A farmer owns 30 acres of land. Of the 30 acres, only 65% can be farmed. How many acres are available for farming?

17-15 =2

 he would exceed by 2 a day

The triangle ABC is mapped to A'B'C' through a 180-degree rotation about the origin, as all the points' x and y coordinates have changed signs, consistent with this transformation.

To determine which transformations can map the original triangle ABC to the new triangle A'B'C', we must closely examine the coordinates given and analyze the possible transformations.

Looking at the coordinates:

A(2, 2) to A'(-2, -2) suggests a reflection over the origin, which can be considered as a 180-degree rotation around the origin.

B(4, 1) to B'(-1, -4) also suggests a similar transformation, as the x and y values are negated and swapped in position.

C(4, 5) to C'(-5, -4) follows the same pattern.

All these transformations indicate that the original triangle has been rotated 180 degrees about the origin. This can also be observed by noting that the x and y coordinates have simply changed their signs, an effect of 180-degree rotation about the origin. This satisfies the claim of the classical geometry theorem which states that such transformations can be expressed as either a translation or a rotation. In this case, it's purely a rotation as there's no translation component.

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

All real numbers have a reciprocal.

But we know that 0 has no inverse, means there is no reciprocal exists for 0.

Because,

[tex]\dfrac{1}{0}=\infty[/tex]

So, 0 is a counter example to the statement.

Hence, Second option is correct.

Answer:

Figure 3.

Step-by-step explanation:

We perform the rotation first.  A 180° rotation about the origin maps every point

(x, y)→(-x, -y).  This means it negates both the x- and y-coordinates.

The pre-image points are:

K(3, -4); L(3, -1); M(5, -1); N(5, -4).  Performing the rotation and negating the coordinates will give us:

K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).

Now we perform the translation.  The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate.  This maps to our new points:

K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)

These are the points of figure 3.

Answer:

end point is (-5/3 , 3)

mid-point: (5/6, 3/2)

Step-by-step explanation:

Answer:

[tex]A. \frac{5}{143}[/tex]

Step-by-step explanation:

Given,

Number of women = 5,

Number of men = 8,

Total persons = 5 + 8 = 13,

∵ Ways of selecting any 3 persons = [tex]^{13}C_3[/tex]

Also, the ways of selecting 3 women = [tex]^5C_3[/tex]

Hence, the probability of selecting 3 women

[tex]=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}[/tex]

[tex]=\frac{^5C_3}{^{13}C_3}[/tex]

[tex]=\frac{\frac{5!}{2!3!}}{\frac{13!}{3!10!}}[/tex]

[tex]=\frac{10}{\frac{13\times 12\times 11}{6}}[/tex]

[tex]=\frac{60}{13\times 12\times 11}[/tex]

[tex]=\frac{5}{143}[/tex]

Hence, OPTION A is correct.

The solution for the expression will be cos Ф - cos Ф.sin² Ф = cos³ Ф.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

The given trigonometric expression will be solved as below,

cos Ф - cos Ф.sin² Ф

We know that, sin² Ф = 1 - cos² Ф

E = cos Ф -  cos Ф( 1-cos² Ф)

E = cos Ф - cos Ф  - cos³ Ф

E = cos³ Ф

Therefore, the expression is cos Ф - cos Ф.sin² Ф = cos³ Ф.

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Answer:

It takes to the plane [tex]162.792[/tex] seconds to fly once around a circle whose radius is 2850 m at a speed of [tex](110)\frac{m}{s}[/tex]

Step-by-step explanation:

The first step in this exercise is to find the total distance that the plane will fly.

This distance is equal to the perimeter of a circle whose radius is 2850 m.

Given a circle of radius R, the perimeter ''P'' can be calculated as :

[tex]P=\pi .d=\pi  .2.R[/tex]

Where ''d'' is the diameter of the circle that is equal to 2.R

The distance that the plane will fly in the exercise is :

[tex]P=\pi .2.R=\pi .2.(2850m)=17907.078m[/tex]

Now, the speed is equal to distance divided by time.

[tex]speed=\frac{distance}{time}[/tex]

We have the speed of the plane and the distance (that is the perimeter ''P'' of the circle). We only need to replace this values in the equation and find the time variable.

[tex](110)\frac{m}{s}=\frac{(17907.078)m}{t}[/tex]

[tex]t=\frac{(17907.078)m}{(110)\frac{m}{s}}=(162.792)s[/tex]

[tex]t=(162.792)s[/tex]

We find that the time is [tex]162.792[/tex] seconds.

To find 'z', utilise the properties of a parallelogram where opposite sides are equal. Setting these sides equal to each other and solving for 'z' provides the answer, 'z' = 3.5.

In this problem, you're given a quadrilateral ABCD for which you are supposed to find the value of 'z' when the quadrilateral is a parallelogram. In a parallelogram, the opposite sides are equal. Therefore, we can set AB = CD and BC = AD, and then solve for 'z'. From AB = CD (13w + 5 = 13w + 5), no information is required as their lengths are already equal. From BC = AD (5z - 2 = 3z + 5), solving for 'z' would give us 'z' = 7/2 or 3.5.

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To find the probability of selecting 9 or more girls out of 14 newborn babies, sum the probabilities for selecting 9 to 14 girls from the given table.

To find the probability of selecting 9 or more girls out of 14 babies, we need to calculate the sum of the probabilities of selecting 9, 10, 11, 12, 13, and 14 girls. Refer to the given table that summarizes the probabilities for each value of x. Add the probabilities for these values to get the probability of selecting 9 or more girls.

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