a rectangular laboratory has a length equal to one and a half times its width and a perimeter of 40m. find its length and width respectively?

Answer: its the last answer I got it right

The coordinates of an image dilated about the origin is given by multiplying the coordinates of the preimage by the scale factor

The coordinates where P' should be is (-6.5, 4.5)

The reason the above values is correct is as follows:

Question: The diagram in the question appear missing, a sample diagram of a trapezoid PQRS, having coordinates; P(-3, 3), Q(6, 3), R(9, 0), S(-5, 0)

The coordinates of the vertices of the image are multiplied using the given scale factor about the origin and 2 is subtracted from the x-values the as follows;

The coordinates of the image as follows;

\(\begin{array}{|l|cl|}Preimage \ (x, y)&&Image = \left (x \times \dfrac{3}{2} - 2,\ y \times \dfrac{3}{2} \right)\\P(-3, \ 3)&&P'(-6.5, \ 4.5)\\Q(6, \ 3)&&Q'(7, \ 4.5)\\R(9, \ 0)&&R'(11.5, \ 0)\\S(-5, \ 0)&&S'(-9.5, \ 0)\end{array}\right]\)

Therefore, the coordinates where P' should be is (-6.5, 4.5)

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To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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The complete factorization of the polynomial is:

h(x) = (x - 3)*(x - 1)*(x + 2)

Here we have the polynomial:

g(x)= x³ - 2x² - 5x + 6

And we know that x = 3 is a zero, then (x - 3) is a factor.

So if f(x) = a*x² + b*x + c

We can write:

h(x) = (x - 3)*f(x)

Let's find f(x).

Expanding that:

x³ - 2x² - 5x + 6 = (x - 3)*(a*x² + b*x + c)

x³ - 2x² - 5x + 6 = ax³ + bx² + cx - 3ax² - 3bx - 3c

x³ - 2x² - 5x + 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c

Comparing like terms, we can see that:

a = 1

b - 3 a = -2

c - 3b = -5

-3c = 6

With the first and last equation we can get:

a = 1

c = 6/-3 = -2

Now with one of these values and the second or third equation we can find the value of b.

b - 3 a = -2

b - 3*1 = -2

b - 3 = -2

b = -2 + 3 = 1

Then:

f(x)  = x² + x - 2

The zeros of this quadratic function are given by:

x = -1±3 / 2

so, we get,

x = (-1 + 3)/2 = 1

x = (-1 - 3)/2 = -2

Then we can factorize this as:

f(x) = (x - 1)*(x + 2)

And then we can write h(x) as:

h(x) = (x - 3)*(x - 1)*(x + 2)

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complete question:

For the polynomial below, 3 is a zero.

g(x)= x³ - 2x² - 5x + 6

Express g (x) as a product of linear factors.

Answer:

I only, know one of them....

Step-by-step explanation:

Based on the information given about the fraction, the number of boxes that are needed will be 171 boxes.

From the information, it was stated that headphones at a factory are packed into small boxes measuring one-third cubic foot.

Therefore, the number of boxes of headphones that can fill a cargo truck measuring 57 cubic feet will be 57 divided by 1/3.

= 57 × 3

= 171

Therefore, 171 boxes are needed.

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Answer:Some functions have asymptotes because the denominator equals zero for a particular value of x or because the denominator increases faster than the numerator as x increases.

Step-by-step explanation:

Answer:

orange juice is better than Apple Juice

Answer:

(-6,-9)

Step-by-step explanation:

Answer:

Most you can do is factor out the x and turn it into   x (3x + 7)

roots would be x = 0 and x = -7/3

Answer:  x(3x+7)

Step-by-step explanation:

You would factor the x out of both of your values and put on the outside of the parenthesis. And you put the two numbers that you have left inside of the parenthesis. And that is as far down as this function can be factored.

Answer:

what is force ? write its S.I unit

Answer:

2 3

2 3

-2 - 1.5 0

4 5

Step-by-step explanation:

-10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 1 0

Answer:

B

Step-by-step explanation:

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

The way to represent this it is

\( 12.33 - \frac{0.27}{\sqrt{n} } < \mu < 12.33 + \frac{0.27}{\sqrt{n} } \)

Step-by-step explanation:

From the question we are told that

The sample mean is

The standard deviation is

Given that the confidence level is 95% then the level of significance is mathematically represented as

\(\alpha = (100-95)\)

\(\alpha = 0.05\)

The critical value for \(\frac{\alpha }{2}\) is obtained from the normal distribution table that value is

\(Z_{\frac{\alpha }{2} } = 1.96\)

Now the margin of error is mathematically represented as

\(E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }\)

\(E = \frac{0.27}{\sqrt{n} }\)

Now the error range to show a 95% confidence is mathematically represented as

\(\= x - E < \mu < \= x + E\)

           \( 12.33  -   \frac{0.27}{\sqrt{n} } <  \mu < 12.33  +   \frac{0.27}{\sqrt{n} } \)

Here notice that the significant figure is keep to three to match the significant figure of the given values

Answer:

4 L 600 mL

Step-by-step explanation:

1 L = 1000 mL

so 27 L 600 mL = 27000 + 600 = 27600 mL

27600/6 = 4600 mL

4 L 600 mL.

The equation for hyperbola with given foci is \(\frac{(x+3)^{2}}{49}-\frac{(y-6)^{2}}{32}=1\)

What is hyperbola?

In analytical geometry, a hyperbola is a conic section that results from the intersection of a plane with a double right circular cone at an angle that touches both of the cone's halves. The two distinct unbounded curves that result from the intersection of the plane and cone are known as hyperbolas.

The standard equation of a horizontal hyperbola with center (h,k) is

\(\frac{(x-h)^{2}}{a^{2} } -\frac{(y-k)^{2}}{b^{2} }=1\)

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is 2a= 4-(-10)

2a=14

a=7

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is \((\frac{-10+4}{2} , \frac{6+6}{2} )= (-3,6)\)

Now, we need to use the relation a^2+b^2=c^2 in order to find b^2.

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

c= 6-(-3)=9

So, 7^2+b^2=9^2

b^2= 9^2-7^2

b^2= 81-49

b^2= 32

Hence, on substituting the obtained values in the standard equation of hyperbola, we get

\(\frac{(x-(-3))^{2} }{7^{2}}-\frac{(y-6)^{2} }{32} =1\)

\(\frac{(x+3)^{2} }{49}-\frac{(y-6)^{2} }{32} =1\)

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Answer:

The best first step would be to multiply the second equation by -2

Step-by-step explanation:

The best first step would be to multiply the second equation by -2

then you would have the following

\(\ \ \ \ \ \ 4x - 5y = 2 \\-2*(2x)+ (-2)*y = (-2)*3\)

and when you multiply it is easy to eliminate because you will get

   \(4x - 5y = 2 \\-4x -2y = 6\)

and if you sum the equations you get

-7y = 8

so that is a single variable equation which is easier to solve.

Answer:

Step-by-step explanation:

To determine the most you should pay for the annuity, you can use the present value formula for an annuity.

PV = C * [(1 - (1 + r)^(-n)) / r]

where PV is the present value, C is the annual cash flow, r is the interest rate, and n is the number of periods.

In this case, C is $1,000, r is 6%, and n is 5 years. Plugging these values into the formula, we get:

PV = $1,000 * [(1 - (1 + 0.06)^(-5)) / 0.06]

PV = $4,212.10

Therefore, the most you should pay for the annuity is $4,212.10. If you pay more than this amount, you would be better off investing your money elsewhere at a 6% interest rate.

Answer:

Percent increase = 30%

Step-by-step explanation:

Given that:

Old price of toy = £50

New price of toy = £65

Difference = New price - Old price

Difference = 65 - 50

Difference = £15

Percent increase = \(\frac{Difference}{Old\ price}*100\)

Percent increase = \(\frac{15}{50}*100\)

Percent increase = 0.3 * 100

Percent increase = 30%

Hence,

Percent increase = 30%

Answer:

4x + 3y

Step-by-step explanation:

Answer:

4x+3y

Step-by-step explanation:

Answer:

AC = 13.3

Make proportional relationship:

\(\dfrac{\text{AB}}{\text{AC}} =\dfrac{\text{AM}}{\text{AN}}\)

Insert values

\(\rightarrow\dfrac{10}{\text{AC}} =\dfrac{6}{8}\)

Cross multiply

\(\rightarrow \text{AC}=\dfrac{10(8)}{6}\)

Simplify

\(\rightarrow \text{AC}=13.3\)

Answer:

2.75

Step-by-step explanation:

21.50 - 18.75 = $2.75

CAN I HAVe BRAINLIEST

Complete question is;

A labourer is paid rs. 8 per hour for an 8 hour day and ½ times that rate for each hour in excess of 8 hours in a single day. if the labourer received rs. 80 for a single day's work, how long did he work on that day?

Answer:

Total working time for the day = 12 hours

Step-by-step explanation:

Money paid to the labourer for initial 8 hrs of work = 8 × 8 = rs. 64.

Now, we are told that he receives rs. 80 in total for that day. And that he receives ½ times the initial rate for each extra hour after the initial 8 hour period.

Thus;

½ × 8 × y = (80 - 64)

Where y is the duration of extra hours.

So;

4y = 16

y = 16/4 hours

y = 4 hours

Now, since extra hours = 4 hours and normal working hours = 8 hours.

Then, total working time for that day = 8 + 4 = 12 hours

A company did a study on the physical activity level and weight gain of its employees. Age was not considered, so it might be an example of a confounding variable.

A confounding variable is an unmeasured third variable that influences, or confounds, the relationship between an independent and a dependent variable. For example, in a study looking at the relationship between smoking and lung cancer, age may be a confounding variable because people who smoke tend to be older than those who do not.

This would mean that age is influencing both smoking and the risk of lung cancer, so the true effect of smoking on the risk of lung cancer cannot be determined without taking age into account. The presence of a confounding variable can distort the results of an experiment and lead to inaccurate conclusions.

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Answer:
It would have to be B?

Step-by-step explanation:

can’t divide by zero, that’s undefinable.

The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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