The table shows information about the masses of some dogs.

a) Work out the minimum number of dogs that could have a mass of more than

27 kg

b) Work out the maximum number of dogs that could have a mass of more than

27 kg

a) The domain and the range of the function are given as follows:

b) The zero of the function is given as follows: (3,0).

c) The behaviors are given by these following intervals:

d) The extremas are given as follows:

e) The function is neither even nor odd.

The domain of a function is the set that contains all the input values for the function, hence in the graph it is given by the values of x.

The range of a function is the set that contains all the output values for the function, hence in the graph it is given by the values of y.

The zeros are the points of the function at which it either crosses or touches the x-axis.

The function is increasing when the graph is moving up, and decreasing it the graph is moving down.

The extremas are given as follows:

The function is classified as even, odd or neither as follows:

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The value of x in this problem is 2.

Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.

Use the transposing method to isolate the variable x and then solve for it.

distribute brackets on both sides of the equation.

= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x

= 15x - 10 = 10 + 6 + 2x

collect terms in x to the left side and numeric values to the right side.

= 15x - 2x = 10 + 6 + 10

= 13x = 26

= x = 26/13 = 2

Therefore the final value of x in this equation will be 2.

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x² + 4x + 4, this is a perfect square trinomial, which is expressed as

(x + 2)²

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Given that,

x² + 4x + 4

= (x)² + 2(2x) + 4

= (x)² + 2(x)(2) + 2²

This is similar to a² + 2ab + b² = (a + b)²

so, we can write:

= (x + 2)²

= (x + 2) (x + 2)

so, this is a perfect square trinomial.

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Answer:

yes, the board is long enough

Step-by-step explanation:

5.5 in x 4 walls = 22 inches

The board is 24.5 in, so there is enough.

24.5 > 22, there is an extra 2.5 in left over.

The spring constant is 30 N/m and the stretch when the 420 N force is applied is 14 cm.

The force needed or applied to compress or extend a spring on any attached object is known as the spring force.

A spring exerts an equal and opposite force on an object when the object exerts a force on it. It always takes action to get mass back to where it should be for equilibrium. 

Given that when 180 N force is applied the spring stretched by 6 cm. The spring stretch when the 420 N force is applied is calculated as,

First, calculate the spring constant,

F = kx

180 = k x 6

k = 30 N / m

Calculate the deformation,

x = F / k

x = 420 / 30

x = 14 cm

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Answer:

Step-by-step explanation:

Divide: 18 ÷3=?

The answer is 6

The terms of the expression are 5x², 9x and 6

Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.

They are also known to be made up of arithmetic operation, such as;

It is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.

They can be regrouped by the addition of  their coefficients. Like terms are those that has the same variables to the same powers or coefficients.

The types are;

5x², 9x and 6

Thus, they are 5x², 9x and 6

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The value of x in the shape we have here is given as 18.7 cm

In this question we are to find the value of x using the values that we already have in the shape.

The base of the diagram has its length as 40 cm.

The shape is made up of two right angled triangles.

since the top of the shape is 26 m, the triangles would be gotten by

40 - 26 = 14

14 / 2 = 7cm

each rectangular base is therefore 7 cm

we have to solve for the value of x using the Pythagorean theorem

hence we would have:

7² + x² = 20²

49 + x² = 400

x² = 400 - 49

x² = 351

x = 18.7 cm

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The required slope of the linear equation is -3 which values shown in the table.

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The table is given in the question as follows:

x          y

-4       -15

-2        9

0         3

2        -3

4         -9

As per the question, we take the given points are (0, 3) and (4, -9).

So we can substitute these values into the formula:

m = (-9 - 3) / (4 - 0)

m = -12 / 4

Apply the division operation, and we get

m = -3

Therefore, the required slope of the linear equation is -3.

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The best answer from the choices provided is a = plus-or-minus 16 . Option C

A quadratic equation can be defined as an equation that can be rearranged in a standard form

Such that;

These quadratic equation are also described as polynomial equation having its highest degree as 2.

From the information given, we have that;

3a² - 21 = 27

collect like terms

3a² = 27 + 21

Add the values

3a² = 48

Divide both sides by 3

a² = 48/3

a² = 16

Hence, the value is a² = 16

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The Fraction for the given word problem is x/y = 9/11

A fraction, which derives from the Latin word fractus, meaning "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in everyday speech.

Let the fraction be x/y

The numerator of a fraction is 2 minus its denomination.

⇒ x = y - 2 .....(i)

When 3 is subtracted from numerator and from denomination the new fraction obtained is 3/4

⇒ x - 3/y - 3 = 3/4

Can also be written as

⇒ 4(x + 3) = 3(y - 3)

⇒ 4x - 12 = 3y - 9

⇒ 4x - 3y = -9 + 12

⇒ 4x - 3y = 3 .....(ii)

Substitute the value of (i) in (ii)

⇒ 4x - 3y = 3

⇒ 4(y - 2) - 3y = 3

⇒ 4y - 8 - 3y = 3

⇒ y - 8 = 3

⇒ y = 3 + 8

⇒ y = 11

Putting the value of y in (i).

⇒ x = y - 2

⇒ x = 11 - 2

⇒ x = 9

Hence, Fraction = x/y = 9/11

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The scale factor of the drawing of the neighborhood park would be = 2000.

The scale factor is defined as the ratio between the scale of the original object and the new object, which represents it but in a different size (larger or smaller).

The width of the neighborhood park. in real life = 8 meters

To convert 8 meters to millimetres is to multiply by 1000

= 8 × 1000 = 8000 mm

The scale factor = 4 × X = 8000

make X the subject of formula;

X = 8000/4

X = 2000.

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Answer:

Enlargment and 5/4

Step-by-step explanation:

15%

If you take fiction plus non fiction it equals 10k books. 1500/10000 is 15%

If the leg of the triangle is equal to a, then:

The second leg is also equal to a.

the given hypotenuse is a√2.

The given area is equal to a²/2; and

The perimeter equals a (2 + √2).

Now, looks easy, but from where does it come? There are various of methods to prove that equation, the most popular of them are:

By using the Pythagorean theorem, we can do that.

As you know one leg length a, then you know the length of the other as well, as both of them are equal.

The given 45 45 90 triangle shows the remaining parameters. Now you know that:

hypotenuse length is - 9 in * √2 = 12.73 in.

area is - 9 in * 9 in / 2 = 40.5 in²; and

perimeter - 9 in + 9 in + 9 in * √2 = 30.73 in.

Find the hypotenuse from the Pythagorean theorem:

a² + b² = c² => a² + a² = c² so c = √(2a²) = a√2

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Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that a taxi charges a flat rate of $1.75 and an additional $0.65 per mile.

Eli has at most $10 to spend on the cab ride

We need to find how far could he travel

1.75+0.65x≤10

Subtract 1.75 on both sides

0.65x≤10-1.75

0.65x≤8.25

x≤8.25/0.65

x≤12.6

So he could travel 12 miles.

Three-fourths times x added to two times x is more than eleven

3/4x+2x>11

Hence,  Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven

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Answer:

hhhhhhhhhhhhhhhh hhhhhhhhhhh

Step-by-step explanation:

hhhhhhhhh hhhhhhhhh hhhhhhh hhhhhh

Answer: a) AE || BC     b)AB=BC      c)AE⊥ED &ED⊥CD

Step-by-step explanation:

a) The line segments that have the arrow sign on them mean that they are parallel, so AE || BC ( || = parallel to).

b) When two line segments have a dashed line on it, it shows that they are the same length, so AB is equal to BC.

c) when two segments intersect with a 90° angle, they are perpendicular, so AE⊥ED &ED⊥CD(⊥ = perpendicular to).

Answer:

0.0558

Step-by-step explanation:

3% is out of hundred so we multiply

3%×1.86=0.0558

Checking:

0.0558÷1.86=0.03

0.03=3%

Logs are a type of mathematical operation used to solve exponential equations.

Logs are written as log boxes, where b is the base. The base is the number that the logarithm is being calculated concerning. The x is the number that the logarithm is calculated. Logarithms allow us to convert multiplication and division problems into addition and subtraction.

For example, log2 (8) can be calculated by taking the logarithm of 2, which is 0.301029996, and then multiplying it by 8, which is 2.408239965. This means that log2 (8) is equal to 2.408239965.

Another example is log10 (100). This can be calculated by taking the logarithm of 10, which is 1 and then multiplying it by 100, which is 100.

This means that log10 (100) is equal to 100. Logs are an important tool in mathematics and are used in a variety of fields, such as chemistry, engineering, and economics.

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Answer:

Step-by-step explanation:

no

Answer:

22:18

Step-by-step explanation:

In this case, firstly you have to add 11 and 9 together, which makes 20.

Then, 40 ( number of sweets ), divided by 20 gives us 2.

This means that every piece, or block, of our ratio will be 2.

Therefore, the last step is multiplying 11x2 and 9x2.

So, Andy has 22 sweets an Trevor has 18.

The probability is 0.3845.The probability of anything occurring is known as probability.

Explanation:

2/52 * 10/52  = 20/52 = 0.3845.

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Step-by-step explanation:

20 workers finish work in 21 days.

the necessary work effort is 20×21 = 420 workdays.

the same effort is needed even if the overall time is shorter.

x workers in 15 days.

x × 15 = 420

x = 420/15 = 28 workers.

so, 28-20 = 8 additional workers are needed to finish the work in 15 days.

Answer:

18.84

Step-by-step explanation:

x is the hypotenuse of the triangle.

For the 48° angle, 14 is the opposite leg.

The trigonometric ratio that relates the opposite leg to the hypotenuse is the sine.

sin 48° = opp/hyp

sin 48° = 14/x

x × sin 48° = 14

x = 14/sin 48°

x = 18.84

A basis for the eigenspace corresponding to a = 11 is (1, -2, 0) and a basis for the eigenspace corresponding to a = 2 is (0,1,1).

An eigenspace is the set of all vectors that are multiplied by a matrix and remain unchanged. In this case, the eigenspace is the set of all vectors that when multiplied by the matrix A will result in a vector with a scalar multiple of the eigenvalue. The eigenvalue is found by solving the characteristic equation, which is the determinant of the matrix minus the eigenvalue multiplied by the identity matrix.

For the matrix A, the eigenvalues are 11 and 2. The corresponding eigenspace for each eigenvalue is then found by solving the homogeneous system of equations. For a = 11, the solution to the system is (1, -2, 0) and for a = 2, the solution is (0,1,1). Both of these vectors form a basis for the corresponding eigenspaces.

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The 4th interval is called perfect

The perfect fourth interval consists of two notes with five steps distance.

The 4th interval is called perfect

The perfect fourth interval consists of two notes with five steps distance. For example, C to F note will result in this musical interval. The perfect fourth include one more semi-step compared to the major third  and two semi-steps less compared to the perfect fifth .

The reason for the name perfect goes back to the Medieval. The unison, fourth, fifth and octave were considered most consonant and therefore were given the name perfect. Perfect fourth is “perfect” in the sense that is almost sounds as the unison interval. The perfect fourth interval is abbreviated  (an alternate spelling is augmented third).

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The y-intercept of the quadratic function f(x) = (x - 6)(x + 2) is -12.

The y-intercept of a quadratic function is the point at which the graph of the function crosses the y-axis. This means that when x = 0, the value of y is equal to the y-intercept. In the case of the function f(x) = (x - 6)(x + 2), when x = 0, the value of y is equal to -12. This means that the y-intercept of the function is -12. To find the y-intercept, we can also substitute 0 for x in the equation, which would give us 0 = (0 - 6)(0 + 2), which simplifies to 0 = -12, and thus the y-intercept is -12.

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Answer:

483000

Step-by-step explanation:

To write a linear expression in standard form, rearrange the terms in alphabetical order.

Answer:

48300000

We can write the above number as

4.83 x 10000000

=4.83 x 10 ^7

Answer:

2800

Step-by-step explanation:

20% of 14,000 is 2800

Multiply both sides by 14,000, then divide the left side to get the result.

Answer:

2800

is what the calculator says

Answer: 256b

Step-by-step explanation: So, first we need to find the square root of 16b.

That'd be 4b, because a square root is when a number can be divided by a number, such as 4 can go into 16 4 times, and like 5 can go into 25 5 times. So, we got 4b

So, 4 to the power of 4 (ignore the b right now) is the same as 4 x 4 x 4 x 4.

So simplified, that'd be 16 x 4 (64). So, 64 x 4 = 256.

So, I'd be 256b