (80 - 2x)

= 80x - 2(x)²

= -2x² + 80x

dA/dx = -2x² + 80x

A' = -4x + 80

-4x = -80

x = 80/4

x = 20 m

Substitute x = 20 in equation (2)

y = 80 - 2(20)

y = 40 m  

So, the area should be,

A = 20 × 40

A = 600 m².

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Answer:4.05

Step-by-step explanation: Walnut divided by 2 is 0.9 and Oak is 0.9. Maple is 0.45 and Spruce. All that is added up to 4.05

Answer:

552 mph

Step-by-step explanation:

414 / 3/4 = 414 * 4/3 = 1656/3 = 552

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

tan x= -3/1

So, H = √1 + 9 = √10

sin x= -3/ √10 and cos x= 1/ √10

So, sin 2x= 2 sin x cos x =2 ( -3/ √10 )(1/ √10) = -3/10

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 9/10)

                  = -8/10

and, tan 2x = sin 2x/ cos 2x =  -3/10 / ( -8/10) = 3/8

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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