200 T-hirt have been bought for a Fun Run at a cot of £400 plu VAT at

17. 5%. The cot of entry for the run i £5 per peron. What i the minimum number of entrie needed in order to cover the total cot of the T-hirt?

The roots of the given quadratic equation are x = -2/3 and x = -2.

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is a quadratic equation as follows -

3x² + 7 = - 8x + 3

The given quadratic equations are -

3x² + 7 = - 8x + 3

3x² + 8x = 3 - 7

3x² + 8x + 4 = 0

(x + 2/3)(x + 2) = 0

(x + 2/3) = 0   and   (x + 2) = 0

x = -2/3   and   x = -2    

Therefore, the roots of the given quadratic equation are x = -2/3 and x = -2.

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If [tex]$\mathrm{x} \neq 3$[/tex], the expression [tex]$\frac{2 x^3+7 x^2-3 x-25}{x+3}$[/tex] is equivalent to [tex]$2 x^2+x-6-\frac{7}{x+3}$$[/tex].

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.

A mathematical sentence with variables, numbers, or both is known as an expression. Operation can also be a part of an expression, although an equal sign is never present in an operation. A mathematical expression that demonstrates the equality of two expressions is called an equation. There is a sign of equality in equations.

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

Let the equation be

[tex]$\frac{2 x^3+7 x^2-3 x-25}{x+3}[/tex]

simplifying the equation, we get

[tex]$& \text { Divide } \frac{2 x^3+7 x^2-3 x-25}{x+3}=2 x^2+\frac{x^2-3 x-25}{x+3} \\[/tex]

[tex]$& =2 x^2+\frac{x^2-3 x-25}{x+3}[/tex]

[tex]$& \text { Divide } \frac{x^2-3 x-25}{x+3}=x+\frac{-6 x-25}{x+3} \\[/tex]

[tex]$ =2 x^2+x+\frac{-6 x-25}{x+3}[/tex]

Divide [tex]$\frac{-6 x-25}{x+3}=-6+\frac{-7}{x+3}$[/tex]

[tex]$=2 x^2+x-6+\frac{-7}{x+3}$$[/tex]

Simplifying the equation, we get

[tex]$=2 x^2+x-6-\frac{7}{x+3}$$[/tex]

Therefore, the correct answer is option 1) [tex]$2 x^2+x-6-\frac{7}{x+3}$$[/tex].

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The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

What is polynomial?

A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.

We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.

Let 2 and √3 are the roots of the polynomial so,

x = 2,  x = √3

⇒ x - 2 = 0,  x - √3 = 0

⇒ (x - 2)(x - √3) = 0

x^2 - √3x - 2x + 2√3 = 0

Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

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y = -1/2x is the equation of example of the direct variation.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

Given four linear equations in them we need to state which equation is an example of direct variation.

The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Or in other words, the direct variation equation always passes through the origin point of a cartesian plane or (0, 0).

Therefore, in the given options y = -12/x is the only equation that is an example of direct variation.

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The description of isometry and transformations is as follows,

isometry mean A distance-preserving transformation between metric spaces is known as isometry, congruence, or congruent transformation.

The transformation, or f, is a function that maps to itself: X  X. Following the transformation, the pre-image X transforms into the image X. Any or all of the operations like translation, rotation, reflection, and dilation can be used in this transformation. A function is translated by moving it in a particular direction, rotated by spinning it about a point, reflection by reflecting the function, and dilation by scaling it.

Isometry: If two distinct points, a and b, were to be mapped to the same point, then the coincidence axiom of the metric d would be violated. This proof is similar to the proof that an order embedding exists between partially ordered sets. Clearly, a topological embedding exists for each and every isometry between metric spaces.

A bijective isometry is a global isometry, isometric isomorphism, or congruence mapping. A global isometry, like any other bijection, has a function inverse. A global isometry is also the inverse of a global isometry.

Types of transformations;

Transformation of Reflection: The term "reflection" refers to the kind of transformation that takes place when every point in the shape is reflected over a line. The image is on the opposite side of the line from the pre-image but at the same distance from the line when the points are reflected over it. An image point (q,p) is reflected from each point (p,q).

Transformation of Rotation: Rotation is the transformation that rotates each point of the shape by a predetermined number of degrees around that point. When the number of degrees is positive, the shape rotates counterclockwise, and when the number of degrees is negative, the shape rotates clockwise.

Transformation of Translation:  Sliding occurs when a 2-d shape is translated. Let's look at how the vertices of the blue and red figures are positioned in relation to one another in order to describe their relative positions. By comparing its position to the positions of A, B, and C, we must determine their positions.

Hence the basic description of transformation is as follows.

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The required weight of the dollar amount of Stock C is $64.96.

The Correct option is (B).

In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.

Given:

Investment Amount Invested ROR

Stock A     $1,800     1.5%

Stock B     $4,600     3.7%

Stock C     $580        11.2%

Stock D     $1,122      −2.8%

According to the question,

Weight of dollar amount of Stock C

= 580 × 11.2%

= 580 x 0.112

= $64.96

Hence, the required weight is $64.96.

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Answer:

22

Step-by-step explanation:

34-12=22 you just basically subtract 34 and 12 and it gives you 22 but theres the equation too

Dimensions of the parallelogram are:

Its perimeter is:

Its area is:

Perimeter is 2 times greater:

Area is 2*2 = 4 times greater:

Perimeter is 3 times greater:

Area is 3*3 = 9 times greater:

Perimeter is 2 times smaller:

Area is 2*2 = 4 times smaller:

Answer:

the equation of the line is y = -7x - 2.

Step-by-step explanation:

To find the equation of the line with slope -7 that passes through the point (4, -30), we can use the point-slope form of a line.

The point-slope form of a line is:

y - y1 = m(x - x1)

where:

(x1, y1) is a point on the line

m is the slope of the line

Substituting the given values, we get:

y - (-30) = (-7)(x - 4)

Expanding the right side, we get:

y + 30 = -7x + 28

Combining like terms, we get:

y = -7x - 2

So the equation of the line is y = -7x - 2.

The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.

It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.

Recall that Area, A = length × width.

Therefore, since length = 6 (√(x + 2)) units

The width = (5 √(x + 2) ) units

Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )

= 30 (x + 2) square units

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Answer: 88

Step-by-step explanation:

Answer: 88

Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88

280t + 320t = 1,000 is distance equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart.

What does distance mean in a nutshell?

Distance is the overall movement of an object without consideration of direction.

                      Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.

At 10:00 a.m. two planes leave an airport. If the northbound plane flies at 280 mph and the southbound at 320 mph

Let 't' be the time taken when they are 1000 miles apart

the northbound plane flies at 280 mph

Distance  = speed * time

distance covered by northbound plane D1= 280 * t= 280t

the southbound at 320 mph

distance covered by southbound plane D2=320 t

Distance is 1000 miles apart

D1 + D2= 1000

280t + 320t = 1,000

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Answer:

[tex]x=\dfrac{\log 6}{\log 23}[/tex]

Step-by-step explanation:

Given exponential equation:

[tex]23^x=6[/tex]

[tex]\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies\log_{23}6=x[/tex]

[tex]\textsf{Given change of base formula}: \quad \log_by=\dfrac{\log y}{\log b}}[/tex]

Apply the given change of base formula:

[tex]\implies x=\dfrac{\log 6}{\log 23}[/tex]

The option that shows that the set of irrational numbers under addition is not closed is B. π + π.

All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to express an irrational number as the ratio of two integers. The collection of real numbers known as irrational numbers, where p and q are integers, are those that cannot be expressed as fractions, such as p/q.

The example of "π + π" shows that the set of irrational numbers under addition is not closed, because the result of adding two irrational numbers (π + π) is an irrational number (2π) which is not included in the set of irrational numbers.

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Answer:

------------------------------------

There is no indication that the given triangles are congruent.

We can see one angle of each triangle is marked as congruent and that is is. No more evidences of congruence and therefore we state the triangles are not congruent.

This is a choice C.

1. The best geometric model for the rail road is C. Line

2. Two straight lines cannot go through any two points. It is false.

3. The length of the cake is A. 5.5 inches.

4. The vertical angles are AHC and GHE.

The best geometric model for a set of railroad tracks would likely be a line, as it represents the linear path that the tracks follow. A point would not be appropriate as it does not represent the length or direction of the tracks, and a plane would not be necessary as the tracks are linear and exist in a three-dimensional space.

It should be noted that two straight lines cannot go through any two points. Only one line can. The length of the cake will be:

= 6.0 - 0.5

= 5.5

It should be noted that vertical angles are equal. This was Illustrated as AHC and GHE.

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Answer:

12.

Step-by-step explanation:

right!!

Answer:

11

Step-by-step explanation:

remember that the absolute value function always gives a positive value, that is

| - a | = | a | = a

substitute the given values into the expression

- a² - 2bc - | c |

= - (- 2)² - 2(3)(- 3) - | - 3 |

= - (4) - 2(- 9) - | 3 |

= - 4 + 18 - 3

= 14 - 3

= 11

Answer:

C

Step-by-step explanation:

Put in the form y/x and you should have equivalent fraction

12/4 = 3

15/5 = 3

18/6 = 3

When the fractions are simplified, they all equal 3.

Answer: Toni invested in pounds= $1350

Step-by-step explanation:rate of compound interest=4%

Step-by-step explanation:

Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula:  

Given equation is in the form of

where P is the amount invested

'r' is the rate of interest

t is the time taken

P= 1350 is the initial amount invested

1+r= 1.04  (subtract 1 from both sides)

multiply it by 100 to get percentage

r= 4%

I just search it bc my brain dosent work any more

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7). A mathematical expression is a statement that contains a minimum of two numbers .

A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression is (Number/Variable, Math Operator, Number/Variable). A mathematical expression is a statement that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions. A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6.

given

The correct response is 4 less than 7, since 4 is less than 7.

Thus, 7-4=3 could be considered.

The first section of 7–4 appears to be answer B.

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7).

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Answer:

$302

Step-by-step explanation:

p(x) 3x^4 = x^4-3x^2+5

We put 3 in for x and solve

3(3)^4 = 3^4 -3(3)^2 + 5

3(81) = 81 -3(9) + 5

243 = 81 - 27 + 5

243 = 59

Then we add 243 with 59 and get

$243 + $59 = $302

So, they spend together $302

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Answer:

Step-by-step explanation:

Answer: 3

Step-by-step explanation:You can't start at station 0 or 1, as there is not enough gas to travel to the next station.

Let's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4

Travel to station 0. Your tank = 4 - 3 + 2 = 3

Travel to station 1. Your tank = 3 - 3 + 3 = 3

You cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.

Therefore, you can't travel around the circuit once no matter where you start.

Answer:

1,520 pounds

Step-by-step explanation:

40x 38 = 1520

Permutations for each word can be calculated by considering the number of unique letters in it and taking factorial of it.

a) Inverary: There are 8 letters in the name "Inverary" (I, N, V, E, R, A, R, Y), so there are 8! (8 factorial) permutations of all the letters in the name. This equals 40320 permutations.

b) Beamsville: There are 9 letters in the name "Beamsville" (B, E, A, M, S, V, I, L, E), so there are 9! (9 factorial) permutations of all the letters in the name. This equals 362880 permutations.

c) Mattawa: There are 7 letters in the name "Mattawa" (M, A, T, T, A, W, A), so there are 7! (7 factorial) permutations of all the letters in the name. This equals 5040 permutations.

d) Penetanguishene: There are 14 letters in the name "Penetanguishene" (P, E, N, E, T, A, N, G, U, I, S, H, E, N), so there are 14! (14 factorial) permutations of all the letters in the name. This equals 87178291200 permutations.

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Answer:

41,500 people

Step-by-step explanation:

First you find 3% of 36,000= 1,080

Then you do 1080 x 5= 4,500

Then finally do 36,000 + 4,500= 41,500

On solving the provided question we cans ay thatVertical Angles: TZU, XZW Adjacent Angles: TZU, UZV are Vertical angle and adjacent angle.

What is Vertical angle and adjacent angle,?

Vertical angles are two angles that share the same vertex and are formed by two intersecting lines. They are congruent (i.e. have the same measure) and are opposite each other

Adjacent angles are two angles that share a common vertex and side, but do not overlap. They are also called "next to" or "sharing an arm" angles.

Fig 1:

Vertical Angles: NMJ, LMK

Adjacent Angles: NMJ, JMK

Fig 2:

Vertical Angles: DEA, CEB

Adjacent Angles: DEA, AEB

Fig 3:

Vertical Angles: LQM, PQN

Adjacent Angles: LQM, MQN

Fig 4:

Vertical Angles: TZU, XZW

Adjacent Angles: TZU, UZV

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